AACIMP 2010 Summer School lecture by Ruben Tikidji-Hamburyan. "Physics, Chemistry and Living Systems" stream. "Introduction to Modern Methods and Tools for Biologically Plausible Modeling of Neurons and Neural Networks" course. Part 2. More info at http://summerschool.ssa.org.ua

1. Southern Federal University
A.B.Kogan Research Institute for Neurocybernetics
Laboratory for Detailed Analysis and Modeling of
Neurons and Neural Networks
Introduction to modern methods and
tools for biologically plausible
modeling of neurons and neural
networks
Lecture II
Ruben A. Tikidji – Hamburyan
rth@nisms.krinc.ru
2010

2. Previous lecture in a nutshell
1. There is brain in head of human and animal. We use it for thinking.
2. Brain is researched at different levels. However physiological methods
is constrained. To avoid this limitations mathematical modeling is
widely used.
3. The brain is a huge network of connected cells. Cells are called
neurons, connections - synapses.
4. It is assumed that information processes in neurons take place at
membrane level. These processes are electrical activity of neuron.
5. Neuron electrical activity is based upon potentials generated by
selective channels and difference of ion concentration in- and outside
of cell.
6. Dynamics of membrane potential is defined by change of
conductances of different ion channels.
7. The biological modeling finishes and physico-chemical one begins at
the level of singel ion channel modeling.

3. Previous lecture in a nutshell
8. Instead of detailed description of each ion channel by energy function
we may use its phenomenological representation in terms of dynamic
system. This first representation for Na and K channels of giant squid
axon was supposed by Hodjkin&Huxley in 1952.
9. However, the H&H model has not key properties of neuronal activity.
To avoid this disadvantage, this model may be widened by additional
ion channels. Moreover, the cell body may be divided into
compartments.
10.Using the cable model for description of dendrite arbor had blocked
the researches of distal synapse influence for ten years up to 80s and
allows to model cell activity in dependence of its geometry.
11.There are many types of neuronal activity and different classifications.
12.The most of accuracy classification methods use pure mathematical
formalizations.
13.Identification of network environment is complicated experimental
problem that was resolved just recently. The simple example shows
that one connection can dramatically change the pattern of neuron
output.

4. Phenomenological models of neuron
Is it possible to model only phenomena of neuronal activity
without detailed consideration of electrical genesis?

5. Hodjkin-Huxley style models
Reduction of base equations or/and number of compartments
or/and simplification of equations for currents
Speed up and dimension of network
Accuracy neuron description
Simplification
Sophistication
Description of neuron dynamics by formal function
Integrate-and-Fire style models

6. FitzHugh-Nagumo's model
R. FitzHugh
«Impulses and physiological states in models of nerve membrane»
Biophys. J., vol. 1, pp. 445-466, 1961.
2 3
v '=ab vc v d v −u u' =  e v−u 

7. Izhikevich's model
Eugene M. Izhikevich
«Which Model to Use for Cortical Spiking Neurons?»
IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 15, NO. 5, SEPTEMBER 2004
2
v ' =0.04 v 5 v140−u
u ' =ab v−u where a,b,c,d – model parameters
if v30 then v=c ,u=ud

8. Izhikevich's model

9. Integrate-and-Fire model
Simple integrator:
du
 = ∑ I syn−ut 
⌠ dt
│dt
⌡
Threshold function – short circuit of membrane:
if u then u=0

10. Integrate-and-Fire model
Simple integrator:
du
 = ∑ I syn−ut 
⌠ dt
│dt
⌡
Threshold function – short circuit of membrane:
if u then u=0

11. Modified Integrate-and-Fire model
Master and slave integrators
dut  r duap 1
 =rI t  uap t −ut  −ut ap =  u t −uap t 
dt r ap dt ap
Adaptive threshold
{
a
dui t  r  ut −ui t  if utui t 
= =ui t cth
dt a
f
 ut−ui t if ut ui t 
Pulse generator:
 du (t ) 1 u ap (t ) − u (t ) u (t ) 2U s τ fire
 = I (t ) + − + если t − t ' <
dt C CR ap τs τ fire 2

 du (t ) 1
 u ap (t ) − u (t ) u (t ) 2U s τ fire
 = I (t ) + − − если < t − t ' < τ fire
dt C CR ap τs τ fire 2

 du (t ) 1 u ap (t ) − u (t ) u (t )
 = I (t ) + − во всех остальных случаях
 dt
 C CR ap τ

