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Computational investigation of cholinergic modulation of the hippocampus and directional encoding of touch in somatosensory cortex

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Computational investigation of cholinergic modulation of the hippocampus and directional encoding of touch in somatosensory cortex

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Content Computational Investigation of Cholinergic Modulation of the Hippocampus and Directional
Encoding of Touch in Somatosensory Cortex
by
Adam Mergenthal
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
August 2024
Copyright 2024 Adam Mergenthal

Dedication
To my Mother, Father, Sister, and all of the other people in my life who have blessed me with unwavering
support. Your patience and love has always been appreciated.
ii

Acknowledgements
I would like to acknowledge the following people who have made professional contributions to the completion of this work:
– Dr Jean-Marie Bouteiller and Dr Theodore Berger for guiding and supporting my work.
– The members of the Berger lab who have provided years of both professional advice and friendship.
– Dr Andrew Hires for guidance and insight while I worked through the analysis in Chapter 3. Dr
Jonathan Cheung, Dr Phillip Maire, Dr Samson King, and the other members of the Hires lab who
were involved in the recording of the experimental data analyzed in Chapter 3 of this document.
– Dr Allen Gulledge for providing cell recordings which were used in calibrating the model found in
Chapter 2 of this document.
iii

Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Cholinergic Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Sources of Cholinergic Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Receptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Whisking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Whisker organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Vibrissa structure and mechanoreceptors . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Pathways to the S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.4 Location Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 2: A Computational Model of the Cholinergic Modulation of CA1 Pyramidal Cell Activity 7
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Calibrating the endoplasmic reticulum . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Calibrating intracellular calcium and indicator model . . . . . . . . . . . . . . . . . 16
2.3.3 Calibrating calcium release and spike acceleration . . . . . . . . . . . . . . . . . . 19
2.3.4 Depolarization activated calcium store replenishment . . . . . . . . . . . . . . . . 25
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Acetylcholine and cell excitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 Intracellular calcium release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.1 Novel additions to CA1 compartmental model . . . . . . . . . . . . . . . . . . . . . 37
2.5.2 Predictions from model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.3 Refining model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.4 Future uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
iv

Chapter 3: Encoding of Whisker Touch Direction in Layer 5 of Somatosensory cortex . . . . . . . 43
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Experimental model and subject details . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Animal Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.3 Behavior, videography, and electrophysiology . . . . . . . . . . . . . . . . . . . . . 46
3.3.4 In vivo loose-seal juxtacellular recordings . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.5 Quantification and statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.5.1 Touch-response window . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.5.2 Tuning curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.5.3 Directional selectivity of responses . . . . . . . . . . . . . . . . . . . . . 49
3.3.5.4 Pre-touch velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.5.5 Location and directional preference . . . . . . . . . . . . . . . . . . . . . 51
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter 4: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
A Additional Cholinergic Model Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
B Cholinergic Model Parameters and Reaction Equations . . . . . . . . . . . . . . . . . . . . 83
C Additional Whisker Analysis Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
v

List of Tables
B.1 Table of mechanism initial concentrations. † initial value varies with the ratio of section
volume to section surface area. * value is nonzero only for experiments requiring a
simulated fluorescence signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
B.2 Table of mechanism kinetic parameters, conductances, and diffusion, with their respective
sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
vi

List of Figures
2.1 Mechanisms of CA1 pyramidal cell modulation by M1 MAChRs. A) Flowchart description
of the steps between M1 activation and modulated membrane potential. B) Illustrated stages
of activation: Left Before activation the cell is at rest with Kv7 channels open. Center M1
activation leads to hydrolysis of PIP2 from cell membrane (inhibiting Kv7 channels) and the
release of intracellular Ca2+ (activating SK channels) through the generation of IP3. Right
As Ca2+ is extruded from the intracellular space SK channels close while Kv7 channels
remain closed. C) Membrane potential at different stages of activation. D) Intracellular
calcium levels at different stages of activation. . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 A) Visualization of mechanisms included in expanded CA1 pyramidal cell calcium
model. B) Results of tuning model mechanisms that replenish calcium stores in the
endoplasmic reticulum without action potentials. Plotted value is simulated calcium stored
in endoplasmic reticulum over time (x-axis=50 sec, y-axis=50 µM). Target data is based
on experiments in [61]. C) Results of tuning model mechanisms that determine calcium
dynamics following an action potential. Plotted value is the percent change in fluorescence
of a simulated calcium indicator (OGB-1) over time (Scale: x-axis=1 sec, y-axis=10% change
in fluorescence). Target data is based on results from [62] . . . . . . . . . . . . . . . . . . . 13
2.3 Comparison of dynamics after a simulated 50 msec 100 µM ACh pulse. A) Activated
PLC dynamics using original parameter values from [74] (red dash) to recalibrated
parameter values used in final model (black solid). B) IP3 dynamics using either the original
parameters (red dash), increased PLC activation parameters (blue dash- dot), or increased
PLC activation parameters along with increased hydrolysis rate (k
P LC) (black solid) C)
PIP2 dynamics using either using either the original parameters (red dash), increased PLC
activation parameters (blue dash-dot), increased PLC activation parameters along with
increased hydrolysis rate (k
P LC) (grey dot), or all increased parameters including those
that drive synthesis of PIP2 (black solid). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 A) Experimental recording of CA1 pyramidal cell responding to a 40 msec pulse of 100 µM
while driven to spiking. B) Model response to 50 msec pulse of 100 µM ACh while cell
is driven to regular spiking. C) Comparison of instantaneous firing rate of experimental
response and model response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
vii

2.5 Simulated response to phasic (50 msec) exposure at varying concentrations of acetylcholine.
A) Cell membrane potential with no other stimulation besides acetylcholine pulse. B)
Simulated intracellular calcium release. C) Peak hyperpolarization and depolarization
values at different concentrations of acetylcholine. D) The peak intracellular calcium
concentration following acetylcholine pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 Simulated response to phasic (50 msec) exposure of varying concentrations of acetylcholine.
A) Cell injected with a current amplitude such that it spikes at a steady rate of 10 Hz.
Current injection is present throughout simulation B) Repeat of experiment with the
addition of a 100 µM acetylcholine pulse that starts at t = 1 second and lasts for the duration
of the simulation. C) Instantaneous firing rate over time for different concentrations of
ACh. This rate is the inverse of the inter spike interval. D) The peak spike acceleration
increased with higher concentrations of ACh. E) The duration of the pause in spiking
versus the concentration of ACh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.7 A) Time series of intracellular calcium concentration after phasic (50 msec) exposure to
ACh. B) Peak cytosol calcium versus the concentration of the phasic ACh pulse. . . . . . . 31
2.8 Measuring reduction in rheobase due to tonic acetylcholine exposure. A) A 200 msec
current pulse of varying amplitude is applied at a time sufficiently after the start of a
simulated acetylcholine exposure such that the system is at steady state. A binary search
was performed to find the minimum current injection amplitude which would generate an
action potential. B) Cell rheobase decreases with increased concentration of acetylcholine. 32
2.9 Increasing the concentration of tonic acetylcholine increases the input resistance of the cell
model as measured at the soma. Input resistance was measured by performing a series of
somatic current injections and then performing linear regression on the relation between
membrane depolarization to current amplitude. The values plotted are the slopes of the
estimated linear functions. The current amplitudes used were 0, -100, and 100 pA. . . . . . 32
2.10 Measuring depolarization and hyperpolarization after tonic (60 second) exposure to
acetylcholine. A) Simulated response of somatic membrane potential to different
concentrations. B) Amplitude of steady depolarization and temporary hyperpolarization
versus acetylcholine concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.11 Increasing the concentration of tonic acetylcholine increases spike rate for a given injected
current amplitude. A) Cell injected with a current amplitude such that it spikes at a steady
rate of 10 Hz. Current injection is present throughout simulation. B) Repeat of experiment
with the addition of a 100 µM acetylcholine pulse that starts at t = 1 second and lasts for the
duration of the simulation. C) The maximum spike frequency acceleration vs acetylcholine
concentration. Spike frequency acceleration was measured as the percent increase from the
rate before acetylcholine exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.12 Acetylcholine leads to the release of intracellular calcium. All sections in the apical
trunk and soma were simultaneously exposed to a 50 msec pulse of 100 µM ACh. A)
Simulated time course of intracellular calcium after acetylcholine exposure. More distal
sections achieve higher concentrations more rapidly than somatic sections. B) Display of
concentrations in all model compartments at different time steps throughout calcium wave. 36
viii

3.1 A) Illustration of the touch discrimination task. B) Example trial showing variables of
interest and examples of a protracting and a retracting touch event. C) Post stimulus
time histogram showing each cell’s mean firing when aligned by time from touch. Cells
have been grouped by their response type (i.e. excited, unaffected, or inhibited) with
touch excited cells grouped at the top and touch inhibited cells shown at the bottom. D)
Percentage of recorded Layer 5 pyramidal cells demonstrating touch response types. E)
Distribution across touch- modulated (excited or inhibited) cells of the mean addition
spikes seen after touch. A negative value suggests the cell is inhibited by touch. The dotted
line indicates the mean additional spikes (0.38 spikes/touch) seen across the population
of the recorded touch modulated cells. F) Distribution across touch excited cells of mean
latency from touch to measurably increased activity. G) Distribution of mean duration of
touch excited cells’ increased activity after touch. . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 A) Spike raster plots of cells demonstrating strong retraction selectivity (top), strong
protraction selectivity (bottom), and no directional preference (center). The spiking
activity are aligned by the time of touch at t=0 and sorted by the pre-touch velocity
with the most negative (fastest retraction) at the bottom. B) Mean touch response (mean
spike rate in response window) split into three ranges of pre-touch speed. Ranges were
chosen such that the distribution of pre-touch speed across all recorded touches would
be equally divided into 3 populations. Cells are the same as those shown in A. C) Mean
additional spikes after touch split by direction for significantly touch modulated cells.
Filled points had a significant directional preference based on a Wilcoxon rank sum
test. D) Normalized distribution of relative direction modulation indices compared to a
bootstrapped shuffle (mean of distribution, black dotted line, mean of bootstrapped shuffle,
gray dashed line). Negative values suggest a bias to retraction, while positive values suggest
bias to protraction. E) Normalized touch responses vs pre-touch whisker speed for all touch
modulated cells. Each cell’s values were normalized by that cell’s maximum response rate
in either direction. Dark lines show the mean of the normalized values within each speed
bin for each direction F) Distribution of the mean differences between each cell’s speed bin
values. A negative value suggests a bias towards retraction while a positive value suggests
a bias towards protraction (mean of distribution, black dotted line, mean of bootstrapped
shuffle, gray dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
ix

3.3 A) Cell firing rate plotted against touch location for cells showing significant location
tuning. B) Preferred location (Location bin with maximum firing rate) versus relative
direction modulation index for cells demonstrating location tuning. The blue shaded
region shows cells with stronger responses to retracting touches (rdmi value < 0.0) while
the orange region shows cells with stronger responses to protracting touches (rdmi >
0.0). The population’s mean rdmi value is shown as a dotted line demonstrating a bias
towards protraction. C) Distribution of preferred touch locations. The distribution of
protraction- preferring cells (rdmi > 0.0) is shown in orange, while the distribution for
retraction- preferring cells (rdmi < 0.0) is shown in blue. D) Distribution of the median
whisker location during whisking. E) Mean pre-touch velocity sorted by location for
all (top), protracting (middle), and retracting (bottom) touches for each cell in A. The
column labeled “mean” shows the mean value across the population in each level. F) The
proportion of all touches that are protracting versus the location. G) Relative direction
modulation index versus touch location. Cells have been split into three groups based on
the value of the mean direction modulation index across sampled locations (mldmi) (top
mldmi > 0.1, middle |mldmi| < 0.1, bottom mldmi < -0.1) While most cells demonstrate
consistent directional preference across locations, some cells have distinct ranges where a
particular each direction generates a stronger response. H) Scatter of preferred location
across all touches versus mean location directional modulation index. The white space
shows -0.1 < mldmi < 0.1. Gray dotted line shows population mean, demonstrating a bias
towards protraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 A) Cell firing rate plotted against touch location for all touches (top), only protracting
touches (middle), and only retracting touches (bottom). Firing rate has been normalized
by the maximum rate within each column of each subplot. B) Example plots of directional
location tuning curves for cells that demonstrate high correlation (left plots) and
anticorrelation (right plots). Shaded regions in upper plots show the 95% confidence
interval. C) Distribution of correlation between directional location curves for cells shown
in A along with a distribution generated by bootstrapped shuffle. D) Comparison of cells’
preferred locations. Separate histograms show the distributions of the preferred locations
for cells that show significant location tuning in only one direction. The scatter plots the
preferred location for each directional tuning curve for cells with significant location
tuning in both directions. E) Distribution of the correlations between directional location
tuning curves for cells that have significant tuning in both directions (scatter plot of D)
plotted against a distribution generated by a bootstrapped shuffle. . . . . . . . . . . . . . . 58
A.1 Visualization of compartmental model with expanded calcium dynamics. . . . . . . . . . . 79
A.2 A) Schematic representation of M1 receptor model including the mechanisms for the G
protein cascade, PIP2 synthesis, and IP3 breakdown. The number next to each reaction
is the entry in B.2 in which the reaction kinetic parameters can be found. B) Schematic
representation of IP3R model used in model. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
A.3 Comparison of concentration responses with original oxotremorine-m parameters in blue
and new acetylcholine responses in green. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
x

A.4 The inclusion of the SOCE mechanism allows for the rapid refilling of lumenal calcium if
the cell is depolarized. A) A cell will be unable to repeatedly release intracellular calcium
if it remains at near resting membrane potentials, but B) can perform repeated release if
driven to spike. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
C.1 A) Spike raster plots of cells demonstrating strong retraction selectivity (top), strong
protraction selectivity (bottom), and no directional preference (center). Figures in the left
column show only the first touch within each trial. Figures on the right show all trials. The
range of pre-touch time plotted in these figures has been extended from 25 ms to 100 ms to
aid in understanding the cause of pre-touch directional selectivity seen in Figure 3.2A. The
spiking activity has been aligned by the time of touch at t=0 and sorted by the pre-touch
velocity with most negative (fastest retraction) at the bottom. . . . . . . . . . . . . . . . . 92
C.2 Mean pre-touch velocity versus location. The three figures on the top middle demonstrate
the mean velocity vs location for protraction preferring cells while cells with no direction
preference and retraction preference are respectively shown in the bottom left and bottom
right. For each group of the three the top subplot shows mean velocity for all touches,
the middle subplot shows the mean velocity for protracting touches, while the bottom
subplot shows the mean velocity for retracting touches. Areas shown in white do not have
recordings of that cell’s response to touches in that location and direction. . . . . . . . . . 93
C.3 Touch location tuned cells split by directional preference. Cells were sorted based on the
mean location direction modulation index where values above zero indicate cells that on
average have higher firing rates in responses to protracting touches across all measured
locations and values less than zero indicate cells that have on average higher firing rates in
response to retracting touches across all measured locations. . . . . . . . . . . . . . . . . . 93
C.4 A) Population distribution of touches vs touch phase and touch location. B) Population
distribution of touches vs pre-touch velocity and touch location. . . . . . . . . . . . . . . . 94
xi

