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Dependence of rabbit retinal synchrony on visual stimulation parameters
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Dependence of rabbit retinal synchrony on visual stimulation parameters
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Content
DEPENDENCE OF RABBIT RETINAL SYNCHRONY ON VISUAL STIMULATION
PARAMETERS
by
Susmita Chatterjee
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
August 2008
Copyright 2008 Susmita Chatterjee
ii
Dedication
I would like to dedicate my work at USC to several people who mean a great deal to me.
Firstly, it would be my parents and my brother who have taught me to always dream big
and encouraged me emotionally both during the highs and the lows. Vivek: for believing
in me and being there when I needed him the most. Dr David Merwine: for teaching me
his skills selflessly with a lot of patience and enthusiasm. Finally, Dr Norberto Grzywacz,
my advisor for teaching me life’s lesson on how to be a good researcher and most
importantly to be a good human being.
iii
Acknowledgements
I want to take this opportunity to express my gratitude and appreciation to all the
people who have helped me throughout the course of my doctoral studies. At first, I
would like to thank my thesis committee Dr Norberto Grzywacz, Dr Judith Hirsch, Dr
Bartlett Mel, Dr James Weiland, Dr David D’Argenio and Dr David Merwine, for their
valuable help and suggestions through the numerous discussions that we have had
together. I want to thank Dr Frank Amthor for collaborating with me and for always
encouraging my work.
I consider myself very fortunate to have met and worked with a great set of
people in my lab: Dr Eun –Jin Lee, Dr Monica Padilla, Xiwu Cao, Joaquin Rapela,
Junkwan Lee ,Jeff Wurfel and Denise Steiner .They have been like my family here at
USC .I am very certain that they will remain my friends and colleagues for life.
I would also like to extend my deepest gratitude to Ed and Carlos from the
animal facility department for always helping me with the rabbits when ever I asked
them.
iv
Table of Contents
Dedication ii
Acknowledgements iii
List of Figures vi
List of Tables viii
Abstract ix
Chapter One: Introduction 1
1.1 Synchronous activity in the neurons 1
1.2 Synchrony in the retina 3
1.3 Mechanism and retinal circuitry leading to synchrony 4
1.4 Specific Aims 5
Chapter Two: Methodology 7
2.1 Animals 7
2.2 Preparation and recording 8
2.3 Stimulus 10
2.3.1 Static edges 11
2.3.2 Low contrast stimuli 11
2.3.3 Discontinuous edges 11
2.4 Finding receptive field of cells 13
2.5 Distance between cells 15
2.6 Spatial relationship between cells 15
2.7 Cross-covariance measurements 15
2.8 Calculation of expected hits 18
2.9 Quantitative analysis of low contrast synchrony 19
2.10 Model Simulations 20
2.10.1 Stimulus for simulation 21
2.10.2 Bipolar-cell filter 21
2.10.3 Excitatory-amacrine-cell filter 23
2.10.4 Inhibitory-amacrine-cell filter 24
2.10.5 Ganglion-cell filter 25
2.10.6 Parameters 26
Chapter Three: Properties of stimulus-dependent synchrony in
populations of ganglion cells 27
3.1 Correlation for constant illumination, light steps
and moving extended edges 27
3.2 Synchrony at different time scales 29
3.3 Quantification of correlation indices 31
v
Chapter Four: Enhancement and suppression of synchrony 34
Chapter Five: Distance and directional-dependence of synchrony 37
5.1 Distance-dependence of correlated activity 37
5.2 Directional-dependence of correlated activity 39
Chapter Six: Synchrony for static edges 42
Chapter Seven: Low contrast synchrony in the retina 44
7.1 Correlation at low contrast 44
7.2 Strength of correlation at low contrast 45
7.3 Directional-dependence of correlation
as a function of contrast 48
Chapter Eight: Possible mechanism of synchrony 50
8.1 Retinal circuitry for synchrony 51
Chapter Nine: Modeling the phenomenology of
stimulus-specific synchrony 54
9.1 Spatial relationship between bipolar, excitatory-amacrine,
inhibitory-amacrine, ganglion cells in the model 54
9.2 Control 56
9.3 Correlation for light step and moving extended edge 59
9.4 Quantification of responses and
correlation index across contrasts 60
9.5 Enhancement and suppression of synchrony 61
9.6 Experimental predictions 63
9.6.1 Effect of integration window to elicit
suppression of synchrony 64
9.6.2 Synchrony for discontinuous edge 65
Chapter Ten: Experimental tests for the predictions of the model 67
10.1 Varying the integration window for
suppression of synchrony 67
10.2 Correlation for continuous and discontinuous edges 68
Chapter Eleven:Conclusion 72
11.1 Stimulus and class-dependent synchrony 72
11.2 Rationale behind circuitry leading to
stimulus-specific synchrony 73
11.3 Model simulation and its tests 74
11.4 Possible roles of stimulus-dependent synchrony 75
11.5 Future directions of this work 77
References 79
vi
List of Figures
Figure 2.1: Stimuli for discontinuous edge 12
Figure 2.2: Schematic relationship of stimuli, motion responses
and mapped receptive fields 13
Figure 3.1: Stimulus-dependent synchrony in ganglion-cell responses 28
Figure 3.2: Synchrony at different time scales 30
Figure 3.3: Quantification of synchrony over the populations of cells 32
Figure 4.1: Enhancement and suppression of synchrony 35
Figure 5.1: Distance-dependence of synchronous activity 38
Figure 5.2: Directional-dependence of synchrony 40
Figure 6.1: Synchrony for static edges 43
Figure 7.1: Low contrast synchrony in ganglion cell 45
Figure 7.2: Low contrast synchrony in different classes of cells 46
Figure 7.3: Population plot for all the pairs of cells in the study 47
Figure 7.4: Directional –dependence of synchrony across contrasts 49
Figure 8.1: Amacrine-cell network model for synchrony 52
Figure 9.1: Schematic spatial relationship between cells in the retina 55
Figure 9.2.1: Intracellular voltages and conductances of cells for full-field 57
Figure 9.2.2: Intracellular voltages and conductances of cells for
moving extended edges 58
Figure 9.3: Stimulus-specific synchrony in the simulation 60
Figure 9.4: Quantification of responses and correlation indices
in the simulation 61
vii
Figure 9.5: Enhancement and suppression of synchrony in the model 62
Figure 9.6.1: Effect of increasing the width of integration 64
Figure 9.6.2: Discontinuous edge stimuli in the simulation 66
Figure 10.1: Effect of integration window in the experiment 68
Figure 10.2.1: Correlations in the presence of occlusions 69
Figure 10.2.2: Quantification of correlation for continuous and
discontinuous edges 70
Figure 10.2.3: Correlation for different positions of the occluder 71
viii
List of Tables
Table 1: Parameters of simulation 26
ix
Abstract
Neighboring retinal ganglion cells often spike synchronously, but the possible
function and mechanism of this synchrony is unclear. Recently, the strength of the fast
correlation between On-Off directionally selective cells of the rabbit retina was shown to
be stimulus dependent. Here, we extend that study, investigating stimulus-dependent
correlation among multiple ganglion-cell classes, using multi-electrode recordings. The
work towards this dissertation generalized those for directionally selective cells. All cell
pairs exhibiting significant spike synchrony did it for an extended edge but rarely for full-
field stimuli. The strength of this synchrony did not depend on the amplitude of the
response and correlations could be present even when the cells' receptive fields did not
overlap. We found that motion is not necessary for synchrony, i.e., it can occur with static
flashes of bars. In addition, correlations tended to be orientation selective in a manner
predictable by the relative positions of the receptive fields. Interestingly, extended edges
and full-field stimuli produced significantly greater and smaller correlations than
predicted by chance respectively. We observed synchrony for edges at contrasts as low as
10% making them viable for natural image contrast statistics. We propose an amacrine-
network model for the enhancement and depression of correlation. We find that with
reasonable biophysical assumptions, the simulation of the network model will exhibit
stimulus-appropriate facilitation and suppression of synchrony. The model further
provides verifiable predictions for the rate of fast synchrony for discontinuous edges. We
have supported the predictions of the model with experimental data and found fast ms-
x
synchrony to disappear for discontinuous edge. Such an apparently purposeful control of
correlation adds evidence for retinal synchrony playing a functional role in vision
1
Chapter One: Introduction
1.1 Synchronous activity in neurons
Millions of neurons are involved in the processing of information in the animal
and human brain. These neurons must communicate amongst themselves to know the
information processed by each other. The most plausible mechanism for such a large-
scale integration is the formation of dynamic links mediated by synchrony over multiple
frequency bands (Varela et al., 2001). Neurons can exhibit a wide range of oscillations
(theta to gamma-band oscillations ~4-70 Hz) and these oscillations can enter into precise
synchrony over a limited period of time (millisecond scale). Brain oscillations at different
frequencies are one of the most promising candidate mechanisms explaining the neural
basis for higher-level information processing. Various studies in the cat visual cortex
(Brosch, M et al., 1995, Eckhorn, R., 1994.(et al.,1988,1992 ),Gray et al., 1989) and the
monkey cortex (Kreiter and Singer, 1992) have shown that synchronous oscillating
activity amongst neurons may contribute to the communication of these neurons (Singer,
1999, Engel et al.,1991a).
For example, the synchronous firing of neurons in the visual cortex has received
considerable attention as a possible route towards conceptual binding stimuli (Eckhorn et
al., 1988; 1993; Eckhorn, 1994; Engel et al., 1991a, b; Fries et al., 1997; Gray et al.,
1989; Kreiter and Singer, 1996). For instance, Wolf Singer and colleagues demonstrated
that neurons in the cat brain fired synchronously when the bars moved together (Kreiter
and Singer, 1996) over their receptive field but fired asynchronously when two
independent images of a bar moved in different directions .It appeared that the monkeys
2
were aware that the two separate bars in contrast to the single bar represent two aspects of
the same object and encoded it through the synchrony of firing. Eckhorn and others have
demonstrated that 40–80 Hertz synchronous oscillations link distant neurons involved in
registering different aspects (color, shape, movement, velocity etc.) of the same visual
perceptions and thereby bind together features of a sensory stimulus (Eckhorn et al.,
1988; Singer, 1998).
In the study of Amthor et al., 2005 in the retina, the authors postulated that the
theories proposing synchronous firing for object binding in visual cortex have been
criticized sometimes .For instance, for the production of sub-millisecond synchrony in
the cortex, the distances of centimeters between the retina and the cortex, and the multi-
millisecond transmission delays over such distances has to be accounted for. One thought
is that the retinal output already contains synchrony in the firing response of the cells.
The task of separated cortical cells might then be to select, tune or amplify the already
present synchrony.
Physiological (Cleland et al. 1971a; Mastronarde 1987, 1992) as well as anatomic
(Hamos et al. 1987) studies show convergence between retinal ganglion cells and
geniculate neurons which may suggest that while some geniculate neurons receive input
from only one retinal ganglion cell which is well explored but, many others receive
converging input from two or more ganglion cells. Therefore, convergence may
also be important in the transmission of information from retina to LGN.
3
1.2 Synchrony in the retina
With advanced recording techniques, synchronous firing in populations of
neurons has been found at all levels of the visual pathway including the retinal output.
Multi- and dual-electrode recordings in a number of species have shown that some
classes of neighboring retinal ganglion cells exhibit correlated spiking, both
spontaneously and in response to light stimuli (Arnett & Spraker, 1981; Mastronarde,
1983; Meister et al., 1995; Brivanlou et al., 1998; Neuenschwander et al., 1999; DeVries,
1999; Alonso et al., 1996; Hu EH & Bloomfield, 2003; Amthor et al., 2005; Ackert et al.,
2006)..Different studies have proposed contrasting theories and functions for retinal
synchrony.
For instance, Meister et al. (1995; Meister, 1996) proposed that correlated spikes
carry fine-grained spatial information. De Vries., 1999 showed how certain stimuli can
activate neighboring OFF cells simultaneously through their receptive field centers. More
recently, Ackert et al., 2006 have argued that de-synchronization of responses between
On directionally selective (DS) ganglion cells for stimuli moving in the null direction
could be used by higher visual centers as a possible code for motion direction. They
postulated that the de-synchronization might be the key component in detecting a visual
motion signal. Amthor et al. (2005) demonstrated that the On-Off DS ganglion-cell class
in the rabbit retina shows stimulus-dependent spike correlations. DS-ganglion-cell
responses showed significant millisecond correlations when long bars (that extended
beyond the RFs of the cells) moved through both RFs simultaneously. Stimulation by
large flashing spots elicited responses that typically showed little correlated firing.
According to Amthor et al. (2005), one possible interpretation of this result is that the
4
correlated firing is a signal to higher visual centers that the outputs of the two DS
ganglion cells should be “bound” together, as they occur due to the contour of a common
object. The authors also argued that the stimulus-dependent synchrony in the retinal
ganglion–cell output is ideal for detection by known lateral-geniculate-nucleus and
visual-cortex mechanisms (Alonso et al., 1996, 2001; Dan et al., 1998; Usrey et al., 1998,
1999, 2000).In a separate study by Schwartz et al., 2007, the authors have demonstrated
that the synchrony in the retina to signal motion reversal. In contrast, it has also been
suggested from analyses based on information theory that correlated spikes carry little
information that is not already available from individual cell firing rates (Nirenberg et al,
2001).
