University of Southern California Dissertations and Theses

Functional impacts of morphology on synaptic transmission

(USC Thesis Other)

Functional impacts of morphology on synaptic transmission

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand com er and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to
order.
UMI
A Bell & Howell Information Company
300 North Zeeb Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/521-0600
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FUNCTIONAL IMPACTS OF MORPHOLOGY ON
SYNAPTIC TRANSMISSION
Copyright 1998
by
Taraneh GhafFari-Farazi
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
in Partial Fulfillment of the
Requirements for the Degree
Master o f Science
in
Biomedical Engineering
University of Southern California
December 1998
Taraneh GhafFari-Farazi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 13 94780
UMI Microform 1394780
Copyright 1999, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This thesis, written by
TVtR.At4e H _______________
under the guidance of his/her Faculty Committee
and approved by all its members, has been
presented to and accepted by the School of
Engineering in partial fulfillm ent o f the re
quirements fo r the degree of
fdT_ _______ \*.___________
T ?) ______
Da te _ __
Faculty Committee
'Dr. T. u j. 'B-ee
Chairman
D r. L_- sow
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ACKNOWLEDGEMENTS
There are many people I would like to acknowledge who helped contribute to this
research project.
First and foremost, I would like to thank my advisor, Dr. Theodore Berger, whose
patience and guidance made this thesis possible.
Secondly, I would like to thank Dr. Jim-Shih Liaw, whose experience and keen
insight helped me tremendously.
Thirdly, I would like to thank Dr. Larry Swanson, who also helped me a great deal
in this research effort.
Finally, I would like to thank the members of Dr. Berger’s lab and my family for
their patience and support.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ii
TABLE OF CONTENTS
• ACKNOWLEDGEMENTS ............................................................................... ii
• LIST OF FIGURES ............................................................................................ iv
• ABSTRACT ........................................................................................................ v
• INTRODUCTION .............................................................................................. 1
• Literature review 7
• METHOD ............................................................................................................ 9
• Overview of the model 10
• Construction of the 2D model 11
• Calcium diffusion 12
• Calcium current and pumps 13
• Neurotransmitter release 14
• RESULTS ........................................................................................................... 15
• Differential probability of release 15
• Geometric features influential in calcium dynamics 16
• Spatial features in the partitioned synapse 19
• Paired pulse simulation 20
• Constant frequency simulation 21
• Calcium pump distribution simulation 22
• DISCUSSION ..................................................................................................... 23
• Accomplishments of the model 23
• Possible mechanism involved in perforations 24
• Future work 25
• BIBLIOGRAPHY .................................................................................................49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF FIGURES
Figure
Page Number
L Synapse Model
8
2. EM of the Partitioned Synapse
9
3. Computer Generated Terminal
10
4. Calcium Distribution
11-13
5. Release Model
16
6. Differential Release in Partitioned Synapse
18
7. “Wall” Effect
20
8. Compartmentalization Effect
21
9. “Pocket” Size
23
10. “Neck” Size
24
11. Site 3 Moved in Partitioned Synapse
26
12. Compartments Eliminated
28
13. Paired Pulse
30
14. Paired Pulse Facilitation
31
15. Constant Frequency Stimulation
33
16. Constant Frequency Stimulation-2
34
17. Effect of Calcium Pumps
36
18. Effect of Scattered Calcium Pumps
37
19. Effect of Uniform Calcium Pumps
38
20. Effect of Calcium Pumps 2
40
21. Effect of Calcium Pumps 3
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
Structural modification has been consistently reported in relation to neural
plasticity, as well as, learning and memory; however, the mechanism by which
morphological alterations influence synaptic function remain unknown. Given that the
primary means of transporting free ions inside living cells is diffusion, morphologic
changes affect the diffusion pattern and local distribution of free ions by modifying the
geometric boundary of the diffusion medium. As a result, any pre- and postsynaptic
processes that depend on the spatio-temporal distribution of free ions are affected. The
aim of this study is to 1) develop a mathematical model of a synapse, capable of simulating
synaptic transmission and predicting postsynaptic potentials, while incorporating
morphologic parameters, and 2) use the model to analyze the impact of changes in
synaptic morphology on synaptic plasticity. Simulation results of the model reveals that
there are multiple morphological features that affect the diffusion pattern of calcium and
neurotransmitter release. Some spatial features affect the release process on a short time
scale and some affect the release on a long time scale, leading to various synaptic
dynamics. In addition, distribution of calcium pumps with respect to the release sites
affects the probability of neurotransmitter release.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
INTRODUCTION
Neurons transmit information via synapses, and it is through the integration of
these signals that higher functions emerge. Functions like the brain’s enormous ability to
process and store new information, and learn new tasks depend on signal transmission
between neurons and the function of their synapses. A century ago, Cajal laid the
foundation for today’s neuroscience when he demonstrated that neurons are not in
cytoplasmic continuity, but are in networks with specialized contacts. The notion that
formation of learning and memory in the brain is mediated by neuronal plasticity was
refined through the years as scientists found more compelling evidence for its support,
both conceptually, and with neurophysiological experiments (McCulloch & Pitts, 1943;
Konorski, 1948; Hebb, 1949; Kandel & Tauc, 1965; Bliss & Lomo, 1973). Although
many different forms of synaptic plasticity have been identified, mechanisms that induce
some form of modification in synapdc contacts are not well understood. Changes in
synaptic contacts may be viewed as essential elements in information processing of the
brain since by affecting synaptic transmission, they alter the outcome of the signal
integration in the brain. In particular, structural changes in the synapse directly affect
synaptic transmission by altering diffusion pattern of free ions. Considering that the
primary means of transporting free ions inside living cells is by diffusion, morphologic
changes affect the diffusion pattern and local distribution of free ions by modifying the
geometric boundary of the diffusion medium. As a result, any pre- and postsynaptic
processes that depend on the spatio-temporal distribution of free ions are affected. Even
though such structural modification has been consistently reported in relation to
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
plasticity, as well as, learning and memory, the mechanism by which the morphological
alterations influence synaptic function remain unknown. Technological limitations, make
it very difficult to experimentally find the functional relevance of morphologic alterations