Abstract
Pyramidal cells are a diverse class of excitatory neurons that are the main sources for non-local axonal
projections from the neocortex and hippocampus. The pyramidal cells of the CA1 region in the hippocampus
and thick tufted Layer 5 pyramidal cells in the cortex share several characteristics that suggest the nature
of the input-output transformation they perform from incoming synaptic activity to generation of action
potentials would operate under similar principles. This work seeks to develop a deeper understanding of
these cell types in two ways. First we calibrated a mechanistic computational model of CA1 pyramidal
cells to replicate experimental observations of their modulation by acetylcholine. This model combined
biochemical cascades of intracellular events activated by cholinergic input to accurately replicate the
experimentally observed changes in the electrophysiological properties of the cell. This work resulted
in a novel CA1 pyramidal cell model expanded through the explicit modeling of cholinergic-dependent
molecular interactions involved in healthy cognitive function and disease. Through this expanded model,
we come closer to simulating these diseases and gaining the knowledge required to develop novel treatments
targeting the cholinergic pathway. The second portion of this work analyzed experimental recordings from
layer 5 pyramidal cells (L5) in the barrel cortices of head-fixed mice while these animals performed a task
that required determining whisker location during touch. This analysis built on prior work demonstrating
the ability of L5 cells to encode a target’s location along the anteroposterior axis following touch. The
presented analysis found that a cell’s touch location encoding was significantly correlated across directions,
xii

but that individual cells demonstrated a variable amount of preference for a particular direction. From these
results we go on to suggest experimentally testable hypotheses for the origin of this directional preference.
xiii

Chapter 1
Introduction
The following chapters focus on two disparate efforts to further understanding of the function of pyramidal
cells in the brain. Chapter 2 details the development and calibration of a mechanistically detailed computational model of a portion of the way cholinergic modulation alters the behavior of CA1 hippocampal
pyramidal cells. Chapter 3 describes the results of an analysis of cell recordings from Layer 5 pyramidal
cells in the barrel cortex of mice. This analysis explores how the direction of whisker motion is coupled
with the cells’ encodings of a target object’s location following whisker contact. Despite the cell types
explored in these efforts being in structurally and functionally very different regions of the brain, both are
subject to cholinergic modulation [1, 2, 3] and demonstrate dendritic spiking in the apical tuft [4, 5]. Due to
these shared characteristics, understanding aspects of each cell type can inform about the other and lead
to insights about the direction of further research. To aid the reader in understanding these efforts, brief
summaries of relevant background information have been provided.
1.1 Cholinergic Modulation
The neurotransmitter acetylcholine (ACh) is critical for a number of cognitive functions. However, despite
acetylcholine being a subject of study for decades, there still remains a holistic understanding in how the
various mechanisms of cholinergic modulation are meant to functionally alter the targeted cell networks.
1

1.1.1 Sources of Cholinergic Projections
While cholinergic cells are present in several regions of the brain, the primary source for cholinergic
projections to neocortex and hippocampus is the basal forebrain[6, 7, 8]. 3D reconstructions of cholinergic
projections originating in the medial septum (MS) and diagonal band (DB) (two basal forebrain nuclei)
showed projections to cortical, subcortical, and hippocampal regions [8]. Local cholinergic cells were also
present in the somatosensory cortex and other cortical regions [8].
1.1.2 Receptors
Cholinergic receptors are divided into two classes, nicotinic and muscarinic. Nicotinic acetylcholine
receptors (nAChRs) are so named due to nicotine being an agonist. These receptors are pentameric with
either homomeric or heteromeric combinations of subunits. All nAChRs are ionotropic, selective for cations,
with varying levels of calcium permeability depending on each subtype’s subunit composition cite. There
are 5 types of muscarinic acetylcholine receptors (mAChRs) designated M1-M5. The M1, M3, and M5
mAChRs are metabotropic receptors coupled to Gαq/11 proteins. The activation of the associated cascade
allows these mAChRs to interact with a variety of intracellular mechanisms [9, 10]. The M2 and M4 mAChRs
are coupled to Gαi/o proteins leading to their activation triggering a completely different reaction cascade.
1.1.3 Modulation
Cholinergic neuromodulation of excitatory cell activity can be summarized as acting through a few methods.
The most direct is the activation of nAChRs on the postsynaptic side of glutamatergic synapses. This
leads to enhanced synaptic activation and can alter spike timing dependent plasticity [11, 12]. M1 mAChR
activation and the resulting cascade alters the behavior of a variety of different voltage gated ion channels,
resulting in greater excitability of the dendritic compartments within which activated receptors are present
[3, 13, 14]. Additionally, as M1 activation can lead to the release of calcium, a secondary messenger involved
2

in a variety of intracellular mechanisms, it can trigger a variety of mechanisms related to plasticity. M2 and
M4 mAChRs have been found in presynaptic terminals, and their activation have been associated with the
inhibition of neurotransmitter from those terminals [15, 3]. Finally several subtypes of nAChRs have been
found in interneurons [16, 17]. Activation of these receptors can lead to shifting levels of inhibition across
an excitatory cell’s dendritic arbor as locations are newly inhibited or disinhibited.
This variety of effects on the level of both the individual and cell networks leads to difficulty in
untangling what role cholinergic modulation plays in each network’s healthy functioning. The work
discussed in Chapter 2 seeks to provide a basis from which to model these varying effects and explore how
the interactions and dysfunctions of the various mechanisms alter a neuron cell network’s behavior.
1.2 Whisking
The analysis found in Chapter 3 expands current understanding of the way that a whisker’s movements
and interactions with objects are encoded and transformed into a perception of the animal’s environment.
The dataset analyzed in that chapter is made up of recordings from the primary somatosensory cortex
(S1). This is a higher order brain region, so the signal from the primary sensory neurons (PSNs) has passed
through several stages of processing before it reaches the cells in the S1. What follows is a summary of the
current understanding concerning the whisking somatosensation, so the reader can better understand the
nature of that work.
1.2.1 Whisker organization
While the recordings analyzed in Chapter 3 were done in the S1 of mice, rats and mice are both used in
experiments exploring whisker somatosensation. Both species typically have 30 whiskers or macrovibrissae
per side of the face. Many mammal species have macrovibrissae and how they are arranged in the mystacial
pad varies from species to species [18]. However, the rat and the mouse have largely similar arrangements
3

[19, 18]. Except for the four most caudal vibrissae, the vibrissae are organized into five easily defined rows.
Each vibrissa in these rows is labeled by a letter signifying the row (A being the most dorsal row, E being
the most ventral) and number (with 1 at the most caudal position in the row and increasing in value moving
rostrally). The four most caudal vibrissae don’t align neatly with the rows, and when labeling them the
conventions are to either use greek letters (from most dorsal to most ventral α, β, γ, andδ) with numbers
only used for the rows, or to include each whisker as a member of a row and start the numbering there.
Regardless of the labeling convention used, it is important to understand that in the S1 each vibrissa has a
dedicated region, or barrel, and these barrels are arranged such that they replicate the spatial relationships
of the vibrissae in the mystacial pad [20]. This has led to the portion of the S1 involved with whisking to be
labeled the barrel cortex.
Whisking is driven by the antiphasic activation of two groups of muscles [21]. The intrinsic muscles are
described as running around the follicle root like a "sling" [22]. Contraction of the intrinsic muscles causes
the follicle to pivot at the point it passes through the skin such that these contractions cause the follicle to
protract forward. The extrinsic muscles run just below the skin and their contractions are responsible for the
retraction of the vibrissae. Motor signal is brought to these muscles by the facial motor nerve. An interesting
aspect of the musculature of the mystacial pad is that the receptors associated with proprioception in other
muscles (spindles and intrafusal fibers) are only found at extremely low densities [23]. This low density
seemingly means that the state of muscle contraction is not used in the encoding of the positioning of the
whisker. Instead, whisking somatosensation relies on a different set of mechanoreceptors.
1.2.2 Vibrissa structure and mechanoreceptors
whisking has been shown to be an incredibly sensitive tactile sensory modality [24, 25, 26]. The mechanoreceptors that encode the forces of the whisker’s interactions with objects and surfaces are located at the
base of the follicle. Before discussing these mechanoreceptors, it should be mentioned that the follicle
4

itself is structured to improve tactile sensitivity as the curve and taper of the follicle allows interactions at
different distances along the whisker (arclengths) to be transmitted to the mechanorecepters as distinct
combinations of forces [27]. These mechanoreceptors come in two classes, Merkel endings and lanceolate
endings. Merkel endings surround the base of the follicle in two locations, the ring sinus and the rete-ridge
collar. The distribution of the Merkel endings at these locations allows them to be sensitive to bending
moments and lateral forces that the whisker experiences, while the lanceolate endings are more responsive
to the axial forces [28, 29]. The activation of these mechanoreceptors is transmitted by their associated
afferents to neurons in the trigeminal ganglion.
1.2.3 Pathways to the S1
Each vibrissae receives around 100-200 axons originating from PSNs in the trigeminal ganglion [30]. At this
level, the PSNs are primarily sensitive to a single vibrissa but can integrate information from its primary
vibrissa’s neighbor and can encode a angular selectivity [31, 32, 29]. Additionally, these cells are capable of
high spike-timing precision [33].
The activity of the PSNs in the trigeminal ganglion then project into at least three parallel pathways
that all eventually reach the S1. While other pathways have been suggested, the main three have been
labeled the lemniscal, paralemniscal, and extralemniscal pathways. The lemniscal pathway goes from the
trigeminal nucleus principalis (PrV) in the brainstem to the dorsomedial ventral posteromedial nucleus
(VPMdm) of the thalamus [34, 35]. The cells in this pathways encode the phase of whisking, but also reliably
encoding the timing of touch [23, 36]. Projections from the VPMdm target Layer 1 and Layer 4 of the barrel
cortex. The paralemniscal pathway runs from the spinal trigeminal nucleus (SpV) through the posterior
medial nucleus of the thalamus (POm) [34, 35]. The cells in this pathway encode whisking activity, but at
lower firing rates than that in the VPMdm [23, 36]. The extralemniscal pathway runs from the interpolaris
(SpVi) to the ventrolateral sector of the VPM (VPMvl) [37]. These cells encode touch properties.
5

1.2.4 Location Tuning
There is no stage along the pathways through which re-afferent signals reach the somatosensory cortex
that seems to encode the location of touch relative to the animal. That tactile encoding does appear in the
Layer 5 pyramidal cells of the barrel cortex, however [38]. This raises the question of how this location
encoding is arising. Is bottom up information sufficient to drive this encoding in the S1? Layer 5 pyramidal
cells also receive top down signals from the motor cortex [39] which has been shown to enhance L5 cell
dendritic activity during active whisking [5]. How L5 cells transform these signals to produce a perception
of touch location is not fully understood. The work described in 3 was done to explore how these aspects
of touch may be interacting to produce this location tuning.
6

Chapter 2
A Computational Model of the Cholinergic Modulation of CA1 Pyramidal
Cell Activity
2.1 Abstract
Dysfunction in cholinergic modulation has been linked to a variety of cognitive disorders including
Alzheimer’s disease. The important role of this neurotransmitter has been explored in a variety of experiments, yet many questions remain unanswered about the contribution of cholinergic modulation to
healthy hippocampal function. To address this question, we have developed a model of CA1 pyramidal
neuron that takes into consideration muscarinic receptor activation in response to changes in extracellular
concentration of acetylcholine and its effects on cellular excitability and downstream intracellular calcium
dynamics. This model incorporates a variety of molecular agents to accurately simulate several processes
heretofore ignored in computational modeling of CA1 pyramidal neurons. These processes include the
inhibition of ionic channels by phospholipid depletion along with the release of calcium from intracellular
stores (i.e. the endoplasmic reticulum). This paper describes the model and the methods used to calibrate its
behavior to match experimental results. The result of this work is a compartmental model with calibrated
mechanisms for simulating the intracellular calcium dynamics of CA1 pyramidal cells with a focus on
those related to release from calcium stores in the endoplasmic reticulum. From this model we also make
7

various predictions for how the inhibitory and excitatory responses to cholinergic modulation vary with
agonist concentration. This model expands the capabilities of CA1 pyramidal cell models through the
explicit modeling of molecular interactions involved in healthy cognitive function and disease. Through
this expanded model we come closer to simulating these diseases and gaining the knowledge required to
develop novel treatments.
2.2 Introduction
Acetylcholine (ACh) directly modulates the activity of neurons within every subregion of the hippocampus,
including both principal neurons and interneurons [40, 41]. The dense distribution of the cholinergic
terminals within the hippocampus suggests that this neurotransmitter plays an important role in healthy
hippocampal functioning. This important role is further evidenced by the correlation of dysfunctions
reported in cholinergic terminals with cognitive impairment. The progression of Alzheimer’s disease
(AD) has long been associated with the decline of cholinergic markers in the hippocampus [42]. Other
cognitive disorders such as depression and schizophrenia are also associated with alterations in cholinergic
disregulation [43]. On an even broader scale, changes in cholinergic expression are associated with the
cognitive decline due to advanced age [42]. The variety of cognitive dysfunctions related to ACh suggests
that it plays not only an important, but a complex role. In a two-year double-blind study, 35% of patients
taking an acetylcholinesterase inhibitor to slow cognitive decline due to AD had a recurrence of major
depressive episodes vs 19% of those on a placebo [44]. In other words, a drug meant to counteract one
form of cholinergic dysfunction exacerbated a separate form of cholinergic dysfunction. Developing better
treatments for these disorders requires a better understanding of the dynamics of healthy cholinergic
modulation.
Currently, ACh is understood to play a role in a variety of cognitive processes. We will summarize
some of these effects briefly but for fuller reviews, see [45, 46]. Acetylcholine has long been understood to
8

be involved in the generation of theta oscillations (4-12 Hz) in the hippocampus. Theta oscillations are
theorized to organize memory encoding and retrieval into distinct phases [47]. Acetylcholine seems to
be involved with the generation of the lower frequency portion of theta oscillations, as these frequencies
can be blocked by the cholinergic receptor antagonist atropine [48]. On a behavioral level, the blockade
of cholinergic receptors in animal models leads to a variety of memory deficits involving both spatial
navigation and the acquisition of conditioned fear responses [45, 49]. These effects result from the activation
of a variety of cholinergic receptors in the hippocampus. These receptors can be sorted into two types.
The first type, nicotinic receptors, act as ionotropic receptors and allow the passage of ions through the
plasma membrane. In the CA1, nicotinic receptors primarily modulate interneuron activity [50], but they
also appear in low densities on pyramidal cells [51]. The second type, muscarinic receptors, have a much
larger effect in modulating CA1 pyramidal cell activity [3]. These receptors are G protein coupled receptors
with their activation setting off a cascade of intracellular reactions. Among the five subtypes of muscarinic
acetylcholine receptors (mAChRs), the subtypes that primarily modulate CA1 pyramidal activity are the
M1 and M4 mAChRs. M4 mAChRs suppress glutamatergic release from excitatory synapses originating
from the CA3 subregion [3]. M1 mAChRs are present throughout the cell’s morphology and alter its overall
excitability along with altering the intracellular calcium dynamics [3]. Thus the M1 mAChRs are responsible
for the majority of the cholinergic response in this cell type.
The M1 mAChR, as a G-protein coupled receptor, activates a cascade of intracellular reactions [9, 10].
It is through these reactions that the M1 receptor is able to modulate the behavior of a variety of ion
channels. Teithehe M-current was given that name due to muscarinic receptors suppressing its activity
[52]. Inhibition of this current in CA1 pyramidal cells through bath application of the M-current antagonist
XE991 lead to a depolarized resting membrane potential and increased spiking activity [53]. This current
was also shown to be inhibited after bath application of the muscarinic agonist Oxotremorine-M (Oxo-M)
[54]. The channels responsible for the M-current, Kv7 Potassium channels, require phosphatidylinositol
9

