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Neural basis of number sense in zebrafish

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Neural basis of number sense in zebrafish

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Content Neural Basis of Number Sense in Zebrafish
By
Peter Luu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MOLECULAR BIOLOGY)
December 2024

Acknowledgements
I would like to express my deepest gratitude to my advisors, Thai Truong and Scott Fraser,
whose unwavering support, guidance, and encouragement have been instrumental in the
completion of this work. Your insightful advice and constructive feedback have helped shape the
direction of my research, and I am immensely grateful for the opportunity to learn under your
mentorship.
I am also indebted to the members of my dissertation committee, Don Arnold and Dion
Dickman, as well as my collaborators, Giorgio Vallortigara and Caroline H. Brennan for their
valuable time, input, and encouragement throughout this process. Your expertise and
suggestions have greatly enriched my work, and I have benefited immensely from your insights.
Special thanks to my colleagues and friends, Chance Jones, Kevin Keomanee-Dizon, Matt
Jones, Brendon Cooper, Falk Schieder, Keon Rabbani, Arkadi Shwartz, Daniel Koo, Wen Shi,
Valeria Komatsu, who have provided not only technical assistance but also moral support during
challenging times. The camaraderie and shared experiences have made this journey
memorable and enjoyable.
I owe a particular debt of gratitude to Anna Nadtochiy and Mirko Zannon, whose in-depth
assistance with detailed image analysis using experimental imaging was crucial to overcoming
many of the challenges encountered during this research. Their expertise, patience, and
willingness to dive into the complexities of image processing were invaluable, and this work
would not have been possible without their significant contributions.
ii

I would also like to acknowledge the financial support from the Human Frontier Science
Program (RPG0008/2017) and the National Institutes of Health (1U01NS122082-01,
1U01NS126562-01), without which this research would not have been possible.
iii

Table of Contents
Acknowledgements …………………………………………………………………………………….…ii
List of Figures …………………………………………………………………………………………….vi
List of Tables …………………………………………………………………………………………….viii
Abstract …………………………………………………………………………………………………...ix
Chapter 1 - Zebrafish as a Neurobehavioral Model for Studying Number
Sense ………………………………………………………………………………………...……………1
1.1 Abstract: Quantity as a Fish Views It: Behavior and Neurobiology…………………………2
1.2 Quantities and Their Ecological Importance in Fish Behavior………………………………2
1.3 The Issue of the Control of Continuous and Discrete Quantities in
Behavioral Studies ………………………………………………………………………………..…5
1.4 Quantitative Abilities in Zebrafish………………………………………………………………9
1.5 Neural Circuits for Quantities in Zebrafish: Prey and Predators’ Studies………………...15
1.6 Neural Circuits for Quantities in Zebrafish: Social Behaviors and the Role
of Sensory Features ………………………………………………………………………………..18
1.7 Neural Correlates of Continuous and Discrete Magnitude in Zebrafish
Adult Brain …………………………………………………………………………………………..24
1.8 Modeling Developmental Dyscalculia in Fish ……………………………………………….27
1.9 Future Directions: New Methodologies in Calcium Imaging for Next-Gen
Studies ………………………………………………………………………………………………32
1.10 Conclusion …………………………………………………………………………………….38
Chapter 2 - Applying Two-Photon Excitation Microscopy to Live Imaging ………………...40
2.1 Abstract: More than double the fun with two-photon excitation microscopy …………….41
2.2 Introduction ……………………………………………………………………………………..41
2.2.1 Principles of fluorescence and TPE microscopy ……………………………………..42
2.3 Wider, faster, deeper - towards volumetric, intravital imaging with TPE
microscopy …………………………………………………………………………………………..50
2.3.1 Wider: TPE light-sheet fluorescence microscopy ……………………………………51
2.3.2 Faster: TPE light-field microscopy …………………………………………………….53
2.3.3 Deeper: Periscopes from microlenses and GRIN lenses …………………………...55
2.4 TPE microscopy and photon counting applications ………………………………………..57
2.4.1 TPE FCS …………………………………………………………………………………57
2.4.2 TPE FLIM …………………………………………………………………………………58
2.5 Maximizing SNR within the limitations of TPE ………………………………………………63
2.5.1 Optimizing SNR and photodamage ……………………………………………………63
2.5.2 Selective excitation by polarized light …………………………………………………66
2.6 Image quality metric …………………………………………………………………………...69
2.7 Quo vadis? What’s next? ……………………………………………………………………..70
iv

Chapter 3 - Neural Basis of Number Sense in Larval Zebrafish ……………………………...73
3.1 Significance …………………………………………………………………………………….74
3.2 Abstract …………………………………………………………………………………………75
3.3 Introduction …………………………………………………………………………………….76
3.4 Results …………………………………………………………………………………………..77
3.5 Discussion ………………………………………………..……………………………………..90
3.6 Methods …………………………………..……………………………………………………..95
3.6.1 Key resources table ……………………………………………………………………..95
3.6.2 Animal care.............................................................................................................95
3.6.3 Calcium imaging .....................................................................................................96
3.6.4 Stimuli Generation ..................................................................................................97
3.6.5 Visual number-based display..................................................................................97
3.6.6 Ethanol administration ............................................................................................98
3.6.7 Cell segmentation ...................................................................................................98
3.6.8 Number neuron selection .......................................................................................99
3.6.9 Brain spatial registration and region segmentation...............................................100
3.6.10 Supervised classification ....................................................................................100
3.6.11 Statistical analysis...............................................................................................101
3.6.12 Acknowledgements ..................................................................................................101
3.6.13 Funding.....................................................................................................................101
3.6.14 Supplementals……………………………………………………………………………..102
Chapter 4 - Conclusion ……..……………………………………………..………………………….119
Reference ………………………………………..………….………………………………………….122
v

List of Tables
Table 2.1: Non-exhaustive list of microscopy vendors offering TPE microscopy
instrumentation highlighting unique features of each ……………………………………………….47
Supplementary Table 3.1. Group averages of identified neurons ...……………………………...111
Supplementary Table 3.2. Total amount of neurons identified in the whole brain ……...………112
Supplementary Table 3.3. Total amount of neurons identified in the forebrain …………………113
Supplementary Table 3.4. Total amount of neurons identified in the midbrain …………………114
Supplementary Table 3.5. Total amount of neurons identified in the hindbrain ………………...115
Supplementary Table 3.6. Comparison of age-related change in number-selective
neurons in subregions of the forebrain ……………………………………………………………...116
Supplementary Table 3.8. Summary of GeNEsIS parameters …………………………………...118
vi

List of Figures
Figure 1.1: Stimuli and neural circuits associated with prey capture in zebrafish
larvae …………………………………………………………………………………………………….16
Figure 1.2: Stimuli and neural circuits involved in social behaviors ………………………………21
Figure 1.3: Schematic representation of the habituation/dishabituation paradigm
used to identify neural correlates associated with a change in discrete and
continuous magnitude in the adult zebrafish brain………………………………………….……….25
Figure 1.4: Whole-brain functional imaging to find neural substrate of zebrafish
numerosity capability …………………………………………………………………………………..37
Figure 2.1: Introduction to TPE microscopy …………………………………………………………48
Figure 2.2: Popularity and needs of TPE microscopy ………………………………………………50
Figure 2.3: From laser point scanning to fast, wide and deep volumetric imaging
in complex samples with TPE …………………………………………………………………………56
Figure 2.4: Combination of TPE with the photon counting techniques FCS and
FLIM 62
Figure 2.5: Optimization of excitation laser polarization for single and multi-focal
microscopy….……………………………………………………………………………………………68
Figure 3.1: Application of two-photon fluorescence light sheet microscopy to
detect neuronal representation of number perception in larval zebrafish ………………………..79
Figure 3.2: Number-selective neurons produce higher Ca2+ activity for preferred
numerosities ……………….…………………………………………………………………………….82
Figure 3.3: Populations of neurons tuned to specific numerosities show
redistribution of number preference during early development ……………………………………83
Figure 3.4: Number-selective neurons are primarily detected in the forebrain
and midbrain……………………….…………………………………………………………………….85
Figure 3.5: Prediction accuracy of the numerical stimuli from Ca2+ activity
using an SVM classifier shows increased performance with age …………………………………88
Figure 3.6: Ethanol alters the activity of number-selective neurons in the
forebrain ……………………….…………………………………………………………………………89
Supplementary Figure 3.1: Sequence of stimuli including all possible
combinations of spread and sizes using a new pattern for each stimulus ……………..……….102
Supplementary Figure 3.2: Segmentation output using CaImAn toolbox ………………………103
Supplementary Figure 3.3: Example traces of geometric controls of the
number-based dot stimuli…………….……………………………………………………………….104
Supplementary Figure 3.4: Tuning curve of 3, 5, and 7 dpf age groups …….…………………..105
Supplementary Figure 3.5: No-stimulus negative control …………………………………………106
vii

Supplementary Figure 3.6: Localization of number-selective neurons at three
stages of development ………………….…..………………………………………………………...108
Supplementary Figure 3.7: Distribution of sub-regional number-selective
neurons normalized by total number-selective neurons in the forebrain …………………….…109
Supplementary Figure 3.8: Distribution on number-selective and all active neurons
across three major brain regions during ethanol administration …………………………………110
Figure 4.1 Using the neural basis of number sense as a foundation for future studies ……….120
viii

Abstract
Numerical cognition is a foundational aspect of animal behavior, influencing survival and
ecological interactions. This dissertation investigates the neural basis of number sense in
zebrafish (Danio rerio), leveraging their genetic tractability, optical transparency, and behavioral
repertoire. Combining advanced two-photon light-sheet microscopy with molecular genetics, we
identify the neural circuits underpinning discrete quantity estimation. We demonstrate that
zebrafish possess specialized neural substrates in the forebrain and midbrain, with responses
modulated by age, developmental stage, and external factors such as ethanol. Our findings
reveal the parallels between zebrafish and higher vertebrates, establishing zebrafish as a robust
model for studying numerical cognition, genetic contributions to developmental dyscalculia, and
neurobiological mechanisms of magnitude estimation. This work not only broadens the
understanding of quantity cognition across species but also proposes zebrafish as a
translational model for neurodevelopmental disorders.
ix

Chapter 1 - Zebrafish as a Neurobehavioral Model for Studying
Number Sense
This chapter introduces zebrafish as an advantageous model for studying number sense due to
their genetic tractability and well-characterized nervous system. The ecological relevance of
numerical cognition in fish is explored, particularly in the context of survival behaviors such as
foraging and predator avoidance. The chapter also outlines the challenges of distinguishing
between continuous and discrete quantities in behavioral studies, which is critical for
understanding the underlying neural mechanisms of quantity estimation.
The work of this chapter is published at Frontiers in Neuroanatomy by:
Andrea Messina
1
, Davide Potrich
1
, Matilde Perrino
1
, Eva Sheardown
2
, Maria Elena Miletto
Petrazzini
3
, Peter Luu
4
, Anna Nadtochiy
4
, Thai V. Truong
4
, Valeria Anna Sovrano
1,5
, Scott E.
Fraser
4
, Caroline H. Brennan
6
, Giorgio Vallortigara
1
1) Centre for Mind/Brain Sciences, University of Trento, Rovereto, Italy
2) Centre for Developmental Neurobiology, Institute of Psychiatry, Psychology and
Neuroscience, New Hunt’s House, Kings College London, London, United Kingdom
3) Department of General Psychology, University of Padova, Padua, Italy
4) Michelson Center for Convergent Bioscience, University of Southern California, Los
Angeles, CA, United States
5) Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
6) School of Biological and Behavioral Sciences, Queen Mary University of London,
London, United Kingdom
1

1.1 Abstract: Quantity as a Fish Views It: Behavior and Neurobiology
An ability to estimate quantities, such as the number of conspecifics or the size of a predator,
has been reported in vertebrates. Fish, in particular zebrafish, may be instrumental in advancing
the understanding of magnitude cognition. We review here the behavioral studies that have
described the ecological relevance of quantity estimation in fish and the current status of the
research aimed at investigating the neurobiological bases of these abilities. By combining
behavioral methods with molecular genetics and calcium imaging, the involvement of the retina
and the optic tectum has been documented for the estimation of continuous quantities in the
larval and adult zebrafish brain, and the contributions of the thalamus and the dorsal-central
pallium for discrete magnitude estimation in the adult zebrafish brain. Evidence for basic
circuitry can now be complemented and extended to research that makes use of transgenic
lines to deepen our understanding of quantity cognition at genetic and molecular levels.
1.2 Quantities and Their Ecological Importance in Fish Behavior
Quantity discrimination is a fundamental aspect of our everyday life. A preference for more or
less of something can be easily observed in non-human animals’ behavior. Extensive evidence
in several species supports the use of quantity estimation during foraging (Bar-Shai et al., 2011;
Garland et al., 2012; Gazzola et al., 2018; Hauser et al., 2000; Stancher et al., 2015; T.-I. Yang
& Chiao, 2016), defensive responses (McComb et al., 1994; Wilson et al., 2002), reproductive
and safety strategies (Carazo et al., 2009; Queiroz & Magurran, 2005; Rooke et al., 2020), and
parental cares (Lyon, 2003). Indeed, the ability to estimate and process the number of elements
2

in a group or the size of another animal (prey or predator) is widespread across different
species, which suggests it may be of highly adaptive value in their ecological niches (Bortot et
al., 2021; Messina, Potrich, Perrino, et al., 2022a; Nieder et al., 2020; Vallortigara, 2017).
In particular, fish have mainly been studied by taking advantage of their social responses. Fish
form shoals (i.e., aggregation of conspecifics) to dilute the risk of being preyed upon (Foster &
Treherne, 1981). Quantity discrimination can, thus, be studied by giving fish the possibility to
join either one of two groups of companions differing in number.
For example, angelfish reliably chooses the larger set of conspecifics in 1 vs. 2 and 2 vs. 3
comparisons but is at random in 3 vs. 4 comparisons (Gómez-Laplaza & Gerlai, 2011a).
Mosquitofish show more accurate performances, discriminating 3 vs. 4 but not 4 vs. 5 (Agrillo et
al., 2008), whereas guppies can discriminate with this ratio (Lucon-Xiccato et al., 2017). These
results indicate that fish show a discriminatory limit of 3–4 elements among small numerosity, as
found in other vertebrate species (Stancher et al., 2015). Fish, however, also proved to be able
to compare sets with large numerosity (>4 elements), showing a ratio-dependent accuracy.
Angelfish can discriminate up to a 0.56 ratio (5 vs. 9) (Gómez-Laplaza & Gerlai, 2011b), while
other species such as guppies (Agrillo et al., 2012), mosquitofish (Agrillo et al., 2008), and
swordtail (Buckingham et al., 2007) show a limit set at 0.5 (one group is two times the other).
Fewer evidence indicates that fish can go higher than 0.67: three-spined sticklebacks
discriminate up to 0.87, showing, however, a progressive accuracy decrease as the ratio
increases (Mehlis et al., 2015). The size of the shoal matters not only to prey but also to
predators. Many fish species suffer a low capture success when attacking groups of prey, due to
known anti-predator benefits of grouping such as predator confusion (Milinski, 1977a, 1977b).
For example, white perch direct more attacks at stragglers than shoals of killifish (Morgan &
Godin, 1985). However, an opposite trend has been found in acaras and pike cichlids that
3

showed to direct their attack toward the larger shoal of prey (Botham et al., 2005; Krause &
Godin, 1995).
The discrimination of food quantities is one of the most relevant abilities from an ecological point
of view. As stated by the theory of optimal foraging, a larger food patch offers a higher energetic
gain (Krebs et al.,1974). Guppies spontaneously select the larger number of food items with
contrasts of 1 vs. 4 and 2 vs. 4 (Lucon-Xiccato et al., 2015). Similarly, angelfish discriminate
between identically sized food quantities with a numerical ratio of up to 0.67 (Gómez-Laplaza et
al., 2018).
Quantity discrimination has also been described in fish concerning parental care: females of
convict cichlid spend more time trying to recover fry from the larger of two groups displaced from
the nest, by up to a 0.67 ratio (6 vs. 9) (Forsatkar et al., 2016). In mating strategy, females of
mouthbrooder cichlid prefer males that show more spots in their tails mimicking the conspecific
eggs (Hert, 1991).
Studies in fish investigating relative quantity judgments revealed that their accuracy parallels
that of many other vertebrates: with small numerosity, discriminative accuracy stands at around
3–4 elements, but when numerosity increases, the discrimination appears to be
ratio-dependent, following Weber’s Law where accuracy decreases as the ratio increases
(Cantlon & Brannon, 2006).
4

1.3 The Issue of the Control of Continuous and Discrete Quantities in
Behavioral Studies
All the studies mentioned in the previous paragraph face a drawback: the discrimination of
relevant ecological stimuli and their numerosity is intertwined with other non-numerical
continuous magnitudes. For example, when the number of conspecifics or food items increases,
other aspects would, most likely, also increase: e.g., the overall volume, area, and perimeter
tend to correlate positively with numerical information. Similarly, if the elements are equally
spaced, the larger group will globally occupy a larger space (also known as convex hull or
sparsity); a balance of the convex hull, on the other hand, leads to having different items’
density. Also, the continuous and discrete aspects of the quantitative features of a stimulus can
interact with one another (Vallortigara et al., 2022). The type of information the animals pay
attention to during discrimination is a challenge for this kind of research.
In food quantity discrimination tasks, both angelfish (Gómez-Laplaza et al., 2019) and guppies
(Lucon-Xiccato et al., 2015) were found to prefer larger-sized food items as opposed to larger
food amounts. As to the control of items’ spatial disposition, when the inter-item distance was
kept constant, angelfish preferred the more numerous to the less numerous set
(Gómez-Laplaza et al., 2018). However, the density of the food elements appeared to be an
important feature for angelfish when dealing with large numbers (e.g., 5 vs. 10), driving the
choice toward the smaller sets with clustered (denser) items concerning the numerically larger
sets with scattered items. The density of the group’s items seems to be particularly relevant for
fish, as well as in social contexts, affecting shoal discrimination in angelfish (Gómez-Laplaza &
Gerlai, 2013) and three-spined stickleback (Frommen et al., 2009).
5

The role of swimming activity (and, thus, the amount of stimulus motion) is another important
non-numerical cue, being usually higher in a larger group. One method to equalize this
continuous variable between the sets is to reduce the water temperature (as the temperature
decreases, fish activity decreases) or to restrict the space occupied by each fish in the stimulus
shoal. When the temperature was manipulated, a loss of preference for the larger shoal was
described in zebrafish (Pritchard et al., 2001). Similarly, mosquitofish and angelfish shoaling
discrimination was affected in large comparisons (respectively, 4 vs. 8 and 5 vs. 10) but not in
small comparisons (2 vs. 3) (Agrillo et al., 2008; Gómez-Laplaza & Gerlai, 2012). However,
when activity was controlled by space restriction, angelfish preferred the larger shoal in both
numerical contrasts (Gómez-Laplaza & Gerlai, 2012).
As to the area of the stimuli, in mosquitofish, this has been controlled for by placing larger
individuals in the numerically smaller stimulus shoal and smaller individuals in the numerically
larger stimulus shoal. In such a condition, fish showed no significant choice preference,
highlighting the relevance of the overall stimuli area and/or the individual size of the stimuli in
discrimination (Agrillo et al., 2008). Similar results were recently obtained in guppies, zebrafish,
Chinese crucian carps, and qingbo (Xiong et al., 2018).
Another technique to prevent fish from using continuous quantities involves reducing the visual
access to the conspecifics by partial occlusion. For example, fish can initially observe two
different numerical shoals simultaneously; then, before allowing individuals to exhibit a
preference between the two sets, some individuals from the larger group are occluded, leaving
the same number of the stimuli visible in the two shoals. In this condition, redtail splitfins chose
the larger shoal in small numerical comparisons (1 vs. 2, 2 vs. 3, but not 3 vs. 4) (Stancher et
al., 2013). Similar performances with both small and large numerosity were obtained in
zebrafish (Potrich et al., 2015) and angelfish (Gómez-Laplaza & Gerlai, 2015), although the
6

latter were less accurate with large numerosity. Using an adaptation of the “item-by-item
presentation” procedure, mosquitofish were exposed to a shoal test task, in which each fish
stimulus was singly confined in separate compartments, with several opaque occluders
positioned in such a way that the test subject could see only one stimulus at a time. Fish were,
therefore, required to add the amount of the seen conspecifics on both sides and compare
them. Mosquitofish spent more time close to the largest shoal in 2 vs. 3 and 4 vs. 8
comparisons (Dadda et al., 2009).
The importance of non-numerical versus numerical information in quantity discrimination may
have ecological reasons. For example, while foraging, it may be more relevant for fish to select
the larger-sized food items instead of the larger numerosity, motivated by the attempt to
maximize energy gained from eating the food while minimizing energy expenditure collecting
and/or protecting the food. Similarly, the density of conspecifics in the shoal could sometimes be
more relevant than pure numerical information to gain protection in the group. Hence, the use of
experimental procedures based on spontaneous preferences for attractive ecological stimuli
prevents us from studying the role of different quantities (number, size, density, etc.). The use of
conditioning procedures might overcome some of these limitations.
During conditioning procedures, animals are typically requested to discriminate between
different sets of elements differing in numerosity by choosing the one associated with a reward
(usually food or a social reward). Using this method, mosquitofish were trained to discriminate
between different sets of two-dimensional stimuli (2 vs. 3) to gain access to social companions
(Agrillo et al., 2009). Fish discriminated between the two numerosity when no control on the
continuous stimulus variables was done but showed a drop in performance when tested after
equalizing some of the continuous quantities. For instance, when the cumulative surface area or
the convex hull (sparsity) were equalized between the groups, performance dropped to chance
7

level and no interference was found when overall perimeter or total brightness were balanced.
Similar results were obtained in the same species when large numerosity was used (4 vs. 8 and
100 vs. 200) (Agrillo et al., 2010). Using a different technique, cavefish were shown to
discriminate between different quantities of vertical sticks associated with a food reward only
when both continuous quantities were correlating with numbers but not when only numerical
information was available (Bisazza, Agrillo, et al., 2014).
The lack of numerical performance found in these studies might outline a fish’s inability to use
numerical cues and/or the fact that numerical information could be taken into account by fish
only when other non-numerical information (such as overall area or convex hull) is not available
(as a last resort strategy). Interestingly, however, when trained with controls for non-numerical
cues from the beginning of the training, mosquitofish and cavefish showed that they can
discriminate based on numerical information alone (Agrillo et al., 2010; Bisazza, Agrillo, et al.,
2014). Moreover, the use of numerical cues alone can be conducive to high accuracy levels
(higher than 90%), provided fish are exposed to extensive training, as shown in guppies
(Bisazza, Agrillo, et al., 2014) and goldfish (DeLong et al., 2017). Furthermore, the hypothesis
that relying on numbers would represent a last resort strategy was tested by Agrillo et al. (2011)
who trained mosquitofish to discriminate between two sets of items making available either only
continuous variables, only numerical information, or both simultaneously. As expected, fish
learned to discriminate more quickly when both numbers and continuous information were
available than when only continuous information or only numerical information could be used.
Interestingly, there was no difference in learning between the two latter conditions, suggesting
that the process of learning numbers is no more cognitively demanding than that of learning
continuous variables (Agrillo et al., 2011).
8

The above mentioned studies in fish attempting to control for non-numerical variables during the
learning process were mainly focused on the overall elements’ area, density, and convex hull
(Agrillo et al., 2012; Bisazza, Tagliapietra, et al., 2014; DeLong et al., 2017). In a recent study,
archerfish were trained to select one of two groups of items (small dots) (3 vs. 6 and 2 vs. 3
elements), with accurate control for all the possible geometrical constraints and their
combinations (elements’ size, overall area, overall perimeter, density, and sparsity), ensuring
that only numerical information was available (Potrich et al., 2022). Results confirmed that
non-numerical cues (including the spatial frequency of the stimuli used) did not correlate with
the archerfish’s performance accuracy, suggesting that the discrimination made by the animals
was based on purely numerical information.
1.4 Quantitative Abilities in Zebrafish
Despite the huge literature on fish quantitative abilities, all the studies mentioned so far are
limited to behavioral observations as none of the studied species is a model in research fields
such as genetics, neurobiology, and neuroimaging.
Concerning this issue, during the last decade, zebrafish (Danio rerio) have gained more
attention as a new powerful model for studying quantitative skills at different levels of
complexity, from genes to behavior. Since its innovative use as a model organism in genetics
and neurodevelopmental biology by George Streisinger in the 1960s (Walker & Streisinger,
1983), the zebrafish have rapidly become an established model for translational neuroscience
(Brock et al., 2017; Fontana et al., 2018; Stewart & Kalueff, 2012) due to multiple advantages
that surpass those in fruit flies and rodents and that make the zebrafish an excellent
9

compromise between system complexity and practicality (Gerlai, 2020; McCammon & Sive,
2015).
Zebrafish are physiologically homologous to mammals and possess all major neurotransmitters,
hormones, and receptors (Alsop & Vijayan, 2009; Panula et al., 2006). The high degree of
protein and genetic homology with humans (Howe et al., 2013), coupled with refined
gene-editing tools and behavioral paradigms, make this species a vertebrate system amenable
to large-scale forward genetic analyses (Kalueff et al., 2013; Sheardown et al., 2022a; Wolman
et al., 2011). Transparency of embryos and larvae enables in vivo functional imaging of neural
activity and establishes the zebrafish as a powerful optogenetic tool. Other advantages include
cost/space efficiency and high fecundity (laying up to 200 eggs a day), which allows
high-throughput screening and rapid development, with completed organogenesis by 5 days
post fertilization (dpf) (Brand et al., 2002; Kimmel et al., 1995). Of relevance to this review,
zebrafish possess an elaborate behavioral repertoire and complex cognitive abilities present in
higher vertebrates, including learning (associative, non-associative, spatial and aversive
learning) (Gerlai, 2016), long-term and short-term memory (Stewart & Kalueff, 2012), and of
course, quantitative skills.
It is worth noting that one of the pivotal studies on quantitative abilities in fish was conducted by
Pritchard et al. (Pritchard et al., 2001) who showed that zebrafish preferred the larger of two
shoals (2 vs. 4) when the water temperature was kept the same. However, this preference was
lost when swimming activity in the larger shoal was reduced by cooling the water, thus providing
the first evidence of the continuous quantities’ influence on discriminative abilities in fish.
10

Since then, binary choice tests, operant training procedures, and habituation-dishabituation
protocols have been adopted to further investigate zebrafish skills and to disentangle the
relative salience of numerical and non-numerical information.
Female zebrafish, tested in a shoal choice task with no control for continuous quantities,
showed a preference for the larger group of social companions for ratios above or equaling 0,5
(0 vs. 4, 1 vs. 4, 2 vs. 8, 2 vs. 6, and 3 vs. 6). Interestingly, as performance broke down in a 4
vs. 8 contrast, the authors suggested that having more than four fish in a shoal did not confer
selective advantage as both groups provided sufficient protection from potential predators, thus
leading zebrafish to treat both shoals equally (Seguin & Gerlai, 2017). As mentioned above,
when Xiong et al. (2018) investigated the role played by the cumulative body surface area in
shoal selection, they found that different species, zebrafish included, relied on non-numerical
information rather than on number when choosing between 2 and 3 conspecifics, thus
confirming the salience of non-numerical information in this type of task.
To prevent zebrafish from using continuous quantities, Potrich et al. (2015) adopted the
procedure previously used with redtail splitfin, in which two numerically different shoals were
partially occluded at the time of choice (Stancher et al., 2013). Male zebrafish tested with this
approach proved to be able to select the larger between two shoals of females when both small
(1 vs. 2 and 2 vs. 3, but not 3 vs. 4) and large numbers of conspecifics (4 vs. 6, 4 vs. 8 but not 6
vs. 8) were presented, thus providing the first evidence of zebrafish ability to rely on working
memory to discriminate among quantities. Furthermore, accuracy was ratio-dependent (US) as
reported in several animal species. It is known that the performance in a quantity discrimination
task can be affected by the experimental procedure used, even within the same species (Agrillo
& Bisazza, 2017; Agrillo & Dadda, 2007). Methodological differences (sexual vs. social context,
11

2 vs. 30 trials for each subject and 23 vs 50-cm-long tank) could then explain the discrepancy
observed in the 4 vs. 8 contrast compared to results obtained by Seguin and Gerlai (2017).
If on the one hand, the numerical ability has been thoroughly investigated in several species
(Agrillo et al., 2017; Messina, Potrich, et al., 2021; Santacà et al., 2021), on the other hand
estimation of continuous quantities has received relatively less attention. Recently, a novel
method has been developed to quickly assess size estimation ability in zebrafish by exploiting
their natural preference for passing through the larger of two holes to move in their environment.
Adult zebrafish showed impressive quantitative abilities in being able to discriminate up to a
ratio of 0.91 with their performance decreasing while increasing the ratio between the smaller
and the larger holes (Santacà et al., 2020). Importantly, the experimental procedure has been
shown to have good retest reliability and to be unaffected by the experience, which is
fundamental in studies testing drug effects on diseases causing cognitive deficits or
investigating the cognitive decline in normal and pathological aging.
Surprisingly, the same accuracy was observed in larvae tested at 21 dpf, whereas larvae at 7
and 14 dpf discriminated up to a ratio of 0.86 (Santacà et al., 2021). Altogether, these results
suggest a limited role of maturation and experience on zebrafish’s ability to estimate areas that
parallel the existence of tectal neurons by selectively responding to item size already during the
first week of life (see paragraph below for more details). This high accuracy seems to be in
contrast with performance observed in juvenile zebrafish tested in a spontaneous choice test to
investigate the ontogeny of numerical competence (Sheardown et al., 2022a). In this study, the
authors adapted the procedure previously used to investigate shoal choice discrimination in
angelfish, in which the stimulus fish were located in individual compartments that limited
movement and avoided fish hiding each other. The results showed that fish from 31 dpf already
chose the larger group in 1 vs 3, 2 vs. 5, and 2 vs. 3, but not 2 vs. 4 contrasts. In a control
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experiment, fish proved unable to discriminate between the shoals (2 vs. 3, 2 vs. 4, and 2 vs. 5)
when the overall space occupied by the social companions was the same. However, they still
chose the larger group in 2 vs. 5 and 2 vs. 3 but not 2 vs. 4 when the overall space was not
controlled for. Furthermore, when the same ratio of 0.5 was maintained but the numerousness
of conspecifics was changed, zebrafish discriminated between 1 vs. 2 and 3 vs. 6 individuals,
failing again in 2 vs. 4. The consistent failure to select the larger group between 2 and 4
individuals, whether controlled for space occupied or not, suggests that the fish did not only rely
on the overall space as 4 fish occupied two times the space. Hence, the authors suggested that
zebrafish may use both numerical and non-numerical information to represent quantities (Agrillo
et al., 2016; Leibovich et al., 2017; Sheardown et al., 2022a) and that attentional constraints and
cognitive and working memory mechanisms may orchestrate numerical competence as
hypothesized in both humans and other animals (Hyde, 2011). However, these results may also
support the hypothesis of distinct quantification systems characterized by domain and task
specificity operating largely independently from the others (Feigenson et al., 2004; Miletto
Petrazzini et al., 2014).
To date, information on zebrafish’s numerical capacities is scarce and only a few studies used
training procedures with stimuli controlled for continuous variables to understand whether
zebrafish can use numerical information alone. Agrillo et al. (2012) first comp first compared the
numerical abilities of five teleost fishes, (guppies, redtail splitfins, angelfish, Siamese fighting
fish, and zebrafish), using the same stimuli, numerical contrasts, and experimental protocol.
Fish initially trained to discriminate between two easy numerical contrasts (5 vs 10 and 6 vs, 12;
ratio: 0.5) were then tested for their ability to generalize the learned rule both to novel larger
numerosities (8 vs. 12 and 9 vs. 12, respectively; ratios: 0.67 and 0.75) and to contrast with
constant ratio (0.5), increasing (25 vs. 50) or decreasing (2 vs. 4) total set size. Although only
minor differences were observed among the five species, the proportion of zebrafish reaching
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the learning criterion was lower compared to the other species. They also performed
significantly worse in a control experiment testing shape discrimination, suggesting that the
observed differences resulted from zebrafish’s difficulty in learning the procedure rather than
from a cross-species variation in the numerical domain (Agrillo et al., 2012). However, it has
recently been shown that zebrafish trained to discriminate between numbers differing by one
unit can successfully distinguish up to 5 vs 6 items (0.83), thus showing excellent learning
abilities and numerical skills similar to those observed in higher vertebrates (Bisazza & Santacà,
2022).
Ordinal abilities have also been investigated in zebrafish (Potrich et al., 2019) as previously
done in guppies (Petrazzini et al., 2015). In this study, zebrafish correctly choose the second
exit in a series of five identically spaced ones along a corridor based on ordinal information
rather than on absolute spatial cues (i.e., total length of the corridor and the distance between
inter-exit distance). However, when the number of exits was increased (from 5 to 9) and the
inter-exit distance was reduced, they relied both on ordinal and relative spatial information, thus
suggesting the use of redundant information to solve a more difficult task (Agrillo et al., 2011;
Suanda et al., 2008).
Finally, a habituation/dishabituation paradigm, commonly used to study numerical abilities in
newborns (de Hevia et al., 2014; Izard et al., 2009), has recently been adapted to explore the
brain regions involved in numerosity discrimination in adult zebrafish through molecular biology
analyses (Messina et al., 2020, 2022) In brief, fish were initially habituated to arrays of 3 or 9
dots, changing in item size, position, and density from trial to trial but keeping the same
numerousness and overall area. Zebrafish showed a general increase in approach when
exposed to a novel stimulus compared to the familiar one even when the stimuli changed in
number, indicating that numerousness was being used by the zebrafish.
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Several authors suggest the existence of a shared non-verbal numerical system among
vertebrates with a possible common genetic basis and evolutionarily conserved neuronal
circuits (Agrillo & Bisazza, 2017; Lorenzi et al., 2021a). The finding that zebrafish’s abilities to
discriminate both continuous and discrete quantities are comparable to those observed in
mammals raises the possibility of using this species as a model to investigate both the neural
circuitry and the genetic mechanisms underpinning numerosity representation and the role of
genes in developmental dyscalculia. Furthermore, some neurodegenerative diseases that have
been associated with impaired abilities to estimate both discrete (Gandini et al., 2009) and
continuous quantities (Barabassy et al., 2010) could potentially be used for an early diagnosis of
disease (Levinoff et al., 2006). The availability of behavioral tools for rapid and easy assessment
of quantitative abilities at an early age that can be used for rapid screening of mutant lines for
candidate genes potentially associated with such diseases can significantly contribute to
progress in biomedical research.
1.5 Neural Circuits for Quantities in Zebrafish: Prey and Predators’
Studies
A key factor for an animal’s survival is prey-predator recognition, an ability that relies on the
detection of both the continuous and discrete features of the stimulus (Cross & Jackson, 2017).
Size and direction are continuous features and have been well-studied in zebrafish where the
location and onset of mediating neurons have been identified (Temizer et al., 2015a, 2015b).
However, the mechanism for detecting discrete quantities is largely unknown and may respond
to approximation and/or subitization, namely the instant recognition of the number of objects
without sequential counting (Piazza, 2010a). Here, we discuss current methodologies and
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studies on prey-predator behaviors, which is summarized in Figure 1.1, and how they can be
applied to better understand the detection of discrete quantities.
Figure 1.1. Stimuli and neural circuits associated with prey capture in zebrafish larvae.
A Looming-evoked escape (–) behavior in zebrafish larvae (Temizer et al., 2015b).
B A schematic representation of moving small or large dots entering the visual field of zebrafish
larvae. Larvae tend to approach (+) small dots and avoid (–) large dots (Barker and Baier,
2015).
C A schematic representation of moving small or large objects in zebrafish larvae. Small objects
elicit an approach (+) interaction and large objects an avoidance (–) interaction (Preuss et al.,
2014).
D Classification of small and large objects in retinotectal circuits of zebrafish larvae eliciting an
appetitive or aversive behavior in zebrafish larvae. Retinal ganglion cells (RGCs) detecting small
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objects project to the external layers of the zebrafish optic tectum. On the contrary, RGCs for
large objects project to the deeper layer of the optic tectum (Preuss et al., 2014).
To represent prey and predator interactions, Niell and Smith (2005) used a variety of dot
stimulations and found four clusters of tectal neurons that respond to the general movement of a
dot, movement in a specific direction, flashing of the dot, or spontaneous darkness (Figure 1.1A;
While these neurons respond intensely to their corresponding categories, they are also
triggered by other stimuli. For example, the cluster responding to the general movement of a dot
also moderately responds to a flashing, static, or looming dot. Interestingly, the study
simultaneously demonstrated the ability to map continuous features to a single neuron using
2-photon calcium imaging. Note, however, that the authors used the calcium indicator dye
OGB1 (Oregon Green BAPTA-1), which may have limited their findings due to its reduced signal
intensity compared to modern genetically encoded calcium indicators (GECI) as they found
large clusters of seemingly unresponsive neurons (T.-W. Chen et al., 2013). Semmelhack et al.
(2014) also found that a small visual area, AF7 (arborization field 7), responds specifically to the
optimal artificial prey stimulus based on size and speed (3° dot moving at 90°/s).
Expanding on Niell and Smith (2005) and Preuss et al. (2014) placed a larger emphasis on
finding tectal neurons mediating size selectivity. The study used spots ranging from 2° to 64°,
incrementing by powers of 2, combined with 2-photon calcium imaging using a GECI. The
authors identified that laterally interconnected neurons in the superficial region of the tectum
were tuned to smaller (<16°) sizes whereas the deeper tectal region housed neurons tuned to
larger (>16°) sizes (Figures 1.1C,D). These results motivate a question: if a single neuron
responds to a single dot, would two visually distinct dots activate two separate tectal neurons? If
so, could these two neurons converge to activate a single neuron?
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Although neural tuning can demonstrate recognition of a given stimulus, a behavioral output
shows that the signal undergoes further processing in other parts of the brain to emit a
response. Barker and Baier’s (2015) study found that interneurons in the tectum are required for
approach or avoidance during prey-predator interactions (Figure 1.1B). Typically, zebrafish
larvae will approach a moving dot smaller than 5° and avoid dots larger than 10° as early as 5
dpf (Barker & Baier, 2015). However, when a specific glutaminergic tectal neuron was ablated,
the authors found an increase in avoidances and a decrease in approaches to small dots. In this
study, the behavior was always evaluated using a single object as the stimulus. This leaves an
open question: can variation in the number of objects influence approach or avoidance? If given
larger groups of small dots, it may be possible for young larvae to approximate or subitize the
quantity of a food source as it is evolutionarily advantageous to be efficient foragers.
The discussed studies primarily focused effort on the optic tectum but multiple aspects of the
nervous system mediate prey-predator recognition. For example, the visual pathway starts at
the retina and primarily connects to the pretectum and the optic tectum, but it then spans to the
less explored forebrain and other areas. While this complicates functional studies of the brain,
faster and broader imaging techniques are being developed to remedy this. By incorporating
proper number-based stimuli with new imaging techniques, it will be possible to characterize the
neuronal substrate responsible also for the detection of discrete quantities.
1.6 Neural Circuits for Quantities in Zebrafish: Social Behaviors and
the Role of Sensory Features
Despite terrific advancements in linking neural circuits with behavior, thanks to novel
methodologies, our knowledge of zebrafish neurobiology exhibits two main gaps (Bollmann,
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2019). First, as already discussed, the majority of studies employing functional imaging take
advantage of the natural transparency of the skin and the skull of larvae up to around 5 dpf.
Therewith, they have concentrated on specific areas that are already mature at that
developmental stage (e.g., optic tectum) while neglecting others that go through major
structural, as well connectivity changes (e.g., telencephalic areas) (Bloch et al., 2020). The
second issue is immediately consequent from the first since the inaccessibility of adult animals
to whole-brain functional imaging prevents scientists from investigating some complex
behaviors that emerge only at a later age (Orger & de Polavieja, 2017; Valente et al., 2012).
Social behavior is one example, given that zebrafish juveniles start to approach groups of
conspecifics at 7 dpf and completely mature social behaviors only at 21 dpf (Dreosti et al.,
2015). The growth of social drive seems to follow an exponential growth between 6 and 24 dpf
(Hinz & de Polavieja, 2017), which parallels the maturation of the nervous system. During this
period, they start to display orientation toward other fish, shoaling, schooling, and a greater
preference for more numerous groups of conspecifics as previously mentioned.
Besides the development of social drive, one central question regarding these behaviors is what
triggers them. The necessity to study social behavior in dynamic contexts has prevented
investigating the role of sensory signals and perceptual processes. However, understanding the
mechanisms and neural circuits involved is a primary issue.
Visual cues are necessary for social behaviors since the removal of illumination or the occlusion
of visual stimuli removed any social preference, orientation, or shoaling behavior in fish (Dreosti
et al., 2015; Harpaz et al., 2021; Larsch & Baier, 2018a). We know that several physical factors
influence social behaviors, such as stimulus size, shape, motion, and color (Abaid et al., 2012;
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Gerlai, 2017). Also, the number of stimuli affects social preference and decision-making
(Arganda et al., 2012; Pritchard et al., 2001).
Interestingly, computer-generated dots exhibiting age-specific characteristic swim kinetics can
elicit shoaling in juvenile (15–27 dpf) or adult zebrafish (Larsch & Baier, 2018b). Reciprocal
interaction is not necessary to start shoaling, while attraction was strongest to dots of 1.8–3.7
mm. This preference mirrors the actual size of body parts more salient for fish (e.g., head,
torso). Consistently, older animals tend to prefer larger dots.
A specific visual circuit involved in the selection of larvae characteristic swim kinetics (bout-like
acceleration) was found in juveniles of 21 dpf (Kappel et al., 2022). Global activity maps by c-fos
in situ hybridization chain reaction (HRC) revealed a cluster of brain areas whose activity was
modulated by virtual and real conspecifics. These involve some evolutionary conserved
hypothalamic components and the optic tectum, the dorsal thalamus (DT), and the posterior
tuberculum, hinting at interesting roles in the visual pathway. Two-photon calcium imaging
confirmed a posterior cluster of neurons in the dorsal thalamus selective for bout swim (bout
preference neurons, BPN). Interestingly, this activation was specific for acceleration at 5 mm/s
fish-like speed and characteristic bout frequency. These neurons are already present in larvae
although at a lower number. Analysis of connectivity by electron microscopy revealed not only
projections from the tectal periventricular neurons to the dorsal thalamus but also connections of
these back to the tectum or directed to the hypothalamus. A possibility is that during
development DT neurons mature projections to hypothalamic as well forebrain areas, such as
the ventral forebrain that are known to be causally involved in social behavior in adults (Stednitz
et al., 2018; Tallafuss et al., 2022). Chemogenetic ablation of tectal cells reduced the number of
BPN active neurons in the dorsal thalamus by more than 80% and determined loss of attraction
toward moving dots in 21 dpf juveniles. Despite the disruption of shoaling and inversion in the
20