12. Modified Integrate-and-Fire model

13. Modified Integrate-and-Fire model

14. Comparative characteristics o
neuron models by Izhikevich

15. Synapses: chemical and electrical

16. Synapses: chemical and electrical

17. Chemical synapse models (ion model)
g s t =g s t s −t  Phenomenological models
I s =g s  u−E s 
g s t =g s u ps ,t  g s t =g s u ps ,t ,[ Ma2 + ]o ,
u ps , t= P u ps , t 
ps 1
u , t=1−
1exp 
u ps−
 
ps 1 ps 2+ ps
u , t=1− u ,t ,[ Ma ]o =u , t  g∞
1exp 
u ps t− t−
  g∞ = 1[ Ma ]o e

2+ − u −1


18. Chemical synapse models
(Phenomenological models)
{
if tt s
{
0 if tt
s 0
{
s
0 if tt t s −t t s −t
I s = t −t
e
s
if other
I s=

t s −t
 
exp 1−
t s −t
  if other
I s=

e
1
−e
1−2
2
if other
{
m s mi
− if t−t sr
dmi t  r  f
I s = mi t =
dt mi
− if t−t sr
f

19. Learning, memory and neural networks
Gerald M. Edelman
The Group-Selective
Theory of Higher Brain
Function
The brain is hierarchy of non-degenerate
neural group

20. Learning, memory and neural networks
Sporns O., Tononi G.,
Edelman G.M.
Theoretical Neuroanatomy:
Relationg Anatomical and
Functional Connectivity in
Graphs and Cortical
Connection Matrices
Cerebral Cortex, Feb 2000;
10: 127 - 141

21. Learning, memory and neural networks
Gerald M. Edelman – Brain Based Device (BBD)
Krichmar J.L., Edelman G.M.
Machine Psychology: Autonomous Behavior,
Perceptual Categorization and Conditioning in a
Brain-based Device
Cerebral Cortex Aug. 2002; v12: n8 818-830

22. Learning, memory and neural networks
Gerald M. Edelman – Brain Based Device (BBD)
McKinstry J.L., Edelman G.M.,
Krichmar J.K.
An Embodied Cerebellar Model
for Predictive Motor Control
Using Delayed Eligibility Traces
Computational Neurosci. Conf.
2006

24. Learning, memory and single neuron
Donald O. Hebb

25. Learning, memory and single neuron
Guo-qiang Bi and Mu-ming Poo
Synaptic Modifications in
Cultured Hippocampal Neurons:
Dependence on Spike Timing,
Synaptic Strength, and
Postsynaptic Cell Type
The Journal of Neuroscience,
1998, 18(24):10464–1047
Long Term Depression Long-Term Potentiation Spike Time-Dependent Plasticity
(LTD) (LTP) (STDP)

26. Learning, memory and single neuron
Gerald M. Edelman – Experimental research
Vanderklish P.W., Krushel L.A., Holst B.H., Gally J. A., Crossin K.L., Edelman
G.M.
Marking synaptic activity in dendritic spines with a calpain substrate exhibiting
fluorescence resonance energy transfer
PNAS, February 29, 2000, vol. 97, no. 5, p.2253 2258

27. Learning and local calcium dynamics
Feldman D.E.
Timing-Based LTP and LTD at
Vertical Inputs
to Layer II/III Pyramidal Cells in
Rat Barrel Cortex
Neuron, Vol. 27, 45–56, (2000)

28. Learning and local calcium dynamics
Shouval H.Z., Bear
M.F.,Cooper L.N.
A unified model of NMDA
receptor-dependent
bidirectional synaptic plasticity
PNAS August 6, 2002 vol. 99
no. 16 10831–10836