Figure 2.1: Mechanisms of CA1 pyramidal cell modulation by M1 MAChRs. A) Flowchart description of the
steps between M1 activation and modulated membrane potential. B) Illustrated stages of activation: Left
Before activation the cell is at rest with Kv7 channels open. Center M1 activation leads to hydrolysis of PIP2
from cell membrane (inhibiting Kv7 channels) and the release of intracellular Ca2+ (activating SK channels)
through the generation of IP3. Right As Ca2+ is extruded from the intracellular space SK channels close
while Kv7 channels remain closed. C) Membrane potential at different stages of activation. D) Intracellular
calcium levels at different stages of activation.
10

4,5-bisphosphate (PIP2) in the cell membrane to maintain its open state. M1 activation leads to the activation
of phospholipase C (PLC) which hydrolyzes PIP2 into inositol(1,4,5)triphosphate (IP3) and diacylglycerol [9,
10]. It is through this depletion of PIP2 that mAChRs inhibit the M-current. Also, by producing IP3, M1
receptors trigger the release of calcium from the endoplasmic reticulum (ER) via IP3 receptors. This leads
to an increase in intracellular calcium which activates calcium dependent potassium (SK) channels. In CA1
pyramidal cells M1 activation is followed by a hyperpolarization which is able to inhibit action potentials.
These hyperpolarizations can be blocked through the application of apamin, an SK channel antagonist [3].
Figure 2.1 provides both a flowchart and a cartoon to illustrate these processes.
One long term goal of our lab has been to create a large scale model of the hippocampus and through
this model, gain a better understanding of the underlying dynamics of this system [55], thereby facilitating
the development of better treatments (electrical or pharmaceutical) to alleviate hippocampal dysfunctions.
Experimental evidence has demonstrated that cholinergic modulation plays an important role in controlling
the dynamics of this system. This has driven the development of this single cell model, which will act as a
foundation for integrating cholinergic modulation into our efforts for a large-scale hippocampal model.
We have chosen to build the single cell model on a biophysically realistic basis wherever possible. This is
for two reasons. First, the collection of experimental data for calibrating a model gives a perspective on
the depth of understanding and raises questions to guide further in vitro or in vivo experimental efforts.
Second, the inclusion of biochemical mechanisms allows for broad parametric manipulations which (i)
facilitate the simulation of pathological processes and disease states and (ii) provide useful insights for the
identification and development of novel treatment options. By creating a biophysically realistic model, we
have developed a tool that allows more cohesive collaboration with other experimental efforts.
What follows is a description of a model for the cholinergic modulation of the somatic activity of
pyramidal cells within the CA1 region of the hippocampus. Within the hippocampus, this cell type is the
11

most studied in terms of cholinergic modulation and will constitute a solid foundation for the construction
of larger cell network models.
2.3 Materials and Methods
The primary task of this research was to evaluate and bring together a variety of mechanisms and models
to accurately capture the dynamic response of CA1 pyramidal cells to acetylcholine. As a starting point, we
used a compartmental model of the CA1 pyramidal cell (mpg141209_A_idA as downloaded from ModelDB)
[56] previously developed for the NEURON simulation environment [57]. We chose to use this simulation
environment as its RXD module [58] allowed us to efficiently expand the model’s intracellular calcium
mechanisms. The code for these simulations was developed in the Python programming language. The base
model included mechanisms for the M-current, SK channels, voltage-gated calcium channels (VGCC). Entry
through VGCCs was the only mechanism through which intracellular calcium increased, while calcium
efflux was simulated as an exponential decay of the intracellular calcium to its resting value. As one of
the focuses of this work was to simulate intracellular calcium release we needed to insert and calibrate
all of the mechanisms for simulating the storage and release of calcium from the endoplasmic reticulum,
buffering the intracellular calcium concentration, and extrusion of excess calcium into the extracellular
space. Without these mechanisms, none of the inhibitory effects seen in 2.1 could be replicated.
These calcium mechanisms were only expanded in the sections that comprise the soma and the first
200 µm of the apical dendritic trunk. Figure S1 illustrates which sections within the full morphology were
given expanded calcium mechanisms. One reason for the decision to only expand the calcium model into
these sections was that the calcium dynamics in these regions are the most studied due their diameters
being large enough for calcium imaging using fluorescent dyes. Second, cholinergic modulation in synaptic
spines seems to play a role in plasticity [59]. However, plasticity in these synapses is also dependent upon
postsynaptic spiking activity. To properly simulate how plasticity is altered by cholinergic modulation
12

Figure 2.2: A) Visualization of mechanisms included in expanded CA1 pyramidal cell calcium model. B)
Results of tuning model mechanisms that replenish calcium stores in the endoplasmic reticulum without
action potentials. Plotted value is simulated calcium stored in endoplasmic reticulum over time (x-axis=50
sec, y-axis=50 µM). Target data is based on experiments in [61]. C) Results of tuning model mechanisms
that determine calcium dynamics following an action potential. Plotted value is the percent change in
fluorescence of a simulated calcium indicator (OGB-1) over time (Scale: x-axis=1 sec, y-axis=10% change in
fluorescence). Target data is based on results from [62]
.
requires we first make a working model of how cholinergic modulation alters cell excitability and spike
generation. Finally, the mechanisms of action differ between synaptic and somatic modulation. For instance,
the hyperpolarization seen at the soma is due to the activation of SK channels as evidenced by its blockade
by apamin [3], while synaptic cholinergic modulation has been tied to the inhibition of SK channels [60].
Calibrating these differing mechanisms requires a separate series of simulations and would be best explained
in a separate work.
Our goal in selecting additional mechanisms was to create a relatively simple model capable of replicating
intracellular calcium dynamics. Disease and age have been reported to alter several of the mechanisms
included (e.g. calcium buffering) [63, 64]. By incorporating mechanistic models for these altered states, we
can explore how the cell behavior changes, and how these changes impact network-level outcomes. Of
importance, fidelity to the biochemistry of the intracellular space must be balanced against the realities of
13

computational modeling. A model that includes all of the known molecular interactions would have too
many parameters to constrain with the available experimental evidence. Additionally, simulations using this
model would be computationally expensive even for a single cell model. In addition, our goal of including
this model into large scale network simulations only exacerbates this limitation. We have thus strived to
include the minimum collection of mechanisms that is necessary for capturing cholinergic modulation in
the soma and apical trunk. Expanding the model to other regions and to include other mechanisms will be
performed in subsequent work. A visualization of the mechanisms in the expanded calcium model can be
found in Figure 2.2, while the concentrations and kinetic parameters for these mechanisms can be found in
Table S1 and Table S2 respectively.
The addition of a mechanism often required constraining parameter values to properly replicate
experimental results. In order to simplify the calibration process, the mechanisms were divided into
groups based upon region of action (e.g. endoplasmic reticulum vs intracellular). These groups were then
calibrated in a specific order, starting from protocols that required the smallest number of mechanisms
and comprised a minimum number of interdependent parameters. For example, the rate at which the
endoplasmic reticulum (ER) regains depleted calcium at rest is based upon the balance between the rate
of calcium uptake from sarco/endoplasmic reticulum calcium pumps (SERCA) versus the rate of calcium
leakage from the ER. Since the conductance of VGCCs does not factor into this result it can be ignored.
Conversely, replicating intracellular calcium transients after an action potential requires constraining
parameters for VGCC conductance and calcium extrusion, in addition to SERCA and ER leak flux, as ER
calcium sequestration alters the dynamics in the intracellular space. Since we could relatively isolate the
ER mechanisms, those parameters were calibrated first. This simplified the calibration of later parameters
based on results that depend on more mechanisms. The following sections describe the mechanisms that
were implemented and the experimental data from which constrained these parameter values.
14

2.3.1 Calibrating the endoplasmic reticulum
The first step in creating the model was to calibrate the parameters pertaining to the ER. We chose to model
the ER as an idealized 10% of the intracellular volume to avoid explicitly modeling the intricate and dynamic
geometry of the ER. Reconstructions of the ER in CA1 pyramidal cells have focused on the organelle’s
volume in either the dendritic branches or synaptic spines while ignoring the volume of the ER in the soma
and apical trunk. Using smaller values for the percentage of ER volume, such as those found in dendritic
reconstructions (2-8% of dendrite volume) [65], decreased the capacity of calcium storage such that the
model could not replicate the amplitude of calcium release events. The 10% value is therefore a compromise
that allows larger intracellular calcium release events while remaining near the experimentally measured
range. The resting concentration inside the ER was initialized at 175 µ M [66]. For the initial calibration,
there were three mechanisms that defined the ER calcium dynamics: calreticulin (CALR) concentration,
SERCA pumps, and calcium leak. The inositol(1,4,5)triphosphate receptor mechanism (IP3R) was calibrated
at a later stage as the IP3R model produced negligible currents at resting IP3 concentrations. CALR acts
as the major calcium buffer in the lumen of the ER and its concentration defines the amount of buffered
calcium reserves for a given lumenal calcium concentration. We used the CALR kinetics and concentration
found in an earlier ER model [67].
15

Expressions 2.1 and 2.2 were used for the SERCA pump mechanism while Expression 2.3 was the
formula used to calculate the leak of calcium from the ER into the cytosol. Expression 2.4 shows the
chemical formula used for CALR binding to calcium.
Ca2+
cyt
k
S
f
−−→ Ca2+
ER (2.1)
k
S
f =
gS · [Ca2+
cyt]
2
[Ca2+
cyt]
2 + 0.00132
(2.2)
Ca2+
ER
k
leak ER
f
−−−−−→ Ca2+
cyt (2.3)
CALR + Ca2+
k
calr
f
−−− ↽−−−⇀
k
calr
b
CALRCa (2.4)
From these mechanisms we calibrated two parameters, gS, the SERCA conductance, and k
leak ER
f
, the
rate of leakage from the ER. Due to the model ER not having a set geometry it also lacks a set surface
area. Therefore these mechanisms were implemented as direct fluxes between the two volumes without
consideration of surface density. To constrain the SERCA and leak mechanisms, we used an experimental
result [61] for which the return of Ca2+
ER to resting concentrations was fit with an exponential function with
a time constant of 59 seconds. This time constant along with the experimental Ca2+
ER resting concentration
gave us a target with which we manually calibrated gS and k
leak ER
f
. The results of this calibration are
illustrated in Figure 2.2B
2.3.2 Calibrating intracellular calcium and indicator model
With the ER related mechanisms calibrated, we moved to calibrating the mechanisms related to the
intracellular space. The major mechanisms of interest in this portion of the model pertain to the extrusion
of excess calcium into the extracellular space (i.e. plasma membrane calcium pumps (PMCA)) and the
conductance of VGCCs. However, experimental evidence to constrain these parameters required the addition
of mechanisms to replicate experiments using fluorescent calcium indicators. Fluorescence measurements
16

constitute the primary method to visualize calcium dynamics. However these indicators act as a high affinity
calcium buffer and alter the very dynamics they are supposed to report. We therefore included mechanisms
to simulate the binding of calcium to Oregon Green BAPTA-1 (OGB-1), as this was the indicator used in the
experimental results we sought to replicate. The kinetic parameters we used for the OGB-1 mechanism
were based on measurements in an intracellular environment as interactions with intracellular ions can
change the affinity from its reported in vitro value [68]. Expression 2.5 was the chemical formula used for
the binding of calcium to OGB-1. According to the product information sheet OGB-1 bound to calcium
fluoresces 14 times the rate of the unbound state [69]. We used this fact to create Expression 2.6, which
provides a method to calculate the simulated fluorescence. With this mechanism we could use fluorescence
experiments that used this calcium indicator to constrain the other intracellular mechanisms. This OGB-1
mechanism for creating a simulated fluorescence was only used in this portion of the calibration process
and was not included in later parameter calibrations.
OGB + Ca2+
k
ogb1
f
−−− ↽−−−⇀
k
ogb1
b
OGBCa (2.5)
F = fmult · OGB1Ca + OGB1 (2.6)
Deciding what concentration of Calbindin-D28k (CB) to use in our simulations was another obstacle.
The presence of CB is among the ways that CA1 pyramidal cells display heterogeneity, with only around
50% of cells expressing this protein [70]. Expression of CB is not correlated with the bursting/regular firing
characteristic that serves as the major dichotomy within CA1 pyramidal cells [71], so the spiking response
of base compartmental model could not be used as a constraint. Additionally CB is mostly mobile, so a large
portion of CB likely diffused out of the cell and into the electrodes used to inject the fluorescent indicators as
demonstrated in [70]. These factors make it difficult to have full confidence in the intracellular concentration
of CB during the fluorescent measurements we used to calibrate the parameters. In simulations replicating
17

fluorescent data, we assumed these cells did express this protein but that the concentration was diminished.
We set the diminished concentration to 20% of its regular value as that proportion was estimated to be
immobile in neurons [72]. Expression 2.7 is the chemical formula for the binding of CB to calcium.
CB + Ca2+
k
cb
f
−−↽−−⇀
k
cb
b
CBCa (2.7)
Expression 2.8 describes the binding of pmca to calcium while expression 2.9 describes the release of
calcium into the extracellular volume. This series of reactions describes how PMCA acts as the mechanism
for the extrusion of calcium from the cytosol to the extracellular space.
PMCA + Ca2+
k
pmca ca
f
−−−−− ↽−−−−−⇀
k
pmca ca
b
PMCACa (2.8)
PMCACa k
pmca rel
−−−−−→ PMCA (2.9)
Among these mechanisms there were two parameters that required calibration. First, we needed to tune
the overall rate of calcium extrusion due to PMCA. While we had the parameters for its binding kinetics,
we needed to tune the overall flux by altering the mechanism’s surface density. Second, we had to alter the
conductances of the VGCCs. In altering the model we had expanded the volume the model tracked while
calculating calcium concentration. The original conductance values were tuned assuming a thin shell on the
inner surface of the cell membrane. This expanded volume required increasing the channel conductances
such that the calcium influx was enough to drive the fluctuations seen in the target experimental data.
As our target for constraining the intracellular calcium dynamics we chose the calcium fluorescence
following an action potential (AP) [62] as this protocol minimized the amount of calcium released from the
ER. These experiments measured fluorescence transients in both the soma and the apical dendritic trunk,
allowing us to calibrate separate parameter values for different section types. To calibrate these mechanisms
18

we induced a simulated AP. We then modified the parameters values by hand until the simulated calcium
fluorescence matched the target data. By altering the VGCC conductances we could alter the overall
amplitude of the calcium transient. Due to differences in target amplitude, separate VGCC conductance
values were calibrated for the soma and apical dendritic trunk. Increasing the density of PMCA decreased
the maximum amplitude of the calcium along with increasing the rate the transient decayed to resting
concentrations. The results of this calibration can be seen in 2.2C.
2.3.3 Calibrating calcium release and spike acceleration
With the components for the calcium dynamics in place, the next step was to calibrate the production of
IP3 following M1 mAChR activation. For the M1 mAChR model we turned to the kinetic models developed
by the Hille lab [73, 9, 10, 74]. This model included mechanisms that describe the process from the receptor
activation by its agonist to PIP2 hydrolysis into IP3 and DAG. A schematic representation of this model
including all of the associated reactions can be found in Figure S2. However, the model required notable
modifications to fit our purpose. First, the Hille model simulated the agonist Oxo-M, not acetylcholine
(ACh). While Oxo-M is an important muscarinic agonist, the goal of simulating endogenous cholinergic
modulation required the mechanism to include ACh. Our work added the action of ACh on the M1 mAChR
model through the calibration of additional parameters. Second, the rate of IP3 production was extremely
slow compared to the behavior seen in CA1 pyramidal cells. Recordings of spiking CA1 pyramidal cells
exposed to brief (40 msec) pulses of ACh were provided by the authors of [75]. From these recordings we
selected a subset of traces demonstrating regular spiking activity where the pre-ACh spiking frequency
was less than 15 Hz. This provided 16 cell voltage traces. From these selected recordings it was determined
that the regenerative release occurred within 200 msec of receptor activation as spikes were inhibited by
this time. Both of these issues required the alteration of parameter values in order to achieve the desired
responses.
19

