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A MILLION-PLUS NEURON MODEL OF THE HIPPOCAMPAL DENTATE GYRUS: ROLE
OF TOPOGRAPHY, INHIBITORY INTERNEURONS, AND EXCITATORY
ASSOCIATIONAL CIRCUITRY IN DETERMINING SPATIO-TEMPORAL DYNAMICS OF
GRANULE CELLS

by

Phillip Hendrickson

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL OF THE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY,
BIOMEDICAL ENGINEERING

May 2016

Copyright 2015, Phillip Hendrickson

Page | 1

Acknowledgements

I want to thank everyone who mentored and supported me throughout my tenure as a Ph.D.
student. To paraphrase an old saying, it takes an entire university to graduate a doctoral
candidate!
Thanks to Dr. Theodore Berger, my doctoral advisor. You’ve believed in me, mentored
me, challenged me, and held me to a high standard. I’ve learned so much from you. Thanks for
helping me see this through to the end!
Thanks to the members of my dissertation committee, Dr. Larry Swanson, Dr. Dong
Song, Dr. Vasilis Marmarelis, and Dr. Aiichiro Nakano. I appreciate your support and
suggestions through the qualifying exam and then the dissertation defense.
Thanks to the many lab members who have provided ideas, collaboration, and social
connection. While I can’t name everyone, I want to particularly thank Gene Yu, who has worked
closely with me on the development of the large-scale hippocampal model.
Thanks to all of the staff members in the Department of Biomedical Engineering. You’ve
always kept things running and made sure I had my t’s crossed and my i’s dotted when it came to
logistics.
Thanks to my four children, Joy, Daniel, Anna, and Todd. For your entire lives, you’ve
known me as a student and been patient with everything that entails!
Page | 2
Thanks to my wife, Kimberly. You’ve always been by my side, giving me your love and
quiet support. Thanks for your close companionship all of these years and seeing this through to
the end with me!
Thanks to the organizations that have provided financial support, including DARPA, the
U.S. Office of Naval Research, the U.S. NIBIB, the U.S. National Institutes of Health, and the
U.S. National Science Foundation.

Page | 3
Contents

Acknowledgements ....................................................................................................................... 1
Contents ......................................................................................................................................... 3
List of Tables ................................................................................................................................. 5
List of Figures ................................................................................................................................ 6
Chapter 1: Introduction ............................................................................................................. 10
1.1 Introduction ......................................................................................................................... 10
1.2 Overview of Hippocampal System ...................................................................................... 10
1.3 Research Objectives ............................................................................................................ 12
1.4 References ........................................................................................................................... 13
Chapter 2. Computational Platform for Neural Modeling ..................................................... 15
2.1 Software Infrastructure ........................................................................................................ 15
2.2 Hardware Infrastructure ....................................................................................................... 16
2.3 References ........................................................................................................................... 19
Chapter 3: A Million-Plus Neuron Model of the Hippocampal Dentate Gyrus:
Critical Role for Topography in Determining Spatio-Temporal Network Dynamics .......... 21
3.1 Abstract ................................................................................................................................ 21
3.2 Introduction ......................................................................................................................... 22
3.3 Methods ............................................................................................................................... 24
A. Model Scale and Features .................................................................................................. 24
B. Granule Cell Morphology .................................................................................................. 25
C. Granule Cell Bioelectric Properties ................................................................................... 26
D. Topography ....................................................................................................................... 28
E. Computational Platform ..................................................................................................... 30
3.4 Results ................................................................................................................................. 31
A. Granule Cell Response to Random Entorhinal Input: Firing in Spatio-Temporal
”Clusters” ............................................................................................................................... 31
B. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Inhibition ................. 34
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C. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Topographic
Organization of Entorhinal Afferents ..................................................................................... 37
D. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Axon
Terminal Field Geometry ....................................................................................................... 38
3.5 Discussion ............................................................................................................................ 39
3.6 References ........................................................................................................................... 42
Chapter 4: Interactions between Inhibitory Interneurons and Excitatory
Associational Circuitry in Determining Spatio-Temporal Dynamics of
Hippocampal Dentate Granule Cells: A Large-Scale Computational Study ........................ 49
4.1 Abstract ................................................................................................................................ 49
4.2 Introduction ......................................................................................................................... 50
4.3 Methods ............................................................................................................................... 53
A. Model Features and Scale .................................................................................................. 53
B. Morphology ....................................................................................................................... 55
C. Topography ........................................................................................................................ 56
D. Bioelectric Properties and Pharmacology ......................................................................... 60
E. Computational Platform ..................................................................................................... 60
4.4 Results ................................................................................................................................. 61
A. Granule Cell Response to Random Entorhinal Input: Firing in Spatio-
Temporal ”Clusters” ............................................................................................................... 61
B. Effect of Feedforward and Feedback Inhibition on Granule Cell Activity ....................... 63
C. Effect of Associational System Excitation on Granule Cell Activity ............................... 70
C1. Re-optimization of Network Parameters ......................................................................... 72
C2. Evaluation of Selected Pathway Functions ..................................................................... 76
4.5 Discussion ............................................................................................................................ 79
A. Effects of Inhibitory Interneuronal Circuitry (Feedforward and Feedback) ..................... 83
B. Effects of Associational Circuitry ..................................................................................... 84
C. Interpretation of “Clusters” of Granule Cell Activity: A Measure of
Network Dynamics ................................................................................................................. 87
4.6 References ........................................................................................................................... 89
Chapter 5: Conclusion ................................................................................................................ 97
Page | 5

List of Tables

Table 2.1: Cost breakdown for different CPUs within a family/architecture. 18
Table 3.1: Morphological Parameters for Dentate Granule Cells 26
Table 3.2: Passive & Active Properties for Dentate Granule Cells 26
Table 3.3: Synaptic Parameters for a 1/10-Scale Network 31
Table 4.1: Synaptic parameters, including numbers of synapses, synaptic weights,
EPSP/IPSP magnitudes and rise/fall times, and reversal potentials
58
Table 4.2: Passive and active biophysical parameters for dentate cells 59
Table 4.3: Summary of changes in network activity due to strengthening and
weakening individual synaptic connections
77

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List of Figures

Figure 1.1: Hippocampal tri-synaptic pathway, with information flowing first from
dentate gyrus (DG), then to CA3, and finally to CA1.
11
Figure 2.1: Comparison of total simulation runtime across two different Intel CPU
architectures. Runtime increases nonlinearly as the total network size increases, but
the E5520, which is a newer-generation CPU, scales better for large numbers of cells.
17
Figure 2.2: CPU price vs. speed curve. There are two main sections of the curve –
the relatively flat part, where speed increases come at a small dollar expense, and the
steep part, where similar speed gains are much more expensive.
18
Figure 2.3: 4,040-CPU Beowulf cluster used to run simulations. NEURON running
over MPI was used to run the simulations, with Python being used to specify the
model and perform data visualization/analysis.
19
Figure 3.1: Two sample dentate granule cell morphologies generated using L-
NEURON with the parameter distributions shown in Table 3.1.
25
Figure 3.2: Granule cell active properties. Top left: When subjected to a current
clamp stimulus at the soma, the granule cell responds by firing an action potential
with a latency of approximately 100 ms. Top right: When the current clamp
amplitude is just over the threshold required to elicit a second AP, its latency is
approximately 350 ms. This matches experimental data (bottom, reproduced from
[50]).
28
Figure 3.3: Summary of the image processing pipeline used to quantify the EC-DG
topography from data obtained from [38]. Not all data is shown. 1) The data in their
anatomical subject maps are digitized and grouped according to injection location. 2)
The maps are projected onto a standard coordinate space. 3) The sets are averaged. 4)
The averaged group data are projected onto an average anatomical map. The compass
represents the rostro-caudal and medio-lateral axes.
29
Figure 3.4: Simulation results for topographically constrained EC-DG networks with
feedforward and feedback inhibition, run at two different scales: 1M granule cells
(top), and 100k granule cells (bottom). At both scales, spatio-temporal clusters appear
in the granule cell activity, despite the random nature of the EC input. In the million-
cell case, only a subset of the full dataset is plotted to keep it from appearing solid
black. Column B: 2D autocorrelations confirm the presence of these clusters.

33
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Figure 3.5: Results of increasing the feedback GABA inhibition. A) The raster plot
of the granule cell output for increasing levels of inhibition. GABA level 1 uses the
original BC-GC conductance values while levels 2-4 use 4, 10, and 20 times larger
conductance values, respectively. B) The 1D DFT plot of the data. As the inhibition
increases, the granule cells develop synchronous firing at 22 Hz.
35
Figure 3.6: Granule cell activity when removing internal and external sources of
inhibition. Top: GABAergic inhibition removed; bottom: both AHP and GABA
removed. Spatio-temporal clusters persist in both cases, as evidenced by both the
raster plots and 2D autocorrelations (B).
36
Figure 3.7: Simulation results for a randomly connected EC-DG network. In this
simulation, the granule cell AHP was removed, as was GABAergic inhibition.
Spatio-temporal clusters are no longer present, having been replaced with bands of
activity with a high level of background activity. In the 2D autocorrelation, what
looked like a typical cluster is now a vertical band. Thus, while there’s still a
temporal variation in granule cell activity, the spatial component is gone.
37
Figure 3.8: Effects of increasing the terminal field extent in the septo-temporal
direction. A) Raster plot of the granule cell output. B) The 2D autocorrelation of the
data. As the terminal field extent increases, the cluster size increases, and this is
reflected by the increase in the spatial extent of the 2D autocorrelation.
38
Figure 4.1: Top – schematic showing local feedback circuits in the dentate gyrus,
with the perforant path providing input to both granule cells and basket cells. The
hierarchical nature of local projections in the dentate gyrus can be seen in the mossy
cell population, which both excites granule cells monosynaptically and inhibits them
disynaptically. Bottom – The number of cells included in the full-scale model
matches numbers reported in anatomical studies.
54
Figure 4.2: Top – summary of mossy cell axonal projection, as a function of septo-
temporal position in the hippocampus. Bottom – summary of axon terminal field
extents along both the septo-temporal and transverse axes of the dentate gyrus.
57
Figure 4.3: Simulation results, at two different scales, for topographically
constrained EC-DG networks with feedforward and feedback inhibition. A1 –
simulation results from 1 million granule cells. Despite the random nature of the
perforant path input, dentate activity in both granule and basket cells consists of
spatio-temporal clusters of spikes. In the million-cell case, only a subset of the full
dataset is plotted to keep it from appearing solid black. B1 – the spatio-termporal
correlation (STC) confirms the existence of clusters. Bottom – Clusters persist when
the network is scaled down to 100k granule cells.

62
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Figure 4.4: Effect of progressively increasing strength of feedback inhibition. As the
amount of inhibition increases (A1 – A4), pronounced rhythmicity develops in both
granule cell and basket cell activity. The presence of this rhythmicity is verified with
frequency analysis (B1 – B4), which shows a peak developing at approximately 18
Hz.
65
Figure 4.5: Effect of increasing strength of perforant path drive in the presence of
strong feedback inhibition. When rhythmicity is present in the network, increasing
the strength of the perforant path excitatory drive (A1 – A4) both strengthens the
rhythmicity and increases its freqeuency. As DFT analysis shows, a small 18 Hz peak
at the base perforant path strength (B1) becomes a much larger peak centered at about
32 Hz. when the synaptic weight of the perforant path input is increased by 20x (B4).
67
Figure 4.6: Effect of increasing the strength of feedforward inhibition. The
feedforward component of basket cell inhibition helps to both desynchronize and
scale down total granule cell activity. As the strength of the feedforward inhibition
increases (A1 – A4), total granule cell activity decreases until there’s almost no
activity in the network. The 18 Hz. peak in the DFTs (B1 – B4) also disappears.
68
Figure 4.7: Large amounts of PP excitation (A1), feedback inhibition (A2), and
feedforward inhibition (A3) in isolation, with corresponding frequency plots (column
B). Of note is the fact that only feedback inhibition can cause oscillatory activity in
the network.
69
Figure 4.8: Initial simulation results after connecting the mossy cell associational
pathway. When EPSP magnitudes are set at values reported in the literature, strong
synchrony develops in all three dentate cell populations (A1). When synaptic weights
are rebalanced to fit the results of the paired-pulse stimulation experiments of
Douglas, McNaughton, and Goddard 1983 (A2), rhythmicity in the network
disappears, replaced by a large variety of spatio-temporal clusters (A3).
71
Figure 4.9: Histogram showing inter-spike intervals for each of the cell populations
in the model. Inter-spike intervals are very small for basket cells and mossy cells
(A1), which makes sense, given that basket cells are fast-spiking interneurons.
Granule cells don’t exhibit many small inter-spike intervals (A2), but rather, show a
peak in the 200 ms – 300 ms range. The distribution of inter-spike intervals for
entorhinal cortical cells looks exponential, which is expected for a group of cells
whose action potentials follow a Poisson process.

74
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Figure 4.10: Simulation results for two dentate networks that only differ in the
topography of the mossy cell projection to granule cells. Top: results when mossy
cell axonal tree extents vary by their location along the septo-temporal axis of the
dentate gyrus, as reported by Zimmer (Zimmer 1971). Bottom: results when mossy
cells are allowed to project randomly to the granule cell population. Note that the size
of the spatio-temporal clusters in granule cells increases substantially in the randomly
connected network, as evidenced by the spatio-temporal correlations (B1, B2).
75
Figure 4.11: Simulation results when strengthening and weakening three individual
synaptic connections in the granule-mossy-basket cell network. All raster plots show
1,000 ms of activity. When the excitatory mossy cell loop is strengthened relative to
the inhibitory basket cell loop, a pattern of theta-modulated gamma oscillations
develops (A3, A4, B2).
80
Figure 4.12: Same simulation results as in Figure 4.11, but showing 4,000 ms of
activity to give a better view of the theta-modulated gamma oscillations.
81
Figure 4.13: DFTs for the data shown in Figures 4.11-4.12. 82

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Chapter 1: Introduction

1.1 Introduction

Neuroscience is a field that, with the advent of computers and the rapid increase in computing
power over the last few decades, lends itself well to modeling. Ever since Alan Hodgkin and
Andrew Huxley published their 1952 paper describing the differential equations governing
sodium and potassium channel dynamics [1], the field has been modeling neurons and their
embedded membrane channels with systems of differential equations whose solutions can be
accurately approximated using computers. Models of single cells have generated insight about
many aspects of neural function, including how neurons generate and propagate action
potentials, how dendrites perform local computations, and how various membrane channels
affect the signal processing characteristics of the cell. More recently, as the prices of large
computer systems has come down, research groups have started moving from modeling single
cells to networks of cells [2]–[4]. This is especially important, as tools to manipulate networks of
neurons – their structure, their composition, and their connectivity – either don’t exist, or have a
variety of issues, leaving models as an ideal tool to manipulate individual components of neural
networks.