characteristic ring of attraction, collision avoidance and escape responses to looming stimuli
were intact, thus suggesting diversification of circuits for these behaviors.
Figure 1.2. Stimuli and neural circuits involved in social behaviors.
A,B Left: Several types of stimuli were presented to the visual field of zebrafish using a virtual
reality assay. Black dots vary in angular size, vertical dimension, horizontal dimension, and
number. At 7 dpf, these stimuli elicited an aversive turn with an increasing probability of
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repulsion with an increase in the retina occupancy. At 21 dpf, stimuli of the same size were
considered attractive. Right: the model proposed by Harpaz et al. (2021) hypothesized the
existence of two different populations in downstream areas that are responsible for attraction or
avoidance of social stimuli. While only the repulsive population is mature at 7 dpf, the balance of
excitation and inhibition of the two populations determines the behavior of the fish at 14–21 dpf.
C Left: black dots with bout-like motion elicited shoaling behavior in juvenile zebrafish, while
continuously moving dots were considered not attractive (Larsch & Baier, 2018b). Right:
Connectivity patterns of dorsal thalamus where Kappel et al. (2021) found a cluster of neurons
selective for bout swim. Rth, rostral thalamus; POA, preoptic area; CMid, caudal midbrain; DT,
dorsal thalamus; OT, optic tectum; Hyp, hypothalamus.
Retinal occupancy and physical features, such as area, shape, and number of stimuli, are
particularly relevant for collective behaviors. By applying a virtual reality assay, Harpaz et al.
(2021) were able to study their role in moving stimuli (black dots) projected to the retinal space
by varying each variable at a time while keeping all the others constant (Figure 1.2). They could
notice that, at 7 dpf, an increment in the angular size increases the probability of an aversive
turn, while, at 21 dpf, dots as large as 45° were considered attractive social stimuli. The vertical
size of the stimuli had a greater relevance for animals. Changing the height of the dot increased
escape behavior in 7–21 dpf, but an increase in width did not have an effect on 7 dpf fish and a
moderate one in 14–21 dpf fish. Concerning the number of dots, animals seemed to compute a
weighted average of the response to each stimulus presented alone, with weight proportional to
its size. Thus, visual occupancy seems primary concerning the number and density of stimuli.
The consistent role of retinal occupancy but the different behavioral responses at 7, 14, and 21
dpf made Harpaz et al. (2021) hypothesize the existence of two different populations in
downstream areas that are responsible for attraction or avoidance toward stimuli (Figure 1.2).
According to this model, retinal ganglion cells map the vertical height of stimuli at each visual
angle and project to two different populations of neurons: repulsive and attractive. There, RGC
activity is first integrated and later averaged by specific units. These output units then send
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excitatory/inhibitory projections to motor centers determining the turning direction of the fish.
While only the repulsive population is mature at 7 dpf, the balance of the two populations
determines the behavior of the fish at 14–21 dpf. According to this model, the quantity
estimation process is already mature at 7 dpf, while the control of behavior changes over
development.
Moving to other sensory modalities, mechanosensitive neuromast cells of the lateral line also
contribute to the perception of conspecifics, modulating the expression of parathyroid hormone
2 (pth2) of the dorsal thalamus neurons in zebrafish (Anneser et al., 2020). Interestingly, Pth2
expression follows a quantitative relationship with the social environment of the animals
throughout all developmental stages (5–21 dpf) and adulthood. Indeed, while isolated fish
showed a rapid reduction of the level of pth2, its expression linearly increased with the number
of fish present. Also, pth2 seems sensitive to the current social setting and its expression is not
altered in the long term. However, when visually stimulated while physically isolated by a glass
barrier, Pth2 levels were not altered. Therefore, pth2 expression seems specific for mechanical
stimulation and strongly tracks the group size of conspecifics. Remarkably, these pth2
expressing neurons overlap with the bout preference cells in the dorsal thalamus (Kappel et al.,
2022). This might suggest the dorsal thalamus as a possible multisensory area integrating
sensory signals of conspecifics. Recently, a loss-of-function mutation in the gene pth2 lowered
shoal cohesion in adults (Anneser et al., 2020), suggesting a role of this hormone in regulating
downstream signals important for shoaling.
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1.7 Neural Correlates of Continuous and Discrete Magnitude in
Zebrafish Adult Brain
Recently, part of the neural network associated with the estimation of continuous and discrete
quantity in the zebrafish brain has been identified (Messina et al., 2020, 2022). Adult zebrafish
were trained to familiarize themselves (habituation phase) with artificial stimuli, small red dots
(three or nine dots) that changed in individual position, density, and size, while maintaining their
numerousness and overall surface from trial to trial. During the subsequent dishabituation
phase, separate groups of fish faced different types of change in the stimuli: a change in
number (nine or three dots with the same overall surface); in size (with the same shape and
number); in shape (squares instead of dots); and no change at all (control group). Combining
this spontaneous habituation/dishabituation paradigm with the evaluation of the expression of
specific markers of neural activity, i.e. the immediate early genes (IEGs) c-fos and egr-1, we
found a specific activation of the thalamus and the most caudal part of the dorso-central (Dc)
pallium in fish facing a change in numerosity (Figure 1.3A) concerning the other experimental
conditions (Messina et al., 2020, 2022). These results agree with evidence reporting the
involvement of thalamic nuclei in 10-year-old children performing quantity estimation in fMRI
studies (Kovas et al., 2009) and with the relevant role of subcortical (and more generally
subpallial) territories in tasks involving magnitude estimation (Lorenzi et al., 2021b; Vallortigara
et al., 2022). Also, they are in line with the response to numerosity shown by single-cell
recording experiments in the parietal and prefrontal cortex in the non-human primate cortex
(Nieder, 2016; Nieder et al., 2002; Nieder & Merten, 2007; Viswanathan & Nieder, 2020) and
young chicks (Kobylkov et al., 2022), and in fMRI experiments in humans (Piazza et al., 2004).
Further research will be needed to clarify the possible homologies/analogies between the
dorso-central pallium (Dc) of zebrafish and the cortical/pallial areas responding to numerosity in
the mammalian and avian brains(Nieder, 2021).
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Figure 1.3. Schematic representation of the habituation/dishabituation paradigm used to
identify neural correlates associated with a change in discrete and continuous magnitude
in the adult zebrafish brain.
A A change in number from 3 (habituation) to 9 (dishabituation) dots elicits an approach
interaction. On the contrary, avoidance of the stimulus is detected in the change from 9 to 3
dots. An evaluation of IEG expressions revealed the main role of the thalamus and the
25

dorso-central pallium (Dc) in the elaboration of changes in discrete quantity (numerosity)
(Messina et al., 2020, 2022).
B A change in size, i.e., a decrease (1/3x) or an increase (3x), revealed the main role of the
retina and the optic tectum in the elaboration of continuous quantity (stimulus size) (Messina et
al., 2020, 2022).
Hodological studies suggest that Dc contains the major descending pathway of the fish pallium
to the optic tectum and medulla oblongata (Harvey-Girard et al., 2012; Ito & Yamamoto, 2009;
Rodríguez et al., 2021; Yamamoto et al., 2007; Yamamoto & Ito, 2005). Intriguingly, we found
that the amount of EGR-1-positive cells in Dc tended to increase with changes from small to
large numerosity and to decrease with changes from a large to a small set of dots, suggesting
that a higher or lower activation of Dc could be related to a higher/lower response of fish motor
responses (approach or avoidance) in association with the direction of the change in
numerosity; this was also supported by different behavioral measures (Messina et al., 2022).
As to the response to continuous quantity as opposed to discrete ones (Figure 1.3B), we found
a selective modulation in the expression levels of IEGs in the retina and the optic tectum in the
groups of zebrafish facing a change in the size of the stimulus (a three-fold increase or
decrease in the size of the individual dots) (Messina et al., 2022). These results support
previous evidence in zebrafish larvae that showed an involvement of the optic tectum in the
categorization of visual targets of different sizes in approach/avoidance behavior (Abbas &
Meyer, 2014; Preuss et al., 2014) . Furthermore, stimulus-size selectivity was also reported in
studies of the intra-tectal circuitry involved in the prey-catching behavior of amphibians
(Cervantes-Pérez et al., 1985; Ewert & Gebauer, 1973) and in single cells recording
experiments in pigeons (Gusel’nikov et al., 1971), suggesting a general mechanism of activation
of tectal circuits about continuous magnitude discrimination in vertebrates (Lorenzi et al.,
2021b).
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Further research is ongoing to detail the ascending and descending pathways driving the
response to continuous and discrete magnitude-related visual stimuli from the retina, through
the thalamic and optic tectum nuclei, toward the dorsal pallium and the premotor and motor
nuclei of the zebrafish brain.
1.8 Modeling Developmental Dyscalculia in Fish
As discussed above, the finding that zebrafish’s abilities to discriminate both continuous and
discrete quantities are comparable to those observed in mammals raises the possibility of using
this species as a model to investigate both the neural circuitry and the genetic mechanisms
underpinning numerosity representation and the role of genes in developmental dyscalculia
(DD). DD is a recently recognized congenital condition that results in an impaired ability to
perform simple arithmetic operations. It describes children who fail to achieve adequate
arithmetic proficiency despite normal intelligence, scholastic opportunity, emotional stability, and
necessary motivation (Diagnostic and Statistical Manual of Mental Disorders, 2013). The
disorder has a high prevalence of 5–7% (Shalev, 2004, 2007).Dyscalculic individuals are found
to be unable to grasp the abstract concept of number (cardinality) by the expected age,
meaning that they will also be unable to learn the place principle (ordinality) and calculation
(Kaufmann et al., 2013; Rubinsten, 2015). These learning difficulties have lifelong
consequences, correlating with socioeconomic status (Ritchie & Bates, 2013). Deficits in
symbolic mathematics have also been found to be associated with low performance in
non-symbolic numerical tasks (Mazzocco et al., 2011; Piazza, 2010a).
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Like other learning disabilities, DD has a significant familial aggregation (Shalev et al., 2001)
with a strong effect of genetic influence (Alarcón et al., 1997; Kovas et al., 2009; Oliver et al.,
2004). This, along with the clinical characterization of dyscalculia as a syndrome, led to
Genome-Wide Association Studies (GWAS) being undertaken. Docherty et al. (2010) used a
twin study to investigate the genes affecting mathematical ability and disability. Twins in England
and Wales were given web-based testing and the National Curriculum Review ratings, which
were combined to give a composite measure of mathematical ability. Stage 1 used the 16th
percentile of the top and bottom performers in the composite score, with 300 subjects for
extremely high and extremely low performance. Stage 2 took the 20th percentile and stage 3
used individuals with a range of abilities. GWAS looking for Single Nucleotide Polymorphisms
(SNPs) associated with mathematical performance in stage 1 found 46 candidate SNPs. These
results were validated in stage 3, where 10 SNPs remained significantly associated with
individual differences in mathematical ability. The nearest genes to these SNPs were MMP7,
GRIK1, DNAH5, SMAD3, ARID1B, FLJ20160, GUCY1A2, NRCAM, DLD, and NUAK1, making
them potential candidates for influencing numerical processing. No overall large effect was
found in the study suggesting the genetic influence on mathematical ability is caused by multiple
Quantitative Trait Loci (QTL) of small effect (Docherty et al., 2010). A more recent GWAS study
was performed by Chen and colleagues. The mathematical abilities of school-age children were
assessed by looking at the midterm and final math exam results in each semester. A combined
meta-analysis identified four SNPs associated with mathematics ability. All these SNPs were
located on the SPOCK1 gene, a gene previously implicated in neurodevelopment through
neurogenesis, now a potential candidate for the development of mathematical ability (H. Chen
et al., 2017).
Other genetic studies have identified candidates for developmental dyscalculia. Quantitative
data on mathematical ability was correlated with genome data of 200 children with dyslexia and
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found that the rs133885 variant in the myosin-18B (MYO18B) gene is the only marker that had
an association with the mathematical ability at a statistically significant level. Neuroimaging of
79 healthy adults showed that carriers of the rs133885 risk allele displayed a reduced depth of
the right intraparietal sulcus, which has been proposed to mediate numerical processing
(Ludwig et al., 2013). A Copy Number Variant (CNV) scan for psychiatric conditions in the
Icelandic population also identified a region in chromosome 15q11.2 between breakpoints 1 and
2 [15q11.2 (BP1-BP2) deletion] in controls with a history of dyslexia and dyscalculia, disrupting
GCP5, CYFIP1, NIPA2, and NIPA1 (Stefansson et al., 2014; Ulfarsson et al., 2017). This region
is a recurrent site for chromosomal rearrangements underlying different neurodevelopmental
conditions.
Another way to identify DD-associated genes is to look at syndromes with a dyscalculia
component and any genes associated with those syndromes. For example, Fragile X syndrome
(FXS) and Prader–Willi Syndrome (PWS) are human genetic disorders that are associated with
poor number cognition. FXS is the most common cause of inherited intellectual disabilities. It is
caused by the expansion of trinucleotide CGG in the fragile X mental retardation 1 gene (FMR1)
(Bagni et al., 2012). Additionally, premutation expansions (55–200 repeats) can cause
neurodevelopmental problems such as deficits in numerical cognition and arithmetic (Cordeiro
et al., 2011; Goodrich-Hunsaker et al., 2011; S. H. Lee et al., 2012; Murphy et al., 2006; K.
Sullivan et al., 2006; Tassone et al., 2014). CYFIP1 interacts with FMR1 as part of the
CYFIP1-FMR1-eIF4E pathway. This pathway affects synaptic plasticity through its role as a
negative regulator of translation. FMR1 binds to CYFIP1, and the FMR1-CYFIP1 complex binds
to the translation initiation factor eIF4E. This inhibits the eIF4E-mediated initiation of translation,
thereby affecting the translation of a large group of target messenger RNAs (mRNAs),
particularly those found at synapses. Known targets include ARC (AKA Arg3.1), MAP1B,
CAMKII, PSD-95, GLUR1, and GLUR2 (Abekhoukh et al., 2017).
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In PWS, although there is a very severe phenotype, mathematical abilities are more impaired
relative to other cognitive functions and approximately 70% of PWS cases are caused by the
deletion of 15q11-13. As mentioned above, CYFIP1 has been found to be one of the 4 genes in
the 15q11.2 copy number variation, which when deleted confers the risk of dyscalculia (Bertella
et al., 2005). The Cytoplasmic FMR1-Interacting Protein (CYFIP) gene is highly conserved and
expressed in the central nervous system. CYFIP1 and CYFIP2 are enriched at inhibitory
synapses and have a role in regulating the balance between excitatory and inhibitory synapses
(Davenport et al., 2019). CYFIP1 and CYFIP2 also consistently appear in the top 10% of hits in
published GWAS studies (H. Chen et al., 2017; Davis et al., 2014), suggesting that they may
play a role in developmental dyscalculia.
In addition to FXS and PWS, individuals with William’s syndrome (WS) have been found to
show dyscalculia phenotypes with a range of deficits and impairments in aspects of their
numerical abilities (Ansari et al., 2007; O’Hearn et al., 2011; Opfer & Martens, 2012). Deficits in
elements of patients with WS’ symbolic (Krajcsi et al., 2009) and non-symbolic (Rousselle et al.,
2013) systems have been observed. Another study found the non-symbolic system (specifically
the ANS) of WS adolescents is functioning at the same level as 2–4-year-old Typical
development (TD) children, whereas the symbolic system is comparatively functioning at a
much similar level to TD 6–9-year-olds. This suggests that WS individuals have greater
impairment in their non-symbolic abilities in comparison to their symbolic abilities (Libertus et al.,
2014).
William’s syndrome (WS) is genetically defined by a typical hemizygous 7q11.23 microdeletion
of 1.55 million base pairs (Mb) that encompasses approximately 28 genes (Bayés et al., 2003).
One of the genes in this microdeletion is BAZ1B (bromodomain adjacent to zinc finger domain,
30

1B), also known as Williams syndrome transcription factor (WSTF) (Kitagawa et al., 2011).
BAZ1B is an evolutionarily conserved protein tyrosine kinase and is expressed throughout
neurodevelopment. WS neurons show defects in differentiation influenced by haploinsufficiency
of BAZ1B with widespread gene expression changes in neural progenitor cells (Lalli et al.,
2016). This haploinsufficiency explains 42% of the transcriptional dysregulation seen in WS
neurons. Another gene in the WS microdeletion is FZD9 (Frizzled class receptor 9) (Kitagawa et
al., 2011). Frizzled receptors are the mediators of the WNT pathways, which play fundamental
roles in cell differentiation and organism development (Corda & Sala, 2017). Patients with WS
found that their neurons had longer dendrites, an increased number of spines along with
aberrant calcium oscillations, and altered network connectivity, which were found to be mediated
by FZD9 (Chailangkarn et al., 2016). Their role in neuron dysfunction in WS highlights these two
genes as potential candidates for a causal role in developmental dyscalculia.
Neural networks are highly conserved across vertebrates, and zebrafish have a relatively simple
neural system and high homology with the human genome (Howe et al., 2013), supporting the
translational validity of the model for functional validation. The establishment and subsequent
optimization of genome editing technologies in zebrafish have enabled reverse genetic
approaches to be used in the model for testing the functional role of GWAS-associated loci
using the highly efficient CRISPR/Cas9 system (Hwang et al., 2013). Reverse genetic
approaches are used to test the hypotheses regarding a causal role, a developmental role, or a
mechanism of action of a candidate gene associated with human disorders. These have been
used to great effect in zebrafish as endophenotypes of disorders can be tested in robust assays
that, coupled with CRISPR/Cas9 loss of function and molecular assays, can define causal
genes involved in the disorders. A gene expression screening of nine genes (baz1b, fzd9, limk1,
tubgcp5, cyfip1, grik1a, robo1, nipa1, and nipa2) is associated with human developmental
dyscalculia (Chai et al., 2003; Docherty et al., 2010; Maver et al., 2019; Tassabehji, 2003),
31

which revealed that most of them are largely distributed in the zebrafish dorsal pallium and five
of them (grik1a, nipa1, nipa2, and robo1) are asymmetrically distributed between the left and the
right hemispheres, opening the way to another crucial theme that links developmental
dyscalculia with brain laterality (Messina, Boiti, et al., 2021; Shalev, 2004; Shalev et al., 1995).
With the establishment of robust assays of numerical abilities in zebrafish, we are well placed to
test the causal roles of candidate genes and their mode of action.
1.9 Future Directions: New Methodologies in Calcium Imaging for
Next-Gen Studies
Recent advancements in live imaging have enabled recording the functional activity map of
large areas, and entire volumes, of the brain of small model organisms (e.g., C. elegans,
drosophila melanogaster, and danio rerio), while the animals undergo naturalistic behavior. This
brain-wide imaging approach enables the exciting prospect of unbiased observation and
identification of the relevant brain substrates that underlie behavior. A comprehensive review of
these imaging advancements is beyond the scope of this contribution and has been done
elsewhere (Weisenburger & Vaziri, 2018). Here, we focus on the discussion of key
developments that could provide relevant advancements for combining imaging of zebrafish
neural circuits with behavior. In particular, given the lack of live imaging studies investigating the
detection of discrete quantities in comparison with the copious literature on size detection, we
suggest an application of these methods for the study of numerosity in zebrafish.
As discussed previously, most zebrafish numerosity or numerosity-related studies have involved
the animal’s visual response to numerosity stimuli. Thus, when imaging this numerosity
response, it is critical to ensure that the animal’s visual response is not compromised by the
32

laser light used to excite the fluorescence signals. Zebrafish can detect wavelengths in the
visible range of ∼400–650 nm (Cameron, 2002), hence ruling out the usage of conventional
1-photon excitation with visible wavelengths. Thus, to avoid interfering with the zebrafish’s visual
response, frequent imaging should be carried out with 2-photon excitation, where the pulsed
laser light has wavelengths in the near-infrared range, ∼800–1,000 nm, which is invisible to the
zebrafish. We will, thus, focus our discussion below mainly on imaging technologies that use
2-photon excitation.
A mainstream of live neuroimaging is the modality of 2-photon excitation point-scanning
microscopy (2p-PSM) (Denk et al., 1990a), where the 3D volume of interest is imaged one voxel
at a time by serially raster-scanning the point over the volume. Recent refinements in better
2-photon laser sources, better photon-counting detectors, and better design of optical detection
pathways to maximize the photon collection efficiency, and a plethora of turn-key user-friendly
commercially-available instruments at affordable prices (Bruzzone et al., 2021; Weisenburger &
Vaziri, 2018), have increasingly made 2p-PSM available to the zebrafish neuroscience
community. In 2p-PSM, the achievable 2D (frame) imaging rate is typical ∼1 Hz with systems
that use a galvanometer scanner and ∼30 Hz with systems that use a resonant scanner. Volume
coverage is achieved by scanning the imaging frame axially, thus achieving a volumetric
imaging rate that scales inversely with the number of z-slices (e.g., 10 z-slices recorded at 1 Hz
frame rate will yield ∼0.1 Hz volumetric rate).
In the effort to improve the imaging speed of 2p-PSM and reduce the potential photodamage
associated with the intense peak laser intensity needed for the point-scanning and
serially-recorded strategies, new parallelized-recorded imaging modalities have been
developed. In 2-photon light-sheet microscopy (2p-SPIM) (Truong et al., 2011a), the excitation is
achieved by scanning a gently-focused pencil-like laser beam to create the sheet-like
33

fluorescence signal along the detection focal plane, which is then imaged by a camera. The
parallelized 2D image collection enables a longer signal integration time for each voxel, thus
requiring a much-reduced peak laser intensity compared with 2p-PSM. Recent implementations
of 2p-SPIM, as applied to brain-wide functional imaging of zebrafish (de Vito et al., 2022;
Keomanee-Dizon et al., 2020a; Wolf et al., 2015a, 2017), have achieved imaging frame rates of
20–150 Hz and volumetric rates spanning ∼1–5 Hz. Importantly, in these studies, the upper limit
of the imaging rate is not dictated by the imaging hardware but rather by the putative threshold
of photodamage, which starts to appear as the laser power is increased.
Taking the parallelized-recording strategy to the third dimension, light field microscopy (LFM) is
an imaging modality that uses a plenoptic (i.e., multi-view) detection strategy to capture an
entire 3D volume of interest in a single 2D camera snapshot and computation to reconstruct the
original image volume (Levoy et al., 2006a). Thus, a typical imaging frame rate of ∼30 Hz will
readily yield a very fast volumetric rate of 30 Hz after reconstruction. While the resolution
achieved is necessarily reduced to provide the extended volume coverage beyond the native
focal plane (as compared to conventional modalities that record only the focal plane),
light-field-based imaging approaches still achieve single-neuron resolution over depths of 100
microns or more in imaging the zebrafish brain (Cong et al., 2017; Prevedel et al., 2014a;
Truong et al., 2020). The latest developments and applications of LFM in neuroimaging of
zebrafish (Lin et al., 2020; Z. Zhang et al., 2021) showed great promise to provide fast,
volumetric imaging of multiple-regions or whole-brain coverage of zebrafish during naturalistic
behavior. Light-field-based selective volume illumination microscopy (SVIM) (Madaan et al.,
2021; Truong et al., 2020) combines the spatially-selective illumination strategy of light-sheet
microscopy with light-field detection to significantly improve the signal contrast while maintaining
the high volumetric imaging rate of LFM. SVIM has also been implemented with 2-photon
excitation, providing a promising way to study visually-sensitive processes, such as numerosity
34

in zebrafish. One general challenge with light-field-based techniques is the substantial amount
of time and computational power needed to carry out the image reconstruction post-acquisition,
which typically requires ∼103 times longer to reconstruct compared to the imaging volumetric
rate. Toward mitigating this computation challenge, a variant of LFM called Fourier-LFM (Cong
et al., 2017; Guo et al., 2019a), by operating with a spatially-invariant point-spread-function,
reduces the reconstruction time by ∼2 orders of magnitude, thus bringing LFM closer to the
wide-spread application to neuroscience research.
The above-described trends in the maturation/development of established/novel imaging
technologies have enabled exciting progress in zebrafish neuroscience in recent years. We
highlight here several of these works. In Lee et al. (2017), 2p-SPIM was used to image 6-dpf
zebrafish undergoing sleep and wake, to monitor the brain-wide activity map as a function of
natural and optogenetically driven sleep. Of note, the 2p-SPIM imaging was gentle and visually
inert, enough to not disrupt the normal sleep/wake behavior of the zebrafish. Wagle et al. (2022)
used 2p-PSM with 5–7-dpf zebrafish to study the brain-wide perception of the emotional valence
of light and found that it is regulated by the distinct hypothalamic corticotropin-releasing factor
neurons. Here, again, the visual inertness of the 2-photon excitation light was critical to enable
brain-wide imaging while the animals were treated to cycles of light/dark stimuli. Finally,
2p-SPIM was used by de Vito et al. (2022) to map the whole-brain activity patterns of 4-dpf
zebrafish undergoing epileptic seizures. The authors characterized the spatial-temporal
dynamics of the pathological seizure activity and identified a previously-unknown caudo-rostral
ictal wave pattern.
Together, the studies described above point to the exciting possibility that the numerosity
capability of zebrafish could be studied using brain-wide functional imaging to identify not only
its neural substrate (i.e., “number cells”) but possibly also the circuits involved in how the animal
35

processes number stimuli. Toward this goal, we have started a research program employing
whole-brain functional imaging to study zebrafish numerosity. We highlight some of our
preliminary results in Figure 1.4. We used the microscopy platform described in
Keomanee-Dizon et al. (2020) to record the whole-brain activity map of awake zebrafish larvae,
which were transgenically labeled with fluorescent calcium indicators. A projector system was
used to present visual numerosity stimuli to the zebrafish (Figure 1.4A). The stimuli consisted of
a particular number of black dots on a diffuse red background, and the repeated presentations
were controlled to find the activity patterns that are intrinsically sensitive to the number of stimuli
and not to other continuous variables of the dot patterns (such as radius, total area, total
perimeter, etc.) (Figure 1.4B). In an exemplary recording, the fish were presented with multiple
trials of blank (no stimulus), 2 dots, blank, and then 5 dots, as depicted in Figure 1.4E. We then
used a T-score-based analysis approach to identify neurons that exhibited a difference in their
activity under the different stimuli (Figure 1.4D). We found that many neurons have differential
activity between 2 dots (or 5 dots) versus blank, particularly in the optic tectum. Promisingly, we
also found neurons, located mainly in the pallium and the habenula (Figure 1.4D), that have
differential activity between 2 vs 5 dots. The forebrain location for these putative number
neurons is consistent with our team’s results in adult zebrafish (Messina, Boiti, et al., 2021;
Messina, et al., 2022), discussed earlier in Section “Neural Correlates of Continuous and
Discrete Magnitude in Zebrafish Adult Brain”. We are poised to confirm and expand the
preliminary results shown here to fully characterize the cellular substrate of the numerosity
capability of the zebrafish larvae.
36

Figure 1.4. Whole-brain functional imaging to find neural substrate of zebrafish
numerosity capability.
A Schematic setup of the 2p-SPIM setup that allows calcium imaging of awake zebrafish larvae
that are subjected to visual numerosity stimuli.
B Examples of the numerosity stimuli, which consist of a particular number of black dots on a
diffuse red background. The visual patterns are controlled for various non-numerosity
37

continuous variables to find the responses that are intrinsic to the recognition of discrete
numbers.
C Schematic drawing of the brain. The forebrain includes the pallium (Pa) and the habenula
(Hb). The midbrain contains the optic tectum (OT).
D Representative results from 8-dpf larvae show neurons that exhibited different levels of
activity during different stimuli (e.g., 2 versus 5 dots, etc.). Green: nuclei of identified neurons.
Magenta: anatomical background generated via the maximum-intensity projection in Z of the
standard deviation projection in time, depicting neurons with time-varying activity. The raw
dataset covers the volume of ∼350 μm × 600 μm × 250 μm (depth), taken with three sections
per volume for 42 min.
E Representative activity traces, of the two neurons selected by arrowheads in panel (D), during
number stimuli. The line graph depicts activity levels as ΔF/F for the time trial as shown,
averaged over n = 50 trials. Neuron 1 (blue arrowhead): higher activity levels during the 5-dot
stimuli compared to the 2-dot stimuli. Neuron 2 (yellow arrowhead): higher activity levels during
the 2-dot stimuli compared to the 5-dot stimuli. P < 0.05, bootstrapping with resampling. Error
bars represent SEM, n = 50. Scale bar in panel (D),100 μm.
1.10 Conclusion
The main goal of this review was to provide a state of the art of our current behavioral and
neurobiological understanding of the mechanisms underlying quantity (discrete and continuous)
encoding and processing in fish.
Although the ability to estimate quantities was documented in both invertebrates and
vertebrates and the involvement of subpallial and pallial brain structures was described in
different taxonomic groups in vertebrates (Lorenzi et al., 2021b; Messina, Boiti, et al., 2021;
Nieder, 2021; Vallortigara et al., 2022), the exact neural circuits devoted to the elaboration of
continuous and discrete magnitudes have not been precisely identified as of yet.
Zebrafish represents an excellent animal model system to investigate the genetics and
molecular mechanisms of behavior and may be instrumental to develop the neurobiology of
38

magnitude cognition with a complete characterization of neurons and neural circuits associated
with quantity discrimination processes, laying the foundations for comparative molecular studies
in other animal species, including humans.
39

Chapter 2 - Applying Two-Photon Excitation Microscopy to Live
Imaging
This chapter focuses on the application of two-photon excitation microscopy (TPE) for imaging
live samples, highlighting the technological advancements that enable high-spatial and temporal
resolution. Through detailed imaging techniques, this chapter provides insight into how TPE
microscopy is used to investigate the neural substrates responsible for numerical cognition in
zebrafish, specifically targeting the processing of continuous and discrete quantities.
This chapter contains work published in Communications Biology - Nature by:
Peter Luu
1,2
, Scott E. Fraser
1,2,3
, Falk Schneider
1,4
1) Translational Imaging Center, Michelson Center for Convergent Bioscience,
2) Department of Biological Sciences, Division of Molecular and Computational Biology,
3) Alfred Mann Department of Biomedical Engineering,
4) Dana and David Dornsife College of Letters, Arts and Sciences,
University of Southern California, Los Angeles, CA, 90089, USA
40

2.1 Abstract: More than double the fun with two-photon excitation
microscopy
For generations researchers have been observing the dynamic processes of life through the
lens of a microscope. This has offered tremendous insights into biological phenomena that span
multiple orders of time- and length-scales ranging from the pure magic of molecular
reorganization at the membrane of immune cells, to cell migration and differentiation during
development or wound healing. Standard fluorescence microscopy techniques offer glimpses at
such processes in vitro, however, when applied in intact systems, they are challenged by
reduced signal strengths and signal-to-noise ratios that result from deeper imaging. As a
remedy, two-photon excitation (TPE) microscopy takes a special place, because it allows us to
investigate processes in vivo, in their natural environment, even in a living animal. Here, we
review the fundamental principles underlying TPE aimed at basic and advanced microscopy
users interested in adopting TPE for intravital imaging. We focus on applications in
neurobiology, present current trends towards faster, wider and deeper imaging, discuss the
combination with photon counting technologies for metabolic imaging and spectroscopy, as well
as highlight outstanding issues and drawbacks in development and application of these
methodologies.
2.2 Introduction
Two-photon excitation (TPE) laser scanning microscopy (LSM) has evolved from a custom tool
to a broadly available imaging modality in the life sciences. Number of users and applications
have grown dramatically in the decades since it was demonstrated by Winfried Denk and his
coworker James “Jim” H. Strickler in the Webb lab (Denk et al., 1990b). TPE microscopy has
emerged as the gold standard for deep tissue and intravital imaging as well as for metabolic
studies. Exemplary applications include imaging of cultured cells(Bousso et al., 2002), imaging
41

of neuronal activity in single cells and tissue slices (Denk et al., 1994, 1995) as well as model
organisms such as mice (Stosiek et al., 2003), rats (M. R. Sullivan et al., 2005), or zebrafish
(Renninger & Orger, 2013; Yoshimatsu et al., 2021), and deep-tissue imaging (Helmchen &
Denk, 2005), even in challenging settings such as following immune cell trafficking in intact
lymph nodes (Miller et al., 2003). In this review, we will first cover the basics of fluorescence and
TPE microscopy and then present many of the growing sets of applications in biological imaging
along with cutting-edge technical developments.
2.2.1 Principles of fluorescence and TPE microscopy
Fluorescence microscopy provides molecular sensitivity and specificity to image a fluorescently
labeled species against background. Typically, a fluorophore absorbs a single photon and emits
a single photon of a longer wavelength, causing a red shift between excitation and emission
termed the Stokes’ shift (Figure 2.1a,b) (Lakowicz, 2006). This Stokes’ shift is the foundation for
contrast in fluorescence microscopy as dichroic mirrors and appropriate filters can be used to
separate the excitation and emission wavelengths. The time delay of a few nanoseconds (ns)
between excitation and emission required for cycling a typical fluorophore from ground state to
excited state and back permits Fluorescence Lifetime Imaging Microscopy (FLIM), which
exploits this characteristic delay as an additional source of contrast (Figure 2.1b). Other
photophysical effects such as phosphorescence (as a result of intersystem-crossing, ICS) might
be used to generate contrast but are less popular because they offer fewer photons per unit
time (Abbasizadeh & Spencer, 2021).
Two-photon excitation (TPE) microscopy is made possible by a fluorophore simultaneously
absorbing two photons of about double the wavelength (half the energy) required for one-photon
excitation (Figure 2.1a,b). This was first predicted by Maria Goeppert-Mayer in the 1930s
(Göppert-Mayer, 1931), whose pioneering work is recognised by naming the unit of the
42

probability of two photon absorption (TPA) after her, GM units (1 GM = 10
-50⋅cm4⋅s) (Zipfel,
Williams, & Webb, 2003). The first experimental demonstration of fluorescence from TPE was
achieved by Kaiser and Garret in europium doped calcium fluoride crystals (CaF2
:Eu
2+
) decades
later (Kaiser & Garrett, 1961). Because of the need for two photons to excite the fluorophore,
the probability of absorption (and subsequent fluorescence emission) depends on the square of
the number of photons reaching the fluorophore simultaneously; thus, two-photon excitation
exhibits a non-linear (quadratic) relationship to the excitation intensity unlike the linear
relationship in one-photon excitation (Zipfel, Williams, & Webb, 2003) (Figure 2.1c, left). The
two-photon absorption cross-sections of typical fluorophores require large, instantaneous
photon densities, which are usually achieved by tightly focusing the beam (mW power) of a
short pulsed laser (~100s fs pulse width, typically pulsing at a repetition rate of ~80 MHz),
concentrating photons both spatially and temporally. Because the photon density falls off by the
square of the distance from the focus, excitation (and fluorescence emission) falls off by the
fourth power of the distance from the focus of the infra-red (IR) laser beam (Diaspro et al.,
2006). This provides optical sectioning comparable to a confocal (one-photon excitation)
microscope which, however, requires a confocal aperture, pinhole, to reject fluorescence excited
above and below the optical section in focus (Figure 2.1c). Given the selective excitation of the
TPE beam, the excited fluorescence can be collected far more efficiently because scattered
emission can also be collected (Figure 2.1d). Thus, TPE reduces out-of-focus excitation
(reducing photobleaching and phototoxicity), increases photon collection efficiency (no pinhole,
collection of full emission peak) (Denk et al., 1990b; Helmchen & Denk, 2005; Mainen et al.,
1999) and extends the depth of imaging because IR photons are more than 10-fold less
scattered than visible light (Helmchen, 2009; Helmchen & Denk, 2005; Key et al., 1991). It
should be noted that more than two photons can be absorbed at the same time which is
exploited in three- and multi-photon microscopy providing an exciting avenue to deep tissue
43

imaging (Hell et al., 1996; Wokosin et al., 1996; Xiao et al., 2023). Here, however, we focus on
the more widespreadly used two-photon excitation.
TPE microscopy is not without its concerns and limitations. The high laser powers required
might result in photodamage, yet the absorption of biological materials of infra-red light is
considered low. It is worth noting that the efficiency of two-photon absorption (action cross
section of the fluorophore in units of GM), a molecular property of the dyes, is small as
compared to absorption in one photon but efforts to improve probes are constantly ongoing
(Benitez-Martin et al., 2020; Mütze et al., 2012; P. Wang et al., 2017; Zipfel, Williams, & Webb,
2003). Given that the two-photon brightness is set by the absolute TPA cross-section and by the
quantum yield, a fluorescent protein that is bright in one photon excitation might not appear as
bright in TPE. Finally, the excitation spectra are not simply double the single photon excitation
spectra; instead, the two-photon excitation spectra often show broadening, variable red-shifting
and unexpected peaks due to different quantum mechanical selection rules governing oneversus two-photon excitation (Chung et al., 2005; Drobizhev et al., 2011; C. Xu & Webb, 1996).
Two-photon absorption processes can often be non-intuitive, as the spectra and extinction
coefficients are not simply related to the one-photon absorption properties of the dyes;
Furthermore, computing two-photon absorption properties, especially for large molecules, is
computationally difficult (Chołuj et al., 2022; Ramos et al., 2023). The spectra and absorption
properties must be determined experimentally, as they may be highly dependent on the details
of the experimental apparatus and the biological environment (Drobizhev et al., 2011; Lakowicz
et al., 1997; C. Xu & Webb, 1996).
A typical TPE setup is similar to a standard confocal laser scanning microscope without the
confocal aperture (Figure 2.1e) (Benninger & Piston, 2013; Helmchen & Denk, 2005). The light
source (laser beam) is moved in the sample space using a galvanometric mirror (galvo) to raster
scan each location in an optical section and construct an image, pixel-by-pixel, using the
44

fluorescence collected onto a detector, typically a photomultiplier tube (PMT), an avalanche
photodiode (APD), or a hybrid detector (e.g., GaAsP). Usually, the detector is moved just behind
the objective as there is no need for a pinhole and rescanning the fluorescence in contrast to
descanned one-photon confocal detection (Figure 2.1e). This non-descanned detection method
minimizes light losses by utilizing the entire light-sensitive area of the detector enabling the
capture of scattered emission light and further minimizes light loss by decreasing the number of
optical elements (mirrors, scan lens, tube lens, etc.) (Figure 2.1d). In addition, fluorescence can
be collected along the optical axis (from above in an inverted microscope configuration) allowing
to collect fluorescence emitted in the direction of the excitation making use of signals otherwise
not captured (Crosignani et al., 2012; Dvornikov et al., 2019).
In the time since the first practical TPE microscope was demonstrated more than three decades
ago, the demand for TPE in biological application never ceased (Figure 2.2a) and new varieties
for in vivo microscopy constantly evolve. The application of TPE microscopy has been
empowered by the availability of robust, tunable, ultrafast IR lasers for excitation and by the
availability of turn-key instrument solutions. At least 10 vendors offer TPE microscopes, with
various specifications and custom options. Some instruments are specifically aimed at biologists
driven by user-friendliness; whereas, others are motivated by users demanding more flexibility
for customization, undaunted by the required expert knowledge in optics and hardware/software
integration (A. D. Edelstein et al., 2014). When choosing two-photon microscopy
instrumentation, one needs to consider user-friendliness, costs, and flexibility (Figure 2.2b).
Furthermore, this choice should be driven by the biological phenomena to be investigated, and
driven by a few questions:
1. Do I need access to the optical path?
2. Do I need the best possible single image or do I need a large set of images (time series
or z-stack)?
45

