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 1. 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 I
Ruben A. Tikidji – Hamburyan
rth@nisms.krinc.ru
2010

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

3. System level
Reception (sense) functions:
vision, hearing, touch, ... Perception.
Cognitive functions:
attention, memory, emotions, speech, thinking ...
Methods: EEG, PET, MRT, ...

4. System level
Mathematical Modeling:
Population models based on collective dynamics
Oscillating networks
Formal neural networks, fuzzy logic

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. Is a brain a set of cells or syncytium?
Single Cell
OR
Syncytium
Muscle Cells Liver Cells Heart Cells
v v

11. Cellular and subcellular levels
Ramon-y-Cajal's paradigm.
Camillo Santiago
Golgi Ramon-y-Cajal
1885 1888 – 1891

12. 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

13. Neuron as alive biological cell

14. Spike generation. Afterpolarization
Synapse Potential impulse
«Action Potential» or Spike
threshold
Afterpolarization

15. Formal description
= Σ

16. Formal description
=
⌠
│Σ
│dt dt
⌡

17. Formal description
= Σ
⌠
│Σ dt
⌡

18. Ions Uin neuron. Reversal potential
NaCl NaCl
C1=1.5 mM/L C2=1.0 mM/L
C1
= RT ln
c
C2
Na+
Na+ = zF U
e
Na+
= 
e c
RT C 1
U= ln
zF C 2

19. Na+ and K+ currents
out
Na+
K+
in
Inside (mM) Outside (mM) Voltage(mV)
Na+ 50 437 56
K+ 397 20 -77
Cl- 40 556 -68

20. Membrane level organization of neuron
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon

21. Membrane level organization of neuron
Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon

22. Ion currents blockage. Spike generation
Current of capacitance
When K+ is blocked. Na+ current.
When Na+ is blocked. K+ current.

23. Ion currents blockage. Spike generation

24. Gate currents and method Patch-Clamp
Erwin Neher
and
Bert Sakmann

25. Gate currents and method Patch-Clamp
Erwin Neher
and
Bert Sakmann

26. Molecular level. The last outpost of
biologically plausible modeling.
E
-
- +
x

27. Molecular level. The last outpost of
biologically plausible modeling.

28. Hodjkin-Huxley equations
Dynamics of gate variables
du
C = g K  E K  Na  E Na  L  E L 
u− g u− g u−
dt
g K = g K n4 g Na= g Na m3 h
df
=  f  f  − f 
1−  u f u
dt
where f – n, m and h respectively
df 1
= − − f ∞ 
f
dt 

f u f u
 u  f  ; f ∞  =
 = f u  u u =
   u
f u f u 

29. 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
h 0.07 e 20
1
J. Physiol. (Lond.), 117:500-544. 3− 0.1u
e
Citation from:Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity» Cambridge University
Press, 2002

30. Non-plausibility of the most biologically
plausible model!
Threshold is depended upon speed of potential raising
Threshold adaptation under prolongated polarization.

31. Non-plausibility of the most biologically
plausible model!

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
I k = g k m h  E k
pk qk
t u−
dm
=  m m  − m  
1−  u m u
dt
dn
=  n n  − n 
1−  u n u
dt

33. 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
I k = g k m h  E k
pk qk
t u−
dm
=  m m  − m  
1−  u m u
dt
dn
=  n n  − n 
1−  u n u
dt

34. The Zoo of Ion Channels
Regular Spiking (RS) Fast Spiking (FS) cell
cell (Na, K, M) (Na, K)
Intrinsically Bursting
Slow firing (SF) cell
(IB) cell (Na, K, M,
(Na, K, h)
CaL)
Rebound bursting Repetitive Bursting
(LTS) cell (Na, K, M, (RB) cell (Na, K, M,
CaT) CaL)

35. Compartment model of neuron
du
C = ∑ i gi  E i
u− 
dt
g m  E m  A  u' 
u− g u− I

36. Compartment model of neuron

37. Cable equation
RL i 
xdx  u , xdx  u, x 
= t − t
ixdx  i  
− x =
∂ 1
= C u , x 
t  u , x  I ext , x 
t − t
∂t RT
C = c dx, RL = rL dx, RT-1 = rT-1 dx, Iext(t, x) = iext(t, x) dx.
∂2 ∂ rL
u, x  c r L u, x  u , x  r L i ext , x 
t = t  t − t
∂x
2
∂t rT
∂ ∂
2
rL/rT = λ 2 и cr = τ u , x   2 u, x  u, x  ext , x 
t = t − 2 t i t
L ∂t ∂x

38. Fist modeling fault
John Carew Eccles
Wilfrid Rall

39. Cell geometry and activity
∂
i xdx  i  C
− x = u , x  ∑ [g i , u , x  E i  I ext , x 
t  t t
u − ]− t
∂t i
∂ ∂
2
u, x  c r L u, x  L ∑ [g i , u , x  E i  r L i ext , x 
t = t r t t
u − ]− t
∂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)

40. 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. Cell geometry and activity

42. Neuron types by Nowak et. al. 2003

43. Neuron types by Nowak et. al. 2003

44. 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

45. 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

46. 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

47. 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

48. Neurodynamics and circuit of cortex
connections
Thomson A.M., Lamy C. 2007

49. Properties of single neuron in network
and network with such elements

50. Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005

51. Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005

52. If the brain were so simple we could understand it,
we would be so simple we couldn't
Lyall Watson