1.2 Overview of Hippocampal System

The hippocampal formation is a small neural system that sits in the temporal cortex of the brain.
Among other things, one of the primary functions of the hippocampus is to assist in the
formation of new declarative memories [5]. It does this by performing a series of
Page | 11
transformations, via several cell layers, on incoming short-term memories to re-encode them into
a form suitable for storage as long-term memories.
In the rat, the hippocampus is composed of a series of repeating intrinsic circuits known
as the tri-synaptic pathway [6] (Figure 1.1). The trisynaptic pathway receives its name because
it’s composed of 3 main regions, which are connected in a largely feed-forward manner. The
dentate gyrus (DG) is the first of these regions/layers, and is dominated by approximately one
million granule cells that receive their major input from layer II lateral and medial entorhinal
cortical (EC) neurons [7]. The main target of the granule cell output, or mossy fibers, is CA3.
CA3 is composed of approximately 330,000 pyramidal cells, which perform the second major
transformation on the set of spike trains representing the memory, before sending projections to
the CA1 region, the final main region in the tri-synaptic pathway. CA1 contains approximately
420,000 pyramidal cells, and performs the final transformation on the memory signal before
sending its output to the subiculum and, eventually, back other layers in the entorhinal cortex.

Figure 1.1: Hippocampal tri-synaptic pathway, with information flowing first from dentate
gyrus (DG), then to CA3, and finally to CA1.

Page | 12

The hippocampus is one of the most well studied systems in the brain; lots of quantitative
data exists about it, the cells that make it up [8]–[10], its structure, and its internal connectivity
[6], [11]. That fact, along with advances in parallelizable software systems for accurately
representing anatomical and physiological characteristics of neural systems, and paired with the
growth of high performance computing systems capable of sustaining the numerical burden of
simulating large-scale neural networks, makes the hippocampus a good brain region to model.

1.3 Research Objectives

One of the contributions of this research has been to endow the lab with computational
capabilities it didn’t previously have, and to start the effort to create a large-scale model of the
rat hippocampus. One of the overarching goals of the group is to create a model that has enough
biological realism such that data it produces gives us insight into how individual components of
the hippocampus combine and interact with each other to generate network- and system-level
spiking activity. A further goal of the group is to make the model general and adaptable enough
that it can be a useful tool to explore a wide variety of research questions for the next several
years.
This dissertation is organized as follows. Chapter 2 describes the infrastructure – the
hardware and software – that was built to support simulations, data analysis, and visualization of
large-scale neural network model data. Chapter 3 describes the implementation of a biologically
realistic model of the rat dentate gyrus, and shows for the first time the critical role that
topography plays in shaping network-level spiking activity. The contents of this chapter were
published in the BRAIN special issue of the IEEE Transactions of Biomedical Engineering.
Page | 13
Chapter 4 describes an expansion of the original dentate network to include both feedforward
and feedback inhibition from the local basket cell network and the mossy cell associational
system, and shows how rich oscillatory dynamics can evolve from a relatively small number of
interacting local circuits. The contents of this chapter were published in a research topic on the
dentate gyrus and its local circuits in Frontiers in Systems Neuroscience. Finally, chapter 5
summarizes the findings from the research and provides concluding comments.

1.4 References
[1] A. Hodgkin and A. Huxley, “A Quantitative Description Of Membrane Current And Its
Application To Conduction And Excitations In Nerve,” J. Physiol., pp. 500–544, 1952.
[2] H. Markram, “The blue brain project.,” Nat. Rev. Neurosci., vol. 7, no. 2, pp. 153–60, Feb.
2006.
[3] E. M. Izhikevich and G. M. Edelman, “Large-scale model of mammalian thalamocortical
systems.,” Proc. Natl. Acad. Sci. U. S. A., vol. 105, no. 9, pp. 3593–8, Mar. 2008.
[4] R. Ananthanarayanan, S. K. Esser, H. D. Simon, and D. S. Modha, “The Cat is Out of the
Bag : Cortical Simulations with 10 9 Neurons , 10 13 Synapses,” Proceedings of the
Conference on High Performance Computing Networks, 2009.
[5] H. Eichenbaum, “The hippocampus and mechanisms of declarative memory.,” Behav.
Brain Res., vol. 103, no. 2, pp. 123–33, Sep. 1999.
[6] D. G. Amaral and M. P. Witter, “The three-dimensional organization of the hippocampal
formation: A review of anatomical data,” Neuroscience, vol. 31, no. 3, pp. 571–591, 1989.
[7] D. G. Amaral, H. E. Scharfman, and P. Lavenex, “The dentate gyrus: fundamental
neuroanatomical organization (dentate gyrus for dummies).,” Prog. Brain Res., vol. 163,
pp. 3–22, Jan. 2007.
[8] R. S. Williams and S. Matthysse, “Morphometric analysis of granule cell dendrites in the
mouse dentate gyrus.,” J. Comp. Neurol., vol. 215, no. 2, pp. 154–64, Apr. 1983.
[9] X. G. Li, P. Somogyi, a Ylinen, and G. Buzsáki, “The hippocampal CA3 network: an in
vivo intracellular labeling study.,” J. Comp. Neurol., vol. 339, no. 2, pp. 181–208, Jan.
1994.
Page | 14
[10] J. C. Magee and D. Johnston, “Characterization of single voltage-gated Na+ and Ca2+
channels in apical dendrites of rat CA1 pyramidal neurons.,” J. Physiol., vol. 487 ( Pt 1,
pp. 67–90, Aug. 1995.
[11] P. E. Patton and B. McNaughton, “Connection matrix of the hippocampal formation: I.
The dentate gyrus.,” Hippocampus, vol. 5, no. 4, pp. 245–86, Jan. 1995.

Page | 15
Chapter 2. Computational Platform for Neural Modeling

2.1 Software Infrastructure

As computer hardware has increased in performance over the past 50 years, a plethora of
software tools have been developed to model neurons and neural networks. Many of these
packages share a core set of functionality, such as the ability to model sub-cellular processes like
synaptic and trans-membrane channel dynamics, the ability to represent whole cells as either a
series of interconnected compartments or with simplified “integrate-and-fire” dynamics, and the
ability to connect single cells to form networks [1]. These packages differ, though, in the amount
of usability, approachability, performance, and scalability they provide to the research
community. They also vary in their popularity among research groups.
At the outset of this research effort, we conducted a comparative survey of the main
simulation packages, and selected NEURON [2], [3] as the simulator to develop the large-scale
hippocampus model on. It was chosen because it appeared to have the most extensive and well-
rounded functionality of any simulator at the time, runs efficiently, is parallelizable via MPI
bindings [4], scales well on multi-processor machines and clusters [5], is being actively
developed and supported, has been used to publish more than a thousand research papers [6], and
has an online repository where users can make their models available to the wider research
community [7].
In addition to NEURON, the Python programming language was selected as our tool for
data analysis and visualization. Python, which is a well supported, easy-to-learn, and
extendable/modular general programming language, has found strong traction in the scientific
and high-performance computing fields [9], [10]. Because of this, and because NEURON has
Page | 16
been implemented as a Python module [8], we use it, along with scientific and visualization-
oriented modules, to 1) specify our large-scale hippocampal model, 2) run analyses on data
produced by simulations, and 3) create plots and other visualizations of that data.

2.2 Hardware Infrastructure

With the software toolset selected, the next challenge was to build a computer cluster capable of
supporting simulations with cellular networks consisting of more than a million multi-
compartmental neurons. The performance of the NEURON engine on parallel hardware has been
well characterized by its developers [5], and depends on multiple factors, including system
architecture (number of CPUs, CPU instruction set, amount of RAM, and network bandwidth),
number and complexity of individual cell models, and complexity of the cellular network. In
particular, that study concluded that NEURON simulations are typically CPU-bound, which
makes raw CPU performance important, and that larger amounts of on-board CPU cache can
improve performance.
To verify these conclusions, and to compare the performance of individual CPU models
with each other, we benchmarked a randomly connected neuronal network consisting of copies
of a published CA1 pyramidal cell [11] on a variety of computer hardware. Though NEURON
can be compiled to run on processors with the x86 and power instruction sets, IBM processors
were prohibitively expensive, so benchmarks were limited to CPUs from Intel and AMD.
NEURON doesn’t run on the ARM or Sun SPARC architectures, so they similarly weren’t
included. For a series of simulations in which the number of CPUs remained constant, but the
size of the model increased, the time required to complete each simulation also increased
proportionally. However, the Intel CPU model with the larger cache and the newer architecture
Page | 17
scaled to large network sizes better (see Figure 2.1). AMD processors didn’t outperform Intel
processors, even though they have more CPU cores. We attribute this to a less efficient CPU
architecture for the types of simulations we perform.

Figure 2.1: Comparison of total simulation runtime across two different Intel CPU architectures.
Runtime increases nonlinearly as the total network size increases, but the E5520, which is a
newer-generation CPU, scales better for large numbers of cells.

A cost analysis was also performed, as a lower performing processor may turn out to
provide the greatest benefit if its cost is low enough that many more can be purchased, compared
to a better performing, but more expensive model. Table 2.1 shows a breakdown of cost for
several processors within a family. These processors share the same micro-architecture and
cache size, but only vary in their clock speed. As Figure 2.2 shows, for lower clock speeds, the
price increases slowly with modest speed gains, but then hits a “corner,” after which costs
increases dramatically for very small increases in speed. Thus, it makes the most financial sense
to buy nodes whose CPUs fall as close to that corner, in the flat section of the curve, as possible.
0
2000
4000
6000
8000
10000
12000
14000
512 2048
Run Time (s)
Total Number of Cells
Total run1me
(E5410)
Total run1me
(E5520)
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Table 2.1: Cost breakdown for different CPUs within a family/architecture.

CPU model CPU speed (GHz) Price ($) price/GHz ratio
XEON E5405 2.00 $249.10 124.55
XEON E5410 2.33 $307.40 131.93
XEON E5420 2.50 $349.80 139.92
XEON E5430 2.66 $498.20 187.29
XEON E5440 2.83 $752.60 265.94
XEON E5450 3.00 $975.20 325.07

Figure 2.2: CPU price vs. speed curve. There are two main sections of the curve – the relatively
flat part, where speed increases come at a small dollar expense, and the steep part, where similar
speed gains are much more expensive.

In the end, two separate purchases were made over a 6-month period. The cluster, in its
current state, has 394 dual quad-core Intel-based nodes and 74 dual hexa-core Intel-based nodes,
for a total of 4,040 processor cores. The system has 8.1 TeraB of distributed RAM, 73.1 TeraB
of distributed disk space, and a maximum theoretical performance of 38.82 teraflops. All nodes
are connected to a high-speed, low-latency 10G Myrinet networking backbone. These nodes are
$0.00
$200.00
$400.00
$600.00
$800.00
$1,000.00
$1,200.00
2.00 2.20 2.40 2.60 2.80 3.00
Price ($)
Speed (GHz)
CPU price ($) vs speed (GHz)
Price ($)
Page | 19
housed, maintained and monitored on a 24/7 basis in USC’s high-performance computing
(HPCC) facility (Figure 2.3).

Figure 2.3: 4,040-CPU Beowulf cluster used to run simulations. NEURON running over MPI
was used to run the simulations, with Python being used to specify the model and perform data
visualization/analysis.

2.3 References
[1] R. Brette, M. Rudolph, T. Carnevale, M. Hines, D. Beeman, J. M. Bower, M. Diesmann,
A. Morrison, P. H. Goodman, F. C. Harris, M. Zirpe, T. Natschläger, D. Pecevski, B.
Ermentrout, M. Djurfeldt, A. Lansner, O. Rochel, T. Vieville, E. Muller, A. P. Davison, S.
El Boustani, and A. Destexhe, “Simulation of networks of spiking neurons: a review of
tools and strategies.,” J. Comput. Neurosci., vol. 23, no. 3, pp. 349–98, Dec. 2007.
[2] M. L. Hines and N. T. Carnevale, “The NEURON simulation environment.,” Neural
Comput., vol. 9, no. 6, pp. 1179–209, Aug. 1997.
[3] N. Carnevale and M. Hines, The NEURON book. .
[4] M. L. Hines and N. T. Carnevale, Translating network models to parallel hardware in
NEURON., vol. 169, no. 2. 2008, pp. 425–55.
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[5] M. Migliore, C. Cannia, W. W. Lytton, H. Markram, and M. L. Hines, “Parallel network
simulations with NEURON.,” J. Comput. Neurosci., vol. 21, no. 2, pp. 119–29, Oct. 2006.
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2003.

Page | 21
Chapter 3: A Million-Plus Neuron Model of the Hippocampal
Dentate Gyrus: Critical Role for Topography in Determining
Spatio-Temporal Network Dynamics

3.1 Abstract

This chapter describes a million-plus granule cell compartmental model of the rat hippocampal
dentate gyrus, including excitatory, perforant path input from the entorhinal cortex, and
feedforward and feedback inhibitory input from dentate interneurons. The model includes
experimentally determined morphological and biophysical properties of granule cells, together
with glutamatergic AMPA-like EPSP and GABAergic GABAA-like IPSP synaptic excitatory
and inhibitory inputs, respectively. Each granule cell was composed of approximately 200
compartments having passive and active conductances distributed throughout the somatic and
dendritic regions. Modeling excitatory input from the entorhinal cortex was guided by axonal
transport studies documenting the topographical organization of projections from subregions of
the medial and lateral entorhinal cortex, plus other important details of the distribution of
glutamatergic inputs to the dentate gyrus. Information contained within previously published
maps of this major hippocampal afferent were systematically converted to scales that allowed the
topographical distribution and relative synaptic densities of perforant path inputs to be
quantitatively estimated for inclusion in the current model. Results showed that when medial and
lateral entorhinal cortical neurons maintained Poisson random firing, dentate granule cells
expressed, throughout the million-cell network, a robust, non-random pattern of spiking best
described as spatio-temporal “clustering”. To identify the network property or properties
responsible for generating such firing “clusters”, we progressively eliminated from the model
Page | 22
key mechanisms such as feedforward and feedback inhibition, intrinsic membrane properties
underlying rhythmic burst firing, and/or topographical organization of entorhinal afferents.
Findings conclusively identified topographical organization of inputs as the key element
responsible for generating a spatio-temporal distribution of clustered firing. These results
uncover a functional organization of perforant path afferents to the dentate gyrus not previously
recognized: topography-dependent clusters of granule cell activity as “functional units” or
“channels” that organize the processing of entorhinal signals. This modeling study also reveals
for the first time how a global signal processing feature of a neural network can evolve from one
of its underlying structural characteristics.