3. Do I need flexibility in wavelength or do I always use the same fluorophores?
Commercial vendors can help customize their solutions to the researcher’s needs but identifying
these needs is paramount before deciding on equipment. Table 2.1 outlines a few of the
available implementations with distinct features. Given these gateway offerings, it seems like a
perfect time for optical veterans and for novice microscopists to start working with TPE
microscopy.
46

Table 2.1: Non-exhaustive list of microscopy vendors offering TPE microscopy
instrumentation highlighting unique features of each.
Vendor Model(s) Notable features
3i VIVO Multiphoton - Very flexible, customisable
platform
- Integrated adaptive optics
Bruker Ultima Series - Rotating nosepiece
- Remote focussing
Leica Microsystems SP8 / Stellaris 8 DIVE - Fully integrated with confocal LSM
- Up to 4 non-descanned detectors
- FLIM acquisition and analysis
packages
Nikon AX R MP - Resonance scanner (720 fps at
512 x 16 pixels)
- Tilting nosepiece
- Array detector for increased SNR
and resolution (NSPARC)
Olympus FVMPE-RS - Broad transmission 400 nm -1600
nm
- Multichannel IR excitation
Prospective
Instruments
MPX - Compact and fully integrated
system
- FLIM capable
Sutter Instruments MOM/DF Scope - Moveable objective
- Collection of emitted light above &
below the sample for increased
detection efficiency/SNR
Thorlabs Bergamo II Series
Mesoscope
- Flexible geometry with rotating
body
- Extended depth of field using
Bessel beam
- Dual plane imaging
- Remote focussing
- TPE random access modality
Zeiss NLO module for LSM 980
(nonlinear optical
microscopy)
- Integrated with LSM platform
- Combination with airyscan offers
increased resolution and speed
47

48

Figure 2.1: Introduction to TPE microscopy.
a Hypothetical excitation (solid blue and orange lines) and emission spectra (solid green line) of
a fluorophore in one-photon and two-photon excitation (one-photon and two-photon excitation
maxima indicated as blue and orange dashed lines, respectively) and typical emission collection
(green bars, bottom).
b Simplified Jablonski diagram showing the ground state (S0
), first excited state (S1
), triplet state
(T1
) and vibrational states (thin lines). Absorption of one or two photons of the right energy
excites the molecule and allows for fluorescence and phosphorescence (return to ground state)
after energy dissipation through vibrational states. Inter system crossing (ICS) can take the
molecule into a long-lived dark-state. From the excited states molecules can react further by
photo-bleaching (loss of fluorescence). The bottom panel outlines approximate time-scales for
the processes shown in the Jablonski diagram.
c Principles of one-photon and two-photon excitation and emission at the focal plane and
out-of-focus. One-photon absorption increases linearly with incident laser light whereas
two-photon absorption increases non-linearly (quadratically) with incident laser light (left
panels). In TPE microscopy, this allows for fluorescence excitation only at the focal spot. In
one-photon excitation, this highlights the increased photo-bleaching due to out-of-focus
excitation (gray). Further this explains the necessity for an aperture in standard confocal
detection (see d).
d Scheme of a typical detection in one- and two-photon excitation experiments: in one-photon
configuration, a pinhole rejects out-of-focus light whereas in TPE microscopy fluorescence only
originates in the focal plane, thus additional scattered photons can be collected, increasing
detection efficiency.
e Scheme of a typical TPE laser scanning microscope. Depicted are beam path, TPE laser
properties, non-descanned detection, and digital image reconstruction. For comparison with
conventional confocal LSM, the position of the descanned detection (before the galvo mirror) is
indicated by a green dashed line (meaning in descanned detection the main dichroic mirror and
the detectors would be moved to this position).
49

Figure 2.2: Popularity and needs of TPE microscopy
a Cumulative citations of reference of Denk et al. Science (1990). This hallmark paper
introduced TPE laser scanning microscopy and the use of non-linear microscopy to biological
samples. Number of citations were exported from Google Scholar.
b Needs and trade-offs in biological application of TPE microscopy: There is a demand for
low-cost equipment that has to be balanced with user-friendliness (ie., turn-key instrumentation)
and the flexibility (e.g., tuneable wavelengths, filters, photon counting applications). Commercial
and home-built setups typically cover different regimes of the needs.
2.3 Wider, faster, deeper - towards volumetric, intravital imaging with
TPE microscopy
Complex biological processes occur across a wide range of time scales, in all three spatial
dimensions, which often limits comprehensive studies. Biological processes encompass
phenomena like hormone release, calcium waves, differentiation, and apoptosis that unfold over
time-scales ranging from milliseconds to hours or even days. While studying fixed samples at
multiple time points is a potential approach to reconstruct such dynamics, the sheer number of
samples required poses challenges for reproducibility. Consequently, current research
necessitates imaging tools capable of rapidly capturing 3D samples at cellular resolution,
enabling the investigation of dynamic, biological processes.
Conventional TPE laser scanning microscopy, while offering excellent pixel resolution, suffers
from slow imaging speed due to point-by-point scanning and the use of the same objective for
excitation and detection (Figure 2.3a). The most straight-forward solution towards increasing
speed is scanning faster. Resonance galvanometric scanners are typically used for this
purpose. They can achieve kHz scan rates, but are limited to specified field of views (FOVs) and
sampling rates; they also shorten the pixel dwell time dramatically (i.e., reducing the time
fluorescence can be recorded from each pixel). As the single-point scanning seems to be the
main limitation several remedies have been developed to overcome this issue. Firstly,
multi-focal schemes allow to distribute the focal area to different positions, for instance, through
50

a micro lens array/disk, a beam splitter, beam shaping, or a set of mirrors(Bewersdorf et al.,
1998, 2006; D. Chen et al., 2020; R. Lu et al., 2017; Niesner et al., 2007; Wu et al., 2020). An
elegant scanless solution is to image an area instead of a single point in widefield-type
illumination, for example, using temporal focussing(Oron et al., 2005; Zhu et al., 2005). To
achieve sufficient photon density for TPE at the focal plane in widefield, the excitation pulses are
first dispersed and then temporally compressed along the optical axis using a combination of
low NA objective and reflective grating(Papagiakoumou et al., 2020). Such schemes allow
simultaneous acquisition of multiple spatial locations or a plane at the cost of a lower
signal-to-noise ratio (SNR) due to a smaller energy density at every focal volume. To spatially
multiplex detection, multi-focal schemes employ cameras (CMOS, CCD sensors) as opposed to
point detectors (PMTs, APDs) found in conventional laser scanning microscopes. This comes at
the cost of decreased spatial resolution as scattered fluorescence may cause a blurred signal
when detected on a camera. In summary, applying TPE to faster imaging modalities demands a
balance between the photon density required for TPA while generating multiple focal points or
an entire plane as in TPE light-sheet microscopy.
2.3.1 Wider: TPE light-sheet fluorescence microscopy
Light-sheet fluorescence microscopy (LSFM) is an ideal approach to reliably capture transient
biological processes of cells across hundreds of micrometers in 3D(Daetwyler & Fiolka, 2023).
LSFM (also known as Selective Plane Illumination Microscopy) uses a thin sheet of light to
excite fluorophores within a focal plane while reducing out-of-focus excitation. The excited focal
plane is then captured as a 2D image using a CMOS or CCD sensor rather than a point
detector, increasing both frame and volumetric acquisition rate. Because only the focal plane is
excited, LSFM has true optical sectioning where background fluorescence is greatly
reduced(Cox, 1984). Optical sectioning of LSFM reduces photodamage by three orders of
51

magnitude when comparing one-photon excitation LSFM to confocal microscopy(Reynaud et
al., 2008). When combined with TPE, photodamage, reduces by five-fold when compared with
conventional TPE laser scanning microscopy(Stelzer et al., 2021; Truong et al., 2011a).
TPE-LSFM further enhances imaging depth and SNR, while eliminating the need for visible
excitation laser which can be a potential confounding factor in light-sensitive samples(Denk &
Detwiler, 1999) or behavioral experiments. Recent notable applications have applied TPE-LSFM
to light-sensitive behavioral studies that require imaging large regions such as the whole brain
during seizure(de Vito et al., 2022), sleep(D. A. Lee et al., 2017b), phototaxis(Wolf et al., 2015b)
and visual number sense(Messina, Potrich, Perrino, et al., 2022b).
A challenge in TPE-LSFM is maintaining a sufficiently high photon density for excitation. In the
first implementation, a light sheet is created by focusing the excitation beam through two
cylindrical lenses to first create a line and then a sheet, fluorescence is detected orthogonally
through a second objective on a camera(Palero et al., 2010) (Figure 2.3b). However, a
cylindrical lens reduces the photon density, and consequently, decreases the fluorescence
signal due to the quadratic dependence of TPE. To increase the photon density, the focal point
of the TPE laser focus can be shaped (axially extended) into a micrometer-thin beam of light
and can be quickly moved (scanned) laterally to create a “virtual light-sheet” that provides even
illumination and higher photon density when compared to using cylindrical lenses(Keller et al.,
2008; Keller & Stelzer, 2010; Maruyama et al., 2014; Truong et al., 2011a)(Figure 2.3c). The
emitted fluorescence from the scanned area is integrated on the camera and the use of a low
NA illumination objective partially mitigates the degradation of lateral resolution (Truong et al.,
2011).
Both LSFM modalities allow for increased spatial and temporal sampling (~4 orders of
Magnitude(de Vito et al., 2022; Rocha-Mendoza et al., 2015)) with the drawback of lower energy
density and thus fluorescent light flux in a given focal point as compared to LSM approaches.
52

Volumetric imaging is achieved by either mechanically moving the sample through the focal
plane or simultaneously moving both the detection objective with a piezo element and
excitation sheet using a galvanometric mirror to achieve volumetric acquisition speed of 0.5 Hz
at 400 × 800 × 250 µm3
in 52 z-sections (Keomanee-Dizon et al., 2020). Higher volumetric
acquisition speed can be achieved by replacing the piezo element with an electrotunable lens to
gain speed of up to 5 Hz at 600 × 800 × 150 µm3
in 31 z-sections (de Vito et al., 2022; Fahrbach
et al., 2013).
2.3.2 Faster: TPE light-field microscopy
Light-field microscopy (LFM) is an innovative technique that enhances the acquisition rate of 3D
imaging by allowing targeted volume excitation without the need for time-consuming z-scanning.
In traditional 3D imaging, the sequential scanning through voxels, lines, or planes creates a
bottleneck, slowing down the imaging process. For example, LSFM requires scanning plane by
plane (axially) to capture a 3D volume, thus this approach is limited by the exposure time
required for each frame or z-section to gather sufficient photons. To address this issue,
detection can be integrated with light-field technology. LFM captures both 2D spatial and 2D
angular information of light emitted from the sample, effectively preserving 3D characteristics
within a single camera frame(Levoy et al., 2006b). LFM is typically implemented in widefield
illumination with a microlens array (MLA) inserted in the image plane before the camera,
redistributing the light on the chip based on the illuminated volume in the sample plane (Figure
2.3d). While this technique sacrifices some lateral and axial resolution, a single snapshot can be
subsequently reconstructed into a detailed 3D volume, effectively aligning the acquisition speed
with the camera's frame rate (Broxton et al., 2013).
Adding TPE to LFM increases the imaging depth while reducing out-of-focus illumination.
Conventional implementations of LFM use widefield illumination(Prevedel et al., 2014b),
however, in TPE a high photon density must be maintained. Therefore, different illuminations
53

schemes similar to LSFM methods have been employed; for example, the excitation laser is
extended axially and scanned laterally (Figure 2.3e,f). The TPE beam scanning can be
effectively applied in both multi-objective setups (Figure 2.3e) and single-objective setups
(Figure 2.3f).
TPE LFM has the potential to non-invasively record millisecond events of thousands of cells
across hundreds of cubic microns but the technology is still in its infancy. The volumetric
imaging speed is constrained by the number of emitted photons from the fluorophores in the
sample and detection efficiency of the camera. Brighter and faster fluorescent proteins and
sensors are constantly being developed. The fastest calcium sensor can record single neuron
firing speeds of up to 50Hz(Y. Zhang et al., 2023). Similarly, higher quantum efficiency (>90%)
cameras using backside illumination CMOS sensors are now more accessible (e.g., Sona-11
Series, Andor; ORCA-Fire, Hamamatsu). Another limitation of LFM is the lengthy volume
reconstruction time which requires extensive computations and expert knowledge(Prevedel et
al., 2014b). To speed up computation time, Guo et al.(Guo et al., 2019b) employed a Fourier
imaging scheme to decrease reconstruction time by 100-fold. In conventional LFM, the MLA is
placed at the native image plane (NIP) (Broxton et al., 2013). In Fourier LFM, the MLA is placed
at the back focal plane of the Fourier lens. In the Fourier domain, the signals can be processed
in parallel, meaning that multiple computations can happen simultaneously to decrease
reconstruction time. There is a lot of ongoing work to improve lightfield technology to make it
accessible and user-friendly, for example, a graphical user interface implementation for
reconstruction is now available in napari (Napari LF - Napari Plugin - Geneva Schlafly, Amitabh
Verma, Rudolf Oldenbourg, n.d.). We eagerly await to see the next generation of LFM
technologies for imaging fast dynamic processes.
54

2.3.3 Deeper: Periscopes from microlenses and GRIN lenses
While TPE microscopy improves penetration depth as compared to single photon excitation to
hundreds of microns, optical aberrations in highly scattering tissue with non-uniform refractive
index distribution degrade resolution. Incorporation of adaptive optics (AO) can help correct for
these aberrations and allow for high-resolution imaging at depth (Hampson et al., 2021; Qin, He,
et al., 2020; Yao et al., 2023). However, many processes still remain out of reach. For example,
to image millimeters deep into the cortex of an animal by conventional two-photon a
considerable amount of scattering tissue must be surgically removed (Oheim et al., 2001; G.
Yang et al., 2013). This invasive procedure provides access but might perturb the system. An
emerging technology to provide higher imaging depths are gradients of refractive index (GRIN)
lenses (Jung & Schnitzer, 2003; Levene et al., 2004). These optical elements are cylindrically
shaped lenses varying the refractive index orthogonally to the optical axis. Implanting such a
lens into tissue allows it to relay light from deep inside the sample to the imaging objective
(Figure 2.3g). Thus, it can be viewed as TPE endoscopy enabling us to investigate processes
deep in tissue over weeks and months post-implantation of the GRIN lens. While getting the
lens in place is an invasive procedure and the alignment of objective and GRIN lenses is
challenging, it is thus far the only way to obtain fluorescence imaging information at such depths
in intact non-transparent animals. The effective light throughput and resolution will be influenced
by the properties of the GRIN lens such as numerical aperture or field curvature. Combination of
this technology with AO (Qin, Chen, et al., 2020), improving the field of view (Y. Lu et al., 2022),
imaging speed (Chien et al., 2021) and resolution (Meng et al., 2019) of GRIN lens systems and
fiber based alternatives (Bijoch et al., 2023) are active and exciting areas of research. Often,
imaging requires immobilization of the specimen, for example the mouse, which can be
circumvented by head-mounted TPE microscopes allowing to image brain activity in freely
moving animals (Helmchen et al., 2001; McCullough et al., 2022; Silva, 2017).
55

Figure 2.3: From laser point scanning to fast, wide and deep volumetric imaging in
complex samples with TPE.
a Scheme for conventional TPE laser scanning microscopy which requires scanning of the
excitation/emission (orange ellipse) through x,y, and z dimension and collection of every single
point onto a point detector.
b Scheme for TPE light-sheet excitation and detection using a camera. Scanning is only
required in z-dimension.
c TPE scheme for digitally scanned light-sheet. The virtual sheet is created by scanning an
extended TPE beam in y-dimension faster than the camera frame rate (orange double-arrow).
56

Volumetric imaging is achieved by scanning in z-dimension. The camera detection integrates
multiple scans of the beam in y-dimension into a single frame.
d Scheme for scanless volumetric detection using light-field technology. The microlens array in
front of the camera allows capturing z information from an excited volume at the expense of
lateral resolution. A volume of illumination is generated by quickly scanning the virtual sheet
along the z axis to excite and capture a volume in a single snapshot. “Human brain outline in
lateral view” by an unknown author from Wikimedia Commons licensed under CC0 1.0.
e,f Combination of light-field detection with two (e) or one (f) objective digitally scanned
light-sheet excitation while selectively exciting a volume of interest.
g TPE laser scanning microscopy in combination with an implanted GRIN lens for deep tissue
imaging in live animals. WD: working distance, GRIN: gradient of refractive index.
2.4 TPE microscopy and photon counting applications
Cells, tissues and organisms rely on the fast reorganization of biomolecules on time-scales
beyond the capabilities of conventional imaging techniques. Fluorescence correlation
spectroscopy (FCS) and fluorescence lifetime imaging microscopy (FLIM) offer access to these
rapid time-scales as they are able to probe transient changes in molecular interactions or in the
molecular environment. In FCS, photons are analyzed with respect to the start of the experiment
(macrotime, seconds to minutes), and in FLIM, photon arrival times after exciting laser pulse
(microtime, nano-seconds) are measured (Figure 2.4a). Conveniently, these advanced photon
counting techniques can be readily coupled to typical TPE laser scanning microscopes allowing
us to eavesdrop on biological processes deep in tissue: FCS can be used to investigate
diffusion dynamics, concentrations, or oligomerization in vivo (Elson, 2011; Lakowicz, 2006;
Urbančič et al., 2021), FLIM can be used to add extra contrast to the image and report on the
local environment of the fluorophores (Datta et al., 2020; Lakowicz, 2006).
2.4.1 TPE FCS
FCS is a point measurement technique to characterize molecular diffusion dynamics and
concentrations. The laser focus is parked at a specified location (e.g. in the center of the field of
view) and the fluorescence intensity over time is recorded, essentially performing a very fast
57

imaging scan (sub-μs) of a single pixel (Figure 2.4a ) (Magde et al., 1972; Mørch & Schneider,
2023; Urbančič et al., 2021). Analyzing the intensity fluctuations caused by molecules diffusing
in and out of the focus yields information on kinetic (diffusion coefficient) and thermodynamic
(concentration, brightness/oligomeric state) properties of the system. These parameters are
obtained by fitting the autocorrelation curves to an appropriate model (Mørch & Schneider,
2023; Sankaran & Wohland, 2023; Urbančič et al., 2021) and can then be statistically compared
for different conditions.
TPE naturally extends the capabilities of FCS because it (i) inherently constraints the
fluorescence to a sharp sub-femto-liter volume, necessary to obtain the intensity fluctuations to
analyze for FCS (ii) results in no out-of-focus excitation, causing less photodamage, less
accumulative photobleaching (less change in concentration over time), and less background
fluorescence, (iii) shows no artifacts from scattered laser light as excitation and emission
wavelength are far apart, and (iv) improves penetration through thicker samples (Berland et al.,
1995, 1996). TPE FCS has been used to study diffusion dynamics in the cytoplasms or
membranes of living cells (Berland et al., 1995; J.-H. Chen et al., 2015; Schwille et al., 1999; Wu
et al., 2009), embryos (Petrásek et al., 2008), and throughout organisms (Shi et al., 2009; X.
Wang et al., 2023). We expect with the availability of turn-key instruments to see a renaissance
of the application of this technology as well as the increase in use of related techniques such as
scanning FCS (sFCS) (Berland et al., 1996; Mørch & Schneider, 2023; Petrášek & Schwille,
2008; Ruan et al., 2004) or raster image correlation spectroscopy (RICS) (Digman et al., 2005;
Obashi et al., 2019) that provide spatial context to the FCS data.
2.4.2 TPE FLIM
FLIM reports intensity and fluorescence lifetime for every pixel providing additional means to
generate contrast in the image. The fluorescence lifetime refers to the time a fluorophore
spends in an excited state S1 before returning to the ground state S0
(see also Figure 2.1b). The
58

fluorescence lifetime is a molecular property of the fluorophore and its local environment
(Berezin & Achilefu, 2010; Valeur & Berberan‐Santos, 2012). It can be used to add contrast to
the image, to allow discrimination of two dyes with similar emission wavelengths but different
lifetimes (for example removal of autofluorescence with characteristic lifetime), or to report on
changes in the local environment of the fluorophore such as viscosity, pH, or binding (Valeur &
Berberan‐Santos, 2012) (Figure 2.4b).
FLIM data can be recorded in the time domain (using a pulsed laser and photon counting) or in
the frequency domain (using excitation modulation and measuring the phase shift between
excitation and emission). Both approaches can be coupled to TPE laser scanning microscopy in
a readily integrated microscope or added as an LSM upgrade kit (typical vendors for these
options include: Becker and Hickl, PicoQuant, ISS, Leica). In the more widely used time domain
measurements, the time delay of emitted photons with respect to the excitation pulse is
analyzed for every pixel (microtime, Figure 2.4a) (Becker, 2012; Lakowicz, 2006; Sun et al.,
2011). Building a histogram of the emitted photon arrival times after laser pulse is called time
correlated single photon counting (TCSPC). The decay curve is fitted with appropriate models
(e.g., multi-exponential function) to obtain the fluorescence lifetime per pixel (Figure 2.4a
bottom, Figure 2.4b left). Obtaining valid results from this approach requires careful attention to
the photon statistics; collecting a sufficient number of photons per pixel to yield an accurate
fluorescence lifetime estimate is crucial and can be time consuming. Further, it is important to
consider that more photons are required to differentiate small lifetime differences (e.g., 1.2 ns
versus 1.4 ns) as compared to large lifetime differences (e.g., 1 ns and 5 ns) (Datta et al., 2020;
Köllner & Wolfrum, 1992). Therefore, FLIM acquisitions are usually an order of magnitude
slower, as compared to using the intensity image (ie., in conventional confocal imaging),
hampering studies of fast (sub-second) biological processes with FLIM. However new photon
counting hardware (commercial options include: Becker and Hickl, SPC-QC-008; Leica
59

Microsystems, FALCON; PicoQuant, PicoHarp 330) and corrections for photon counting at high
photon fluxes (deadtime and pile-up corrections) (Isbaner et al., 2016; Patting et al., 2018) are
becoming available.
Analyzing FLIM data can alternatively be performed using the fitting-free phasor approach
(Figure 2.4b, right) (Digman et al., 2008). In essence, the phasor analysis uses a Fourier
transform to approximate the fluorescence decay in each pixel. In this process a decay curve
(often >200 photon bins per pixel) is compressed to two phasor coefficients (real and imaginary
part of the phasor, usually termed G and S respectively, see Figure 2.4b) (Ranjit et al., 2018).
This process is performed for every pixel. Filtering the phasor coefficients (the G and S images,
e.g., using a median filter) helps improve the SNR (Digman et al., 2008; P. Wang et al., 2021).
Mono-exponential lifetimes fall on the semi-circle whereas bi-exponential lifetimes fall within. A
combination of two mono-exponential lifetimes maps within the circle but can be decomposed
into the original components as well as their fractions estimated (Figure 2.4b bottom). The key
point of the phasor transform is that pixels showing similar lifetimes / fluorescence properties will
have similar G and S values on the phasor plot and can be analyzed together. These pixels can
be far apart in the original image. In this way the phasor transform helps to elucidate spatial
patterns, number of components with distinct lifetimes, and their interactions in the sample. No
fitting of the data is performed, making it a fast, unbiased and convenient way to explore the
data rather than focusing on determination of exact lifetimes.
Imaging of autofluorescent, endogenous compounds can provide insights into cellular
physiology. However, these molecules often need to be excited in the UV range (using one
photon excitation). TPE FLIM enables such measurements without exposing the sample to
extended UV irradiation. While TPE FLIM has also been used with fluorescent biosensors (P. R.
Evans et al., 2019; Koveal et al., 2020; Laviv et al., 2020; Laviv & Yasuda, 2021), we focus here
on the application in label-free microscopy using intrinsic biomarkers (Heikal, 2010; Zipfel,
60

Williams, Christie, et al., 2003). In metabolic imaging, for example, the cofactors NADH and
NADPH are excited around 740 nm (Azzarello et al., 2022; Ranjit et al., 2019; Stringari et al.,
2011; Stringari, Nourse, et al., 2012). Their lifetime can be used to infer metabolic state of a cell
or tissue (Figure 2.4c) (Datta et al., 2020; Georgakoudi & Quinn, 2023; Kolenc & Quinn, 2019;
Stringari, Nourse, et al., 2012) as these compounds change fluorescence lifetime when binding
to metabolic enzymes of the oxidative phosphorylation pathway (Oxphos) (Lakowicz et al.,
1992; Leben et al., 2019). The more NADH is free in a cell, the less Oxphos is in progress, the
more glycolysis is performed (Figure 2.4c). Using FLIM, cells or tissues can be profiled for
metabolic state under various conditions such as during glucose shock (see example in Figure
2.4d)(Stringari, Nourse, et al., 2012), infection (Liublin et al., 2022; Miskolci et al., 2022),
differentiation (Liu et al., 2018; Sánchez-Ramírez et al., 2022; Stringari, Edwards, et al., 2012;
Wright et al., 2012), diabetes (Z. Wang et al., 2021), drug treatments (Pham et al., 2021;
Stringari, Nourse, et al., 2012), or in the context of neuro-pathophysiology (Bernier et al., 2020;
Chakraborty et al., 2016; Cleland et al., 2021; Liaudanskaya et al., 2023; Yaseen et al., 2013).
While examining NADH lifetime can provide valuable insights, imaging conditions especially
when fixation or embedding is required need to be carefully evaluated (Sánchez-Hernández et
al., 2023). As the autofluorescence of this endogenous compound is dim, the phasor analysis
has over the past years evolved to the gold standard to process and analyze such low SNR
FLIM data (Figure 2.4b,c) (Digman et al., 2008; Scipioni et al., 2021)
61

Figure 2.4: Combination of TPE with the photon counting techniques FCS and FLIM
a The pulsed excitation and resulting fluorescence in TPE microscopy can be combined with
FCS and FLIM. In FCS the fluorescence time trace at a fixed point in space is analysed by
means of temporal autocorrelation. Fitting the resulting autocorrelation curve by an appropriate
model gives information on the diffusion coefficient, concentration and oligomeric state
(brightness) of moving particles in the sample. Histogramming the photon arrival times after
62

laser pulses allows for the investigation of the fluorescence lifetime of the observed
fluorophores.
b The pixels in FLIM imaging contain lifetime values in addition to the intensity values. For every
pixel a lifetime decay (photon counting histogram can be calculated). A convenient way to
compress the data is to map the decay curves via Fourier transform onto the phasor space.
Mono-exponential lifetimes lie on the universal circle. Combination of lifetimes (or
multi-exponential decays) map within the circle.
c Application of Phasor-FLIM imaging to investigate metabolic state of cells by exploiting the
autofluorescence of bound and unbound NADH. The more NADH is bound, the more oxidative
phosphorylation (Oxphos) is performed revealing the metabolic phenotype (ie., Oxphos versus
glycolysis). Lifetimes can be false-colored using the phasor plot and remapped onto the FLIM
image to identify spatial patterns.
d Example of metabolic imaging of NIH3T3 cells in low or high glucose media (images on the
left) and corresponding phasor coordinates of the pixel containing fluorescence (right). NADH
was imaged using 740 nm excitation. False coloring using a magenta to blue look up table is
applied to the phasor cloud remapping the pixels from phasor to image space. This allows the
identification of pixels with more free NADH (meaning more glycolytic cells, short NADH lifetime)
and pixels with more bound NADH (meaning more oxidative phosphorylation, long NADH
lifetime). This panel was adapted from reference (Stringari, Nourse, et al., 2012) Stringari et al.
(2012), PLOS ONE https://doi.org/10.1371/journal.pone.0048014 published under CC BY 4.0
https://creativecommons.org/licenses/by/4.0/
2.5 Maximizing SNR within the limitations of TPE
Equally important to enhancing temporal and spatial sampling is the pursuit of optimal image
quality, SNR, while ensuring the health and integrity of the sample. These factors need to be
balanced to ensure collection of meaningful biological data. This section addresses two
frequently underestimated yet resolvable concerns: photodamage and photo selectivity.
2.5.1 Optimizing SNR and photodamage
Understanding the processes involved in the photodamage from TPE can be challenging as it
introduces photodamage both linearly and nonlinearly with increasing excitation power.
Generally, photodamage results from two distinct processes: photothermal and photochemical
effects(Débarre et al., 2014). Photothermal damage results from laser heating outpacing the
63

dissipation of the heat, and typically follows a time-averaged photon absorption process (linear
effect)(Karu, 1999; Koester et al., 1999; Podgorski & Ranganathan, 2016; Schmidt & Oheim,
2020). Photochemical effects result from the ionization of molecules and formation of reactive
oxygen species (ROS) through multiphoton absorption processes (nonlinear effect)(Botchway et
al., 2010; Débarre et al., 2014; Donnert et al., 2007; Hopt & Neher, 2001; König et al., 1997;
Patterson & Piston, 2000; Shafirovich et al., 1999; Stennett et al., 2014; Talone et al., 2021).
One approach to minimize nonlinear photodamage is to decrease the photon density of a single
pulse (or peak power). The peak power (𝑃 can be described by:
𝑝𝑒𝑎𝑘
)
𝑃 (1)
𝑝𝑒𝑎𝑘
∝
𝑃
𝑚𝑒𝑎𝑛
τ · 𝑓
Where laser pulse repetition rate = 𝑓 , mean laser power (pulse + inter-pulse interval) = 𝑃 , 𝑚𝑒𝑎𝑛
and pulse width = τ.
The easiest means to decrease linear photodamage is to decrease 𝑃 , ideally while keeping 𝑚𝑒𝑎𝑛
𝑃 constant, as fluorescence signal is dependent on both and (Gasparoli et
𝑝𝑒𝑎𝑘
(𝑆) 𝑃
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
al., 2020; Maioli et al., 2020; Song et al., 2023):
𝑆 ∝ (2)
𝑃
𝑚𝑒𝑎𝑛
2
τ · 𝑓
2
To maintain or increase signal while minimizing damage, adjusting 𝑃 or by modifying
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
only the laser output at the source is inadequate. A far better approach is to utilize a pulse
compensator to change pulse width (τ) to increaser 𝑃 without increasing , and/or a
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
64

pulse picker to decrease the repetition rate 𝑓 to maintain 𝑃 but decrease .(Song et al.,
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
2023)
Adjustments of 𝑃 and must be empirically determined for different experiments
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
because the TPE focal point (photon density) at the sample may vary. The variation is due to
the sample type, objective NA, and illumination scheme (point scanning, lightsheet, lightfield,
temporal focusing) (de Vito et al., 2022; Ji et al., 2008; Maioli et al., 2020; Schmidt & Oheim,
2020). In practice, we adjust 𝑃 and by first determining what type of photodamage is
𝑝𝑒𝑎𝑘
𝑃
𝑚𝑒𝑎𝑛
occurring within the sample. Linear photodamage from TPE excitation is similar to
photoablation, where the damage area results in a small cavity, typically appearing as a dark
non-fluorescent region (Marshall et al., 2022). Nonlinear photodamage is more complex to judge
and may result in either darkening or intensifying the local signals due to the photochemical
effects. Photobleaching is only one of the signatures of photochemical damage, and the most
accessible sign of nonlinear photodamage (Kuznetsova et al., 2015; Magidson & Khodjakov,
2013). However, the absence of photobleaching does not necessarily guarantee the absence of
nonlinear photodamage as other molecules may be affected before the fluorophore(Laissue et
al., 2017). Another challenge in determining nonlinear photodamage, are studies using Ca
2+
indicators, as photobleaching can be difficult to assess because the baseline fluorescent change
can be a complex mixture of linear and nonlinear effects (Koester et al., 1999; Schmidt &
Oheim, 2020). One convenient method to determine the photodamage type, is to image the
sample with a continuous wave laser of the same 𝑃 (eg. by disabling mode-locking of the 𝑚𝑒𝑎𝑛
laser source). It is good practice after TPE microscopy to perform a viability or behavioral assay
to determine the health of the sample (Laissue et al., 2017).
65

2.5.2 Selective excitation by polarized light
An often overlooked phenomenon in fluorescence microscopy is photoselection caused by the
linear polarization of the excitation light. This phenomenon can preferentially excite certain
fluorophore orientations, due to their dipole moments, leading to fluorescence emission
anisotropy (Lakowicz, 2006). The orientation of the transition dipole moment of the fluorophore
not only describes the shift in electron density upon excitation but also determines dye
excitation efficiency (Khoroshyy et al., 2023). The most efficient excitation takes place when the
transition dipole moment of the fluorophore aligns with the polarization direction of the light.
Fluorescence emission is also oriented, with the photons emitted in the plane perpendicular to
the transition dipole moment (Figure 2.5a,b). For such fluorescence emission anisotropy to
occur, the fluorescence lifetime must be shorter than the rotational diffusion times (the average
time required for the molecule to complete a rotation). The rapid tumbling motions of dyes in
solution would randomize these orientations, which is why the contribution from photo-selection
is often under-appreciated.
Because the laser light typically used to excite fluorophores is linearly polarized, the preferential
excitation of fluorophores that are bound to or embedded in targets result in intensity variations
in the sample. In epifluorescence microscopy, this can be easily demonstrated with a labeled
model membrane system, such as giant unilamellar vesicles (GUVs). A fluorophore, such as
Fast-DiO, oriented radially within the GUV membrane shows the expected fluorescence
emission anisotropy (Figure 2.5d,e); the non-selected direction is almost completely dark. A
quarter-wave plate offers an easy solution for this issue in epifluorescence microscopy by
creating circularly polarized light (Paquette et al., 2018; Zeng et al., 2011) (Figure 2.5c,f),
permitting the laser to excite all dye orientations.
Line-scanning microscopy techniques like orthogonal-plane LSFM or oblique plane microscopy
(OPM) can leverage photoselection to minimize laser power and photodamage while
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maximizing the fluorescence signal intensity. Unlike in epifluorescence, the solution is not to
excite as many fluorophores as possible but to excite only those fluorophores that most
efficiently emit fluorescence light towards the camera direction (Vito et al., 2020a). For
example, one can selectively excite fluorophores that will emit fluorescence light radially on a
2D plane by using a half-wave plate to control the directions of linearly polarized light. If not
optimized in this fashion, the detected fluorescence can be reduced for the same number of
excited dyes, because of their decreased emission towards the detection camera (Figure 2.5g).
Optimal efficiency of fluorescence collection should result from linearly polarized light oriented to
best excite fluorophores that will emit fluorescence light radially on the xz plane (Figure 2.5h).
This effect has been demonstrated using an orthogonal-plane LSFM to image jGCaMP7f calcium
indicators in a 7-day post-fertilization zebrafish midbrain (Figure 2.5i,j). While its impact in single
objective TPE OPM has yet to be demonstrated, we expect it should be similarly improved as
compared to two objective orthogonal LSFM (Kumar et al., 2018; Yu et al., 2017). In short,
optimizing the linear polarization direction during one- or two-photon excitation will maximize the
fluorescence signal collection, which is particularly important for TPE because the higher laser
powers increase the risk of photodamage.
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Figure 2.5: Optimization of excitation laser polarization for single and multi-focal
microscopy.
a-c Epifluorescence microscopy. Excitation and detection light travel through the same
objective. Horizontally polarized excitation laser (a) vertically polarized excitation laser (b)
circularly polarized excitation laser (c).
d-f Example image of equatorial plane of a giant unilamellar vesicle (GUV) taken with
epifluorescence microscopy. GUV consists of an unsaturated phospholipid
(1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC), is labeled with Fast-DiO and excited with
68

