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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 I
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Brain as an object of research
● System level – to research the brain as awhole
● Structure level: a) anatomicalb) functional
● Populations, modules and ensembles● Cellular● Subcellular
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System level
Reception (sense) functions: vision, hearing, touch, ... Perception.
Cognitive functions: attention, memory, emotions, speech, thinking ...
Methods: EEG, PET, MRT, ...
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System level
Mathematical Modeling:Population models based on collective dynamicsOscillating networksFormal neural networks, fuzzy logic
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Structure level
Anatomical Functional
Methods of research and modelinguse and combine methods of both system and population levels
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Populations, modules and ensembles
Research methods:Focal macroelectrode records from intact brainMarking by selective dyesSpecific morphological methods
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Populations, modules and ensembles
Modeling methods:Formal neural networksBiologically plausible models:
Population or/and dynamical modelsModels with single cell accuracy (detailed models)
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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
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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
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Cellular and subcellular levelsRamon-y-Cajal's paradigm.
SantiagoRamon-y-Cajal
1888 – 1891
CamilloGolgi1885
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Cellular and subcellular levelsRamon-y-Cajal's paradigm.
Soma of neuron
Dendrite tree or arbor of neuron:the set of neuron inputs
Axon hillock,The impulse generating zone
Axon, the nerve:output of neuron
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Neuron as alive biological cell
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Spike generation. Afterpolarization
threshold
Afterpolarization
Potential impulse«Action Potential» or Spike
Synapse
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Formal description
Σ=
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Formal description
= ⌠│dt⌡
⌠│Σ dt⌡
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Formal description
Σ= ⌠│Σ dt⌡
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Ions in neuron. Reversal potential
NaClC
1=1.5 mM/L
NaClC
2=1.0 mM/L
U
Na+
Na+
Na+
c=RT lnC1
C 2
e=zF U
e=c
U=RTzF
lnC1
C 2
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Na+ and K+ currents
out
in
K+
Na+
Inside (mM) Outside (mM) Voltage(mV)50 437 56397 20 -7740 556 -68
Na+
K+
Cl-
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Membrane level organization of neuron
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
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Membrane level organization of neuron
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
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Current of capacitance
When K+ is blocked. Na+ current.
When Na+ is blocked. K+ current.
Ion currents blockage. Spike generation
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Ion currents blockage. Spike generation
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Gate currents and method Patch-Clamp
Erwin Neherand
Bert Sakmann
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Erwin Neherand
Bert Sakmann
Gate currents and method Patch-Clamp
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Molecular level. The last outpost of biologically plausible modeling.
-
+-
E
x
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Molecular level. The last outpost of biologically plausible modeling.
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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
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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
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Threshold is depended upon speed of potential raising
Threshold adaptation under prolongated polarization.
Non-plausibility of the most biologically plausible model!
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Non-plausibility of the most biologically plausible model!
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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
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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
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Cdudt
=∑ig i u−E i
gm u−Emg Au−u' I
Compartment model of neuron
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Compartment model of neuron
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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
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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.
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=200msRaxial 150Ώcm (6.66 mScm)
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Cell geometry and activity
Soma Dendrite
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)
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Cell geometry and activity
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Neuron types by Nowak et. al. 2003
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Neuron types by Nowak et. al. 2003
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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.
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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
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Neurodynamics and circuit of cortex connections
West D.C., Mercer A., Kirchhecker S., Morris O.T., Thomson A.M.
Layer 6 Cortico-thalamic Pyramidal CellsPreferentially Innervate Interneurons andGenerate Facilitating EPSPs
Cerebral Cortex February 2006;16:200--211
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Neurodynamics and circuit of cortex connections
Somogyi P., Tamas G., Lujan R., Buhl E.H.Salient features of synaptic organisation in the cerebral cortexBrain Research Reviews 26 (1998). 113 – 135
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Properties of single neuron in network and network with such elements
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Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
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Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005