3.2 Introduction

Developing large-scale, quantitatively based models of neural systems has become a realizable
goal in recent years [1]–[3], largely because of three major developments: (i) data collection over
the course of the past several decades has led to substantial databases of anatomical and
physiological properties for many neural systems [4]–[11]; (ii) the development of sophisticated
and parallelizable software systems for representing these anatomical and physiological
characteristics [12]–[15]; (iii) the continued growth of high performance computing systems
capable of sustaining the numerical burden of such large-scale models [16], [17].
One of the most extensively studied regions of the brain is the hippocampal formation.
Numerous anatomical analyses over the course of the last century have documented the classes,
numbers, and organization of principal neurons [18]–[22] and interneurons [23], [24] in this
limbic region. Extensive studies at the electron microscopic level have provided knowledge of
the numbers, densities, membrane locations, and neurotransmitter properties of synapse
Page | 23
populations [25]–[29]. Despite this wealth of knowledge, there have been few detailed,
quantitative models of the hippocampal system. Those that have been developed have been
limited to subregions of the hippocampus, understandably given the complexity of the system.
These initial models have been successful in providing insights into functional properties of the
hippocampus at a subsystems level [30]–[33].
Here we describe the first step in an implementation of a full-scale model of the
hippocampal formation. We have dealt with the first stage in what has been termed the intrinsic
“tri-synaptic pathway” of the hippocampus, i.e., the “perforant path” excitatory projections from
the entorhinal cortex (EC) to granule cells of the dentate gyrus (DG), including inhibitory
feedback from DG interneurons. Our model is based on the hippocampal formation of the rat, as
the majority of quantitative anatomical information available is for the rat species. We have
taken into consideration a number of factors concerning the EC-DG projection in an attempt to
attain a model that is as biologically realistic as is achievable given current knowledge. In
general, these factors include: the number and ratio of layer II EC neurons and dentate granule
cells; the ratio of inhibitory interneurons and dentate granule cells; the dendritic morphological
structure and morphological variability of granule cells; the terminal field distributions of EC
layer II cells; the synaptic density of EC layer II cells onto dentate granule cells; the passive
membrane properties of granule cells; both somatic and dendritic active conductances
responsible for the action potential and for other voltage-dependent properties.
One other anatomical feature that also is the focus of the present study concerns the
topographical organization of EC-DG projections. Topography of anatomical connections, i.e.,
the point-to-point relation of typically non-uniform synaptic connectivity between any two brain
regions, is a property of nearly all mammalian brain systems, and is distinctly different for each.
The topography of EC-DG projections in the rat has been studied elegantly and reported
Page | 24
previously [34]–[38]. The question being asked in the present study is the functional
consequence of that topography. To our knowledge, the issue of the functional significance of
the topographical organization of a projection system has yet to be addressed quantitatively for
any brain system, and is an issue particularly well-suited for a large-scale, structural-functional
model. We show here that the topographical characteristics of EC projections to the DG impose
quantifiable boundaries on the spatio-temporal properties of granule cell network activity.
Findings conclusively identified topographical organization of inputs as the key element
responsible for generating a spatio-temporal distribution of clustered firing. As such, these
results uncover a functional organization of perforant path afferents to the DG not previously
recognized: topography-dependent clusters of granule cell activity as “functional units” or
“channels” that organize the processing of EC signals.

3.3 Methods
A. Model Scale and Features

Models of the EC-DG system were completed according to two scales – one with 1,000,000
granule cells, i.e., equivalent to the number of cells in one hemisphere of the rat hippocampus
[7], [39], and one with 100,000 granule cells, i.e., equivalent to 1:10 scale to accelerate
simulation time. All results reported here were observed at both scales. All networks studies
were composed of dentate granule cells and inhibitory interneurons, with excitatory input to
granule cells modeled after the organization of layer II EC afferents. In general terms, the models
featured complex and variable morphologies for granule cells, multiple active conductances
distributed non-uniformly throughout granule cell membranes, interneurons configured (as cell
Page | 25
bodies only) to provide both feed-forward and feedback inhibition, and either randomly or
topographically organized excitatory input to network neurons. Specifics are provided below.

B. Granule Cell Morphology

The morphological characteristics of hippocampal dentate granule cells have been studied in
depth and with quantitative detail [40]–[42]. Example three-dimensional dendritic structure was
obtained from sample reconstructed neurons labeled using a variety of methodologies and
available through neuromorpho.org [5]. To incorporate morphological diversity in the granule
cell population, however, the L-NEURON tool [43] was used. L-NEURON allows for the
generation of unique dendritic and axonal trees based on sampling from a set of statistical
distributions that describe their fundamental structural parameters [43], [44]. Table 3.1 shows the
distributions used for each of the granule cell parameters, while Figure 3.1 shows a sample of L-
NEURON generated granule cell somata and dendritic trees. Only the somata of basket cells
were modeled as part of the present study, so no basket cell dendritic structures were included;
no cells were given an explicit axon.

Figure 3.1: Two sample dentate granule cell morphologies generated using L-NEURON with
the parameter distributions shown in Table 3.1.

Page | 26
Table 3.1: Morphological Parameters for Dentate Granule Cells

Variable Distribution Mean/Min Std. Dev./Max
Soma Diameter Gaussian 9.00 2.00
Number of Stems Uniform 2.00 4.00
Stem initial diameter Gaussian 1.51 0.79
Branching diameter Gaussian 0.49 0.28
IBF branch length Gaussian 10.70 8.40
Term. branch length Gaussian 10.70 8.40
Daughter ratio Uniform 1.00 2.00
Taper ratio Gaussian 0.10 0.08
Rall power Constant 1.50 ---
Bifurcation amp. Gaussian 42.00 13.00
Tree elev. (narrow) Gaussian 10.00 2.00
Tree elev. (medium) Gaussian 42.00 2.00
Tree elev. (wide) Gaussian 75.00 2.00

C. Granule Cell Bioelectric Properties

Biophysical properties for each of the cell types in the model were taken from previously
published experimental data and from previously published mathematical models of the DG [4],
[45]–[52]. Table 3.2 shows the channel distribution for granule cells, while Table 3.2 and Figure
3.2 show key passive and active properties for one instance of a granule cell.

Table 3.2: Passive & Active Properties for Dentate Granule Cells

Property / Mechanism Soma GCL Inner 1/3 Middle 1/3 Outer 1/3
Soma S.A. (cm
2
) 4.97E-4
Soma Volume (cm
3
) 1.11E-6
R.M.P. (mV) -75.01
R
in
(M-Ohms) 185.86
Membrane time const. (ms) 31.0
Latency to first AP (ms) 100.0
C
m
(uF/cm
2
) 9.8 9.8 15.68 15.68 15.68
Ra (ohm-cm) 210 210 210 210 210
Leak (S/cm
2
) 2.9E-4 2.9E-4 4.6E-4 4.6E-4 4.6E-4
Sodium (S/cm
2
) 0.84 0.126 0.091 0.056 ---
Delayed Rectifier K (slow) (S/cm
2
) 6.0E-3 6.0E-3 6.0E-3 6.0E-3 8.0E-3
Page | 27
Delayed Rectifier K (fast) (S/cm
2
) 0.036 9.0E-3 9.0E-3 2.25E-3 2.25E-3
A-type K (S/cm
2
) 0.108 --- --- --- ---
L-type Ca (S/cm
2
) 2.5E-3 3.8E-3 3.8E-3 2.5 ---
N-type Ca (S/cm
2
) 1.5E-3 7.4E-4 7.4E-4 7.4E-4 7.4E-4
T-type Ca (S/cm
2
) 7.4E-5 1.5E-4 5.0E-4 1.0E-3 2.0E-3
Ca-dependent K (S/cm
2
) 1.0E-3 4.0E-4 2.0E-4 --- ---
Ca- and V- dependent K (S/cm
2
) 1.2E-4 1.2E-4 2.0E-4 4.8E-4 4.8E-4
Tau for decay of intracell. Ca (ms) 10.0 10.0 10.0 10.0 10.0
Steady-state intracell. Ca (mol) 5.0E-6 5.0E-6 5.0E-6 5.0E-6 5.0E-6

The modeled network used AMPA and GABAergic synapses for connectivity. We
modeled the postsynaptic conductance as a sum of two exponentials, with the rise time, fall time
and maximum conductance, optimized to match experimentally recorded EPSPs and IPSPs in
both granule and basket cells [53]–[58], to the extent such data was available. At certain levels of
basket cell inhibition, whether feedforward or feedback, there was pronounced synchrony in
network activity (see Figure 3.5). Because highly synchronous firing was not the focus of the
present study, and without complete knowledge of IPSP size for granule cells, we scaled the
basket cell inhibition until the persistent synchrony disappeared. Because axons were only
implicitly modeled, a delay to postsynaptic activation was added to account for axonal
conduction of action potentials. In the million-granule-cell model, the number of synapses in the
network corresponded to the number of reported spines on granule cells [27], [42], [59]. In the
1:10 scale model, we scaled the number of synapses down by a factor of 10, while
simultaneously increasing peak synaptic conductance by a factor of 10. Table 3.3 shows the
relevant synaptic parameters for the network.
Page | 28

Figure 3.2: Granule cell active properties. Top left: When subjected to a current clamp stimulus
at the soma, the granule cell responds by firing an action potential with a latency of
approximately 100 ms. Top right: When the current clamp amplitude is just over the threshold
required to elicit a second AP, its latency is approximately 350 ms. This matches experimental
data (bottom, reproduced from [50]).

D. Topography

The EC is divided into two areas termed the lateral entorhinal cortex (LEC) and the medial
entorhinal cortex (MEC). Anatomically, the LEC lies rostral and lateral to the MEC. Both areas
contribute to the perforant path that projects onto the DG in a laminar manner. The LEC
primarily targets the outer third of the molecular layer of the DG, and the MEC primarily targets
the middle third [60], [61]. This laminar organization is present in our model.
Page | 29

Figure 3.3: Summary of the image processing pipeline used to quantify the EC-DG topography
from data obtained from [38]. Not all data is shown. 1) The data in their anatomical subject maps
are digitized and grouped according to injection location. 2) The maps are projected onto a
standard coordinate space. 3) The sets are averaged. 4) The averaged group data are projected
onto an average anatomical map. The compass represents the rostro-caudal and medio-lateral
axes.

Two additional features of the EC-DG projection were used to define its topography.
First, there was the relationship between the position of the presynaptic inputs (cell bodies) and
the position of their projections (axons) onto the postsynaptic population. Second, there was the
geometry of the axon terminal field. The combination of the two features constrained the subset
of the DG population with which a given presynaptic neuron can synapse.
Experimental analyses have revealed that EC input to the DG is distributed with a non-
random topography. In general, the lateral regions of the LEC and the lateral/caudal regions of
the MEC project to the septal portion of the DG, and the medial regions of the LEC and the
medial/rostral regions of the MEC project to the temporal portion of the DG (Figure 3.3).
Dolorfo and Amaral characterized this topography in rats, and their work is the basis of the
specific topographical relationships implemented here, though we verified the generality of the
Dolorfo and Amaral findings with those of other researchers [34]–[38]. Dolorfo and Amaral
found that any injection within a particular septo-temporal quartile of the DG resulted in the
Page | 30
same characteristic labeling of EC. Therefore, the data were divided into sets based on the
quartiles in which the injection sites were located in order to calculate the mean EC area that
projected to a given quartile. However, because each injection was performed on a different rat,
each brain map had a different size and shape. In order to quantify this work, an image
processing pipeline was designed that digitized the brain maps, projected the individual
anatomical brain maps onto a common standard coordinate system, calculated the mean of the
data, and projected the resulting data back onto an average anatomical map (Figure 3.3). An
average anatomical map was calculated by computing the mean of all of the dimensions of the
individual anatomical subject maps.
To determine the axon distribution, the maps were converted into probabilities where the
intensity, or darkness, of the pixel corresponded to the probability that an EC neuron located
within would send its axon to a particular quartile of the DG. The specific point within the
quartile to which the axon is sent is referred to as the “perforation point.”
Upon reaching the perforation point, the axon branches out into the terminal field. The
terminal field was limited to between 1.0 and 1.5 mm in the septo-temporal direction and
encompassed the entire transverse width of the DG within this extent. The constraints were based
on morphological and anatomical studies that characterized individual axon morphologies and
the overall patterns of projection [61], [62].

E. Computational Platform

All simulations were run on a high-performance compute cluster consisting of 394 dual quad-
core Intel-based nodes and 74 dual hexa-core Intel-based nodes, for a total of 4,040 processor
cores. The system has 8.1 TeraB of distributed RAM, 73.1 TeraB of distributed disk space, and a
Page | 31
maximum theoretical performance of 38.82 teraflops. All nodes are connected to a high-speed,
low-latency 10G Myrinet networking backbone. These nodes are housed, maintained and
monitored in facilities operated by the University of Southern California Center for High-
Performance Computing and Communications. We used version 7.3 of the NEURON simulation
engine [12], [63] to run all simulations, and used Python 2.7 for model specification, data
visualization, and analysis [64], [65].
Table 3.3: Synaptic Parameters for a 1/10-Scale Network

Synapse Counts:
GC # spines - inner 1/3: 115 - 135 GC to BC 50 - 140
GC # spines - middle 1/3: 105 - 120 MEC to BC 10 - 20
GC # spines - outer 1/3: 110 - 130 LEC to BC 10 - 20
BC to GC: 4 - 8
Synaptic Weights (S/cm
2
):
MEC to GC: 1.17E-4 GC to BC: 1.13E-3
LEC to GC: 1.5E-4 MEC to BC: 4.21E-5
BC to GC: 5.45E-5 LEC to BC: 4.21E-5
EPSP/IPSP Rise Time (ms):
MEC to GC: 1.05 GC to BC: 0.1
LEC to GC: 1.05 EC to BC: 1.05
BC to GC: 1.05
EPSP/IPSP Decay Time (ms):
MEC to GC: 5.75 GC to BC: 0.59
LEC to GC: 5.75 EC to BC: 18
BC to GC: 5.75
Reversal Potentials (mV):
MEC to GC: 0 GC to BC: -75
LEC to GC: 0 EC to BC: 0

3.4 Results
A. Granule Cell Response to Random Entorhinal Input: Firing in Spatio-Temporal ”Clusters”

Initial simulations of granule cell network dynamics to EC input involved both medial and lateral
entorhinal (MEC & LEC) neurons firing at a mean frequency of 3.0 Hz, accelerated (by design)
Page | 32
over the course of approximately the first 1000 ms of the simulation. Four (4.0) seconds of time
were simulated in all results presented here. Entorhinal inputs were topographically organized
according to the relations described in the Methods. Basket cells were configured to provide both
feedforward and feedback inhibition. All active granule cell membrane properties included those
described in Table 3.2. Simulation results with a one million granule cell population revealed
that despite continued Poisson EC input, granule cells discharged in a decidedly non-random,
non-uniform manner. As shown in Figure 3.4 (top), granule cells throughout the entire septo-
temporal extent of the DG fired in what we call here spatio-temporal “clusters,” i.e., irregular
periods of spiking and non-spiking lasting approximately 50-100 ms “on” and 50-75 ms “off”.
The granule cells engaged in firing changed spatial location along the septo-temporal axis, as
evidenced by the apparent “drift” in patterned firing in Figure 3.4A and other similar figures.
The appearance of clustered spiking in response to Poisson EC input was not specific to million-
granule cell populations, but was equally apparent for simulations involving 100k granule cells
as well (Figure 3.4, bottom).
In some cases, the appearance of spatial-temporal clusters did not appear immediately
with the onset of EC input, but instead only appeared after a period of highly rhythmic granule
cell activity. In those cases, granule cell spiking started after approximately 200 ms, reaching a
maximum at approximately 300 ms. At this time point granule cell output was highly
synchronous, with granule cells along the entire extent of the septo-temporal axis firing at a high
rate for a duration of approximately 100 ms. Approximately midpoint in this initial 100 ms of
extended firing, basket cells fired synchronously as well, leading to a termination of extended
granule cell firing. After a few more periods of synchronous granule cell discharge alternating
with periods of heightened basket cell output the system appears to reach an equilibrium (after
Page | 33
800-900 ms into the simulation). It is at this point that a steady-state of “clustered” spike
discharges emerges and continues.