in synaptic plasticity. However, mathematical modeling o f synaptic transmission is more
feasible and can help answer some of the questions surrounding this topic. For example, a
modeling study was used by Liaw and colleagues (Xie et al., 1997) to explain puzzling
experimental data. The study revealed that during expression of STP and LTP, AMP A
receptor channels are relocated in order to become more geometrically aligned with the
presynaptic release sites. The study also demonstrated the importance of spatial relation
o f synaptic elements in plasticity. Similarly, the aim o f this study is to 1) develop a
mathematical model of a synapse, capable of simulating synaptic transmission and
predicting postsynaptic potentials, while incorporating morphologic parameters, and 2)
use the model to analyze the impact of changes in synaptic morphology on synaptic
plasticity while addressing the following issues:
• Presynaptic calcium dynamics
How the diffusion pattern of intracellular calcium is affected by morphologic changes
in the presynaptic terminal and calcium buffering.
• Calcium pump distribution
How changes in pump distribution affects calcium dynamics and the release of
neurotransmitters.
• Neurotransmitler release
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
How the release probability and the actual release are affected by the morphologically
induced changes in calcium dynamics.
• Nenrotransmiller re-uptake
• Neurotransmitler transporters on presynaptic terminal
• Glia cells
Whether there is a functional significance in relation to transporter localization and
neurotransmitter re-uptake and how that is affected by morphological changes in the
terminal.
• Postsynaptic receptors/potential
How the postsynaptic potential is affected by pre- and postsynaptic ultra-structural
modifications.
• Second messenger systems
How the second messenger system signaling is affected by morphologic changes in the
postsynaptic spine.
There are many different processes at the molecular level that underlie synaptic
transmission, such that to address the above issues, a comprehensive model of a synapse
with sufficient details in both the presynaptic and postsynaptic components is required.
Such a model will be a valuable tool to study morphological impacts on synaptic
transmission and synaptic dynamics. Information gained about synaptic dynamics may
lead to insights in neuronal information processing and explain the significance of
morphologic restructuring in the process of learning and memory. With all of its
complexity, the brain’s functionality may rely on a set of much simpler mechanisms, and
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by modeling a synapse, a great deal can be learned about some of those underlying
mechanisms.
Literature review
Several studies, including our previous model, have described mathematical
models of calcium diffusion and neurotransmitter release and addressed different issues
involved in release. However, all of these models consider a much simpler geometric
shape for the synapse. A three dimensional diffusion model of a squid giant synapse with
radial symmetry was developed to predict calcium dynamics in the presynaptic terminal
and the time course of transmitter release and facilitation (Zucker and Stockbridge, 1983).
A similar model was later employed to study the number of calcium channels that are
likely to activate due to a given depolarization step and the effect of the depolarization on
neurotransmitter release (Zucker and Fogelson, 1986). A diffusion-reaction model of
crayfish neuromuscular junction was used to demonstrate that neurotransmitter release is
enhanced when active zones are closer to each other due to spatial overlapping of
localized calcium clouds (Cooper et al., 1996). A mathematical model of neurotransmitter
release showed a fourth power relationship between intracellular calcium concentration
and the release (Bertram et al., 1996). In a previous study, conducted by J.-S. Liaw and
colleagues, presynaptic mechanisms involved in release were investigated using a two
dimensional model of neurotransmitter release and facilitation. Although these modeling
studies are different from one another (in their mathematical approach and in what they
model; i.e., NMJ vs. CNS synapse), their primary focus is to study the underlying
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mechanisms of neurotransmitter release and the importance of calcium dynamics in this
process. Since calcium dynamics are determined by the diffusion pattern, variations in the
geometric boundary of the diffusion medium affect calcium dynamics. Therefore,
inclusion of a realistic synaptic geometry in modeling can be very beneficial in studying the
transmitter release.
Numerous studies have reported structural changes in the synapse, namely
perforated synapses, and their involvement in plasticity. A large incidence of postsynaptic
density (PSD) perforations, that increased in number after a lesion in entorhinal cortex,
were identified in the rat dentate gyrus (Nieto-Sampedro et al., 1982). Similar findings
were reported in the visual cortex of rabbits following light/dark rearing (Mueller et al.,
1981), visual cortex of rats following prolonged exposure to a visually enriched
environment (Greenough et al., 1979; Schwartz and Rothblat, 1980), and in the motor and
visual cortices of mature rabbit with development (Mueller et al., 1981; Vrensen et al.,
1980). Geinisman and coworkers identified a novel synaptic subtype that exhibited
partitioned PSDs (Geinisman, 1993), and reported an increase in the number of these
perforated and partitioned synapses, one hour after induction of LTP in the rat dentate
gyrus (Geinisman et al., 1993). Despite the compelling evidence relating structural
modification to synaptic plasticity, the mechanisms by which perforated and partitioned
synapses contribute to synaptic plasticity remain unknown. Given the sensitivity of
diffusion to changes in the geometric boundary of diffusion medium, an accurate structural
representation in a synapse model can help to elucidate the relevance of partitioning in
synaptic plasticity.
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
METHOD
Due to the difficulty of solving partial differential equation for diffusion with time
varying boundary conditions over a highly irregular geometry, most models, including our
previous model, assume a regular domain (i.e., sphere, cylinder, & rectangular prism).
The method of choice to solve the diffusion in this project, is use of MATLAB PDE
(Partial Differential Equation) toolbox. PDE solver is capable of solving the diffusion
equation through a diffusion medium of irregular shape. The diffusion medium is specified
with the "Constructive Solid Geometry" modeling paradigm, which is discretized using the
"Finite Element Method" for solving the diffusion equation according to the boundary and
initial conditions. Any two dimensional geometrical boundary, such as the presynaptic
terminal, is constructed by way of drawing basic geometrical shapes (circle, ellipse,
rectangle, polygon), and overlapping them to combine or subtract from each other to
make up complex geometric shapes.
Incorporation of geometric parameters in the model is not without a cost. A
synapse is a three dimensional structure which has been implemented as a two dimensional
slice in the model due to the complex computation involved in solving the diffusion
equation with time varying boundary conditions in an asymmetric diffusion medium. A 2D
model can, however, adequately represent the synapse considering that the diffusion of
particles such as calcium and neurotransmitters in every dimension is identical to the other