950 nm. Horizontally polarized (d) vertically polarized (e) circularly polarized, simulated image
(f). Scale bar, 10µm.
g,h Multifocal orthogonal LSFM. Excitation and detection light travel through different objectives.
Horizontally polarized excitation laser (g) vertically polarized excitation laser (h).
i,j Example image of a 7-day post-fertilization zebrafish midbrain expressing pan-neuronal
H2B::jGCaMP7f (Dana et al., 2019a) taken with orthogonal LSFM. The sample is illuminated by
a single lightsheet from bottom of the image at 920 nm with 175 mW of power. Example image
is averaged across 30 seconds showing a single z-plane of a volumetric time series taken at 1
volume per second. Scale bar, 100µm.
a-c,g,h Green arrows show one possible radial emission direction; Green ellipsoid has the
highest fluorescence emission probability perpendicular to the dipole moment, at the ellipsoid’s
equator. Circularly polarized light was adapted from “Clockwise circularly polarized light” by
Dave3457, Wikimedia Commons, licensed under CC BY-SA 4.0.
2.6 Image quality metric
The imaging community has strived to achieve FAIR (Findability, Accessibility, Interoperability,
and Reusability) practices. The impact of FAIR practices has been demonstrated impressively in
structural biology, where every structure deposited into the protein database is accompanied by
quality metrics such as resolution, R-value etc. This allows for meta-analyses, joint refinement of
structures, fostering collaborations, and direct comparisons between datasets. Similar efforts in
fluorescence microscopy have been underway, but with far less acceptance in the field
(Kemmer et al., 2023; Sasaki, 2022). Likely, it will take more proactive involvement of publishers
and funding agencies to mandate FAIR practices and to convince the user community. We
believe that this would represent a game changer for reproducibility and transparency, making
us hope it will not be too long before the TPE microscopy community adapts standardization
routines, published along the data, that will allow us to quantitatively compare datasets and
results.
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2.7 Quo vadis? What’s next?
Application, further advancement, and replacement of technologies are best dictated by the
biology under investigation. For TPE microscopy such improvements have largely been driven
by the neuro-science community and their endeavors to map whole-brain activity. This has
resulted in technology to go faster and deeper, as well as pushed more towards volumetric
imaging.
Instrumentation including optics and electronics for TPE microscopy as well as the acquisition
schemes are constantly improving. This has been carried by an open-source culture that helps
drive innovation and affordability of custom setups (Diederich et al., 2022; Panier et al., 2023).
Technology advancements such as the use of single photon avalanche diode (SPAD) arrays
(instead of single point detectors) should provide a wealth of new information in laser scanning
microscopes (Bruschini et al., 2019; Koho et al., 2020). While technology improvements will
keep pushing the edge of possibilities a few milliseconds and microns at a time, in our opinion,
ground-breaking, biological insights will arise from:
i) Applying appropriate technologies to the right biological question/system
ii) New probes, labeling strategies, and optogenetic modifications
iii) Better image and signal processing algorithms readily integrated in TPE microscopes
The choice of microscopy modality determines the dynamic range and information content that
can be extracted from biological experiments. Imaging with TPE has many advantages over
single-photon excitation and has become the preferred method for deep tissue imaging.
Furthermore, it can be straight-forwardly combined with harmonic generation microscopy
allowing for additional label-free contrast in tissues (James & Campagnola, 2021; Zipfel,
Williams, Christie, et al., 2003). Now the challenge is to decide in which applications the
advantages outweigh the expenses of TPE and which modalites (e.g., point scanning versus
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light-sheet) should be considered. Not every sample necessitates the most advanced imaging
methodology, as the same conclusions might be reached with a simpler approach. We would
like to emphasize that designing the experiment and choosing the required imaging modality
carefully is crucial to discovery and can save a lot of time and money. Typical questions to keep
in mind should include:
What spatial and temporal resolution do I need?
What field of view and imaging depth do I need?
Does cross-excitation matter?
Do I need optical sectioning?
What would the disadvantages in one-photon excitation be?
Developments of new probes, sensors, and labeling strategies will enable new insights into
biological processes. Currently, brighter, more photo-stable fluorescent proteins and sensors
(e.g., calcium or voltage imaging) already revolutionize what can be measured on conventional
instruments (Bando et al., 2021; S. W. Evans et al., 2023; Farrants et al., 2023; Kagiampaki et
al., 2023; Maiti et al., 2023; Oliinyk et al., 2022). An exciting direction is the use of red-shifted
probes to exploit the red part of the visible light spectrum (>600 nm) (Adesnik & Abdeladim,
2021; W. Yang & Yuste, 2018). Red-shifted probes allow for less scattering and absorption as
well as better penetration depth. While development of brighter red fluorescent proteins is well
underway and new detector technology starts to overcome the low quantum efficiency of
standard PMTs in this regime, further improvements will have a major impact and essentially
add another channel to experiments (Farrants et al., 2023; Maiti et al., 2023; Oliinyk et al.,
2022). Moreover, the use of smart probes and biosensors that report on changes in sample
properties such as pH value, temperature or viscosity will provide new insights on the local
environment around a protein of interest(Juvekar et al., 2021; Mercadé-Prieto et al., 2017;
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Roffay et al., 2023). Similar to metabolic imaging, using the right probe can unlock more
information than just the spatial distribution of the fluorophore. Furthermore, photostimulation
(e.g., uncaging of neurotransmitters or calcium, optogenetic manipulation through
channelrhodopsins) offers exciting strategies to precisely control cellular signaling in space and
time (Janicek et al., 2021; Matsuzaki & Kasai, 2011; Oron et al., 2012; W. Yang et al., 2018).
TPE spectra are broad and a single wavelength can excite multiple fluorophores (cross
excitation). The emission spectra of the excited fluorescent proteins can be highly overlapping
which is a challenge in any multi-color fluorescence microscopy experiment. Recent advances
in unmixing algorithms promise to overcome this issue and make most of overlapping emission
signals (Chiang et al., 2023; Cutrale et al., 2017; Rakhymzhan et al., 2021). Hyper-spectral
approaches use, for example, detector banks or prisms and cameras to record emission
intensity in spectral bins instead of a single channel. This allows for unmixing of different
fluorophores and removal of autofluorescence (Hedde et al., 2021; Kubo et al., 2021).
Furthermore, the combination of spectral and lifetime detection offers new avenues to
multiplexing in biological imaging (Chiang et al., 2023; Scipioni et al., 2021). We believe that
these technologies will be integrated in turn-key systems and improve TPE imaging. However,
we do emphasize that code and analysis pipelines should be open-source and easily accessible
to anyone; this is crucial for quality control and reproducibility.
Overall, it is the perfect time to dive deeper into biological tissues using TPE microscopy. We
hope to leave the reader with some two-photon excitement for recent advancements in
technology, their applications, and an appreciation for their current limitations.
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Chapter 3 - Neural Basis of Number Sense in Larval Zebrafish
This chapter represents the core component of my PhD research, where I explore the neural
mechanisms underlying number sense in larval zebrafish. By combining a deep understanding
of zebrafish biology with advanced optical imaging techniques, I have been able to investigate
the neurons responsible for numerical perception. The work presented here has culminated in
findings that are currently under submission for publication.
Authors:
Peter Luu
1,2
, Anna Nadtochiy
1,3
, Mirko Zanon
4,1
, Noah Moreno
1
, Andrea Messina
4
, Maria Elena
Miletto Petrazzini
5
, Jose Vicente Torres Perez
5
, Kevin Keomanee-Dizon
1,6
, Matthew Jones
1
,
Caroline H. Brennan
5
, Giorgio Vallortigara
4
, Scott E. Fraser
1,2,3
, Thai V. Truong
1,2
Corresponding Authors: sfraser@provost.usc.edu, tvtruong@usc.edu
Affiliation:
1 Translational Imaging Center, Michelson Center for Convergent Bioscience, University of
Southern California, Los Angeles, CA, USA
2 Molecular and Computational Biology, University of Southern California, Los Angeles, CA,
USA
3 Quantitative and Computational Biology, University of Southern California, Los Angeles, CA,
USA
4 Centre for Mind/Brain Sciences, University of Trento, Rovereto, Italy
5 School of Biological and Behavioral Sciences, Queen Mary University of London, London,
United Kingdom
6 Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA
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3.1 Significance
● Numerically responsive neurons are detected by 3 days post-fertilization (dpf) in
zebrafish
○ Number-selective neurons preferring quantities greater than one increases after
3 dpf
● Neurons that are highly responsive to specific numbers of objects are mainly localized to
the forebrain and midbrain
● Number stimulus can be decoded from Ca
2+ activity and show increased performance
with age
● Administration of ethanol decreases the activity of number-selective neurons in the
forebrain
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3.2 Abstract
Number sense, the ability to discriminate the quantity of objects, is crucial for survival. To
understand how neurons work together and develop to mediate number sense, we used
two-photon fluorescence light sheet microscopy to capture the activity of individual neurons
throughout the brain of larval Danio rerio, while displaying a visual number stimulus to the
animal. We identified number-selective neurons as early as 3 days post-fertilization and found a
proportional increase of neurons tuned to larger quantities after 3 days. We used machine
learning to predict the stimulus from the neuronal activity and observed that the prediction
accuracy improves with age. We further tested ethanol’s effect on number sense and found a
decrease in number-selective neurons in the forebrain, suggesting cognitive impairment. These
findings are a significant step towards understanding neural circuits devoted to discrete
magnitudes and our methodology to track single-neuron activity across the whole brain is
broadly applicable to other fields in neuroscience.
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3.3 Introduction
Understanding quantity, whether discrete (countable) or continuous, is fundamental for survival,
e.g. for avoiding predators, finding food, mating, and other group behaviors (Alder & Rose,
2000; Cross & Jackson, 2017; Edwards et al., 2002; Templeton & Greene, 2007). Quantity
estimation, often referred to as the Approximate Number System (ANS), allows both humans
and animals to intuitively estimate numerosity, or quantity of objects in a set, without precise
counting (Brannon & Merritt, 2011; Piazza, 2010b; Piazza et al., 2004). The ANS develops
during early infancy, highlighting its importance as a foundational aspect of cognition (F. Xu &
Spelke, 2000). The ANS forms the basis of survival instincts to complex mathematical abilities,
ultimately shaping how we perceive and interact with the world (Bonny & Lourenco, 2013;
Feigenson et al., 2004; Szkudlarek & Brannon, 2017).
Current studies are limited to identifying individual neurons or specific brain regions responsible
for number sense, but understanding how a network of number-selective neurons functions
across the entire brain remains elusive (Ditz & Nieder, 2015, 2016; Messina, et al., 2022a,
2022b; Pfeifer et al., 2018; Piazza et al., 2004; Viswanathan & Nieder, 2013). In primates,
Viswanathan & Nieder (2013) showed a visual sense of number mapped to the parietal and
prefrontal cortices. Expanding on this, recent studies suggest that visual number processing
extends beyond these regions and involves the superior colliculus, a deep subcortical area
(Collins et al., 2017; Georgy et al., 2016). In birds, involvement of several pallial regions has
been recently documented by early gene expression (Lorenzi et al., 2024). While the use of
electrodes can access individual neurons at multiple regions, it is difficult to unbiasedly capture
all neurons especially without neuron damage after implantation (Eles et al., 2018; Ferguson et
al., 2019; Goss-Varley et al., 2017). Capturing neuronal activity across the whole brain would
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enable researchers to map neural circuits involved in ANS processing with unparalleled
precision in both encoding and representation..
To address this, we developed and optimized a two-photon fluorescence light sheet microscopy
(2P-LSFM) platform (Keomanee-Dizon et al., 2020c; Messina, Potrich, Perrino, et al., 2022c;
Truong et al., 2011b; Vito et al., 2020b) and a customized data analysis pipeline. This allowed
for noninvasive imaging of the functional activity of nearly all neurons across the whole brain in
larval zebrafish (Danio rerio) with single-neuron resolution. Larval zebrafish offer many
advantages as a model system for studying neural processes such as transparency, genetic
tractability, and drug screening applications (Kawakami, 2005; Lubin et al., 2021; Trinh & Fraser,
2013; Weber & Köster, 2013). By expressing a nuclear-localized calcium indicator
(H2B-jGCaMP7f) (Dana et al., 2019b), we were able to monitor whole-brain neuronal activity in
response to non-symbolic, visual numerical stimuli. While no studies have shown any ability to
discriminate different numerosities at an early age (<7 days post-fertilization (dpf)) in zebrafish,
it must develop before the behavior becomes apparent (Adam et al., 2024; Lorenzi et al., 2023;
Lucon-Xiccato et al., 2023; Sheardown et al., 2022b). Here, we aim to identify these
number-neurons, across the brain, in real time as the animal processes a visual number
stimulus, to improve our understanding of the neural basis of number sense.
3.4 Results
3.4.1 Using two-photon fluorescence light sheet microscopy to identify
number neurons in larval zebrafish
We used our custom-developed 2P-LSFM to record whole-brain neuronal activity of
agarose-embedded zebrafish at age 3, 5, and 7 dpf, while the animals were presented with
visual numerical stimuli based on dots (Figure 1a, Methods: Calcium imaging). Imaging was
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acquired at a 1-Hz whole-brain volumetric rate, and the entire imaging experiment lasted for 90
minutes, as the numerical stimuli sequenced from one to five dots. When the quantity of dots
changes, non-numerical geometric effects co-vary and can confound the numerical effects. For
example, two circles have a higher combined area than one circle of the same diameter. To
account for geometric effects, the number-based dot stimuli controlled for both numerical and
non-numerical variables (i.e. for continuous physical variables that co-vary with numerosity)
(Zanon et al., 2022). The non-numerical variables were divided into spread and size of the
individual dots. The Angular diameter of the dots was kept at a minimum of 5° (angular degree)
above the visual acuity threshold of 2-3° (Haug et al., 2010). The spread of the dots includes
convex hull and distance between the dots, while the dot size includes constant radius, total dot
area, and total dot perimeter (Figure 1b). The stimuli sequence includes all possible
combinations of spread and sizes using a new pattern for each stimulus (Supplementary Figure
1). To account for any intrinsic neural oscillatory signal that might have a repetitive pattern in
phase with the stimulus display, the inter-stimulus interval followed a pseudo-random sequence.
We applied and optimized several publicly available Python tools and software for managing,
processing, and analyzing volumetric movie data and neuronal signals. We used VoDEx
(Nadtochiy et al., 2023) to manage the 4D (volumetric movie) data and stimuli annotations.
Advanced Normalization Tools (Avants et al., 2009) was used to spatially align and correct for
motion artifacts in 4D datasets. Registration of multiple samples onto a representative brain
template was performed using ITK-SNAP (Yushkevich et al., 2006).
To segment for the signals from individual neurons, we applied the Python toolbox for
large-scale Calcium Imaging Analysis (CaImAn) (Giovannucci et al., 2019). See Methods for full
details. Figure 1c, d, e shows example images of the raw image data with whole-brain coverage
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at cellular resolution. The resulting processed segmentation is shown in Supplementary Figure
2.
Figure 3.1. Application of two-photon fluorescence light sheet microscopy to detect
neuronal representation of number perception in larval zebrafish.
a Schematic of the two-photon light sheet fluorescence microscope. The sample is excited by
two orthogonal 920 nm scanning lasers aided by a physical eye-shaped mask that blocks laser
illumination of the eyes (Methods: Calcium imaging). Stimulus is displayed on the right side of
the larval fish. Bottom-left: brightfield image of the mounted sample, scale bar = 200 μm.
Center-bottom: stimulus projection image, scale bar = 10 mm. Bottom-right: Dorsal view of the
sample relative to the stimulus direction and excitation laser. A = anterior, P = posterior, D =
dorsal, V = ventral, L = left, R = right.
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b Continuous geometric parameters used to control for non-numerical covariables when
changing quantities of objects. Convex hull and inter-distance controls spread of the dots, while
radius, total area and perimeter controls for the dot size. See Method: Stimuli Generation.
c Example maximum image projection (MIP) of a 7 dpf zebrafish brain. Top, dorsal view, MIP
along the dorsal/ventral axis; middle, frontal view, MIP along the rostral/caudal axis; bottom,
lateral view, MIP along the left/right axis. Images were averaged over 60 seconds. Scale bar =
100 μm.
d,e Magnified image showing cellular resolution. (d) forebrain (e) tectum from (c). Left, dorsal
view of a single plane; middle, frontal view of a single plane along the green dash lines; right,
lateral view of a single plane along cyan dash line. Scale bar = 50 μm.
3.4.2 Neurons correlating to number stimuli are detected early in
development
To identify neurons specifically responsive to changes in numerosity (Figure 2a, Supplementary
Figure 3) from those responsive to geometric changes, we applied a two-way permutation
ANOVA. Neurons were filtered based on a significant main effect for changes in numerosity (p <
0.01), without exhibiting significant main or interaction effects due to geometric changes. We
define these filtered neurons as “number-selective neurons”. As an example, we present the
significant main effect for changes in numerosity during the stimulus onset for a 7 dpf larva
(Figure 2b). The analysis window of 3 seconds accounts for the typical ~2 second decay time
constant (Dana et al., 2019c; E. Yang et al., 2022). In general, a significant Ca
2+
response to a
numerical stimulus was detected 0-3 seconds from the stimulus onset.
On average, we identified 1300±300, 800±100, 550±100 number-selective neurons, among
14000±2700, 17000±1300, 17000±2000 detected active neurons in 3, 5, and 7 dpf larval
zebrafish, respectively (n=5 for each age group) (Supplementary Table 1-5). Due to the varying
expression levels of H2B::GCaMP across individual fishes and varying signal-to-noise ratios
due to development of the skin (Li & Uitto, 2014) and head (Kimmel et al., 1995), quantification
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of number-selective neurons are normalized by number preference, detected active neurons,
and regions for each sample. Example Ca
2+ signal traces and tuning curves of neurons tuned to
1-5 objects for one fish are shown in Figure 2c. Neurons showing a peak Ca
2+
response to a
specific numerosity is defined as tuned or having preference to that numerosity. Tuning curves
show a gradual decrease in Ca
2+
response for numerosities further from the preferred
numerosity (Figure 2d; for population tuning see Supplementary Figure 4).
As the zebrafish larval age increases across 3, 5, and 7 dpf, we found that the proportion of
neurons tuned to numerosities of two or more shows a trending increase with age (3dpf:4%;
5dpf:12%; 7dpf:14%) (Figure 3a). When comparing the tuning preferences of the
number-selective neurons (Figure 3b), we found a significant decrease of 1-tuned neurons in 3
dpf (96 ± 1%) compared to 5 (88 ± 2%) and 7 (86 ± 5%) dpf groups (p < 0.05). For 3-tuned
neurons, we found a significant increase in 7 dpf (5 ± 1%) compared to the 3 dpf (0.2 ± 0.1%)
group (p < 0.01).
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Figure 3.2. Number-selective neurons produce higher Ca
2+ activity for preferred
numerosities.
a Single neuron fluorescence intensity trace of Ca
2+ activity during numerical stimuli. Neurons
responsive to numerical stimuli show a Ca
2+ spike after the stimulus onset.
b Statistical significance of number selectivity over time during stimulus onset in one example 7
dpf larvae. Rows represent individual neurons (n = 599) centered around the stimulus onset
(peristimulus). Stimulus starts at time = 0 and lasts for 1 second. Black solid line on top
indicates a 3-second analysis window used to detect number-selective neurons with a two-way
permutation ANOVA to account for the rise and decay time of the Ca
2+
response.
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c Ca
2+ activity trace of 5 example neurons with preference to 1-5 dots. Traces are centered
around the stimulus onset (peristimulus) for preferred and non-preferred numerosities. Neuron
preferences were selected by the highest average activity for a numerosity. Top labels indicate
the number of dots presented, and each color represents the specific number tuning (1 = red, 2
= cyan, 3 = green, 4 = yellow, 5 = magenta). Baseline for ∆F/F is calculated by averaging the 3
time points prior to the stimulus onset (dotted vertical line). Black line indicates the average
across 48 trials.
d Tuning curves of each of the five neurons from c. Each entry is the average of the 3-second
analysis window for each numerosity presentation (n = 3 * 48 numerosities). Error bar = SEM.
Figure 3.3. Populations of neurons tuned to specific numerosities show redistribution of
number preference during early development.
a Proportion of number-selective neurons as a percentage of all detected number-selective
neurons across 3, 5, and 7 dpf. 1-tuned neurons = red, 2-tuned neurons = cyan, 3-tuned
neurons = green, 4-tuned neurons = yellow, 5-tuned neurons = magenta. n = 5.
b Percentages of number-selective neurons preferring specific numerosities for 3-, 5-, and 7
dpf. Percentages are expressed as a proportion to all detected number-selective neurons.
Pairwise comparisons were performed using a Mann-Whitney U-test for each numerosity,
multiple comparisons were adjusted using a Bonferroni correction (alpha = 0.016). Error bars =
SEM, n = 5, * = p < 0.05, ** = p < 0.01.
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3.4.3 Number-selective neurons primarily localize to the forebrain and
midbrain
Number-selective neurons were detected across the forebrain, midbrain, and hindbrain of 3, 5,
and 7 dpf groups. To show the locations of the number-selective neurons, we registered all
imaged samples onto the respective brain templates of each age group (see Methods) and
mapped out the centroids of all identified neuronal nuclei (Figure 4a-b, Supplementary Figure
5). We found a majority of number-selective neurons were localized to the forebrain and
midbrain (Figure 4c). For all three age groups, the forebrain (3dpf:28 ± 4%; 5dpf:45 ± 5%;
7dpf:39 ± 6%) and midbrain (3dpf: 65 ± 5%; 5dpf: 49 ± 6%; 7dpf: 45 ± 4%) had proportionally
more number-selective neurons than the hindbrain (3dpf: 7 ± 2%; 5dpf: 6 ± 2%; 7dpf: 15 ± 5%)
(p ≤ 0.01). We did not identify any apparent mapping based on preferred numerosities
(Supplementary Figure 6). In the 3 dpf group, we found significantly less neurons in the
forebrain than the midbrain (p < 0.001).
Building upon these findings, we further investigated the subregions of the forebrain (eminentia
thalami, hypothalamus, pallium, pretectum, thalamus, subpallium) and found no significant
changes with age (Supplementary Figure 7, Supplementary Table 6).
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Figure 3.4. Number-selective neurons are primarily detected in the forebrain and
midbrain.
a The 3D map of the brain was divided into three major brain regions (forebrain, midbrain,
hindbrain). Solid lines indicate delineation of major brain regions, dash lines indicate
overlapping regions.
b Locations of number-selective neurons in three different individual larval zebrafish at three
stages of development, representing the results as point maps in orthographic projections. The
white circles represent the centers of each identified number-selective neuron. Columns indicate
age. Scale bar: 100 µm.
c Comparison of number-selective neuron distribution across brain regions of three stages of
development. Number-selective neurons per region are normalized by the total number of
number-selective neurons detected in the whole brain. Comparisons were performed using a
two-way ANOVA for age and brain region followed by Tukey’s HSD. Error bars = SEM, n = 5, * =
p < 0.05, ** = p < 0.01.
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3.4.4 Number stimulus can be decoded from number-selective neurons
To determine if the Ca
2+ activity of number-selective neurons across the brain is sufficient to
predict the correct number of dots shown during a visual stimulus, we trained a support vector
machine (SVM) supervised classifier to estimate the visual stimulus from the recorded activities
(Kirschhock & Nieder, 2022). The features were extracted averaging the Ca
2+ activity of all
identified number-selective neurons for each preferred numerosity (Figure 5a, Methods). The
Ca
2+ activity averages for number preferences 1-5 serve as the five input features and are used
to predict six types of stimuli (1, 2, 3, 4, 5 dot, no dot). The classifier was trained on four out of
five individual zebrafish in each age group and tested on the remaining one, enabling
generalized testing across conspecifics.
To assess the performance of the SVM classifier, we used a confusion matrix to evaluate the
classifier accuracy (Figure 5b, c, d, e). The confusion matrix shows the prediction instances
(columns) during a visual numerical dot stimulus or “true label” (rows). Each entry of the matrix’s
main diagonal shows correct prediction of the true labels. By averaging the diagonal entries, the
overall classifier accuracy can be obtained. At 3 dpf, the prediction accuracy was above chance
level (16.7%) for the numerosities 1 (50%), 2 (30%), 3 (30%), and 5 (32%) (Figure 5b). At 5 dpf,
the general is similar but with an increase in accuracy: 1 (61%), 2 (43%), 3 (44%), and 5 (41%)
(Figure 5c). At 7 dpf, for numerosities greater than 2 we see a general increase in accuracy: 1
(56%), 2 (44%), 3 (52%), 4 (37%), and 5 (52%) (Figure 5c). The prediction improvement is
confirmed by the overall classifier accuracy increasing with age (42%, 48%, 55% for 3, 5, and 7
dpf, respectively) (Figure 5f, Supplementary Table 7).
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87

Figure 3.5. Prediction accuracy of the numerical stimuli from Ca
2+ activity using an SVM
classifier shows increased performance with age.
a Feature extraction of Ca
2+ activity from numerically-tuned neurons. For each training and
testing instance, the average Ca
2+ activity of each neuron population tuned to the 5 numerosities
was calculated and shown as a percentage of ∆F/F (5 input features). The visual stimulus (1, 2,
3, 4, 5, background/no dot) serves as the true label for each instance. Each sample larval fish is
comprised of 288 instances (48 repetition * 6 visual stimulus type). Cross validation was
performed using a leave-one-out cross validation where training was performed on the data
from 4 of 5 larval fish and tested on the excluded sample, then repeated on a different excluded
sample.
b, c, d, e Confusion matrix of the support vector machine (SVM) classifier of 3, 5, and 7 dpf
groups and a shuffled 7 dpf group. The percentage indicates the number of predictions out of
the total instances of each true label. Random chance = 16.7%.
f Overall SVM classification accuracies for the three age groups. Dash line indicates chance
level, calculated as the accuracy of shuffled data from the 7 dpf group.
3.4.5 Ethanol inhibits number-selective neurons in the forebrain
Acute ethanol exposure affects learning and memory processing in zebrafish (Sartori et al.,
2022). To understand how this affects number-selective neurons we examined the effect of
ethanol on number-selective neurons of 7 dpf larvae compared to the untreated larvae.
Location of detected number-selective neurons in the forebrain is noticeably less when treated
with 1.5% ethanol (Figure 6a). The percentage of number-selective neurons in the
ethanol-treated group (10%) showed a significant decrease in the forebrain when compared to
detected active neurons in the forebrain brain (20%) and the forebrain of untreated group (39%)
(n=5 for each treatment group) (Figure 6b, Supplementary Figure 8). To measure the predictive
capacity of number-selective neurons of an ethanol-treated group, we trained a supervised
classifier to predict the visual stimulus using the Ca
2+ activity (Figure 6c). The overall accuracy
of the ethanol-treated group (41%) was decreased compared to the untreated group (55%)
(Figure 6d). This effect is mainly driven by the decreased accuracy when predicting
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numerosities of 3, 4, and 5. These results suggest ethanol may impair the function of
number-selective neurons.
Figure 3.6. Ethanol alters the activity of number-selective neurons in the forebrain.
a Location of number-selective neurons in three different brain regions in a single 7 dpf larval
zebrafish treated with ethanol. Refer to the caption for Figure 4b for a detailed description.
b Percentage of number-selective neurons in the forebrain during ethanol treatment.
Number-selective and active neurons in the forebrain are normalized to all number-selective or
active neurons (respectively) across the whole brain. Pairwise comparisons were performed
using a Mann-Whitney U-test with a Bonferroni correction for multiple comparisons (alpha =
0.17). Error bars represents SEM, n = 5, ** denotes p < 0.01.
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c Confusion matrix of the SVM classifier of the numerical stimuli using Ca
2+ activity during
ethanol treatment. Refer to the caption for Figure 5b, c, d, e for a detailed description.
d Overall SVM classification accuracies for the 7 dpf EtOH treatment groups. Dash line
indicates chance level, calculated as the accuracy of shuffled data from the 7 dpf untreated
group.
3.5 Discussion
In this study, we investigated the neural basis of number sense in larval zebrafish, focusing on
the tuning of neurons to specific visual-based numerosities under different conditions. Our work
has, for the first time, discovered the existence of number-selective neurons in larval zebrafish.
The fast volumetric imaging rate of one volume per second and the high signal-to-noise ratio of
light sheet microscopy enabled whole-brain recording and segmentation of approximately
17,500 active neurons per larva. The use of two-photon excitation allowed for increased depth
of coverage (deeper imaging) and reduced visual artifacts compared to one-photon excitation
(Truong et al., 2011b; Vito et al., 2022; Wolf et al., 2015c).
Consistent with studies using chick models (Kobylkov et al., 2022) and human infants (Izard et
al., 2009; F. Xu & Spelke, 2000), we detected number-selective neurons during early
post-embryonic (equivalent to post-natal) stages in zebrafish. Notably, the existence of these
number-selective neurons at 3 dpf precedes any known numerically-driven behaviors such as
hunting and shoaling (which start at 5 and ~24 dpf, respectively) (Adam et al., 2024; Borla et al.,
2002; Lucon-Xiccato et al., 2023; Sheardown et al., 2022b), underscoring the fundamental role
and necessity of early numerical cognition for survival.
Consistent with studies using chick models (Kobylkov et al., 2022) and human infants (Izard et
al., 2009; F. Xu & Spelke, 2000), we detected number-selective neurons during early
post-embryonic (equivalent to post-natal) stages in zebrafish. Notably, we observed these
90

neurons at 3 dpf, which is before the onset of known numerically-driven behaviors that typically
begin at 7 dpf (Adam et al., 2024; Lucon-Xiccato et al., 2023). This finding suggests that the
development of these neurons precedes and potentially facilitates these behaviors, highlighting
the critical importance of early numerical cognition for survival.
The proportion of neurons tuned to numerosities of two or more shows a trending increase with
age (Figure 3a). A significantly increased proportion of neurons preferring 3 objects was
detected after 3 dpf (Figure 3b). These results suggest number-selective neurons develop in an
ordinal fashion with age. An interesting question for future studies is whether this increase is
due to the generation of new neurons preferring higher numerosities or the re-tuning of existing
neurons. This could be resolved by application and further refinement of our experimental
platform to observe number-selective neurons in the same zebrafish longitudinally over
development time.
The increased proportion of neurons preferring larger numerosities (>2) developing after 3 dpf
may be caused by an improvement in visual acuity rather than changes to number-selective
neurons. However, the zebrafish eye is emmetropic at 3 dpf (Easter & Nicola, 1996), and no
differences in visual acuity were detected when comparing larvae at 4, 5, and 6 dpf (Haug et al.,
2010). Furthermore, recognition of 5 dots does not require finer visual acuity than 2 dots when
maintaining equivalent inter-distances (Figure 1c). Because we detected neurons preferring 2
dots in 3 dpf larvae, the increase of neurons preferring larger numerosities in older larvae is
unlikely to be caused by improved visual acuity.
We identified number-selective neurons localized throughout the forebrain and midbrain (Figure
4b). In the 3 dpf group, we found significantly less neurons in the forebrain compared to the
midbrain, whereas in the 5 and 7 dpf groups, the forebrain contained a similar proportion of
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these neurons (Figure 4c), likely due to the forebrain being more developed in the older fish
(Cheng et al., 2014). Further analysis of the forebrain subregions found no significant
age-related changes in (Supplementary Figure 7, Supplementary Table 6). These results
suggest that while overall development affects neuron distribution, the specific sub regional
changes may not happen until the brain matures beyond 7 dpf.
In the mammalian brain, most number processing is to our knowledge localized to the prefrontal
and parietal cortices (Nieder et al., 2002; Piazza et al., 2004). In non-mammals, such as
zebrafish, the pallium generally fulfills the role of the prefrontal cortex (Medina et al., 2019).
However, the non-mammalian brain lacks a structure that is directly analogous to the parietal
lobe; instead, the optic tectum of the midbrain serves many cortical functions such as sensory
processing and spatial perception (Förster et al., 2020; Gazzola et al., 2018; Muto et al., 2013).
In line with our result of finding number-selective neurons in the midbrain, emerging studies
suggest subcortical and optic tectal involvement in visuospatial processing on numerosities
(Bengochea et al., 2023; Bengochea & Hassan, 2023; Collins et al., 2017; Lorenzi et al.,
2021b). This suggests that the optic tectum participates in more complex functions than its
long-studied roles in visual mapping and sensory integration.
To assess the predictive capabilities of the number-selective neurons across 3, 5, and 7 dpf
zebrafish, we trained a supervised classifier using their underlying Ca
2+ activity. The prediction
accuracy of the classifier increases with age for 2-5 objects, indicating that higher
number-selective neurons become more specific (generating more action potentials in response
to specific numerical stimuli) as the larval zebrafish matures. Similar to the findings of number
sense in crows (Kirschhock & Nieder, 2022), our results show that most misclassifications
occurred near the correct choice, suggesting a numerical distance effect (i.e. discrimination
errors arise between closer numerosities) (Moyer & Landauer, 1967; Nieder, 2011). From 3 to 5
92

dpf, the average prediction accuracy of 2, 3, and 5 objects increased from ~30% to ~43%, but
interestingly the accuracy of 4 objects remained near random chance (17%) until 7 dpf.
A plausible explanation for the decreased accuracy of 4 objects for 5 dpf fish is that numerosity
of 4 represents a transition point between Object Tracking System/Parallel Individuation System
(OTS/PIS) and Approximate Number System (ANS) (Feigenson et al., 2004; Hyde, 2011;
Sheardown et al., 2022a). The OTS/PIS is thought to be responsible for tracking and
representing small quantities of objects with high precision, typically up to four items. Whereas
the ANS operates on an approximate level, allowing for rapid estimation of small (<4) and large
(>4) numerical magnitudes beyond the capacity of the OTS/PIS. If the OTS develops ordinally
then neurons preferring 4 objects would develop last whereas neurons preferring 5 objects
would have emerged earlier with the ANS.
When larval zebrafish were exposed to ethanol, the activity of number-selective neurons
decreased in the forebrain (Figure 6a-b). Given ethanol's well-known propensity to inhibit
information processing in the frontal lobe of humans (Koelega, 1995; Tzambazis & Stough,
2000), it is likely that the number-selective neurons in the forebrain, which are implicated in
complex higher-order functions such as learning and memory (Dempsey et al., 2022; Rodríguez
et al., 2002), are selectively affected. When predicting the stimulus from the Ca
2+ activity using
an SVM classifier, the overall accuracy decreases for larger numerosities (>2) (Figure 6c).
Interestingly, the prediction accuracy of 1 dot showed improvement. One possible explanation is
ethanol treatment is inhibiting the number-selective neurons part of the ANS system that prefer
1, leaving OTS neurons remaining which have a more precise representation of numbers
(Feigenson et al., 2004).
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Our findings contribute to the growing understanding of the developmental stages of cognitive
abilities in vertebrates, offering new insights into how early neural circuits involved in numerosity
evolve even before behaviorally measurable traits emerge. The identification of
number-selective neurons in larval zebrafish as early as 3 dpf, well before the onset of
numerically-driven behaviors, emphasizes the critical role of early neural development in the
establishment of cognitive functions necessary for survival. This study not only adds to the
foundational knowledge of numerical cognition in non-mammalian species but also opens
avenues for comparative studies across vertebrate models, including primates and humans, to
explore the evolutionary conservation of these neural circuits.
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3.6 Methods
3.6.1 Key resources table
Reagent type
(species) or resource
Designation Source or reference Identifiers
Genetic reagent
(Danio rerio)
Zebrafish:
Tg(elavl3:H2B::jGCa
MP7f)
(Dana et al., 2019c;
E. Yang et al., 2022),
gift from David
Prober
RRID:Addgene_1044
88
Python Library Analysis tools:
ANTs
(Avants et al., 2009) https://github.com/AN
TsX/ANTs
Python library Analysis tools:
NuMan
https://github.com/Le
monJust/numan
Python library Analysis tools:
numan_plus
https://github.com/Mir
koZanon/numan_plus
Python library Analysis tool:
seaborn
(Waskom, 2021) https://seaborn.pydat
a.org/index.html
Python library Data management:
VoDEx
(Nadtochiy et al.,
2023)
https://github.com/Le
monJust/vodex
Python library Cell Segmentation (Giovannucci et al.,
2019)
https://github.com/flat
ironinstitute/CaImAn
Python library Stimuli presentation:
PsychoPy
(Peirce et al., 2019) https://psychopy.org/i
ndex.html
Software/Python
Library
Image analysis
toolkit: ITK-SNAP
(Yushkevich et al.,
2006)
http://www.itksnap.or
g/
Software Microscope GUI,
µManager
(A. Edelstein et al.,
2010a)
https://doi.org/10.100
2/0471142727.mb142
0s92
Software Stimuli generation:
GeNEsIS
(Zanon et al., 2022) https://github.com/Mir
koZanon/GeNEsIS
3.6.2 Animal care
Casper zebrafish (Danio rerio) expressing a pan-neural, nuclear-localized fluorescence Ca
2+
reporter (elavl3:H2B::jGCaMP7f) was a gift from the lab of David Prober at California Institute of
95