Figure 3.4: Simulation results for topographically constrained EC-DG networks with
feedforward and feedback inhibition, run at two different scales: 1M granule cells (top), and
100k granule cells (bottom). At both scales, spatio-temporal clusters appear in the granule cell
activity, despite the random nature of the EC input. In the million-cell case, only a subset of the
full dataset is plotted to keep it from appearing solid black. Column B: 2D autocorrelations
confirm the presence of these clusters.

Quantitative analyses verified the existence of clusters of spike firing. 2D autocorrelation
allows an analysis of the data in both spatial and temporal dimensions, and was used to analyze
most of the results presented here. It was constructed by computing every pairwise cross-
correlation of discretized spike trains in a random sample of 10,000 neurons. The spike trains
were discretized by counting the number of spikes elicited by a particular neuron within a bin
size of 5 ms. The resulting cross-correlations were sorted by the distance between the neuron
pairs and were further binned using a resolution of 0.05 mm. The mean cross-correlation within
each bin was computed.
Page | 34
The right-hand column of Figure 3.4 shows the 2D autocorrelations for the million-cell
and 100k-cell simulations. What emerges from the analysis is something that looks like a typical
cluster for each of the datasets: in the million-cell case, clusters are roughly elliptical, with a
temporal width of approximately 40-50 ms and a spatial height of 1-2 mm. The analysis looks
very similar for the 100k-cell simulation, which verifies that clusters exist and are similar at both
simulation scales.
Further analysis was performed on the 100k-cell dataset using DENCLUE 2.0, a density-
based cluster identification algorithm [66]. For this application, a Gaussian density kernel was
used. Analyses show that a) clusters exist, and b) they appear in a wide variety of sizes, though
their basic shape remains similar. Statistical analysis of the identified clusters shows that inter-
centroid cluster time is 11±12 ms, and that the density of spikes within a cluster is approximately
12±9 spikes/ms-mm.

B. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Inhibition

Following this initial characterization, we conducted experiments designed to identify the
mechanisms underlying granule cell clustered spiking: what was responsible for transforming
continuous random spike firing into non-continuous, non-periodic, clusters of spikes? A first
hypothesis concerned a possible role for GABAergic inhibition, given the strong effect of
interneuron activity in synchronizing granule cell activity in the early stages of the simulation.
Indeed, when feedback inhibition was increased by 4-10 times that used in initial simulations,
longer periods of synchronous activity, marked by multiple bands of high activity followed by
bands of almost zero activity in the DG followed (Figure 3.5A). This pattern of bands eventually
becomes asynchronous, though, giving rise to spatio-temporal clusters similar to the ones we see
Page | 35
with less inhibition. When we increase inhibition to a level 20 times greater than normal,
however, the synchrony persists for the entire duration of the simulation.

Figure 3.5: Results of increasing the feedback GABA inhibition. A) The raster plot of the
granule cell output for increasing levels of inhibition. GABA level 1 uses the original BC-GC
conductance values while levels 2-4 use 4, 10, and 20 times larger conductance values,
respectively. B) The 1D DFT plot of the data. As the inhibition increases, the granule cells
develop synchronous firing at 22 Hz.

One-dimensional discrete Fourier transforms (DFTs) were used to analyze the temporal
frequency spectrum of the spike data. They were computed using a spike density matrix. The
matrix was constructed by counting the total number of spikes elicited within a spatio-temporal
bin with a resolution of 0.05 mm and 2 ms. The 1D DFT was computed for each row of the
matrix resulting in the temporal frequency spectrum at a particular septo-temporal location on
the DG. The mean of all of the resulting DFTs was then computed.
Page | 36
As Figure 3.5B shows, as the amount of GABAergic inhibition increases in the network,
a small peak at approximately 22 Hz turns into a sharp one, followed by another sharp peak at
about 45 Hz with even more inhibition. This points to oscillations occurring in the low to
medium range of the gamma band. This GABA-dependent rhythmicity has been described
previously [67], [68].
Given the synchrony introduced into granule cell spiking as a result of feedback
inhibition, we decided to remove sources of inhibition to see whether the cluster activity would
also disappear. There are two sources of inhibition in dentate granule cells: external inhibition,
from the basket cell population, and internal inhibition, due to the afterhyperpolarization (AHP)
that granule cells experience after one or more action potentials (APs). As Figure 3.6 illustrates,
spatio-temporal clusters persist with one or both of these sources of inhibition absent from the
network.

Figure 3.6: Granule cell activity when removing internal and external sources of inhibition. Top:
GABAergic inhibition removed; bottom: both AHP and GABA removed. Spatio-temporal
clusters persist in both cases, as evidenced by both the raster plots and 2D autocorrelations (B).

Page | 37
C. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Topographic Organization
of Entorhinal Afferents

We next turn to topography as the potential source of clustering. As Figure 3.7 shows, when the
constraints placed on EC-to-DG connectivity are removed, thus allowing a randomly connected
network where any EC neuron can synapse onto any dentate granule cell, the clusters that have
always been present in the output disappear, and bands of activity appear in their place. The 2D
autocorrelation corroborates this: while there’s still a small amount of temporal structure in the
network activity, it’s 8x-10x weaker than in any of the topographically constrained cases, and the
spatial component has completely disappeared – what once looked like an elliptical cluster in the
2D autocorrelation has become a band that occupies the full septo-temporal extent of DG. Thus,
it is the topography of the EC-DG projection that’s responsible for the emergence of spatio-
temporal clusters, even when the input to the network is random.

Figure 3.7: Simulation results for a randomly connected EC-DG network. In this simulation, the
granule cell AHP was removed, as was GABAergic inhibition. Spatio-temporal clusters are no
longer present, having been replaced with bands of activity with a high level of background
activity. In the 2D autocorrelation, what looked like a typical cluster is now a vertical band.
Thus, while there’s still a temporal variation in granule cell activity, the spatial component is
gone.

Page | 38
D. Mechanisms Responsible for Spatio-Temporal Clustered Spiking: Axon Terminal Field
Geometry

The previous results establish that the emergence of clusters in the spatio-temporal pattern of the
granule cell output is caused by topography. An immediate question that came to mind, given
these results, is how the parameters of the topography might influence the size and shape of the
clusters. The following set of simulations varied the axons’ terminal field extents in the septo-
temporal axis to investigate the contributions of the terminal field geometry to the emergence of
spatio-temporal clusters. These simulations did not include basket cells.

Figure 3.8: Effects of increasing the terminal field extent in the septo-temporal direction. A)
Raster plot of the granule cell output. B) The 2D autocorrelation of the data. As the terminal field
extent increases, the cluster size increases, and this is reflected by the increase in the spatial
extent of the 2D autocorrelation.

Page | 39
The results clearly show a dependence between the terminal field size and the cluster size
(Figure 3.8). As the size of the terminal field increases, the cluster size increases. Furthermore,
the density of the cluster decreases as the cluster size increases. This is verified given that each
simulation resulted in approximately the same number of spikes (1,580,000±30,000 spikes with a
range of 1,560,000 – 1,650,000 spikes). An increase in cluster size for the same number of spikes
per time signifies a decrease in cluster density.
The 2D autocorrelation demonstrates the relationship between spatio-temporal correlation
and the terminal field extent. The analysis shows that the extent of the spatial correlation
between one neuron and any other neuron increases as the terminal field increases. Also, the
terminal field does not appear to affect the extent of the temporal correlation. However, the
maximum of the 2D autocorrelation decreases as the terminal field extent increases. An
approximately 10-fold decrease in the peak correlation is seen between a terminal field extent of
0.5 mm and 5 mm.

3.5 Discussion

The study described here is based on the creation of a large-scale, compartmental neuron model
of the EC-DG projection system of the hippocampal formation. We have intended for the model
to be large-scale in the sense of including a total number of dentate granule cells, GABAergic
interneurons, and EC axons that are equivalent to those found in one hemisphere of the rat brain.
We have intended the model to be biologically realistic with respect to the numbers and ratios of
different classes of neurons, granule cell dendritic morphologies, classes and distributions of
somatic and dendritic conductances, and the presence of feedforward and feedback GABAergic
interneurons. In this its first generation of development and use, the model has uncovered a
Page | 40
functional organization of perforant path afferents to the DG not previously recognized: a spatio-
temporal clustering of granule cell spiking on the order of 11 ms between clusters and 12
spikes/ms-mm within clusters. These findings are important in several respects. First, these
spatio-temporal clusters of active granule cells represent “functional units” or “channels” that
organize the processing of EC signals. Second, results of the present study clearly demonstrate
that the spatio-temporal clustering property of the EC-DG pathway depends primarily on the
topographic organization of perforant path afferents. This is the first time that a functional
characteristic of a cortical projection has been linked specifically to topographic features of that
projection. Third, this organizational property of the EC-DG pathway is apparent only when
structural-functional relations are examined at large-scales. Smaller scale models would not have
revealed the clustering phenomenon, and thus, these results point to the importance of large-scale
modeling of cortical systems.
The model described in this report is not complete in the sense that there are several
features of the biological dentate gyrus not included in the present model, and that ultimately
may modify and extend the results reported here. One of these features includes other classes of
interneurons within the dentate hilus that are activated by granule cells and/or perforant path
axons, and that provide feedback to granule cells. Most prominent among these are mossy cells
[69] which are the source of the dentate commissural-associational system [70] and that
terminate throughout the inner one-third of the molecular layer [71]. This cell population lies
beneath the granule cell layer, and is excitatory to both dentate granule cells and inhibitory
interneurons [72], [73]. Additional types of hilar cells are not included in the present model, e.g.,
hilar perforant path-associated (HIPP) interneurons that provide inhibitory input to granule cells
in the inner and outer thirds of the molecular layer, respectively [29], [74]. The precise role that
Page | 41
these and other types of interneurons [23] play, if any, in modulating the spatio-temporal
“cluster” firing of granule cells has yet to be determined.
Another difference between the present model and one that is completely biologically
faithful concerns NMDA receptor-channels on the dendrites of granule cells. The current model
has only AMPA receptor-channels mediating EC-DG glutamatergic synaptic transmission. The
NMDA receptor subtype is activated preferentially by higher frequencies of afferent input [75],
[76], so the shape and/or size of clusters may change with the inclusion of NMDA receptor
subtypes. Future experiments will determine this, and may be conducted with higher mean
frequencies of EC input.
These additional anatomical and biophysical properties of the DG will be included in
future models, and ultimately will be examined for their influence on the topography-dependent
clustered firing of granule cells.
Electrophysiological recordings from neurons within the hippocampal formation in the
behaving animal have identified a number of correlates affiliated with animals’ learned behavior
[77]–[79], spatial location [80], or spatio-temporal properties of the animal learned behavior
[81]–[83]. Other studies have explored the anatomical distribution of spatial firing patterns of
neurons in the hippocampus [84], [85]. Many of these observations have been extended to EC,
parahippocampal and perirhinal cortices [86]–[88]. Differences between the EC and
hippocampal cortical correlates must be attributable to neural processing performed by
connections between the two structures, with the DG playing a major role [89]. Although
speculative, it may be neural processing micro-structures like the EC-DG cluster firing channels
described here that are in part responsible for the EC-to-hippocampal pyramidal cell
transformations observed to date.

Page | 42
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Chapter 4: Interactions between Inhibitory Interneurons and
Excitatory Associational Circuitry in Determining Spatio-Temporal
Dynamics of Hippocampal Dentate Granule Cells: A Large-Scale
Computational Study

4.1 Abstract

This chapter reports on findings from a million-cell granule cell model of the rat dentate gyrus
that was used to explore the contributions of local interneuronal and associational circuits to
network-level activity. The model contains experimentally derived morphological parameters for
granule cells, which each contain approximately 200 compartments, and biophysical parameters
for granule cells, basket cells and mossy cells that were based both on electrophysiological data
and previously published models. Synaptic input to cells in the model consisted of glutamatergic
AMPA-like EPSPs and GABAergic-like IPSPs from excitatory and inhibitory neurons,
respectively. The main source of input to the model was from layer II entorhinal cortical
neurons. Network connectivity was constrained by the topography of the system, and was
derived from axonal transport studies, which provided details about the spatial spread of axonal
terminal fields, as well as how subregions of the medial and lateral entorhinal cortices project to
subregions of the dentate gyrus. Results of this study show that strong feedback inhibition from
the basket cell population can cause high-frequency rhythmicity in granule cells, while the
strength of feedforward inhibition serves to scale the total amount of granule cell activity.
Results furthermore show that the topography of local interneuronal circuits can have just as
strong an impact on the development of spatio-temporal clusters in the granule cell population as
the perforant path topography does, both sharpening existing clusters and introducing new ones
with a greater spatial extent. Finally, results show that the interactions between the inhibitory and
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associational loops can cause high frequency oscillations that are modulated by a low-frequency
oscillatory signal. These results serve to further illustrate the importance of topographical
constraints on a global signal processing feature of a neural network, while also illustrating how
rich spatio-temporal and oscillatory dynamics can evolve from a relatively small number of
interacting local circuits.