two dimensions; and by solving the diffusion equation for two dimensions, one can draw
conclusions about the diffusion in the third dimension. Given the geometrical
representation of the model, the boundary and initial conditions, and the coefficients of the
6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
diffusion equation, PDE toolbox will generate a triangular mesh over the described 2D
geometry, discretize the equation, and produce an approximation to the solution.
Substantial work is required to specify time varying boundary conditions occurring
at the appropriate boundary element. The toolbox sets up a boundary condition matrix
that contains the value of the boundary condition coefficient for every boundary element.
By calculating the coefficient values and updating this matrix at every time step, time
varying boundary conditions may be incorporated into the diffusion equation. Such a
capability allows for inclusion of a variety of time varying boundary conditions for one
structure, to model processes such as ionic channels and pumps, neurotransmitter
transporters, immobile buffers, etc. The model includes a method to couple the diffusion
of calcium with a set of ordinary differential equations describing the chemical interactions
between calcium and various molecules to predict neurotransmitter release probability.
With the extended functionality that has been developed, a synapse with arbitrary shape
and with any number of presynaptic and postsynaptic processes can be defined and used to
study how spatial factors regulate the synaptic transmission and how alterations of these
factors may serve as a basis for synaptic plasticity.
Overview of the model
The model represents a two dimensional cross-section of a partitioned synapse
that includes several elements such as calcium channels, calcium pumps, calcium buffers,
and neurotransmitter release sites (Fig. 1). Each calcium channel represents a population
of channels to accommodate the required intracellular calcium concentration required for
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
release. Calcium buffers are assumed to be distributed uniformly in the cytoplasm, and
calcium pumps are assumed to be uniformly distributed along the terminal membrane,
but excluded from the vicinity of the release site. There is one release site associated
with every calcium channel which is placed 10 nm away from the channel. The input to
the model is a set of depolarization steps and the model computes the calcium dynamics
in the cytoplasm and the time course of its interactions with various molecules, and
produces the resulting probability of neurotransmitter release.
Dendritic Spine
Presynaptic Terminal
Na
Second
(essenger
Ca:
Na
Figure 1. Two dimensional cross-section of a synapse with
presynaptic calcium channels, pumps, buffers, release sites, and
postsynaptic receptors.
Construction of the 2-D model
An EM picture (Geinisman, 1993) of a hippocampal synapse (Fig. 2) after high
frequency stimulation was used to create a presynaptic terminal on the GUI (graphic user
interface) of MATLAB PDE toolbox. Since the terminal shape is highly irregular,
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
constructive solid geometry was utilized to sketch the terminal as accurately as possible
(Fig. 3). Calcium channels, calcium pumps, and neurotransmitter release sites were
placed on the boundary of the drawn terminal based on the location of PSDs in the EM
picture. Kinetics of calcium conductance and pumps were incorporated into the
boundary conditions at the appropriate boundary elements. The diffusion coefficient was
specified to include the appropriate rate of calcium buffering. Given the geometrical
representation of the terminal, the boundary and initial conditions, and the coefficients of
the diffusion equation, a triangular mesh was generated over the described two
dimensional geometry to discretize the diffusion equation and produce an approximation
to the solution using MATLAB PDE. The mesh is generated such that the triangles near
the calcium channels and release sites are higher in number and smaller in size. In
addition to the nonuniform triangulation, the mesh is refined until the smallest boundary
element is just smaller than 0.5 nm wide in order to minimize the approximation error.
Geinisman 1993
Figure 2. Electron micrograph of a hippocampal
synapse in the dentate gyrus after induction of LTP.
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R1
Figure 3. Computer generated model of the
presynaptic terminal taken from the synapse in Figure 2;
R l, R2, and R3 stand for the three release sites that are
near three population of calcium channels and correspond
to the post synaptic densities observed in the EM picture.
Calcium diffusion
After entering the presynaptic terminal, free calcium ions diffuse into the
intracellular space and are quickly bound to the calcium buffers. This process is
simulated by solving the diffusion equation for calcium
at ox-ay
where c(x,y,t) is the calcium concentration inside the diffusion medium at time t at
location (x,y), Dc is the diffusion coefficient of free calcium ions (6x10^ era2 /sec;
Hodgkin and Keynes, 1957), and B(t) is the calcium buffering process which are
assumed to be immobile and uniformly distributed in the cytoplasm. Given that the
process of calcium binding to buffers occurs in a much faster time scale than the
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
diffusion, local equilibrium is reached between free and bound calcium ions (Crank,
1975) and therefore, the above equation can be simplified to
9c(x,y,r) ^ D. 3c2(x,y,r)
dt 1 + p ' dx-dy
where /? is the ratio of bound to free calcium in the cytoplasm. Matlab PDE solver
computes an approximation to the solution of the above equation given the initial and
boundary conditions. Thus, the spatial and temporal distribution of calcium inside the
presynaptic terminal is determined by solving the above equation over a triangular grid,
representing the diffusion medium, using PDE toolbox (Fig. 4).
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B.
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
D.
Figure 4, A,B,C,D. Snap shots of calcium diffusion pattern as it enters
the presynaptic terminal through the calcium channels generated by the
model. The terminal is located in the X-Y plane and the Z axis shows the
amount of calcium particles entered the cell shortly after a depolarization
step; A) Snap shot of calcium concentration 0.445 ms after the beginning of
the input train. B) Snap shot of calcium concentration 2.95 ms after the first
depolarization step (the first pulse lasts from 0.5 to 1.5 ms, and the second
pulse lasts from 5.5 to 6.5 ms-- simulation ends at 15 ms). C) Snap shot of
calcium diffusion pattern 3.695 ms after the first depolarization step. D)
Snap shot 8.45 ms after the second depolarization step.
Calcium current and pumps
The calcium current in the model is determined by
[3]
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where G is the number of channels in the open state, and j is the rate of flow through a
single channel as described by Llinas and colleagues (Llinas et al., 1981).
Parameter values in the above equations are the same as those indicated by Llinas, unless
specified otherwise. Calcium current, as obtained in equation [3] is converted to the
number of calcium particles that enter the cell per unit of time and passed on to the PDE
toolbox in the boundary condition at the appropriate boundary element to model calcium
channels. Since calcium current changes with time, the boundary conditions are re
evaluated and updated at every time step.