Technology. Larval fish were raised accordingly to establish methods (Avdesh et al., 2012) with
modifications: 13:11 hr (light:dark) and fed dry food twice daily after 5 days post-fertilization
(dpf). Experiments used zebrafish ranging from 3-7 dpf. Sex is not defined at this stage of
development. Larvae were raised in 50 mL petri dishes with approximately 50 larvae per dish.
E3 medium (5 mM NaCl, 0.17 mM KCl, 0.33 mM CaCl2, 0.33 mM MgSO4). All animal
procedures conformed to the institutional guidelines set by the University of Southern California
Department of Animal Research.
3.6.3 Calcium imaging
Zebrafish larvae were embedded in 2% low-melting-point agarose (Invitrogen cat 16520100)
and mounted in a custom sample holder. During image acquisition, the larvae were perfused
with oxygenated water using a peristaltic pump and heated to 28C. Image acquisition was
performed on a custom-built microscope (Keomanee-Dizon et al., 2020c) that was further
modified by optimizing the polarization and additional laser pulsing to increase the fluorescence
signal (Luu et al., 2024; Vito et al., 2020b, 2022). The sample was imaged via two-photon
excitation using a Chameleon Ultra II Ti:Sapphire laser (Coherent) at 920 nm with approximately
300 mW peak power and 180 mW average power (combined excitation laser at the sample after
splitting). Emitted light was bandpass filtered at 525 ± 45 nm and collected using a 20x 1.0 NA
water dipping objective (Olympus). Continuous images were acquired at a rate of 1 second per
volume, in which a volume is composed of 60 z-slices at 540 x 296 pixels across 230 µm (~900
x 500 x 230 µm3, equating to a 3.83-µm-thick section) at a pixel resolution of 1.68 µm. The
acquisition time per sample is approximately 90 minutes excluding a 30-minute acclimation
period totaling ~100gb of data. Software control and hardware synchronization for image
acquisition was performed as previously described (Keomanee-Dizon et al., 2020c) using
µManager (A. Edelstein et al., 2010b) and LabVIEW.
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3.6.4 Stimuli Generation
Dot patterns were generated using GeNEsIS (Zanon et al., 2022) and controlled for convex hull,
inter-distance, total area, total perimeter, and radius in (Figure 1b) . Convex hull describes the
smallest convex polygon that encloses all of the elements, inter-distance is the average
distance between the elements. Total area equates average brightness and cumulative surface
area for different numerosities. Total perimeter equates the cumulative circumference of all the
elements for different numerosities. The parameters are summarized in Supplementary Table 8.
Note: parameter values apply by use case (“1” dot stimuli does not have convex hull or
inter-distance parameters, constant radius does not use radius variability). Angular diameter of
dots were kept above 5° to maintain visibility (Haug et al., 2010) and below 18° to minimize an
escape response (Temizer et al., 2015c). Numerical elements were colored black on a red
background to simulate objects' contrast in the natural environment and to prevent disassembly
of the photoreceptor of the photoreceptor (Emran & Dowling, 2010).
3.6.5 Visual number-based display
Visual stimuli were projected onto a diffuser placed 19 mm away from the larvae (figure 1a). The
diffuser is made of cellulose acetate (Scotch Magic tape) that faces the right eye of the larval
fish and is placed orthogonally to its body axis. Illumination was generated using a Qumi Q5
LED Projector (Vivitek) and bandpass filtered at 660 ± 45 nm (Thorlabs).
Each numerical stimulus is presented 48 times following a pseudo-random order. The stimulus
is displayed for 1 second followed by varying inter-stimulus intervals of a blank red background
between 15-30 seconds. The display area is 22 mm in diameter or 66° in angular diameter.
Stimulus control was performed using the PsychoPy toolkit (Peirce et al., 2019).
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3.6.6 Ethanol administration
To determine the appropriate ethanol concentration, we adapted methods from previous studies
(Dlugos & Rabin, 2003; Vossen et al., 2022) to assess larval zebrafish swimming behavior and
mortality after treatment. In triplicates, five 7 dpf zebrafish were immersed in 15 mm x 100 mm
Petri dishes containing 1, 1.5, and 2% ethanol in E3 media for 1.5 hours (image acquisition
duration). We then screened for hyperactivity by gently tapping on the Petri dish and chose the
1.5% ethanol concentration for this study. Before image acquisition, the zebrafish were treated
with 1.5% ethanol 30 minutes prior and then continuously perfused with oxygenated E3 media
containing 1.5% ethanol during imaging.
3.6.7 Cell segmentation
The datasets were first motion corrected using Advanced Normalization Tools (Avants et al.,
2009). Cell segmentation was performed using a python library designed for calcium imaging
(CaImAn) (Giovannucci et al., 2019). CaImAn consists of a series of functions enabling the
separation of neurons using Ca
2+ activity in time and space by applying non-negative matrix
factorization. Prior to cell segmentation, the data size was reduced by selecting only the time
points around the stimulus presentation (3 s before stimulus + 1 s stimulus + 5 s post-stimulus;
see Figure 2). The final volumetric time series was reduced from 5,472 s to 2160 s (9 s window
X 5 numerosities X 48 repetitions). Large data handling and annotation were managed using an
inhouse python library that facilitated image processing (Nadtochiy et al., 2023).
The segmentation was performed in 2D where each time point consisted of 60 z-slices with the
following parameters: ‘decay_time’ = 5 (length of a typical transient in seconds); ‘gSig’ = 3x3
(expected half size of neurons in pixels); min_SNR = 1.5 (signal to noise ratio to accept a
component); rval_thr = 0.85 (space correlation threshold to accept a component). The ‘K’
98

parameter is the expected number of cells to be segmented that serves as a starting point for
optimization. Since the number of cells expected in each z-slice varies, the 'K' parameter is
estimated based on the standard deviation of Ca
2+
flux in each z-slice over time. The standard
deviation image is thresholded (min_std + 0.08*(max_std - min_std)) resulting in an image with
pixels that represent cells with Ca
2+
flux. The maximum number of the resulting pixels are then
divided by ‘gSig’ to approximate the number of cells per z-slice. Since a single cell’s Ca
2+ signal
can span across 2-3 z-slices, we eliminate duplicates by merging cells with both a centroid
distance less than 1 pixel and with a Ca
2+ activity correlation coefficient higher than 0.95.
3.6.8 Number neuron selection
Identification of numerically-tuned neurons involved additional preprocessing steps that
removed camera shot noise and established a baseline fluorescence. To remove false positive
segmented cells caused by the camera shot noise (identified as segmented cells that were
found outside of the brain), we calculated the coefficient of variation (CV), the ratio of the
standard deviation to the mean, for each timepoint in the peristimulus windows. We found a CV
of 0.05 was sufficient to remove false positive cells related to shot noise. Baseline fluorescence
(F0
) was defined as the average of three time points before the visual stimulus around the
stimulus presentation (peristimulus window) for each numerosity.
To differentiate neurons responsive to numerosity from those responsive to nonnumerical
covariables (size and spread), we utilized a two-way permutation ANOVA. This involved
randomizing the labels associated with the data and calculating the F-value. We repeated this
process 10,000 times to construct a null distribution based on simulated F-values to which the
actual F-value was compared to get the p-value. The criteria for identifying a number-selective
neuron must have a significant main effect for the numerical stimulus (alpha = 0.01), a
non-significant main effect for the nonnumerical covariables, and no interaction effect.
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3.6.9 Brain spatial registration and region segmentation
All samples were first registered to a brain template of each respective age group with ITKsnap
(Yushkevich et al., 2006) using the average Ca
2+ signal in time. All identified neuron centers
were remapped to the final brain template to compare across different fish. To identify
subregions of the forebrain, we registered the brain templates to the mapZebrain atlas (Kunst et
al., 2019) using affine transformation, then selected the available subregion Boolean masks.
3.6.10 Supervised classification
To test the predictive properties of the number-selective neurons, we applied a support vector
machine (SVM) based supervised classifier using a linear kernel. The classifier used the
underlying Ca
2+ activity to predict the visual number-based stimulus. To extract the features, we
calculated the average Ca
2+ activity of the neurons tuned to each of the five numerosities during
a 2-second window encompassing the 1-second visual stimulus and the following post-stimulus
second. These five average activities served as input features for the SVM. The six classes
(true labels) consisted of the five numerosities (1-5 objects from the visual stimulus) and the
average Ca
2+ activity during the frames preceding the stimulus representing the no stimulus or
background baseline.
We trained the SVM model on each experimental group (3 dpf, 5 dpf, 7 dpf, 7 dpf + EtOH) to
classify trials based on the five extracted features. We applied a leave-one-out cross-validation
scheme, where the model was trained on data from four fish within a group and tested on the
remaining fish. This procedure was repeated five times, each time excluding a different fish. The
final confusion matrices (Figures 4b-d, and 5c) were obtained by combining the test results from
all five repetitions.
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3.6.11 Statistical analysis
Statistical analyses and graph preparation were conducted using:
Python - seaborn library (Waskom, 2021), Inkscape.
3.6.12 Acknowledgements
I would like to express my deepest gratitude to my collaborators and mentors who made this
project possible. Special thanks to the David Prober lab for providing the zebrafish used in this
study. I would also like to acknowledge Falk Schneider for assistance with editing the
manuscript.
3.6.13 Funding
Alfred E. Mann Doctoral Fellowship to KKD
Human Frontier Science Program
Grant RGP0008/2017 to CB, SEF, GV
ERC European Union's Horizon 2020 research and innovation program
Grant agreement 833504 – SPANUMBRA to GV, CB
FARE–Ricerca in Italia: Framework per l'Attrazione ed il Rafforzamento delle Eccellenze per la
ricerca in Italia, III edizione, project "NUMBRISH–The neurobiology of numerical cognition:
searching for a molecular genetic signature in the zebrafish brain" Prot. R20YL9WN9N to GV.
National Institutes of Health 1U01NS122082-01, 1R34NS126800-01 to TVT.
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3.6.14 Supplementals
Supplementary Figure 3.1. Sequence of stimuli including all possible combinations of
spread and sizes using a new pattern for each stimulus.
Each stimulus lasts for 1 second, and the inter-stimulus duration varies between 15 and 27
seconds. A stimulus cycle is 684 seconds in total when including both convex hull and
inter-distance controls. When a pseudo-random cycle is repeated, a novel dot pattern is
displayed. The cycle is repeated 8 times per sample.
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Supplementary Figure 3.2. Segmentation output using CaImAn toolbox.
Black circles indicate neuron centers. White boundaries indicate segmented Ca
2+ signal.
103

Supplementary Figure 3.3. Example traces of geometric controls of the number-based
dot stimuli
Ca
2+ signal traces from a number-selective neuron which responds to changes in number rather
than geometric variations (covariates). Black lines indicate the mean Ca
2+ signal during any
stimuli presentation, while red lines indicate the mean Ca
2+ signal specific to the geometric
covariates. Gray bars indicate stimulus onset, tick marks represent seconds, error bars indicate
the standard error of the mean (SEM).
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Supplementary Figure 3.4. Tuning curve of 3, 5, and 7 dpf age groups
Overall tuning curves, averaged across five fish per age group, represent the normalized
average Ca
2+ activity of all number-selective neurons in response to stimuli at different
numerical distances from the preferred numerosity. The response of a neuron to its preferred
numerosity is represented by 0. See Supplementary Table 1 and 2 for neuron counts.
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Supplementary Figure 3.5. No-stimulus negative control
Locations of number-selective neurons in one larval zebrafish as orthographic projections
without presenting number stimuli. The white circles represent the centers of each identified
number-selective neuron. Scale bar: 100 µm.
106

107

Supplementary Figure 3.6. Localization of number-selective neurons at three stages of
development
a The 3D map of the brain was divided into three major brain regions (forebrain, midbrain,
hindbrain). Solid lines indicate delineation of major brain regions, dash lines indicate
overlapping regions.
b Locations of number-selective neurons in three different individual larval zebrafish at three
stages of development, representing the results as point maps in orthographic projections. The
individual-colored dots represent the centers of each number-selective neuron extracted using
the pipeline presented in Figure 2a. Columns indicate age; neurons responding with specific
number tunings are shown as rows. Scale bar: 100 µm.
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Supplementary Figure 3.7. Distribution of sub-regional number-selective neurons
normalized by total number-selective neurons in the forebrain.
See Supplementary Table 6 for p-values and f-scores.
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Supplementary Figure 3.8. Distribution on number-selective and all active neurons
across three major brain regions during ethanol administration.
Comparison of number-selective neuron distribution across brain regions between ethanol
groups. Number-selective neurons per region is normalized by the total number of
number-selective neurons detected (white bar) or all detected neurons (gray bar). Pairwise
comparisons were performed using a Mann-Whitney U-test with a Bonferroni correction for
multiple comparisons (alpha = 0.17). Error bars represents SEM, n = 5, ** denotes p < 0.01.
110

Supplementary Table 3.1. Group averages of identified neurons.
Negative control group underwent normal acquisition protocol with only a visible red background
and no dot stimulus.
Number-selective neurons Active neurons
dpf Average SEM Average SEM
3 766 306 13840 2697
5 796 101 16747 1254
7 550 108 16650 1989
7 (negative
control)
6 1 13689 634
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Supplementary Table 3.2. Total amount of neurons identified in the whole brain.
Entries show 5 samples for each condition.
Sample id Condition All neurons 1-tuned 2-tuned 3-tuned 4-tuned 5-tuned
hz04 3dpf 18104 1043 54 2 2 6
hz05 3dpf 14981 2181 51 9 6 4
hz12 3dpf 2346 362 1 0 0 0
hz13 3dpf 14467 834 10 2 2 5
hz14 3dpf 19303 1731 135 5 0 2
hz06 5dpf 20603 925 120 5 3 5
hz08 5dpf 19598 478 40 0 0 2
hz15 5dpf 15221 877 74 102 4 1
hz28 5dpf 13613 539 19 27 6 5
hz29 5dpf 14701 669 21 50 5 3
hz01 7dpf 23980 599 8 57 4 6
hz02 7dpf 16359 436 15 16 9 8
hz09 7dpf 14874 564 18 14 1 2
hz11 7dpf 17769 775 63 20 1 3
hz17 7dpf 10269 90 26 11 2 4
hz18 no_stim 16061 0 1 1 1 1
hz19 no_stim 13386 1 1 1 0 2
hz20 no_stim 13247 1 1 2 3 2
hz21 no_stim 11689 0 0 1 2 0
hz22 no_stim 14062 1 0 2 0 7
hz33 etoh_7dpf 15282 80 6 4 2 0
hz34 etoh_7dpf 16740 368 132 24 1 3
hz35 etoh_7dpf 19178 336 38 18 9 0
hz36 etoh_7dpf 13645 265 22 4 4 5
hz37 etoh_7dpf 15861 163 51 10 3 0
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Supplementary Table 3.3. Total amount of neurons identified in the forebrain.
Entries show 5 samples for each condition.
Sample id Condition Forebrain 1-tuned 2-tuned 3-tuned 4-tuned 5-tuned
hz04 3dpf 3468 303 7 2 2 0
hz05 3dpf 2363 776 5 2 2 2
hz12 3dpf 220 58 1 0 0 0
hz13 3dpf 3671 179 2 0 2 3
hz14 3dpf 3643 714 32 1 0 1
hz06 5dpf 7095 596 4 0 1 1
hz08 5dpf 6546 225 0 0 0 2
hz15 5dpf 3495 355 14 2 0 0
hz28 5dpf 4925 304 6 5 2 4
hz29 5dpf 4871 257 3 0 1 3
hz01 7dpf 8046 363 4 2 2 3
hz02 7dpf 4160 82 3 0 3 4
hz09 7dpf 6296 266 1 1 1 0
hz11 7dpf 5292 293 2 2 0 0
hz17 7dpf 3788 54 0 0 0 3
hz18 no_stim 6949 0 1 1 1 1
hz19 no_stim 4493 1 1 1 0 2
hz20 no_stim 4602 1 1 2 3 2
hz21 no_stim 4260 0 0 1 2 0
hz22 no_stim 4448 1 0 2 0 7
hz33 etoh_7dpf 3997 11 0 2 0 0
hz34 etoh_7dpf 3354 62 1 1 1 0
hz35 etoh_7dpf 2816 21 11 12 2 0
hz36 etoh_7dpf 2528 6 0 0 1 2
hz37 etoh_7dpf 3580 11 4 0 1 0
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Supplementary Table 3.4. Total amount of neurons identified in the midbrain.
Entries show 5 samples for each condition.
Sample id Condition Midbrain 1-tuned 2-tuned 3-tuned 4-tuned 5-tuned
hz04 3dpf 3665 660 29 0 0 0
hz05 3dpf 3554 1163 41 7 2 0
hz12 3dpf 741 288 0 0 0 0
hz13 3dpf 4378 632 7 0 0 2
hz14 3dpf 4392 927 94 1 0 1
hz06 5dpf 6323 298 116 3 0 2
hz08 5dpf 3502 203 40 0 0 0
hz15 5dpf 5847 513 59 100 4 0
hz28 5dpf 2603 171 12 20 2 0
hz29 5dpf 3889 402 17 48 2 0
hz01 7dpf 5936 166 2 52 2 3
hz02 7dpf 3263 218 1 3 5 4
hz09 7dpf 2468 242 13 8 0 2
hz11 7dpf 4653 418 46 7 1 3
hz17 7dpf 1614 29 21 11 0 1
hz18 no_stim 1817 0 0 0 0 0
hz19 no_stim 1972 0 0 0 0 0
hz20 no_stim 1103 0 0 0 0 0
hz21 no_stim 2620 0 0 0 0 0
hz22 no_stim 1813 0 0 0 0 0
hz33 etoh_7dpf 5306 68 4 1 1 0
hz34 etoh_7dpf 4442 292 123 22 0 0
hz35 etoh_7dpf 6022 274 26 3 3 0
hz36 etoh_7dpf 4951 242 22 0 1 1
hz37 etoh_7dpf 4325 131 39 9 0 0
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Supplementary Table 3.5. Total amount of neurons identified in the hindbrain.
Entries show 5 samples for each condition.
Sample id Condition Hindbrain 1-tuned 2-tuned 3-tuned 4-tuned 5-tuned
hz04 3dpf 10971 660 29 0 0 0
hz05 3dpf 9064 1163 41 7 2 0
hz12 3dpf 1385 288 0 0 0 0
hz13 3dpf 6418 632 7 0 0 2
hz14 3dpf 11268 927 94 1 0 1
hz06 5dpf 7185 298 116 3 0 2
hz08 5dpf 9550 203 40 0 0 0
hz15 5dpf 5879 513 59 100 4 0
hz28 5dpf 6085 171 12 20 2 0
hz29 5dpf 5941 402 17 48 2 0
hz01 7dpf 9998 166 2 52 2 3
hz02 7dpf 8936 218 1 3 5 4
hz09 7dpf 6110 242 13 8 0 2
hz11 7dpf 7824 418 46 7 1 3
hz17 7dpf 4867 29 21 11 0 1
hz18 no_stim 7295 0 0 0 0 0
hz19 no_stim 6921 0 0 0 0 0
hz20 no_stim 7542 0 0 0 0 0
hz21 no_stim 4809 0 0 0 0 0
hz22 no_stim 7801 0 0 0 0 0
hz33 etoh_7dpf 5979 68 4 1 1 0
hz34 etoh_7dpf 8944 292 123 22 0 0
hz35 etoh_7dpf 10340 274 26 3 3 0
hz36 etoh_7dpf 6166 242 22 0 1 1
hz37 etoh_7dpf 7956 131 39 9 0 0
115

Supplementary Table 3.6. Comparison of age-related change in number-selective
neurons in subregions of the forebrain.
Kruskal–Wallis test across age groups (n=5) for each region, adjusted for multiple comparisons
using Bonferroni correction with alpha = 0.00625.
Region F value p value
Dorsal Telencephalon (Pallium) 3.42 0.18
Eminentia Thalami 6.74 0.03
Hypothalamus 8.3 0.02
Posterior Tuberculum (Basal Part of
Prethalamus and Thalamus)
0.82 0.66
Pretectum 0.26 0.88
Prethalamus (Ventral Thalamus) 1.46 0.48
Thalamus (Dorsal Thalamus) 4.02 0.13
Ventral Telencephalon (Subpallium) 5.89 0.05
116

Supplementary Table 3.7. Summary of confusion matrix score.
This table presents the fraction of prediction instances using performance metrics such as
precision, recall, and F1-score. Precision indicates the proportion of correctly predicted positive
observations to the total predicted positives (i.e., the accuracy of positive predictions). Recall
(also known as sensitivity) represents the proportion of correctly predicted positive observations
to all observations in the actual class (i.e., the ability to find all relevant instances). The F1-score
is the harmonic mean of precision and recall, providing a single metric that balances both
concerns.
117

Supplementary Table 3.8. Summary of GeNEsIS parameters.
GEnerator of Numerical ElementS Images Software (GeNEsIS) is a custom program written in
Matlab to create stimuli with different numerosity and controlled or constrain physical stimuli
characteristics.
Parameter Pixels cm
Convex hull 100 4.84
Inter-distance 9 1.98
Constant radius 1.2 0.05808
Total area 26 5.72
Total perimeter 31 6.82
Radius variability 0.2 0.044
Mean inter-distance 1.1 0.242
Mean radius 0.8 0.176
Arena radius 10 2.2
Arena dimension (pixel) 10 2.2
Pixel_X screen 1280 16
Pixel_Y screen 720 9
118

Chapter 4 - Conclusion
The research presented in this dissertation explores the neural basis of number sense in
zebrafish, contributing to our understanding of how numerical cognition is processed in a
vertebrate model. Through a combination of behavioral experiments and advanced imaging
techniques, this study has uncovered significant insights into the neural circuits involved in
quantity estimation and how these circuits are organized in the zebrafish brain.
In Chapter 1, we provided an overview of zebrafish as a neurobehavioral model for studying
number sense, emphasizing their suitability due to their genetic tractability and
well-characterized nervous system. The ecological relevance of quantity estimation in fish
behavior was discussed, along with the challenges associated with controlling for continuous
and discrete quantities in behavioral studies. The chapter also highlighted the potential of
zebrafish as a model organism for investigating developmental dyscalculia, a condition
characterized by impaired numerical abilities.
Chapter 2 focused on the application of two-photon excitation microscopy for live imaging in
zebrafish, showcasing the methodological advancements that have allowed for more precise
and comprehensive imaging of neural activity during behavior. The integration of these
techniques has provided a deeper understanding of the neural substrates underlying numerical
perception, particularly in relation to continuous and discrete quantities.
The core findings of this research were presented in Chapter 3, where we demonstrated the
neural basis of number sense in zebrafish through detailed experimental analysis. The
identification of specific brain regions, such as the optic tectum and dorsal pallium, involved in
quantity processing, as well as the modulation of these regions in response to changes in
119

numerical stimuli, represents a significant advancement in the field of comparative neurobiology.
These findings suggest that zebrafish possess neural mechanisms for numerical cognition that
are homologous to those found in mammals, providing a platform for future studies (Figure 4.1).
Figure 4.1 Using the neural basis of number sense as a foundation for future studies.
The findings in this dissertation (green check marks) provide a platform for many other future
studies ranging from developmental studies to modeling disabilities and exploring drug effects
on neural circuits.
Building on the foundation of this work, several promising research directions emerge that could
significantly broaden our understanding of numerical cognition and its underlying mechanisms.
One immediate avenue involves using the neural substrates identified in this study to explore
how external factors such as developmental stressors (e.g., ethanol exposure) or behavioral
conditions (e.g., sleep deprivation) impact number neurons. These studies could reveal critical
insights into how environmental and physiological states influence cognitive abilities, with
potential applications in developmental biology and neurology.
Another compelling direction is the integration of advanced molecular techniques to map neural
circuits with greater precision. Multiplexed imaging using molecular markers could facilitate
tracking neural activity across entire circuits and over developmental stages, enhancing our
understanding of how neural connectivity evolves to support numerical cognition. Furthermore,
120

genetic tools could be leveraged to investigate specific mutations, such as those linked to
developmental dyscalculia, offering a zebrafish model for studying human learning disorders.
Future studies will also focus on the translational potential of these findings. The identification of
conserved mechanisms for numerical cognition provides an exciting opportunity to develop
zebrafish as a model for testing pharmacological interventions. Investigating the effects of
nootropics or depressants, for example, could provide insight into therapeutic strategies for
treating cognitive impairments. In parallel, these efforts may also uncover new biomarkers for
early diagnosis of neurodevelopmental or neurodegenerative conditions linked to numerical
cognition deficits.
In conclusion, this dissertation provides a comprehensive analysis of the neural basis of number
sense in zebrafish, offering valuable insights into the underlying mechanisms of numerical
cognition. The findings have significant implications for both basic research and potential clinical
applications, particularly in the context of developmental disorders. Future research should
continue to build on these findings, exploring the genetic and molecular pathways involved in
numerical cognition and expanding the use of zebrafish as a model for studying cognitive
functions.
121

References
Abaid, N., Bartolini, T., Macrì, S., & Porfiri, M. (2012). Zebrafish responds differentially to a
robotic fish of varying aspect ratio, tail beat frequency, noise, and color. Behavioural
Brain Research, 233(2), 545–553. https://doi.org/10.1016/j.bbr.2012.05.047
Abbas, F., & Meyer, M. P. (2014). Fish vision: Size selectivity in the zebrafish retinotectal
pathway. Current Biology: CB, 24(21), R1048-1050.
https://doi.org/10.1016/j.cub.2014.09.043
Abbasizadeh, N., & Spencer, J. A. (2021). Two-Photon Phosphorescence Lifetime Microscopy.
Advances in Experimental Medicine and Biology, 3233, 63–82.
https://doi.org/10.1007/978-981-15-7627-0_4
Abekhoukh, S., Sahin, H. B., Grossi, M., Zongaro, S., Maurin, T., Madrigal, I., Kazue-Sugioka,
D., Raas-Rothschild, A., Doulazmi, M., Carrera, P., Stachon, A., Scherer, S., Drula Do
Nascimento, M. R., Trembleau, A., Arroyo, I., Szatmari, P., Smith, I. M., Milà, M., Smith,
A. C., … Bardoni, B. (2017). New insights into the regulatory function of CYFIP1 in the
context of WAVE- and FMRP-containing complexes. Disease Models & Mechanisms,
10(4), 463–474. https://doi.org/10.1242/dmm.025809
Adam, E., Zanon, M., Messina, A., & Vallortigara, G. (2024). Looks like home: Numerosity, but
not spatial frequency guides preference in zebrafish larvae (Danio rerio). Animal
Cognition, 27(1), 53. https://doi.org/10.1007/s10071-024-01888-0
Adesnik, H., & Abdeladim, L. (2021). Probing neural codes with two-photon holographic
optogenetics. Nature Neuroscience, 24(10), Article 10.
https://doi.org/10.1038/s41593-021-00902-9
Agrillo, C., & Bisazza, A. (2017). Understanding the origin of number sense: A review of fish
studies. Philosophical Transactions of the Royal Society of London. Series B, Biological
Sciences, 373(1740), 20160511. https://doi.org/10.1098/rstb.2016.0511
Agrillo, C., & Dadda, M. (2007). Discrimination of the larger shoal in the poeciliid fish Girardinus
falcatus. Ethology Ecology & Evolution, 19(2), 145–157.
https://doi.org/10.1080/08927014.2007.9522574
Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2008). Do fish count? Spontaneous
discrimination of quantity in female mosquitofish. Animal Cognition, 11(3), 495–503.
https://doi.org/10.1007/s10071-008-0140-9
Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2009). Use of number by fish. PloS One, 4(3),
e4786. https://doi.org/10.1371/journal.pone.0004786
Agrillo, C., Miletto Petrazzini, M. E., & Bisazza, A. (2016). Chapter 7—Number Versus
Continuous Quantities in Lower Vertebrates. In A. Henik (Ed.), Continuous Issues in
Numerical Cognition (pp. 149–174). Academic Press.
https://doi.org/10.1016/B978-0-12-801637-4.00007-X
Agrillo, C., Miletto Petrazzini, M. E., & Bisazza, A. (2017). Numerical abilities in fish: A
methodological review. Behavioural Processes, 141(Pt 2), 161–171.
122

https://doi.org/10.1016/j.beproc.2017.02.001
Agrillo, C., Piffer, L., & Bisazza, A. (2010). Large number discrimination by mosquitofish. PloS
One, 5(12), e15232. https://doi.org/10.1371/journal.pone.0015232
Agrillo, C., Piffer, L., & Bisazza, A. (2011). Number versus continuous quantity in numerosity
judgments by fish. Cognition, 119(2), 281–287.
https://doi.org/10.1016/j.cognition.2010.10.022
Agrillo, C., Piffer, L., Bisazza, A., & Butterworth, B. (2012). Evidence for two numerical systems
that are similar in humans and guppies. PloS One, 7(2), e31923.
https://doi.org/10.1371/journal.pone.0031923
Alarcón, M., DeFries, J. C., Light, J. G., & Pennington, B. F. (1997). A twin study of mathematics
disability. Journal of Learning Disabilities, 30(6), 617–623.
https://doi.org/10.1177/002221949703000605
Alder, T. B., & Rose, G. J. (2000). Integration and recovery processes contribute to the temporal
selectivity of neurons in the midbrain of the northern leopard frog, Rana pipiens. Journal
of Comparative Physiology. A, Sensory, Neural, and Behavioral Physiology, 186(10),
923–937. https://doi.org/10.1007/s003590000144
Alsop, D., & Vijayan, M. M. (2009). Molecular programming of the corticosteroid stress axis
during zebrafish development. Comparative Biochemistry and Physiology. Part A,
Molecular & Integrative Physiology, 153(1), 49–54.
https://doi.org/10.1016/j.cbpa.2008.12.008
Anneser, L., Alcantara, I. C., Gemmer, A., Mirkes, K., Ryu, S., & Schuman, E. M. (2020). The
neuropeptide Pth2 dynamically senses others via mechanosensation. Nature,
588(7839), 653–657. https://doi.org/10.1038/s41586-020-2988-z
Ansari, D., Donlan, C., & Karmiloff-Smith, A. (2007). Typical and Atypical Development of Visual
Estimation Abilities. Cortex, 43(6), 758–768.
https://doi.org/10.1016/S0010-9452(08)70504-5
Arganda, S., Pérez-Escudero, A., & de Polavieja, G. G. (2012). A common rule for decision
making in animal collectives across species. Proceedings of the National Academy of
Sciences of the United States of America, 109(50), 20508–20513.
https://doi.org/10.1073/pnas.1210664109
Avants, B. B., Tustison, N., Song, G., & others. (2009). Advanced normalization tools (ANTS).
Insight j, 2(365), 1–35.
Avdesh, A., Chen, M., Martin-Iverson, M. T., Mondal, A., Ong, D., Rainey-Smith, S., Taddei, K.,
Lardelli, M., Groth, D. M., Verdile, G., & Martins, R. N. (2012). Regular Care and
Maintenance of a Zebrafish (Danio rerio) Laboratory: An Introduction. Journal of
Visualized Experiments : JoVE, 69, 4196. https://doi.org/10.3791/4196
Azzarello, F., Pesce, L., De Lorenzi, V., Ferri, G., Tesi, M., Del Guerra, S., Marchetti, P., &
Cardarelli, F. (2022). Single-cell imaging of α and β cell metabolic response to glucose in
living human Langerhans islets. Communications Biology, 5(1), Article 1.
https://doi.org/10.1038/s42003-022-04215-w
123

Bagni, C., Tassone, F., Neri, G., & Hagerman, R. (2012). Fragile X syndrome: Causes,
diagnosis, mechanisms, and therapeutics. The Journal of Clinical Investigation, 122(12),
4314–4322. https://doi.org/10.1172/JCI63141
Bando, Y., Wenzel, M., & Yuste, R. (2021). Simultaneous two-photon imaging of action
potentials and subthreshold inputs in vivo. Nature Communications, 12(1), Article 1.
https://doi.org/10.1038/s41467-021-27444-9
Barabassy, A., Beinhoff, U., & Riepe, M. W. (2010). Cognitive estimation in aged patients with
major depressive disorder. Psychiatry Research, 176(1), 26–29.
https://doi.org/10.1016/j.psychres.2008.06.045
Barker, A. J., & Baier, H. (2015). Sensorimotor Decision Making in the Zebrafish Tectum.
Current Biology, 25(21), 2804–2814. https://doi.org/10.1016/j.cub.2015.09.055
Bar-Shai, N., Keasar, T., & Shmida, A. (2011). The use of numerical information by bees in
foraging tasks. Behavioral Ecology, 22(2), 317–325.
https://doi.org/10.1093/beheco/arq206
Bayés, M., Magano, L. F., Rivera, N., Flores, R., & Pérez Jurado, L. A. (2003). Mutational
mechanisms of Williams-Beuren syndrome deletions. American Journal of Human
Genetics, 73(1), 131–151. https://doi.org/10.1086/376565
Becker, W. (2012). Fluorescence lifetime imaging – techniques and applications. Journal of
Microscopy, 247(2), 119–136. https://doi.org/10.1111/j.1365-2818.2012.03618.x
Bengochea, M., & Hassan, B. (2023). Numerosity as a visual property: Evidence from two highly
evolutionary distant species. Frontiers in Physiology, 14.
https://doi.org/10.3389/fphys.2023.1086213
Bengochea, M., Sitt, J. D., Izard, V., Preat, T., Cohen, L., & Hassan, B. A. (2023). Numerical
discrimination in Drosophila melanogaster. Cell Reports, 42(7), 112772.
https://doi.org/10.1016/j.celrep.2023.112772
Benitez-Martin, C., Li, S., Dominguez-Alfaro, A., Najera, F., Pérez-Inestrosa, E., Pischel, U., &
Andréasson, J. (2020). Toward Two-Photon Absorbing Dyes with Unusually Potentiated
Nonlinear Fluorescence Response. Journal of the American Chemical Society, 142(35),
14854–14858. https://doi.org/10.1021/jacs.0c07377
Benninger, R. K. P., & Piston, D. W. (2013). Two-Photon Excitation Microscopy for the Study of
Living Cells and Tissues. Current Protocols in Cell Biology / Editorial Board, Juan S.
Bonifacino ... [et Al.], 0 4, Unit. https://doi.org/10.1002/0471143030.cb0411s59
Berezin, M. Y., & Achilefu, S. (2010). Fluorescence Lifetime Measurements and Biological
Imaging. Chemical Reviews, 110(5), 2641–2684. https://doi.org/10.1021/cr900343z
Berland, K. M., So, P. T., Chen, Y., Mantulin, W. W., & Gratton, E. (1996). Scanning two-photon
fluctuation correlation spectroscopy: Particle counting measurements for detection of
molecular aggregation. Biophysical Journal, 71(1), 410–420.
https://doi.org/10.1016/S0006-3495(96)79242-1
Berland, K. M., So, P. T., & Gratton, E. (1995). Two-photon fluorescence correlation
spectroscopy: Method and application to the intracellular environment. Biophysical
124

Journal, 68(2), 694. https://doi.org/10.1016/S0006-3495(95)80230-4
Bernier, L.-P., York, E. M., Kamyabi, A., Choi, H. B., Weilinger, N. L., & MacVicar, B. A. (2020).
Microglial metabolic flexibility supports immune surveillance of the brain parenchyma.
Nature Communications, 11(1), Article 1. https://doi.org/10.1038/s41467-020-15267-z
Bertella, L., Girelli, L., Grugni, G., Marchi, S., Molinari, E., & Semenza, C. (2005). Mathematical
skills in Prader-Willi Syndrome. Journal of Intellectual Disability Research: JIDR, 49(Pt
2), 159–169. https://doi.org/10.1111/j.1365-2788.2004.00634.x
Bewersdorf, J., Egner, A., & Hell, S. W. (2006). Multifocal Multi-Photon Microscopy. In J. B.
Pawley (Ed.), Handbook Of Biological Confocal Microscopy (pp. 550–560). Springer US.
https://doi.org/10.1007/978-0-387-45524-2_29
Bewersdorf, J., Pick, R., & Hell, S. W. (1998). Multifocal multiphoton microscopy. Optics Letters,
23(9), 655–657. https://doi.org/10.1364/OL.23.000655
Bijoch, Ł., Włodkowska, U., Kasztelanic, R., Pawłowska, M., Pysz, D., Kaczmarek, L.,
Lapkiewicz, R., Buczyński, R., & Czajkowski, R. (2023). Novel Design and Application of
High-NA Fiber Imaging Bundles for In Vivo Brain Imaging with Two-Photon Scanning
Fluorescence Microscopy. ACS Applied Materials & Interfaces, 15(10), 12831–12841.
https://doi.org/10.1021/acsami.2c22985
Bisazza, A., Agrillo, C., & Lucon-Xiccato, T. (2014). Extensive training extends numerical
abilities of guppies. Animal Cognition, 17(6), 1413–1419.
https://doi.org/10.1007/s10071-014-0759-7
Bisazza, A., & Santacà, M. (2022). Zebrafish excel in number discrimination under an operant
conditioning paradigm. Animal Cognition, 25(4), 917–933.
https://doi.org/10.1007/s10071-022-01602-y
Bisazza, A., Tagliapietra, C., Bertolucci, C., Foà, A., & Agrillo, C. (2014). Non-visual numerical
discrimination in a blind cavefish (Phreatichthys andruzzii). The Journal of Experimental
Biology, 217(Pt 11), 1902–1909. https://doi.org/10.1242/jeb.101683
Bloch, S., Hagio, H., Thomas, M., Heuzé, A., Hermel, J.-M., Lasserre, E., Colin, I., Saka, K.,
Affaticati, P., Jenett, A., Kawakami, K., Yamamoto, N., & Yamamoto, K. (2020).
Non-thalamic origin of zebrafish sensory nuclei implies convergent evolution of visual
pathways in amniotes and teleosts. eLife, 9, e54945. https://doi.org/10.7554/eLife.54945
Bollmann, J. H. (2019). The Zebrafish Visual System: From Circuits to Behavior. Annual Review
of Vision Science, 5, 269–293. https://doi.org/10.1146/annurev-vision-091718-014723
Bonny, J. W., & Lourenco, S. F. (2013). The Approximate Number System and its Relation to
Early Math Achievement: Evidence from the Preschool Years. Journal of Experimental
Child Psychology, 114(3), 375–388. https://doi.org/10.1016/j.jecp.2012.09.015
Borla, M. A., Palecek, B., Budick, S., & O’Malley, D. M. (2002). Prey Capture by Larval
Zebrafish: Evidence for Fine Axial Motor Control. Brain Behavior and Evolution, 60(4),
207–229. https://doi.org/10.1159/000066699
Bortot, M., Regolin, L., & Vallortigara, G. (2021). A sense of number in invertebrates.
Biochemical and Biophysical Research Communications, 564, 37–42.
125

https://doi.org/10.1016/j.bbrc.2020.11.039
Botchway, S. W., Reynolds, P., Parker, A. W., & O’Neill, P. (2010). Use of near infrared
femtosecond lasers as sub-micron radiation microbeam for cell DNA damage and repair
studies. Mutation Research, 704(1–3), 38–44.
https://doi.org/10.1016/j.mrrev.2010.01.003
Botham, M. S., Kerfoot, C. J., Louca, V., & Krause, J. (2005). Predator choice in the field;
grouping guppies, Poecilia reticulata, receive more attacks. Behavioral Ecology and
Sociobiology, 59(2), 181–184. https://doi.org/10.1007/s00265-005-0018-7
Bousso, P., Bhakta, N. R., Lewis, R. S., & Robey, E. (2002). Dynamics of thymocyte-stromal cell
interactions visualized by two-photon microscopy. Science (New York, N.Y.), 296(5574),
1876–1880. https://doi.org/10.1126/science.1070945
Brand, M., Granato, M., & Nüsslein-Volhard, C. (2002). Keeping and raising zebrafish. In C.
Nüsslein-Volhard & R. Dahm (Eds.), Zebrafish: A Practical Approach (p. 0). Oxford
University Press. https://doi.org/10.1093/oso/9780199638086.003.0002
Brannon, E. M., & Merritt, D. J. (2011). Evolutionary foundations of the approximate number
system. In Space, time and number in the brain: Searching for the foundations of
mathematical thought (pp. 207–224). Elsevier Academic Press.
https://doi.org/10.1016/B978-0-12-385948-8.00014-1
Brock, A. J., Sudwarts, A., Parker, M. O., & Brennan, C. H. (2017). Zebrafish Behavioral Models
of Ageing. In A. V. Kalueff (Ed.), The rights and wrongs of zebrafish: Behavioral
phenotyping of zebrafish (pp. 241–258). Springer International Publishing.
https://doi.org/10.1007/978-3-319-33774-6_11
Broxton, M., Grosenick, L., Yang, S., Cohen, N., Andalman, A., Deisseroth, K., & Levoy, M.
(2013). Wave optics theory and 3-D deconvolution for the light field microscope. Optics
Express, 21(21), 25418–25439. https://doi.org/10.1364/OE.21.025418
Bruschini, C., Homulle, H., Antolovic, I. M., Burri, S., & Charbon, E. (2019). Single-photon
avalanche diode imagers in biophotonics: Review and outlook. Light: Science &
Applications, 8(1), Article 1. https://doi.org/10.1038/s41377-019-0191-5
Bruzzone, M., Chiarello, E., Albanesi, M., Miletto Petrazzini, M. E., Megighian, A., Lodovichi, C.,
& Dal Maschio, M. (2021). Whole brain functional recordings at cellular resolution in
zebrafish larvae with 3D scanning multiphoton microscopy. Scientific Reports, 11(1),
11048. https://doi.org/10.1038/s41598-021-90335-y
Buckingham, J., Wong, B., & Rosenthal, G. (2007). Shoaling decisions in female swordtails:
How do fish gauge group size? Behaviour, 144(11), 1333–1346.
https://doi.org/10.1163/156853907782418196
Cameron, D. A. (2002). Mapping absorbance spectra, cone fractions, and neuronal
mechanisms to photopic spectral sensitivity in the zebrafish. Visual Neuroscience, 19(3),
365–372. https://doi.org/10.1017/s0952523802192121
Cantlon, J. F., & Brannon, E. M. (2006). Shared system for ordering small and large numbers in
monkeys and humans. Psychological Science, 17(5), 401–406.
https://doi.org/10.1111/j.1467-9280.2006.01719.x
126