4.2 Introduction

We recently reported on the first generation of a large-scale, biologically realistic compartmental
neuron model of the rat hippocampal dentate gyrus (Hendrickson et al. 2015). This model
included one million granule cells, axons from 112k entorhinal cortical neurons (layer II), and 6k
inhibitory interneurons configured synaptically as basket cells of the dentate gyrus. Entorhinal
axons provide glutamatergic, excitatory input to granule cells. In the model, basket cells were in
appropriate numbers relative to granule cells (i.e., matching an experimentally known ratio), and
were arranged in both GABAergic feedforward (relative to entorhinal afferents) and feedback
(relative to granule cell efferents) synaptic relations (Seress and Pokorný 1981; Zipp et al. 1989;
Lübbers and Frotscher 1987). Basket cell axons terminate around the somata and axon initial
segments of granule cells, and thus are a powerful source of inhibitory modulation of entorhinal-
driven granule cell output (Ribak et al. 1978; Ribak and Seress 1983).
Dentate afferents from the entorhinal cortex arise from both its medial and its lateral
subdivisions, and terminate in the middle and the outer thirds, respectively, of the dendrites of
dentate granule cells (Steward 1976; Hjorth-Simonsen and Jeune 1972; Hjorth-Simonsen 1972;
Witter 2007). The inner third of granule cell dendrites is innervated by associational and
commissural fibers arising from neurons intrinsic to the dentate hilus (Berger et al. 1981).
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Associational fibers arise from neurons ipsilateral to a given hemisphere (Zimmer 1971);
commissural fibers arise from contralateral sites (Gottlieb and Cowan 1973). Both associational
and commissural fibers arise from the same cells of origin within the dentate hilus, namely,
mossy cells (though other hilar neurons also may contribute) (Ribak et al. 1985; Swanson et al.
1981). Mossy cells are distributed loosely within the hilus in the rat, but are located more
compactly in the polymorphic layer of the rabbit and other species that are higher on the
phylogenetic scale, and that have a more well-organized hilar region (Berger et al. 1981; Amaral
et al. 2007).
Terminating within the inner one-third of the molecular layer, associational-commissural
afferents directly excite granule cells (Scharfman 1994; Soriano and Frotscher 1994; Ribak and
Shapiro 2007; Buckmaster et al. 1992). However, inhibitory interneurons embedded beneath the
granule cells send their dendrites through the granule cell layer and up into the molecular layer as
well (Scharfman 1991; Leranth et al. 1990). Thus, associational-commissural inputs can directly
activate both excitatory and inhibitory components of dentate circuitry (Scharfman 1995). In
fact, it has been shown previously that suprathreshold excitation of dentate granule cells by
entorhinal afferents can be determined by the balance between associational-commissural input
to excitatory (granule cells) and inhibitory (interneurons) dentate elements (Douglas et al. 1983).
In total, then, at the level of the dentate gyrus there are two major interneuron “loops”
contributing to the modification and transmission of entorhinal information to the pyramidal cell
populations of Ammon’s horn. The first includes the feedforward and feedback inhibitory
pathways enveloping the dentate granule cell population; the second is the mossy cell
associational-commissural system. Because mossy cells terminate monosynaptically onto both
granule cells and basket cells, there is at least a partial hierarchical organization of the mossy cell
system in relation to the basket cell-granule cell feedforward-feedback pathways. The impact of
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these two control pathways is complex and not easily deduced. A functional understanding of
these two interneuron pathways is made even more difficult because selective experimental
manipulation of some or most of this circuitry is not readily accomplished with current
technology. Transgenic mouse lines and viral vectors can be used to impair the expression of
specific synaptic receptors, but they cannot selectively alter specific cell types (Fuchs et al. 2007;
Korotkova et al. 2010; Caputi et al. 2012; Murray et al. 2011; Wulff et al. 2009). Optogenetics
can be used to modify interneurons to be susceptible to modulation using light, but currently the
technique can only target broadly defined and overlapping interneuron groups that are
identifiable by the expression of certain molecular markers and would not be able to specifically
affect, for example, mossy cells exclusively (Tang et al. 2014; Allen and Monyer 2015). The
nature and relative contributions of the basket cell and mossy cell systems to granule cell output,
despite being difficult to elucidate, are remarkably important given that these pathways are the
main arbiters of entorhinal input to the CA3/4 pyramidal cell regions. In addition, the dentate
hilar zone is the major target for noradrenergic and serotonergic brainstem afferents that have a
powerful modulatory influence on hippocampal function (Moore et al. 1978; Loy et al. 1980;
Moore and Bloom 1979; Azmitia and Segal 1978). These challenges to a more precise definition
of basket cell-interneuron and mossy cell-associational pathway functions we feel argues
strongly for a mathematical modeling approach. There is a wealth of quantitative anatomical
information in the hippocampal literature as to the numbers and densities of neurons and
interneurons, morphology of dendrites and distribution of dendritic spines, classes and
distributions of synapses, etc., required for such a model to successfully address the issues at
hand. Finally, a recent compartmental neuron model of the dentate gyrus, which included the
contribution of basket cells and mossy cells to hippocampal epileptic activity, provides guidance
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for a new, comprehensive modeling study of the functional properties of the associational and
basket cell control systems (Santhakumar et al. 2005; Dyhrfjeld-Johnsen et al. 2007).
The goal of the present analysis is to expand our previous large-scale, compartmental
neuron model of the dentate gyrus to include both the basket cell-inhibitory circuitry and the
mossy cell-associational system. By systematically varying parameters of the mossy cell and
basket cell pathways, we hope to provide better insight into their respective and collective
functional roles in modifying the dynamics of entorhinal-dentate spatio-temporal activity
patterns.
In brief, our analyses revealed that the feedforward component of the inhibitory circuit
serves to scale the total amount of granule cell activity, with the ability to shut it down almost
completely, while the feedback component has the ability to introduce high-frequency
rhythmicity in the network. The associational pathway, in partnership with the inhibitory
network, has the ability to both sharpen spatio-temporal clusters that exist due to the connectivity
constraints imposed by the perforant path topography, and to introduce new clusters that span a
greater portion of the septo-temporal extent of the dentate gyrus. Furthermore, by varying the
relative strength of the inhibitory and excitatory associational input to granule cells, it’s possible
to introduce high-frequency rhythmicity that’s modulated by a slowly varying oscillatory signal.

4.3 Methods
A. Model Features and Scale

The dentate model consisted of granule cells, basket cells, and mossy cells with input arriving
from axons organized as those from layer II neurons of the entorhinal cortex (EC). The EC cell
axons provided monosynaptic excitatory input to both granule cells and basket cells. Granule
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cells provided excitatory input to both basket cells and mossy cells, and basket cells provided
inhibitory input to granule cells. Thus, granule cells received both feedforward and feedback
inhibition via the basket cell population. Mossy cells provided excitatory input to both granule
cells and basket cells (Figure 4.1).

Figure 4.1: Top – schematic showing local feedback circuits in the dentate gyrus, with the
perforant path providing input to both granule cells and basket cells. The hierarchical nature of
local projections in the dentate gyrus can be seen in the mossy cell population, which both
excites granule cells monosynaptically and inhibits them disynaptically. Bottom – The number of
cells included in the full-scale model matches numbers reported in anatomical studies.

Simulations were performed at two scales: a full scale containing cell numbers equivalent
to those found in a single, adult rat hippocampus (one hemisphere) and a reduced scale
containing 1/10
th
of the number of cells. The 1:10 scale was used to decrease computation time.
However, all results reported here were observed at both scales. The numbers of cells included in
the simulations can be found in Figure 4.1. Simulations were performed using the NEURON
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(v7.3) simulation environment (Carnevale and Hines 2006; Migliore et al. 2006); Python (v2.7)
was used for model specification, data visualization, and data analyses (Hines et al. 2009;
Oliphant 2007).

B. Morphology

Granule cell morphologies were generated using the L-Neuron tool following the methods of
Ascoli and Krichmar, 2000 and modifications of L-Neuron described in our previous work
(Hendrickson et al. 2015). Parameters describing the dendritic arbor of granule cells were
obtained from a database of reconstructed granule cells and were input into L-Neuron to create
individual, and presumably unique, morphologies for each granule cell modeled. Granule cell
models were discretized using NEURON, resulting in individual models that each contained over
200 compartments. Basket cells and mossy cells were modeled as single compartment somata, so
they were not conceived of as having any dendritic structures. The decision to include somata
only for these two cell types was driven by the relatively low number of dendritic reconstructions
available in databases like NeuroMorpho.org from which to draw statistics.
No cells in the model were given explicit axon compartments. Instead, axons were
functionally present in the form of propagation delays that postponed the time between the
generation of a presynaptic action potential and subsequent initiation of the postsynaptic
potential. The delay was calculated using reported action potential conduction velocities and the
path length traveled between the pre- and post-synaptic neurons.

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C. Topography

To generate connectivity between neurons, the densities of axon terminal fields were modeled as
distributions that governed the probability of connection to postsynaptic neurons within the
target field. The distributions were parameterized to match the anatomical extent of axon
terminal fields.
The perforant path projection describing the topographical connectivity between the
medial entorhinal cortex (MEC), the lateral entorhinal cortex (LEC), and the dentate gyrus was
implemented using data from a study that involved systematic injections of retrograde tracer
throughout the septo-temporal axis of the dentate gyrus in rats (Dolorfo and Amaral 1998). The
procedure describing the quantification and implementation of the data to the model’s
connectivity is specified in detail in a previous publication (Hendrickson et al. 2015). The MEC
and LEC axon terminals were made to synapse within laminar portions of the dentate molecular
layer as described by others (Hjorth-Simonsen and Jeune 1972; Witter 2007). MEC axons
targeted dendritic segments located within the middle third of the molecular layer; LEC axons
targeted dendritic segments located within the outer third. The axon terminal field was
distributed across the entire transverse extent of the DG and extended 1-1.5 mm in the septo-
temporal direction (Tamamaki and Nojyo 1993).
Granule cells send their axons into the hilus where branching occurs; axon terminals of
these branches synapse with cells including, but not limited to, basket cells and mossy cells
(Seress and Pokorný 1981; Lübbers and Frotscher 1987). The axon terminals of basket cells
target the granule cell layer, synapsing with the somata and near the initial axon segments of
granule cells (Ribak and Seress 1983). The connection between basket cells and granule cells
comprise the feedback inhibition circuit in our model. The dendrites of basket cells also extend
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into the molecular layer allowing the EC to innervate the basket cells (Zipp et al. 1989); this
provides the feedforward inhibitory circuitry.

Figure 4.2: Top – summary of mossy cell axonal projection, as a function of septo-temporal
position in the hippocampus. Bottom – summary of axon terminal field extents along both the
septo-temporal and transverse axes of the dentate gyrus.

Mossy cell dendrites are restricted to the hilus, but their axons extend into the molecular
layer, predominantly in the inner third (Ribak and Shapiro 2007; Buckmaster et al. 1996). The
septo-temporal extent of the mossy cell axons changes based on the septo-temporal cell body
position. In general, mossy cells located more septally have axons that extend up to 2/3 of the
dentate, while mossy cells located more temporally target only approximately 1/3 or less of the
dentate gyrus (Zimmer 1971). The variation of the mossy cell axon extents are summarized in
Figure 4.2. Within the inner third of the dendritic field, axon terminals contact both granule cell
and basket cell dendrites (Scharfman 1995), and compose the associational pathway in the
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network. The parameters for the EC, granule, basket, and mossy cell axon distributions are
summarized in Figure 4.2. Connectivity was further determined using anatomically derived
convergence and divergence values reported in the literature. Convergence refers to the number
of presynaptic inputs that a neuron will receive from a given cell type; divergence refers to the
number of postsynaptic targets that a neuron will contact of a given cell type. These values are
summarized in Table 4.1.

Table 4.1: Synaptic parameters, including numbers of synapses, synaptic weights, EPSP/IPSP
magnitudes and rise/fall times, and reversal potentials.

Synapse counts:
GC # spines - inner 1/3 1150 - 1350 GC to BC 500 - 1400
GC # spines - middle 1/3 1050 - 1200 MEC to BC 100 - 200
GC # spines - outer 1/3 1100 - 1300 LEC to BC 100 - 200
BC to GC 40 - 80
MC to GC 750 - 850 MC to BC 950 - 1050
Synaptic weights:
MEC to GC 1.17E-5 GC to BC 1.13E-4
LEC to GC 1.50E-5 MEC to BC 4.21E-6
BC to GC 1.09E-5 LEC to BC 4.21E-6
GC to MC 2.00E-5 MC to GC 1.17E-6
MC to BC 2.27E-5
EPSP/IPSP rise time (ms):
MEC to GC 1.05 GC to BC 0.1
LEC to GC 1.05 EC to BC 1.05
BC to GC 1.05
EPSP/IPSP fall time (ms):
MEC to GC 5.75 GC to BC 0.59
LEC to GC 5.75 EC to BC 18
BC to GC 5.75
Reversal Potentials (mV):
MEC to GC 0 GC to BC 0
LEC to GC 0 EC to BC 0
BC to GC -75

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Table 4.2: Passive and active biophysical parameters for dentate cells.