Calcium pumps are assumed to be distributed uniformly on the terminal
membrane; however, they are eliminated from the neighborhood of the calcium channel
and release site complex to a radius of 60 nm. Calcium pumping rate used in previous
models range from 80 to 2 nm/msec (Yamada and Zucker, 1992; Pamas et al., 1989;
Zucker and Fogelson, 1985; Zucker and Stockbridge, 1983). In this model, we varied
the pumping rate within the above range. Similar to the calcium influx, calcium
pumping was modeled by specifying the rate in the boundary condition at every element
[4]
[5]
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
on the boundary except where the pumping is not present (i.e., neighborhood of the
calcium channeL and release site complex).
Neurotransmitter release
The process of neurotransmitter release and its time course is described by a set
of equations developed by J.-S. Liaw for a mathematical model of synapse, in a previous
study:
k f c *
Ca2 + + X_V<±>CaX_V + Ca2+ <^>Ca^X_V [6]
J L , f c - ,
n(Ca^X)_V-%n(Ca,X)_V'£>I [7]
where X is the synaptotagmin, V is the synaptic vesicle, n(Ca2X)_V* is the number of
vesicles in the open state allowing neurotransmitter release, and / is the insensitive state
of the fusion pore. Although synaptotagmin is the only vesicle protein that is included in
the above equations, the binding/unbinding rates are specified to account for all proteins
involved in the release process, to predict the time course of neurotransmitter release. To
this end, the kinetic parameters of calcium interaction with various molecules (e.g.,
synaptotagmin; Fig. 5) which trigger neurotransmitter release are described by fitting
simulation results with experimental data on the time course of response to a pair of
depolarization steps delivered at 5 msec apart (Pamas et al., 1989).
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Cytoskeleton
Synapsins
Synaptic
Vesicle
Synaptobrevin
(VAMP) '
Synapto tagmln
NSF/SNAP
Complex
Synaptophysin
- Synaptophilln
■ Neuroxln
Synataxin
Presynaptic
Mem brane
Calcium
Channel
Figure 5. Molecules associated with synaptic vesicle and release.
RESULTS
Thus far, only the presynaptic component of the model has been developed.
However, some of the issues mentioned early on, such as morphological effects on
calcium dynamics, neurotransmitter release, and calcium pump distribution may be
addressed with the present model. To this end, several simulation studies were
conducted and the result are as follows.
Differential Probability of Release
To test the hypothesis that local structure in the partitioned synapse affects calcium
diffusion and, therefore release, an arbitrary input pattern (i.e., a 200 msec long train of
depolarization steps shown in the bottom panel of Fig. 6-B) was chosen. The probability
of neurotransmitter release was then calculated for the three calcium channel-release site
complexes in the terminal (Fig. 3). The peak amplitude of release probability due to a
single depolarization step (Fig. 6-A) for site #1 was higher than that of site #2 by 32% and
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that of site #3 by 19%. However, the peak response of site #1 to subsequent
depolarization steps (Fig. 6-B) varied with respect to site #3 (i.e., beginning at 15 msec,
for a period of 30 msec, site #3’s peak response was higher than that o f site #1). This
variation is caused by differences in local calcium concentration between different sites
which indicates that local geometry has an impact on calcium dynamics. Given the highly
nonlinear relationship between neurotransmitter release probability and calcium
concentration intracellularly, changes in calcium dynamics produce different release
probabilities for different release sites of the same terminal.
Geometric Features — influential in calcium dynamics
To isolate morphologic features that account for changes in calcium dynamics, a
series of computer simulations using simple geometric shapes as the presynaptic terminal
were conducted and the release probability for a given input pattern was calculated,
varying only one spatial feature at a time.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
Release Probability, CH1 Release Probability, CH2 Release Probability, CH3
x10'
4
3
2
1
0
0 1 2 3 4 5
msec
B
K10-4 Release Probability
x 1(T
4
3
2
1
0
0 1 2 3 4 5
msec
4
3
2
1
0
0 1 2 3 4 5
msec
a
7
6
6
4
3
2
1
0
180 200 0 140 160 20 80 100 120 40 60
msec
m V Input
0
-70
MJULIM M l M J___L
20 40 60 80 100 120 140 160 180 200
msec
Figure 6. A) Probability of release for all three sites in the partitioned synapse due to
a single depolarization step. B) Probability of release due to a train of depolarization
steps, for sitel and site3.
The first set of simulations were designed to test the idea that the partition membrane wall
can affect calcium dynamics and, therefore, alter the release probability. As such, a simple
geometrical shape, such as a rectangle, was used as the presynaptic terminal. One calcium
channel and one release site (10 nm apart) were placed at a distance of 3X from the edge
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o f the terminal (Fig. 7-A), and the probability of release for a given input train shown in
Fig. 7-B was computed. In two other experiments, the calcium channel-release site
complex was moved closer and closer to the edge of the rectangular terminal, and the
simulation was repeated. Comparison of the release probability curves indicates that the
release site closest to the edge have the highest probability of neurotransmitter release.
This increase in release probability is due to the increase in local calcium concentration
caused by the edge of the terminal which acts as a barrier, blocking calcium diffusion in
that direction. The same concept may be applied to the release sites in a partitioned
synapse that are near the partition membrane wall.
The next simulation was to investigate the effect of compartmentalization in
general. For this purpose, a simple rectangular geometry with a small compartment in one
side was used as the presynaptic terminal. Two calcium channel-release site complexes
were placed as shown in figure 8-A. Comparison of the release probability curves of the
two sites shows a higher probability for neurotransmitter release for the site located in the
small compartment (Fig. 8-B). The compartment acts as a pocket, accumulating calcium,
which increases the likelihood of having neurotransmitter release. Applying this
simulation result to partitioned synapses, one can predict that small pocket like cavities
that exist in such synapses cause free calcium ions to not diffuse away and thus increase
the release probability.
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission.
A
B
_ X
2
A A
R1
i— X
R2
3X
R3
x 10 R e lease Probability
8
7
6
5
4
3
2
1
0
— R1
— R2
— R3
200 120 140 160 180 100
m sec
Input
h mi h h A A A A A A I I I I
-
0 20 40 60 80 100 120 140 160 180 200
msec
to
o
Figure 7. Proximity to adjacent partition membrane, A) Release site was placed at
3X, X, and 0.5X from the edge of the terminal, B) Comparison of the release probability
for the three locations,
owner. Further reproduction prohibited without permission. O
■ o
*
R1
B.
I
C o n tr o l
x 1 0 Release P r o b a b i l i t y
8
7
6
5
4
3
2
1
0
R1
C o n tr o l
160 140 180 200 100 120
m sec
mV
0
-70
In p u t
S J L J J L J J J l J U U l f t J U L
( 1 f t
0 20 40 60 80 100 120 140 160 180 200
msec
to
Figure 8. Local volume effect, A) Release site U1 is partitioned from the rest of the
terminal. B) Comparison o f the release probability for the two release sites depicted in A,
After demonstrating the effect of local volume on release, the relationship between