1.3 Mechanisms and retinal circuitry leading to synchrony
Numerous studies have investigated the neural circuitry behind correlated activity
in the retina (Meister., et al 1995, Brivanlou et al., 1998, DeVries., 1999). Brivanlou et
al., 1998 identified at least three mechanisms that contribute towards concerted firing in
the salamander and the cat retina. Electrically coupled cells with large dendrite overlap
can produce sub-millisecond delay synchrony. Correlations, on a time scale between 2 to
10 ms, are caused by a common input to the recorded ganglion cells from an electrically-
coupled interneuron. Finally, the authors suggested that broad or slow correlations with
time scales of 50-100 ms are mostly created from divergent inputs using a chain of
chemical synapses.
In contrast, the lack of obligatory synchrony in the rabbit retina (Amthor et al.,
2005) for both stimuli argues against gap junctions as an exclusive mechanism. Further,
5
they found long-range synchrony between cells with receptive fields separated by
maximum distances up to 600 µm. Thus, stimulus-specific synchrony at least in the rabbit
retina cannot be explained by electrical coupling between cells.
Various examination and pharmacological manipulation of synchrony have
revealed properties of the neurons and circuits in which they are found. Meister et al.,
1995 showed that synchronous spikes in two RGCs can encode a spatial receptive field
that is different from the RFs of either neuron considered in isolation. In a separate study,
Liu et al., 2007 have demonstrated that the intensity of the medium correlations could be
strengthened when exogenous GABA was applied and attenuated when GABA receptors
were blocked by picrotoxin in the chicken retina. Ackert et al, 2006 have shown that null
stimulus movement evokes a GABAergic inhibition that temporally shifts the firing of
ON DS cell neighbors, resulting in a desynchronization of spike activity.
Pharmacological studies (Amthor et al., 2005) have provided evidence that a common
cholinergic input produces fast-ms correlation in nearby ganglion cells, with GABAergic
input suppressing synchronous activity.
1.4 Specific aims
In this doctoral dissertation, we extended the results of Amthor et al. (2005) in
several directions. The objective for the work has the following nine specific aims.
1. To investigate stimulus-dependent synchrony across population of ganglion cells;
2. Does the difference in synchrony arise from an enhancement of synchrony or
suppression of synchrony?
3. To study distance and directional dependence of synchrony;
6
4. Is motion necessary for synchrony?
5. Are the contrasts that are commonly found in natural image contrast statistics enough
to produce synchrony?
6. To find the possible mechanism of stimulus-specific synchrony;
7. Modeling the phenomenology of stimulus-specific synchrony;
8. To test the model predictions with physiological data;
9. To discuss the possible new roles of synchrony with regard to this study;
7
Chapter Two: Methodology
In this chapter, we will discuss all the procedures shared by the different
experiments towards this doctoral dissertation. The results of the various experiments
have been described in the subsequent chapters .We have described in detail the statistics
and equations that we have used . We have made frequent reference to this chapter for
purposes of methodology through out this dissertation.
2.1 Animals
We used adult Dutch-belt pigmented rabbits of either sex, weighing between 1-3
kg. All surgical and experimental procedures were in conformance with the Guide for
the Care and Use of Laboratory Animals (National Institutes of Health) and were
approved by the Institutional Animal Care and Use Committee (IACUC) at the
University of Southern California or the University of Alabama at Birmingham. The
animal care facilities at both universities were fully accredited by the American
Association for Accreditation of Laboratory Animal Care (AAALAC) during data
collection. The animals were dark adapted for 30 min before surgery, and all surgery was
done in dim red light. The animals were initially anesthetized using Ketamine and
Xylazine, given I.P. with a dosage of (50mg/kg) and (5mg/kg), respectively. Afterwards,
Pentobarbital Sodium (1ml/kg) was injected in the marginal ear vein to obtain deep
anesthesia. Anesthesia was checked by testing for corneal reflexes and reactions to a paw
pinch. After confirming a lack of reflexive movement, an eye was enucleated, and the
animal subsequently killed with an I.V. overdose of Pentobarbital Sodium.
8
2.2 Preparation and recording
For eyecup recordings, an eye was enucleated, hemisected, devitreated, and
everted over a latex dome as previously described (Amthor et al., 2005). For isolated
retinal recordings, the retina was gently separated from the pigment epithelium and then
placed, ganglion-cell side down, over a hole punched in a Whatman Filter paper. The
filter paper was then flipped and mounted in the recording chamber so that the ganglion
cells would be accessible through the hole. The isolated retina was placed in the
recording chamber within 5 min of interrupting the blood supply in vivo. Once in the
chamber or on the latex dome, the retina was continuously superfused with oxygenated
bicarbonate-buffered Ames solution (Sigma) at 37
0
C at a flow rate of 3-5 ml/min.
Eyecups produced reliable response for over 12 hrs, while isolated retinas remained
healthy for about 6 hr post isolation.
Extracellular recordings from the eyecup were made using a transparent multi-
electrode array (Amthor et al., 2003). Recordings from the isolated retina were obtained
with a commercial multi-electrode array (Cyberkinetics) having a 10 × 10 grid with 200-
µm inter-electrode spacing. An array was lowered onto the ganglion-cell layer and fixed
in position when responses were recorded on a maximum number of electrodes.
Recordings were obtained in the central retina just above the visual streak. Retinal cell
classes were identified and classified using criteria described previously (Amthor et al.,
1989; Merwine et al., 1995). In brief, cells were classified into concentric or complex
cell classes using full-field step and moving grating stimuli. Further, cells were
categorized to be brisk if their peak firing rate was greater than 25 spikes/sec and
sluggish otherwise. We distinguished sustained and transient cells based on whether their
9
maintained activity was above or below 25% of their peak activity 200ms after the peak
onset.
We analyzed data from thirteen isolated retinas and six eyecups in this study. We
obtained high quality receptive-field maps and observed robust responses in 142 cells
from the isolated retinas and 30 cells from the eyecups. There were 127 possible pairs of
cells from the isolated retina and 15 from the eyecup that could be chosen for analysis. A
pair would be a candidate for analysis if the cells were within 600 µm of each other
(center to center). Moreover, the cells had to be of the appropriate response sign to have
a possible temporal overlap in their light-driven responses. We obtained largely similar
results from cells in the two preparations. However, because we have more data from the
isolated retina, we only quantify its pairs in the rest of this paper. Of the 107 available
pairs, 66 showed statistically significant correlations with our criteria.
For eyecup recordings, data were digitized and spike times detected using custom-
template software described elsewhere (Amthor et al, 2003). For isolated-retina
recordings, selected channels of data were digitized with a commercial data-acquisition
system (Cyberkinetics). A custom analysis program sampled the data at 10 kHz
(Guillory and Normann, 1999) and stored the recordings for later analysis. We
performed spike sorting offline using the customized program, POWERNAP
(Cyberkinetics), and then used MATLAB (The Math Works Inc., Natick, MA) to analyze
the data set.
10
2.3 Stimulus
Light stimuli were provided by an RGB monitor (Accusync LCD 51V, NEC) with
a refresh rate of 60Hz. The monitor image was reflected off a half-silvered mirror under
the microscope stage, and focused on the photoreceptor layer of the retina by the
condenser lens to produce an image of 3 × 3 mm on the retina.
We wrote our code for stimulus control in MATLAB, using the Psychophysics
Toolbox extensions (Brainard, 1997; Pelli, 1997). The stimuli included constant
illumination at the mean background intensity, full-field steps, and moving square-wave
gratings. We displayed the full-field step stimulus with 1000-ms ON period and 1000-ms
OFF period for fifty trials. The light step was at 80% contrast. We used the light step
stimulus both to begin classifying the ganglion cells and to investigate stimulus-
dependent response correlations.
Each cell's RF size and position was next determined by analyzing responses to
fifty presentations of a very low spatial-frequency square-wave grating (0.14cycle/mm)
drifting upwards, downwards, leftwards, and rightwards. This grating was such that a
single dark or bright edge was present on the screen at any given time (temporal
frequency = 0.069 Hz, and same contrast and mean illumination as above). A higher
spatial-frequency square-wave grating (0.71 cycle/mm; 0.42 Hz) was shown moving in
24 directions for 50 trials (same contrast and mean illumination as above). This stimulus
aided in classifying cells with complex RFs, and responses to it were analyzed to study
correlations to moving edges. Pilot experiments were performed using different spatial
and temporal frequencies of the grating to determine the optimal frequencies for driving
cell responses.
11
2.3.1 Static edges
For the static edge stimulus, we delivered the square-wave grating (0.71
cycle/mm; 0.42 Hz at 80% contrast) with contrast reversal. By using contrast reversal
instead of motion, we could test whether static edges could elicit synchrony, i.e., whether
motion was necessary. The spatial frequency was such that the RF of a cell saw at most
one edge. To ensure that the edge simultaneously crossed the centers of the RFs of two
cells, we presented the gratings at four equally spaced phases for each orientation. The
whole procedure was then repeated for 12 orientations of the grating in a pseudorandom
order. The presentations were in 50-cycle (100 reversals) blocks, each with a fixed phase
and orientation. The period of a cycle was 2000 ms.
2.3.2 Low contrast stimuli
For studies of synchrony using low contrasts we showed full-field steps, moving
square-wave gratings at 5%, 7%, 12%, 25%, 51%, 82% and 100% contrasts. Contrast
modulations were defined by (L
max
- L
min
)/(L
max
+ L
min
) and was increased or decreased
from the mean background illumination of 9.10 Cd/m
2
. The different contrasts were
interleaved and shown in a random sequence to avoid any effects of adaptation.
2.3.3 Discontinuous edges
We put over the square wave grating an occluding long bar of a width of 120 µm such
that it is perpendicular to the direction of motion (Fig 2.1). The occluding bar has the
same luminance as the background. The occlusions are periodic and spaced at 100 µm
from beginning to beginning. We show the moving grating with the occlusions at a given
12
phase for 25 cycles. We then shift the occlusion by 100 µm and repeat the motion of the
edge for another 25 cycles. This fine increment in position enables the occluding edge to
Figure 2.1: Stimuli for discontinuous edge: We show a square wave grating with the presence of an occluder. The
circles are schematic representation of the receptive field of ganglion cells. The gray horizontal bar is the occluder.
be between every two RF centers for at least one of the phases, causing edge
discontinuity. We repeated this procedure for 12 directions in a pseudorandom order. The
randomization of phases and directions help to keep the measurements periods of
relatively stable retinal sensitivities. We repeat the procedure without the occlusions to
compare synchronization with and without them.
Figure 2.2 shows a schematic illustration of the relationship between our main
stimuli and the positions of cells. In 2.2A left, a full-field light step covers the receptive
fields of cells 1, 2, and 3 entirely. In 2.2A right, a single edge of the drifting, high
spatial-frequency grating enters the RFs of the two cells 1 and 2 simultaneously for a
particular direction of motion, as opposed to the sequential stimulation of cells 1 and 3
for this direction
13
2.4 Finding the receptive field of each cell
The borders of each cell's RF were rapidly determined based on cell responses
being strongest when an edge crosses into the excitatory RF (Rodieck and Stone, 1965).
We thus presented edges (very low spatial-frequency square-wave gratings) moving
slowly upwards, downwards, leftwards, or rightwards. When an edge with appropriate
contrast moved into the RF of a cell, it gave a response, indicating the border of the RF.
Figure 2.2: Schematic relationship of stimuli, motion responses, and mapped receptive fields. [A] Relationship of three
receptive fields (1, 2 and 3) with the light-step full-field stimulus (left) and the moving extended edge (right – grating).
The arrow indicates a particular direction of motion and the time course of the steps of light appear schematically
below the full-field stimulus. [B] Post-stimulus time histograms (PSTH) for four motion directions (indicated by
arrows) of a low spatial-frequency grating. The white, vertical, dashed line indicates the statistically determined start
of the transient response in each direction. [C] Receptive-field map extrapolated from the motion responses. The four
tangents to the map indicate the grating edge location at the onset of the transient response (corrected for the delay of
the step response).
14
Figure 2.2B shows histograms of the responses of a cell to each direction of motion. The
starting time of the response in each direction (indicated by the dashed line on the
histogram) was translated into a spatial position, using the known spatial and temporal
frequencies of the grating, and its phase. Moreover, we used the measured delay of
response to the full-field step to account for the delay between penetration of the RF by
the edge and the beginning of the response. Figure 2.2C shows the rectangle defined by
the horizontal and vertical RF borders derived from the responses of Fig. 2.2B. In this
work, we define the RF as the largest ellipse embedded on this rectangle (Fig. 2.2C).
Because the rectangle arises from the onsets of response from the background activity,
we were careful to detect them in a statistically robust manner (Liu et al., 2006). The
background firing rate, i.e., the baseline, was first estimated as the median of the
distribution of the neural activity during the response to the motion. Because the median
is a robust statistical estimator, it captures a property of the majority of the response, i.e.,
of the baseline. We then determined the median absolute deviation (MAD) of the
response distribution (Sprent., 1993). The MAD is a statistically robust measure of
response deviation (like standard deviation, but robust) and thus, also captures variations
of the baseline. To detect the border of the RF, we searched for the first histogram bin
that was more than 3.8 MAD’s above the baseline (Sprent, 1993). We avoided picking
up false positives by requiring that the subsequent bin also passed the 3.8 MAD
criterions. This MAD level corresponds to a p < 0.0005 chance that the background firing
is detected as the beginning of the response by chance (Sprent, 1993).
15
2.5 Distance between cells
To measure the distance dependence of correlation, we calculated a ratio called Spacing
‘s,’ similar to that used by De Vries (1999). This ratio estimates distance between each
pair of cells as
s =
d
r1+ r2
- Equation 1
where d is the length of the line connecting the RF centers (i.e., the distance between
them), and r1 and r2 are their distances to the nearest points where this line intersects the
RF ellipses. Therefore, the definition in Eq. 1 gives the distance between RFs relative to
their sizes. We then plotted the strength of synchrony between cells as a function of this
relative distance.
