Molekuláris bionika és infobionika szakok tananyagának komplex

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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 

[e-mail] 

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.

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