the size of the compartment or pocket to the probability of release became important. To
address this point, the area of the terminal in the previous simulation was increased (Fig.
9-A) and the simulation with the same input train was repeated. Comparison of the
resulting release probability curve with that of the previous simulation shows a decrease in
peak amplitudes (Fig. 9-B). This result clearly demonstrates the effect of
compartmentalization size on calcium dynamics and therefore probability of release. In a
larger pocket, calcium can diffuse further away from the release site and thus decrease the
likelihood of probability of binding to synaptotagmin and triggering release. Partitioned
synapses, by creating small pockets, entrap free calcium ions and increase the efficacy of
the synaptic connection of increasing the probability of release.
Another important issue with respect to the compartmentalization is the size of the
“neck”. In the next simulation, the size of the neck, the opening though which the small
pocket is connected to the rest of the terminal, was increased (Fig. 10-A). This caused a
decrease in the release probability, indicating that small pockets with small necks make the
terminal more efficient in releasing neurotransmitter than large pockets with large necks
(Fig. 10-B).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 2
copyright owner. Further reproduction prohibited without permission.
Contro
Control
X 10
R e le a s e Probability
8
7
6
5
4
3
2
1
0
R2
140 180 60 120 160 200 40 80 100
msec
Input
ro
U U ILUL J l I L
20 40 60 80 100 120 140 160 180 200
m sec
to
O J
Figure 9. Effect o f "pocket" size. A) R l is placed in a larger "pocket" compared to
R2. B) Comparison of the release probabilities in both cases.
o f th e copyright owner. Further reproduction prohibited without permission.
R1 Control
Wide Neck
B.
Control
R e l e a s e P r o b a b i l i t y x 10
8
7
6
5
4
3
2
1
0
Control
mV
0 20
Input
40 60 80 100
m sec
120 140 160 180 200
-70
y y mi
M l
juui j i I L
20 40 60 80 100
m sec
120 140 160 180 200
Figure 10. Effect o f "neck" size. A) R 1 is placed in a pocket where the openning or
the neck is narrow compared to R2. B) Comparison of the release probabilities in both
cases,
to
4 ^
The following is a summary o f identified spatial features that can modify the
magnitude of the release probability:
• Proximity to adjacent “partition membrane wall” (Fig. 7)
As the calcium channel-release site was moved closer to the nearby membrane
wall, the peak amplitude of the release probability increased.
• Local volume (Fig. 8)
The calcium channel-release site that was positioned at a relatively small pocket
like cavity had a higher probability of neurotransmitter release than those
positioned at an open space.
• “Pocket” size (Fig. 9)
As the size of the pocket decreased, the probability of neurotransmitter release
increased over time.
• “Neck” size (Fig. 10)
As the diameter of the neck decreased, the probability of neurotransmitter release
increased over time.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission.
9 1 ----------------1 ----------------^ ------------------------------------------------------------------------------------- -------------
8
7
6
5
4
3
2
1
°0 20 40 60 80 100 120 140 160 180 200
mV
0
-70
0 20 40 60 80 100 120 140 160 180 200
m sec
Figure ll, A) Release site #3 is moved to a new location, not near a partitioning
membrane, B) The release probability at the new location is compared to the original,
to
C T l
m sec
Input
n mi mu h h n a n n 1
B
v i(i8 R e l e a s e P r o b a b i l i t y
Geinisman 1993
R3
(new location)
Spatial Features in the Partitioned Synapse
The differential release probability observed in the partitioned synapse (Fig. 6-B),
may be due to one, or a combination, of the above listed spatial features. In order to test
this idea, calcium channel-release site #3 in the partitioned synapse was moved
approximately 300nm to the right (Fig. 11-A), and the release probability at the new
location was calculated. Comparison of the new release probability for site #3 to it
original release probability shows a decrease in magnitude (Fig. 11-B). By moving the
calcium channel and the release site to the new location, the diffusion blockade effect of
the “adjacent partition membrane wall” was removed, enabling calcium ions to diffuse
farther away, and thus the release probability was decreased.
The effect of local volume and partitioning is demonstrated by modifying the
boundary of the Geinisman geometry (Fig. 12-A). By eliminating the compartments in the
terminal, the difference in the peak amplitude of probability of release between site #1 and
#3 was decreased (Fig. 12-B). This simulation clearly shows the impact of the partitioning
on calcium dynamics and the release probability. However, the small difference between
the peak amplitude of the two release probability curves is due to the asymmetry of the
terminal and the location of the two sites relative to each other and the terminal boundary.
Having demonstrated the effect of morphology on neurotransmitter release,
questions may be raised with respect to the input frequency dependence of the observed
effects. To tackle this issue, the following two sets of simulations were conducted: paired
pulse facilitation and constant frequency trains.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
release sites.
Paired Pulse Simulation
Here, a series of PPF simulations for the partitioned geometry for various inter-
stimulus intervals (ISI=2, 5, 10, 15, 20, 30, 40, 50, 75, 100, 150, 200, 300, 400, and 500
msec) were performed. Comparisons of the peak release probabilities due to the second
pulse (Fig. 13) show that, with the exception of three ISIs (5, 10, and 15 msec), the peak
response of site #1 was higher than that of #3 by at least 6.5% (ISI = 2 msec). This
difference went up to 17.5% for ISI = 500 msec. The high release probability of site #1
for the second pulse compared to site #3 may be explained by the “local volume” effect.
Since site #1 is partially isolated from the rest of the terminal, free calcium ions are
contained in the compartment and thus the probability o f calcium ions binding to
synaptotagmin and triggering release is increased. Site #3 however, is exposed to a larger
diffusion area and thus free calcium ions are diffused far away, given enough time in
between the two sequential depolarization steps (i.e., large ISIs). For this reason, the
peak release probability of this site did not reach as high as that of site #1. Due to the high
release probability of site #1 compared to site #3 for the first pulse, it can be predicted that
the facilitation for this site should be lower that site #3. Review of the paired pulse
facilitation calculated for the partitioned synapse for a range of ISI values confirms the
above prediction (Fig. 14).
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Rel. probability due t o the 2nd pulse
6.00E-05
5.00E-05
4.00E-05
3.00E-05
2.00E-05
1.00E-05
O .O O E + O O CH3_P2
CH2_P2
CHI P2
IS I (msec)
Figure 13. Magnitude of the release probability due to the second pulse.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
u.
CH3_PPF
CH2_PPF
CHI PPF
20
40
IS I (msec)
Figure 14. Paired Pulse Facilitation for all three release sites.
Constant Frequency Simulation
In this set of simulations, the input consisted of 10 depolarization steps (-70 to 0
mV) delivered at a constant frequency (f=10, 20, 40, 50, 80, 100, 200, 250, and 400 Hz).
The resulting release probabilities for all three sites were calculated and magnitudes of all
ten peaks for all frequencies were recorded. Although the peak amplitude of release
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