Cell
Type Property/Mechanism Soma GCL Inner 1/3 Middle 1/3 Outer 1/3
Granule
cell
Soma S.A. (cm2) 4.97E-04
Soma Volume (cm3) 1.11E-06
R.M.P. (mV) -75.01
Rin (M-Ohms) 185.86
Membrane time constant (ms) 31
Latency to first AP (ms) 100
Cm (uF/cm2) 9.8 9.8 15.68 15.68 15.68
Ra (ohm-cm) 210 210 210 210 210
Leak (S/cm2) 2.90E-04 2.90E-04 4.57E-04 4.57E-04 4.57E-04
Sodium (S/cm2) 0.84 0.126 0.091 0.056 ---
Delayed Rectifier K (slow) 0.006 0.006 0.006 0.006 0.008
Delayed Rectifier K (fast) 0.036 0.009 0.009 0.00225 0.00225
A-type K (S/cm2) 0.108 --- --- --- ---
L-type Ca (S/cm2) 0.0025 0.00375 0.00375 0.00025 ---
N-type Ca (S/cm2) 1.47E-03 7.35E-04 7.35E-04 7.35E-04 7.35E-04
T-type Ca (S/cm2) 0.000074 0.00015 0.0005 0.001 0.002
Ca-dependent K (SK) 0.001 0.0004 0.0002 --- ---
Ca- and V- dependent K (BK) 1.20E-04 1.20E-04 2.00E-04 4.80E-04 4.80E-04
Tau for decay of Ca (ms) 10 10 10 10 10
Steady-state Ca (mol) 5.00E-06 5.00E-06 5.00E-06 5.00E-06 5.00E-06
Mossy
cell
Soma S.A. (cm2) 2.51E-03
Soma Volume (cm3) 2.51E-05
R.M.P. (mV) -64.75
Cm (uF/cm2) 0.6
Ra (ohm-cm) 100
Leak (S/cm2) 1.10E-05
Sodium (S/cm2) 0.12
Delayed Rectifier K (fast) 5.00E-04
A-type K (S/cm2) 1.00E-05
L-type Ca (S/cm2) 6.00E-04
N-type Ca (S/cm2) 5.00E-05
Ca-dependent K (SK) 1.60E-03
Ca- and V- dependent K (BK) 1.65E-02
Tau for decay of Ca (ms) 10
Steady-state Ca (mol) 5.00E-06

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D. Bioelectric Properties and Pharmacology

Biophysical parameters for each of the cell types in the model were derived from previously
published experimental data and from previously published computational models of the DG
(Hendrickson et al. 2015; Dyhrfjeld-Johnsen et al. 2007; Santhakumar et al. 2005). Table 4.2
shows both the channel distributions for the cell types, and key passive and active properties
assumed for each cell type.
Synapses were modeled as mechanisms whose activation would result in a conductance
change that followed a time-course approximated by the difference of two exponentials.
Excitatory connections were represented as AMPA synapses while inhibitory connections were
represented as GABA
A
receptor synapses. For simplicity, neither NMDA nor GABA
B
receptors
were included in the model, though they will be included in the future. Initially, the rise/fall
times, maximum conductances, and reversal potentials were initially adjusted to match
experimental recordings of excitatory and inhibitory postsynaptic potentials (EPSPs and IPSPs)
in the soma of the relevant cell types. However, these parameters resulted in an overtly
synchronous network not consistent with biological recordings. An alternate optimization was
performed that used the results of an experimental paradigm designed by McNaughton (Douglas
et al. 1983) to balance the excitation and inhibition of the associational mossy cell network (see
Results).

E. Computational Platform

All simulations were run on a high-performance computer cluster consisting of 394 dual quad-
core Intel-based nodes and 74 dual hexa-core Intel-based nodes, for a total of 4,040 processor
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cores. The system has 8.1 TeraB of distributed RAM, 73.1 TeraB of distributed disk space, and a
maximum theoretical performance of 38.82 teraflops. All nodes are connected to a high-speed,
low-latency 10G Myrinet networking backbone. These nodes are housed, maintained and
monitored in facilities operated by the University of Southern California Center for High-
Performance Computing and Communications (USC HPCC Center).

4.4 Results
A. Granule Cell Response to Random Entorhinal Input: Firing in Spatio-Temporal ”Clusters”

Initial simulations of granule cell network dynamics to EC input involved both medial and lateral
entorhinal (MEC & LEC) neurons firing in a Poisson fashion with a mean frequency of 3.0 Hz,
slowly accelerated from 0.0 Hz (by design) over the course of the first 1,000 ms of the
simulation. This was performed as a means to reduce what was observed in preliminary studies
to be a strong transient response of the system to a step function input if EC input was allowed to
start at maximum from zero. The transient response of the network was oscillatory, and the
ramping input was a means to mitigate that effect. Four seconds (4.0 s) of neural time were
simulated for all conditions presented here. In order to complete simulations at the million-cell
scale, approximately 84,000 CPU hours were required per simulation. This corresponds to 28
hours of wall time when using 3,000 processors. At the 100k-cell scale, approximately 7,200
CPU hours were required, corresponding to approximately 6 hours of wall time with 1,200
processors. Simulation results with a one million granule cell population revealed that despite
continued Poisson EC input, granule cells discharged in a decidedly non-random, non-uniform
manner. As shown in Figure 4.3 (top), granule cells throughout the entire longitudinal extent of
the DG fired in spatio-temporal “clusters,” i.e. local regions of spatio-temporally dense activity.
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The clusters are organized in irregular patterns persisting for approximately 50-100 ms and
separated by periods of lower density activity lasting 50-75 ms. The appearance of clustered
spiking in response to Poisson EC input was not specific to million-granule cell populations, but
was equally apparent for simulations involving 100k granule cells as well (Figure 4.3, bottom).
Despite the presence of spatio-temporal clusters at both scales, though, there were some
differences in network activity. At the million-cell scale, there was more intra-cluster activity in
the granule cell population, and sparser basket cell activity, than appeared in the 100k results.

Figure 4.3: Simulation results, at two different scales, for topographically constrained EC-DG
networks with feedforward and feedback inhibition. A1 – simulation results from 1 million
granule cells. Despite the random nature of the perforant path input, dentate activity in both
granule and basket cells consists of spatio-temporal clusters of spikes. In the million-cell case,
only a subset of the full dataset is plotted to keep it from appearing solid black. B1 – the spatio-
termporal correlation (STC) confirms the existence of clusters. Bottom – Clusters persist when
the network is scaled down to 100k granule cells.

Quantitative analyses verified the existence of clusters of spike firing. A 2D spatio-
temporal correlation (STC) was used, which provided an analysis of the data in both spatial and
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temporal dimensions. It was constructed by computing every pairwise cross-correlation of
discretized spike trains in a random sample of 10,000 neurons. The spike trains were discretized
by counting the number of spikes elicited by a particular neuron within a bin size of 5 ms. The
resulting cross-correlations were sorted by the distance between the neuron pairs and were
further binned using a resolution of 0.05 mm. The mean cross-correlation within each bin was
then computed. The STC represents the average spatial and temporal correlation that any
particular neuron has with its neighbors.
The right-hand column of Figure 4.3 shows the STCs for the million-cell and 100k cell
simulations, respectively. For any given neuron, a spatial correlation persists for 1 mm with a
temporal correlation lasting up to 25 ms, resulting in the elliptical STC that is depicted.
Furthermore, the spatial and temporal extent of the correlation roughly matches the size and
shape of the clusters seen in the raster plots. This analysis verifies the existence of the clusters in
the data sets. The similarity in the STC for the million and 100k cell simulations indicates that
the clusters are present at both scales and validates, to an extent, the scaling methodology that
was used such that any emergent properties that arise in the million cell simulations would not be
lost when scaling the simulations down to 100k.

B. Effect of Feedforward and Feedback Inhibition on Granule Cell Activity

One of the most significant forms of interneuron modulation of granule cell activity has been
inhibition due to GABAergic interneurons (Andersen et al. 1964; Kosaka et al. 1984; Gamrani et
al. 1986; Sloviter and Nilaver 1987; Milner and Bacon 1989; Traub et al. 1996). Given the strong
effect that such local interneuron activity is likely to play in modulating granule cell firing, we
conducted experiments designed to further examine the role of inhibition on spatio-temporal
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network activity in the hippocampal dentate gyrus. The inhibition that the basket cell population
monosynaptically provides to the granule cells can be initiated through several pathways. In the
following sets of simulations, two pathways were investigated: feedback inhibition, due to the
innervation of basket cells by granule cells, and feedforward inhibition, due to innervation of
basket cells by the perforant path. Several sets of simulations were run to explore the
contributions of each of these components of the inhibitory network: one, where the maximum
conductance of the basket cell input to granule cells was incrementally increased; two, where the
strength of entorhinal input to basket cells was increased; and three, where the strength of the
entorhinal input to granule cells was increased. None of the simulations in this section included
mossy cells.
At the base level of feedback inhibition with no feedforward inhibition, granule cell
activity behaves similarly to previous results. Following a transient response characterized by a
slow, large rise and fall of total activity and increased cluster sizes that span up to 8 mm in
length, the activity develops into a steady-state consisting of irregular patterns of clusters that are
1-2 mm in size. As the strength of feedback inhibition was increased, however, a marked
synchrony in network activity developed, with granule cells across the entire longitudinal extent
of the dentate gyrus firing within a 20-30 ms time window followed by a cessation of activity for
approximately 30-40 ms. Increasing the inhibition further strengthened this synchrony. These
periodic oscillations were caused by a phasic excitation-inhibition cycle maintained by the
feedback inhibition between granule cells and basket cells. Basket cells would fire in response to
their activation by the granule cells, and this in turn would cause basket cells to inhibit the
granule cells to stop firing. Increasing inhibition also decreased the total level of granule cell
activity, as reflected in the number of generated spikes over each 4-second simulation; it
decreased by 25%, from 742,778 to 557,669.
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Figure 4.4: Effect of progressively increasing strength of feedback inhibition. As the amount of
inhibition increases (A1 – A4), pronounced rhythmicity develops in both granule cell and basket
cell activity. The presence of this rhythmicity is verified with frequency analysis (B1 – B4),
which shows a peak developing at approximately 18 Hz.

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Discrete Fourier transforms (DFTs) were used to analyze the temporal frequency
spectrum of the spike data and quantify the oscillations of the simulations. They were computed
using a spike density matrix. The matrix was constructed by counting the total number of spikes
elicited within a spatio-temporal bin having a resolution of 0.05 mm and 8 ms. The DFT was
computed for each row of the matrix, resulting in a frequency spectrum for each septo-temporal
location on the DG. Because the spectra at each row were similar, the means of all of the DFTs
were computed.
As Figure 4.4 shows, feedback GABAergic inhibition introduced a peak oscillation at 17-
18 Hz. Increasing the inhibition did not change the location of the peak but rather sharpened, or
decreased the width of the peak. At the highest level of feedback inhibition tested, a smaller
secondary peak formed at approximately 35 Hz. The sharpening of the peak and the appearance
of the second peak, likely a harmonic of the first peak, are evidence that feedback inhibition
introduces oscillation at a certain frequency, but other factors are involved in mediating at which
frequency the oscillation occurs, as is demonstrated below.
While the feedback inhibitory circuit appears to be a primary cause of synchrony in the
network, the strength of perforant path input to the DG, on its own, did not. Stronger excitatory
input only increased the amount of total spiking activity in the granule cell population, increasing
it from 742,778 spikes to 4,464,558 spikes over a 10 times increase in PP drive, without ever
introducing synchronous activity (see Figure 4.7). However, when synchrony was already
present in the network, increasing the strength of the entorhinal input to DG drove the network
into both faster and stronger rhythmicity, shifting it from 17-18 Hz at its base strength to 31-32
Hz when 20 times stronger (see Figure 4.5). Thus, in the presence of periodic behavior,
feedforward excitation was able to modulate the frequency of oscillation using random,
uncorrelated activity. However, it was unable to induce oscillatory behavior alone.
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Figure 4.5: Effect of increasing strength of perforant path drive in the presence of strong
feedback inhibition. When rhythmicity is present in the network, increasing the strength of the
perforant path excitatory drive (A1 – A4) both strengthens the rhythmicity and increases its
freqeuency. As DFT analysis shows, a small 18 Hz peak at the base perforant path strength (B1)
becomes a much larger peak centered at about 32 Hz. when the synaptic weight of the perforant
path input is increased by 20x (B4).

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Figure 4.6: Effect of increasing the strength of feedforward inhibition. The feedforward
component of basket cell inhibition helps to both desynchronize and scale down total granule cell
activity. As the strength of the feedforward inhibition increases (A1 – A4), total granule cell
activity decreases until there’s almost no activity in the network. The 18 Hz. peak in the DFTs
(B1 – B4) also disappears.

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Figure 4.7: Large amounts of PP excitation (A1), feedback inhibition (A2), and feedforward
inhibition (A3) in isolation, with corresponding frequency plots (column B). Of note is the fact
that only feedback inhibition can cause oscillatory activity in the network.

Feedforward inhibition had a decidedly different effect on network activity. As Figure 4.6
shows, progressively increasing the strength of the perforant path projection to basket cells
greatly decreased the overall level of granule cell activity; at its base strength, the granule cell
population produced 742,778 spikes over a 4-second period. With 5 times stronger entorhinal
input, only 82,040 spikes were generated, a nine-fold decrease in granule cell activity. With 10
times stronger entorhinal input, granule cell activity was almost completely suppressed. The
feedforward component of the inhibitory connection was also able to terminate synchrony caused
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by feedback inhibition as seen in Figure 4.6. Increasing the strength of perforant path input to the
basket cells decoupled the basket cells from granule cell activity and prevented the phasic
excitation-inhibition that caused the oscillation via feedback inhibition.

C. Effect of Associational System Excitation on Granule Cell Activity

The dentate gyrus has a known excitatory feedback circuit via the associational pathway. Mossy
cells receive input from granule cells and provide excitatory feedback to granule cells. The next
series of simulations was designed to study the effect of the interactions between the GABAergic
inhibitory and the associational excitatory circuits. However, the associational pathway is more
complex than acting merely as a feedback excitation circuit. Mossy cells also innervate basket
cells, so that this cell population provides both direct feedback excitation and indirect feedback
inhibition to granule cells. Incorporating mossy cells considerably increases the complexity of
the model, almost doubling the number of types of synaptic connections and thus, increasing the
dimensionality of parameter space to explore. Initial results with the mossy cell network, when
EPSP magnitudes between mossy cells and granule cells were set according to values reported in
the literature (Scharfman et al. 1990; Scharfman 1995), was strong synchrony in all three of the
cell body populations in the DG. As Figure 4.8, top shows, the granule cell population was the
first to fire in response to perforant path stimulation. Those spikes, though low in number, were
enough to stimulate a strong burst of activity in the mossy cell population, which, in turn,
reinforced the activity in the granule cells. Both populations likely contributed to the burst of
activity from basket cells. After a period of approximately 50 ms, the burst of granule cell
activity suddenly stopped, either due to basket cell inhibition and/or the synchronized
hyperpolarization of the entire granule cell population. This cycle repeated itself every 100 ms, a
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finding that was corroborated by the frequency analysis, which showed a 10 Hz spike in the GC,
BC and MC populations.

Figure 4.8: Initial simulation results after connecting the mossy cell associational pathway.
When EPSP magnitudes are set at values reported in the literature, strong synchrony develops in
all three dentate cell populations (A1). When synaptic weights are rebalanced to fit the results of
the paired-pulse stimulation experiments of Douglas, McNaughton, and Goddard 1983 (A2),
rhythmicity in the network disappears, replaced by a large variety of spatio-temporal clusters
(A3).