29. Learning and local calcium dynamics
Mizuno T., KanazawaI., Sakurai M.
Differential induction of LTP and LTD is not
determined
solely by instantaneous calcium concentration: an
essential involvement of a temporal factor
European Journal of Neuroscience, Vol. 14, pp.
701-708, 2001
Kitajima T., Hara K.
A generalized Hebbian rule for activity-
dependent synaptic modification
Neural Network, 13(2000) 445 - 454

30. Learning and local calcium dynamics

31. Learning and local calcium dynamics
Urakubo H., Honda M., Froemke R.C., Kuroda S.
Requirement of an Allosteric Kinetics of NMDA Receptors for Spike Timing-Dependent Plasticity
The Journal of Neuroscience, March 26, 2008 v. 28(13):3310 –3323

32. Learning and local calcium dynamics
Letzkus J.J., Kampa B.M., Stuart
G.J.
Learning Rules for Spike Timing-
Dependent Plasticity
Depend on Dendritic Synapse
Location
The Journal of Neuroscience, 2006
26(41):10420 –1042

33. Learning and local calcium dynamics
Letzkus J.J., Kampa B.M., Stuart
G.J.
Learning Rules for Spike Timing-
Dependent Plasticity
Depend on Dendritic Synapse
Location
The Journal of Neuroscience, 2006
26(41):10420 –1042

34. Learning and Memory
Frey & Morris, 1997
Open issues

35. Learning and Memory
Open issues
from: Frankland & Bontempi (2005)

36. Tools for biologically plausible modeling
Simulator Publicat Versi First Latest Primary License MS Mac OS X Linux Other Active Language
ions on release release author Windows Community
Emergent (formerly AisaMin 4.0 1986 2008 Dr. Randy GNU GPL XP, 2003, Intel, PPC Any, Any Unix emergent- C++
PDP++ and PDP) gusORei O'Reilly Vista Fedora, users list,
lly07 Ubuntu Wiki
GENESIS (the GEneral Beeman 2.3 1988 2007 Dr. James GNU GPL Cygwin Intel, PPC Yes Any Unix SourceForge C
NEural SImulation EtAl07 Bower & list
System) Dr. Dave
Beeman
NEURON (originally Hines93 6.2 1986 2008 Dr. Michael GNU GPL 95+ Intel, PPC Debian Any Unix NEURON C, C++
CABLE) HinesCa Hines Forum
rnevale9
7
HinesEt
Al06
SNNAP (Simulator for Unknow 8.1 2001 2007 Dr. John Proprietary Java Java Java Java Available Java
Neural Networks and n Byrne & Dr. but defunct
Action Potentials) Douglas
Baxter
Catacomb2 (Components Unknow 2.111 2001 2003 Robert GNU GPL Java Java Java Java No Java
And Tools for Accessible n Cannon
COmputer Modeling in
Biology
Topographica Neural BednarE 0.9.4 1998 2008 Dr. James A. GNU GPL Vista, XP, Build from Build from Build from Mailing list, Python/C++
Map Simulator tAl04 Bednar NT source source source boards
NEST (NEural Diesman 2.0 2004 2006 Unknown Proprietary Unknown Unknown Unknown Any Unix, NEST-users Unknown
Simulation Tool) nEtAl95 build from list
Diesman source
nGewalti
g02
Gewaltig
EtAl02D
jurfeldt0
8
http://grey.colorado.edu/emergent/index.php/Comparison_of_Neural_Network_Simulators