probability for a given input frequency kept on increasing for each release site (Fig. 15),
the difference in peak amplitude between site #1 and #3 for the last four depolarization
steps became steady. A comparison of the difference between site #1 and #3 in release
probability (due to the last four pulses in the input train) for all input frequencies shows
that site #3 has a higher facilitation for high frequency input trains (80-400 Hz) than site
#1; and site #1 has a higher facilitation for low frequency input trains (10-50 Hz) than site
#3 (Fig. 16). This result gives an interesting twist to the idea o f increased response due to
adjacent membrane wall. For short-term intervals (f > 80 Hz), the peak amplitude of the
release probability for site #3 exceeded that of site #1, indicating a frequency dependent
increase in local calcium concentration, induced by the adjacent partition membrane wall
next to the release site #3. In addition, being adjacent to the partition membrane wall, site
#3 is exposed to a relatively large area of the terminal, requiring high frequency stimulus
to increase local calcium concentration. For low frequency stimulus, there is enough time
between sequential depolarization steps for the calcium to diffuse away and decrease the
local calcium concentration, causing a decrease in the release probability.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
Prob(R3)-Prob(Rl) I n %
30
20
10
0
10
■ 2 0
■ 3 0
10 8 6 4 2 0
peck
— flO_CH3-CHl
— f20_CH3-CH 1
— * —f40_CH 3-CHI
— f50_CH3-CH 1
— *£—f80_CH3-CH 1
flOO_CH3-CHl
— f200_CH3-CHl
— B — f250_CH3-CH 1
— A -f400 CH3-CH1
Figure 15. Percentage difference in probability of release between
every peak for all frequencies.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
Figure 16. Percentage difference in release probability for the last four
depolarization steps.
Calcium Pump Distribution Simulation
Given that spatial distribution of calcium is affected by morphologic parameters of
the terminal, location and rate of processes that directly alter calcium concentration, such
as calcium pumps, will affect the local calcium distribution and ultimately affect synaptic
dynamics. To study this issue, several simulations on the partitioned synapse with various
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
calcium pump rates and distributions were conducted, keeping the input train identical in
all simulations. In the first three simulations, the pumping rate used was 20 nm/msec
(Zucker and Fogelson, 1986), but the distribution of the pump was varied. When the
pump was assigned to be uniformly distributed across the terminal membrane, the release
probability peaks of site #1 was higher than that of site #3 (Fig. 17). However, having
pumps in between the release site and calcium channels seems self-defeating and
unrealistic; so, in the next simulation the pump was moved to two patches of 200-300 nm
long, placed in between the three release sites (Fig. I8_A). The result showed that for the
first half of the simulation, site #3 had a higher release probability than site #l(Fig. 18_B).
However, in the second half of the simulation, this relationship is reversed, indicating a
great deal of sensitivity in release probability to pump distribution. When the pumps were
distributed uniformly across the terminal with the exception of 20nm radius of the calcium
channels and release sites, release probability of site #1 became dominant with respect site
#3 (Fig. 19).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission.
8
7
6
5
4
3
2
1
°0 20 40 60 80 100 120 140 160 180 200
t (msec)
(mV)
0
-70
0 20 40 60 80 100 120 140 160 180 200
Figure 17, Probability of release in the partitioned synapse when calcium pumps (rate =
20 nm/msec) are distributed uniformly on the terminal membrane,
nput tram
y _ j j _ J U L _
mu i n
i i a
-
-
y in-s R e le a s e probability
' 1 ' I I '' I 1 ' J ' I ' T I ' ■ ' i r r j r I , n - , I | I I |
---------------R1 -
----------------R3 _
L O
Os
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
A.
B.
Location ofthe calcium pumps
x10 .4 R e le ase probability
- R3
0.6
0.6
0.4
0.2
80 100 120 140 160 180 40 60 200
Input train
msec
y
msec
200
Figure 18. Probability of release in the partitioned synapse when calcium pumps (rate
20 nm/ms) are placed only on the membrane in between the three sites,
u >
CN
T — CO
01 01
C O
CO
o O
O < D
C O
o
CO
Q.
C M
O in co CO N O
1 1 I 1
<=
=
=
i 1
o
o
^r
o
C O
CN 3
II
-5
C O
B
In
C O
Un B
c
C O
Q . O
E
CN
3 C O
c l
B
3
Q -
;5 U
o
CO
X
U
o
c
o
o
r*
§
> kn
X )
o
C O E
Q -
o
C O
C
E
" 5
" 3
o
3
c H
. 2 - 2
CO
o
3
o
c o
■ 3 * c o
C L
a
c
o
C O
• 3
o
CO
o
.£
CJ
3 kn
o c
" O
C O
C O
o
2
a
*E
3
c
c o
C O
o
-o
c
o o C
CO
3
J3
15
C O
- O
-O
3
C O
•3
O
E
3
o O
k*
CL,
o
kn
C O
C O
CJ
CN
u
o
o
3
«
C O -a
k~
g c
3 3
CD
i Z
E
c
>
E
o
Similar to pump distribution, the pumping rate is another important factor in
calcium dynamics, especially when considered in conjunction with geometric parameters.
For the next two computer simulations, the pumping rate was changed to lOnm/msec, and
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the distribution was kept uniform except in the vicinity of the calcium channels and release
sites. In the first experiment, the pumping was turned off from a 20nm radius around the
channel and release site (Fig. 20), and in the second, it was turned off from a 60nm radius
around the channel and release site(Fig. 21). The results suggest that the effect of the
calcium pump on release somehow depends on the morphologic parameters associated
with the specific release site. For example, comparison of the magnitude of release
probability due to the seventh input step, shows that changing the “pump off region” from
20 to 60nm increased the release probability of site #3 by nearly 100%. However, the
release probability of site #1 was much less sensitive to the change, and it only increased
by 30%.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
R e l e a s e probability
R3 -
0.7
0.6
0.4
0.2
180 200 60 80 100
t (msec)
120 140 160 20 40
(mV)
0
-70
0 20 40 60 80 100 120 140 160 180 200
Figure 20. Probability o f release in the partitioned synapse when calcium pumps (rate = 10
nm/mscc) are distributed uniformly on the terminal membrane, except in a 20 nm radius
around the calcium channels and release sites.
Input train
y y m iiflii A A A 1 1 A
_ _
-
o
Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission.
y in-4 R e l e a s e probability
1.6
1.4
1.2
1
0,8
0,6
0,4
0,2
0 ,
U lJLjy
A
f t
O '-----------------4+ v f t llv — 4 lJ
R1
R3
'v,,
'0 20 40 60 80 100
t (msec)
120 140 160 180 200
nput train
y n a f t a m
A A A 1 1 :
-
(mV)
0
-70
20 40 60 80 100 120 140 160 180 200
Figure 21, Probability o f release in the partitioned synapse when calcium pumps (rate = 10
nm/mscc) are distributed uniformly on the terminal membrane, except in a 60 nm radius
around the calcium channels and release sites.
DISCUSSION:
Accomplishments of the model
Theoretical calculations based on this model 1) demonstrated how morphologic
parameters in a synapse can alter the probability of neurotransmitter release, 2) identified
spatial features (local volume, proximity to adjacent partition membrane, pocket size, and
neck size) that are effective in modifying calcium dynamics, 3) revealed that the release
sites of the partitioned synapse exhibited different release probability to the same input,
and showed 4) facilitation in the release probability that is sensitive to the input frequency,
and finally 5) determined importance of calcium pump distribution with respect to the
location of calcium channels and release sites.
Structural changes in synapses indirectly contribute to synaptic plasticity by
altering spatial distribution of calcium intracellularly and changing the probability of