Carazo, P., Font, E., Forteza-Behrendt, E., & Desfilis, E. (2009). Quantity discrimination in
Tenebrio molitor: Evidence of numerosity discrimination in an invertebrate? Animal
Cognition, 12(3), 463–470. https://doi.org/10.1007/s10071-008-0207-7
Cervantes-Pérez, F., Lara, R., & Arbib, M. (1985). A neural model of interactions subserving
prey-predator discrimination and size preference in anuran amphibia. Journal of
Theoretical Biology, 113(1), 117–152. https://doi.org/10.1016/S0022-5193(85)80080-1
Chai, J.-H., Locke, D. P., Greally, J. M., Knoll, J. H. M., Ohta, T., Dunai, J., Yavor, A., Eichler, E.
E., & Nicholls, R. D. (2003). Identification of four highly conserved genes between
breakpoint hotspots BP1 and BP2 of the Prader-Willi/Angelman syndromes deletion
region that have undergone evolutionary transposition mediated by flanking duplicons.
American Journal of Human Genetics, 73(4), 898–925. https://doi.org/10.1086/378816
Chailangkarn, T., Trujillo, C. A., Freitas, B. C., Hrvoj-Mihic, B., Herai, R. H., Yu, D. X., Brown, T.
T., Marchetto, M. C., Bardy, C., McHenry, L., Stefanacci, L., Järvinen, A., Searcy, Y. M.,
DeWitt, M., Wong, W., Lai, P., Ard, M. C., Hanson, K. L., Romero, S., … Muotri, A. R.
(2016). A human neurodevelopmental model for Williams syndrome. Nature, 536(7616),
338–343. https://doi.org/10.1038/nature19067
Chakraborty, S., Nian, F.-S., Tsai, J.-W., Karmenyan, A., & Chiou, A. (2016). Quantification of
the Metabolic State in Cell-Model of Parkinson’s Disease by Fluorescence Lifetime
Imaging Microscopy. Scientific Reports, 6(1), Article 1. https://doi.org/10.1038/srep19145
Chen, D., Segovia-Miranda, F., Walker, N., Valenzuela, J. I., Zerial, M., & Myers, E. W. (2020).
Bridging scales in scattering tissues via multifocal two-photon microscopy (p.
2020.06.11.146704). bioRxiv. https://doi.org/10.1101/2020.06.11.146704
Chen, H., Gu, X.-H., Zhou, Y., Ge, Z., Wang, B., Siok, W. T., Wang, G., Huen, M., Jiang, Y., Tan,
L.-H., & Sun, Y. (2017). A Genome-Wide Association Study Identifies Genetic Variants
Associated with Mathematics Ability. Scientific Reports, 7, 40365.
https://doi.org/10.1038/srep40365
Chen, J.-H., Kellner, Y., Zagrebelsky, M., Grunwald, M., Korte, M., & Walla, P. J. (2015).
Two-Photon Correlation Spectroscopy in Single Dendritic Spines Reveals Fast Actin
Filament Reorganization during Activity-Dependent Growth. PLOS ONE, 10(5),
e0128241. https://doi.org/10.1371/journal.pone.0128241
Chen, T.-W., Wardill, T. J., Sun, Y., Pulver, S. R., Renninger, S. L., Baohan, A., Schreiter, E. R.,
Kerr, R. A., Orger, M. B., Jayaraman, V., Looger, L. L., Svoboda, K., & Kim, D. S. (2013).
Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature, 499(7458),
295–300. https://doi.org/10.1038/nature12354
Cheng, R.-K., Jesuthasan, S. J., & Penney, T. B. (2014). Zebrafish forebrain and temporal
conditioning. Philosophical Transactions of the Royal Society B: Biological Sciences,
369(1637), 20120462. https://doi.org/10.1098/rstb.2012.0462
Chiang, H. J., Koo, D. E. S., Kitano, M., Burkitt, S., Unruh, J. R., Zavaleta, C., Trinh, L. A.,
Fraser, S. E., & Cutrale, F. (2023). HyU: Hybrid Unmixing for longitudinal in vivo imaging
of low signal-to-noise fluorescence. Nature Methods, 20(2), Article 2.
https://doi.org/10.1038/s41592-022-01751-5
Chien, Y.-F., Lin, J.-Y., Yeh, P.-T., Hsu, K.-J., Tsai, Y.-H., Chen, S.-K., & Chu, S.-W. (2021). Dual
127

GRIN lens two-photon endoscopy for high-speed volumetric and deep brain imaging.
Biomedical Optics Express, 12(1), 162–172. https://doi.org/10.1364/BOE.405738
Chołuj, M., Alam, Md. M., Beerepoot, M. T. P., Sitkiewicz, S. P., Matito, E., Ruud, K., & Zaleśny,
R. (2022). Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths
Based on Popular Density Functional Approximations. Journal of Chemical Theory and
Computation, 18(2), 1046–1060. https://doi.org/10.1021/acs.jctc.1c01056
Chung, S.-J., Rumi, M., Alain, V., Barlow, S., Perry, J. W., & Marder, S. R. (2005). Strong,
low-energy two-photon absorption in extended amine-terminated cyano-substituted
phenylenevinylene oligomers. Journal of the American Chemical Society, 127(31),
10844–10845. https://doi.org/10.1021/ja052926i
Cleland, N. R. W., Al-Juboori, S. I., Dobrinskikh, E., & Bruce, K. D. (2021). Altered substrate
metabolism in neurodegenerative disease: New insights from metabolic imaging. Journal
of Neuroinflammation, 18(1), 248. https://doi.org/10.1186/s12974-021-02305-w
Collins, E., Park, J., & Behrmann, M. (2017). Numerosity representation is encoded in human
subcortex. Proceedings of the National Academy of Sciences of the United States of
America, 114(14), E2806–E2815. https://doi.org/10.1073/pnas.1613982114
Cong, L., Wang, Z., Chai, Y., Hang, W., Shang, C., Yang, W., Bai, L., Du, J., Wang, K., & Wen,
Q. (2017). Rapid whole brain imaging of neural activity in freely behaving larval zebrafish
(Danio rerio). eLife, 6, e28158. https://doi.org/10.7554/eLife.28158
Corda, G., & Sala, A. (2017). Non-canonical WNT/PCP signalling in cancer: Fzd6 takes centre
stage. Oncogenesis, 6(7), e364. https://doi.org/10.1038/oncsis.2017.69
Cordeiro, L., Ballinger, E., Hagerman, R., & Hessl, D. (2011). Clinical assessment of DSM-IV
anxiety disorders in fragile X syndrome: Prevalence and characterization. Journal of
Neurodevelopmental Disorders, 3(1), 57–67. https://doi.org/10.1007/s11689-010-9067-y
Cox, I. J. (1984). Scanning optical fluorescence microscopy. Journal of Microscopy, 133(2),
149–154. https://doi.org/10.1111/j.1365-2818.1984.tb00480.x
Crosignani, V., Dvornikov, A., Aguilar, J. S., Stringari, C., Edwards, R., Mantulin, W. W., &
Gratton, E. (2012). Deep tissue fluorescence imaging and in vivo biological applications.
Journal of Biomedical Optics, 17(11), 116023.
https://doi.org/10.1117/1.JBO.17.11.116023
Cross, F. R., & Jackson, R. R. (2017). Representation of different exact numbers of prey by a
spider-eating predator. Interface Focus, 7(3), 20160035.
https://doi.org/10.1098/rsfs.2016.0035
Cutrale, F., Trivedi, V., Trinh, L. A., Chiu, C.-L., Choi, J. M., Artiga, M. S., & Fraser, S. E. (2017).
Hyperspectral phasor analysis enables multiplexed 5D in vivo imaging. Nature Methods,
14(2), Article 2. https://doi.org/10.1038/nmeth.4134
Dadda, M., Piffer, L., Agrillo, C., & Bisazza, A. (2009). Spontaneous number representation in
mosquitofish. Cognition, 112(2), 343–348.
https://doi.org/10.1016/j.cognition.2009.05.009
Daetwyler, S., & Fiolka, R. P. (2023). Light-sheets and smart microscopy, an exciting future is
128

dawning. Communications Biology, 6(1), Article 1.
https://doi.org/10.1038/s42003-023-04857-4
Dana, H., Sun, Y., Mohar, B., Hulse, B. K., Kerlin, A. M., Hasseman, J. P., Tsegaye, G., Tsang,
A., Wong, A., Patel, R., Macklin, J. J., Chen, Y., Konnerth, A., Jayaraman, V., Looger, L.
L., Schreiter, E. R., Svoboda, K., & Kim, D. S. (2019a). High-performance calcium
sensors for imaging activity in neuronal populations and microcompartments. Nature
Methods, 16(7), Article 7. https://doi.org/10.1038/s41592-019-0435-6
Dana, H., Sun, Y., Mohar, B., Hulse, B. K., Kerlin, A. M., Hasseman, J. P., Tsegaye, G., Tsang,
A., Wong, A., Patel, R., Macklin, J. J., Chen, Y., Konnerth, A., Jayaraman, V., Looger, L.
L., Schreiter, E. R., Svoboda, K., & Kim, D. S. (2019b). High-performance calcium
sensors for imaging activity in neuronal populations and microcompartments. Nature
Methods, 16(7), 649–657. https://doi.org/10.1038/s41592-019-0435-6
Dana, H., Sun, Y., Mohar, B., Hulse, B. K., Kerlin, A. M., Hasseman, J. P., Tsegaye, G., Tsang,
A., Wong, A., Patel, R., Macklin, J. J., Chen, Y., Konnerth, A., Jayaraman, V., Looger, L.
L., Schreiter, E. R., Svoboda, K., & Kim, D. S. (2019c). High-performance calcium
sensors for imaging activity in neuronal populations and microcompartments. Nature
Methods, 16(7), 649–657. https://doi.org/10.1038/s41592-019-0435-6
Datta, R., Heaster, T. M., Sharick, J. T., Gillette, A. A., & Skala, M. C. (2020). Fluorescence
lifetime imaging microscopy: Fundamentals and advances in instrumentation, analysis,
and applications. Journal of Biomedical Optics, 25(7), 071203.
https://doi.org/10.1117/1.JBO.25.7.071203
Davenport, E. C., Szulc, B. R., Drew, J., Taylor, J., Morgan, T., Higgs, N. F., López-Doménech,
G., & Kittler, J. T. (2019). Autism and Schizophrenia-Associated CYFIP1 Regulates the
Balance of Synaptic Excitation and Inhibition. Cell Reports, 26(8), 2037-2051.e6.
https://doi.org/10.1016/j.celrep.2019.01.092
Davis, O. S. P., Band, G., Pirinen, M., Haworth, C. M. A., Meaburn, E. L., Kovas, Y., Harlaar, N.,
Docherty, S. J., Hanscombe, K. B., Trzaskowski, M., Curtis, C. J. C., Strange, A.,
Freeman, C., Bellenguez, C., Su, Z., Pearson, R., Vukcevic, D., Langford, C., Deloukas,
P., … Spencer, C. C. A. (2014). The correlation between reading and mathematics ability
at age twelve has a substantial genetic component. Nature Communications, 5, 4204.
https://doi.org/10.1038/ncomms5204
de Hevia, M. D., Izard, V., Coubart, A., Spelke, E. S., & Streri, A. (2014). Representations of
space, time, and number in neonates. Proceedings of the National Academy of Sciences
of the United States of America, 111(13), 4809–4813.
https://doi.org/10.1073/pnas.1323628111
de Vito, G., Turrini, L., Müllenbroich, C., Ricci, P., Sancataldo, G., Mazzamuto, G., Tiso, N.,
Sacconi, L., Fanelli, D., Silvestri, L., Vanzi, F., & Pavone, F. S. (2022). Fast whole-brain
imaging of seizures in zebrafish larvae by two-photon light-sheet microscopy. Biomedical
Optics Express, 13(3), 1516–1536. https://doi.org/10.1364/BOE.434146
Débarre, D., Olivier, N., Supatto, W., & Beaurepaire, E. (2014). Mitigating phototoxicity during
multiphoton microscopy of live Drosophila embryos in the 1.0-1.2 µm wavelength range.
PloS One, 9(8), e104250. https://doi.org/10.1371/journal.pone.0104250
DeLong, C. M., Barbato, S., O’Leary, T., & Wilcox, K. T. (2017). Small and large number
129

discrimination in goldfish (Carassius auratus) with extensive training. Behavioural
Processes, 141(Pt 2), 172–183. https://doi.org/10.1016/j.beproc.2016.11.011
Dempsey, W. P., Du, Z., Nadtochiy, A., Smith, C. D., Czajkowski, K., Andreev, A., Robson, D. N.,
Li, J. M., Applebaum, S., Truong, T. V., Kesselman, C., Fraser, S. E., & Arnold, D. B.
(2022). Regional synapse gain and loss accompany memory formation in larval
zebrafish. Proceedings of the National Academy of Sciences, 119(3), e2107661119.
https://doi.org/10.1073/pnas.2107661119
Denk, W., Delaney, K. R., Gelperin, A., Kleinfeld, D., Strowbridge, B. W., Tank, D. W., & Yuste,
R. (1994). Anatomical and functional imaging of neurons using 2-photon laser scanning
microscopy. Journal of Neuroscience Methods, 54(2), 151–162.
https://doi.org/10.1016/0165-0270(94)90189-9
Denk, W., & Detwiler, P. B. (1999). Optical recording of light-evoked calcium signals in the
functionally intact retina. Proceedings of the National Academy of Sciences, 96(12),
7035–7040. https://doi.org/10.1073/pnas.96.12.7035
Denk, W., Strickler, J. H., & Webb, W. W. (1990a). Two-photon laser scanning fluorescence
microscopy. Science (New York, N.Y.), 248(4951), 73–76.
https://doi.org/10.1126/science.2321027
Denk, W., Strickler, J. H., & Webb, W. W. (1990b). Two-Photon Laser Scanning Fluorescence
Microscopy. Science, 248(4951), 73–76. https://doi.org/10.1126/science.2321027
Denk, W., Sugimori, M., & Llinás, R. (1995). Two types of calcium response limited to single
spines in cerebellar Purkinje cells. Proceedings of the National Academy of Sciences of
the United States of America, 92(18), 8279. https://doi.org/10.1073/pnas.92.18.8279
Diagnostic and Statistical Manual of Mental Disorders. (n.d.). DSM Library. Retrieved March 11,
2024, from
https://dsm.psychiatryonline.org/doi/book/10.1176/appi.books.9780890425596
Diaspro, A., Bianchini, P., Vicidomini, G., Faretta, M., Ramoino, P., & Usai, C. (2006).
Multi-photon excitation microscopy. BioMedical Engineering OnLine, 5, 36.
https://doi.org/10.1186/1475-925X-5-36
Diederich, B., Müllenbroich, C., Vladimirov, N., Bowman, R., Stirling, J., Reynaud, E. G., &
Andreev, A. (2022). CAD we share? Publishing reproducible microscope hardware.
Nature Methods, 19(9), Article 9. https://doi.org/10.1038/s41592-022-01484-5
Digman, M. A., Caiolfa, V. R., Zamai, M., & Gratton, E. (2008). The phasor approach to
fluorescence lifetime imaging analysis. Biophysical Journal, 94(2), L14-16.
https://doi.org/10.1529/biophysj.107.120154
Digman, M. A., Sengupta, P., Wiseman, P. W., Brown, C. M., Horwitz, A. R., & Gratton, E.
(2005). Fluctuation Correlation Spectroscopy with a Laser-Scanning Microscope:
Exploiting the Hidden Time Structure. Biophysical Journal, 88(5), L33–L36.
https://doi.org/10.1529/biophysj.105.061788
Ditz, H. M., & Nieder, A. (2015). Neurons selective to the number of visual items in the corvid
songbird endbrain. Proceedings of the National Academy of Sciences of the United
States of America, 112(25), 7827–7832. https://doi.org/10.1073/pnas.1504245112
130

Ditz, H. M., & Nieder, A. (2016). Sensory and Working Memory Representations of Small and
Large Numerosities in the Crow Endbrain. The Journal of Neuroscience: The Official
Journal of the Society for Neuroscience, 36(47), 12044–12052.
https://doi.org/10.1523/JNEUROSCI.1521-16.2016
Dlugos, C. A., & Rabin, R. A. (2003). Ethanol effects on three strains of zebrafish: Model system
for genetic investigations. Pharmacology Biochemistry and Behavior, 74(2), 471–480.
https://doi.org/10.1016/S0091-3057(02)01026-2
Docherty, S. J., Davis, O. S. P., Kovas, Y., Meaburn, E. L., Dale, P. S., Petrill, S. A., Schalkwyk,
L. C., & Plomin, R. (2010). A genome-wide association study identifies multiple loci
associated with mathematics ability and disability. Genes, Brain, and Behavior, 9(2),
234–247. https://doi.org/10.1111/j.1601-183X.2009.00553.x
Donnert, G., Eggeling, C., & Hell, S. W. (2007). Major signal increase in fluorescence
microscopy through dark-state relaxation. Nature Methods, 4(1), Article 1.
https://doi.org/10.1038/nmeth986
Dreosti, E., Lopes, G., Kampff, A. R., & Wilson, S. W. (2015). Development of social behavior in
young zebrafish. Frontiers in Neural Circuits, 9, 39.
https://doi.org/10.3389/fncir.2015.00039
Drobizhev, M., Makarov, N. S., Tillo, S. E., Hughes, T. E., & Rebane, A. (2011). Two-photon
absorption properties of fluorescent proteins. Nature Methods, 8(5), Article 5.
https://doi.org/10.1038/nmeth.1596
Dvornikov, A., Malacrida, L., & Gratton, E. (2019). The DIVER Microscope for Imaging in
Scattering Media. Methods and Protocols, 2(2), 53. https://doi.org/10.3390/mps2020053
Easter, S. S., & Nicola, G. N. (1996). The development of vision in the zebrafish (Danio rerio).
Developmental Biology, 180(2), 646–663. https://doi.org/10.1006/dbio.1996.0335
Edelstein, A., Amodaj, N., Hoover, K., Vale, R., & Stuurman, N. (2010a). Computer Control of
Microscopes Using µManager. Current Protocols in Molecular Biology, 92(1),
14.20.1-14.20.17. https://doi.org/10.1002/0471142727.mb1420s92
Edelstein, A., Amodaj, N., Hoover, K., Vale, R., & Stuurman, N. (2010b). Computer Control of
Microscopes Using µManager. Current Protocols in Molecular Biology, 92(1),
14.20.1-14.20.17. https://doi.org/10.1002/0471142727.mb1420s92
Edelstein, A. D., Tsuchida, M. A., Amodaj, N., Pinkard, H., Vale, R. D., & Stuurman, N. (2014).
Advanced methods of microscope control using μManager software. Journal of
Biological Methods, 1(2), e10. https://doi.org/10.14440/jbm.2014.36
Edwards, C. J., Alder, T. B., & Rose, G. J. (2002). Auditory midbrain neurons that count. Nature
Neuroscience, 5(10), 934–936. https://doi.org/10.1038/nn916
Eles, J. R., Vazquez, A. L., Kozai, T. D. Y., & Cui, X. T. (2018). In vivo imaging of neuronal
calcium during electrode implantation: Spatial and temporal mapping of damage and
recovery. Biomaterials, 174, 79–94. https://doi.org/10.1016/j.biomaterials.2018.04.043
Elson, E. L. (2011). Fluorescence Correlation Spectroscopy: Past, Present, Future. Biophysical
Journal, 101(12), 2855–2870. https://doi.org/10.1016/j.bpj.2011.11.012
131

Emran, F., & Dowling, J. E. (2010). Larval zebrafish turn off their photoreceptors at night.
Communicative & Integrative Biology, 3(5), 430–432.
https://doi.org/10.4161/cib.3.5.12158
Evans, P. R., Yan, L., & Yasuda, R. (2019). Imaging Neuronal Signal Transduction Using
Multiphoton FRET-FLIM. In E. Hartveit (Ed.), Multiphoton Microscopy (pp. 111–130).
Springer. https://doi.org/10.1007/978-1-4939-9702-2_6
Evans, S. W., Shi, D.-Q., Chavarha, M., Plitt, M. H., Taxidis, J., Madruga, B., Fan, J. L., Hwang,
F.-J., van Keulen, S. C., Suomivuori, C.-M., Pang, M. M., Su, S., Lee, S., Hao, Y. A.,
Zhang, G., Jiang, D., Pradhan, L., Roth, R. H., Liu, Y., … Lin, M. Z. (2023). A positively
tuned voltage indicator for extended electrical recordings in the brain. Nature Methods,
20(7), 1104–1113. https://doi.org/10.1038/s41592-023-01913-z
Ewert, J.-P., & Gebauer, L. (1973). Größenkonstanzphänomene im Beutefangverhalten der
Erdkröte (Bufo bufo L.). Journal of comparative physiology, 85(3), 303–315.
https://doi.org/10.1007/BF00694236
Fahrbach, F. O., Voigt, F. F., Schmid, B., Helmchen, F., & Huisken, J. (2013). Rapid 3D
light-sheet microscopy with a tunable lens. Optics Express, 21(18), 21010–21026.
https://doi.org/10.1364/OE.21.021010
Farrants, H., Shuai, Y., Lemon, W. C., Hernandez, C. M., Yang, S., Patel, R., Qiao, G., Frei, M.
S., Grimm, J. B., Hanson, T. L., Tomaska, F., Turner, G. C., Stringer, C., Keller, P. J.,
Beyene, A. G., Chen, Y., Liang, Y., Lavis, L. D., & Schreiter, E. R. (2023). A modular
chemigenetic calcium indicator enables in vivo functional imaging with near-infrared light
(p. 2023.07.18.549527). bioRxiv. https://doi.org/10.1101/2023.07.18.549527
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive
Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Ferguson, M., Sharma, D., Ross, D., & Zhao, F. (2019). A Critical Review of Microelectrode
Arrays and Strategies for Improving the Neural Interface. Advanced Healthcare
Materials, 8(19), e1900558. https://doi.org/10.1002/adhm.201900558
Fontana, B. D., Mezzomo, N. J., Kalueff, A. V., & Rosemberg, D. B. (2018). The developing
utility of zebrafish models of neurological and neuropsychiatric disorders: A critical
review. Experimental Neurology, 299(Pt A), 157–171.
https://doi.org/10.1016/j.expneurol.2017.10.004
Forsatkar, M. N., Nematollahi, M. A., & Bisazza, A. (2016). Quantity discrimination in parental
fish: Female convict cichlid discriminate fry shoals of different sizes. Animal Cognition,
19(5), 959–964. https://doi.org/10.1007/s10071-016-0997-y
Förster, D., Helmbrecht, T. O., Mearns, D. S., Jordan, L., Mokayes, N., & Baier, H. (2020).
Retinotectal circuitry of larval zebrafish is adapted to detection and pursuit of prey. eLife,
9, e58596. https://doi.org/10.7554/eLife.58596
Foster, W. A., & Treherne, J. E. (1981). Evidence for the dilution effect in the selfish herd from
fish predation on a marine insect. Nature, 293(5832), 466–467.
https://doi.org/10.1038/293466a0
Frommen, J. G., Hiermes, M., & Bakker, T. C. M. (2009). Disentangling the effects of group size
132

and density on shoaling decisions of three-spined sticklebacks (Gasterosteus aculeatus).
Behavioral Ecology and Sociobiology, 63(8), 1141–1148.
https://doi.org/10.1007/s00265-009-0767-9
Gandini, D., Lemaire, P., & Michel, B. F. (2009). Approximate quantification in young, healthy
older adults’, and Alzheimer patients. Brain and Cognition, 70(1), 53–61.
https://doi.org/10.1016/j.bandc.2008.12.004
Garland, A., Low, J., & Burns, K. C. (2012). Large quantity discrimination by North Island robins
(Petroica longipes). Animal Cognition, 15(6), 1129–1140.
https://doi.org/10.1007/s10071-012-0537-3
Gasparoli, F. M., Escobet-Montalbán, A., Early, J., Bruce, G. D., & Dholakia, K. (2020). Is laser
repetition rate important for two-photon light sheet microscopy? OSA Continuum, 3(10),
2935–2942. https://doi.org/10.1364/OSAC.405369
Gazzola, A., Vallortigara, G., & Pellitteri-Rosa, D. (2018). Continuous and discrete quantity
discrimination in tortoises. Biology Letters, 14(12), 20180649.
https://doi.org/10.1098/rsbl.2018.0649
Georgakoudi, I., & Quinn, K. P. (2023). Label-Free Optical Metabolic Imaging in Cells and
Tissues. Annual Review of Biomedical Engineering, 25, 413–443.
https://doi.org/10.1146/annurev-bioeng-071516-044730
Georgy, L., Celeghin, A., Marzi, C. A., Tamietto, M., & Ptito, A. (2016). The superior colliculus is
sensitive to gestalt-like stimulus configuration in hemispherectomy patients. Cortex; a
Journal Devoted to the Study of the Nervous System and Behavior, 81, 151–161.
https://doi.org/10.1016/j.cortex.2016.04.018
Gerlai, R. (2016). Learning and memory in zebrafish (Danio rerio). Methods in Cell Biology, 134,
551–586. https://doi.org/10.1016/bs.mcb.2016.02.005
Gerlai, R. (2017). Zebrafish and relational memory: Could a simple fish be useful for the
analysis of biological mechanisms of complex vertebrate learning? Behavioural
Processes, 141(Pt 2), 242–250. https://doi.org/10.1016/j.beproc.2017.01.016
Gerlai, R. (2020). Evolutionary conservation, translational relevance and cognitive function: The
future of zebrafish in behavioral neuroscience. Neuroscience and Biobehavioral
Reviews, 116, 426–435. https://doi.org/10.1016/j.neubiorev.2020.07.009
Giovannucci, A., Friedrich, J., Gunn, P., Kalfon, J., Brown, B. L., Koay, S. A., Taxidis, J., Najafi,
F., Gauthier, J. L., Zhou, P., Khakh, B. S., Tank, D. W., Chklovskii, D. B., &
Pnevmatikakis, E. A. (2019). CaImAn an open source tool for scalable calcium imaging
data analysis. eLife, 8, e38173. https://doi.org/10.7554/eLife.38173
Gómez-Laplaza, L. M., Díaz-Sotelo, E., & Gerlai, R. (2018). Quantity discrimination in angelfish,
Pterophyllum scalare: A novel approach with food as the discriminant. Animal Behaviour,
142, 19–30. https://doi.org/10.1016/j.anbehav.2018.06.001
Gómez-Laplaza, L. M., & Gerlai, R. (2011a). Can angelfish (Pterophyllum scalare) count?
Discrimination between different shoal sizes follows Weber’s law. Animal Cognition,
14(1), 1–9. https://doi.org/10.1007/s10071-010-0337-6
133

Gómez-Laplaza, L. M., & Gerlai, R. (2011b). Spontaneous discrimination of small quantities:
Shoaling preferences in angelfish (Pterophyllum scalare). Animal Cognition, 14(4),
565–574. https://doi.org/10.1007/s10071-011-0392-7
Gómez-Laplaza, L. M., & Gerlai, R. (2012). Activity counts: The effect of swimming activity on
quantity discrimination in fish. Frontiers in Psychology, 3, 484.
https://doi.org/10.3389/fpsyg.2012.00484
Gómez-Laplaza, L. M., & Gerlai, R. (2013). Quantification abilities in angelfish (Pterophyllum
scalare): The influence of continuous variables. Animal Cognition, 16(3), 373–383.
https://doi.org/10.1007/s10071-012-0578-7
Gómez-Laplaza, L. M., & Gerlai, R. (2015). Angelfish (Pterophyllum scalare) discriminate
between small quantities: A role of memory. Journal of Comparative Psychology
(Washington, D.C.: 1983), 129(1), 78–83. https://doi.org/10.1037/a0038228
Gómez-Laplaza, L. M., Romero, L., & Gerlai, R. (2019). The role of item size on choosing
contrasted food quantities in angelfish (Pterophyllum scalare). Scientific Reports, 9(1),
15305. https://doi.org/10.1038/s41598-019-51753-1
Goodrich-Hunsaker, N. J., Wong, L. M., McLennan, Y., Srivastava, S., Tassone, F., Harvey, D.,
Rivera, S. M., & Simon, T. J. (2011). Young adult female fragile X premutation carriers
show age- and genetically-modulated cognitive impairments. Brain and Cognition, 75(3),
255–260. https://doi.org/10.1016/j.bandc.2011.01.001
Göppert-Mayer, M. (1931). Über Elementarakte mit zwei Quantensprüngen. Annalen Der
Physik, 401(3), 273–294. https://doi.org/10.1002/andp.19314010303
Goss-Varley, M., Dona, K. R., McMahon, J. A., Shoffstall, A. J., Ereifej, E. S., Lindner, S. C., &
Capadona, J. R. (2017). Microelectrode implantation in motor cortex causes fine motor
deficit: Implications on potential considerations to Brain Computer Interfacing and
Human Augmentation. Scientific Reports, 7(1), 15254.
https://doi.org/10.1038/s41598-017-15623-y
Guo, C., Liu, W., Hua, X., Li, H., & Jia, S. (2019a). Fourier light-field microscopy. Optics
Express, 27(18), 25573–25594. https://doi.org/10.1364/OE.27.025573
Guo, C., Liu, W., Hua, X., Li, H., & Jia, S. (2019b). Fourier light-field microscopy. Optics
Express, 27(18), 25573–25594. https://doi.org/10.1364/OE.27.025573
Gusel’nikov, V. I., Morenkov, É. D., & Gutsu, I. P. (1971). Responses of neurons in the pigeon’s
optic tectum to visual stimuli. Neurophysiology, 3(1), 78–83.
https://doi.org/10.1007/BF01065595
Hampson, K. M., Turcotte, R., Miller, D. T., Kurokawa, K., Males, J. R., Ji, N., & Booth, M. J.
(2021). Adaptive optics for high-resolution imaging. Nature Reviews Methods Primers,
1(1), Article 1. https://doi.org/10.1038/s43586-021-00066-7
Harpaz, R., Nguyen, M. N., Bahl, A., & Engert, F. (2021). Precise visuomotor transformations
underlying collective behavior in larval zebrafish. Nature Communications, 12(1), 6578.
https://doi.org/10.1038/s41467-021-26748-0
Harvey-Girard, E., Giassi, A. C. C., Ellis, W., & Maler, L. (2012). Organization of the gymnotiform
134

fish pallium in relation to learning and memory: IV. Expression of conserved transcription
factors and implications for the evolution of dorsal telencephalon. The Journal of
Comparative Neurology, 520(15), 3395–3413. https://doi.org/10.1002/cne.23107
Haug, M. F., Biehlmaier, O., Mueller, K. P., & Neuhauss, S. C. (2010). Visual acuity in larval
zebrafish: Behavior and histology. Frontiers in Zoology, 7(1), 8.
https://doi.org/10.1186/1742-9994-7-8
Hauser, M. D., Carey, S., & Hauser, L. B. (2000). Spontaneous number representation in
semi-free-ranging rhesus monkeys. Proceedings. Biological Sciences, 267(1445),
829–833. https://doi.org/10.1098/rspb.2000.1078
Hedde, P. N., Cinco, R., Malacrida, L., Kamaid, A., & Gratton, E. (2021). Phasor-based
hyperspectral snapshot microscopy allows fast imaging of live, three-dimensional tissues
for biomedical applications. Communications Biology, 4(1), Article 1.
https://doi.org/10.1038/s42003-021-02266-z
Heikal, A. A. (2010). Intracellular coenzymes as natural biomarkers for metabolic activities and
mitochondrial anomalies. Biomarkers in Medicine, 4(2), 241–263.
https://doi.org/10.2217/bmm.10.1
Hell, S. W., Bahlmann, K., Schrader, M., Soini, A., Malak, H. M., Gryczynski, I., & Lakowicz, J.
R. (1996). Three-photon excitation in fluorescence microscopy. Journal of Biomedical
Optics, 1(1), 71–74. https://doi.org/10.1117/12.229062
Helmchen, F. (2009). Two-Photon Functional Imaging of Neuronal Activity. In R. D. Frostig (Ed.),
In Vivo Optical Imaging of Brain Function (2nd ed.). CRC Press/Taylor & Francis.
http://www.ncbi.nlm.nih.gov/books/NBK20230/
Helmchen, F., & Denk, W. (2005). Deep tissue two-photon microscopy. Nature Methods, 2(12),
Article 12. https://doi.org/10.1038/nmeth818
Helmchen, F., Fee, M. S., Tank, D. W., & Denk, W. (2001). A miniature head-mounted
two-photon microscope. High-resolution brain imaging in freely moving animals. Neuron,
31(6), 903–912. https://doi.org/10.1016/s0896-6273(01)00421-4
Hert, E. (1991). Female choice based on egg-spots in Pseudotropheus aurora Burgess 1976, a
rock-dwelling cichlid of Lake Malaŵi, Africa. Journal of Fish Biology, 38(6), 951–953.
https://doi.org/10.1111/j.1095-8649.1991.tb03634.x
Hinz, R. C., & de Polavieja, G. G. (2017). Ontogeny of collective behavior reveals a simple
attraction rule. Proceedings of the National Academy of Sciences of the United States of
America, 114(9), 2295–2300. https://doi.org/10.1073/pnas.1616926114
Hopt, A., & Neher, E. (2001). Highly nonlinear photodamage in two-photon fluorescence
microscopy. Biophysical Journal, 80(4), 2029–2036.
Howe, K., Clark, M. D., Torroja, C. F., Torrance, J., Berthelot, C., Muffato, M., Collins, J. E.,
Humphray, S., McLaren, K., Matthews, L., McLaren, S., Sealy, I., Caccamo, M.,
Churcher, C., Scott, C., Barrett, J. C., Koch, R., Rauch, G.-J., White, S., … Stemple, D.
L. (2013). The zebrafish reference genome sequence and its relationship to the human
genome. Nature, 496(7446), 498–503. https://doi.org/10.1038/nature12111
135

Hwang, W. Y., Fu, Y., Reyon, D., Maeder, M. L., Tsai, S. Q., Sander, J. D., Peterson, R. T., Yeh,
J.-R. J., & Joung, J. K. (2013). Efficient genome editing in zebrafish using a
CRISPR-Cas system. Nature Biotechnology, 31(3), 227–229.
https://doi.org/10.1038/nbt.2501
Hyde, D. (2011). Two Systems of Non-Symbolic Numerical Cognition. Frontiers in Human
Neuroscience, 5. https://www.frontiersin.org/articles/10.3389/fnhum.2011.00150
Isbaner, S., Karedla, N., Ruhlandt, D., Stein, S. C., Chizhik, A., Gregor, I., & Enderlein, J.
(2016). Dead-time correction of fluorescence lifetime measurements and fluorescence
lifetime imaging. Optics Express, 24(9), 9429–9445.
https://doi.org/10.1364/OE.24.009429
Ito, H., & Yamamoto, N. (2009). Non-laminar cerebral cortex in teleost fishes? Biology Letters,
5(1), 117–121. https://doi.org/10.1098/rsbl.2008.0397
Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract
numbers. Proceedings of the National Academy of Sciences of the United States of
America, 106(25), 10382–10385. https://doi.org/10.1073/pnas.0812142106
James, D. S., & Campagnola, P. J. (2021). Recent Advancements in Optical Harmonic
Generation Microscopy: Applications and Perspectives. BME Frontiers, 2021, 3973857.
https://doi.org/10.34133/2021/3973857
Janicek, R., Agarwal, H., Gómez, A. M., Egger, M., Ellis-Davies, G. C. R., & Niggli, E. (2021).
Local recovery of cardiac calcium-induced calcium release interrogated by
ultra-effective, two-photon uncaging of calcium. The Journal of Physiology, 599(16),
3841–3852. https://doi.org/10.1113/JP281482
Ji, N., Magee, J. C., & Betzig, E. (2008). High-speed, low-photodamage nonlinear imaging using
passive pulse splitters. Nature Methods, 5(2), Article 2.
https://doi.org/10.1038/nmeth.1175
Jung, J. C., & Schnitzer, M. J. (2003). Multiphoton endoscopy. Optics Letters, 28(11), 902–904.
https://doi.org/10.1364/ol.28.000902
Juvekar, V., Lim, C. S., Lee, D. J., Song, D. H., Noh, C.-K., Kang, H., Shin, S. J., & Kim, H. M.
(2021). Near-Infrared Ratiometric Two-Photon Probe for pH Measurement in Human
Stomach Cancer Tissue. ACS Applied Bio Materials, 4(3), 2135–2141.
https://doi.org/10.1021/acsabm.0c01546
Kagiampaki, Z., Rohner, V., Kiss, C., Curreli, S., Dieter, A., Wilhelm, M., Harada, M., Duss, S.
N., Dernic, J., Bhat, M. A., Zhou, X., Ravotto, L., Ziebarth, T., Wasielewski, L. M.,
Sönmez, L., Benke, D., Weber, B., Bohacek, J., Reiner, A., … Patriarchi, T. (2023).
Sensitive multicolor indicators for monitoring norepinephrine in vivo. Nature Methods,
1–11. https://doi.org/10.1038/s41592-023-01959-z
Kaiser, W., & Garrett, C. G. B. (1961). Two-Photon Excitation in CaF2:Eu2+. Physical Review
Letters, 7(6), 229–231. https://doi.org/10.1103/PhysRevLett.7.229
Kalueff, A. V., Gebhardt, M., Stewart, A. M., Cachat, J. M., Brimmer, M., Chawla, J. S.,
Craddock, C., Kyzar, E. J., Roth, A., Landsman, S., Gaikwad, S., Robinson, K., Baatrup,
E., Tierney, K., Shamchuk, A., Norton, W., Miller, N., Nicolson, T., Braubach, O., …
136

Zebrafish Neuroscience Research Consortium. (2013). Towards a comprehensive
catalog of zebrafish behavior 1.0 and beyond. Zebrafish, 10(1), 70–86.
https://doi.org/10.1089/zeb.2012.0861
Kappel, J. M., Förster, D., Slangewal, K., Shainer, I., Svara, F., Donovan, J. C., Sherman, S.,
Januszewski, M., Baier, H., & Larsch, J. (2022). Visual recognition of social signals by a
tectothalamic neural circuit. Nature, 608(7921), 146–152.
https://doi.org/10.1038/s41586-022-04925-5
Karu, T. (1999). Primary and secondary mechanisms of action of visible to near-IR radiation on
cells. Journal of Photochemistry and Photobiology B: Biology, 49(1), 1–17.
https://doi.org/10.1016/S1011-1344(98)00219-X
Kawakami, K. (2005). Transposon tools and methods in zebrafish. Developmental Dynamics:
An Official Publication of the American Association of Anatomists, 234(2), 244–254.
https://doi.org/10.1002/dvdy.20516
Keller, P. J., Schmidt, A. D., Wittbrodt, J., & Stelzer, E. H. K. (2008). Reconstruction of Zebrafish
Early Embryonic Development by Scanned Light Sheet Microscopy. Science, 322(5904),
1065–1069. https://doi.org/10.1126/science.1162493
Keller, P. J., & Stelzer, E. H. K. (2010). Digital scanned laser light sheet fluorescence
microscopy. Cold Spring Harbor Protocols, 2010(5), pdb.top78.
https://doi.org/10.1101/pdb.top78
Kemmer, I., Keppler, A., Serrano-Solano, B., Rybina, A., Özdemir, B., Bischof, J., El Ghadraoui,
A., Eriksson, J. E., & Mathur, A. (2023). Building a FAIR image data ecosystem for
microscopy communities. Histochemistry and Cell Biology.
https://doi.org/10.1007/s00418-023-02203-7
Keomanee-Dizon, K., Fraser, S. E., & Truong, T. V. (2020a). A versatile, multi-laser
twin-microscope system for light-sheet imaging. Review of Scientific Instruments, 91(5),
053703. https://doi.org/10.1063/1.5144487
Keomanee-Dizon, K., Fraser, S. E., & Truong, T. V. (2020b). A versatile, multi-laser
twin-microscope system for light-sheet imaging. Review of Scientific Instruments, 91(5),
053703. https://doi.org/10.1063/1.5144487
Keomanee-Dizon, K., Fraser, S. E., & Truong, T. V. (2020c). A versatile, multi-laser
twin-microscope system for light-sheet imaging. Review of Scientific Instruments, 91(5),
053703. https://doi.org/10.1063/1.5144487
Key, H., Davies, E. R., Jackson, P. C., & Wells, P. N. (1991). Optical attenuation characteristics
of breast tissues at visible and near-infrared wavelengths. Physics in Medicine and
Biology, 36(5), 579–590. https://doi.org/10.1088/0031-9155/36/5/002
Khoroshyy, P., Martinez-Seara, H., Myšková, J., & Lazar, J. (2023). Dynamics of transition
dipole moment orientation in representative fluorescent proteins. Physical Chemistry
Chemical Physics, 25(33), 22117–22123. https://doi.org/10.1039/D3CP01242E
Kimmel, C. B., Ballard, W. W., Kimmel, S. R., Ullmann, B., & Schilling, T. F. (1995). Stages of
embryonic development of the zebrafish. Developmental Dynamics: An Official
Publication of the American Association of Anatomists, 203(3), 253–310.
137

https://doi.org/10.1002/aja.1002030302
Kirschhock, M. E., & Nieder, A. (2022). Number selective sensorimotor neurons in the crow
translate perceived numerosity into number of actions. Nature Communications, 13(1),
6913. https://doi.org/10.1038/s41467-022-34457-5
Kitagawa, H., Fujiki, R., Yoshimura, K., Oya, H., & Kato, S. (2011). Williams syndrome is an
epigenome-regulator disease. Endocrine Journal, 58(2), 77–85.
https://doi.org/10.1507/endocrj.k10e-393
Kobylkov, D., Mayer, U., Zanon, M., & Vallortigara, G. (2022). Number neurons in the
nidopallium of young domestic chicks. Proceedings of the National Academy of Sciences
of the United States of America, 119(32), e2201039119.
https://doi.org/10.1073/pnas.2201039119
Koelega, H. S. (1995). Alcohol and vigilance performance: A review. Psychopharmacology,
118(3), 233–249. https://doi.org/10.1007/BF02245951
Koester, H. J., Baur, D., Uhl, R., & Hell, S. W. (1999). Ca2+ Fluorescence Imaging with Picoand Femtosecond Two-Photon Excitation: Signal and Photodamage. Biophysical
Journal, 77(4), 2226–2236. https://doi.org/10.1016/S0006-3495(99)77063-3
Koho, S. V., Slenders, E., Tortarolo, G., Castello, M., Buttafava, M., Villa, F., Tcarenkova, E.,
Ameloot, M., Bianchini, P., Sheppard, C. J. R., Diaspro, A., Tosi, A., & Vicidomini, G.
(2020). Two-photon image-scanning microscopy with SPAD array and blind image
reconstruction. Biomedical Optics Express, 11(6), 2905–2924.
https://doi.org/10.1364/BOE.374398
Kolenc, O. I., & Quinn, K. P. (2019). Evaluating Cell Metabolism Through Autofluorescence
Imaging of NAD(P)H and FAD. Antioxidants & Redox Signaling, 30(6), 875–889.
https://doi.org/10.1089/ars.2017.7451
Köllner, M., & Wolfrum, J. (1992). How many photons are necessary for fluorescence-lifetime
measurements? Chemical Physics Letters, 200(1), 199–204.
https://doi.org/10.1016/0009-2614(92)87068-Z
König, K., So, P. T., Mantulin, W. W., & Gratton, E. (1997). Cellular response to near-infrared
femtosecond laser pulses in two-photon microscopes. Optics Letters, 22(2), 135–136.
https://doi.org/10.1364/ol.22.000135
Kovas, Y., Giampietro, V., Viding, E., Ng, V., Brammer, M., Barker, G. J., Happé, F. G. E., &
Plomin, R. (2009). Brain correlates of non-symbolic numerosity estimation in low and
high mathematical ability children. PloS One, 4(2), e4587.
https://doi.org/10.1371/journal.pone.0004587
Koveal, D., Díaz-García, C. M., & Yellen, G. (2020). Fluorescent Biosensors for Neuronal
Metabolism and the Challenges of Quantitation. Current Opinion in Neurobiology, 63,
111–121. https://doi.org/10.1016/j.conb.2020.02.011
Krajcsi, A., Lukács, A., Igács, J., Racsmány, M., & Pléh, C. (2009). Numerical abilities in
Williams syndrome: Dissociating the analogue magnitude system and verbal retrieval.
Journal of Clinical and Experimental Neuropsychology, 31(4), 439–446.
https://doi.org/10.1080/13803390802244126
138