37. Tools for biologically plausible modeling
Simulator Publicat Vers First Latest Primary License MS Mac OS X Linux Other Active Language
ions ion release release author Windows Community
KInNeSS - KDE Gorchote 0.3.4 2004 2008 Dr. Anatoli GNU GPL No No KDE 3.1 No No C++
Integrated chnikov Gorchetchni required
NeuroSimulation EtAl04G kov
Software rossberg
EtAl05
XNBC VibertAz 9.10 1988 2006 Dr. Jean- GNU GPL 9x, 2000, Build from RPM Tru 64, No C++
my92Vib -h François XP source (Fedora), Ultrix, AIX,
ertEtAl9 VIBERT Build from SunOS,
7VibertE source HPux
tAl01
PCSIM: A Parallel neural Unknow 0.5.0 2008 2008 Dr. Dejan GNU GPL No No Build from No No Python/C++
Circuit SIMulator n Pecevski source
Dr. Thomas
Natschlager
NeuroCAD Unknow 0.00. 2003 2007 Dr. Ruben GNU GPL No No Yes Any Unix No C
n 21a Tikidji -
Hamburyan
http://grey.colorado.edu/emergent/index.php/Comparison_of_Neural_Network_Simulators

38. NeuroCAD – Problem definition
To create a computer environment, combining
flexibility and universality of script machines,
with efficacy of monolithically compiled, high
optimized application.
It would be very nice, if found solution allows to perform
computations in homogeneous, heterogeneous and SMP
system. Thereby parallelism is included in background of
NeuroCAD project.

39. NeuroCAD – how to make model?
Step I:
Select and export required
modules from modules
data bases as c-code and
compile it Modules
(shared objects files *.so)
Step V:
Step II: Make modules runtime
Link its by NeuroCAD Engine scheduler and run.
Step III:
Export variable blocks
in shared memory of
NeuroCAD Engine Step IV:
Connect
variables.
Step IV:
Connect variables.
shared memory

40. NeuroCAD Benchmarks
NeuroCAD vs. GENESIS ~ 5 – 15 times
NeuroCAD -normal NeuroCAD – tab Neuron – tab
0.2740 0.1955 1.1740
1 0.71 4.28NeuroCAD -normal
1 6.01 NeuroCAD – tab
1 Neuron – tab
http://nisms.krinc.ru/neurocad.org
rth@nisms.krinc.ru

41. The big model of Purkinje Cell
E. DeSchutter J.M. Bower
«An Active Membrane Model of the Cerebellar Purkinje Cell»
J. Neurophysiology Vol. 71, No. 1, January 1994.
● 1600 compartments
● 12 types of ion channels
●
Ca2+ concentration dynamics
●
Ca2+ dependent K+ channels
● Two synaptic types
● Three types of dendritic zones
● More than 60 tests and real data
comparisons (runtime for some
tests in 1994 was approximately
two weeks)

42. The big model of Purkinje Cell
E. DeSchutter J.M. Bower
«An Active Membrane Model of the Cerebellar Purkinje Cell»
J. Neurophysiology Vol. 71, No. 1, January 1994.

43. The big model of Purkinje Cell
E. DeSchutter J.M. Bower
«An Active Membrane Model of the Cerebellar Purkinje Cell»
J. Neurophysiology Vol. 71, No. 1, January 1994.

44. The big model of Purkinje Cell
E. DeSchutter J.M. Bower
«An Active Membrane Model of the Cerebellar Purkinje Cell»
J. Neurophysiology Vol. 71, No. 1, January 1994.

45. Detailed model of thalamo-cortical part of cat vision system
S. Hill, G. Tononi
«Modeling Sleep and Wakefulness in the Thalamocortical System»
J. Neurophysiology Vol. 93, 1671-1698, 2005.
● approximately 65000 neurons
● approximately 1.5 million synapses
● ration number of neurons in model
and average cat 1:9
● Three cortex layers and two thalamus
layers with modeling of primary and
secondary zones of visual perception
● Neuron model – hybrid of H-H and IaF with 4 types of ion channels.
● 5 types of synapses. Synaptic model includes mediator waste effect.
● Predominant anisotropy of network with local formed ensembles.

46. Detailed model of thalamo-cortical part of cat vision system

49. ”I have all this data – cell types, firing properties,
connectivity, dendritic excitability, synaptic dynamics, .....
But I don’t understand it. I need to model it”
”У меня есть все эти данные – типы клеток,
условия их срабатывания, связи, возбудимость
дендритов, динамика синапсов, .....
Но я не могу понять этого. Я вынужден это
моделировать”
Bert Sakmann, 2001, Jerusalem