Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 2

Southern Federal University

Laboratory of neuroinformatics ofsensory and motor systems

A.B.Kogan Research Institute for Neurocybernetics

Ruben A. Tikidji – [email protected]

Introduction to modern methods and tools for biologically plausible modeling

of neural structures of brain

Part II

Previous lecture in a nutshell1. 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.

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.

Previous lecture in a nutshell

Phenomenological models of neuronIs it possible to model only phenomena of neuronal activity

without detailed consideration of electrical genesis?

Hodjkin-Huxley style models

Integrate-and-Fire style models

Acc

urac

y ne

uron

des

crip

tion

Sim

plifi

catio

n

Sop

hist

icat

ion

Reduction of base equations or/and number of compartments

or/and simplification of equations for currents

Spe

ed u

p an

d di

men

sion

of

net

wor

k

Description of neuron dynamics by formal function

FitzHugh-Nagumo's modelR. FitzHugh«Impulses and physiological states in models of nerve membrane» Biophys. J., vol. 1, pp. 445-466, 1961.

v '=ab vc v2d v3

−u u'= e v−u

Izhikevich's model

v '=0.04 v25v140−u

u '=a bv−uif v30 then v=c ,u=ud

where a,b,c,d – model parameters

Eugene M. Izhikevich«Which Model to Use for Cortical Spiking Neurons?»IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 15, NO. 5, SEPTEMBER 2004

Izhikevich's model

Integrate-and-Fire model

⌠│dt⌡

dudt

=∑ I syn−u t

Simple integrator:

Threshold function – short circuit of membrane:

if u thenu=0

Integrate-and-Fire model

⌠│dt⌡

dudt

=∑ I syn−u t

Simple integrator:

Threshold function – short circuit of membrane:

if u thenu=0

Master and slave integrators

du t dt

=rI t rrap

uap t −u t −ut ap

duap

dt=

1ap

u t −uap t

Adaptive threshold

dui t

dt={

ar

ut −uit if u t ui t

a f

u t −ui t if u t ui t =uit cth

−−

+=

<−<−−−

+=

<−+−−

+=

случаяхостальныхвсехвоtu

CR

tututI

Cdt

tdu

ttеслиUtu

CR

tututI

Cdt

tdu

ttеслиUtu

CR

tututI

Cdt

tdu

ap

ap

firefire

fire

s

sap

ap

fire

fire

s

sap

ap

τ

)()()()(

1)(

τ'2τ

τ

2

τ

)()()()(

1)(

2τ

'τ

2

τ

)()()()(

1)(

Pulse generator:

Modified Integrate-and-Fire model

Modified Integrate-and-Fire model

Modified Integrate-and-Fire model

Com

para

tive

char

acte

ristic

s of

ne

uron

mod

els

by

Izhi

kevi

ch

Synapses: chemical and electrical

Synapses: chemical and electrical

Chemical synapse models (ion model)

I s=g s u−E s g st =g st s−t

g st =g su ps , t

Phenomenological models

u ps , t =1−1

1expups−

u ps , t =1−1

1exp upst− t −

g st =g su ps , t ,[Ma2+]o ,

u ps , t =P u ps ,t

u ps , t ,[Ma2+]o=u ps , t g∞

g∞=1expu [Ma2+]o

−1

Chemical synapse models (Phenomenological models)

I s={ 0 if tt s

e t s−t if otherI s={

0 if tt s

t s−t

exp1− t s−t if other

I s={0 if tt s

e

t s−t1 −e

t s−t2

1−2

if other

dmi t

dt={

ms

r

−mi

f

if t−t sr

−mi

f if t−t sr

I s=mi t

Learning, memory and neural networksGerald M. Edelman

The brain is hierarchy of non-degenerate neural group

The Group-Selective Theory of Higher Brain

Function

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

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

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

Learning, memory and single neuron

Donald O. Hebb

Learning, memory and single neuron

Guo-qiang Bi and Mu-ming Poo

Synaptic Modifications in Cultured Hippocampal Neurons:Dependence on Spike Timing, Synaptic Strength, andPostsynaptic Cell Type

The Journal of Neuroscience, 1998, 18(24):10464–1047

Long Term Depression(LTD)

Long-Term Potentiation(LTP)

Spike Time-Dependent Plasticity(STDP)

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

Learning and local calcium dynamicsFeldman D.E.

Timing-Based LTP and LTD at Vertical Inputsto Layer II/III Pyramidal Cells in Rat Barrel Cortex

Neuron, Vol. 27, 45–56, (2000)

Learning and local calcium dynamicsShouval H.Z., Bear M.F.,Cooper L.N.

A unified model of NMDA receptor-dependentbidirectional synaptic plasticity

PNAS August 6, 2002 vol. 99 no. 16 10831–10836

Learning and local calcium dynamicsMizuno T., KanazawaI., Sakurai M.

Differential induction of LTP and LTD is not determinedsolely by instantaneous calcium concentration: anessential 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

Learning and local calcium dynamics

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

Learning and local calcium dynamics

Letzkus J.J., Kampa B.M., Stuart G.J.

Learning Rules for Spike Timing-Dependent PlasticityDepend on Dendritic Synapse Location

The Journal of Neuroscience, 2006 26(41):10420 –1042

Learning and local calcium dynamics

Letzkus J.J., Kampa B.M., Stuart G.J.

Learning Rules for Spike Timing-Dependent PlasticityDepend on Dendritic Synapse Location

The Journal of Neuroscience, 2006 26(41):10420 –1042

Frey & Morris, 1997

Learning and MemoryOpen issues

from: Frankland & Bontempi (2005)

Learning and MemoryOpen issues