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C1. Re-optimization of Network Parameters

Such a strongly synchronous, highly rhythmic state of dentate firing is non-physiological,
according to multiple analyses in freely moving animals (Deadwyler et al. 1976; Deadwyler et al.
1979). In order to move the network to a non-synchronous, less excitatory state, synaptic
conductances were rebalanced to correspond with data published from experiments in which
both the perforant path and contralateral mossy cell population were stimulated in vivo and the
granule cell population response was recorded (Douglas et al. 1983). These experimental results
show that, while the commissural (and, by extension, associational) afferents to DG have both an
excitatory and inhibitory influence on granule cells, the predominant effect is inhibitory:
activation of commissural inputs to dentate can prevent perforant path stimulation from reaching
threshold. They further show that the amount of inhibition is dependent on the length of the
delay between stimulation of the contralateral hippocampus and stimulation of the perforant
path. Re-balancing of synaptic weights in the dentate model involved increasing the strength of
GABAergic inhibition of granule cells by basket cells while decreasing the strength of the
projection from mossy cells to granule cells. To evaluate the re-balancing process, an initial
control simulation was run where commissural activation was not simulated, and the total
number of granule cell spikes was counted. When input from the commissural pathway was
introduced and as the delay between commissural and perforant path input start times was
increased, the total number of granule cells spikes was tallied and converted into a percentage
relative to the number of spikes generated in the control simulation. The procedure was
considered complete when the simulation curve matched that of the experimental findings (see
Figure 4.8, middle).
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Figure 4.8, bottom shows simulation results from the rebalanced network. These results
show a pronounced lack of synchrony and, in general, sparser activity throughout the network,
though the spatio-temporal clusters present in Figure 4.3 (and others) persisted. The granule cell
network generated a total of 928,832 spikes over 4 seconds, a 1.25x increase over the non-
associational system network. The clusters, too, have sharper edges (i.e., activity both starts and
terminates more suddenly) than clusters from non-associational projection network. The clusters
also exhibited a mix of sizes dependent on their septo-temporal location. “Non-associational”
clusters tended to remain 1-2 mm in length, but the introduction of associational projections
caused larger clusters (3-5 mm) to appear. The larger clusters appeared exclusively in the septal
two-thirds of the dentate, which is related to associational projection topography. Associational
projections in the septal two-thirds have a greater axon terminal field size (up to 7.5 mm)
(Zimmer 1971), which can introduce spatial correlations spanning a greater distance and result in
larger clusters. When local topographic constraints on mossy cell connectivity were removed, the
balance of cluster types shifted strongly towards those with a larger spatial extent (see Figure
4.10), a result that emphasizes once again the importance of topography on the development of
spatio-temporal cluster functionality (Hendrickson et al. 2015).
In addition, the clusters emerging from mossy cell activity look somewhat different from
granule cell clusters driven by only perforant path excitation; instead of an elliptical or ovular
shape, mossy cell activity have “C” shaped clusters (see, for example, Figures 4.8 and 4.10). The
“C” shape implies that these clusters have an initiation point where activity begins which spreads
almost symmetrically in both directions longitudinally away from this initiation point. The curve
of the “C” was due to the temporal delay of the activity as it spread from the initiation point.

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Figure 4.9: Histogram showing inter-spike intervals for each of the cell populations in the
model. Inter-spike intervals are very small for basket cells and mossy cells (A1), which makes
sense, given that basket cells are fast-spiking interneurons. Granule cells don’t exhibit many
small inter-spike intervals (A2), but rather, show a peak in the 200 ms – 300 ms range. The
distribution of inter-spike intervals for entorhinal cortical cells looks exponential, which is
expected for a group of cells whose action potentials follow a Poisson process.

An inter-spike interval analysis of the dentate network with associational projections was
calculated. As Figure 4.9 shows, the histogram of inter-spike intervals for the perforant path
input follows an exponential curve with a long tail. Inter-spike intervals range from as small as
0.1 ms to as large as 3,194.9 ms, thus spanning a wide range of frequencies. The granule cell
population shows a distribution of inter-spike intervals with a long tail, similar to the perforant
path input, but with much fewer small intervals. It has a peak in the 200-400 ms range. Basket
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and mossy cells have a large concentration of inter-spike intervals less than 100 ms, which drops
off almost entirely by 400-500 ms.

Figure 4.10: Simulation results for two dentate networks that only differ in the topography of the
mossy cell projection to granule cells. Top: results when mossy cell axonal tree extents vary by
their location along the septo-temporal axis of the dentate gyrus, as reported by Zimmer (Zimmer
1971). Bottom: results when mossy cells are allowed to project randomly to the granule cell
population. Note that the size of the spatio-temporal clusters in granule cells increases
substantially in the randomly connected network, as evidenced by the spatio-temporal
correlations (B1, B2).

At a population level, a unique pattern of activity emerged that was not present in the
network without the associational system. More evident in the interneuron activity, there were
regions of inactivity lasting approximately 200-250 ms that were interposed between regions of
activity. During these silent intervals, the granule cell population also exhibited a reduced
activity. However, granule cell clusters still persisted whether or not the population was in its
higher or lower activity states, though the clusters were shorter longitudinally during the low
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activity states. This highlights the influence of mossy cells on cluster size. While mossy cell
activity is present, granule cell clusters are larger than when mossy cells are silent. This overall
pattern of high/low or active/inactive states represents a slower oscillation that had not been seen
in any simulations until the introduction of the mossy cell-based associational system.

C2. Evaluation of Selected Pathway Functions

Using the rebalanced synaptic conductances, a series of experiments were performed to observe
the effects of altering the strengths of individual connections between cell types. The rebalanced
synaptic conductances will be referred to as the “base weights” when comparing the next set of
simulations. While all seven synaptic connections were manipulated, only three of those
manipulations are reported on in detail here. See Figures 4.11-4.13 for those details – Figure 4.11
shows a 1,000-ms view of each of the relevant datasets, Figure 4.12 shows a 4,000-ms view of
those same data, and Figure 4.13 shows the DFTs for each of the datasets. See Table 4.3 for a
summary of the effects of manipulating each of the seven connections.
The second row of Figures 4.11-4.13 shows the result of both strengthening and
weakening the direct, excitatory projection from mossy cells to granule cells. When the mossy
cell drive to granule cells is decreased, regions of interneuron inactivity no longer appeared.
Likewise, there were no periods during which the granule cell population underwent a lower
activity state. Otherwise, the granule cells still exhibited clustered behavior, and the “C” clusters
in the mossy cells remained. This was similar to the network activity in the previous network
during regions of interneuron activity. Total granule cell activity also decreased by 22%.
Increasing the strength of the excitatory feedback to granule cells extended the length of
interneuron inactivity significantly. Though the length of the silent interval was similar to that of
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the base weights near the beginning of the simulation, the interval increased in length from 250
ms to 1,200 ms by the end of the simulation. During the silent intervals, granule cells exhibited
sparse but clustered activity patterns, similar to that found for the base weights. However, the
patterns generated by all cell types during intervals when the interneurons were active changed
dramatically. These active interneuron intervals, lasting 100-200 ms, are composed of multiple
waves of synchronous activity. Although most of the activity is concentrated during the active
interneuron intervals, the total granule cell activity increased by 27%, indicating that the activity
during the active interneuron intervals is dense.
Table 4.3: Summary of changes in network activity due to strengthening and weakening
individual synaptic connections

Connection
Increase/Decrease
Weight? Effect
MC --> GC
Increase
Strong high-frequency activity modulated by low-frequency
oscillation. High-frequency bursts are highly synchronous.
Decrease
Less, but more regular GC activity; spatio-temporal clusters
slightly more "fuzzy;" fewer long (3-4 mm) clusters.
GC --> MC
Increase
Slight increase in both mossy and basket cell activity, with
corresponding decrease in granule cell activity. Otherwise, little
discernable difference in activity.
Decrease
Slight decrease in both mossy and basket cell activity.
Otherwise, little discernable difference.
MC --> BC
Increase GC activity is more regular; no other strong differences.
Decrease
Strong high-frequency activity modulated by low-frequency
oscillation. Low frequency component is higher than in MC--
>GC and BC-->GC cases, while high frequency component is
slower.
GC --> BC
Increase Very regular activity in all three dentate cell populations.
Decrease
Low-frequency oscillation modulates strength and density of
spatio-temporal clusters in granule cells.
BC --> GC
Increase
Spatio-temporal clusters have sharpter tailing edges, with less
inter-cluster activity.
Decrease
Strong high-frequency activity modulated by low-frequency
oscillation. Synchrony in high-frequency activity not as strong as
for MC-->GC case.

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The third row of Figures 4.11-4.13 shows the result of manipulating the strength of the
mossy cell projection to basket cells. This change affected the inhibitory aspect of the
associational pathway in the network. Halving the strength of the mossy-basket connection
enhanced the silent interneuron intervals relative to the network with base synaptic weights. The
intervals increased in length to 250-350 ms but also became more numerous; the active
interneuron intervals became shorter. Also, granule cell activity during the silent interneuron
intervals remained clustered. The direction of this change is similar to that when the MC-GC
connection was strengthened, though there were differences. Instead of exhibiting bands of
activity that extended across the entire longitudinal extent, granule cell clusters of many sizes
occurred, ranging from 1-8 mm. Furthermore, the intervals had a greater regularity than the MC-
GC case which had silent intervals that increased in length over time. Total granule cell activity
increased by 12%. In both instances (i.e. either weakening the MC-BC connection or
strengthening the MC-GC connection), the net effect of these changes was to tip the balance
towards the associational excitatory loop relative to the inhibitory loop. However, changing the
MC-GC connection affected a direct excitatory connection while changing the MC-BC
connection altered an indirect inhibition as well as causing disinhibition. Doubling the strength
of the mossy-basket connection resulted in a similar effect as decreasing the strength of the
mossy-granule connection. The silent interneuron intervals disappeared and the clustering
behavior remained unchanged. Granule cell activity decreased by 14%.
The last row of Figures 4.11-4.13 shows the result of manipulating the strength of the
basket cell projection to granule cells. This affects both the basket-granule feedback circuit as
well as associational inhibition as the basket cells mediate inhibition for both circuits. Decreasing
the strength of basket-granule inhibition had an effect similar to strengthening mossy-granule
cell connection; short periods of high activity occurred, interspaced with longer periods of little
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to no activity. Again, weakening BC inhibition caused the network to favor the associational
excitatory loop over of the inhibitory loop; decreasing the BC-GC inhibition disinhibited the
network. However, the silent interneuron interval was much greater when the BC-GC inhibition
was decreased. Initially having a length of 600 ms, the next silent interneuron interval lasted for
2,000 ms. Furthermore, total granule cell activity increased by 49%, which was greater than the
increase caused by the MC-GC manipulation. Another difference lay within the patterns of
activity during the active interneuron interval. Granule cell activity occurred as unconnected but
distinct clusters as opposed to unbroken bands that spanned the entire longitudinal extent.
Following the above trend, increasing the strength of the basket cell projection to granule cells
had a similar effect as decreasing the mossy cell projection to granule cells. The silent
interneuron interval disappeared and the total granule cell activity decreased by 18%. Because
the basket cells were driven by both granule cells and mossy cells, the sensitivity of the BC-GC
connection may be greater than the MC-GC connection, which was driven by granule cells alone,
and this could account for the more drastic changes that occurred by varying the BC-GC
connection.

4.5 Discussion

The dentate gyrus is an integral part of the hippocampal formation, as it both transforms
incoming information from the entorhinal cortex and transmits it to subsequent areas of
hippocampus. This circuit plays a critical role in the formation of new long-term memories and
has two local feedback loops that modulate its activity. Our goal with this study has been to
explore the effects of both the inhibitory and associational circuits on network level activity in
the dentate gyrus. With respect to inhibitory feedback, basket cells were chosen for the initial
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Figure 4.11: Simulation results when strengthening and weakening three individual synaptic
connections in the granule-mossy-basket cell network. All raster plots show 1,000 ms of activity.
When the excitatory mossy cell loop is strengthened relative to the inhibitory basket cell loop, a
pattern of theta-modulated gamma oscillations develops (A3, A4, B2).

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Figure 4.12: Same simulation results as in Figure 4.11, but showing 4,000 ms of activity to give
a better view of the theta-modulated gamma oscillations.

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Figure 4.13: DFTs for the data shown in Figures 4.11-4.12.

implementation of the model as it is the most numerous and most well-known inhibitory
feedback element. With respect to the associational system, mossy cells are regarded as the main
source of these projections, though evidence exists that other interneurons also contribute to this
pathway (Amaral 1979; Berger et al. 1981; Swanson et al. 1981). These loops are organized in a
hierarchical fashion, which makes it difficult to determine experimentally the role that each plays
in the spatio-temporal spiking dynamics of granule cells. A mathematical model, however, lends
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itself exactly to this kind of study because cellular properties and synaptic connections can be
selectively manipulated to observe their effect on network function.

A. Effects of Inhibitory Interneuronal Circuitry (Feedforward and Feedback)

Our computational model has revealed two key roles for the inhibitory interneuronal circuitry.
First, feedback inhibition is necessary to generate rhythmicity in the granule cell population. In
generating that rhythmic activity, the feedback inhibitory loop fundamentally changes network
activity; instead of generating spatio-temporal clusters spanning 1-2 mm of the septo-temporal
extent of the hippocampus, activity now occurs as bands that span its entire length. Similar large-
scale spatial synchronization of principle cells, due to GABAergic feedback inhibition, has been
shown in network models of CA3 (Traub et al. 1987) and of visual cortex (Bush and Douglas
1991). In both of those models, however, the presence or absence of rhythmicity was studied
with cells that exhibit strong bursting activity. In the present model, rhythmicity develops despite
the lack of bursting spike behavior in principal cells. Evidence of GABAergic interneuron-
interneuron synapses (Cobb et al. 1997) inspired additional studies that investigated inhibitory
interneuron coupling on gamma generation which demonstrated an important role for these
synapses in a more robust generation of gamma over a broader range (Bartos et al. 2001; Bartos
et al. 2002). Basket cell-to-basket cell coupling was not incorporated in the present study.
Other studies have focused on interconnected networks of interneurons as the source of
large-scale synchrony in neuronal networks (Wang and Buzsaki 1996; Traub et al. 1996). Those
computational studies found that, among the factors that influence the frequency of rhythmicity,
strength of afferent input plays a role. The results of this current study corroborate these prior
findings – in the presence of strong feedback inhibition, perforant path excitation of granule cells
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both strengthens and increases the frequency of rhythmicity. However, unlike those models, we
find that, when paired with Poisson distributed spiking input from the entorhinal cortex,
feedback inhibition from basket cells, on its own, is also sufficient to generate rhythmicity – no
additional interneuron types are needed.
The second key finding from our study of inhibitory interneuron circuitry is that
feedforward inhibition plays an important role in scaling the total amount of granule cell activity.
At progressively higher levels of feedforward inhibition, granule cell activity decreases until it is
almost completely inhibited. This phenomenon can be explained by the fact that entorhinal input
to the basket cell population helps to decouple it from the granule cell activity that normally
drives it. The scaling effect of feedforward inhibition has been shown in a simple circuit
previously (Buzsáki 1984). In that review paper, the author hypothesized that feedforward
inhibitory mechanisms, where they occur in the hippocampus, can be important from an external
control standpoint – they can allow other areas of the brain to effectively shut off portions of the
hippocampus. This is especially true in the dentate gyrus, which is the first area of the
hippocampus that signals originating in other portions of the brain see. Based on these results,
feedforward inhibition could be hypothesized to act as a homeostatic mechanism to prevent overt
synchronized oscillation and hyperexcitability in granule cells. Increased activation of granule
cells would also increase GABAergic inhibition. Also, in the presence of synchronized
oscillation, feedforward inhibition can terminate synchrony, as was demonstrated.

