Southern Federal University Laboratory of neuroinformatics of sensory and motor systems A.B.Kogan Research Institute for Neurocybernetics Ruben A. Tikidji – Hamburyan [email protected]Introduction to modern methods and tools for biologically plausible modeling of neural structures of brain Part I
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Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 1
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Southern Federal University
Laboratory of neuroinformatics ofsensory and motor systems
Population or/and dynamical modelsModels with single cell accuracy (detailed models)
Cellular and subcellular levels
Research methods:Extra- and intracellular microelectrode recordsDyeing, fluorescence and luminescence microscopySlice and culture of tissueGenetic researchResearch with Patch-Clamp methods from cell as a whole up to
selected ion channel Biochemical methods
Cellular and subcellular levels
Modeling methods:Phenomenological models of single neurons and synapsesModels with segmentation and spatial integration of cell bodyModels of neuronal membrane locusModels of dynamics of biophysical and biochemical processes in
synapsesModels of intracellular components and reactionsQuantum models of single ion channels
Cellular and subcellular levelsRamon-y-Cajal's paradigm.
SantiagoRamon-y-Cajal
1888 – 1891
CamilloGolgi1885
Cellular and subcellular levelsRamon-y-Cajal's paradigm.
Soma of neuron
Dendrite tree or arbor of neuron:the set of neuron inputs
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
Membrane level organization of neuron
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
Current of capacitance
When K+ is blocked. Na+ current.
When Na+ is blocked. K+ current.
Ion currents blockage. Spike generation
Ion currents blockage. Spike generation
Gate currents and method Patch-Clamp
Erwin Neherand
Bert Sakmann
Erwin Neherand
Bert Sakmann
Gate currents and method Patch-Clamp
Molecular level. The last outpost of biologically plausible modeling.
-
+-
E
x
Molecular level. The last outpost of biologically plausible modeling.
Hodjkin-Huxley equationsDynamics of gate variables
Cdudt
=g K u−E K g Nau−E NagL u−E L
g Na=gNa m3 hg K=g K n4
dfdt
=1− f f u− f f u
where f – n, m and h respectivelydfdt
=−1 f − f ∞
u =1
f u f u; f ∞u=
f u
f u f u= f u
u
First activation and inactivation functions.
α(u) β(u)
n0.1−0.01u
e1−0.1u−12.5−0.1u
e2.5−0.1u−1
m2.5−0.1u
e2.5−0.1u−1 4e−u18
h 0.07 e−u20
1
e3−0.1u1
Hodgkin, A. L. and Huxley, A. F. (1952).
A quantitative description of ion currents and its applications to conduction and excitation in nerve membranes.
J. Physiol. (Lond.), 117:500-544.
Citation from:Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity» Cambridge University Press, 2002
Threshold is depended upon speed of potential raising
Threshold adaptation under prolongated polarization.
Non-plausibility of the most biologically plausible model!
Non-plausibility of the most biologically plausible model!
The Zoo of Ion ChannelsGerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
Cambridge University Press, 2002
Cdudt
= I i∑kI k t
I k t =g k m pk hqk u−E k
dmdt
=1−mm u−mmu
dndt
=1−nnu−nnu
The Zoo of Ion ChannelsGerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
Cambridge University Press, 2002
Cdudt
= I i∑kI k t
I k t =g k m pk hqk u−E k
dmdt
=1−mm u−mmu
dndt
=1−nnu−nnu
Cdudt
=∑ig i u−E i
gm u−Emg Au−u' I
Compartment model of neuron
Compartment model of neuron
Cable equationRL i xdx =u t , xdx −u t , x
i xdx −i x =
=C∂
∂ tu t , x
1RTu t , x −I ext t , x
C = c dx, RL = r
L dx, R
T
-1 = rT
-1 dx, Iext
(t, x) = iext
(t, x) dx.
∂2
∂ x 2 u t , x =c r L∂
∂ tu t , x
r LrTu t , x −r L iext t , x
rL/rT = λ2 и crL = τ∂
∂ tu t , x =
∂2
∂ x 2u t , x −
2u t , x iext t , x
Cell geometry and activityi xdx −i x =C
∂
∂ tu t , x ∑
i[ g i t , uu t , x −E i ]−I ext t , x
∂2
∂ x2u t , x =c r L
∂
∂ tu t , x r L∑
i[g i t , uu t , x −E i ]−r L iext t , x
Ion channels from Mainen Z.F., Sejnowski T.J. Influence of dendritic structureon firing pattern inmodelneocortical neurons // Nature, v. 382: 363-366, 1996.
Na 20(pS/μm2)Ca 0.3(pS/μm2)KCa 3(pS/μm2)KM 0.1(pS/μm2)KV 200(pS/μm2)L 0.03(mS/cm2)
Na 20(pS/μm2)Ca 0.3(pS/μm2)KCa 3(pS/μm2)KM 0.1(pS/μm2)L 0.03(mS/cm2)
Cell geometry and activity
Neuron types by Nowak et. al. 2003
Neuron types by Nowak et. al. 2003
Bannister A.P.Inter- and intra-laminar connections of pyramidal cells in the neocortexNeuroscience Research 53 (2005) 95–103
How to identify the neurons and connections.
How to identify the neurons and connections.
D. Schubert, R. Kotter, H.J. Luhmann, J.F. StaigerMorphology, Electrophysiology and Functional Input Connectivity of Pyramidal Neurons Characterizes a Genuine Layer Va in the Primary Somatosensory CortexCerebral Cortex (2006);16:223--236
Neurodynamics and circuit of cortex connections
West D.C., Mercer A., Kirchhecker S., Morris O.T., Thomson A.M.