release. Depending on the specific geometric shape, the effect on calcium dynamics will
be different: some spatial features affect the release probability on a short-time scale and
others have a long-term effect, which results in various synaptic dynamics. Partitioned
synapses have a higher efficacy than non-partitioned synapses not only because of having
multiple release sites, but also because of their morphological characteristics. PPF and
constant frequency simulations indicated that release sites of the partitioned synapse are
sensitive to the frequency of the input. For example, site #1 had the highest release
probability peaks for low frequency input, where as site #3 had the highest release
probability for high frequency input. This structurally induced sensitivity to input
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequency provides the synapse with another mechanism for synaptic dynamics, and
therefore neuronal information processing.
Possible mechanism involved in perforations
Synaptic perforations are reportedly observed after the induction o f LTP. Several
models describing the mechanism of perforation consider the spine apparatus as a possible
mechanism underlying the pre- and postsynaptic membrane growth and partitioning of the
PSDs (Carlin and Siekevitz, 1983; Dyson and Jones, 1984). Here, another possible
mechanism involved in perforation is presented. Considering that the process of vesicle
recycling is slower than vesicle membrane fusion and release, repeated vesicle release
caused by the high frequency stimulation (to induce LTP) will result in the addition of
presynaptic membrane without allowing for expansion of its intracellular content. Since
the presynaptic and the postsynaptic membranes at the synapse are anchored to one
another by anchoring proteins, the postsynaptic spine head is forced to somehow
compensate for the presynaptic membrane growth. This may serve as a driving force
triggering the spine apparatus to synthesize protein and insert membrane right on to the
PSD to counterbalance the presynaptic membrane growth. As a result, there will be an
increase in both the presynaptic and postsynaptic membranes of the synapse, which
naturally has to fold. The possibility of this suggestion is strengthened when size of
vesicles and terminal bouton is considered. Serial EM study of rat hippocampal neurons
show that the average surface area o f a spine head is 0.6 lp.m2 (Harris and Stevens, 1989).
The average diameter of a vesicle is reported to be between 40 to 50nm (Jahn and Sudhof,
1994). Assuming that LTP is induced by 40 pulses at 100Hz and that one vesicle is
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
released for each pulse, then a total of 40 vesicle membranes are added to the terminal
membrane (i.e., addition of a total o f 0.25(xm2 in surface area). This would result in a
41% increase in surface area of the axonal terminal if its surface area is similar to the
surface area of the spine head.
Future work
So far, the findings of this study are based on the presynaptic component of the
model. The other two major components of the model, namely synaptic cleft and
postsynaptic spine, are to be developed. Processes such as synaptic vesicle depletion and
mobilization, vesicle recycling, neurotransmitter diffusion across synaptic cleft,
neurotransmitter uptake by glia cells and presynaptic transporters, postsynaptic receptor
channels such as AMP A and NMDA, and kinetics of transmitter binding to the
postsynaptic receptors are part of the future work on the model. Implementation of these
elements in the model will help to see the effect of ultra-structural modification beyond the
presynaptic terminal and release. Given the influence of geometry on the release
probability, the location of molecules (i.e., their location with respect to the PSD and the
geometric shape of the terminal) that directly affect the local concentration of calcium and
neurotransmitters, such as calcium pumps and neurotransmitter transporters, will be
important issues to investigate further. Changes in neurotransmitter release and uptake
may alter postsynaptic response, and with the extended functions of the model these
questions can be addressed.
Other applications of this model include transporter localization research. EM
studies of dopamine transporter localization show that this transporter is extensively
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
localized on the plasma membrane of the axonal terminals, lateral to the site of contact
(Nirenberg et ah, 1996). With the geometric capabilities that this model has in handling
diffusion, modeling studies of dopaminergic synapses with localized transporters may help
answer questions regarding dopamine transporter localization and their role in Parkinson’s
disease.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
BIBLIOGRAPHY
1. Bertram, R., Sherman, A. & Stanley, E. F. (1996) Journal o f Neurophysiology 75,
1919-1931.
2. Bliss, T. V. P. & Lomo, T. (1973) Journal o f Physiology, London 232, 331-356.
3. Buchs, P.-A. & Muller, D. (1996) Proceedings o f the National Academy o f Science,
USA 93, 8040-8045.
4. Carlin, R. K. & Siekevitz, P. (1983) Proceedings o f the National Academy o f Science
80, 3517-3521.
5. Cooper, R. L., Winslow, J. L., Govind, C. K. & Atwood, H. L. (1996) Journal o f
Neurophysiology 75, 2451-2466.
6. Dyson, S. E. & Jones, D. G. (1984) Developmental Brain Research 13, 125-137.
7. Geinisman, Y., Detoledomorrell, L., Morrell, F., Heller, R. E., Rossi, M. & Parshali,
R. F. (1993) Hippocampus 3, 435-446.
8. Geinisman, Y. (1993) Hippocampus 3, 417-434.
9. Geinisman, Y., Detoledomorrell, L., Morrell, F., Persina, I. S. & Beatty, M. A. (1996)
Journal O f Comparative Neurology 368, 413-423.
10. Greenough, W. T., Juraska, J. M. & Volkmar, F. R. (1979) Behavioral and Neural
Biology 26, 287-297.
11. Harris, K. M. & Stevens, J. K. (1989) Journal o f Neuroscience 9, 2982-2997.
12. Hebb, D. O. (1949) Wiley, New York .
13. Kandel, E. R. & Tauc, L. (1965).
14. Konorski, J. (1948) Cambridge U niversity.
15. Llinas, R., Steinberg, I. Z. & Walton, K. (1981) Biophysical Society 33, 289-322.
16. McCulloch, W. S. & Pitts, W. (1943) Bull. Math. Biophysics 5, 115-133.
17. Muller, L., Pattisellano, A. & Vrensen, G. (1981) Brain Research 205, 39-48.
18. Nieto-Sampedro, M., Hoff, S. F. & Cotman, C. W. (1982) Proceedings o f the
National Academy o f Science, USA 79, 5718-5722.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19. Nirenberg, M. J., Vaughan, R. A., Uhl, G. R., Kuhar, M. J. & Pickel, V. M. (1996)
Journal o f Neuroscience 16, 436-447.
20. Paraas, H., Hovav, G. & Pamas, I. (1989) Biophysical Society 5, 859-874.
21. Schwartz, M. L. & Rothblat, L. A. (1980) Experimental Neurology 68, 136-146.
22. Vrensen, G., Nunes Cardozo, J., Muller, L. & Van der Want, J. (1980) Brain
Research 184, 23-40.
23. Xie, X. P., Liaw, J.-S., Baudry, M. & Berger, T. W. (1997) Proceedings o f the
National Academy o f Science, USA 94, 6983-6988.
24. Yamada, W. M. & Zucker, R. S. (1992) Biophysical Society 61, 671-682.
25. Zucker, R. S. & Stockbridge, N. (1983) Journal o f Neuroscience 3, 1263-1269.
26. Zucker, R. S. & Fogelson, A. L. (1986) Proceedings o f the National Academy o f
Science, USA 83, 3032-3036.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
IMAGE EVALUATION
TEST TARGET (Q A -3 )
1 . 0
l.l
1.25
“ O S
is H i
1*1
If
1 .4
1 23
[ 2.2
2.0
1 . 8
1 .6
150mm
A P P L I E D A IIVHGE . Inc
1653 East Main Street
- = ~- Rochester. NY 14609 USA
_ £ = = ! = : Phone: 716/482-0300
- = ~ - = Fax: 716/288-5989
0 1993. Applied Image. Inc., All Rights R eserved
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