B. Effects of Associational Circuitry

Adding local associational circuitry to the otherwise large-scale model of the dentate gyrus
revealed several key roles for the mossy cell population in shaping the spatio-temporal dynamics
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of granule cells. First, as was clear in our previous study of entorhinal projections to the dentate,
topography of associational connections was found to play an important a role in shaping the
clusters of spiking activity in the granule cell population (Hendrickson et al. 2015). In addition to
the 1-2 mm clusters that appear from the topographic organization of the perforant path
projection, new clusters that span 4-6 mm of the septo-temporal extent of the hippocampus
appear when associational connections are included. These clusters form predominately at the
septal end of the hippocampus, where mossy cell axonal fields have a similarly large spread.
When projections from mossy cells to granule cells are randomized, small clusters virtually
disappear anywhere there is mossy cell activity, and are replaced with clusters that have a very
large spatial extent.
Second, clusters of granule cell activity evoked by perforant path input had boundaries
that were considerably “sharper” in the presence of mossy cell circuitry. This effect appeared to
be due to mossy cells evoking a strong response from the basket cell population, which more
rapidly inhibited granule cell activity on the trailing end of a given cluster. In addition, because
of the relative ease with which granule cells depolarize any given mossy cell to threshold, they
facilitate a more sudden onset of spiking activity in the granule cell population at the beginning
of each cluster.
Third, incorporating the associational system into the network leads to the appearance of
power in the lower theta frequency band of the Fourier transform of the population response. The
frequency spectra for the cases in which feedforward and feedback inhibition and perforant path
excitatory drive were investigated did not include this lower theta activity. Instead, feedback
inhibition gives rise to oscillations in the gamma range, as is consistent with several other
computational studies that identified GABAergic inhibition from basket cells as the source of
gamma oscillations using single compartment models (Wang and Buzsaki 1996; Tiesinga and
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José 2000; Maex and De Schutter 2003; Bartos et al. 2007). Only after mossy cells are included
in the network does power in the theta range appear. In fact, the simulations demonstrate a theta-
gamma network oscillation generated by the interactions of the mossy, basket, and granule cells
(Figure 4.12). Through granule cell excitation, the mossy cells mediate both a positive feedback
loop, via a direct monosynaptic connection onto granule cells, and a negative feedback loop, via
a disynaptic connection in which mossy cells excite basket cells that subsequently inhibit granule
cells. By altering the balance between the positive and negative feedback loops, the amount of
theta and gamma in the network can be altered. Increasing the strength of the positive feedback
loop relative to the mossy cell-controlled negative feedback loop increases the amount of theta.
This can be achieved either by increasing the strength of the mossy cell drive to the granule cells
or by decreasing the strength of the mossy cell drive to the basket cells. Affecting these synaptic
weights in the opposite direction decreased theta. Thus, these simulations suggest that mossy
cells within a granule cell-basket cell network can potentially serve a role in regulating theta.
This potential link between theta oscillations and mossy cells has not been fully explored
previously, though a former study has shown that mossy cells preferentially fire during cycles of
theta (Soltesz et al. 1993). Other studies have identified phasic input from the medial septal
nucleus and the nucleus of the diagonal band as sources of theta to the dentate (Pernía-Andrade
and Jonas 2014; Stewart and Fox 1990), but as these two areas were not included in the model,
they could not be the source of theta in these results.
Finally, we note that the dentate system can enter an aberrant bursting state reminiscent
of epileptic activity within a relatively large range of parameter values. This is notable because
much of the experimental work published on hippocampal mossy cells has been grounded in
studying their role in the formation of epilepsy after blunt head trauma. Two alternate theories
have been proposed. One, known as the “dormant basket cell” theory, proposes that, due to
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mossy cell loss that results from blunt head trauma, inhibitory interneurons that are normally
innervated by mossy cells lose that excitatory input, resulting in lower levels of granule cell
inhibition and thus, greater activity (Sloviter 1991; Sloviter et al. 2003). An alternate theory,
known as the “irritable mossy cell” theory, holds that not all mossy cells are lost after blunt head
trauma, and that those remaining become hyper-excited, leading to over stimulation of the
granule cell population (Santhakumar et al. 2000). Based on the results of the associational
pathway simulations, it seems likely that both of these theories have validity, as epileptic-like
activity appears both when the strength of mossy cell input to granule cells is increased and when
either mossy cell input to basket cells or basket cell input to granule cells is decreased.

C. Interpretation of “Clusters” of Granule Cell Activity: A Measure of Network Dynamics

Our goal is to understand how multiple, specific neurobiological mechanisms that are known to
comprise the hippocampal formation interact to produce network dynamics. In this model we
have incorporated as many important details as possible regarding the morphology of the
dendritic and axonal processes, the biophysical properties of cellular membranes with respect to
passive electrical characteristics (membrane resistance and capacitance) and active membrane
processes (voltage-dependent and ion-dependent conductances), the spatial distribution of
synaptic inputs in dendritic regions, the topographic distribution of synaptic connections between
populations of neurons, the ratio of principal neurons to interneurons, etc. Predicting how
network dynamics emerge from the interaction of these various mechanisms requires driving
these network elements with an input signal. It is obvious that the nature of the interaction
between components of the network – and thus, the expression of the very network dynamics in
question – will depend to a large extent on the input signal itself. This problem of how to
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separate network dynamics from the nature of the test signal used to obtain their expression is a
problem of long standing in the field of biomedical engineering (Marmarelis and Marmarelis
1978; Marmarelis 2004; Sclabassi et al. 1988; Marmarelis and Berger 2005). One of the key
solutions is the use of randomized inputs which provides a basis for input strength, and/or input
pattern, or some other parameter of the input signal, to be equalized as much as possible. Thus,
in the present analysis, the input signal was a series of impulses having randomly varying inter-
impulse intervals. As a result, the input signal varies widely (in this case from 0.1 msec to
3,194.9 msec), and remains reasonably unbiased. The wide range of randomized input signals
maximizes the probability that most mechanisms of a neural system will be activated. For
example, random input signals ensure not only that monosynaptically stimulated cells are subject
to frequency-dependent release of neurotransmitter (e.g., well-known paired pulse potentiation
and similar phenomena) and to frequencies sufficient for activating receptor-channels with
voltage-dependence or voltage-dependent blockade (e.g., NMDA), but also so that different
components of a given network are activated transsynaptically through as many different
pathways and circuits as possible (see Yeckel and Berger 1998). For these reasons, the net
functional consequence of using random input signals is that any resulting network behavior will
reflect contributions from a great many of the mechanisms, neurons, and/or circuits comprising
the network. This is why, in fact, the “clusters” of granule cell activity represent a reasonable
index of network dynamics, perhaps better than any alternative index.
In addition, although being mostly analyses on the system and signal level, our model
also provides a valuable platform for studying the computational and cognitive functions of the
hippocampus. For example, the dentate gyrus has long been postulated to play a role in pattern
separation or sparsification for memory formations (McNaughton and Morris 1987, O’Reill and
McClelland 1994, Treves and Rolls 1992). However, most previous theoretical and
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computational studies have utilized simple connectivity schemes between the entorhinal cortex
and dentate gyrus, and highly abstracted neuron models. The exact nature of pattern separation
remains unclear. By contrast, our model is built with anatomically constrained EC-dentate
connectivity and eletrophysiologically accurate neuron models, and thus can be used to
quantitatively investigate how pattern separation is performed by the EC-dentate system and
provide predictions that can be more readily verified with experimental studies.

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Chapter 5: Conclusion

The research presented in this dissertation is significant for several reasons. First, the creation of
the necessary computational foundation to support such a model has endowed the lab with
capabilities that it didn’t previously have. Indeed, the development of the large-scale
compartmental model of the rat dentate gyrus has been made possible by two developments in
the computing field: (1) the development of parallelizable software systems for representing
anatomical and physiological characteristics of neural systems; and (2) the continued growth of
high performance computing systems capable of sustaining the numerical burden of simulating
such large-scale models.
Second, the model has been developed with sufficient biological detail to allow the data it
generates to increase our insights about how individual components of the dentate gyrus network
combine and interact to influence spiking activity on a system level. The results from the initial
model implementation show, for the first time, the critical role that the topography of the
perforant path connection plays in the development of spatio-temporal clusters in the granule cell
population. These clusters represent “functional units” that organize the processing of signals
originating in the entorhinal cortex and link a functional characteristic of a cortical projection to
its topographical features. The results from the simulations with feedforward and feedback
inhibition show how strong feedback inhibition can introduce synchrony into the network, while
feedback inhibition can both reduce the amount of synchrony and scale the total amount of
granule cell spiking activity. The introduction of the mossy cell associational system shows that
mossy cell topography may play a role in the creation of spatio-temporal clusters in granule cells,
introducing clusters with a spatial extent of 4-5 mm, where only smaller clusters were present
previously. They may also play a role in shaping existing spatio-temporal clusters, sharpening
Page | 98
both their leading and trailing temporal edges. Results first show that the interactions of the
associational system with the inhibitory system can introduce rich oscillatory dynamics into the
network, with oscillations in the gamma band being modulated by oscillations in the theta band.
These insights may be useful because they could (1) increase our understanding of how neural
systems in the brain function in both healthy and diseased states, (2) suggest experimental work
that might be performed to verify the data the model generates, and (3) enable advances in both
medicine and computing.
Finally, the model has been developed to be sufficiently general and adaptable so that
other scientific questions can be explored. For example, inclusion of NMDA receptor channels in
granule cell dendrites may alter the size and/or shape of spatio-temporal clusters. Changing the
dynamics of synapses and/or trans-membrane ion channels, as some pharmaceuticals do, may
alter the amount of background (ie, non-cluster) spiking, or change the level of spiking within
clusters. Modeling disease states, in which certain cell types are lost, can be accomplished
relatively easily, as could a quantitative investigation of how pattern separation is performed by
the EC-dentate system. Adding additional sub-regions of the hippocampus, starting with CA3,
would also be valuable, as the types and numbers of cells in CA3 are very different from those of
DG, as are the topographies of the mossy fiber and perforant path projections.

Abstract (if available)

Abstract This dissertation describes a million-plus granule cell compartmental model of the rat hippocampal dentate gyrus, including excitatory, perforant path input from the entorhinal cortex, and feedforward and feedback inhibitory input from dentate interneurons. The model includes experimentally determined morphological and biophysical properties of granule cells, basket cells and mossy cells, together with glutamatergic AMPA‐like EPSP and GABAergic GABAA‐like IPSP synaptic excitatory and inhibitory inputs, respectively. Each granule cell was composed of approximately 200 compartments having passive and active conductances distributed throughout the somatic and dendritic regions. Modeling excitatory input from the entorhinal cortex was guided by axonal transport studies documenting the topographical organization of projections from subregions of the medial and lateral entorhinal cortex, plus other important details of the distribution of glutamatergic inputs to the dentate gyrus. Information contained within previously published maps of this major hippocampal afferent were systematically converted to scales that allowed the topographical distribution and relative synaptic densities of perforant path inputs to be quantitatively estimated for inclusion in the current model. Results were divided between simulations studying the effect of topography on the spatio‐temporal dynamics of granule cells, and simulations studying the contributions of the local interneuronal and associational circuits to network‐level activity. Results from the topography‐related simulations showed that when medial and lateral entorhinal cortical neurons maintained Poisson random firing, dentate granule cells expressed, throughout the million‐cell network, a robust, non‐random pattern of spiking best described as spatio‐temporal “clustering”. To identify the network property or properties responsible for generating such firing “clusters”, we progressively eliminated from the model key mechanisms such as feedforward and feedback inhibition, intrinsic membrane properties underlying rhythmic burst firing, and/or topographical organization of entorhinal afferents. Findings conclusively identified topographical organization of inputs as the key element responsible for generating a spatio‐temporal distribution of clustered firing. These results uncover a functional organization of perforant path afferents to the dentate gyrus not previously recognized: topography‐dependent clusters of granule cell activity as “functional units” or “channels” that organize the processing of entorhinal signals. This modeling study also reveals for the first time how a global signal processing feature of a neural network can evolve from one of its underlying structural characteristics. Results from the local circuit simulations show that strong feedback inhibition from the basket cell population can cause high‐frequency rhythmicity in granule cells, while the strength of feedforward inhibition serves to scale the total amount of granule cell activity. Results furthermore show that the topography of local interneuronal circuits can have just as strong an impact on the development of spatio‐temporal clusters in the granule cell population as the perforant path topography does, both sharpening existing clusters and introducing new ones with a greater spatial extent. Finally, results show that the interactions between the inhibitory and associational loops can cause high frequency oscillations that are modulated by a low‐frequency oscillatory signal. These results serve to further illustrate the importance of topographical constraints on a global signal processing feature of a neural network, while also illustrating how rich spatio‐temporal and oscillatory dynamics can evolve from a relatively small number of interacting local circuits.

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Creator Hendrickson, Phillip J. (author)

Core Title A million-plus neuron model of the hippocampal dentate gyrus: role of topography, inhibitory interneurons, and excitatory associational circuitry in determining spatio-temporal dynamics of granul...

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 02/12/2016

Defense Date 11/17/2015

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Tag associational‐commissural fibers,cluster analysis,compartmental model,dentate gyrus,dynamics,entorhinal cortex,gamma,hippocampus,inhibition,interneurons,mathematical model,Model,neuroanatomy,OAI-PMH Harvest,oscillations,rhythmicity,spatio‐temporal pattern,spike,synchrony,topographical organization,topography

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Advisor Berger, Theodore W. (committee chair), Marmarelis, Vasilis (committee member), Nakano, Aiichiro (committee member), Song, Dong (committee member), Swanson, Larry (committee member)

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