In [10] the authors used fluorescence resonance energy transfer (FRET) to measure the binding of M1
mAChRs to Oxo-M. A separate study performed an analysis of ACh binding to M1 using similar FRET
techniques [76]. From this study we took the half maximal effective concentration value of ACh and used
that value to calibrate the parameters for agonist binding the receptor (see reaction 1 in Table S2). The
change in the receptor’s response to agonist concentration can be seen in Figure S3.
The discrepancy between the rapid release of intracellular calcium after M1 activation seen in CA1
pyramidal cells and the slow generation of IP3 in the [74] model was solved by increasing a subset of kinetic
parameters in two portions of the M1 model. This discrepancy is most likely due to the original model being
constrained to fit the response within sympathetic neurons. Activation of M1 channels in this neuron type
leads to PIP2 depletion but not large releases of intracellular calcium. The rate of PLC activity will differ
depending on the specific isozymes present within the cell type. Hippocampal cells contain PLC isozymes
which are activated by increased intracellular calcium [77], creating a positive feedback for the hydrolysis
of PIP2. It stands to reason that PIP2 hydrolysis would be triggered more rapidly than in the original model.
The first portion of the model that needed faster dynamics was the activation and inactivation of PLC
through its binding and unbinding to the G protein. Expressions 2.10 and 2.11 describe these reactions.
PLC + Gα−GTP k
P LCassoc
−−−−−−→ Gα−GTP−PLC (2.10)
Gα−GDP−PLC k
P LCdiss
−−−−−−→ Gα−GDP + PLC (2.11)
From these reactions we recalibrated the two forward rates (k
P LCassoc and k
P LCdiss). If we examine
the original dynamics as seen in Figure 2.3A and 2.3B, one can see that the PLC activation peaks around 2
seconds after the ACh pulse and that IP3 levels peak around the same time. However, looking at the cell
recordings (see Figure 2.4A for an example), by this time the calcium transients have already largely ended
20

by 2 seconds as the cells have largely resumed spiking by then. Using the original parameter values led to
a longer weak release of calcium from the ER as opposed to the approximately 1 second duration strong
release we required to reach higher (> 1µM) intracellular calcium concentrations. The two parameters
were therefore both increased by a factor of 10. The difference in dynamics can be seen in 2.3A.
The second portion of the M1 model that required changed kinetics was the hydrolysis of PIP2 into
DAG and IP3. Expressions 2.12 and 2.13 describe this reaction.
PIP2
k
P LC
−−−→ IP3 + DAG (2.12)
k
P LC = rP LC ∗ Gα-GTP-PLC (2.13)
Here the parameter, rP LC, was increased by a factor of 100. If we look at Figure 2.3B, we can see how this
altered the dynamics of the reaction. By increasing the rate of the hydrolysis along with increasing the
rates in expressions 2.10 and 2.11, the production of IP3 occurred far more rapidly and was largely complete
within two seconds of the ACh pulse. This also rapidly depleted the PIP2 as seen in Figure 2.3C.
The next goals were to calibrate the calcium release required for spike inhibition and the rate of PIP2
synthesis. This latter process controls the rate of reactivation of the M-current, and thereby controls the
duration of spike acceleration. With the rate of IP3 increased in previous calibration steps, overall IP3
levels were controlled by altering the total concentrations of IP3 Kinase (IP3K) (expressions 2.16, 2.17,
and 2.18) and IP 5-phosphatase (IP5P) (expressions 2.14, 2.15). Similar reasoning to the increased rate of
IP3 production drove tuning the rate of IP3 removal. The concentration of IP3 needed to return to near
resting levels quickly enough that calcium release ended within seconds of the ACh pulse. This allowed
21

Figure 2.3: Comparison of dynamics after a simulated 50 msec 100 µM ACh pulse. A) Activated PLC
dynamics using original parameter values from [74] (red dash) to recalibrated parameter values used
in final model (black solid). B) IP3 dynamics using either the original parameters (red dash), increased
PLC activation parameters (blue dash- dot), or increased PLC activation parameters along with increased
hydrolysis rate (k
P LC) (black solid) C) PIP2 dynamics using either using either the original parameters (red
dash), increased PLC activation parameters (blue dash-dot), increased PLC activation parameters along
with increased hydrolysis rate (k
P LC) (grey dot), or all increased parameters including those that drive
synthesis of PIP2 (black solid).
22

Figure 2.4: A) Experimental recording of CA1 pyramidal cell responding to a 40 msec pulse of 100 µM
while driven to spiking. B) Model response to 50 msec pulse of 100 µM ACh while cell is driven to regular
spiking. C) Comparison of instantaneous firing rate of experimental response and model response.
23

mechanisms to restore calcium to the ER and also allowed the cell’s activity to sharply transition from
hyperpolarization to accelerated spiking.
IP5P + IP3
k
ip5p
f
−−− ↽−−−⇀
k
ip5p
b
IP5P−IP3 (2.14)
IP5P−IP3
k
ip2
−−→ IP5P + IP2 (2.15)
IP3K + 2 Ca2+
k
ip3k ca
f
−−−−− ↽−−−−−⇀
k
ip3k ca
b
IP3K−2 Ca2 (2.16)
IP3K−Ca2 + IP3
k
ip3k ip3
f
−−−−− ↽−−−−−⇀
k
ip3k ip3
b
IP3K−2 Ca2−IP3 (2.17)
IP3K−Ca2−IP3
k
ip4
−−→ IP3K−Ca2 + IP4 (2.18)
The mechanism for calcium efflux through IP3 receptors is described by expressions 2.19 and 2.20. Here
ROpen refers to the open state of the full kinetic model. For the full kinetic scheme of the IP3 receptor
model see Figure S2B.
Ca2+
ER
k
IP 3R
f
−−−−→ Ca2+
cyt (2.19)
k
IP3R
f = gIP3R · ROpen (2.20)
By manipulating the maximum flux, gIP3R, and the rate of IP3 breakdown we were able to produce
calcium transients with peaks reached greater than 1 µM that resolved within the desired duration range
(1-3 seconds).
The final set of parameters we altered to replicate the CA1 pyramidal cells’ behavior were involved in
the synthesis of PIP2. The resynthesis of PIP2 is due to activity in the ER that varies with the proteins a cell
type expresses [78]. As these species are not characterized within the CA1 pyramidal cell, we chose to use
24

the mechanisms present in the model and to calibrate the kinetic parameters to match the behavior seen in
in vitro experiments. The following expressions describe these reactions.
PI k
4K
−−→ PI(4) P (2.21)
PI(4) P k
5K
−−→ PIP2 (2.22)
PI(4) P k
4P
−−→ PI (2.23)
PIP2
k
5P
−−→ PI(4) P (2.24)
From these expressions four parameters needed to be recalibrated (k
4K, k
5K, k
4P , and k
5P ). These
parameters were recalibrated based upon the rate the instantaneous firing rate (IFR) returned to its pre-ACh
value. In our model, this increased spiking is due to the inhibition of the M-current following PIP2 depletion.
By simulating the original experiments used in [75], we could replicate the altered spiking behavior and
calibrate the kinetic parameters for PIP2 synthesis so that the resolution of spike acceleration matched the
experimental results. Figure 2.3C shows how the recalibrated parameters changed the synthesis of PIP2.
Figure 2.4 shows a simulated experiment along with an example of a cell recording that demonstrates the
model’s ability to replicate the changes to IFR over time.
2.3.4 Depolarization activated calcium store replenishment
The final mechanism we resolved to include in this model was the role of store operated calcium entry
(SOCE). Briefly, this is a process by which the depletion of lumenal calcium causes the activation of calcium
channels on the plasma membrane. These channels are positioned in membrane junctions or regions where
the distance between the plasma and ER membrane is less than 100 nm. This allows the calcium that
enters through SOCE to almost directly enter the ER without altering the overall intracellular calcium
25

concentration. For a more in depth review of this process see [79]. Interestingly this process is also
dependent on depolarization of the cell [80]. Without depolarization, repeated phasic exposure fails to
demonstrate repeated hyperpolarizing responses to intracellular calcium release.
While this process is well documented and the responsible actors have been partly identified, the
kinetics of this process have not been quantified. Not including a mechanism to replicate SOCE would make
it impossible to simulate network activity with synaptic release of ACh, as the cell model would only be
able to respond to one release event. To overcome this limitation we included a mechanism that replicated
the behavior of SOCE without explicitly modeling the underlying molecular events. This mechanism is
based on a series of assumptions.
• Depolarization is required for activation [80].
• Hyperpolarization does not cause a leak from intracellular stores.
• CaER depletion is required for activation [79].
• The action of this mechanism bypasses the intracellular calcium concentration as calcium directly
moves from the extracellular space to the ER lumen.
Expression 2.25 was the mechanism we used which fit the above criteria.
dCa2+
ER = gSOCE · ln(1 + e
vm−vinit ) · e
−(CaER−Cad
)
kSOCE (2.25)
This mechanism avoids alterring the intracellular calcium concentration by directly changing the value of
CaER. Through the use of a softplus function this mechanism will have minimum activation except when
the cell’s membrane potential is depolarized from it’s resting value (vinit). Also as CaER approaches its
resting value, this mechanism deactivates, ensuring it is maximally activated after calcium store depletion.
As seen in Figure S4 this mechanism allows repeated hyperpolarizations following intracellular calcium
26

release if the cell depolarizes, but intracellular calcium release cannot repeatedly occur if the cell maintains
a near resting membrane potential. This replicates behavior seen in cortical pyramidal cells [80].
2.4 Results
2.4.1 Acetylcholine and cell excitability
With the compartmental model able to replicate experimental responses of CA1 cells, we sought to explore
how variations in the concentration of ACh would alter the model’s behavior. As our model only captures
the modulation in the soma, axon, and apical trunk of the cell, we focused on simulating how ACh alters
the cell’s excitability. Experiments tend to use agonist concentrations that will drive a significant and
unambiguous response. These experimental concentrations may not be biologically relevant, however.
While some measurements of in vivo ACh concentrations have been made, these measurements were made
under the assumption of volumetric transmission. Recent work, however, has demonstrated that cholinergic
terminals form synapses, undermining this volumetric assumption [41]. It therefore remains unclear what
concentrations muscarinic receptors see during cognition. This particular aspect will be further discussed
later. To avoid testing an exact concentration profile we sought to explore how our model responds to a
wide range of concentrations. We also explored how the model behaved differently under a synaptic release
of ACh versus a steady state exposure. Short pulses (50 msec) replicated a simultaneous synaptic release
we termed "phasic", while long term (>5 seconds) exposures simulated a steady state exposure referred to
as "tonic" exposure.
We first replicated phasic exposure while the cell is at a resting membrane potential. Figure 2.5
demonstrates how the model replicates these changes to membrane potential. At 100 µ M the model
produces a -9.05 mV hyperpolarization followed by a depolarization of 1.98 mV. From Figure 2.5 C and D it
is clear that the amplitudes of these reactions are highly concentration dependent. From Figure 2.5D its
27

Figure 2.5: Simulated response to phasic (50 msec) exposure at varying concentrations of acetylcholine.
A) Cell membrane potential with no other stimulation besides acetylcholine pulse. B) Simulated intracellular calcium release. C) Peak hyperpolarization and depolarization values at different concentrations of
acetylcholine. D) The peak intracellular calcium concentration following acetylcholine pulse.
28

clear that for concentrations less than 0.1 µ M, the release of calcium from intracellular stores is negligible
and consequently no hyperpolarization occurs. In Figure 2.5C we see that the hyperpolarizing effect is
induced at lower concentrations (EC50=0.499 µM) than the depolarization (EC50=1.95 µM). This suggests
that for cells at rest, within a certain range of concentrations, short pulses of acetylcholine would only have
an inhibitory effect on the cell without producing much excitatory modulation.
We then sought to explore how phasic ACh exposure would alter the spiking activity of the cell model.
We ran a series of simulations in which current injections drove the cell to spike at a constant rate of 10 Hz.
At the 1 second mark we then modeled the injection of a 50 msec pulse of ACh with each simulation having
a different concentration. The results of these simulations can be seen in Figure 2.6. Looking at Figure 2.6C,
we can see that once spiking resumes, the IFR increases rapidly reaching a peak around 2 to 3 seconds after
the ACh pulse. The increased firing rate then slowly returned to its baseline rate over several seconds. We
calculated the peak percent increase in IFR, or spike acceleration, for each simulated concentration. As
shown in Figure 2.6D, this value formed a smooth sigmoidal curve when plotted against concentration.
The duration of the spike inhibition, seen in Figure 2.6E varied in a way similar to the variation seen in
the resting conditions, abruptly beginning at concentrations above 0.1 µM. That spike inhibition begins so
abruptly means that for ACh concentrations of 0.1 µM or less the firing rate will have noticeably increased
without a period of spike inhibition. Additionally, while the peak acceleration followed a sigmoidal curve,
the longest spike inhibition occured at 1 µM, with the duration of inhibition decreasing thereafter.
If we examine Figure 2.7 we can see the cause of this nonlinearity. In 2.7A we can see that as the
concentration of the ACh pulse increases, the peak concentration of the intracellular calcium transient
increases. Figure 2.7B demonstrates that these peak values form a sigmoidal curve. However, while the
peak values is increasing, the duration of the calcium transient is also decreasing. This is due to larger ACh
pulses driving increased IP3 production and thereby causing a more rapid depletion of ER calcium stores. As
the stores are depleted, the calcium transient begins to decay. It is this accelerated depletion of ER calcium
29

Figure 2.6: Simulated response to phasic (50 msec) exposure of varying concentrations of acetylcholine. A)
Cell injected with a current amplitude such that it spikes at a steady rate of 10 Hz. Current injection is
present throughout simulation B) Repeat of experiment with the addition of a 100 µM acetylcholine pulse
that starts at t = 1 second and lasts for the duration of the simulation. C) Instantaneous firing rate over
time for different concentrations of ACh. This rate is the inverse of the inter spike interval. D) The peak
spike acceleration increased with higher concentrations of ACh. E) The duration of the pause in spiking
versus the concentration of ACh.
30

Figure 2.7: A) Time series of intracellular calcium concentration after phasic (50 msec) exposure to ACh. B)
Peak cytosol calcium versus the concentration of the phasic ACh pulse.
which leads to the shorter duration of inhibition for higher concentrations of ACh. This nonlinearity in
spike inhibition could have interesting implications for network activity, and will be a subject of discussion
later in this paper.
Under tonic exposure to ACh, we noted multiple ways that the cell model displayed increased excitability.
As can be seen in Figure 2.8 the rheobase (defined here as the minimum amplitude of a 200 msec current
pulse required to elicit an action potential) decreased with increasing concentrations of ACh. Starting
at a value of 263 pA, the rheobase decreased 40.5% to a value of 156 pA with 14.3 nM of ACh producing
half of the maximum decrease. The cell model also demonstrated increased excitability, illustrated by an
increase of 39.1% in the input resistance measured at the soma. The increase in simulated input resistance
can be see in Figure 2.9. This increased excitability plateaus in the high hundred nanomolar range with
the increased excitability starting within nanomolar concentrations. This suggests that even relatively
31