2.6 Spatial relationship between cells
To study the direction dependence of correlation, we first determined the angle of the line
connecting the centers of the receptive fields in each cell pair. We then added and
subtracted 90 degrees from this angle. The resulting angles were the two opposite
directions of motion that would simultaneously cross over both receptive-field centers.
We then compared these directions with those of the grating motion that caused
significant correlations.
2.7 Cross-covariance measurements
One tool that we used to measure the strength of fast correlation was the cross-covariance
function. In this study, cross-covariance functions were computed for spike trains of
16
pairs of cells as previously described (Grzywacz et al., 2000, Amthor et al., 2005). Here,
we briefly explain the Amthor-et-al method to compute cross-covariance functions,
providing its rationale. In most studies of synchrony, stimulus-driven correlations due to
just co-stimulation of cells that causes covariation in their firing rates are not of primary
interest. Most studies focus instead on the relationship between the firing rates due to
inter-cellular connectivity in the neural circuitry. A method to eliminate correlations that
are due to stimulus-induced relationship is to compute shuffle-corrected cross-covariance.
Amthor et al. compute this cross-covariance from two numbers. The first (C
I,1,2
(τ
m
)) is
the number of times a spike in Cell 2 has a delay of τ
m
± ∆τ/2 from a spike in Cell 1 in
the same trial, where ∆τ is typically a small time interval. The second (C
E,1,2
(τ
m
)) is the
same number, but such that spikes of Cell 1 are from different trials from those of Cell 2.
In other words, C
I,1,2
(τ
m
) and C
E,1,2
(τ
m
) are respectively the total number of intra-trial
and extra-trial spike matches (shuffle-corrected) with delay τ
m
. In the procedure of
Amthor et al., the number of matches from across trials is subtracted from within-trial
matches (with appropriate normalization for chance matches) and subsequently binned in
an histogram (with bin size = ∆τ). This subtraction gives cross-covariance based only on
physical connectivity between neurons, since the subtracted extra-trial matches reflect
solely the stimulus-driven correlation.
Mathematically, we estimate cross-covariance as
( )
) 1 (
) ( ) (
1
) (
2 , 1 , 2 , 1 ,
2 , 1
−
−
∆
=
M M
C
M
C
X
m E m I
m
τ τ
τ
τ - Equation 2
where M is the number trials, i.e., of stimulus repetitions. We use ∆τ = 1 ms, and -25 ms
≤ τ
m
≤ 25 ms for most of our correlation plots in this paper. This choice of temporal
17
parameters results in 51 shuffle-corrected correlation bins. In one plot, however,, we use
∆τ = 50 ms, and -1025 ms ≤ τ
m
≤1025 ms. This choice of broader temporal values results
in 41 shuffled-corrected bins and allows us to study covariance in coarser temporal
scales. To determine whether the covariance in a particular delay bin was statistically
significantly different from zero, we used the intra-trial (C
I,1,2
(τ
m
)) and extra-trial
(C
E,1,2
(τ
m
) ) match counts, and the same two-sided χ
2
test as explained elsewhere
(Grzywacz and Sernagor, 2000; Amthor et al., 2005). The test is of whether when one
makes an intra-trial measurement, the probability of finding a match is the same as the
one to find a match in an extra-trial measurement. (In other words, the null hypothesis is
that intra-trial matches occur by chance.) We used a stringent criterion of p < 0.0002 to
consider a bin to have a statistically significant covariance. Finally, we performed a
normalization procedure to compare the covariogram results from different retinas and
across different cells. This procedure used the most widely cited cross-correlation metric
in the literature, namely, the cross-covariance normalized by the standard deviation
(Johnson & Wichern 1992). In the procedure (Aertsen et al., 1989), we calculated
) 0 ( ) 0 (
) (
) (
ˆ
2 , 2 1 , 1
2 , 1
2 , 1
X X
X
X
m
m
τ
τ = - Equation 3
where X
i,i
is just the variance of the response in Cell i (i = 1,2). Equation 3 has a
normalization for τ
m
= 0, i.e., a value from -1 to 1 which is equivalent to the correlation
coefficient. For other τ
m
, Eq. 3 has no normalization, but we will show empirically that
the results are typically statistically indistinguishable from 0.
18
2.8 Calculation of expected hits
Another tool that we used to measure the strength of fast correlation was the “hits”
histogram. Hits took place when two spikes in a pair of cells occurred within a window
of w = 2 ms of each other. The histogram of these hits showed the time during the
response when the correlated events occurred. We plotted the hits histogram
superimposed on the post-stimulus time histogram (PSTH) of the cells. Both the PSTH
and the hits histogram used bins of duration D = 20 ms. Because two spikes of a hit
could fall in different bins, to avoid double counting, we counted a hit for a bin only if
Cell 1’s spikes fell there.
We also tested whether a particular visual stimulus caused more or less hits than
expected by chance. To calculate the bin-wise expected number of hits from the light
responses, we took into account the number of spikes produced by each cell per
millisecond per trial. To estimate this number, we first measured the number of spikes in
D=20ms bins over M = 50 trials. We then performed a piecewise constant approximation
of the firing rate. (The approximation was for the same 20-ms intervals for Cell 1 but
extrapolated to 24 ms for Cell 2. This extrapolation took into account cases in which
Cell-2 hit spikes fell outside the 20-ms bin.) With these estimated firing rates, we
proceeded to estimate the expected number of hits. For this estimation, we assumed the
two cells to fire independently. Moreover, we assumed that the number of spikes in each
given 4-ms bin obeyed a Poisson distribution with mean much smaller than 1. (The bins
in this calculation were of 4 ms, since a hit could occur if a spike in Cell 2 occurred
within ±2 ms of a given spike in Cell 1). This was because the probability of a particular
spike falling in our 4-ms bin of interest was very small. The distribution was Poisson,
19
since the number of spikes in all 20 ms in all fifty trials was large. With the
independence and small-mean Poisson assumptions, the bin-wise expected number of hits
was
DM
S wS
N
2 1
2
= - (Equation 4)
where S
i
was the total number of spikes for Cell i in the 20- ms window over all M trials.
The derivation of this equation used the approximated Poisson-distribution equality of
mean and probability of a success for small means. This derivation also used the
multiplication rule for independent probabilities.
To test statistically whether the number of observed events was larger or smaller
than expected, we used the Poisson distribution. To test for facilitation of synchrony, we
calculated the probability p that a Poisson distribution with the expected mean could
cause a number of hits larger or equal than observed. To test for suppression of
synchrony, we calculated the opposite. These calculations were performed for each bin
and a statistically significant difference was considered to have occurred if p < 0.05.
Similarly, we considered the integrated number of expected hits and compared it with the
integrated number of observed hits. This comparison is possible, because the sum of
Poisson variables is a Poisson variable.
2.9 Quantitative analysis for low contrast synchrony
Plots were made of the normalized cross-correlation index–versus contrast curve
for all the pairs of cells in this study section. We used jack-knife statistics to get the
mean value of the correlation-index for all of the correlation-versus contrast curves. We
20
fit each of the curves to an equation so that we could determine the slope and the
saturation value for the strength of correlation for each pair.
contrast k
contrast k
y
+
=
2
* 1
+ k3 - Equation 5
We also plotted the correlation index as a function of direction of motion for all
the pairs in the study. The direction of motion yielding statistically significant correlation
defined either a bimodal or a unimodal profile. These tuning curves were fitted to a
simple linear combination of two von Mises-type functions (von Mises, 1918) (Eq. 6) and
that defined a bimodal tuning profile with a set of parameters {b, k1,k2,µ1, 1 κ , 2 κ ,µ2)
(Amirkian et al., 2000). We can vary the parameters that adjust the position (µ1, µ2),
shape (k1, k2) and depth (K1, K2) for each of the modes independently.
) 2 cos( 2 exp( 2 ) 1 cos( 1 exp( 1 µ θ κ µ θ κ − + − + = k k b y - Equation 6
Using the ki, which is a width parameter, we calculated the half-width of the tuning curve
at half-height of the maximal response using the following formula (Wang et al., 2007)
] / ) 5 . 0 arccos[(ln 5 . 0
5 . 0
k k + = θ - Equation 7
where k > -0.5ln0.5
2.10 Model simulation
We built a retinal model (Figure 8.1) that provides quantitative explanation of the
stimulus-specific synchrony illustrated in this dissertation. We simulated the model with
a moving edge and full-field square-wave modulation which are 2D arrays. All the cells
21
were simulated as a single RC compartment. The parameters for the simulation have been
given in Table 2.1 at the end of this chapter.
2.10.1 Stimulus for simulation
We used moving edge and full-field square-wave modulation for the stimulus
similar to the stimuli used by Chatterjee et al., 2007.
Full-field:
I(x, y, t) =
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
= +
+
< < +
otherwise b
n
f
d n
t
f
n
if a
,
.... 3 , 2 , 1 , 0 ; 1 1 ,
-Equation 8
Moving-edge:
y orient x orient ramp * ) sin( * ) cos( − =
-Equation 9
) 2 / * sin( ) , , ( pi sf ramp t y x I + Φ + =
-Equation 10
) 2 / ) 1 ) , , ( (( ) , , ( + = t y x I round t y x I
-Equation 11
2.10.2 Bipolar cell filter
All the cells were simulated as a single RC compartment. These filters were linear
filters with separable spatial and temporal components. The spatial components of the
receptive fields of these cells were described by a difference of Gaussians (DoG). In the
cartesian coordinates, with origin at the center of the receptive field, spatial filter
implemented by such a cell may be written as:
22
))
2
( exp( 2 ))
1
( exp( 1
2 2 2 2
σ σ
y x
K
y x
K DoG
+
− −
+
− = -Equation 12
where K1 >> K2 and σ2 > σ1.
The first and second Gaussian accounts for the center and surround sensitivity. K1 is
made greater than K2 to ensure that there are responses from the bipolar cell even when
simulated by the full-field stimulus.
The bipolar cells were built as a spatiotemporal filter.
))] exp( [( * ) 2 , 1 , 2 , 1 : , ( ) , , (
b
t
t K K y x DoG t y x B
τ
σ σ
−
=
Equation 13
where τ is the decay constant of the temporal filter
Photoreceptor noise (Minke et al., 1975, Barlow et al., 1993) have been
incorporated by adding Poisson noise (ξ ) to the input of the bipolar cells. ξ , reflected
departure from the mean of the Poisson distribution. The magnitude of Poisson noise
varies across the stimulus, as it depends on the image intensity.
) , , ( ) , , ( ) , , ( t y x t y x I t y x I ξ + =
Equation 7
where I (x, y, t) represents the mean stimulus at every position and time and ξ is the
poisson noise that is added to the stimulus, i.e I + ξ has a Poisson distribution.
The response of the bipolar cells is the product of the convolution of the stimulus
with the spatio-temporal filter:
) , , ( ) , , ( ) ( τ τ − =
∫∫ ∫
t y x I t y x dxdyB d t R
b
Equation 14
23
All the synapses in the simulation are conventional synapse and follow a
relationship as follows:
)) ) ( ( exp( 1
) (
2 _ , 1 _ 1 _ 2 _ , 1 _
2 _ , 1 _
2 _ , 1 _
cell cell cell cell cell
cell cell
cell cell
t R k
A
t R
θ − − +
= Equation 15
where, A
cell_1,cell_2
>0 is the synaptic gain, k
cell_1,cell_2
is the slope of the synapse input-
output relationship and
2 _ , 1 _ cell cell
θ is the synaptic threshold .The notation cell_1 and
cell_2 denote the pre-synaptic and post-synaptic cells considered for the synapse
respectively.
2.10.3 Excitatory Amacrine Cell
Cell Ae has been built as a leaky integrate and fire neuron (LIF) and is
represented as follows:
Ae m m W t R t R
dt
dAe
cell cell b Ae
− =
∑
) ' , ( ) ( ) (
2 _ , 1 _
τ Equation 16
where,
Ae
τ is the time constant of the decay of the membrane potential
2
2 _ , 1 _
2 2
2
) ) ( ) ((
exp( ) ' , (
cell cell
l j k i
m m W
σ
− + − −
= -Equation 17
W (m, m’) –is symmetric unless specified and gives the connection strength which are
implemented as Gaussian functions of the Euclidian distance between the Cartesian
position of the pre-synaptic cell (i, j) and the post-synaptic cell (k, l).
2 _ , 1 _ cell cell
σ is the
Gaussian radius of the interaction .The spatial extent of synaptic interactions depended on
the input and the output radii of the post-synaptic and pre-synaptic cell types. In this case
24
cell_1, cell_2 represents the interaction between the bipolar cell filter and excitatory
amacrine cell filter.
For the excitatory amacrine cell, the resting membrane potential of Ae
mem
is -
65mv and when, Ae > Ae
thresh
, 35 = Ae mv
The membrane potential is reset to the resting membrane potential after an action
potential has been generated. An action potential (spike) is produced only when the
membrane potential exceeds the threshold (Ae
thresh
).Spike that is generated in the Ae cell
is propagated to ganglion cells within a spatial radius.
2.10.4 Inhibitory amacrine cell filter
The inhibitory neuron Ai is built to be a non-spiking neuron. The bipolar cells
make synapse with neighboring inhibitory A
inh
cell represented as follows:
) ' , ( ) ( ) ( ) (
2 _ , 1 _
,
m m W t R t R t A
cell cell
y x
b inh ∑
= Equation 18
W (m, m’) and R
cell_1, cell_2
, determines the connection strength and synaptic connections
respectively; where cell_1 and cell_2 represent bipolar cell and inhibitory amacrine cell
respectively. The connection strength parameter
2 _ , 1 _ cell cell
σ is very small and hence
bipolar cells make very local synaptic connections with inhibitory amacrine cell.