Krause, J., & Godin, J.-G. J. (1995). Predator preferences for attacking particular prey group
sizes: Consequences for predator hunting success and prey predation risk. Animal
Behaviour, 50(2), 465–473. https://doi.org/10.1006/anbe.1995.0260
Krebs, J. R., Ryan, J. C., & Charnov, E. L. (1974). Hunting by expectation or optimal foraging? A
study of patch use by chickadees. Animal Behaviour, 22, 953-IN3.
https://doi.org/10.1016/0003-3472(74)90018-9
Kubo, T., Temma, K., Smith, N. I., Lu, K., Matsuda, T., Nagai, T., & Fujita, K. (2021).
Hyperspectral two-photon excitation microscopy using visible wavelength. Optics Letters,
46(1), 37–40. https://doi.org/10.1364/OL.413526
Kumar, M., Kishore, S., Nasenbeny, J., McLean, D. L., & Kozorovitskiy, Y. (2018). Integrated
one- and two-photon scanned oblique plane illumination (SOPi) microscopy for rapid
volumetric imaging. Optics Express, 26(10), 13027–13041.
https://doi.org/10.1364/OE.26.013027
Kunst, M., Laurell, E., Mokayes, N., Kramer, A., Kubo, F., Fernandes, A. M., Förster, D.,
Maschio, M. D., & Baier, H. (2019). A Cellular-Resolution Atlas of the Larval Zebrafish
Brain. Neuron, 103(1), 21-38.e5. https://doi.org/10.1016/j.neuron.2019.04.034
Kuznetsova, D. S., Shirmanova, M. V., Dudenkova, V. V., Subochev, P. V., Turchin, I. V.,
Zagaynova, E. V., Lukyanov, S. A., Shakhov, B. E., & Kamensky, V. A. (2015).
Photobleaching and phototoxicity of KillerRed in tumor spheroids induced by continuous
wave and pulsed laser illumination. Journal of Biophotonics, 8(11–12), 952–960.
https://doi.org/10.1002/jbio.201400130
Laissue, P. P., Alghamdi, R. A., Tomancak, P., Reynaud, E. G., & Shroff, H. (2017). Assessing
phototoxicity in live fluorescence imaging. Nature Methods, 14(7), Article 7.
https://doi.org/10.1038/nmeth.4344
Lakowicz, J. R. (Ed.). (2006). Principles of Fluorescence Spectroscopy. Springer US.
https://doi.org/10.1007/978-0-387-46312-4
Lakowicz, J. R., Gryczynski, I., Malak, H., Schrader, M., Engelhardt, P., Kano, H., & Hell, S. W.
(1997). Time-Resolved Fluorescence Spectroscopy and Imaging of DNA Labeled with
DAPI and Hoechst 33342 Using Three-Photon Excitation. Biophysical Journal, 72(2 Pt
1), 567–578.
Lakowicz, J. R., Szmacinski, H., Nowaczyk, K., & Johnson, M. L. (1992). Fluorescence lifetime
imaging of free and protein-bound NADH. Proceedings of the National Academy of
Sciences, 89(4), 1271–1275. https://doi.org/10.1073/pnas.89.4.1271
Lalli, M. A., Jang, J., Park, J.-H. C., Wang, Y., Guzman, E., Zhou, H., Audouard, M., Bridges, D.,
Tovar, K. R., Papuc, S. M., Tutulan-Cunita, A. C., Huang, Y., Budisteanu, M., Arghir, A., &
Kosik, K. S. (2016). Haploinsufficiency of BAZ1B contributes to Williams syndrome
through transcriptional dysregulation of neurodevelopmental pathways. Human
Molecular Genetics, 25(7), 1294–1306. https://doi.org/10.1093/hmg/ddw010
Larsch, J., & Baier, H. (2018a). Biological Motion as an Innate Perceptual Mechanism Driving
Social Affiliation. Current Biology: CB, 28(22), 3523-3532.e4.
https://doi.org/10.1016/j.cub.2018.09.014
139

Larsch, J., & Baier, H. (2018b). Biological Motion as an Innate Perceptual Mechanism Driving
Social Affiliation. Current Biology: CB, 28(22), 3523-3532.e4.
https://doi.org/10.1016/j.cub.2018.09.014
Laviv, T., Scholl, B., Parra-Bueno, P., Foote, B., Zhang, C., Yan, L., Hayano, Y., Chu, J., &
Yasuda, R. (2020). In Vivo Imaging of the Coupling between Neuronal and CREB
Activity in the Mouse Brain. Neuron, 105(5), 799-812.e5.
https://doi.org/10.1016/j.neuron.2019.11.028
Laviv, T., & Yasuda, R. (2021). Imaging neuronal protein signaling dynamics in vivo. Current
Opinion in Neurobiology, 69, 68–75. https://doi.org/10.1016/j.conb.2021.02.002
Leben, R., Köhler, M., Radbruch, H., Hauser, A. E., & Niesner, R. A. (2019). Systematic Enzyme
Mapping of Cellular Metabolism by Phasor-Analyzed Label-Free NAD(P)H Fluorescence
Lifetime Imaging. International Journal of Molecular Sciences, 20(22), 5565.
https://doi.org/10.3390/ijms20225565
Lee, D. A., Andreev, A., Truong, T. V., Chen, A., Hill, A. J., Oikonomou, G., Pham, U., Hong, Y.
K., Tran, S., Glass, L., Sapin, V., Engle, J., Fraser, S. E., & Prober, D. A. (2017a).
Genetic and neuronal regulation of sleep by neuropeptide VF. eLife, 6, e25727.
https://doi.org/10.7554/eLife.25727
Lee, D. A., Andreev, A., Truong, T. V., Chen, A., Hill, A. J., Oikonomou, G., Pham, U., Hong, Y.
K., Tran, S., Glass, L., Sapin, V., Engle, J., Fraser, S. E., & Prober, D. A. (2017b).
Genetic and neuronal regulation of sleep by neuropeptide VF. eLife, 6, e25727.
https://doi.org/10.7554/eLife.25727
Lee, S. H., DeCandia, T. R., Ripke, S., Yang, J., Schizophrenia Psychiatric Genome-Wide
Association Study Consortium (PGC-SCZ), International Schizophrenia Consortium
(ISC), Molecular Genetics of Schizophrenia Collaboration (MGS), Sullivan, P. F.,
Goddard, M. E., Keller, M. C., Visscher, P. M., & Wray, N. R. (2012). Estimating the
proportion of variation in susceptibility to schizophrenia captured by common SNPs.
Nature Genetics, 44(3), 247–250. https://doi.org/10.1038/ng.1108
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of
magnitude”: The role of continuous magnitudes in numerical cognition. The Behavioral
and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960
Levene, M. J., Dombeck, D. A., Kasischke, K. A., Molloy, R. P., & Webb, W. W. (2004). In vivo
multiphoton microscopy of deep brain tissue. Journal of Neurophysiology, 91(4),
1908–1912. https://doi.org/10.1152/jn.01007.2003
Levinoff, E. J., Phillips, N. A., Verret, L., Babins, L., Kelner, N., Akerib, V., & Chertkow, H. (2006).
Cognitive estimation impairment in Alzheimer disease and mild cognitive impairment.
Neuropsychology, 20(1), 123–132. https://doi.org/10.1037/0894-4105.20.1.123
Levoy, M., Ng, R., Adams, A., Footer, M., & Horowitz, M. (2006a). Light field microscopy. ACM
Transactions on Graphics, 25(3), 924–934. https://doi.org/10.1145/1141911.1141976
Levoy, M., Ng, R., Adams, A., Footer, M., & Horowitz, M. (2006b). Light field microscopy. ACM
Transactions on Graphics, 25(3), 924–934. https://doi.org/10.1145/1141911.1141976
Li, Q., & Uitto, J. (2014). Zebrafish as a Model System to Study Skin Biology and Pathology.
140

Journal of Investigative Dermatology, 134(6), 1–6. https://doi.org/10.1038/jid.2014.182
Liaudanskaya, V., Fiore, N. J., Zhang, Y., Milton, Y., Kelly, M. F., Coe, M., Barreiro, A., Rose, V.
K., Shapiro, M. R., Mullis, A. S., Shevzov-Zebrun, A., Blurton-Jones, M., Whalen, M. J.,
Symes, A. J., Georgakoudi, I., Nieland, T. J. F., & Kaplan, D. L. (2023). Mitochondria
dysregulation contributes to secondary neurodegeneration progression post-contusion
injury in human 3D in vitro triculture brain tissue model. Cell Death & Disease, 14(8),
Article 8. https://doi.org/10.1038/s41419-023-05980-0
Libertus, M. E., Feigenson, L., Halberda, J., & Landau, B. (2014). Understanding the mapping
between numerical approximation and number words: Evidence from Williams syndrome
and typical development. Developmental Science, 17(6), 905–919.
https://doi.org/10.1111/desc.12154
Lin, Q., Manley, J., Helmreich, M., Schlumm, F., Li, J. M., Robson, D. N., Engert, F., Schier, A.,
Nöbauer, T., & Vaziri, A. (2020). Cerebellar Neurodynamics Predict Decision Timing and
Outcome on the Single-Trial Level. Cell, 180(3), 536-551.e17.
https://doi.org/10.1016/j.cell.2019.12.018
Liu, Z., Pouli, D., Alonzo, C. A., Varone, A., Karaliota, S., Quinn, K. P., Münger, K., Karalis, K. P.,
& Georgakoudi, I. (2018). Mapping metabolic changes by noninvasive, multiparametric,
high-resolution imaging using endogenous contrast. Science Advances, 4(3), eaap9302.
https://doi.org/10.1126/sciadv.aap9302
Liublin, W., Rausch, S., Leben, R., Lindquist, R. L., Fiedler, A., Liebeskind, J., Beckers, I. E.,
Hauser, A. E., Hartmann, S., & Niesner, R. A. (2022). NAD(P)H fluorescence lifetime
imaging of live intestinal nematodes reveals metabolic crosstalk between parasite and
host. Scientific Reports, 12(1), Article 1. https://doi.org/10.1038/s41598-022-10705-y
Lorenzi, E., Perrino, M., Messina, A., Zanon, M., & Vallortigara, G. (2023). A Kaspar Hauser
experiment for innateness of numerical cognition (p. 2023.12.06.570352). bioRxiv.
https://doi.org/10.1101/2023.12.06.570352
Lorenzi, E., Perrino, M., Messina, A., Zanon, M., & Vallortigara, G. (2024). Innate responses to
numerousness reveal neural activation in different brain regions in newly-hatched
visually naïve chicks. Heliyon, 10(14). https://doi.org/10.1016/j.heliyon.2024.e34162
Lorenzi, E., Perrino, M., & Vallortigara, G. (2021a). Numerosities and Other Magnitudes in the
Brains: A Comparative View. Frontiers in Psychology, 12.
https://www.frontiersin.org/articles/10.3389/fpsyg.2021.641994
Lorenzi, E., Perrino, M., & Vallortigara, G. (2021b). Numerosities and Other Magnitudes in the
Brains: A Comparative View. Frontiers in Psychology, 12.
https://www.frontiersin.org/articles/10.3389/fpsyg.2021.641994
Lu, R., Sun, W., Liang, Y., Kerlin, A., Bierfeld, J., Seelig, J. D., Wilson, D. E., Scholl, B., Mohar,
B., Tanimoto, M., Koyama, M., Fitzpatrick, D., Orger, M. B., & Ji, N. (2017). Video-rate
volumetric functional imaging of the brain at synaptic resolution. Nature Neuroscience,
20(4), Article 4. https://doi.org/10.1038/nn.4516
Lu, Y., Wei, X., Li, W., Wu, X., Chen, C., Li, G., Huang, Z., Li, Y., Zhang, Y., & Gan, W.-B. (2022).
Large-volume and deep brain imaging in rabbits and monkeys using COMPACT
two-photon microscopy. Scientific Reports, 12(1), Article 1.
141

https://doi.org/10.1038/s41598-022-20842-z
Lubin, A., Otterstrom, J., Hoade, Y., Bjedov, I., Stead, E., Whelan, M., Gestri, G., Paran, Y., &
Payne, E. (2021). A versatile, automated and high-throughput drug screening platform
for zebrafish embryos. Biology Open, 10(9), bio058513.
https://doi.org/10.1242/bio.058513
Lucon-Xiccato, T., Dadda, M., Gatto, E., & Bisazza, A. (2017). Development and testing of a
rapid method for measuring shoal size discrimination. Animal Cognition, 20(2), 149–157.
https://doi.org/10.1007/s10071-016-1050-x
Lucon-Xiccato, T., Gatto, E., Fontana, C. M., & Bisazza, A. (2023). Quantity discrimination in
newly hatched zebrafish suggests hardwired numerical abilities. Communications
Biology, 6(1), 1–8. https://doi.org/10.1038/s42003-023-04595-7
Lucon-Xiccato, T., Miletto Petrazzini, M. E., Agrillo, C., & Bisazza, A. (2015). Guppies
discriminate between two quantities of food items but prioritize item size over total
amount. Animal Behaviour, 107, 183–191. https://doi.org/10.1016/j.anbehav.2015.06.019
Ludwig, K. U., Sämann, P., Alexander, M., Becker, J., Bruder, J., Moll, K., Spieler, D., Czisch,
M., Warnke, A., Docherty, S. J., Davis, O. S. P., Plomin, R., Nöthen, M. M., Landerl, K.,
Müller-Myhsok, B., Hoffmann, P., Schumacher, J., Schulte-Körne, G., & Czamara, D.
(2013). A common variant in myosin-18B contributes to mathematical abilities in children
with dyslexia and intraparietal sulcus variability in adults. Translational Psychiatry, 3(2),
e229. https://doi.org/10.1038/tp.2012.148
Luu, P., Fraser, S. E., & Schneider, F. (2024). More than double the fun with two-photon
excitation microscopy. Communications Biology, 7(1), 364.
https://doi.org/10.1038/s42003-024-06057-0
Lyon, B. E. (2003). Egg recognition and counting reduce costs of avian conspecific brood
parasitism. Nature, 422(6931), 495–499. https://doi.org/10.1038/nature01505
Madaan, S., Keomanee-Dizon, K., Jones, M., Zhong, C., Nadtochiy, A., Luu, P., Fraser, S. E., &
Truong, T. V. (2021). Single-objective selective-volume illumination microscopy enables
high-contrast light-field imaging. Optics Letters, 46(12), 2860–2863.
https://doi.org/10.1364/OL.413849
Magde, D., Elson, E., & Webb, W. W. (1972). Thermodynamic Fluctuations in a Reacting
System—Measurement by Fluorescence Correlation Spectroscopy. Physical Review
Letters, 29(11), 705–708. https://doi.org/10.1103/PhysRevLett.29.705
Magidson, V., & Khodjakov, A. (2013). Chapter 23—Circumventing Photodamage in Live-Cell
Microscopy. In G. Sluder & D. E. Wolf (Eds.), Methods in Cell Biology (Vol. 114, pp.
545–560). Academic Press. https://doi.org/10.1016/B978-0-12-407761-4.00023-3
Mainen, Z. F., Maletic-Savatic, M., Shi, S. H., Hayashi, Y., Malinow, R., & Svoboda, K. (1999).
Two-photon imaging in living brain slices. Methods (San Diego, Calif.), 18(2), 231–239,
181. https://doi.org/10.1006/meth.1999.0776
Maioli, V., Boniface, A., Mahou, P., Ortas, J. F., Abdeladim, L., Beaurepaire, E., & Supatto, W.
(2020). Fast in vivo multiphoton light-sheet microscopy with optimal pulse frequency.
Biomedical Optics Express, 11(10), 6012–6026. https://doi.org/10.1364/BOE.400113
142

Maiti, A., Buffalo, C. Z., Saurabh, S., Montecinos-Franjola, F., Hachey, J. S., Conlon, W. J., Tran,
G. N., Hassan, B., Walters, K. J., Drobizhev, M., Moerner, W. E., Ghosh, P., Matsuo, H.,
Tsien, R. Y., Lin, J. Y., & Rodriguez, E. A. (2023). Structural and photophysical
characterization of the small ultra-red fluorescent protein. Nature Communications,
14(1), Article 1. https://doi.org/10.1038/s41467-023-39776-9
Marshall, A. R., Maniou, E., Moulding, D., Greene, N. D., Copp, A. J., & Galea, G. L. (2022).
Two-photon cell and tissue level laser ablation methods to study morphogenetic
biomechanics. Methods in Molecular Biology (Clifton, N.J.), 2438, 217–230.
https://doi.org/10.1007/978-1-0716-2035-9_14
Maruyama, A., Oshima, Y., Kajiura-Kobayashi, H., Nonaka, S., Imamura, T., & Naruse, K.
(2014). Wide field intravital imaging by two-photon-excitation digital-scanned light-sheet
microscopy (2p-DSLM) with a high-pulse energy laser. Biomedical Optics Express,
5(10), 3311–3325. https://doi.org/10.1364/BOE.5.003311
Matsuzaki, M., & Kasai, H. (2011). Two-photon uncaging microscopy. Cold Spring Harbor
Protocols, 2011(5), pdb.prot5620. https://doi.org/10.1101/pdb.prot5620
Maver, A., Čuturilo, G., Kovanda, A., Miletić, A., & Peterlin, B. (2019). Rare missense TUBGCP5
gene variant in a patient with primary microcephaly. European Journal of Medical
Genetics, 62(12), 103598. https://doi.org/10.1016/j.ejmg.2018.12.003
Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired Acuity of the Approximate
Number System Underlies Mathematical Learning Disability (Dyscalculia). Child
Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x
McCammon, J. M., & Sive, H. (2015). Challenges in understanding psychiatric disorders and
developing therapeutics: A role for zebrafish. Disease Models & Mechanisms, 8(7),
647–656. https://doi.org/10.1242/dmm.019620
McComb, K., Packer, C., & Pusey, A. (1994). Roaring and numerical assessment in contests
between groups of female lions, Panthera leo. Animal Behaviour, 47(2), 379–387.
https://doi.org/10.1006/anbe.1994.1052
McCullough, C. M., Ramirez-Gordillo, D., Hall, M., Futia, G. L., Moran, A. K., Gibson, E. A., &
Restrepo, D. (2022). GRINtrode: A neural implant for simultaneous two-photon imaging
and extracellular electrophysiology in freely moving animals. Neurophotonics, 9(4),
045009. https://doi.org/10.1117/1.NPh.9.4.045009
Medina, L., Abellán, A., & Desfilis, E. (2019). Evolution of Pallial Areas and Networks Involved in
Sociality: Comparison Between Mammals and Sauropsids. Frontiers in Physiology, 10,
894. https://doi.org/10.3389/fphys.2019.00894
Mehlis, M., Thünken, T., Bakker, T. C. M., & Frommen, J. G. (2015). Quantification acuity in
spontaneous shoaling decisions of three-spined sticklebacks. Animal Cognition, 18(5),
1125–1131. https://doi.org/10.1007/s10071-015-0884-y
Meng, G., Liang, Y., Sarsfield, S., Jiang, W., Lu, R., Dudman, J. T., Aponte, Y., & Ji, N. (2019).
High-throughput synapse-resolving two-photon fluorescence microendoscopy for
deep-brain volumetric imaging in vivo. eLife, 8, e40805.
https://doi.org/10.7554/eLife.40805
143

Mercadé-Prieto, R., Rodriguez-Rivera, L., & Chen, X. D. (2017). Fluorescence lifetime of
Rhodamine B in aqueous solutions of polysaccharides and proteins as a function of
viscosity and temperature. Photochemical & Photobiological Sciences, 16(11),
1727–1734. https://doi.org/10.1039/C7PP00330G
Messina, A., Boiti, A., & Vallortigara, G. (2021). Asymmetric distribution of pallial-expressed
genes in zebrafish (Danio rerio). The European Journal of Neuroscience, 53(2),
362–375. https://doi.org/10.1111/ejn.14914
Messina, A., Potrich, D., Perrino, M., Sheardown, E., Miletto Petrazzini, M. E., Luu, P.,
Nadtochiy, A., Truong, T. V., Sovrano, V. A., Fraser, S. E., Brennan, C. H., & Vallortigara,
G. (2022a). Quantity as a Fish Views It: Behavior and Neurobiology. Frontiers in
Neuroanatomy, 16. https://www.frontiersin.org/articles/10.3389/fnana.2022.943504
Messina, A., Potrich, D., Perrino, M., Sheardown, E., Miletto Petrazzini, M. E., Luu, P.,
Nadtochiy, A., Truong, T. V., Sovrano, V. A., Fraser, S. E., Brennan, C. H., & Vallortigara,
G. (2022b). Quantity as a Fish Views It: Behavior and Neurobiology. Frontiers in
Neuroanatomy, 16. https://www.frontiersin.org/articles/10.3389/fnana.2022.943504
Messina, A., Potrich, D., Perrino, M., Sheardown, E., Miletto Petrazzini, M. E., Luu, P.,
Nadtochiy, A., Truong, T. V., Sovrano, V. A., Fraser, S. E., Brennan, C. H., & Vallortigara,
G. (2022c). Quantity as a Fish Views It: Behavior and Neurobiology. Frontiers in
Neuroanatomy, 16. https://www.frontiersin.org/articles/10.3389/fnana.2022.943504
Messina, A., Potrich, D., Schiona, I., Sovrano, V. A., Fraser, S. E., Brennan, C. H., &
Vallortigara, G. (2020). Response to change in the number of visual stimuli in zebrafish:A
behavioural and molecular study. Scientific Reports, 10(1), 5769.
https://doi.org/10.1038/s41598-020-62608-5
Messina, A., Potrich, D., Schiona, I., Sovrano, V. A., Fraser, S. E., Brennan, C. H., &
Vallortigara, G. (2022). Neurons in the Dorso-Central Division of Zebrafish Pallium
Respond to Change in Visual Numerosity. Cerebral Cortex (New York, N.Y.: 1991),
32(2), 418–428. https://doi.org/10.1093/cercor/bhab218
Messina, A., Potrich, D., Schiona, I., Sovrano, V. A., & Vallortigara, G. (2021). The Sense of
Number in Fish, with Particular Reference to Its Neurobiological Bases. Animals: An
Open Access Journal from MDPI, 11(11), 3072. https://doi.org/10.3390/ani11113072
Miletto Petrazzini, M. E., Agrillo, C., Piffer, L., & Bisazza, A. (2014). Ontogeny of the capacity to
compare discrete quantities in fish. Developmental Psychobiology, 56(3), 529–536.
https://doi.org/10.1002/dev.21122
Milinski, M. (1977a). Do all Members of a Swarm Suffer the same Predation?1. Zeitschrift Für
Tierpsychologie, 45(4), 373–388. https://doi.org/10.1111/j.1439-0310.1977.tb02027.x
Milinski, M. (1977b). Experiments on the Selection by Predators against spatial Oddity of their
Prey1. Zeitschrift Für Tierpsychologie, 43(3), 311–325.
https://doi.org/10.1111/j.1439-0310.1977.tb00078.x
Miller, M. J., Wei, S. H., Cahalan, M. D., & Parker, I. (2003). Autonomous T cell trafficking
examined in vivo with intravital two-photon microscopy. Proceedings of the National
Academy of Sciences of the United States of America, 100(5), 2604–2609.
https://doi.org/10.1073/pnas.2628040100
144

Miskolci, V., Tweed, K. E., Lasarev, M. R., Britt, E. C., Walsh, A. J., Zimmerman, L. J.,
McDougal, C. E., Cronan, M. R., Fan, J., Sauer, J.-D., Skala, M. C., & Huttenlocher, A.
(2022). In vivo fluorescence lifetime imaging of macrophage intracellular metabolism
during wound responses in zebrafish. eLife, 11, e66080.
https://doi.org/10.7554/eLife.66080
Mørch, A. M., & Schneider, F. (2023). Investigating Diffusion Dynamics and Interactions with
Scanning Fluorescence Correlation Spectroscopy (sFCS). In C. T. Baldari & M. L. Dustin
(Eds.), The Immune Synapse: Methods and Protocols (pp. 61–89). Springer US.
https://doi.org/10.1007/978-1-0716-3135-5_5
Morgan, M. J., & Godin, J.-G. J. (1985). Antipredator Benefits of Schooling Behaviour in a
Cyprinodontid Fish, the Banded Killifish (Fundulus diaphanus). Zeitschrift Für
Tierpsychologie, 70(3), 236–246. https://doi.org/10.1111/j.1439-0310.1985.tb00515.x
Moyer, R. S., & Landauer, T. K. (1967). Time required for Judgements of Numerical Inequality.
Nature, 215(5109), 1519–1520. https://doi.org/10.1038/2151519a0
Murphy, M. M., Mazzocco, M. M. M., Gerner, G., & Henry, A. E. (2006). Mathematics learning
disability in girls with Turner syndrome or fragile X syndrome. Brain and Cognition, 61(2),
195–210. https://doi.org/10.1016/j.bandc.2005.12.014
Muto, A., Ohkura, M., Abe, G., Nakai, J., & Kawakami, K. (2013). Real-Time Visualization of
Neuronal Activity during Perception. Current Biology, 23(4), 307–311.
https://doi.org/10.1016/j.cub.2012.12.040
Mütze, J., Iyer, V., Macklin, J. J., Colonell, J., Karsh, B., Petrášek, Z., Schwille, P., Looger, L. L.,
Lavis, L. D., & Harris, T. D. (2012). Excitation spectra and brightness optimization of
two-photon excited probes. Biophysical Journal, 102(4), 934–944.
https://doi.org/10.1016/j.bpj.2011.12.056
Nadtochiy, A., Luu, P., Fraser, S. E., & Truong, T. V. (2023). VoDEx: A Python library for time
annotation and management of volumetric functional imaging data. Bioinformatics,
btad568. https://doi.org/10.1093/bioinformatics/btad568
napari LF - napari Plugin—Geneva Schlafly, Amitabh Verma, Rudolf Oldenbourg. (n.d.).
Retrieved July 18, 2023, from https://www.napari-hub.org/plugins/napari-LF
Nieder, A. (2011). Chapter 8—The Neural Code for Number. In S. Dehaene & E. M. Brannon
(Eds.), Space, Time and Number in the Brain (pp. 103–118). Academic Press.
https://doi.org/10.1016/B978-0-12-385948-8.00008-6
Nieder, A. (2016). The neuronal code for number. Nature Reviews. Neuroscience, 17(6),
366–382. https://doi.org/10.1038/nrn.2016.40
Nieder, A. (2021). Neuroethology of number sense across the animal kingdom. The Journal of
Experimental Biology, 224(Pt 6), jeb218289. https://doi.org/10.1242/jeb.218289
Nieder, A., Freedman, D. J., & Miller, E. K. (2002). Representation of the quantity of visual items
in the primate prefrontal cortex. Science (New York, N.Y.), 297(5587), 1708–1711.
https://doi.org/10.1126/science.1072493
Nieder, A., & Merten, K. (2007). A Labeled-Line Code for Small and Large Numerosities in the
145

Monkey Prefrontal Cortex. Journal of Neuroscience, 27(22), 5986–5993.
https://doi.org/10.1523/JNEUROSCI.1056-07.2007
Nieder, A., Wagener, L., & Rinnert, P. (2020). A neural correlate of sensory consciousness in a
corvid bird. Science (New York, N.Y.), 369(6511), 1626–1629.
https://doi.org/10.1126/science.abb1447
Niell, C. M., & Smith, S. J. (2005). Functional imaging reveals rapid development of visual
response properties in the zebrafish tectum. Neuron, 45(6), 941–951.
https://doi.org/10.1016/j.neuron.2005.01.047
Niesner, R., Andresen, V., Neumann, J., Spiecker, H., & Gunzer, M. (2007). The Power of Single
and Multibeam Two-Photon Microscopy for High-Resolution and High-Speed Deep
Tissue and Intravital Imaging. Biophysical Journal, 93(7), 2519–2529.
https://doi.org/10.1529/biophysj.106.102459
Obashi, K., Matsuda, A., Inoue, Y., & Okabe, S. (2019). Precise Temporal Regulation of
Molecular Diffusion within Dendritic Spines by Actin Polymers during Structural Plasticity.
Cell Reports, 27(5), 1503-1515.e8. https://doi.org/10.1016/j.celrep.2019.04.006
O’Hearn, K., Hoffman, J. E., & Landau, B. (2011). Small Subitizing Range in People with
Williams syndrome. Visual Cognition, 19(3), 289–312.
https://doi.org/10.1080/13506285.2010.535994
Oheim, M., Beaurepaire, E., Chaigneau, E., Mertz, J., & Charpak, S. (2001). Two-photon
microscopy in brain tissue: Parameters influencing the imaging depth. Journal of
Neuroscience Methods, 111(1), 29–37. https://doi.org/10.1016/s0165-0270(01)00438-1
Oliinyk, O. S., Baloban, M., Clark, C. L., Carey, E., Pletnev, S., Nimmerjahn, A., & Verkhusha, V.
V. (2022). Single-domain near-infrared protein provides a scaffold for antigen-dependent
fluorescent nanobodies. Nature Methods, 19(6), Article 6.
https://doi.org/10.1038/s41592-022-01467-6
Oliver, B., Harlaar, N., Hayiou Thomas, M. E., Kovas, Y., Walker, S. O., Petrill, S. A., Spinath, F.
M., Dale, P. S., & Plomin, R. (2004). A Twin Study of Teacher-Reported Mathematics
Performance and Low Performance in 7-Year-Olds. Journal of Educational Psychology,
96(3), 504–517. https://doi.org/10.1037/0022-0663.96.3.504
Opfer, J. E., & Martens, M. A. (2012). Learning without representational change: Development
of numerical estimation in individuals with Williams syndrome. Developmental Science,
15(6), 863–875. https://doi.org/10.1111/j.1467-7687.2012.01187.x
Orger, M. B., & de Polavieja, G. G. (2017). Zebrafish Behavior: Opportunities and Challenges.
Annual Review of Neuroscience, 40, 125–147.
https://doi.org/10.1146/annurev-neuro-071714-033857
Oron, D., Papagiakoumou, E., Anselmi, F., & Emiliani, V. (2012). Chapter 7—Two-photon
optogenetics. In T. Knöpfel & E. S. Boyden (Eds.), Progress in Brain Research (Vol. 196,
pp. 119–143). Elsevier. https://doi.org/10.1016/B978-0-444-59426-6.00007-0
Oron, D., Tal, E., & Silberberg, Y. (2005). Scanningless depth-resolved microscopy. Optics
Express, 13(5), 1468–1476. https://doi.org/10.1364/OPEX.13.001468
146

Palero, J., Santos, S. I. C. O., Artigas, D., & Loza-Alvarez, P. (2010). A simple scanless
two-photon fluorescence microscope using selective plane illumination. Optics Express,
18(8), 8491–8498. https://doi.org/10.1364/OE.18.008491
Panier, T., Migault, G., Hubert, A., Trentesaux, H., Beaudou, B., Debrégeas, G., & Bormuth, V.
(2023). A Versatile and Open Source One- and Two-Photon Light-Sheet Microscope
Design (p. 2023.07.10.548107). bioRxiv. https://doi.org/10.1101/2023.07.10.548107
Panula, P., Sallinen, V., Sundvik, M., Kolehmainen, J., Torkko, V., Tiittula, A., Moshnyakov, M., &
Podlasz, P. (2006). Modulatory neurotransmitter systems and behavior: Towards
zebrafish models of neurodegenerative diseases. Zebrafish, 3(2), 235–247.
https://doi.org/10.1089/zeb.2006.3.235
Papagiakoumou, E., Ronzitti, E., & Emiliani, V. (2020). Scanless two-photon excitation with
temporal focusing. Nature Methods, 17(6), Article 6.
https://doi.org/10.1038/s41592-020-0795-y
Paquette, S. T., Dawes, R. P., Sundar, I. K., Rahman, I., Brown, E. B., & White, P. M. (2018).
Chronic cigarette smoke exposure drives spiral ganglion neuron loss in mice. Scientific
Reports, 8(1), Article 1. https://doi.org/10.1038/s41598-018-24166-9
Patterson, G. H., & Piston, D. W. (2000). Photobleaching in Two-Photon Excitation Microscopy.
Biophysical Journal, 78(4), 2159–2162. https://doi.org/10.1016/S0006-3495(00)76762-2
Patting, M., Reisch, P., Sackrow, M., Dowler, R., Koenig, M., & Wahl, M. (2018). Fluorescence
decay data analysis correcting for detector pulse pile-up at very high count rates. Optical
Engineering, 57(3), 031305. https://doi.org/10.1117/1.OE.57.3.031305
Peirce, J., Gray, J. R., Simpson, S., MacAskill, M., Höchenberger, R., Sogo, H., Kastman, E., &
Lindeløv, J. K. (2019). PsychoPy2: Experiments in behavior made easy. Behavior
Research Methods, 51(1), 195–203. https://doi.org/10.3758/s13428-018-01193-y
Petrásek, Z., Hoege, C., Mashaghi, A., Ohrt, T., Hyman, A. A., & Schwille, P. (2008).
Characterization of protein dynamics in asymmetric cell division by scanning
fluorescence correlation spectroscopy. Biophysical Journal, 95(11), 5476–5486.
https://doi.org/10.1529/biophysj.108.135152
Petrášek, Z., & Schwille, P. (2008). Photobleaching in Two-Photon Scanning Fluorescence
Correlation Spectroscopy. ChemPhysChem, 9(1), 147–158.
https://doi.org/10.1002/cphc.200700579
Petrazzini, M. E. M., Lucon-Xiccato, T., Agrillo, C., & Bisazza, A. (2015). Use of ordinal
information by fish. Scientific Reports, 5, 15497. https://doi.org/10.1038/srep15497
Pfeifer, J. H., Allen, N. B., Byrne, M. L., & Mills, K. L. (2018). Modeling Developmental Change:
Contemporary Approaches to Key Methodological Challenges in Developmental
Neuroimaging. Developmental Cognitive Neuroscience, 33, 1–4.
https://doi.org/10.1016/j.dcn.2018.10.001
Pham, D. L., Miller, C. R., Myers, M. S., Myers, D. M., Hansen, L. A., & Nichols, M. G. (2021).
Development and characterization of phasor-based analysis for FLIM to evaluate the
metabolic and epigenetic impact of HER2 inhibition on squamous cell carcinoma
cultures. Journal of Biomedical Optics, 26(10), 106501.
147

https://doi.org/10.1117/1.JBO.26.10.106501
Piazza, M. (2010a). Neurocognitive start-up tools for symbolic number representations. Trends
in Cognitive Sciences, 14(12), 542–551. https://doi.org/10.1016/j.tics.2010.09.008
Piazza, M. (2010b). Neurocognitive start-up tools for symbolic number representations. Trends
in Cognitive Sciences, 14(12), 542–551. https://doi.org/10.1016/j.tics.2010.09.008
Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for
approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555.
https://doi.org/10.1016/j.neuron.2004.10.014
Podgorski, K., & Ranganathan, G. (2016). Brain heating induced by near-infrared lasers during
multiphoton microscopy. Journal of Neurophysiology, 116(3), 1012–1023.
https://doi.org/10.1152/jn.00275.2016
Potrich, D., Rugani, R., Sovrano, V. A., Regolin, L., & Vallortigara, G. (2019). Use of numerical
and spatial information in ordinal counting by zebrafish. Scientific Reports, 9(1), 18323.
https://doi.org/10.1038/s41598-019-54740-8
Potrich, D., Sovrano, V. A., Stancher, G., & Vallortigara, G. (2015). Quantity discrimination by
zebrafish (Danio rerio). Journal of Comparative Psychology (Washington, D.C.: 1983),
129(4), 388–393. https://doi.org/10.1037/com0000012
Potrich, D., Zanon, M., & Vallortigara, G. (2022). Archerfish number discrimination. eLife, 11,
e74057. https://doi.org/10.7554/eLife.74057
Preuss, S. J., Trivedi, C. A., vom Berg-Maurer, C. M., Ryu, S., & Bollmann, J. H. (2014).
Classification of Object Size in Retinotectal Microcircuits. Current Biology, 24(20),
2376–2385. https://doi.org/10.1016/j.cub.2014.09.012
Prevedel, R., Yoon, Y.-G., Hoffmann, M., Pak, N., Wetzstein, G., Kato, S., Schrödel, T., Raskar,
R., Zimmer, M., Boyden, E. S., & Vaziri, A. (2014a). Simultaneous whole-animal 3D
imaging of neuronal activity using light-field microscopy. Nature Methods, 11(7),
727–730. https://doi.org/10.1038/nmeth.2964
Prevedel, R., Yoon, Y.-G., Hoffmann, M., Pak, N., Wetzstein, G., Kato, S., Schrödel, T., Raskar,
R., Zimmer, M., Boyden, E. S., & Vaziri, A. (2014b). Simultaneous whole-animal 3D
imaging of neuronal activity using light-field microscopy. Nature Methods, 11(7), Article 7.
https://doi.org/10.1038/nmeth.2964
Pritchard, V. L., Lawrence, J., Butlin, R. K., & Krause, J. (2001). Shoal choice in zebrafish,
Danio rerio: The influence of shoal size and activity. Animal Behaviour, 62(6),
1085–1088. https://doi.org/10.1006/anbe.2001.1858
Qin, Z., Chen, C., He, S., Wang, Y., Tam, K. F., Ip, N. Y., & Qu, J. Y. (2020). Adaptive optics
two-photon endomicroscopy enables deep-brain imaging at synaptic resolution over
large volumes. Science Advances, 6(40), eabc6521.
https://doi.org/10.1126/sciadv.abc6521
Qin, Z., He, S., Yang, C., Yung, J. S.-Y., Chen, C., Leung, C. K.-S., Liu, K., & Qu, J. Y. (2020).
Adaptive optics two-photon microscopy enables near-diffraction-limited and functional
retinal imaging in vivo. Light: Science & Applications, 9(1), Article 1.
148

https://doi.org/10.1038/s41377-020-0317-9
Queiroz, H., & Magurran, A. E. (2005). Safety in numbers? Shoaling behaviour of the
Amazonian red-bellied piranha. Biology Letters, 1(2), 155–157.
https://doi.org/10.1098/rsbl.2004.0267
Rakhymzhan, A., Acs, A., Hauser, A. E., Winkler, T. H., & Niesner, R. A. (2021). Improvement of
the Similarity Spectral Unmixing Approach for Multiplexed Two-Photon Imaging by Linear
Dimension Reduction of the Mixing Matrix. International Journal of Molecular Sciences,
22(11), 6046. https://doi.org/10.3390/ijms22116046
Ramos, T. N., Franco, L. R., Silva, D. L., & Canuto, S. (2023). Calculation of the one- and
two-photon absorption spectra of water-soluble stilbene derivatives using a multiscale
QM/MM approach. The Journal of Chemical Physics, 159(2), 024309.
https://doi.org/10.1063/5.0152308
Ranjit, S., Datta, R., Dvornikov, A., & Gratton, E. (2019). Multicomponent Analysis of Phasor
Plot in a Single Pixel to Calculate Changes of Metabolic Trajectory in Biological
Systems. The Journal of Physical Chemistry A, 123(45), 9865–9873.
https://doi.org/10.1021/acs.jpca.9b07880
Ranjit, S., Malacrida, L., Jameson, D. M., & Gratton, E. (2018). Fit-free analysis of fluorescence
lifetime imaging data using the phasor approach. Nature Protocols, 13(9), 1979–2004.
https://doi.org/10.1038/s41596-018-0026-5
Renninger, S. L., & Orger, M. B. (2013). Two-photon imaging of neural population activity in
zebrafish. Methods, 62(3), 255–267. https://doi.org/10.1016/j.ymeth.2013.05.016
Reynaud, E. G., Kržič, U., Greger, K., & Stelzer, E. H. K. (2008). Light sheet‐based
fluorescence microscopy: More dimensions, more photons, and less photodamage.
HFSP Journal, 2(5), 266–275. https://doi.org/10.2976/1.2974980
Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading
achievement to adult socioeconomic status. Psychological Science, 24(7), 1301–1308.
https://doi.org/10.1177/0956797612466268
Rocha-Mendoza, I., Licea-Rodriguez, J., Marro, M., Olarte, O. E., Plata-Sanchez, M., &
Loza-Alvarez, P. (2015). Rapid spontaneous Raman light sheet microscopy using
cw-lasers and tunable filters. Biomedical Optics Express, 6(9), 3449–3461.
https://doi.org/10.1364/BOE.6.003449
Rodríguez, F., López, J. C., Vargas, J. P., Gómez, Y., Broglio, C., & Salas, C. (2002).
Conservation of Spatial Memory Function in the Pallial Forebrain of Reptiles and
Ray-Finned Fishes. The Journal of Neuroscience, 22(7), 2894–2903.
https://doi.org/10.1523/JNEUROSCI.22-07-02894.2002
Rodríguez, F., Quintero, B., Amores, L., Madrid, D., Salas-Peña, C., & Salas, C. (2021). Spatial
Cognition in Teleost Fish: Strategies and Mechanisms. Animals: An Open Access
Journal from MDPI, 11(8), 2271. https://doi.org/10.3390/ani11082271
Roffay, C., García-Arcos, J. M., Chapuis, P., López-Andarias, J., Schneider, F., Colom, A.,
Tomba, C., Meglio, I. D., Dunsing, V., Matile, S., Roux, A., & Mercier, V. (2023). Technical
insights into fluorescence lifetime microscopy of mechanosensitive Flipper probes (p.
149