The relation between presynaptic terminal morphology and dynamics of neurotransmitter release: A mathematical modeling study

PDF

Effects of prenatal cocaine exposure in quantitative sleep measures in infants

PDF

Cytoarchitecturally conformal multielectrode arrays for neuroscience and neural prosthetic applications

PDF

Dynamics of the newly formed neuromuscular synapse

PDF

Decomposition Of Neuronal Function Using Nonlinear Systems Analysis

PDF

Contributions of active dendrites and structural plasticity to the neural substrate for learning and memory

PDF

Initiation of apoptosis by application of high-intensity electric fields

PDF

Assessment of minimal model applicability to longitudinal studies

PDF

A finite element model of the forefoot region of ankle foot orthoses fabricated with advanced composite materials

PDF

Age and neurotransmitter modulation of release at excitatory striatal synapses

PDF

Evaluation of R.F. transmitters for optimized operation of muscle stimulating implants

PDF

A user interface for the ADAPT II pharmacokinetic/pharmacodynamic systems analysis software under Windows 2000

PDF

Characteristics and properties of modified gelatin cross-linked with saline for tissue engineering applications

PDF

Cellular kinetic models of the antiviral agent (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA)

PDF

Acidity near degrading poly(DL-lactide-co-glycolide): An in vivo and in vitro study

PDF

Building a biological hybrid biosensor using nonlinear system analysis of the CA1 hippocampal neural network

PDF

A kinetic model of AMPA and NMDA receptors

PDF

Contact pressures in the distal radioulnar joint as a function of radial malunion

PDF

Empirical evaluation of neuromusculoskeletal models for functional electrical stimulation of the lower limb

PDF

Computation and validation of circulating blood volume with the indocyanine green dilution technique

Asset Metadata

Creator Ghaffari-Farazi, Taraneh (author)

Core Title Functional impacts of morphology on synaptic transmission

School Graduate School

Degree Master of Science

Degree Program Biomedical Engineering

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

Tag biology, neuroscience,engineering, biomedical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Berger, Theodore W. (committee chair), Liaw, J.S. (committee member), Swanson, Larry (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-28039

Unique identifier UC11337593

Identifier 1394780.pdf (filename),usctheses-c16-28039 (legacy record id)

Legacy Identifier 1394780.pdf

Dmrecord 28039

Document Type Thesis

Rights Ghaffari-Farazi, Taraneh

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA