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Modeling Neurons and Networks
What Algorithms Does the
Brain
Use for Information Processing?
Szabolcs Káli
Institute of Experimental Medicine, HAS
Department of Cellular and Network Neurobiology
Budapest, Hungary
kali@koki.hu
Summary —This document describes the
teaching materials we developed to introduce
the basic concepts of computational neurosci-
ence to Master's level students at the Faculty of
Information Technology at Pázmány Péter
Catholic University.
Keywords - Neurobiology; theory; computer
simulation; biophysics; dynamical systems
I.
I
NTRODUCTION
The subject named “Modelling Neurons
and Networks” is intended to provide an intro-
ductory treatment of several important topics
in computational (also called theoretical) neu-
roscience. These topics include cellular bio-
physics, the processing of synaptic inputs in
single neurons, the dynamics of feedforward
and recurrent neuronal networks, and some
basic mechanisms of learning and memory.
On the other hand, several equally important
topics, such as the coding and decoding of
information in neuronal spike trains, are only
touched upon, and could easily serve as the
core of a second subject.
The subject introduces students to the rep-
ertoire of methods which are routinely used in
the theoretical analysis of the function of the
nervous system. Competent use of essential
mathematical tools, user-level computer skills,
as well as some knowledge of basic neurobi-
ology are presumed, but all of these compe-
tencies are further developed during the
course.
II.
C
ONTENTS OF THE
S
UBJECT
A.
Prerequisites
Before taking this course, students should
have completed their basic university-level
mathematical training, including the following
subjects: linear algebra, differential equations,
probability theory, and numerical methods.
They are also assumed to be familiar with the
basic facts, concepts, and experimental meth-
ods of neuroscience. Finally, they are sup-
posed to be competent in the use of personal
computers. Some other skills, such as experi-
ence with Linux/UNIX operating systems, and
knowledge of certain branches of theoretical
physics (such as dynamical systems) and engi-
neering (such as signal processing), are also
useful and likely to enrich the learning experi-
ence.
B.
Course topics
The contents of this subject include many
of the topics which are traditionally taught in
courses titled “Computational neuroscience”
or “Theoretical Neuroscience” around the
world. The present course bears a different
title partly to emphasize the fact that it focuses
on a subset of the possible topics, providing
ample insight into known mechanisms of in-
formation processing in single nerve cells and
biological neural networks, while neglecting
other important fields such as the information-
theoretical description of neural coding and
decoding, or biologically-based models of
cognitive processes and behavior.
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In somewhat more detail, the course deals
with the following topics:
1. Detailed models of single neurons:
Biophysical
foundations
of
neuronal activity
Signal propagation in passive
dendrites: the cable equation
Signal propagation in the axon: the
Hodgkin-Huxley model
Multicompartmental
modeling,
neural simulators
The diversity of ion channels and
their role in neuronal function
Processing and integration of
excitatory and inhibitory synaptic
inputs
Understanding excitable neurons as
dynamical systems
2. Modeling network dynamics using
simplified model neurons
Rhythmic network activity and
synchronization
Attractor dynamics as the basis of
short-term and long-term memory
Computations in feedforward and
recurrent networks
3. Modeling synaptic plasticity and
learning
Biophysical
mechanisms
of
neuronal plasticity
Dynamics of the synaptic matrix in
neuronal networks
III.
T
EACHING
M
ATERIALS
In the context of the TÁMOP project, we
developed a new set of English slide presenta-
tions, organized into twelve topics, and com-
prising a total of approximately 450 slides.
Besides explanatory text, the slides contain
over 100 figures, and approximately 200 equa-
tions. To our knowledge, the material dis-
cussed is not covered by any single existing
textbook or teaching aid. Rather, the course
combines material which may be found in
popular textbooks with the description of im-
portant recent results from the primary litera-
ture, and adds several unpublished examples
from the author's own research. In addition,
four of the slide presentations actually contain
detailed guides to hands-on experimentation
with (two different types of) neural simulation
software, meant to be taught in a computer lab
environment. These computer-based exercises
complement the more traditional lecture for-
mat of the other presentations. They are sup-
posed to bring about a deeper understanding of
the concepts encountered during the lectures
via guided exercises and independent explora-
tion, introduce some additional concepts, and,
importantly, familiarize the students with pro-
grams which have become widely used re-
search tools in the computational neuroscience
community.