2022.09.28.509885). bioRxiv. https://doi.org/10.1101/2022.09.28.509885
Rooke, R., Rasool, A., Schneider, J., & Levine, J. D. (2020). Drosophila melanogaster behaviour
changes in different social environments based on group size and density.
Communications Biology, 3(1), 304. https://doi.org/10.1038/s42003-020-1024-z
Rousselle, L., Dembour, G., & Noël, M.-P. (2013). Magnitude representations in Williams
syndrome: Differential acuity in time, space and number processing. PloS One, 8(8),
e72621. https://doi.org/10.1371/journal.pone.0072621
Ruan, Q., Cheng, M. A., Levi, M., Gratton, E., & Mantulin, W. W. (2004). Spatial-temporal
studies of membrane dynamics: Scanning fluorescence correlation spectroscopy
(SFCS). Biophysical Journal, 87(2), 1260–1267.
https://doi.org/10.1529/biophysj.103.036483
Sánchez-Hernández, A., Polleys, C. M., & Georgakoudi, I. (2023). Formalin fixation and paraffin
embedding interfere with the preservation of optical metabolic assessments based on
endogenous NAD(P)H and FAD two-photon excited fluorescence. Biomedical Optics
Express, 14(10), 5238–5253. https://doi.org/10.1364/BOE.498297
Sánchez-Ramírez, E., Ung, T. P. L., Alarcón del Carmen, A., del Toro-Ríos, X., Fajardo-Orduña,
G. R., Noriega, L. G., Cortés-Morales, V. A., Tovar, A. R., Montesinos, J. J.,
Orozco-Solís, R., Stringari, C., & Aguilar-Arnal, L. (2022). Coordinated metabolic
transitions and gene expression by NAD+ during adipogenesis. Journal of Cell Biology,
221(12), e202111137. https://doi.org/10.1083/jcb.202111137
Sankaran, J., & Wohland, T. (2023). Current capabilities and future perspectives of FCS:
Super-resolution microscopy, machine learning, and in vivo applications.
Communications Biology, 6(1), Article 1. https://doi.org/10.1038/s42003-023-05069-6
Santacà, M., Agrillo, C., Miletto Petrazzini, M. E., & Bisazza, A. (2020). The ontogeny of
continuous quantity discrimination in zebrafish larvae (Danio rerio). Animal Cognition,
23(4), 731–739. https://doi.org/10.1007/s10071-020-01384-1
Santacà, M., Dadda, M., Miletto Petrazzini, M. E., & Bisazza, A. (2021). Stimulus characteristics,
learning bias and visual discrimination in zebrafish (Danio rerio). Behavioural Processes,
192, 104499. https://doi.org/10.1016/j.beproc.2021.104499
Sartori, B. M., Júnior, R. E. M., Paiva, I. M., Moraes, I. B., Murgas, L. D. S., & Brunialti Godard,
A. L. (2022). Acute Ethanol Exposure Leads to Long-Term Effects on Memory, Behavior,
and Transcriptional Regulation in the Zebrafish Brain (SSRN Scholarly Paper 4265391).
https://doi.org/10.2139/ssrn.4265391
Sasaki, A. (2022). Recent advances in the standardization of fluorescence microscopy for
quantitative image analysis. Biophysical Reviews, 14(1), 33–39.
https://doi.org/10.1007/s12551-021-00871-0
Schmidt, E., & Oheim, M. (2020). Infrared Excitation Induces Heating and Calcium Microdomain
Hyperactivity in Cortical Astrocytes. Biophysical Journal, 119(11), 2153–2165.
https://doi.org/10.1016/j.bpj.2020.10.027
Schwille, P., Haupts, U., Maiti, S., & Webb, W. W. (1999). Molecular dynamics in living cells
observed by fluorescence correlation spectroscopy with one- and two-photon excitation.
150

Biophysical Journal, 77(4), 2251–2265.
Scipioni, L., Rossetta, A., Tedeschi, G., & Gratton, E. (2021). Phasor S-FLIM: A new paradigm
for fast and robust spectral fluorescence lifetime imaging. Nature Methods, 18(5), Article
5. https://doi.org/10.1038/s41592-021-01108-4
Seguin, D., & Gerlai, R. (2017). Zebrafish prefer larger to smaller shoals: Analysis of quantity
estimation in a genetically tractable model organism. Animal Cognition, 20(5), 813–821.
https://doi.org/10.1007/s10071-017-1102-x
Semmelhack, J. L., Donovan, J. C., Thiele, T. R., Kuehn, E., Laurell, E., & Baier, H. (2014). A
dedicated visual pathway for prey detection in larval zebrafish. eLife, 3, e04878.
https://doi.org/10.7554/eLife.04878
Shafirovich, V., Dourandin, A., Luneva, N. P., Singh, C., Kirigin, F., & Geacintov, N. E. (1999).
Multiphoton near-infrared femtosecond laser pulse-induced DNA damage with and
without the photosensitizer proflavine. Photochemistry and Photobiology, 69(3),
265–274. https://doi.org/10.1562/0031-8655(1999)069<0265:mniflp>2.3.co;2
Shalev, R. S. (2004). Developmental dyscalculia. Journal of Child Neurology, 19(10), 765–771.
https://doi.org/10.1177/08830738040190100601
Shalev, R. S. (2007). Prevalence of developmental dyscalculia. In Why is math so hard for some
children? The nature and origins of mathematical learning difficulties and disabilities (pp.
49–60). Paul H. Brookes Publishing Co.
Shalev, R. S., Auerbach, J., & Gross-Tsur, V. (1995). Developmental dyscalculia behavioral and
attentional aspects: A research note. Journal of Child Psychology and Psychiatry, and
Allied Disciplines, 36(7), 1261–1268. https://doi.org/10.1111/j.1469-7610.1995.tb01369.x
Shalev, R. S., Manor, O., Kerem, B., Ayali, M., Badichi, N., Friedlander, Y., & Gross-Tsur, V.
(2001). Developmental dyscalculia is a familial learning disability. Journal of Learning
Disabilities, 34(1), 59–65. https://doi.org/10.1177/002221940103400105
Sheardown, E., Torres-Perez, J. V., Anagianni, S., Fraser, S. E., Vallortigara, G., Butterworth, B.,
Miletto-Petrazzini, M. E., & Brennan, C. H. (2022a). Characterizing ontogeny of quantity
discrimination in zebrafish. Proceedings of the Royal Society B: Biological Sciences,
289(1968), 20212544. https://doi.org/10.1098/rspb.2021.2544
Sheardown, E., Torres-Perez, J. V., Anagianni, S., Fraser, S. E., Vallortigara, G., Butterworth, B.,
Miletto-Petrazzini, M. E., & Brennan, C. H. (2022b). Characterizing ontogeny of quantity
discrimination in zebrafish. Proceedings of the Royal Society B: Biological Sciences,
289(1968), 20212544. https://doi.org/10.1098/rspb.2021.2544
Shi, X., Shin Teo, L., Pan, X., Chong, S.-W., Kraut, R., Korzh, V., & Wohland, T. (2009). Probing
events with single molecule sensitivity in zebrafish and Drosophila embryos by
fluorescence correlation spectroscopy. Developmental Dynamics, 238(12), 3156–3167.
https://doi.org/10.1002/dvdy.22140
Silva, A. J. (2017). Miniaturized two-photon microscope: Seeing clearer and deeper into the
brain. Light: Science & Applications, 6(8), Article 8. https://doi.org/10.1038/lsa.2017.104
Song, J., Kang, J., Kang, U., Nam, H. S., Kim, H. J., Kim, R. H., Kim, J. W., & Yoo, H. (2023).
151

SNR enhanced high-speed two-photon microscopy using a pulse picker and time gating
detection. Scientific Reports, 13, 14244. https://doi.org/10.1038/s41598-023-41270-7
Stancher, G., Rugani, R., Regolin, L., & Vallortigara, G. (2015). Numerical discrimination by
frogs (Bombina orientalis). Animal Cognition, 18(1), 219–229.
https://doi.org/10.1007/s10071-014-0791-7
Stancher, G., Sovrano, V. A., Potrich, D., & Vallortigara, G. (2013). Discrimination of small
quantities by fish (redtail splitfin, Xenotoca eiseni). Animal Cognition, 16(2), 307–312.
https://doi.org/10.1007/s10071-012-0590-y
Stednitz, S. J., McDermott, E. M., Ncube, D., Tallafuss, A., Eisen, J. S., & Washbourne, P.
(2018). Forebrain Control of Behaviorally Driven Social Orienting in Zebrafish. Current
Biology: CB, 28(15), 2445-2451.e3. https://doi.org/10.1016/j.cub.2018.06.016
Stefansson, H., Meyer-Lindenberg, A., Steinberg, S., Magnusdottir, B., Morgen, K., Arnarsdottir,
S., Bjornsdottir, G., Walters, G. B., Jonsdottir, G. A., Doyle, O. M., Tost, H., Grimm, O.,
Kristjansdottir, S., Snorrason, H., Davidsdottir, S. R., Gudmundsson, L. J., Jonsson, G.
F., Stefansdottir, B., Helgadottir, I., … Stefansson, K. (2014). CNVs conferring risk of
autism or schizophrenia affect cognition in controls. Nature, 505(7483), 361–366.
https://doi.org/10.1038/nature12818
Stelzer, E. H. K., Strobl, F., Chang, B.-J., Preusser, F., Preibisch, S., McDole, K., & Fiolka, R.
(2021). Light sheet fluorescence microscopy. Nature Reviews Methods Primers, 1(1),
Article 1. https://doi.org/10.1038/s43586-021-00069-4
Stennett, E. M. S., Ciuba, M. A., & Levitus, M. (2014). Photophysical processes in single
molecule organic fluorescent probes. Chemical Society Reviews, 43(4), 1057–1075.
https://doi.org/10.1039/c3cs60211g
Stewart, A. M., & Kalueff, A. V. (2012). The developing utility of zebrafish models for cognitive
enhancers research. Current Neuropharmacology, 10(3), 263–271.
https://doi.org/10.2174/157015912803217323
Stosiek, C., Garaschuk, O., Holthoff, K., & Konnerth, A. (2003). In vivo two-photon calcium
imaging of neuronal networks. Proceedings of the National Academy of Sciences,
100(12), 7319–7324. https://doi.org/10.1073/pnas.1232232100
Stringari, C., Cinquin, A., Cinquin, O., Digman, M. A., Donovan, P. J., & Gratton, E. (2011).
Phasor approach to fluorescence lifetime microscopy distinguishes different metabolic
states of germ cells in a live tissue. Proceedings of the National Academy of Sciences,
108(33), 13582–13587. https://doi.org/10.1073/pnas.1108161108
Stringari, C., Edwards, R. A., Pate, K. T., Waterman, M. L., Donovan, P. J., & Gratton, E. (2012).
Metabolic trajectory of cellular differentiation in small intestine by Phasor Fluorescence
Lifetime Microscopy of NADH. Scientific Reports, 2(1), Article 1.
https://doi.org/10.1038/srep00568
Stringari, C., Nourse, J. L., Flanagan, L. A., & Gratton, E. (2012). Phasor Fluorescence Lifetime
Microscopy of Free and Protein-Bound NADH Reveals Neural Stem Cell Differentiation
Potential. PLOS ONE, 7(11), e48014. https://doi.org/10.1371/journal.pone.0048014
Suanda, S. H., Tompson, W., & Brannon, E. M. (2008). Changes in the Ability to Detect Ordinal
152

Numerical Relationships Between 9 and 11 Months of Age. Infancy: The Official Journal
of the International Society on Infant Studies, 13(4), 308–337.
https://doi.org/10.1080/15250000802188800
Sullivan, K., Hatton, D., Hammer, J., Sideris, J., Hooper, S., Ornstein, P., & Bailey, D. (2006).
ADHD symptoms in children with FXS. American Journal of Medical Genetics. Part A,
140(21), 2275–2288. https://doi.org/10.1002/ajmg.a.31388
Sullivan, M. R., Nimmerjahn, A., Sarkisov, D. V., Helmchen, F., & Wang, S. S.-H. (2005). In Vivo
Calcium Imaging of Circuit Activity in Cerebellar Cortex. Journal of Neurophysiology,
94(2), 1636–1644. https://doi.org/10.1152/jn.01013.2004
Sun, Y., Day, R. N., & Periasamy, A. (2011). Investigating protein-protein interactions in living
cells using fluorescence lifetime imaging microscopy. Nature Protocols, 6(9), Article 9.
https://doi.org/10.1038/nprot.2011.364
Szkudlarek, E., & Brannon, E. M. (2017). Does the approximate number system serve as a
foundation for symbolic mathematics? Language Learning and Development : The
Official Journal of the Society for Language Development, 13(2), 171–190.
https://doi.org/10.1080/15475441.2016.1263573
Tallafuss, A., Stednitz, S. J., Voeun, M., Levichev, A., Larsch, J., Eisen, J., & Washbourne, P.
(2022). Egr1 Is Necessary for Forebrain Dopaminergic Signaling during Social Behavior.
eNeuro, 9(2), ENEURO.0035-22.2022. https://doi.org/10.1523/ENEURO.0035-22.2022
Talone, B., Bazzarelli, M., Schirato, A., Dello Vicario, F., Viola, D., Jacchetti, E., Bregonzio, M.,
Raimondi, M. T., Cerullo, G., & Polli, D. (2021). Phototoxicity induced in living HeLa cells
by focused femtosecond laser pulses: A data-driven approach. Biomedical Optics
Express, 12(12), 7886–7905. https://doi.org/10.1364/BOE.441225
Tassabehji, M. (2003). Williams-Beuren syndrome: A challenge for genotype-phenotype
correlations. Human Molecular Genetics, 12 Spec No 2, R229-237.
https://doi.org/10.1093/hmg/ddg299
Tassone, F., Hagerman, P. J., & Hagerman, R. J. (2014). Fragile x premutation. Journal of
Neurodevelopmental Disorders, 6(1), 22. https://doi.org/10.1186/1866-1955-6-22
Temizer, I., Donovan, J. C., Baier, H., & Semmelhack, J. L. (2015a). A Visual Pathway for
Looming-Evoked Escape in Larval Zebrafish. Current Biology, 25(14), 1823–1834.
https://doi.org/10.1016/j.cub.2015.06.002
Temizer, I., Donovan, J. C., Baier, H., & Semmelhack, J. L. (2015b). A Visual Pathway for
Looming-Evoked Escape in Larval Zebrafish. Current Biology: CB, 25(14), 1823–1834.
https://doi.org/10.1016/j.cub.2015.06.002
Temizer, I., Donovan, J. C., Baier, H., & Semmelhack, J. L. (2015c). A Visual Pathway for
Looming-Evoked Escape in Larval Zebrafish. Current Biology, 25(14), 1823–1834.
https://doi.org/10.1016/j.cub.2015.06.002
Templeton, C. N., & Greene, E. (2007). Nuthatches eavesdrop on variations in heterospecific
chickadee mobbing alarm calls. Proceedings of the National Academy of Sciences of the
United States of America, 104(13), 5479–5482.
https://doi.org/10.1073/pnas.0605183104
153

Trinh, L. A., & Fraser, S. E. (2013). Enhancer and gene traps for molecular imaging and genetic
analysis in zebrafish. Development, Growth & Differentiation, 55(4), 434–445.
https://doi.org/10.1111/dgd.12055
Truong, T. V., Holland, D. B., Madaan, S., Andreev, A., Keomanee-Dizon, K., Troll, J. V., Koo, D.
E. S., McFall-Ngai, M. J., & Fraser, S. E. (2020). High-contrast, synchronous volumetric
imaging with selective volume illumination microscopy. Communications Biology, 3(1),
74. https://doi.org/10.1038/s42003-020-0787-6
Truong, T. V., Supatto, W., Koos, D. S., Choi, J. M., & Fraser, S. E. (2011a). Deep and fast live
imaging with two-photon scanned light-sheet microscopy. Nature Methods, 8(9), Article
9. https://doi.org/10.1038/nmeth.1652
Truong, T. V., Supatto, W., Koos, D. S., Choi, J. M., & Fraser, S. E. (2011b). Deep and fast live
imaging with two-photon scanned light-sheet microscopy. Nature Methods, 8(9), Article
9. https://doi.org/10.1038/nmeth.1652
Tzambazis, K., & Stough, C. (2000). Alcohol impairs speed of information processing and
simple and choice reaction time and differentially impairs higher-order cognitive abilities.
Alcohol and Alcoholism (Oxford, Oxfordshire), 35(2), 197–201.
https://doi.org/10.1093/alcalc/35.2.197
Ulfarsson, M. O., Walters, G. B., Gustafsson, O., Steinberg, S., Silva, A., Doyle, O. M.,
Brammer, M., Gudbjartsson, D. F., Arnarsdottir, S., Jonsdottir, G. A., Gisladottir, R. S.,
Bjornsdottir, G., Helgason, H., Ellingsen, L. M., Halldorsson, J. G., Saemundsen, E.,
Stefansdottir, B., Jonsson, L., Eiriksdottir, V. K., … Stefansson, K. (2017). 15q11.2 CNV
affects cognitive, structural and functional correlates of dyslexia and dyscalculia.
Translational Psychiatry, 7(4), e1109. https://doi.org/10.1038/tp.2017.77
Urbančič, I., Lagerholm, B. C., & Schneider, F. (2021). Fluorescence correlation spectroscopy. In
Imaging Modalities for Biological and Preclinical Research: A Compendium, Volume 1:
Part I: Ex vivo biological imaging. IOP Publishing.
https://doi.org/10.1088/978-0-7503-3059-6ch33
Valente, A., Huang, K.-H., Portugues, R., & Engert, F. (2012). Ontogeny of classical and operant
learning behaviors in zebrafish. Learning & Memory (Cold Spring Harbor, N.Y.), 19(4),
170–177. https://doi.org/10.1101/lm.025668.112
Valeur, B., & Berberan‐Santos, M. N. (2012). Molecular Fluorescence (1st ed.). John Wiley &
Sons, Ltd. https://doi.org/10.1002/9783527650002
Vallortigara, G. (2017). Comparative cognition of number and space: The case of geometry and
of the mental number line. Philosophical Transactions of the Royal Society of London.
Series B, Biological Sciences, 373(1740), 20170120.
https://doi.org/10.1098/rstb.2017.0120
Vallortigara, G., Lorenzi, E., Messina, A., & Perrino, M. (2022). Magnitudes for Nervous
Systems: Theoretical Issues and Experimental Evidence. Current Directions in
Psychological Science, 31(5), 405–410. https://doi.org/10.1177/09637214221102146
Viswanathan, P., & Nieder, A. (2013). Neuronal correlates of a visual “sense of number” in
primate parietal and prefrontal cortices. Proceedings of the National Academy of
Sciences, 110(27), 11187–11192. https://doi.org/10.1073/pnas.1308141110
154

Viswanathan, P., & Nieder, A. (2020). Spatial Neuronal Integration Supports a Global
Representation of Visual Numerosity in Primate Association Cortices. Journal of
Cognitive Neuroscience, 32(6), 1184–1197. https://doi.org/10.1162/jocn_a_01548
Vito, G. de, Ricci, P., Turrini, L., Gavryusev, V., Müllenbroich, C., Tiso, N., Vanzi, F., Silvestri, L.,
& Pavone, F. S. (2020a). Effects of excitation light polarization on fluorescence emission
in two-photon light-sheet microscopy. Biomedical Optics Express, 11(8), 4651.
https://doi.org/10.1364/BOE.396388
Vito, G. de, Ricci, P., Turrini, L., Gavryusev, V., Müllenbroich, C., Tiso, N., Vanzi, F., Silvestri, L.,
& Pavone, F. S. (2020b). Effects of excitation light polarization on fluorescence emission
in two-photon light-sheet microscopy. Biomedical Optics Express, 11(8), 4651–4665.
https://doi.org/10.1364/BOE.396388
Vito, G. de, Vito, G. de, Vito, G. de, Turrini, L., Turrini, L., Turrini, L., Müllenbroich, C.,
Müllenbroich, C., Müllenbroich, C., Ricci, P., Sancataldo, G., Sancataldo, G.,
Mazzamuto, G., Mazzamuto, G., Tiso, N., Sacconi, L., Sacconi, L., Fanelli, D., Silvestri,
L., … Pavone, F. S. (2022). Fast whole-brain imaging of seizures in zebrafish larvae by
two-photon light-sheet microscopy. Biomedical Optics Express, 13(3), 1516–1536.
https://doi.org/10.1364/BOE.434146
Vossen, L. E., Brunberg, R., Rådén, P., Winberg, S., & Roman, E. (2022). Sex-Specific Effects
of Acute Ethanol Exposure on Locomotory Activity and Exploratory Behavior in Adult
Zebrafish (Danio rerio). Frontiers in Pharmacology, 13.
https://doi.org/10.3389/fphar.2022.853936
Wagle, M., Zarei, M., Lovett-Barron, M., Poston, K. T., Xu, J., Ramey, V., Pollard, K. S., Prober,
D. A., Schulkin, J., Deisseroth, K., & Guo, S. (2022). Brain-wide perception of the
emotional valence of light is regulated by distinct hypothalamic neurons. Molecular
Psychiatry, 27(9), 3777–3793. https://doi.org/10.1038/s41380-022-01567-x
Walker, C., & Streisinger, G. (1983). Induction of Mutations by gamma-Rays in Pregonial Germ
Cells of Zebrafish Embryos. Genetics, 103(1), 125–136.
https://doi.org/10.1093/genetics/103.1.125
Wang, P., Hecht, F., Ossato, G., Tille, S., Fraser, S. E., & Junge, J. A. (2021). Complex wavelet
filter improves FLIM phasors for photon starved imaging experiments. Biomedical Optics
Express, 12(6), 3463–3473. https://doi.org/10.1364/BOE.420953
Wang, P., Xia, Y.-L., Zou, L.-W., Qian, X.-K., Dou, T.-Y., Jin, Q., Li, S.-Y., Yu, Y., Wang, D.-D.,
Luo, Q., Ge, G.-B., & Yang, L. (2017). An Optimized Two-Photon Fluorescent Probe for
Biological Sensing and Imaging of Catechol-O-Methyltransferase. Chemistry – A
European Journal, 23(45), 10800–10807. https://doi.org/10.1002/chem.201701384
Wang, X., Liisberg, M. B., Nolt, G. L., Fu, X., Cerretani, C., Li, L., Johnson, L. A., Vosch, T., &
Richards, C. I. (2023). DNA-AgNC Loaded Liposomes for Measuring Cerebral Blood
Flow Using Two-Photon Fluorescence Correlation Spectroscopy. ACS Nano, 17(13),
12862–12874. https://doi.org/10.1021/acsnano.3c04489
Wang, Z., Gurlo, T., Matveyenko, A. V., Elashoff, D., Wang, P., Rosenberger, M., Junge, J. A.,
Stevens, R. C., White, K. L., Fraser, S. E., & Butler, P. C. (2021). Live-cell imaging of
glucose-induced metabolic coupling of β and α cell metabolism in health and type 2
diabetes. Communications Biology, 4, 594. https://doi.org/10.1038/s42003-021-02113-1
155

Waskom, M. L. (2021). seaborn: Statistical data visualization. Journal of Open Source Software,
6(60), 3021. https://doi.org/10.21105/joss.03021
Weber, T., & Köster, R. (2013). Genetic tools for multicolor imaging in zebrafish larvae. Methods
(San Diego, Calif.), 62(3), 279–291. https://doi.org/10.1016/j.ymeth.2013.07.028
Weisenburger, S., & Vaziri, A. (2018). A Guide to Emerging Technologies for Large-Scale and
Whole-Brain Optical Imaging of Neuronal Activity. Annual Review of Neuroscience, 41,
431–452. https://doi.org/10.1146/annurev-neuro-072116-031458
Wilson, M. L., Britton, N. F., & Franks, N. R. (2002). Chimpanzees and the mathematics of
battle. Proceedings. Biological Sciences, 269(1496), 1107–1112.
https://doi.org/10.1098/rspb.2001.1926
Wokosin, D. L., Centonze, V. E., Crittenden, S., & White, J. (1996). Three-photon excitation
fluorescence imaging of biological specimens using an all-solid-state laser. Bioimaging,
4(3), 208–214.
https://doi.org/10.1002/1361-6374(199609)4:3<208::AID-BIO11>3.0.CO;2-J
Wolf, S., Dubreuil, A. M., Bertoni, T., Böhm, U. L., Bormuth, V., Candelier, R., Karpenko, S.,
Hildebrand, D. G. C., Bianco, I. H., Monasson, R., & Debrégeas, G. (2017).
Sensorimotor computation underlying phototaxis in zebrafish. Nature Communications,
8(1), 651. https://doi.org/10.1038/s41467-017-00310-3
Wolf, S., Supatto, W., Debrégeas, G., Mahou, P., Kruglik, S. G., Sintes, J.-M., Beaurepaire, E., &
Candelier, R. (2015a). Whole-brain functional imaging with two-photon light-sheet
microscopy. Nature Methods, 12(5), 379–380. https://doi.org/10.1038/nmeth.3371
Wolf, S., Supatto, W., Debrégeas, G., Mahou, P., Kruglik, S. G., Sintes, J.-M., Beaurepaire, E., &
Candelier, R. (2015b). Whole-brain functional imaging with two-photon light-sheet
microscopy. Nature Methods, 12(5), 379–380. https://doi.org/10.1038/nmeth.3371
Wolf, S., Supatto, W., Debrégeas, G., Mahou, P., Kruglik, S. G., Sintes, J.-M., Beaurepaire, E., &
Candelier, R. (2015c). Whole-brain functional imaging with two-photon light-sheet
microscopy. Nature Methods, 12(5), 379–380. https://doi.org/10.1038/nmeth.3371
Wolman, M. A., Jain, R. A., Liss, L., & Granato, M. (2011). Chemical modulation of memory
formation in larval zebrafish. Proceedings of the National Academy of Sciences of the
United States of America, 108(37), 15468–15473.
https://doi.org/10.1073/pnas.1107156108
Wright, B. K., Andrews, L. M., Jones, M. R., Stringari, C., Digman, M. A., & Gratton, E. (2012).
Phasor-FLIM analysis of NADH distribution and localization in the nucleus of live
progenitor myoblast cells. Microscopy Research and Technique, 75(12), 1717–1722.
https://doi.org/10.1002/jemt.22121
Wu, J., Corbett, A. H., & Berland, K. M. (2009). The Intracellular Mobility of Nuclear Import
Receptors and NLS Cargoes. Biophysical Journal, 96(9), 3840–3849.
https://doi.org/10.1016/j.bpj.2009.01.050
Wu, J., Liang, Y., Chen, S., Hsu, C.-L., Chavarha, M., Evans, S. W., Shi, D., Lin, M. Z., Tsia, K.
K., & Ji, N. (2020). Kilohertz two-photon fluorescence microscopy imaging of neural
activity in vivo. Nature Methods, 17(3), 287–290.
156

https://doi.org/10.1038/s41592-020-0762-7
Xiao, Y., Deng, P., Zhao, Y., Yang, S., & Li, B. (2023). Three-photon excited fluorescence
imaging in neuroscience: From principles to applications. Frontiers in Neuroscience, 17.
https://www.frontiersin.org/articles/10.3389/fnins.2023.1085682
Xiong, W., Yi, L.-C., Tang, Z., Zhao, X., & Fu, S.-J. (2018). Quantity discrimination in fish
species: Fish use non-numerical continuous quantity traits to select shoals. Animal
Cognition, 21(6), 813–820. https://doi.org/10.1007/s10071-018-1214-y
Xu, C., & Webb, W. W. (1996). Measurement of two-photon excitation cross sections of
molecular fluorophores with data from 690 to 1050 nm. JOSA B, 13(3), 481–491.
https://doi.org/10.1364/JOSAB.13.000481
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition,
74(1), B1–B11. https://doi.org/10.1016/s0010-0277(99)00066-9
Yamamoto, N., Ishikawa, Y., Yoshimoto, M., Xue, H.-G., Bahaxar, N., Sawai, N., Yang, C.-Y.,
Ozawa, H., & Ito, H. (2007). A new interpretation on the homology of the teleostean
telencephalon based on hodology and a new eversion model. Brain, Behavior and
Evolution, 69(2), 96–104. https://doi.org/10.1159/000095198
Yamamoto, N., & Ito, H. (2005). Fiber connections of the anterior preglomerular nucleus in
cyprinids with notes on telencephalic connections of the preglomerular complex. The
Journal of Comparative Neurology, 491(3), 212–233. https://doi.org/10.1002/cne.20681
Yang, E., Zwart, M. F., James, B., Rubinov, M., Wei, Z., Narayan, S., Vladimirov, N., Mensh, B.
D., Fitzgerald, J. E., & Ahrens, M. B. (2022). A brainstem integrator for self-location
memory and positional homeostasis in zebrafish. Cell, 185(26), 5011-5027.e20.
https://doi.org/10.1016/j.cell.2022.11.022
Yang, G., Pan, F., Chang, P. C., Gooden, F., & Gan, W.-B. (2013). Transcranial Two-Photon
Imaging of Synaptic Structures in the Cortex of Awake Head-Restrained Mice. Methods
in Molecular Biology (Clifton, N.J.), 1010, 35–43.
https://doi.org/10.1007/978-1-62703-411-1_3
Yang, T.-I., & Chiao, C.-C. (2016). Number sense and state-dependent valuation in cuttlefish.
Proceedings. Biological Sciences, 283(1837), 20161379.
https://doi.org/10.1098/rspb.2016.1379
Yang, W., Carrillo-Reid, L., Bando, Y., Peterka, D. S., & Yuste, R. (2018). Simultaneous
two-photon imaging and two-photon optogenetics of cortical circuits in three dimensions.
eLife, 7, e32671. https://doi.org/10.7554/eLife.32671
Yang, W., & Yuste, R. (2018). Holographic imaging and photostimulation of neural activity.
Current Opinion in Neurobiology, 50, 211–221.
https://doi.org/10.1016/j.conb.2018.03.006
Yao, P., Liu, R., Broggini, T., Thunemann, M., & Kleinfeld, D. (2023). Construction and use of an
adaptive optics two-photon microscope with direct wavefront sensing. Nature Protocols,
18(12), Article 12. https://doi.org/10.1038/s41596-023-00893-w
Yaseen, M. A., Sakadžić, S., Wu, W., Becker, W., Kasischke, K. A., & Boas, D. A. (2013). In vivo
157

imaging of cerebral energy metabolism with two-photon fluorescence lifetime microscopy
of NADH. Biomedical Optics Express, 4(2), 307–321.
https://doi.org/10.1364/BOE.4.000307
Yoshimatsu, T., Bartel, P., Schröder, C., Janiak, F. K., St-Pierre, F., Berens, P., & Baden, T.
(2021). Ancestral circuits for vertebrate color vision emerge at the first retinal synapse.
Science Advances, 7(42), eabj6815. https://doi.org/10.1126/sciadv.abj6815
Yu, H., Galwaduge, P. T., Voleti, V., Patel, K. B., Li, W., Shaik, M. A., & Hillman, E. M. C. (2017).
Two-photon Swept Confocally Aligned Planar Excitation Microscopy (2P-SCAPE). Optics
in the Life Sciences Congress (2017), Paper NW4C.3, NW4C.3.
https://doi.org/10.1364/NTM.2017.NW4C.3
Yushkevich, P. A., Piven, J., Hazlett, H. C., Smith, R. G., Ho, S., Gee, J. C., & Gerig, G. (2006).
User-guided 3D active contour segmentation of anatomical structures: Significantly
improved efficiency and reliability. NeuroImage, 31(3), 1116–1128.
https://doi.org/10.1016/j.neuroimage.2006.01.015
Zanon, M., Potrich, D., Bortot, M., & Vallortigara, G. (2022). Towards a standardization of
non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to
generate controlled stimuli. Behavior Research Methods, 54(1), 146–157.
https://doi.org/10.3758/s13428-021-01580-y
Zeng, Y., Wang, C., Zhao, F., Huang, X., & Cheng, Y. (2011). Polarization-induced control of
two-photon excited fluorescence in a chiral polybinaphthyl. Optics Letters, 36(15),
2982–2984. https://doi.org/10.1364/OL.36.002982
Zhang, Y., Rózsa, M., Liang, Y., Bushey, D., Wei, Z., Zheng, J., Reep, D., Broussard, G. J.,
Tsang, A., Tsegaye, G., Narayan, S., Obara, C. J., Lim, J.-X., Patel, R., Zhang, R.,
Ahrens, M. B., Turner, G. C., Wang, S. S.-H., Korff, W. L., … Looger, L. L. (2023). Fast
and sensitive GCaMP calcium indicators for imaging neural populations. Nature,
615(7954), Article 7954. https://doi.org/10.1038/s41586-023-05828-9
Zhang, Z., Bai, L., Cong, L., Yu, P., Zhang, T., Shi, W., Li, F., Du, J., & Wang, K. (2021). Imaging
volumetric dynamics at high speed in mouse and zebrafish brain with confocal light field
microscopy. Nature Biotechnology, 39(1), 74–83.
https://doi.org/10.1038/s41587-020-0628-7
Zhu, G., Howe, J. van, Durst, M., Zipfel, W., & Xu, C. (2005). Simultaneous spatial and temporal
focusing of femtosecond pulses. Optics Express, 13(6), 2153–2159.
https://doi.org/10.1364/OPEX.13.002153
Zipfel, W. R., Williams, R. M., Christie, R., Nikitin, A. Y., Hyman, B. T., & Webb, W. W. (2003).
Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence
and second harmonic generation. Proceedings of the National Academy of Sciences,
100(12), 7075–7080. https://doi.org/10.1073/pnas.0832308100
Zipfel, W. R., Williams, R. M., & Webb, W. W. (2003). Nonlinear magic: Multiphoton microscopy
in the biosciences. Nature Biotechnology, 21(11), Article 11.
https://doi.org/10.1038/nbt899
158

Abstract (if available)

Abstract Numerical cognition is a foundational aspect of animal behavior, influencing survival and ecological interactions. This dissertation investigates the neural basis of number sense in zebrafish (Danio rerio), leveraging their genetic tractability, optical transparency, and behavioral repertoire. Combining advanced two-photon light-sheet microscopy with molecular genetics, we identify the neural circuits underpinning discrete quantity estimation. We demonstrate that zebrafish possess specialized neural substrates in the forebrain and midbrain, with responses modulated by age, developmental stage, and external factors such as ethanol. Our findings reveal the parallels between zebrafish and higher vertebrates, establishing zebrafish as a robust model for studying numerical cognition, genetic contributions to developmental dyscalculia, and neurobiological mechanisms of magnitude estimation. This work not only broadens the understanding of quantity cognition across species but also proposes zebrafish as a translational model for neurodevelopmental disorders.

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Creator Luu, Peter (author)

Core Title Neural basis of number sense in zebrafish

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Molecular Biology

Degree Conferral Date 2024-12

Publication Date 11/21/2024

Defense Date 04/01/2024

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag Development,gcamp,larval,light sheet,lightsheet,number sense,numerosity,TPE,two-photon,zebrafish

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Advisor Fraser, Scott E. (committee chair), Arnold, Don (committee member), Dickman, Dion (committee member), Truong, Thai V. (committee member)

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