Figure 2.8: Measuring reduction in rheobase due to tonic acetylcholine exposure. A) A 200 msec current
pulse of varying amplitude is applied at a time sufficiently after the start of a simulated acetylcholine
exposure such that the system is at steady state. A binary search was performed to find the minimum
current injection amplitude which would generate an action potential. B) Cell rheobase decreases with
increased concentration of acetylcholine.
Figure 2.9: Increasing the concentration of tonic acetylcholine increases the input resistance of the cell
model as measured at the soma. Input resistance was measured by performing a series of somatic current
injections and then performing linear regression on the relation between membrane depolarization to
current amplitude. The values plotted are the slopes of the estimated linear functions. The current
amplitudes used were 0, -100, and 100 pA.
32

Figure 2.10: Measuring depolarization and hyperpolarization after tonic (60 second) exposure to acetylcholine. A) Simulated response of somatic membrane potential to different concentrations. B) Amplitude
of steady depolarization and temporary hyperpolarization versus acetylcholine concentration.
33

Figure 2.11: Increasing the concentration of tonic acetylcholine increases spike rate for a given injected
current amplitude. A) Cell injected with a current amplitude such that it spikes at a steady rate of 10 Hz.
Current injection is present throughout simulation. B) Repeat of experiment with the addition of a 100 µM
acetylcholine pulse that starts at t = 1 second and lasts for the duration of the simulation. C) The maximum
spike frequency acceleration vs acetylcholine concentration. Spike frequency acceleration was measured as
the percent increase from the rate before acetylcholine exposure.
34

low background concentrations should be able to alter cell spiking behavior. Long term exposure of ACh
also produced a depolarization that persisted through the duration of exposure. The amplitude of this
depolarization varied as a function of ACh concentration as demonstrated in Figure 2.10. Finally, tonic
exposure caused accelerated spiking for a given amplitude of current injected at the soma. This accelerated
spiking is demonstrated in Figure 2.11.
2.4.2 Intracellular calcium release
Focal application of muscarinic agonists and stimulation of cholinergic terminals were demonstrated to
generate calcium waves that progressed from the apical dendritic trunk to the soma [62]. Our model, as
demonstrated in Figure 2.12, replicates many aspects of these calcium waves. As seen experimentally, the
sections in the apical trunk reached a higher peak calcium concentration more rapidly than the somatic
section. This is likely due to dendritic regions having higher surface area to volume ratios.
35

Figure 2.12: Acetylcholine leads to the release of intracellular calcium. All sections in the apical trunk
and soma were simultaneously exposed to a 50 msec pulse of 100 µM ACh. A) Simulated time course of
intracellular calcium after acetylcholine exposure. More distal sections achieve higher concentrations more
rapidly than somatic sections. B) Display of concentrations in all model compartments at different time
steps throughout calcium wave.
36

2.5 Discussion
2.5.1 Novel additions to CA1 compartmental model
This model includes a number of mechanisms that have largely been absent from previous compartmental
computational models of the CA1 pyramidal cell. In addition to including the M1 mAChR model, the intracellular calcium related mechanisms have been greatly expanded. Among these new calcium mechanisms
were calbindin and PMCA. We have also been able to replicate the calcium wave phenomenon by including
the endoplasmic reticulum. The parameters for these mechanisms were calibrated using experimental
measurements obtained in CA1 pyramidal cells to ensure the resulting model accurately replicates this cell
type’s behavior. The addition of these novel mechanisms allows our model to replicate several molecular
interactions that have been heretofore ignored in whole cell computational models of CA1 pyramidal cells.
2.5.2 Predictions from model
The expanded CA1 pyramidal cell model have allowed us to generate some predictions which could be
tested experimentally. First, the model predicts that intracellular calcium release can be triggered over
a wide range of ACh concentrations. Later experimental evidence may show a more tightly regulated
threshold that the transition between minimum and maximum responses occurs over a narrower range of
concentrations. These hypothetical results would then suggest that there are mechanisms involved which
introduce additional nonlinearities that increase the threshold for calcium release. For example the rate of
PIP2 hydrolysis into IP3 being dependent on calcium would likely cause a sharper threshold for calcium
waves.
A second prediction is that the duration of spike suppression as seen in Figures 2.6E and 2.11D does not
increase monotonically; instead the maximum duration occurs at intermediate concentrations (0.1 µ M
for tonic and 1 µ M for phasic exposure). This result is likely due to the interplay between two competing
processes: regenerative calcium release and the rate of calcium store depletion. The concentrations with
37

the longest suppressions generate enough IP3 to drive regenerative calcium release through IP3Rs while
minimizing the rate of Ca2+ release from intracellular stores. Higher ACh concentrations drive higher IP3
production and so IP3Rs open more fully and deplete intracellular stores more rapidly. This modulation of
the length of inhibition is interesting when considering the possible functional roles calcium waves play in
CA1 pyramidal cells.
If the function of calcium waves is to provide an inhibitory signal, then this inhibitory signal would have
some interesting properties. First, as IP3 is the trigger for this inhibition, multiple sources (whether mGluRs
or mAChRs) could be required to work in concert to generate this signal. The non-monotonically increasing
duration of spike cessation suggests that coactivation of additional IP3 sources after the regenerative calcium
release threshold has been passed may cause a shorter inhibition as the additional IP3 will only lead to faster
calcium stores depletion. Second, the rate at which intracellular calcium stores are depleted depends upon
the amount of calcium stored. A cell with more calcium buffered in the ER will have a longer inhibitory
reaction to cholinergic modulation. Since every action potential increases the amount of calcium in the
ER, calcium waves would be longer for cells that have had more action potentials in the recent past. This
mechanism would thereby act as an internal inhibition which encodes each cell’s past activity. These
two properties suggest scenarios where cholinergic modulation causes shorter inhibition for cells that are
currently receiving a large glutamatergic signal but have not been spiking much in the past while cells
that have been consistently spiking and only receive cholinergic modulation are inhibited for a longer
period. The implications of these properties may have a crucial impact on the downstream effects of calcium
homeostasis, amongst which are excitotoxicity and learning and memory; these aspects will be studied in
later work (see section ’Future Uses’ below).
38

2.5.3 Refining model
In developing this model there have been gaps in experimental evidence which have made it difficult
to model all of the experimental reactions to cholinergic modulation. First of all the dynamics of the
phosphoinositides in the CA1 pyramidal cell plasma membranes are not well understood. This has forced
us to make assumptions based on electrophysiological results, but further research into this area would
aid in refining the model. As the ER plays a role in the production of these phospholipids, it is likely
that the depletion of calcium stores leads to changed dynamics. Indeed experiments in CA1 pyramidal
cells have suggested that prolonged activation of mAChRs can drive oscillations in PIP2 levels [81]. The
signaling cascade that drives these oscillations, however, is not well understood and therefore could not be
included in this model iteration. As these dynamics become better understood, more explicit cascades can
be incorporated into the model allowing for a better simulation of the depletion and synthesis of PIP2.
Tonic cholinergic activation was also shown to inhibit the early portions of slow afterhyperpolarization
(sAHP) following trains of action potentials [3]. Experimental evidence suggests this sAHP is largely due to
sodium-potassium exchange pumps [82, 83]. It is unclear how these exchange pumps interact with the
mechanisms involved with mAChR activation. Without this clearer understanding, we have no way to
properly calibrate the level of sAHP inhibition to variations in ACh concentration.
The model could also be expanded through adding mechanisms which model mitochondrial calcium
dynamics. The mitochondria, along with being vital for the energy metabolism of the cell, play a large
role in calcium dynamics through interactions with the ER [84]. As mitochondrial dysfunction has a well
established link with Alzheimer’s disease [85], this expansion would provide a method for exploring the
functional consequences to network behavior and how best to intercede.
39

2.5.4 Future uses
Though the present work is a significant advancement for modeling the interactions between cholinergic input, intracellular calcium, and neuronal dynamics, the model is far from encompassing all of the
mechanisms that participate in cholinergic response. Yet this work represents a framework within which
additional mechanisms can be added as the knowledge of the system evolves. We have sought to use best
practices while generating the code base to facilitate its understanding and allow future users to expand
upon its capabilities. The current cell model focused on cholinergic modulation in the apical dendritic trunk
and the somatic region and consequently does not incorporate the modulation of synaptic transmission.
Experimental evidence has shown that in synapses originating from the CA3 region, the activation of
presynaptic M4 mAChRs suppresses the amplitude of excitatory postsynaptic potentials (EPSPs) [3]. This
signal suppression has been suggested to shift control of CA1 pyramidal cell activity away from the CA3
toward synaptic inputs from the entorhinal cortex (EC). This is theorized to set the CA1 network into a
state more conducive for encoding the sensory information encoded by the EC synapses [86]. However,
the synaptic connections from the EC are located in the most distal portions of the CA1 pyramidal cell
dendritic tree. In order for these inputs to become dominant, the CA1 pyramidal cell would need to become
more sensitive to distal inputs. Our model has demonstrated that it is capable of replicating an increased
excitability as measured by increased input resistance and lower rheobase at higher concentrations of ACh.
This increased excitability, in conjunction with suppressed CA3 synaptic activity would replicate increased
sensitivity to distal inputs. Our model thereby constitutes a solid foundation for future work exploring the
consequences of this modulation for the integration of inputs from EC versus CA3.
Additionally, synaptic connections from CA3 pyramidal cells to CA1 pyramidal cells demonstrate
plasticity that is dependent upon postsynaptic calcium concentrations [87]. M1 mAChRs are known to
be present at these synapses [88] and have been linked to both long-term potentiation and long-term
depression [59]. Our lab has already developed a kinetic model for the postsynaptic calcium seen in the
40

spine head [89]. While this previous model did not include any mechanisms to link M1 activation to
intracellular calcium release, these missing mechanisms could easily be added. This would allow us to
expand upon previous modeling efforts that sought to tie calcium dynamics to plasticity [90] to explore
how cholinergic modulation alters the network dynamics through long term changes in connectivity.
Another direction of interest would consist of expanding the model to explicitly model cholinergic
synapses. Currently our simulations treat acetylcholine concentration as a fixed value which we change
in a step-wise manner. The addition of cholinergic synapses would allow us to explore how the model
responds to varying synaptic parameters. For example, tonic ACh concentration is based upon both the
amount of ACh released but also the rate of hydrolysis due to acetylcholinesterase (AChE). This enzyme is
the target for a class of drugs, AChE inhibitors, used in the treatment of AD. Exploring how these drugs
alter CA1 network dynamics could point to better treatment strategies. Additionally, cholinergic synapses
have been shown to cotransmit ACh with GABA [91, 41]. This cotransmission could have dramatic effects
on network coherence.
Finally, although pyramidal cells are the most numerous cell type in the CA1, they are not alone. There
are a variety of interneuron cell types which are also the subject of cholinergic modulation. If ACh does play
a role in shifting the focus of information processing from synapses from the CA3 to synapses from the EC,
interneurons likely contribute to this process. This is due to certain interneurons’ ability to disinhibit CA1
pyramidal cells (e.g. CCK+ Basket Cells [92]). Furthermore, interneurons also participate in the generation
of network oscillations which help organize network processes (e.g. OLM cells [93]). Understanding how
these cells, through ACh modulation regulate the overall network activity would aid our understanding of
the complex role ACh plays in the hippocampus.
41

Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial
relationships that could be construed as a potential conflict of interest.
Author Contributions
AM and J-MB: concept and design of study; AM: data acquisition; AM and J-MB: analysis and/or interpretation of data; AM and J-MB: drafting of the manuscript; AM, J-MB, GY, and TB: critical revision; AM, J-MB,
GY, and TB: approval of the manuscript to be published.
Acknowledgements
We would like to thank Dr. Allan Gulledge for providing cell recordings which aided in this project.
Computation for the work described in this paper was supported by the University of Southern California’s
Center for High-Performance Computing (https://hpcc.usc.edu).
Funding
Work supported by NIBIB grants U01 GM104604, P41 EB001978-24 and Army Research Office Grant
W911NF2110091.
Data Availability Statement
Model scripts and code will be made available in the future on the ModelDB platform.
42

Chapter 3
Encoding of Whisker Touch Direction in Layer 5 of Somatosensory cortex
3.1 Abstract
Whisking allows animals to detect the location of objects touched by a vibrissa even in absolute darkness.
Prior work has shown a subset of Layer 5B pyramidal cells in the barrel cortex encode the location of
touch along the anteroposterior axis. However, the origin of this encoding is not fully understood. This
work explores the consistency of these cells’ encoding of touch location when controlling for the pre-touch
whisk direction (protraction or retraction). We find that cells have high correlation between the touch
location tuning curves, but that cells often have a preferred direction that generates stronger responses
across the location range. We also find the distribution of the preferred touch location is also skewed such
that retraction preferring cells are concentrated in the posterior locations. We go on to discuss possible
sources for this directional preference and suggest methods to test these hypotheses experimentally.
3.2 Introduction
Locating objects is a fundamental tactile-motor task. Rodents can discriminate the location of objects
touched with a single whisker [94]. Despite decades of research into this system the origin, structure, and
distribution of the neural representation of object position within the brain is still not fully understood.
43

Neurons within layer 5 of primary somatosensory cortex (S1) are known to encode the azimuthal
position of touched objects with bursts of touch-evoked action potentials that are specific to particular
locations along the azimuthal axis [38]. However, the origin of this population code for object position
within L5 remains unclear. One possibility is that the positional tuning is inherited from bottom-up sensory
input. In this model, touches at different locations along the axis drive differing patterns of follicle strain,
and thus different patterns of primary sensory neuron (PSN) activity [95, 96]. These PSN patterns are then
separated into location correlates by filtering circuits between the PSNs and L5 of S1 [23]. Rotation of
the whisker along its longitudinal axis during free whisking provides a plausible source for a consistent
mapping between the azimuthal angle and differing patterns of PSN activation [97]. These cycles of whisker
motion (whisking) can be mapped to a unit circle, with each moment corresponding to azimuth along the
circle. During free whisking, whisking phase and angle can be predicted from recordings of individual
sensory afferents [33, 28]. Moreover, excitatory neurons in S1 show significant tuning to whisking phase
that tiles the entire unit circle [38]. Finally, many neurons in S1 show directional tuning, where protraction
touch drives different response magnitudes than retraction touches [25].
In an alternative model of positional tuning, bottom-up sensory input from touch acts as a gate for
top-down whisker positional information arising from primary motor cortex (M1) to propagate from tuft
dendrites into the soma of L5 pyramidal neurons. Here, the specifics of what pattern of PSNs gets activated
would have less influence on the positional tuning than where the whisker was scanning when touch
occurs. Consistent with this model, behavioral analysis shows that the number of touches made, combined
with the midpoint of whisking at touch onset, best predicts the animals choice during tactile position
discrimination [94]. M1 encodes whisker positional information [39] and makes strong synaptic connections
to L5 tuft dendrites [5]. Silencing L5 tuft dendrites has been shown to degrade whisker position encoding
and discrimination behavior performance [98]. Tuning of L5 neurons to whisker position during free
whisking is independent of positional tuning during touch [38].
44

Here, we provide further evidence in support of a touch-gated positional tuning model. We examine
touch responses of L5 excitatory neurons during azimuthal object localization while controlling for variation
in touch intensity, force, and direction. We find that most L5 neurons exhibit substantial directional tuning,
with protraction-selective neurons overrepresented in the population. However, this directional tuning is
highly correlated with preferred object location. Within individual neurons, the preferred object location is
maintained regardless of touch direction. As protraction and retraction touches activate highly distinct
patterns of PSNs [32, 29], and location tuning is preserved across these two classes of touches, we conclude
in a central rather than peripheral origin of object location tuning in L5 S1 neurons.
3.3 Materials and Methods
3.3.1 Experimental model and subject details
The results of two separately published experiments were pooled for this analysis [38, 99]. The specifics
of the experimental procedures are detailed in the respective publications, but a summary is provided
here. Transgenic mice (strain varied by experiment), both male and female, of at least 3 mo of age were
used for both experiments. A head-plate implantation procedure was conducted as described by [100].
Postoperatively, mice were housed with littermates or singly housed if fighting occurred. Mice were
provided food ad libitum and water restricted to 1 mL per day for 1 wk before training and recording. A
daily health and weight assessment was completed to ensure mice were healthy.
3.3.2 Animal Task
Both experiments trained mice to perform a whisker-based go/no-go object-localization task. Using a single
whisker (C2), water-restricted mice were motivated to whisk and identify the location of a smooth vertical
pole (0.6 mm diameter) 7–12 mm lateral from the whisker pad. The pole moved along the anteroposterior
axis and was positioned using stepper linear actuators with 99 nm resolution, 25 µm accuracy, and <5 µm
45

repeatability (Zaber NA11B30-T4). To avoid potential ultrasonic cues associated with stepper motor
movement, the pole was jittered 0–127 microsteps (0–25 µm) on each trial. A pneumatic linear slider (Festo)
was used to raise the pole vertically into touch reach for each trial. The Festo also provided a sound cue on
pole presentation onset.
Specific pole locations rewarded mice with water, punished mice with a time-out (2 s), or had no effect
based on the mouse’s decision to lick or withhold licking. In a go/no-go paradigm, four trial outcomes exist.
In a minority of sessions in which the animals were trained, the close posterior 5 mm of pole locations (go)
were rewarded with water rewards upon licking (hit) or had no effect if mice withheld licking (miss). The
far anterior 5 mm of pole locations (no-go) were punished with time-out (false alarm) or had no effect if
mice withheld licking (correct rejection). For the remaining sessions, rewards and punishment were given
regardless of the pole location—go trials and no-go trials had overlapping pole locations.
3.3.3 Behavior, videography, and electrophysiology
Animal behavior, videography, and electrophysiology were synchronized and recorded. The equipment
varied between the experiments, and are detailed in the respective publications. After trial initiation
electrophysiology recording of single-unit activity was synchronized to high speed video capture (1000 fps)
of whisker motion.
The video of whisker motion was recorded from an overhead view and spanned the time prior to pole
onset to the end of the response window. Whisker shape and position were traced and tracked using
Janelia Farm’s Whisker Tracker (https://www.janelia.org/open-science/whisk-whisker-tracking). A mask
was traced around the edge of the fur to reduce tracking noise. The whisker angle is quantified at the
intersection between the mask and the whisker. The whisker midpoint, instantaneous phase, and amplitude
were decomposed from the bandpass- and zero phase–filtered (6–60 Hz, Butterworth) whisker-angle time
series using the Hilbert Transform (MATLAB 2020a/2023b: Hilbert). Whisking amplitude and phase are
46

defined as the magnitude and phase angle (radians) of the Hilbert Transform of the whisker-angle time
series, respectively. A phase value of 0 is the most protracted location of the whisk cycle, π and −π are the
most retracted positions, and the positive/negative sign defines retraction/protraction whisking directions
respectively. The whisking midpoint is the filtered (6–60 Hz) difference between the whisker-angle time
series and bandpass-filtered signal. Whisker curvature is the amount of bending of the whisker measured
3–5 mm lateral from the whisker mask.
The precise millisecond of touch was then calculated either by using custom software tools or manual
curation of images of interactions between the whisker and pole.
3.3.4 In vivo loose-seal juxtacellular recordings
All animals used in this study were adult male or female transgenic mice. Following head-plate surgery,
mice were trimmed to one whisker (C2), and intrinsic signal imaging was used to target the associated
barrel column. A single whisker was maintained throughout training and recording. Prior to recording,
animals were anesthetized (2% isoflurane) and a small craniotomy (200–300 µm) was made above the barrel
column associated with the C2 whisker. On the first day of recording, animals were allowed to recover for
1 h before recording. The number of recordings repeated per animal varied by experiment.
To sample single-unit spiking activity in a manner unbiased by firing rate, blind juxtacellular loose-seal
patch recordings were targeted to L5 neurons using patch pipettes (Warner Instruments; 5–8 MΩ) filled
with 0.9% saline (Growcells). Electrical recordings were acquired and amplified using MultiClamp 700b
and Headstage CV-7B. The pipette axis was aligned parallel to the C2 barrel column at 35°. To perform an
unbiased sampling of L5, we recorded from any isolated unit. An isolated unit was identified by an increase
in resistance to 13–20 MΩ. These units then identified as excitatory cells using methods that depended on
the genetics of the mice used.
47

3.3.5 Quantification and statistical analysis
3.3.5.1 Touch-response window
A smoothed (Bayesian adaptive regression splines (BARS); [101]) response –50 to 50 ms around touch
was used to evaluate the touch-response window. This window was generated two ways: one with all
touches and one with the first touch only for cases in which first touches are not captured adequately. The
touch-response window was defined as any time point from 5–50 ms post-touch in the smoothed response
that exceeded baseline (–50 to 0 ms pre-touch) +/- the 95% confidence interval. Then, the response windows
were manually curated to best fit the probability density function of touches in cases where the initial
approaches again failed to capture the window of the response. Any cells not assigned a touch response
window due to non-response were assigned a response window that was the median of all response windows
within the dataset.
3.3.5.2 Tuning curves
A tuning curve is a response (firing rate) as a function of a stimulus (e.g., touch location). For a single
neuron, 5% of sampled touches define a point along the touch-tuning curve. This method ensured 20
equally sampled bins of stimulus (e.g., whisker position) and response (firing rates) values. The response is
defined as the firing rate within the touch-response window for touch tuning. The median touch-response
window is 10–30 ms post-touch. The stimulus value is defined as the median of the stimulus in each sampled
bin. Response values are defined as the mean of the responses in each sampled bin. Tuning curves were
generated by smoothing the stimulus and response values using BARS. Neurons that had mean whisking
responses less than 1 Hz were not evaluated.
We used a two-step process to define whether a neuron was significantly tuned to a specific location.
We first performed a one-way ANOVA at an alpha level of 0.01 to identify if any angle/position’s firing rate
at touch or during free-whisking significantly differed from another angle/position’s. If a neuron passed this
48

first test, we moved on to the second step of the evaluation. In the second step, we shuffled touch/whisking
responses 1,000 times and evaluated F-values from a one-way ANOVA. If the observed F-value was above
the 95th percentile of the shuffled population distribution of F-values, we deemed the neuron as tuned. This
second evaluation further ensures that the tuning we observed was not due to noise in neural responses. A
neuron was considered significantly location-tuned if it passed both tests. Tuning preference is the location
of the peak response of the tuning curve. To define the width of the tuning, a multiple comparison test
using a Tukey-Kramer-type critical value was used to identify the first bins in both directions that were
significantly different from the peak value. If no bins were significant, no modulation width was defined.
Max and min responses were calculated from BARS-fitted tuning curves. The absolute modulation depth
was calculated as the min response subtracted from the max response (max-min). The modulation depth
was calculated as the min response subtracted from the max response, divided by the min response added
to the max response ((max-min)/max+min).
A Shapiro-Wilk test was used at several steps to assess normality; in most cases, normality could not be
determined, and a non-parametric test was used to test significance.
3.3.5.3 Directional selectivity of responses
The direction of each touch was determined by taking the mean value of the whisker velocity for the five
time steps directly preceding touch (pre-touch velocity). Positive mean values were labeled as protracting
touches while negative values were labeled as retracting touches.
As a first measure of a cell’s directional selectivity, we took the mean touch response (mean spike rate in
response window) across protracting touches (rpro) and the mean touch response across retracting touches
(rret) and calculated the relative direction modulation index using equation 3.1.
49

rdmi =
mpro − mret
rpro + rret
(3.1)
This measure varies in value from -1 to 1, where a cell with a rdmi value of -1 only responds to retracting
touches and a cell with a value 1 only responds to protracting touches. Since a cell’s response is correlated
to a variety of touch characteristics (pre-touch velocity, touch location, whisk amplitude, etc), this measure
is likely biased by any asymmetrical sampling when the data is split by touch direction.
Similarly, we calculated the mean additional spikes generated by touches in either direction. This was
done by multiplying the mean directional response by the duration of the response window to calculate the
mean number of response spikes. The mean additional spikes was calculated as the difference between this
mean number of response spikes and the mean number of spikes that cell generates in the 50 ms before
touch.
3.3.5.4 Pre-touch velocity
To control for directional touches having different distributions of pre-touch speed, we sorted touches into
three bins per direction. The ranges of these bins were chosen to equally split the population’s pre-touch
speed distribution (ignoring direction) into three ranges. Once each cell’s touch responses were split by
touch direction and the pre-touch speeds were sorted into these bins we calculated the mean response rate
for each bin. This provided three points per direction to analyze the relationship between a cell’s touch
response and pre-touch velocity. For each cell we normalized these values by the maximum binned rate in
either direction (rmax), then calculated the mean difference across the velocity bins between protraction
and retraction. The equation of this mean rate difference across speed bins (rspeed) is shown in equation 3.2.
50

rspeed =
1
nbins
nXbins
i=1
rpro,i − rret,i
rmax
(3.2)
Due to the normalization this range of this value will be [-1,1], with positive values representing a trend
towards stronger responses to protracting touches.
3.3.5.5 Location and directional preference
Due to the nature of the performed task, the distribution of recorded touches was not uniform across the
range of locations. This led to the retracting touches being poorly sampled in more anterior locations. We
therefore limited our location analysis to cells that not only demonstrated an overall significant location
preference as described in 3.3.5.2, but also had a majority (≥ 11of20) of the location bins with ≥ 11 samples
in each direction. This ensured that the location preference analysis was not limited to an insufficient range
of locations. Of the 94 cells with significant location preference, 75 cells met this criteria for overlapping
location sampling.
In calculating the rdmi, it is possible that responses in locations that are only sampled for one direction
could bias the final value. To control for this, we separately calculated mean response rate for each location
bin (rl) in each direction. We then calculated the rate difference between protraction and retraction for
location bins that had the minimum number of samples in both directions. The normalized mean value of
these differences or mean location direction modulation index (mldmi) provides a measure of the directional
preference where location preference and differences in sampling across locations are both accounted for.
Equation 3.3 shows the equation used in this calculation.
51

mldmi =
1
nbins
nXbins
i=1
rlpro,i − rlret,i
rlmax
(3.3)
3.4 Results
The analyzed dataset is pooled from a prior report [38] and a new set of recordings [99] using the same
behavioral paradigm (n=191 cells). The dataset comprises juxtacellular loose-seal recordings from optogenetically identified (see Methods 3.3.4) L5 excitatory neurons during a tactile object location discrimination
task ([94]; 3.1A). Mice were head-fixed and performed a go-nogo response task where a thin metal pole was
presented across a linear range of positions along the anteroposterior axis (10 mm range, 4–8 mm radial
distance; 3.1A). Active whisking was required to touch the presented pole, which was reachable in both the
go and nogo location ranges. Mice received a water reward for licking when the pole was in the posterior
half of the range, and a time out if they licked when it was in the anterior half. Whisker motion and pole
touch was imaged at 1000 frames per second and correlated with recorded action potentials (3.1B).
Across the population, 89 neurons (46%) exhibited significant touch-evoked changes in spike rate (41%
excited, 5% inhibited 3.1C,D). Across the population of touch excited neurons, touch evoked a mean increase
of 0.38±0.56 spikes per touch (3.1E). Post-touch elevation in spike rates lasted from 3–45 ms (mean 16.9 ms)
with a latency of 4–36 ms (mean 12.0 ms; 3.1F).
During active whisking, the whiskers move forward (protraction) and backward (retraction) in a
continuous cycle. This results in two distinct classes of touches with distinct patterns of forces on the
follicle for the same pole location due to the direction of whisker travel. The majority of touch-responsive
neurons were selective to touch direction (3.2D). Across the population, protraction touches evoked an
average of 0.35 additional spikes, while retraction touches evoked an average of 0.19 additional spikes
(3.2C). Comparison of relative firing rates in touch response windows for protraction and retraction touches
52

Figure 3.1: A) Illustration of the touch discrimination task. B) Example trial showing variables of interest
and examples of a protracting and a retracting touch event. C) Post stimulus time histogram showing
each cell’s mean firing when aligned by time from touch. Cells have been grouped by their response type
(i.e. excited, unaffected, or inhibited) with touch excited cells grouped at the top and touch inhibited cells
shown at the bottom. D) Percentage of recorded Layer 5 pyramidal cells demonstrating touch response
types. E) Distribution across touch- modulated (excited or inhibited) cells of the mean addition spikes seen
after touch. A negative value suggests the cell is inhibited by touch. The dotted line indicates the mean
additional spikes (0.38 spikes/touch) seen across the population of the recorded touch modulated cells. F)
Distribution across touch excited cells of mean latency from touch to measurably increased activity. G)
Distribution of mean duration of touch excited cells’ increased activity after touch.
53

Figure 3.2: A) Spike raster plots of cells demonstrating strong retraction selectivity (top), strong protraction
selectivity (bottom), and no directional preference (center). The spiking activity are aligned by the time of
touch at t=0 and sorted by the pre-touch velocity with the most negative (fastest retraction) at the bottom.
B) Mean touch response (mean spike rate in response window) split into three ranges of pre-touch speed.
Ranges were chosen such that the distribution of pre-touch speed across all recorded touches would be
equally divided into 3 populations. Cells are the same as those shown in A. C) Mean additional spikes after
touch split by direction for significantly touch modulated cells. Filled points had a significant directional
preference based on a Wilcoxon rank sum test. D) Normalized distribution of relative direction modulation
indices compared to a bootstrapped shuffle (mean of distribution, black dotted line, mean of bootstrapped
shuffle, gray dashed line). Negative values suggest a bias to retraction, while positive values suggest bias
to protraction. E) Normalized touch responses vs pre-touch whisker speed for all touch modulated cells.
Each cell’s values were normalized by that cell’s maximum response rate in either direction. Dark lines
show the mean of the normalized values within each speed bin for each direction F) Distribution of the
mean differences between each cell’s speed bin values. A negative value suggests a bias towards retraction
while a positive value suggests a bias towards protraction (mean of distribution, black dotted line, mean of
bootstrapped shuffle, gray dashed line)
54

confirmed a significant bias in population response to protraction touches (3.2D). To determine if this
protraction bias was explained by systematic differences in the magnitude of impact forces between
protraction and retraction, we compared touch responses between matched pre-touch positive and negative
velocities (3.2B). Spiking responses to both classes of touches were weakly correlated to speed (3.2E).
However, the population bias towards protraction responses was maintained between paired velocity bands
(3.2E, F). Thus, directionally selective touch responses reflect intrinsic differences in sensitivity to touch
characteristics rather than extrinsic differences in those characteristics.
Beyond direction, touches also occur in different locations relative to the body. Excitatory neurons
in L5 of S1 are tuned to the azimuthal location of objects during protraction touches [38]. Of the touchresponsive neurons analyzed here, 94 cells showed significant tuning to the position of touched objects.
These positional preferences tiled the range of touch locations across the population (3.3A). Remarkably,
directionally-selective neurons were unevenly distributed across this range of location preferences (3.3B).
Retraction selective neurons were significantly overrepresented in the posterior location preferring range,
while protraction-selective neurons were overrepresented in anterior range (3.3B,C). The dividing line
between these two distributions roughly aligned with the median position of the whisker during active
whisking (3.3D). Thus, protraction touch responses tended to be stronger in the latter half of the protraction
movement, and retraction responses stronger in the latter half of the retraction movement.
Could this relationship between position and directional preference be explained by a systematic
variation in impact force across the whisk cycle? There was a gradient of pre-touch velocity for both
directions. Protraction touches had lower pre-touch velocity, and thus lower impact force, in posterior
locations (3.3E; C.2), with a nearly constant average pre-touch velocity in the anterior 2/3rd of the exploration
range. Yet, there was no systematic relationship between the preferred touch location and this velocity
distribution (3.3E2). For retraction touches, the highest speed at touch also occurred in anterior locations,
while location preference clustered in the posterior range. Thus, retraction touch location tuning was
55

Figure 3.3: A) Cell firing rate plotted against touch location for cells showing significant location tuning.
B) Preferred location (Location bin with maximum firing rate) versus relative direction modulation index
for cells demonstrating location tuning. The blue shaded region shows cells with stronger responses
to retracting touches (rdmi value < 0.0) while the orange region shows cells with stronger responses to
protracting touches (rdmi > 0.0). The population’s mean rdmi value is shown as a dotted line demonstrating
a bias towards protraction. C) Distribution of preferred touch locations. The distribution of protractionpreferring cells (rdmi > 0.0) is shown in orange, while the distribution for retraction- preferring cells (rdmi
< 0.0) is shown in blue. D) Distribution of the median whisker location during whisking. E) Mean pre-touch
velocity sorted by location for all (top), protracting (middle), and retracting (bottom) touches for each cell in
A. The column labeled “mean” shows the mean value across the population in each level. F) The proportion
of all touches that are protracting versus the location. G) Relative direction modulation index versus touch
location. Cells have been split into three groups based on the value of the mean direction modulation index
across sampled locations (mldmi) (top mldmi > 0.1, middle |mldmi| < 0.1, bottom mldmi < -0.1) While most
cells demonstrate consistent directional preference across locations, some cells have distinct ranges where
a particular each direction generates a stronger response. H) Scatter of preferred location across all touches
versus mean location directional modulation index. The white space shows -0.1 < mldmi < 0.1. Gray dotted
line shows population mean, demonstrating a bias towards protraction.
56

anti-correlated with the pre-touch velocity. Together these data conclude that location tuning is independent
of touch velocity.
Protraction touches are more likely to occur in anterior positions, and vice versa for retraction touches
(3.3F). We considered whether this uneven distribution of touch directions interacting with an underlying
object position tuning produced the relationship between touch direction and location preference. We
controlled for this by examining the directional tuning of each neuron across binned object locations.
With few exceptions, directional preferences were maintained across touch locations (3.3G). The average
tuning across positions, which removes the potential influence of uneven distributions of touch directions,
recapitulated the population relationship between directional tuning and preferred touch location (3.3H).
The above analyses establish that directional tuning in individual neurons is maintained regardless of
the position of touch. What of the converse? Is positional tuning maintained regardless of touch direction?
To assess the impact that directional tuning had on location preference, we compared touch location tuning
for all touches, vs. protraction or retraction only touches (3.4A, C.2, normalized to the all directions group).
While the population tuning preference was less organized, the overall positional preferences were largely
maintained for both protraction and retraction. Across all location tuned neurons, the shape of location
tuning curves for protraction vs. retraction touches were highly correlated (3.4B, significantly more than
expected from a shuffled population (3.4C). Moreover, in the set of cells that were significantly tuned to
location for both protraction and retraction touches alone, the maximally preferred location was highly
correlated between directions (3.4D,E). Thus while the direction of touch influences the overall magnitude
of spiking response, additional mechanisms must underlie object location tuning.
57

Figure 3.4: A) Cell firing rate plotted against touch location for all touches (top), only protracting touches
(middle), and only retracting touches (bottom). Firing rate has been normalized by the maximum rate
within each column of each subplot. B) Example plots of directional location tuning curves for cells that
demonstrate high correlation (left plots) and anticorrelation (right plots). Shaded regions in upper plots
show the 95% confidence interval. C) Distribution of correlation between directional location curves for
cells shown in A along with a distribution generated by bootstrapped shuffle. D) Comparison of cells’
preferred locations. Separate histograms show the distributions of the preferred locations for cells that
show significant location tuning in only one direction. The scatter plots the preferred location for each
directional tuning curve for cells with significant location tuning in both directions. E) Distribution of
the correlations between directional location tuning curves for cells that have significant tuning in both
directions (scatter plot of D) plotted against a distribution generated by a bootstrapped shuffle.
58

3.5 Discussion
Touch direction selectivity of neurons in S1 has long been observed for both passive deflections in anesthetized [102, 103] and active touch in awake rodents [104]. In complementary work, protraction touch
responses to contact with a pole show positional selectivity, with a full range of azimuthal location represented across the population. Here, we show that positional selectivity intersects with direction selectivity
to produce a highly structured ordering of directional preference with positional preference across the
population of Layer 5 excitatory neurons in S1. This invites two questions: what is the mechanistic origin
of this ordering, and what are its functional implications?
The origin of the ordering is constrained by several observations about its structure. The positional
and directional tuning is largely unaffected by particular variations in how the whisker interacts with the
object. Within individual neurons, directional tuning is maintained regardless of whisker velocity at impact
(Figure 3.2E, F), and where the object is located (Figure 3.3G). This implies that direction selectivity has
a distinct origin from position selectivity. Force patterns and strain in the follicle differ on protraction
versus retraction touches [32, 28]. Directional selectivity to touch is seen at all stages of the sensory input
chain, from primary sensory neurons [29] to and across all layers of S1 in the canonical touch processing
circuit [104, 105]. The simplest interpretation of these facts suggest that directional selectivity emerges
from patterns of mechanotransduction in the follicle and propagates upwards, perhaps with filtering and
other modifications, to the L5 neurons of S1.
Intriguingly, object location preference is largely maintained regardless of pretouch velocity (Figure
3.3) or direction of touch (Figure 3.4). This implies that the specific patterns of touch forces that drive
directional selectivity have less of an impact on position selectivity. Physiological and behavioral evidence
[38] suggest that top down signals, potentially from M1 [5, 98], could play a crucial role in establishing
positional selectivity [39, 106].
59

These observations still do not explain why across the population, touch selectivity is highly correlated
to azimuthal position selectivity. The recent finding of a population bias towards protraction-selective
excitation discovered in mice during whisking against textured surfaces [25] suggests one possibility.
There, a phasic volley of local inhibition in S1 occurred in the last quarter of the whisk cycle (near end of
protraction). This could plausibly explain why protraction tuned neurons prefer more anterior regions, as
this maximizes the delay from such a volley, giving an opportunity for release from inhibition. However,
this alone is unable to fully explain the retraction selectivity. Could retraction selective cells be selectively
innervated by a distinct set of inhibitory neurons that fired at the opposite phase (the end of retraction)?
While these were not seen in [25], the nature of the task meant that the curvature was always driven by
varying the amount of protraction into the target while no surface interactions were driven by retractions.
If a retraction associated periodic inhibitory wave were present, one would expect it to be activated by
afferent signals associated with the later half of retraction, which likely would not be present in the task
used in [25], but could be present in the dataset analyzed here. Perhaps the sharply intermittent nature of
touch input against a pole structures inhibition volleys differently than the more continuous sensory input
of a textured surface.
Regarding the functional implications of the location-direction axis, the directional preference distribution seems linked to the conditional probability of touch at an object’s relative position given the
direction of whisking. The relationship between direction and position selectivity is better fit by a binary
transition a the mean whisking azimuthal angle rather than a smooth gradient along the azimuthal axis.
Protraction touches dominate retraction touches at anterior positions, while the proportion of retraction
touches substantially increases as location moves more posterior. The proportion of protraction touches
in posterior locations might be higher under our head-fixed, cue-initiated exploration than during more
natural freely-moving continuous exploration. This is because the resting whisker position is consistently
posterior to the mean whisking position and the whisker is often physically impeded from moving past the
60

pole at the radial distances used in our task. In this model mice have windows of enhanced information
gathering in phase with whisker motion, but direct that window to opposite ends of the whisk-cycle based
on the direction specific probability of whisker-object interactions across locations.
Directional preferences to passive deflections in anesthetized mice are organized within a pinwheel
pattern in superficial layers of S1 [103, 107]. Active touch directional selectivity, however, poorly maps
on to passive deflection tuning in layers 2-4 of S1 [104, 108]. In these layers directional selectivity to
active pole touch with a single whisker is organized with respect to barrel map with protraction preferring
cells distributed towards the C2-C3 border and retraction towards the C1-C2 border. Intriguingly while
[104] found that a majority of L2/3 excitatory cells had strong directional preference our data suggest
L5 cells generally have weak directional preference with few cells responding to touch in only a single
direction 3.2D. This difference could be the result of methodological differences. Such a map has not yet
been observed in L5 due to technical challenges of imaging at that depth from surface in an tangential
plane with standard two-photon microscopy.
The origin of location tuning in L5 neurons is less clear. Calcium imaging of M1 to S1 afferents and
L5 dendrites reveals whisker position signals during touch events [5]. Behavioral correlates of whisker
midpoint is more predictive of L5 object location tuning than other whisking variables [94]. Midpoint
and touch signals could plausibly be integrated in L5 neurons to establish a location code. Thick tufted
layer 5 cells are targeted by projections from both the ventral posterior medial (VPM) and posterior medial
(POm) nuclei of the thalamus [109, 110, 111, 112]. Cells in the VPM encode characteristics of both touch and
whisking. While cells in the POm are associated with only encoding whisking, they are also subject to top
down excitation from S1 L5 cells [113]. It is unclear how this recurrent excitation alters the L5 cells’ touch
location encoding, but it could act as an amplifying mechanism to sharpen encoding or to aid in plasticity.
Finally, we would like to propose future avenues to explore to elucidate the origin of this directional
preference. Despite our best efforts to control for asymmetries in sampling, it’s possible that the distribution
61

of directional preference across the range of locations has been skewed by undersampling responses to
retractions in anterior locations. Driving retraction touches in these locations could prove difficult for the
same reasons that they were undersampled in the combined dataset, so a strategy is required to generate
additional retraction touches. As the origin of directional preference remains unclear, one avenue to explore
is the plasticity of a cell’s preference. Angular selectivity has been shown to be subject to plasticity in
adulthood [107, 114]. If the distribution of a population’s directional preference is due to the conditional
probability of object interaction given the whisk direction and relative position of the object, then this
distribution should be subject to change given altered likelihood. A mechanism that drives additional
retraction touches after whisk initiation could be used to test this hypothesis.
Ethics Statement
All procedures were approved under USC IACUC protocols 20169 and 20788 in accordance with United
States national guidelines issued by Office of Laboratory Animal Welfare of the National Institute of Health.
Lead contact and materials availability
Further information and requests for resources and reagents should be directed to and will be fulfilled by
the lead contact, Samuel Andrew Hires shires@usc.edu.
62

Chapter 4
Conclusions
The work presented in this document furthers the understanding of two aspects of brain function. Here we
will summarize the results of these chapters and suggest directions for future work including ways that the
two efforts could be combined.
The development of a mechanistic model of the M1 mAChR’s modulation of CA1 pyramidal cell
excitability yielded a novel computational model that facilitates investigations of the cholinergic modulation
in the hippocampus and constitutes an in-silico test-bed for therapeutic strategies that target the cholinergic
system. M1 mAChRs are present in a variety of pyramidal cell types throughout the cortex, though the
specific response to ACh and other M1 receptor agonists will vary based on the ion receptors and channels
present in each cell type. Importantly, in conjunction with the CA1 pyramidal cell model and its calibration
with respect to experimental measurements, the methodology presented is fully generalizable and may
thus be used for other cell types.
The work in Chapter 3 demonstrated the relationship between touch location encoding and touch
direction preference in the Layer 5 cells of the barrel cortex. Prior work had demonstrated the touch location
encoding in these cell types [94] and that cells in lower level nuclei demonstrate direction preference before
the re-afferent signal reaches the barrel cortex [23]. The intriguing aspect of the data presented here
is not that cells have directional preference, but that measures of directional preference was fairly low
63

for a majority of the analyzed cells. This implies that for a lot of these cells, the synaptic signal that is
driving their touch reactions is either balanced across the two directions or that the encoding of location is
being driven by an excitatory signal that is whisk direction agnostic. The signal from the motor cortex
seemingly offers such a signal and is known to play a role in L5 cells’ activity [5], but this does not satisfy
a question. Why do touches that can occur at different whisking phases, velocities, and locations (and
therefore generate significantly different re-afferent encodings of force) converge onto a L5 cell so that a L5
cell could have touch location tuning with no directional preference? One way to explore this question is
to see how plasticity plays a role in the directional preference of touch. One limitation of the analyzed data
was the lack of samples of retracting touches at more anterior locations. Correcting for this error likely
requires generating touches at positions where they would normally be biomechanically impossible (e.g.,
by placing the target in the retracting whisker’s path). While this may be physically difficult to achieve, it
would likely allow the animal to experience novel whisker interactions. Recordings from sessions over a
period of time might demonstrate existence and extent of plasticity of this directional preference.
Finally, the results of both efforts may be used to calibrate cholinergic modulation of a computational
model of the Layer 5 thick tufted pyramidal cell. This was unsuccessfully attempted by the author and I
will discuss what difficulties were encountered for those who would attempt this. The model developed in
[115] offers a compartmental model of the desired cell type. However, this cell model lacked the M-current
manipulated to generate the increased excitability and depolarization based on evidence that the associated
ion channels are not present at perisomatic locations. These responses to M1 mAChR agonists have been
shown in this cell type [75], however, so the M1 mAChR must be generating these excitatory responses
through a separate mechanism. While speculating that this increased excitability was being driven by the
activation of TRPC channels, I could not find or generate the experimental data required to confirm this was
the responsible mechanism nor to adequately calibrate a model that uses such a mechanism. While I was
unable to finish pursuing this avenue, I hope later experimentation allows the construction of such a model.
64

One advantage of studying the somatosensory cortex over the CA1 is the relationship between external
measurable variables and single cell activity is (while not transparent) far easier to establish. Shedding
light on cholinergic modulation and its functional impact on the behavior of this cell through the use of a
compartmental model would likely be a worthwhile goal.
65

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77

Appendices
A Additional Cholinergic Model Figures
78

Figure A.1: Visualization of compartmental model with expanded calcium dynamics.
79

Figure A.2: A) Schematic representation of M1 receptor model including the mechanisms for the G protein
cascade, PIP2 synthesis, and IP3 breakdown. The number next to each reaction is the entry in B.2 in which
the reaction kinetic parameters can be found. B) Schematic representation of IP3R model used in model.
80

Figure A.3: Comparison of concentration responses with original oxotremorine-m parameters in blue and
new acetylcholine responses in green.
81

Figure A.4: The inclusion of the SOCE mechanism allows for the rapid refilling of lumenal calcium if the
cell is depolarized. A) A cell will be unable to repeatedly release intracellular calcium if it remains at near
resting membrane potentials, but B) can perform repeated release if driven to spike.
82

B Cholinergic Model Parameters and Reaction Equations
Species Initial Concentration Model Region Source
Calcium 2.0 mM Extracellular [67]
PMCA 2.56e
−5 mM Plasma Membrane Tuned Value
IP5P 2.5e
−4 mM Plasma Membrane Tuned Value
IP3K 1.0e
−3 mM Plasma Membrane Tuned Value
M1 Receptor 79.35 µm−2 Plasma Membrane [74]
G Protein 40.0 µm−2 Plasma Membrane [74]
PLC 15.6 µm−2 Plasma Membrane [74]
PIP2 3232.0 µm−2 † Plasma Membrane [74]
Bound PIP2 6464.0 µm−2 † Plasma Membrane [74]
PI(4)P 4540.0 µm−2 † Plasma Membrane [74]
PI 226975.0 µm−2 † Plasma Membrane [74]
DAG 13.0 µm−2 Plasma Membrane [74]
Calcium 100.0 nM Intracellular [63]
Calbindin-D28k 45.0 µM Intracellular [70]
Oregon Green BAPTA-1 50.0 µM∗
Intracellular [62]
IP3 3.0 nM Intracellular Tuned Value
Calcium 175.0 µM Endoplasmic Reticulum [66]
Calreticulin 86.0 mM Endoplasmic Reticulum [67]
Table B.1: Table of mechanism initial concentrations. † initial value varies with the ratio of section volume
to section surface area. * value is nonzero only for experiments requiring a simulated fluorescence signal.
83

# Reaction name Formula and parameter values Source
1
ACh Binding
to M1 R
ACh + R
k
L1
f
−−↽−−⇀
k
L1
b
RL
k
L1
f = 2.78 mM−1 ms−1
k
L1
b = 2.15 · 10−3 ms−1
Altered
from [9]
2 M1 R Binding to G Protein
R + G
kG1
f
−−↽−−⇀
kG1
b
RG
k
G1
f = 6.8 · 10−3 µm2 ms−1
k
G1
b = 6.8 · 10−3 ms−1
Altered
from [9]
3 ACh Binding to RG
ACh + RG
k
L2
f
−−↽−−⇀
k
L2
b
RGL
k
L2
f = 2.78 mM−1 ms−1
k
G1
b = 2.78 · 10−3 ms−1
Altered
from [9]
4 RL Binding to G
RL + G
kG2
f
−−↽−−⇀
kG2
b
RLG
k
G2
f = 2.7 · 10−5 µm2 ms−1
k
G2
b = 6.8 · 10−3 ms−1
Altered
from [9]
5 RL Binding to Gβγ
RL + Gβγ
kG2b
f
−−− ↽−−−⇀
kG2b
b
RLGβγ
k
G2b
f = 2.7 · 10−5 µm2 ms−1
k
G2b
b = 6.8 · 10−3 ms−1
Altered
from [9]
6 Nucleotide Exchange G
G
kNX RG
−−−−−→ Gβγ + Gα–GTP
k
NX RG = 1.5 · 10−8 ms−1
[9]
84

# Reaction name Formula and parameter values Source
7 Nucleotide Exchange RG
RG kNX RG
−−−−−→ RGβγ + Gα–GTP
k
NX RG = 1.5 · 10−8 ms−1
[9]
8 Nucleotide Exchange RLG
RLG kNX RLG
−−−−−−→ RLGβγ + Gα–GTP
k
NX RLG = 6.5 · 10−4 ms−1
[9]
9
Nucleotide Exchange
Phosphate
Gα–GDP kGT P ase1
−−−−−−→ Gα–GTP
k
NX P = 4.7 · 10−3 ms−1
[9]
10 GTPase1
Gα–GTP kGT P ase1
−−−−−−→ Gα–GDP
k
GT P ase1 = 7.8 · 10−5 ms−1
Altered
from [9]
11 GTPase2
Gα–GTP – PLC kGT P ase2
−−−−−−→
Gα–GDP – PLC
k
GT P ase2 = 4.5 · 10−2 ms−1
Altered
from [9]
12
PLC Association with
Gα-GTP
PLC + Gα–GTP k
P LCassoc
−−−−−−→
Gα–GTP – PLC
k
P LCassoc = 5.0 · 10−2 µm2 ms−1
Altered
from [9]
13
PLC Dissociation from
Gα-GDP
Gα–GDP – PLC k
P LCdiss
−−−−−−→ Gα–GDP +
PLC
k
P LCdiss = 3.55 · 10−3 ms−1
Altered
from [9]
85

# Reaction name Formula and parameter values Source
14 G Protein Reconstitution
Gβγ + Gα–GDP k
reconst
−−−−−→ G
k
reconst = 1.0 · 10−3 µm2 ms−1
[9]
15 Lipid 4-Kinase Activity
PI k
4K
−−→ PI(4) P
k
4K = 6.0 · 10−5 ms−1
Altered
from [74]
16 Lipid 5-Kinase Activity
PI(4) P k
5K
−−→ PIP2
k
5K = 5.0 · 10−4 ms−1
Altered
from [74]
17
Lipid 4-Phosphotase
Activity
PI(4) P k
4P
−−→ PI
k
4P = 3.0 · 10−3 ms−1
Altered
from [74]
18
Lipid 5-Phosphotase
Activity
PIP2
k
5P
−−→ PI(4) P
k
5P = 7.0 · 10−4 ms−1
Altered
from [74]
19 PLC Hydrolyis of PIP2
PIP2
k
P LC
−−−→ IP3 + DAG
k
P LC = 0.03 ∗ Gα-GTP-PLC
Altered
from [74]
20 IP5P Binding to IP3
IP5P + IP3
k
ip5p
f
−−− ↽−−−⇀
k
ip5p
b
IP5P –IP3
k
ip5p
f = 59.0 mM−1 ms−1
k
ip5p
b = 7.2 · 10−2 ms−1
[67]
21 IP2 Formation
IP5P –IP3
k
ip2
−−→ IP5P + IP2
k
ip2 = 1.8 · 10−2 ms−1
[67]
86

# Reaction name Formula and parameter values Source
22
IP3 Kinase Binding to
Calcium
IP3K + 2 Ca2+
k
ip3k ca
f
−−−−− ↽−−−−−⇀
k
ip3k ca
b
IP3K –Ca2
k
ip3k ca
f = 1.11 · 102 mM−1 ms−1
k
ip3k ca
b = 0.1 ms−1
[67]
23 IP3 Kinase Binding to IP3
IP3K –Ca2 + IP3
k
ip3k ip3
f
−−−−− ↽−−−−−⇀
k
ip3k ip3
b
IP3K –Ca2 –IP3
k
ip3k ip3
f = 5.0 · 102 mM−1 ms−1
k
ip3k ip3
b = 8.0 · 10−2 ms−1
[67]
24 IP4 Formation
IP3K –Ca2 –IP3
k
ip4
−−→ IP3K –Ca2 + IP4
k
ip4 = 2.0 · 10−2 ms−1
[67]
25 Degradation of DAG
DAG kDAGase
−−−−−→
k
DAGase = 2.0 · 10−4 ms−1
[74]
26 PIP2 Buffering
PIP2
k
pip2
f
−−− ↽−−−⇀
k
pip2
b
PIP2bound
k
pip2
f = 1.0 · 10−3 µM2 ms−1
k
pip2
b = 2.0 · 10−3 ms−1
[73]
27
PIP2 Binding to
KCNQ Channels
PIP2 + KCNQ
k
kcnq
f
−−−− ↽−−−−⇀
k
kcnq
b
PIP2KCNQ
k
kcnq
f = 5.0 · 10−5 µM2 ms−1
k
kcnq
b = 0.1 ms−1
[73]
87

# Reaction name Formula and parameter values Source
28
Calbindin-D28k
Buffering
CB + Ca2+
k
cb
f
−−↽−−⇀
k
cb
b
CBCa
k
cb high
f = 11.0 mM−1 ms−1
k
cb high
b = 2.607 · 10−3 ms−1
k
cb low
f = 8.7 ms−1
k
cb low
b = 3.57 · 10−2 ms−1
[116]
29 Calreticulin Buffering
CALR + Ca2+
k
calr
f
−−− ↽−−−⇀
k
calr
b
CALRCa
k
calr
f = 1.0 · 10−2 mM−1 ms−1
k
calr
b = 2.0 · 10−2 ms−1
[67]
30 Oregon Green BAPTA-1 binding
OGB + Ca2+
k
ogb1
f
−−− ↽−−−⇀
k
ogb1
b
OGBCa
k
ogb1
f = 10.0 mM−1 ms−1
k
ogb1
b = 4.3 · 10−3 ms−1
[68]
31 PMCA Calcium Binding
PMCA + Ca2+
k
pmca ca
f
−−−−− ↽−−−−−⇀
k
pmca ca
b
PMCACa
k
pmca ca
f = 2.5 · 104 mM−1 ms−1
k
pmca ca
b = 2.0 ms−1
[67]
32
PMCA Extracellular Release
of Ca2+
PMCACa k
pmca rel
−−−−−→ PMCA
k
pmca rel = 5.0 · 102 ms−1
[67]
33 IP3 Receptor Opening
RI + Ca2+
k
ip3r 1
f
−−−− ↽−−−−⇀
k
ip3r 1
b
ROpen
k
ip3r 1
f = 8000.0 mM−1 ms−1
k
ip3r 1
b = 2.0 · 10−3 ms−1
[67]
88

# Reaction name Formula and parameter values Source
34 IP3 Receptor IP3 Binding
R + IP3
k
ip3r 2
f
−−−− ↽−−−−⇀
k
ip3r 2
b
RI
k
ip3r 2
f = 1000.0 · 10−2 mM−1 ms−1
k
ip3r 2
b = 25.8 · 10−3 ms−1
[67]
35 IP3 Receptor Inactivation 1
R + Ca2+
k
ip3r 3
f
−−−− ↽−−−−⇀
k
ip3r 3
b
RC
k
ip3r 3
f = 8.88 · 10−3 mM−1 ms−1
k
ip3r 3
b = 4.995 · 10−3 ms−1
[67]
36 IP3 Receptor Inactivation 2
RC + Ca2+
k
ip3r 4
f
−−−− ↽−−−−⇀
k
ip3r 4
b
RC2
k
ip3r 4
f = 19.98 mM−1 ms−1
k
ip3r 4
b = 9.99 · 10−2 ms−1
[67]
37 IP3 Receptor Inactivation 3
RC2 + Ca2+
k
ip3r 5
f
−−−− ↽−−−−⇀
k
ip3r 5
b
RC3
k
ip3r 5
f = 39.95 mM−1 ms−1
k
ip3r 5
b = 14.985 · 10−2 ms−1
[117]
38 IP3 Receptor Inactivation 4
RC3 + Ca2+
k
ip3r 5
f
−−−− ↽−−−−⇀
k
ip3r 5
b
RC4
k
ip3r 5
f = 59.94 mM−1 ms−1
k
ip3r 5
b = 19.98 · 10−2 ms−1
[67]
39
Calcium flux into ER
due to SERCA
Ca2+
cyt
k
S
f
−−→ Ca2+
ER
k
S
f =
gS·[Ca2+
cyt]
2
[Ca2+
cyt]
2+0.00132
gS = 6.35 · 104 mM−1 ms−1
Altered
from [73]
89

# Reaction name Formula and parameter values Source
40 Leak from ER into Cytosol
Ca2+
ER
k
leak ER
f
−−−−−→
k
leak ER
b
Ca2+
cyt
k
leak ER
f = 2.1 · 103 mM−1 ms−1
Tuned
Value
41
Leak from Extracellular
into Cytosol
dCa2+
cyt = gleak ext · (Caext − Cacyt)
gleak ext = 3.2 · 10−5
Tuned
Value
42 Simulated Fluorescence
F = fmult · OGB1Ca + OGB1
fmult = 14.0
[69]
43
Store Operated Calcium
Entry
dCa2+
ER = gSOCE · ln(1 + e
vm−vinit ) ·
e
−(CaER−Cad
)
kSOCE
gSOCE = 5.0 · 10−4
vinit = −65.0mV
Cad = 0.1mM
kSOCE = 0.015
Tuned
Values
Table B.2: Table of mechanism kinetic parameters, conductances, and diffusion, with their respective sources
90

C Additional Whisker Analysis Figures
91

Figure C.1: A) Spike raster plots of cells demonstrating strong retraction selectivity (top), strong protraction
selectivity (bottom), and no directional preference (center). Figures in the left column show only the first
touch within each trial. Figures on the right show all trials. The range of pre-touch time plotted in these
figures has been extended from 25 ms to 100 ms to aid in understanding the cause of pre-touch directional
selectivity seen in Figure 3.2A. The spiking activity has been aligned by the time of touch at t=0 and sorted
by the pre-touch velocity with most negative (fastest retraction) at the bottom.
92

Figure C.2: Mean pre-touch velocity versus location. The three figures on the top middle demonstrate
the mean velocity vs location for protraction preferring cells while cells with no direction preference and
retraction preference are respectively shown in the bottom left and bottom right. For each group of the
three the top subplot shows mean velocity for all touches, the middle subplot shows the mean velocity
for protracting touches, while the bottom subplot shows the mean velocity for retracting touches. Areas
shown in white do not have recordings of that cell’s response to touches in that location and direction.
Figure C.3: Touch location tuned cells split by directional preference. Cells were sorted based on the mean
location direction modulation index where values above zero indicate cells that on average have higher
firing rates in responses to protracting touches across all measured locations and values less than zero
indicate cells that have on average higher firing rates in response to retracting touches across all measured
locations.
93

Figure C.4: A) Population distribution of touches vs touch phase and touch location. B) Population
distribution of touches vs pre-touch velocity and touch location.
94

Abstract (if available)

Abstract Pyramidal cells are a diverse class of excitatory neurons that are the main sources for non-local axonal projections from the neocortex and hippocampus. The pyramidal cells of the CA1 region in the hippocampus and thick tufted Layer 5 pyramidal cells in the cortex share several characteristics that suggest the nature of the input-output transformation they perform from incoming synaptic activity to generation of action potentials would operate under similar principles. This work seeks to develop a deeper understanding of these cell types in two ways. First we calibrated a mechanistic computational model of CA1 pyramidal cells to replicate experimental observations of their modulation by acetylcholine. This model combined biochemical cascades of intracellular events activated by cholinergic input to accurately replicate the experimentally observed changes in the electrophysiological properties of the cell. This work resulted in a novel CA1 pyramidal cell model expanded through the explicit modeling of cholinergic-dependent molecular interactions involved in healthy cognitive function and disease. Through this expanded model, we come closer to simulating these diseases and gaining the knowledge required to develop novel treatments targeting the cholinergic pathway. The second portion of this work analyzed experimental recordings from layer 5 pyramidal cells (L5) in the barrel cortices of head-fixed mice while these animals performed a task that required determining whisker location during touch. This analysis built on prior work demonstrating the ability of L5 cells to encode a target’s location along the anteroposterior axis following touch. The presented analysis found that a cell’s touch location encoding was significantly correlated across directions, but that individual cells demonstrated a variable amount of preference for a particular direction. From these results we go on to suggest experimentally testable hypotheses for the origin of this directional preference.

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Asset Metadata

Creator Mergenthal, Adam (author)

Core Title Computational investigation of cholinergic modulation of the hippocampus and directional encoding of touch in somatosensory cortex

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Degree Conferral Date 2024-08

Publication Date 07/26/2024

Defense Date 06/04/2024

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

Tag Acetylcholine,barrel cortex,CA1,cholinergic modulation,computational model,hippocampus,OAI-PMH Harvest,pyramidal cell,somatosensory cortex,Touch,whisker

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Bouteiller, Jean-Marie (committee chair), Finley, Stacey (committee member), Hires, Samuel Andrew (committee member), Mel, Bartlett (committee member)

Creator Email armergenthal@gmail.com,mergenth@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113998FYO

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Legacy Identifier etd-Mergenthal-13273

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