Each of the inhibitory amacrine cells make post-synaptic connections with
ganglion cells as shown in Equation 13.
) ' . ( ) ( ) (
2 _ , 1 _
m m W R t A t G
cell cell inh Ainh
= Equation 19
In this case, W (m, m’) is connection strength where when i=k or j=l the strength is zero.
Therefore this connection is asymmetric which means that they connect to ganglion cells
25
that get their input from different bipolar cells from them. Therefore, bipolar cell terminal
will affect amacrine cells that will act on the synaptic potential of displaced ganglion
cells. Cell_1 and cell_2 represents the interaction between the inhibitory amacrine cell
and ganglion cell.
2.10.5 Ganglion cell filter
Ganglion cells make synapses with bipolar cells, excitatory amacrine cells and
inhibitory amacrine cells. The ganglion cells in the model are designed as modified
conductance-based-leaky-integrate–and-fire neuron. The resting membrane voltage
(Vgmem
)
before threshold is at -70mv.
) )( ( ) )( ( ) )( ( ) (
g Ainh Ainh g Ae Ae g B B g r r
g
g
V E t G V E t G V E t G V E G
dt
dV
− + − + − + − = τ
Equation 20
where,
) ' , ( ) ( ) ( ) (
2 _ , 1 _
m m W t R t Rb t G
cell cell B
=
Equation 21
) ' , ( ) ( ) ( ) (
2 _ , 1 _
m m W t R t Ae t G
cell cell Ae
=
Equation 22
) ' , ( ) ( ) ( ) (
2 _ , 1 _
m m W t R t A t G
cell cell inh Ainh
=
Equation 23
Ainh Ae B
E E E , , are the reversal potentials for the bipolar-cell, excitatory-amacrine cell
and inhibitory-amacrine cell respectively. We always have
R Ainh R Ae R B
E andE E E E E < > >
,
Once V
gmem
crosses the threshold (G
thresh
), the ganglion cell fires a spike. We dealt with
two possibilities of building the modified conductance based leaky integrator. First is the
26
introduction of a refractory period after an occurrence of a spike and second is to use
stochasticity into the deterministic LIF model. We have used a 5 ms refractory index
after the occurrence of a spike.
2.10.6 Parameters
Stimulus Bipolar Cell Excitatory
Amacrine Cell
Inhibitory
Amacrine Cell
Ganglion Cell
orient=0deg K1=31.5 A
Ae_ganglion
=2pS A
Ainh_ganglion
=2.5pS E
r
= -50mV
sf=0.5cyc/deg K2=1
ganglion Ae _
θ =30mV
θ
Ainh_ganglion
=10mV
E
Ae
= 0mV
Φ =0
1 σ =4
K
Ae_ganglion
=5 k
Ainh_ganglion
=0.005 E
b
= -40mV
a=8.7Ma
2 σ =16
σ ganglion Ae _
=0.8
σ ganglion Ainh _
=0.5
E
Ainh
= -90mV
b=0.7mA τ
b
=2 Ae
mem
=-65 mv
70 − =
V gmem
mV
d=0.5 A
bipolar_Ae
=2.5 Ae
thresh
= -30 mv G
thresh
=-60mV
f=0.5Hz k
bipolar_Ae
=5
Ae bipolar _
θ =4mV
σ Ae bipor _
=1
A
bipolar_Ainh
=5
k
bipolar_Ainh
=1
Ainh bipolar _
θ =1mV
Ainh bipolar _
σ =0.1
A
bipolar_ganglion
=0.25pS
k
bipolar_ganglion
=5
ganglion bipolar _
θ =1mV
ganglion bipolar _
σ =0.8
Table 1: Parameters for the simulation
27
Chapter Three: Properties of stimulus-dependent synchrony in
populations of ganglion cells
Stimulus-dependent synchrony was observed for pairs of On-Off directionally
selective (DS) ganglion cells of rabbit (Amthor et al., 2005). We wanted to know if
synchrony with the same type of stimulus dependence as in DS cells extended to other
types of cell pairs in the retina.
3.1 Correlations for constant illumination, light steps, and moving extended edges
As Fig. 3.1 illustrates, the answer to this question is positive. Figure 3.1 A is an
example of a pair comprising an On-Off DS cell and an Off brisk cell, while Figure 3.1 B
shows a pair comprising an On-brisk transient cell and an On-Off brisk cell. The figure
shows histogram plots for constant illumination (left), a full-field light-step stimulus
(middle), and for a single direction of motion of the extended edge (right). The direction
of motion for which we illustrate histograms is that which caused the extended edge to
enter both receptive fields simultaneously. As in a previous study (Amthor et al., 2005),
‘hits’ have been superimposed in black on the PSTHs. Hits are the spike occurrences in
one cell that happen within +2 ms of a spike in the other cell. (We will use the hits later
to test whether the probability that spikes are displaying synchrony is greater or smaller
than that predicted by chance.) Finally, the bottom row of each example quantifies
correlation as the normalized cross-covariogram (Eq. 2). When tested under constant
illumination, the cross-covariogram of 21 of 24 pairs showed no significant synchrony at
the 0-ms bin. This lack of correlation occurred despite both cells showing significant
28
spontaneous activity. We obtained a similar lack of fast correlation for 30 of 33 pairs
tested under the light-step full-field stimulus.
Fig 3.1: Stimulus-dependent synchrony in ganglion-cell responses. Data in [A] are from an On/Off-DS and an Off-
Brisk cell pair. Data in [B] are from an On/Off-Brisk and an On-Brisk-Transient cell pair. [A] & [B] Upper panels:
PSTHs for constant illumination (left), full-field step (middle), and moving extended edge (right) stimuli. One cell is
plotted up and the second cell is shown downward on the same temporal axis, while hits are superimposed in black (see
Materials and Methods). [A] & [B] Lower panels: Normalized cross-covariance plots for the constant illumination
(left), full-field step (middle), and moving extended edge (right) stimuli. Asterisks indicate statistical significance
using χ
2
statistics. Hits and cross-covariances show that extended edges but not full fields tend to give rise to
statistically significant synchrony.
This lack of fast correlation was despite the spike responses of the two cells being
strong and overlapping at light onset and offset. The overlap in responses generated
29
time-dependent extra-trial matches (see middle rows of Fig. 3.2 A and B – Brivanlou et
al, 1998; DeVries, 1999).
3.2 Synchrony at different time scales
Figure 3.2, illustrates the correlation elicited by stimulus- and neural-circuitry-
dependent processes. In this figure, we plot and compare the amount of intra-trial
matches, extra-trial matches, and the resultant normalized cross-covariance. We perform
this comparison for the full-field light step and the moving extended edge at 1 and 50 ms
time bins for a pair of cells. The synchrony in the extra-trials histogram is stimulus
driven and arises from the time course of the photoreceptor response (Mastronarde, 1983;
Brivanlou, 1998). In the final, normalized cross-covariogram, this synchrony was
removed by subtracting extra-trial matches from those that occurred within trials. Once
removed, few cell pairs showed significant fast correlations in response to full-field light
steps.
On the other hand, in response to a moving extended edge, all thirty-three pairs
had statistically significant peaks at the 0-ms bin of the 1-ms-bin normalized cross-
covariogram (see left-bottom histogram of Fig. 3.2 B). This synchrony was in addition to
the broad, stimulus-driven correlation in the extra-trial plots (Fig 3.2, middle rows). The
stimulus-driven correlation was very broad due to the extended histogram responses to
the moving edge (Fig 3.1). The significant 0-ms peak in the 1-ms-bin covariogram held
basically for all cell types reported to show fast synchrony by DeVries (1999). In
contrast, we found no significant peaks in the 50-ms-bin covariogram. Therefore, retinal
30
Fig 3.2: Synchrony at different time-scales. The data in this figure is for a single pair of cells for the full-field step [A]
and the moving extended edge [B]. The left and right plots show the analysis in 1- and 50-ms bin widths respectively.
The upper panels of the plots in both [A] and [B] show the intra-trial matches, the middle panels show the extra-trial
matches, and the lower panels show the normalized cross-covariance. Statistical significance is indicated by the
asterisks on the cross-covariance plots. Although the extra-trial histograms show broad time dependence, the
normalized cross-covariance shows only a statistically significant peak around 0 ms. The analysis with 50-ms bins
reveal no significant cross-covariance at long time scales.
ganglion cells did not appear to have any significant circuitry-dependent synchrony at
large time scales. (In the rest of this dissertation, we thus focus our analysis to 1-ms-bin
covariogram.) Finally, on rare occasions, we found significant correlation in random
time bins larger than 10 ms. These correlations occurred for the constant illumination,
31
full-field steps, and extended-edge motions. However, these occurrences were few and
not consistently observed for any of the three stimuli. Similar rare occurrences were also
observed in DS-cell pairs by Amthor et al, (2005). We suspect that such occurrences are
simply chance crossings of our statistical threshold for correlation. Hence, the fast,
neural-circuitry-dependent synchrony observed for pairs of ganglion cells is elicited in a
stimulus-dependent manner. In Figs. 3.1 and 3.2, such synchrony occurs almost
exclusively for moving extended edges.
3.3 Quantification of correlation indices
How strong and how significant is the synchrony across the population of cells in
response to moving extended edges? What is the dependence of synchrony on the
number of spikes generated by each stimulus? Figure 3.3 answers these questions
quantitatively for the 0-ms correlation. Figure 3.3 A shows that the numbers of spikes
elicited by the full-field step and the moving extended edge are almost identical.
Therefore, normalized correlation does not depend on the number of spikes, since
correlation is stronger for moving edges. Figure 3.3 B quantifies this advantage by
plotting correlations elicited by full fields as a function of those elicited by moving edges
for all 33 cells. Most points in this plot fall below a line of slope 1. Consequently,
higher normalized correlation values were obtained in the 0-ms bin for the moving
extended edges than for the full-field stimuli. The mean correlation index observed for
the edge was 0.054, whereas the mean correlation index for the full field was
0.012.Figure 3.3 C quantifies the advantage of moving edges further.
32
Fig 3.3: Quantification of synchrony over the population of cells. [A] Firing responses of each cell for the moving
extended edge and the full-field stimulus. The solid line is the median regression line, and the dashed line corresponds
to a slope of 1 and an intercept of 0. [B] Normalized cross covariance values for individual cell pairs for the moving
extended edge and the full-field stimulus. The dashed lines indicate a slope of 1 and an intercept of 0. [C] χ
2
values for
the test of whether the 0-ms cross-covariances are statistically significantly larger than 0. These values are shown for
all cell pairs for both stimuli. Horizontal lines of p values show statistical criteria for χ
2
. Extended edges had an
advantage over full fields in terms of 0-ms correlation but not in terms of absolute responses.
This figure plots the χ
2
values for all correlation indices (see Chapter 2 after Eq. 2) and
compares these values to lines of constant statistical significance. The χ
2
value for the 0-
ms bin was always higher for the moving extended edge. Only 3 pairs of cells showed
33
significance for the full-field stimulus with the χ
2
test at the p < 0.0002 level and only
one extra pair satisfied the p<0.001 criterion. In contrast, all the pairs except for 2
showed significance at the stringent level of p<0.0002 for the extended edges.
Furthermore, all pairs were significant at p<0.001 for this stimulus.
Thus, although the pairs of cells showed robust and approximately equal firing for
both stimuli, moving extended edges were more effective in generating correlation.
34
Chapter Four: Enhancement and suppression of synchrony
In the previous chapter, we found that some ganglion-cell pairs exhibit
statistically significant positive cross-correlation at short time lags (typically < 1 ms) for
moving or static extended edges (Figs. 3.1, 3.2, 3.3).
The positive cross-correlation is because of “hits” that are spike occurrences in
one cell that happen within +2 ms of a spike in the other cell. Even if the firing of two
cells were independent, “hits” might occur by chance. The fact that we see a positive
cross-covariance at 0 ms for extended edges indicates that they somehow enhance above
chance the probability that two cells fire together. In turn, that we see no covariance for
the full field suggests that this probability is at chance for this condition. However, as
Eq. 2 shows, demonstrating negative cross-covariance may require an impractically large
number of trials. This is because the number of times a spike in Cell 2 has a delay of ±
0.5 ms from a spike in Cell 1 is very small (Figs. 31. and 3.2). Therefore, any
suppression of correlation would involve a small number of missed “hits,” requiring a
large number of trials to prove statistically. We thus searched for an alternate, more
sensitive technique to test suppression. This technique is the analysis of hits histograms
(see Chapter 2, section 1.8). Because this analysis allows us to integrate hits in larger
bins (e.g., 20 ms), it requires much fewer trials.
An illustration of this analysis of hits histograms appears in Fig. 4.1 for two pairs
of cells, for both the full-field light step and the moving extended edge. The top panels
of Figs. 4.1 A and B are as those in Fig. 3.1. In the left bottom panels of these figures,
35
Fig 4.1: Enhancement and suppression of synchrony. [A] & [B]: Upper panels: PSTHs of two cell pairs for full-field
steps (left) and extended-edge motions (right). Hits are superimposed on the histograms as black bins. [A] & [B]:
Lower panels: Plots of the observed (black bars) and expected (white bars) hits for the full-field step (left) and the
extended moving edge (right). The bars are such that the smallest one (black or white) appears on front, so no
occlusion occurs. Asterisks denote statistically significant deviations from chance; using Poisson distribution statistics
(see Results). Extended edges and full fields tend to enhance and suppress synchrony above and below chance
respectively.
36
we plot the observed (closed bars) and the expected (open bars) hits for the full-field
stimulus. The right bottom panel shows similar data but for moving extended edges. For
both pairs of cells, we find fewer observed hits than expected for the full-field stimulus
and more than expected for the moving extended-edge stimulus. However, the
suppression of hits with full field was harder to demonstrate statistically than the
facilitation with edges. We could demonstrate facilitation of hits in all 33 of cells
studied. For example, for the two cell pairs of figure 4.1, the chance probability that the
total number of observed hits would be larger than the expected hits was smaller than
0.004 and 0.0001, respectively. We found the suppression of hits to be statistically
significant for some pairs (e.g., Fig. 8B), weak for others (e.g., Fig. 4.1 A) and some pairs
showed no statistical significance. For the data shown in the bottom left panel of
Fig 4.1 A and Fig 4.1 B , we calculated that the probabilities that the total number of
observed hits is smaller than the expected hits due to chance is less than 0.03 and 4 x 10
-
11
respectively. Of the 33 pairs studied, 17 pairs showed statistically significant
suppression of hits for full temporal integration of the data for p much smaller than
0.0001 and 8 showed for values of p between 0.01 and 0.05 , while the rest did not show
statistical significance for p<0.05 (see Chapter 2 ,section 1.8). Only twenty-one from the
above pairs showed statistically significant suppression of hits in at least one 20-ms bin,
while12 pairs showed no statistically significant effect in the 20-ms bins.
This analysis thus reveals that stimulus-dependence of synchrony arises from
both facilitation of fast correlation in some visual conditions and inhibition in others.
37
Chapter Five: Distance and directional-dependence of synchrony
DeVries (1999) found that only cells with overlapping RFs show significant
synchrony. However, he used white-noise stimuli and at least DS cells behave differently
with extended edges (Amthor et al., 2005). Therefore, we wondered whether only cells
with overlapping RFs would show correlation with our stimuli.
5.1 Distance-dependence of correlated activity
To answer this question, we used the methods described in Fig. 2.2 and Eq. 1 to
quantify distance between RFs. With these methods, a distance of 1 indicates that the
receptive fields of the cells touch each other at their border and there is no spatial
overlap. In turn, distances smaller and larger than 1 indicate the extent by which RFs do
and do not overlap, respectively. Figure 5.1 plots the results, using these distance-
estimation methods. Figure 5.1A shows a plot of the relative RF positions of a cell pair
(DS cell and a non-DS cell) (left), and the cross-covariance plots that result from the
presentation of the full-field (middle) and moving extended-edge (right) stimuli. Fig
5.1B plots the normalized cross-covariances at 0-ms time lag for the best orientation of
the moving extended edges versus the spacing between the cell pairs.
As Fig 5.1A illustrates, one may observe tight synchrony for the moving-edge
stimulus even when the RFs of the cells are non-overlapping. Figure 5.1B reveals that
this finding is common to many cell pairs. For some pairs having non-overlapping RFs,
the correlation coefficient to an extended edge is high (> 0.08). Strong synchrony was
38
present for a distance larger than 1.5 and significant synchrony was observed even at a
normalized distance of 3. However, Fig. 5.1B also shows a fall in correlation strength
Fig 5.1: Distance-dependence of synchronous activity. [A] Receptive-field plots (left) for a pair of non-overlapping
cells. Cross-covariance plots for the pair for a full-field stimulus (middle) and an extended moving edge (right). [B]
Normalized cross-covariance versus inter-cell spacing (relative to receptive-field size – see Chapter 2 , section 1.4) for
all cell pairs for the moving extended edge. Disks represent pairs showing significant synchrony for the moving
extended edge only. Triangles represent those pairs that show significant synchrony for both the full-field step and the
moving extended edge. Synchrony can occur for cells whose receptive fields are so far apart that they significantly do
not overlap.
distance similar to that previously shown by DeVries (1999). Finally, cells exhibiting
correlation for full-field stimuli tend to have RFs that are highly overlapping (triangles in
Fig. 5.1 B). No non-overlapping cells ever exhibited fast correlation for full-field stimuli
39
5.2 Directional dependence of synchrony
If the RFs of two synchronized cells do not overlap, then one should expect the
correlation to be orientation selective. This is because an extended edge would have to
be at the right orientation to stimulate both RFs simultaneously. A similar argument
shows that even if the RFs overlap but are not concentric, then the correlation should be
somewhat orientation selective. Furthermore, if one or both of the cells are DS, then so
would be the correlation. Figure 5.2 shows that these predictions on orientation and
directional selectivity of correlation hold. In Fig. 5.2 A, we plot the positions of two non-
overlapping cells (a pair of non-DS On-Off cells). We show a line joining the centers of
their RFs. The arrows are perpendicular to the line and thus, are indicative of the
directions of motion predicted to yield the highest correlations. We measured these
directions for all the pairs yielding correlation in the study. For the pair illustrated in Fig.
5.2 A, the correlation index varied as a function of direction motion as shown in
Fig. 5.2 B. The direction of motions yielding statistically significant correlation defined a
bimodal profile with peaks at 0º and 120º degrees. These peaks were similar but not
identical to the directions of motion predicted by the arrows in Fig. 5.2 A. For the
population of pairs yielding correlation, we identified pairs to be either unimodal,
bimodal, or trimodal depending on the number of statistically significant peaks in plots
like that in Fig. 5.2 B.
40
Fig 5.2: Directional dependence of synchrony. [A] Receptive-field maps of a pair of cells. The line connects the two
middles of the receptive fields, while arrows indicate directions of motion predicted to elicit maximal synchrony, since
edges would traverse the receptive fields simultaneously. [B] Cross-covariance indices for twenty-four directions of
motion for the cell pair in A. Asterisks denote those directions that have statistically significant synchrony. [C]
Distribution of the number of significant modes in graphs like in B for all synchronized cell pairs in the study. [D]
Distribution of angular differences between the modes of the bimodal pairs in C. [E] Strongest mode of plots like in B
as a function of the closest direction of motion predicted from the receptive-field maps (as in A). [F] Same as in E but
by using the second mode and the second direction predicted from the receptive-field maps. Synchrony is significant
mostly for directions of motion almost perpendicular to the line connecting the middles of the receptive-field maps.
In Fig. 5.2 C, we plot the incidence of unimodal, bimodal, and trimodal pairs.
The majority is bimodal, as predicted by an orientation selective synchrony. To test more
41
finely whether the orientation selectivity prediction holds, Fig. 5.2 D plots the
distribution of the angular differences between the two modes for all bimodal pairs.
These differences peak around 180º, as expected for orientation-selective correlations.
To refine the test further, Fig. 5.2 E plots the strongest mode of plots like that in
Fig. 5.2 B as a function of the closest direction of motion predicted from the RF maps (as
in Fig. 5.2 A). We repeat the same comparison in Fig. 5.2 F, but by using the second
mode and the second direction predicted from the RF maps. That these plots follow a
line of slope 1 and intercept 0 indicate that the geometrical arrangement of correlated
cells give rise to a predictable orientation selectivity of synchrony.
Five of the six pairs of cells giving rise to a single mode in Fig. 5.2 C were found
to contain at least one DS cell. For all pairs where at least one cell was directionally
selective, the optimal-correlation stimulus orientation did not align with the null-
preferred axis of the DS cell. However, retinal DS cells have a particularly broad
directional tuning curve (Grzywacz et al., 2007). Hence, the geometrical arrangement of
RFs should be the determining factor for the optimal orientation of synchrony involving
DS cells.
We have no explanation for why the sixth unimodal pair has only a single mode.
Further, we are not certain what mechanism might underlie trimodal pairs. Nevertheless,
for all trimodal pairs, two of the three modes are again close to those predicted by the
angle of the line joining the RF centers.
42
Chapter Six: Synchrony for static edges
So far, we have reported finding fast synchrony only in response to a moving
extended edge. We wondered whether motion was necessary for generating synchrony.
In a few experiments, we used full-field light-steps, static flashing edges, and
moving extended edges (see Chapter 2, section 1.3.1) to test and compare fast correlation.
In Fig 6.1 A, we show examples of fast correlation across these stimuli for a pair
comprising an OFF brisk-transient and an OFF sluggish ganglion cells. We plot the
PSTHs in the respective upper panels for the full-field light step, static edge, and moving
extended edge as in Fig. 3.1. One observes statistically significant peaks at the 0-ms
delay in the cross-covariogram for both the static and moving edges but not for the full-
field light-step stimulus.
The 9 pairs that were tested with these three stimuli showed 0-ms correlation for
the static edge. Of these 9 pairs, 7 showed 0-ms correlation for the moving edge. Only 1
pair showed correlation for all three stimuli, but the strength of correlation for the full-
field light step was the weakest. In Fig. 6.1 B, we plot the 0-ms static-correlation index
as a function of the same index for moving edges for all the pairs in the study. One
observes that for most pairs, the points of this plot fall above the slope-of-1 line,
indicating slightly higher correlation indices for the static edge. However, the advantage
of static edges in these data is not statistically significant.
We conclude that motion is not necessary for synchrony in the retina and that
extended static edges can cause fast correlation. Hence, if synchrony serves as code in
43
the retina, it does probably not signal motion. For the rest of this dissertation, we have
performed our analysis on moving extended edges.
Fig 6.1: Synchrony for static edges. Data in [A] are from pair comprising an Off brisk-transient and an OFF brisk-
sustained ganglion cells. The upper panels of [A] plot the PSTHs for the full-field step (left), the static edge (middle),
and the moving extended edge (right). Conventions for these panels are as in Fig. 2. The lower panels of [A] plot the
normalized cross-covariance for the three stimuli. As usual, asterisks indicate statistically significant bins. [B] The
normalized cross-covariance for the static edge is plotted against that for the moving edge for all cells in which both
these stimuli were used. The plot is on a log-log scale, with a line indicating a slope of 1 and an intercept of 0. This
plot shows that synchrony for motion is not stronger than synchrony for static edges, indicating that motion is not
necessary for synchrony.
44
Chapter Seven: Low contrast synchrony in the retina
All of the studies until now were performed with stimulus contrast near 100%.
However, natural-image statistics show that the probability of observing a contrast in a
natural image peaks at zero, and falls exponentially as a function of contrast (Balboa &
Grzywacz, 2000, 2003; Ruderman & Bialek, 1994; Zhu & Mumford, 1997). Further,
Tadmor et al. (2000) found that within an area approximately the size of a retinal GC RF,
90% of natural image contrasts were within ± 50%, with a mean contrast around 15%. It
is known that the response properties of sensory neurons are adapted to the statistical
properties of the environment to which they are exposed (Attneave, 1954; Barlow, 1961;
Laughlin, 1981). Hence, this chapter tests the hypothesis that stimulus-dependent
synchrony exists at contrasts that are more commonly observed in natural images.
7.1 Correlation at low contrast
Fig. 7.1A shows the histogram plots for a pair of OFF BT cells in response to
full-field stimulation (left) and a moving extended edge (right) for five different
contrasts. We plotted the motion histograms for an orientation that caused the edge to
enter both cells’ receptive fields simultaneously. Fig. 7.1B plots the normalized cross-
covariance for full-field stimulation (left) and a moving extended edge (right) for the
range of contrasts. We found that 11 of 14 pairs showed no significant correlation at 0
ms for full-field stimulation at any contrast (or for constant light illumination, i.e. 0%
contrast). On the other hand, we found correlation at short time lags (<1ms) for all 14
pairs when stimulated by a moving edge at contrasts above 12%. Hence, as shown before
45
(Amthor et al., 2005; Chatterjee et al., 2007), fast synchrony between pairs of ganglion
cells in the rabbit retina is stimulus dependent. Further correlation can be significant at
very low contrasts.
Fig 7.1: Low contrast synchrony in ganglion cells. Data in Figure 7.1 are from a pair of OFF BT cells. A: PSTHs for
full-field step (left) and moving extended edge (right) stimuli. One cell is plotted up and the second cell is shown
downward on the same temporal axis across 5 contrasts (0%, 12%, 25% 51% and 100%) . B: Normalized cross-
covariance plots for full-field step (left), and moving extended edge (right) stimuli. Asterisks indicate statistical
significance using χ
2
statistics.Synchrony is significant at very low contrast for the moving extended edge.
7.2 Strength of correlation at low contrast
How does the strength of stimulus-dependent correlation vary with contrast? In
Fig. 7.2, we plot the normalized cross-covariance-versus-contrast function for full-field
stimulation (left) and a moving extended edge (right) for 4 different kinds of cell-class
pairs. We consistently observe statistically significant synchrony for the moving
extended edge but not for full-field stimulation. For the pairs that are shown, we observe
a statistical significant synchrony already at 12% contrast. Above 12% the strength of
46
correlation rises with contrast. Both the saturation contrast when it happens and the slope
of the rise vary considerably across these four pairs, and across the population as a whole
(see Fig. 7.3).
Fig 7.2: Low contrast synchrony in different classes of cells: Normalized cross-covariance values across contrast for
many different trials using jackknife statistics are plotted for four different pairs for full-field stimulation (left ) and
moving extended edge (right).The four classes of pairs here are ON Brisk Transient and ON Brisk Sustained, ON
Sluggish Transient and ON Brisk Transient , ON/OFF and OFF Sluggish Transient ,ON/OFF and ON/OFF cell pairs.
The double asterisks mark statistical significance at p<0.0002 criterion, while single asterisks denote significance level
of p<0.05. We observe different trends of how the strength of correlation index changes with contrasts.
Fig. 7.3 quantifies the cross-covariance saturation value and the slope of the correlation-
versus-contrast function for the moving extended edge stimulus. We fit the data with
47
equation 5 (see chapter 2, section 1.9). The addition of the k1 and k3 terms accounts for
the saturation value of the curve, while the initial slope is determined by the ratio of the
k1 and k2 terms. The fits are excellent indication outlying the use of the parameters to
quantify population trends .Figs. 7.3 A, B and C show the fits for the correlation-versus-
contrast curve for three different pairs. Fig. 7.3 D quantifies the saturation value versus
the slope of the curve for the population. We did not plot one pair as it was fit with a
negative slope and was considered an outlier. All other pairs showed a positive slope.
Fig 7.3 : Population plot of all the pairs of cell in this study. Fig3 A ,B and C show a correlation index-versus- contrast
function curve (black) for three different pairs respectively which is fit to equation 4 (Methods) in gray. The error bars
represent the standard errors. The saturation and the value of the slope is indicated in the inset of the graphs. Fig 3D
shows the saturation values and the slopes of the fit for the population of cell. Synchrony across contrast does not
exhibit any relationship between the saturation and the rise for each of the pairs in the study.
48
The mean values for saturation and slope are 0.0615 and 0.006, respectively for
the population. At least for the cell types in this study (Fig 7.3 D), we do not see a sub-
population indicative of any specific correlation between the slope and the saturation
values. The data suggests variability across different cell classes .Additionally there is
also variability across slopes and the saturation value.
7.3 Directional dependence of correlation as a function of contrast
We showed that stimulus-dependent synchrony was also direction dependent (Fig
5.2). A moving extended edge had to be oriented so that it would stimulate both cells
simultaneously. We suggested that synchrony could code for the orientation of the edge,
at least at high contrast (~100%). Fig. 7.4A plots the correlation index as a function of
motion direction of an edge at a single contrast of 25% for a pair of cells. The directions
that yielded significant correlation defined a bimodal profile with peaks at 60 and 210
degrees. We fit equation 5 to the data to get the mode direction and estimates of the error
(represented by the half-width at half-height for each of the two peaks). Figs.7. 4B and C
show that a range of contrasts elicited roughly the same mode direction at each of the two
peaks for this pair. To quantify the behavior across all pairs we subtracted from each
curve like these in Fig 7.4 B and Fig 7.4 C it’s mean across all contrasts. The results for
all curves and for both peaks appear in Fig 7.4 D and E. Eleven of fourteen pairs were
bimodal. One of the pairs showing a bimodal peak displayed a 60 degree difference of
direction between the individual contrasts and the average contrast. That particular pair
was considered an outlier and not shown. As a result of this consideration, fig 7.4 D has
thirteen pairs and Fig 7.4E has ten pairs. The figure demonstrated that for all cell pairs,
49
motion-direction dependence varied by no more than about 40 degree over the range of
contrasts.
Fig 7.4: Directional dependence of synchrony across contrasts. Fig 4A shows the cross-covariances indices for 12
directions of motion for a cell pair in gray. The profile is fit to a von Misses function (Equation 6) in black. Fig 4B and
C plots the mean direction from the fit for the first and the second peak as a function of the contrast respectively. The
error bars are indicative of the half width half height got from the fit. Fig 4D and E shows the difference of the mode
direction for each contrast and the average direction for all the contrast for each of the peak for every pair in the
population as a function of contrasts. Synchrony shows directional dependence across all contrasts
50
Chapter Eight: Possible mechanism of synchrony
We have found significant synchrony can occur for pairs of cells that have no
overlap between their excitatory receptive-field centers (Fig. 5.1). Large-distance
synchrony argues against functional mechanisms such as gap junctions. Ganglion-cell
dendritic trees and receptive fields have roughly the same size (Amthor et al., 1989; Yang
and Masland, 1994). Therefore, large spaces between the latter eliminate the possibility
of direct gap-junction connections. One could postulate a gap-junction-linked chain of
neurons. However, because the typical cross-correlation occurs within 1 ms, spikes
would have to be generated in the in-between cell to arrive simultaneously at the recorded
ones. This in-between-cell-only hypothesis is not parsimonious. If instead, spikes were
generated in one of the cells being recorded, they would arrive with a large delay to the
other cell, splitting the correlation peak. We observe no double-peaked cross-correlation,
consistent with Brivanlou et al. (1998), who failed to see double-peaked cross-correlation
for RF distances larger than 250 µm. A final argument against gap junctions from our
data is that from RF sizes, most of our recorded neurons can be classified as alpha or
wide-field cells (Boycott & Wassle 1974; Xin and Bloomfield, 1997). The majority of
wide-field cells reported by Xin and Bloomfield (1997) show no evidence of being tracer
coupled. In turn, alpha cells have variability in their tracer coupling (Xin and
Bloomfield, 1997).
51
8.1 Retinal circuitry for synchrony
A feasible alternate explanation for the phenomenology of ganglion-cell
synchrony is the model illustrated in Fig 8.1.Imagine that an extended edge entered the
model parallel to the ganglion cells G
1
and G
2
. Such an edge would stimulate strongly
the bipolar cells (Cells B) around G
1
and G
2
because of Mach Bands due to horizontal-
cell-mediated lateral inhibition (Ratliff, 1965; Reifsnider & Tranchina, 1995; Grzywacz
& Balboa, 2002). The strong signals in the bipolar cells could then cause an excitatory
amacrine cell (Cell A
e
) to go over its threshold and generate synchrony by simultaneously
exciting G
1
and G
2
. Cell A
e
could use either spikes or the leading edge of a fast potential
to elicit a common spike in the two ganglion cells.
However, such a rapid-potential amacrine cell (A
e
) cannot be the only process
relevant for ganglion-cell synchronization. We find that moving edges enhance 0-ms
cross-covariance above chance, whereas full-field steps suppress it (Fig. 4.1). Cell A
e
can account for the facilitation but not for the suppression. The latter reflects a negative
correlation, i.e., once a spike occurs in a cell, the chance of a spike occurring in the other
cell falls. The simplest way to implement such a negative correlation is a mutual
inhibition between the circuits leading to G
1
and G
2
. This could arise by the same
mechanisms mediating surround inhibition of ganglion cells (Naka & Witkovsky, 1972;
Werblin, 1974; Werblin & Copenhagen, 1974; Mangel, 1991,.). The mutual inhibition
could happen at multiple retinal levels, but in Fig 8.1, we illustrate it between bipolar
cells through inhibitory neurons (Cells Ai1 and Ai2). Noise in the photoreceptor responses
(Minke et al.1975, Barlow et al., 1993) would break the balance in this mutual-inhibition
computation. Suppose that in Fig. 8.1, noise causes a bipolar cell’s activity to be
52
sufficiently strong to cause a spike in its output ganglion cell. Because of its strong
activity, this bipolar cell will have the tendency to inhibit the other bipolar cells through
the interneuron network. Therefore, the ganglion cells attached to these neighbor bipolar
cells will tend not to fire, leading to negative correlation.
Fig 8.1 :Amacrine-cell network model for synchrony: B represents bipolar cells, A
e
represents an excitatory amacrine
cell, A
i1
and A
i2
are inhibitory amacrine cells, and G
1
and G
2
are ganglion cells. A
e
provides synchrony through a
common input to the ganglion cells by firing fast potentials (possibly spikes). These A
e
fast potentials only occur when
bipolar cells carry large signals (e.g., when stimulated by extended edges). A
i1
and A
i2
provide the mutual-inhibition
network. When synchrony does not occur, the mutual inhibition between the circuits of cells G1 and G2 suppress
chance hits. Whichever of these circuits has the strongest signals (e.g., because of noise), it will tend to cause a spike
in its ganglion cell and to inhibit spikes in the other.
We envision A
e
and the inhibitory network to interact as follows: Outer-retina
inhibition would cause small signals to flow through all bipolar cells for full-field
luminance steps (Werblin, 1974; Thibos & Werblin, 1978; Balboa & Grzywacz, 2000;
Ichinose & Lukasiewicz, 2005). If signals larger than a threshold were required for
activation of A
e
, then this cell would be activated for extended edges but not for full
53
fields. Hence, for full-field responses, the mutual-inhibition network would cause
suppression of synchrony below chance. For contours, A
e
synchronization would
overpower the suppression of synchronization by mutual inhibition. However, although
synchronization would be different for edges and full fields, the amplitude of responses
might be similar, as in Fig. 3.3 A. This is because edges would cause stronger bipolar-
cell responses but also stronger mutual inhibition. This line of reasoning provides further
argument for the relevant mutual inhibition being after A
e
as in Fig. 8.1. Otherwise,
strong responses to edges would be offset by inhibition before reaching A
e
, possibly
preventing it from reaching threshold.
Because bipolar cells tend to be glutamatergic, and thus excitatory (Slaughter &
Miller, 1983; Massey and Miller, 1988; Li et al., 2002), the inhibitory process is likely to
be an amacrine cell instead. Many amacrine cells release GABA or glycine, and are thus
inhibitory (Ball and Brandon, 1986; Wassle et al., 1998; Zhou & Dacheux, 2004;
Vitanova et al., 2004) Consistent with our inhibitory-amacrine hypothesis; Amthor et al.,
(2005) showed that when blocking GABAergic action with picrotoxin, synchrony
emerges for stimuli that normally do not produce it.
54
Chapter Nine: Modeling the phenomenology of stimulus-specific
synchrony
In this chapter, we perform computer simulation of the amacrine-network model
proposed in chapter 8. Our goals were to try to quantitatively account for the stimulus-
dependent correlation data. We simulate a patch of retina using a 3 by 3 network of
bipolar cells, amacrine cells and ganglion cells with stimuli like those in the experiments.
The computer simulated the response by solving a set of differential equations
representing the model (Chapter 2; section1.10). In the simulation, we have considered
only the ON pathway, assuming the OFF pathway to be similar
9.1 Spatial relationship between bipolar, excitatory-amacrine, inhibitory-
amacrine and ganglion cells in the model
In this section, we illustrate the spatial relationships between the various cells in
the simulation (Fig. 9.1). For the sake of simplicity, the model uses a single class of
ganglion cells, with their receptive-field touching at the border. In the simulation, each
bipolar-cell receptive-field is positioned directly over a ganglion cell (one-to-one
correspondence). We also have considered only one type of bipolar cell in the simulation
for simplicity. As with ganglion cells, each inhibitory amacrine cell gets its input from a
single, local bipolar cell (one-to-one correspondence again). This amacrine cell makes
post-synaptic connections asymmetrically with ganglion cells that receive input from
55
other bipolar cells (connection not shown on Fig 9.1, but illustrated on Fig. 8.1). Hence,
each ganglion cell, receives inputs mainly from its four neighbor inhibitory amacrine
cells (a four-to-one convergence). Similarly, each excitatory amacrine cell gets its input
from surrounding four bipolar cells. These amacrine cells are designed to have a large
radial axonal arbor (Xin and Bloomfield, 1997, Bloomfield, 1992) modeled as a Gaussian
profile. The standard deviation of this Gaussian is large enough to provide common
input to ganglion cells up to three standard deviations away from its center. The strength
of the input to the ganglion cell is inversely proportional to the distance of the ganglion
cell from the excitatory amacrine cell.
Figure 9.1: Schematic spatial relationship between cells in the simulations. .Red, large green, and small green
circles are concentric with the receptive fields of the ganglion, bipolar, and inhibitory amacrine cells respectively. The
orange and blue circles are concentric with the receptive fields of the excitatory amacrine cells, with orange and blue
representing cells above and below spiking threshold respectively. Red, yellow, and dark-green regions represent
strongly active ganglion, bipolar, and inhibitory amacrine cells respectively. Light-green regions represent weakly
active bipolar cells. Left: Network stimulated by an edge moving upwards (gray rectangle). Right: Network stimulated
by full-field stimulation. A, B, C & D are the ganglion cells being discussed in the text.
In the left panel of Fig. 9.1, consider Ganglion cells A and B, which have a single edge
entering their receptive fields simultaneously. The bipolar cells that are closer to the edge
56
have a higher graded potential than cells that are further away from the edge. The bipolar
cells with high graded potential will tip the excitatory amacrine cell over threshold. This
cell will thus tend to produce common spikes in all the ganglion cells that fall within its
axonal arbor. In this case, synchronous responses will occur between cells A and B and
cells B and C. Cells A and C will also display synchrony, but its strength will be smaller.
Although cells A and D receive common input from the excitatory amacrine cell; there is
a delay between the activations of their respective bipolar cells. Hence, statistically
significant synchrony for this cell pair may not be seen.The right panel of Fig 9.1, is for
the full-field stimulation. The lower graded potential in the bipolar cells with full fields
does not cause the excitatory amacrine cell to go over the threshold and thus, produce
synchronous spikes.
9.2 Control
To prove the validity of the model, we first show the voltages and the
conductances for each of the components in the network for the full-field and moving
extended-edge stimulation. We want to ensure that the responses are similar to the
literature.
In Fig 9.2 A, we plot the typical intracellular voltages of the bipolar cells for
three repetitions of the full-field stimulation. These cells depolarize with increase of
luminance. The variation in the response of the bipolar cell across trials is a consequence
of the noise added to the visual input (see Chapter 2; section 1.10). The response of the
excitatory amacrine cell is shown in Fig 9.2.1 B. For the full-field stimulation, the
excitatory amacrine cell integrates the input from bipolar cells, but fails to cross the
57
threshold and to produce spikes. Fig 9.2.1 C shows the inhibitory amacrine cell voltage.
The inhibitory amacrine cell gets its input from the closest bipolar cells (see Chapter 2;
section 1.10). The conductance of the bipolar, excitatory amacrine cell and the inhibitory
amacrine cell is shown in Fig 9.2.1 D, E and F. The ganglion cell spike responses are
shown in Fig 9.2.1G.
Fig 9.2.1:Intra-cellular voltages and conductances of cells for full-field. We plot the voltages and conductances for each
of the type of cells in the model at the pre-synaptic and post –synaptic terminal for 3 repetitions of the full-field step
stimulation.
58
Similarly, the individual voltages and conductances for all the components of the
network have been shown for the moving extended edge stimulation in Fig 9.22.
The response features are roughly similar to that of Fig 9.2.1 except that the higher
graded potential in the bipolar cells caused the excitatory amacrine cell to go over
threshold and produce spikes.
Fig 9.2.2: Intra-cellular voltages and conductances of cells for moving extended edge. We plot the voltages and
conductances of each type of cells in the model at the pre-synaptic and post –synaptic terminal for 3 repetitions of
moving extended edge stimulation
59
We set the parameters of the model such that we were able to get equal firing at
the ganglion cell for both the stimuli. The model illustrated in Fig 8.1 was able to
incorporate this feature in the following way. Edges cause stronger bipolar-cell responses
but also stronger mutual inhibition (Fig 9.2.2 A and C) when compared to full-field
stimulation (Fig 9.2.1 A and C). This observation provides further argument for the
relevant mutual inhibition being after A
e
as in Fig.8. 1. Otherwise, strong responses to
edges in the bipolar cell would be offset by inhibition before reaching A
e
, possibly
preventing it from reaching threshold. Also, the higher inhibitory conductance for the
edge plays a role in producing comparable responses (spikes) at the ganglion cells for the
two stimuli.
9.3 Correlation for light step and moving extended edge
We simulated a square patch of 9 ganglion cells with full-field stimuli comprising
a step offset of 1000 ms followed by an onset of 1000 ms. A complete cycle of the
moving edge crossed three neighboring ganglion cells in 2000ms. The post-stimulus time
histogram (PSTH) for an example of 2 pairs of neighboring ganglion cells is shown in
Figure 9.23 (upper panel). The histogram of one cell is plotted upwards and the histogram
for the other cell is shown going downward for the full-field stimulation (left) and the
moving extended edge (right). Figure 9.3 (lower panel) illustrates their normalized cross-
covariance plots. Appropriately we observe no correlation around 0-ms time lag for the
full-field stimulation consistent with the experimental data. This is due to the inability of
excitatory amacrine cell to cross the threshold for the light step. In the case of moving
extended edge, statistically significant 0-ms time lag synchrony is observed.
60
Fig 9.3: Stimulus –specific synchrony in the simulation. Upper panels: PSTHs for full-field step (left), and moving
extended edge (right) stimuli from the simulation. Lower panels: Normalized cross-covariance plots for the full-field
step (left), and moving extended edge (right) stimuli from the simulation. Stimulus-dependent synchrony is observed in
the simulation.
9.4 Quantification of responses and correlation index across contrasts
The stimulus specific synchronies shown in the experiment and simulation are not
due to the difference of responses to the two types stimuli .The number of spikes
averaged over trials were similar for both stimuli for the pairs of cells considered in the
experiment. Figure 9.4A plots the comparison of the average responses for 9 pairs of cells
that were simulated by the two stimuli (full-field and moving edge) across contrasts (0 %,
20%, 40%, 60% and 80%). We observe comparable response strength for the two stimuli
which is consistent with the experiments (Fig 3.3). Figure 9.4B is a plot of the strength of
the normalized cross covariance value for the moving extended edge across contrasts. In
the simulation, we find 60% contrast to produce statistically significant correlation.
Moreover, we find a monotonic increase in the strength of synchrony with contrast, as
observed experimentally (Fig 7.2).
61
Fig 9.4: Quantification of responses and correlation indices in the simulation .A: Firing Responses of a ganglion cell for
full-field stimulation and moving extended edge in the model across contrasts. B: Normalized Cross-covariance values
across contrast for moving extended edge in the model. Response properties of the cells and the strength of correlation
across contrasts is comparable to experimental data.
9.5 Enhancement and suppression of synchrony
We reported enhancement and suppression of synchrony for the moving extended
edge and full-field stimulation respectively in chapter 4.We showed facilitation of hits for
the moving edge although it was harder to demonstrate suppression of hits for full-fields
62
statistically for about half of the pairs. We hypothesized that we would need a large
number of trials to observe suppression experimentally.
Therefore, to demonstrate enhancement and suppression of synchrony with
statistical significance becomes an important feature of the model. In Fig 9.5, we show
the effect of suppression and enhancement of synchrony for a pair of cells. We have used
the same methods as described in detail of Chapter 2, section 1.8 for the analysis.
Fig 9.5: Enhancement or suppression of synchrony in the model.
Upper panel: Cross-covariance for full-field (left) and moving extended edge (right).
Lower panel: Plot of the observed (black bars) and the expected hits (white bars) for the full-field step (left) and
the moving extended edge (right).We observe enhancement and suppression of synchrony for the moving edge and the
full-field stimuli respectively.
63
For the purpose of the simulation, we computed the response over 2000 trials. In
fig 9.5 A, we plot the normalized cross-covariance for the full-field and moving
extended edge stimulations respectively. In fig 9.5 B, left, we calculated the expected
hits and the observed hits. As in the experiment (Fig 4.1,B left),the model yielded
suppression for full-field stimulation .In contrast the model yielded enhancement of
synchrony with moving extended edges (Fig 4.1 ,B right). The suppression of synchrony
(Fig 9.5 B, left) is an effect of inhibitory amacrine cell. On the other hand, enhancement
(Fig 9.5 B, right) is a result of the common input from the excitatory amacrine cell which
produces spikes.
While the model predicts enhancement to be fast as a result of the Ae spike, the
suppression should be slow. In fig 9.5 B left the integration window to calculate
significant suppression is 6ms.We found strong suppression to persist at integration
window longer than 6 ms. To show enhancement of synchrony in fig 9.5 B right, we used
an integration window of 2 ms.This is probable because enhancement is caused from
common input from the excitatory amacrine cell which produces spikes.
9.6 Experimental predictions:
The amacrine-cell network model makes verifiable predictions, which can be tested
experimentally. We make two predictions in this section. Firstly, we want to demonstrate
the effect of the inhibition integration window on suppression. Does the suppression
become stronger with an increase in the integration window? Secondly, we ask if
correlation would hold for discontinuous edges.
64
9.6.1 Effect of integration window width to elicit suppression of synchrony
The idea about increasing the integration window to observe strong suppression
which was not always found in experimental data (chapter 4) was stumbled upon from
the simulations. The suppression of synchrony is from the unbalanced graded potential of
two inhibitory amacrine cells feeding into two separate ganglion cells .The time course of
this potential is determined by the temporal filter of the bipolar cell .In the model, the
bipolar cell will respond to the luminance for 500 ms after the onset of the stimulus. In
Fig 9.6.1, we plot the effect of increasing the integration window to evaluate suppression
of synchrony for a pairs of cells in the simulation.
Fig 9.6.1: Effect of increasing the width of integration
A: Plot of the observed (black) and expected (white) for the full-field step using a 2ms integration window.
B, C, D is similar plots using integration window of 4ms, 6,ms and 20ms respectively. Stronger suppression
was observed for a larger integration window.
65
We set the integration window to 2ms, 4ms, 6ms and 50 ms in Fig A, B, C and D
respectively. We calculate the probabilities that the total number of observed hits is
smaller than the expected hits due to chance for each of the cases (See chapter 4, for more
details). We found the probabilities to be less than 1, 0.9441, 0.0080 and 1.92e-71 for a
delay window of 2ms, 4ms, 6ms and 50 ms respectively. Strong suppression with
statistical significance is observed for a window of 6 ms and more.
9.6.2 Synchrony for discontinuous edges
So far, we have found that pairs of retinal ganglion cells show fast-ms synchrony
for extended edges/contours. In the model, the reason for the synchrony is a spiking
amacrine cell that sits between the two ganglion cells and feeds them both. Hence, the
model would predict that preventing that amacrine cell from firing should eliminate
synchrony. One way to achieve this is to occlude the moving edge between the two
recorded ganglion cells (Fig 9.6.2A – Cells A & B)) .In this case, although the two
receptive fields will be fully stimulated, synchrony would not occur. In Fig 9.6.2B, we
illustrate the relative spatial relationships between the occluder and the receptive fields of
cells in the simulations (see Section 9.1 for more details). Bipolar cells under the occluder
will not have strong graded potentials. Hence, nearby excitatory amacrine cells may not
cross spiking threshold. Consequently, synchrony will not tend to occur for ganglion
cells targeted by those amacrine cells (e.g., Ganglion Cells A and B in Fig. 9.6.2B).
We simulated the model to see if it can predict the strength of the synchrony in
the retina for discontinuous edges. In Fig 9.6.2 C, we plot the cross-covariances plots for
the pair of cell indicated by the electrodes in fig 9.6.2 A. The discontinuity in the edge
66
(left) in comparison to the continuous edge (right) caused fast-ms synchrony to disappear
for the pairs of cells in the simulations. In the next chapter, we have verified these
predictions experimentally.
Fig 9.6.2: A: Discontinuous edge stimulus in the simulation.(A & B indicate the recorded cells).
B: Schematic spatial relationship of cells in the simulation with reference to the occluder (white rectangle) and a single
edge (gray rectangle). See caption of Fig. 9.1 for figure conventions. C: Normalized cross covariance plots. Left:
Discontinuity in the edge caused 0 ms-synchrony to disappear in the model. Right: Fast-ms synchrony for a continuous
edge stimulus persists at 0-ms time lag.
67
Chapter Ten: Experimental tests for the predictions of the model
In chapter 9, we used simulations to see the effect of increasing the integration
window to observe strong suppression of synchrony (See Chapter 4, fig 4.1).We also
made predictions for continuity of edges on retinal synchrony. We found suppression of
synchrony to be stronger and easily demonstrable for larger integration window (See
Chapter 9, fig 9.5.1). We also found fast-ms synchrony to disappear for discontinuous
edges in the simulation (Fig 9.5.2 C). In this chapter, we will test each of the predictions
using physiological experiments in the retina.
10.1 Varying the integration window for suppression of synchrony
We re-ran the hit analysis to compute suppression in those 16 experimental pairs
in which we previously failed to see suppression using a 2ms integration window (see
Chapter 4). We computed suppression for 2ms, 4ms, 10ms and 100 ms window width. In
Fig 10.1 A, we plot the ratio of expected and observed hits as a function of integration
window in a log-log plot. We find that the ratio starts rising to a value greater than one as
we increase the width of the integration window. This means that the number of observed
hits gets smaller than the expected hits. In Fig 10.1B, we plot the probability that the
value of the observed is smaller than the expected due to chance as a function of the
integration window in a logarithmic plot. We find that the observed hits being less than
the expected hits due to chances starts reducing as we go beyond 10ms integration
window. For most pairs we found the chance to be less than 0.05 at earlier delays than
100ms. Suppression of observed hits starts occurring at longer delays.
68
Fig 10.1: Effect of integration window in the experiment. A: Plots the ratio of expected and observed hits
as a function of integration window (at 2ms, 4ms, 10ms and 100ms) in a log-log scale. B: Plots the
probability that observed hits is smaller than expected hits due to chance as a function of integration
window (at 2ms ,4ms 10ms and 100ms) in a log-log scale.
10.2 Correlations for continuous and discontinuous edges
We studied response synchrony between pairs of cells for non-continuous edges
in the retina. We occluded the continuity of the edge strategically such that the occlusion
fell and covered the region between the centers of the two RFs (see Chapter 2, Section
1.3.3 for details). The response synchrony to the occluded motion was compared to that
elicited by continuous edges.
69
In Fig 10.2.1, we show the effect of occlusion for a pair of Off sluggish and Off
Brisk Transient cells (Fig 10.2.1 A ),and On/Off and Off Brisk Transient cells(Fig 10.2.1
B) .The upper panels of figure 10. 2.1 A and 10.2.1 B show plots of the relative RF
positions of the cell pair and the cross-covariance plots that result from the presentation
of the continuous moving edge. As before, we obtain statistically significant synchrony at
0-ms time lags.
Fig 10.2.1: Correlation in the presence of occlusions .Presence of occlusions creating discontinuity of the edge caused
synchrony to disappear for the two pairs of cells. A &B: Upper Panel, Left: Position of RFs relative to each other.
Right: Normalized cross-covariance plots where the asterisks denote significance. A &B: Lower Panel, Left: Position
of RFs relative to the occluder. Right: Normalized cross-covariance plots showing no significant correlation.
70
In the left lower panels of Fig 10.2.1 A and B, we plot the position of the occluder
relative to the position of the RF of the cells. Here, we show those positions of the
occlusion that fall in the middle between the centers of the RF of the two cells. The
occlusions are perpendicular to the orientation of the edge that enters the RFs
simultaneously. The normalized cross-covariance plots in the presence of occlusions (Fig
10.2.1 A and B lower panels, right) do not show significant synchrony at 0 ms time lag.
In all 8 pairs tested in this manner and which showed correlation for continuous
edges, 0-ms correlation disappeared with occlusions. In Fig 10.2.2, we plot the 0-ms
correlation index for continuous and discontinuous moving edges for all the 8 pairs. We
observe that the continuous edge always showed higher correlation indices than for
discontinuity in the edge.
Fig 10.2.2: Quantification of correlation for continuous and discontinuous edges. The normalized cross-covariance
values at 0ms time lag for individual cell pairs for the continuous edge and the discontinuous edge. The values for
continuous edge are always higher than those for discontinuous edges.
71
In 3 separate pairs we found that when the occluding bars did not fall in the
middle between the RFs’ of the two cells, fast- ms correlation persisted. In Fig 10.2.3 A
(left), we plot the position of the occluding bar relative to the RFs of cells. The
normalized cross-covariance shows synchrony at 0 ms time lag (Fig 10.2.3 A, right).
However no obligatory synchrony at 0 ms time lag is observed for the full-field
stimulation for the same pair (Fig 10.2.3, B, right). Therefore, this indicates that the
occlusions have to be positioned such that the continuous edge that enters the RFs’ gets
occluded.
Fig 10.2.3: Correlation for different positions of the occluder. A, Left: Relative position of the occluder and
the RFs. Right: The normalized cross-covariance plot for the pair for moving edge stimulation. The
asterisks denote statistical significance. B, Left: Relative position of the RFs for the same pair of cells for
full-field stimulation. Right: Normalized cross-covariance plots with no significant synchrony.
72
Chapter Eleven: Conclusion
11.1 Stimulus and class-dependent synchrony
Some ganglion-cell pairs exhibit statistically significant positive cross-correlation
at short time lags (typically < 1 ms) for moving or static extended edges (Chapters 3-6
and10). However, these cells rarely do so for constant illumination or full-field
luminance steps. Hence, ganglion cells can exhibit short-time-scale correlation that is
stimulus dependent. This dependence is not influenced by the amount of firing produced
by the various stimuli (Fig. 3.3).Moreover, the stimulus-dependent synchrony occurs
within and between several classes of neurons. This extends a similar previous finding
for On-Off DS cells (Amthor et al., 2005). Other classes of neurons that exhibit such
synchrony in our study largely include pairs of brisk cells with either transient or
sustained firing. Moreover, one sees synchrony between On-Off cells and either On or
Off brisk transient, or On-Off cells (DS or not). Pairs including at least one DS cell were
seen to have the largest cross-covariance among the cell types. Of the 66 possible pairs
that were considered for analysis, most of those that failed to show significant correlation
were sluggish cells of either On, Off, or On-OFF type. The classes of cells that we find
to have significant synchrony are generally consistent with those of DeVries (1999), who
used white-noise stimuli. However, we observe some classes of cells, such as the DS
cells, display synchrony for extended contours but not for white noise (DeVries, 1999).
We found only three pairs in our population to show significant correlation for
constant illumination. This contrasts with the existing literature on correlation from
rabbits (Ackert et al., 2006), and other species like salamander (Meister et al.1996) and
73
cat (Mastronarde et al., 1983). In this literature, one often finds correlations for
stationary full-field steps and/or for constant illumination. One possibility for why we
may have failed in seeing these correlations more consistently is that we did not
specifically target adjacent cells of the same class. Only cells with high RF overlap
exhibit non-extended-edge correlations (Fig. 5.1).Another explanation is that we used a
stringent statistical criterion for detection of correlation. Some pairs showed a tendency
to have elevated correlation around 0 ms, but only a small minority satisfied our stringent
criterion of significance for full-field stimulation.
We found that static extended edges are at least as good as moving extended
edges in eliciting synchrony (Fig. 6.1). Hence, if it serves as code in the retina, synchrony
does probably not signal motion. In contrast, our data is consistent with synchrony
coding detection or localization of long edges or contours.
11.2 Rationale behind circuitry leading to stimulus-specific synchrony
We mention the possibility that A
e
could be a spiking amacrine cell for the
following two reasons: First, spiking amacrine cells have large dendritic trees (Dacey,
1989; Bloomfield, 1992; Cook & Werblin, 1994; Stafford & Dacey, 1997; Mc Neil &
Masland, 1998; Mc Neil et al., 1999) and thus could mediate synchrony over large
distances. Bipolar cells have much smaller RFs (Kolb et al., 1981; Euler et al., 1996; Wu
et al., 2000) and thus, are unlikely to cause large-distance synchrony. Second, if an
amacrine soma generates a spike, it could propagate simultaneously to various dendritic
branches, possibly exciting two ganglion cells at the same time. For synchrony, a spike is
not strictly necessary, as any fast potential may work. However, spikes have the
74
advantage of propagating over large distances without spreading in time. Spiking
amacrine cells of different kinds have been found in the retina (Barnes & Werblin, 1986;
Dacey, 1989; Stafford and Dacey, 1997; Volgyi et al., 2001).
11.3 Model simulation and its tests
We found the role of excitatory amacrine cell Ae, to be crucial in eliciting
synchrony for pairs of ganglion cells. The strength of synchrony strongly depended on
the number of spikes from Ae that feeds in as a common input to pairs of ganglion cells.
This causes strong synchrony at 0-ms time lag. As we increased the threshold such that
fewer number of spike responses occurred in Ae, the significant synchrony disappeared.
This is the case during full-field simulation when none or very few spikes in Ae were
elicited as it did not cross the threshold.
Additionally, full-field stimulation caused suppression of correlation .The
inhibitory amacrine cell that forms a mutual inhibitory network plays an important role in
causing suppression. The inhibitory amacrine cell receives input from local bipolar cells
and makes postsynaptic connections asymmetrically to ganglion cells that connect to
different bipolar cells. The non-linearity property of the synapse between the inhibitory
amacrine cell and ganglion cell helps in making the inhibition for the edge stronger than
full-field step. The strength of inhibition plays an important role in determining equal
responses for the two stimuli (full-field and edge) as in Fig 9.3.
Finally, we have observed that the amount of poisson noise plays a crucial role in
determining the variability in the response of the bipolar cell (Fig 9.1.1 A and Fig 9.1.2
A).The poisson noise is characteristic of the mean of the distribution of the image
75
intensity. Hence the value of the image intensity played an important role. As a
consequence, the variability in the bipolar cell response causes inhibition to be
unbalanced in inhibitory amacrine cells leading to suppression.
The model described in Chapter 8 proposes a new role for retinal lateral
inhibition. Horizontal cells cause lateral inhibition in the outer plexiform layer (Ratliff,
1965, for review Dowling 1987). In turn, amacrine cells can cause inhibition to bipolar
cells, ganglion cells, and other amacrine cells in the inner plexiform layer (Kishida &
Naka, 1967, Miller et al., 1977, Cadwell et al., 1978). Several different theories have
been proposed to understand the goals of lateral inhibition (Srinivasan et al., 1982, Atick
& Redlich, 1992, McCarthy & Owen, 1996, Balboa & Grzywacz, 2000). Such goals
include edge detection and localization, predictive coding, decorrelation, and
maximization of information. We suggest an additional role for lateral inhibition through
our model in Figure 8.1. Lateral inhibition could suppress correlation when a common
contour is not impinging on two ganglion cells.
11.4 Possible roles of stimulus-dependent synchrony
We previously argued (Amthor et al., 2005) that stimulus-dependent
synchrony in DS cells could help the brain begin solving the binding problem (Engel et
al., 1992a, b; Singer and Gray, 1995). Here, we extend the argument to other ganglion-
cell classes. In support of the argument, we found no or weak synchrony for
discontinuous edges when compared with continuous edges in the retina (Fig 10.1.1 and
Fig 10.1.3) in Chapter 10. The observations are similar to observations in cortical
responses (Gray et al., 1989, Engel et al., 1991c, Schwarz and Bolz, 1991). This
76
observation would suggest that the retinal synchrony might provide an initial code for
continuity, which the cortex could then use. In a potent argument against the importance
of synchrony, Nirenberg et al. (2001) showed that 90% of the information in natural
images could be obtained by treating ganglion cells as independent encoders. However,
Amthor et al. (2005) countered that the vast majority of points in a natural image fall
within the interiors of objects (or other homogeneous parts of images, e.g., the sky). Few
points, measured to be around 8% in natural images by Balboa and Grzywacz (2000), fall
on the contours of objects. Thus, the 10% of total information that synchrony carries
may be especially important (e.g., the presence or location of long contours).
Figure 5.2 suggests yet another possible role for ganglion-cell synchrony. The
synchrony between ganglion cells could help determine stimulus orientation. Correlation
is significant for directions of motion roughly perpendicular to the line joining the centers
of the RFs of the synchronized cells (Fig. 5.2). This direction dependence holds even for
cell pairs that are not orientation selective. An interesting possibility is that orientation
selective retinal synchronization is converted into a sub-cortical orientation-biased signal
that could be used by the cortex for its own orientation selectivity. This hypothesis
linking ganglion-cell synchrony to cortical orientation selectivity is consistent with data
showing that the latter has a sub-cortical origin (Hubel & Wiesel, 1962; Reid & Alonso,
1995; Ferster et al., 1996; Erwin & Miller, 1998).
Whatever the role, if synchrony serves as a retinal code then it must function at
contrast levels commonly found in natural environments (Ruderman & Bialek, 1994; Zhu
& Mumford, 1997; Tadmor et al., 2000; Balboa and Grzywacz, 2003).In Chapter 7, we
demonstrated that this is the case, by showing low contrast synchrony in the retinal
77
ganglion cells. In addition we find that correlation strength varies little with contrast,
saturates rapidly at low contrast values. Therefore, retinal synchrony is sensitive enough
to encode the presence of edges in natural scenes. Edges would be encoded in an al-or-
none fashion, i.e., present or not present, based on the existence of correlation.
11.5 Future directions of this work
Firstly, I think that one of the future directions for this study would be
investigating synchrony in the retina for natural images. Recently, several labs have
started redirecting retinal work using natural images. The natural scene is very rich and
has a vast amount of contours and edges. Hence if synchrony is a viable retinal code for
edges at least for the rabbit as indicated by this dissertation, it would have to be present
even for natural images. My lab has recently begun looking at ganglion cell responses for
natural images. The natural image space is complex and I am sure there will be many
surprising results that might support or contradict the data with artificial stimuli.
Secondly it is important to show that if synchrony is a retinal code then it should
be read out by the next levels of the visual pathway (LGN or the early parts of V1).For
example, how does spikes having sub-millisecond delay between two different ganglion
cells interact to cause a spike in the LGN. Alternatively, are the synchronous spikes in
the retinal ganglion cells read only in the early parts of V1?
From this study, we know that synchrony for edges, arises from the common
input of excitatory amacrine cells. It is important to identify the specific type excitatory
and inhibitory amacrine cell that is responsible for synchrony by doing pharmacological
studies using agonist, blockers and bio-markers in vitro.
78
Finally, if one of the functions of retinal synchrony is to code for the presence of
edges, it will be important to validate it with behavioral studies. We can use a drug that
ablates a specific type of excitatory amacrine cell that is responsible for eliciting
synchrony in the retina. We can then perform studies of mouse in a water maze where the
task would be to choose between a discontinuous and continuous edge (fig 10.1 A left ).If
the blocking of the specific amacrine cell causes synchrony to disappear then , the mouse
will not be able to differentiate between the two stimuli. Hence, the proof that synchrony
in the retina plays a role in the behavior of the mouse.
79
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Abstract (if available)
Abstract
Neighboring retinal ganglion cells often spike synchronously, but the possible function and mechanism of this synchrony is unclear. Recently, the strength of the fast correlation between On-Off directionally selective cells of the rabbit retina was shown to be stimulus dependent. Here, we extend that study, investigating stimulus-dependent correlation among multiple ganglion-cell classes, using multi-electrode recordings. The work towards this dissertation generalized those for directionally selective cells. All cell pairs exhibiting significant spike synchrony did it for an extended edge but rarely for full-field stimuli. The strength of this synchrony did not depend on the amplitude of the response and correlations could be present even when the cells' receptive fields did not overlap. We found that motion is not necessary for synchrony, i.e., it can occur with static flashes of bars. In addition, correlations tended to be orientation selective in a manner predictable by the relative positions of the receptive fields. Interestingly, extended edges and full-field stimuli produced significantly greater and smaller correlations than predicted by chance respectively. We observed synchrony for edges at contrasts as low as 10% making them viable for natural image contrast statistics. We propose an amacrine-network model for the enhancement and depression of correlation. We find that with reasonable biophysical assumptions, the simulation of the network model will exhibit stimulus-appropriate facilitation and suppression of synchrony. The model further provides verifiable predictions for the rate of fast synchrony for discontinuous edges. We have supported the predictions of the model with experimental data and found fast ms-synchrony to disappear for discontinuous edge. Such an apparently purposeful control of correlation adds evidence for retinal synchrony playing a functional role in vision.
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Asset Metadata
Creator
Chatterjee, Susmita
(author)
Core Title
Dependence of rabbit retinal synchrony on visual stimulation parameters
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
07/02/2008
Defense Date
05/12/2008
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
amacrine-cell network,ganglion cells,OAI-PMH Harvest,rabbit-retina,stimulus-dependent,synchrony
Language
English
Advisor
Grzywacz, Norberto M. (
committee chair
), D'Argenio, David (
committee member
), Hirsch, Judith A. (
committee member
), Mel, Bartlett W. (
committee member
), Merwine, David K. (
committee member
), Weiland, James D. (
committee member
)
Creator Email
susmitac@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1313
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UC1134727
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etd-Chatterjee-20080702 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-80753 (legacy record id),usctheses-m1313 (legacy record id)
Legacy Identifier
etd-Chatterjee-20080702.pdf
Dmrecord
80753
Document Type
Dissertation
Rights
Chatterjee, Susmita
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
amacrine-cell network
ganglion cells
rabbit-retina
stimulus-dependent
synchrony