Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 1
1. Southern Federal University
A.B.Kogan Research Institute for Neurocybernetics
Laboratory of neuroinformatics of
sensory and motor systems
Introduction to modern methods and
tools for biologically plausible
modeling of neural structures of brain
Part I
Ruben A. Tikidji – Hamburyan
rth@nisms.krinc.ru
2. Brain as an object of research
● System level – to research the brain as a
whole
● Structure level:
a) anatomical
b) functional
● Populations, modules and ensembles
● Cellular
● Subcellular
5. Structure level
Anatomical Functional
Methods of research and modeling
use and combine methods of both system and population levels
6. Populations, modules and ensembles
Research methods:
Focal macroelectrode records from intact brain
Marking by selective dyes
Specific morphological methods
7. Populations, modules and ensembles
Modeling methods:
Formal neural networks
Biologically plausible models:
Population or/and dynamical models
Models with single cell accuracy (detailed models)
8. Cellular and subcellular levels
Research methods:
Extra- and intracellular microelectrode records
Dyeing, fluorescence and luminescence microscopy
Slice and culture of tissue
Genetic research
Research with Patch-Clamp methods from cell as a whole up to
selected ion channel
Biochemical methods
9. Cellular and subcellular levels
Modeling methods:
Phenomenological models of single neurons and synapses
Models with segmentation and spatial integration of cell body
Models of neuronal membrane locus
Models of dynamics of biophysical and biochemical processes in
synapses
Models of intracellular components and reactions
Quantum models of single ion channels
10. Cellular and subcellular levels
Ramon-y-Cajal's paradigm.
Camillo Santiago
Golgi Ramon-y-Cajal
1885 1888 – 1891
11. Cellular and subcellular levels
Ramon-y-Cajal's paradigm.
Dendrite tree or arbor of neuron:
the set of neuron inputs
Soma of neuron
Axon hillock,
The impulse generating zone
Axon, the nerve:
output of neuron
27. Hodjkin-Huxley equations
Dynamics of gate variables
du
C =g K u−E K g Na u− E Na g L u− E L
dt
g K = g K n4 g Na = g Na m3 h
df
=1− f f u− f f u
dt
where f – n, m and h respectively
df 1
=− f − f ∞
dt
1 f u f u
u= ; f ∞ u= =
f u f u f u f u u
28. First activation and inactivation
functions.
α(u) β(u)
Hodgkin, A. L. and Huxley, A. F. 0.1−0.01u 2.5−0.1u
(1952). n
e1−0.1u −1 e 2.5− 0.1u −1
A quantitative description of ion
currents and its applications to 2.5−0.1u −u
m 4e 18
conduction and excitation in nerve e2.5−0.1u −1
membranes.
−u 1
J. Physiol. (Lond.), 117:500-544. h 0.07 e 20 3−0.1u
e 1
Citation from:Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity» Cambridge University
Press, 2002
29. Non-plausibility of the most biologically
plausible model!
Threshold is depended upon speed of potential raising
Threshold adaptation under prolongated polarization.
31. The Zoo of Ion Channels
Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
Cambridge University Press, 2002
du
C = I i∑ k I k t
dt
pk qk
I k t= g k m h u−E k
dm
=1−m m u−m m u
dt
dn
=1−n n u−n n u
dt
32. The Zoo of Ion Channels
Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
Cambridge University Press, 2002
du
C = I i∑ k I k t
dt
pk qk
I k t= g k m h u−E k
dm
=1−m m u−m m u
dt
dn
=1−n n u−n n u
dt
33. Compartment model of neuron
du
C =∑i g i u− E i
dt
g m u− E m g A u−u' I
35. Cable equation
R L i xdx =u t , xdx −ut , x
i xdx −i x =
∂ 1
=C u t , x u t , x −I ext t , x
∂t RT
C = c dx, RL = rL dx, RT-1 = rT-1 dx, Iext(t, x) = iext(t, x) dx.
∂2 ∂ rL
ut , x =c r L ut , x u t , x −r L i ext t , x
∂x
2
∂t rT 2
2 и cr = τ ∂ ∂
rL/rT = λ L u t , x = 2 ut , x − 2 ut , x i ext t , x
∂t ∂x
36. Cell geometry and activity
∂
i xdx −i x =C u t , x ∑ [ g i t , uu t , x −E i ] −I ext t , x
∂t i
2
∂ ∂
ut , x =c r L ut , x r L ∑ [ g i t , uu t , x −E i ] −r L i ext t , x
∂x
2
∂t i
Ion channels from Mainen Z.F., Sejnowski T.J. Influence of dendritic structureon firing pattern in
modelneocortical neurons // Nature, v. 382: 363-366, 1996.
EL= –70, Ena= +50, EK= –90, Eca= +140(mV)
Na: m3h: αm= 0.182(u+30)/[1–exp(–(u+30)/9)] βm= –0.124(u+30)/[1–exp((u+30)/9)]
h∞= 1/[1+exp(v+60)/6.2] αh=0.024(u+45)/[1–exp(–(u+45)/5)]
βh= –0.0091(u+70)/[1–exp((u+70)/5)]
Ca: m2h: αm= 0.055(u + 27)/[1–exp(–(u+27)/3.8)] βm=0.94exp(–(u+75)/17)
αh= 0.000457exp( –(u+13)/50) βh=0.0065/[1+ exp(–(u+15)/28)]
KV: m: αm= 0.02(u – 25)/[1–exp(–(u–25)/9)] βm=–0.002(u – 25)/[1–exp((u–25)/9)]
KM: m: αm= 0.001(u+30)/[1-exp(–(u+30)/9)] βm=0.001 (u+30)/[1-exp((u+30)/9)]
KCa: m: αm= 0.01[Ca2+]i βm=0.02; [Ca2+]i (mM)
[Ca2+]i d[Ca2+]i /dt = –αICa – ([Ca2+]i – [Ca2+]∞)/τ; α=1e5/2F, [Ca2+]∞=0.1μM, τ=200ms
Raxial 150Ώcm (6.66 mScm)
37. Cell geometry and activity
Soma Dendrite
Na 20(pS/μm2) Na 20(pS/μm2)
Ca 0.3(pS/μm2) Ca 0.3(pS/μm2)
KCa 3(pS/μm2) KCa 3(pS/μm2)
KM 0.1(pS/μm2) KM 0.1(pS/μm2)
KV 200(pS/μm2) L 0.03(mS/cm2)
L 0.03(mS/cm2)
41. How to identify the neurons and
connections.
Bannister A.P.
Inter- and intra-laminar connections of
pyramidal cells in the neocortex
Neuroscience Research 53 (2005) 95–103
42. How to identify the neurons and
connections.
D. Schubert, R. Kotter, H.J. Luhmann, J.F. Staiger
Morphology, Electrophysiology and Functional Input
Connectivity of Pyramidal Neurons Characterizes a
Genuine Layer Va in the Primary Somatosensory
Cortex
Cerebral Cortex (2006);16:223--236
43. Neurodynamics and circuit of cortex
connections
West D.C., Mercer A., Kirchhecker S., Morris O.T.,
Thomson A.M.
Layer 6 Cortico-thalamic Pyramidal Cells
Preferentially Innervate Interneurons and
Generate Facilitating EPSPs
Cerebral Cortex February 2006;16:200--211
44. Neurodynamics and circuit of cortex
connections
Somogyi P., Tamas G., Lujan R., Buhl E.H.
Salient features of synaptic organisation in the cerebral cortex
Brain Research Reviews 26 (1998). 113 – 135