Southern Federal University

  A.B.Kogan Research Institute for Neurocybernetics

   Laboratory for Detailed Analysis and ...
Brain as an object of research
      ● System level – to research the brain as a
          whole
      ● Structure level:
...
System level




Reception (sense) functions:
  vision, hearing, touch, ... Perception.
Cognitive functions:
  attention, ...
System level




Mathematical Modeling:
  Population models based on collective dynamics
  Oscillating networks
  Formal n...
Structure level
    Anatomical                            Functional




Methods of research and modeling
  use and combin...
Populations, modules and ensembles




    Research methods:
      Focal macroelectrode records from intact brain
      Ma...
Populations, modules and ensembles




   Modeling methods:
     Formal neural networks
     Biologically plausible models...
Cellular and subcellular levels




Research methods:
  Extra- and intracellular microelectrode records
  Dyeing, fluoresc...
Cellular and subcellular levels




Modeling methods:
  Phenomenological models of single neurons and synapses
  Models wi...
Is a brain a set of cells or syncytium?

                Single Cell

                   OR

                Syncytium



...
Cellular and subcellular levels
    Ramon-y-Cajal's paradigm.
Camillo                     Santiago
 Golgi                 ...
Cellular and subcellular levels
 Ramon-y-Cajal's paradigm.


                 Dendrite tree or arbor of neuron:
          ...
Neuron as alive biological cell
Spike generation. Afterpolarization

       Synapse          Potential impulse
                        «Action Potential» ...
Formal description




     =           Σ
Formal description




     =
                 ⌠
                 │Σ
                 │dt dt
                 ⌡
Formal description




     =           Σ
                 ⌠
                 │Σ dt
                 ⌡
Ions Uin neuron. Reversal potential
NaCl                 NaCl
C1=1.5 mM/L   C2=1.0 mM/L
                                  ...
Na+ and K+ currents
out
            Na+




           K+
  in




       Inside (mM) Outside (mM) Voltage(mV)
Na+        ...
Membrane level organization of neuron
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
Ion currents blockage. Spike generation




            Current of capacitance



            When K+ is blocked. Na+ curr...
Ion currents blockage. Spike generation
Gate currents and method Patch-Clamp




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




 Erwin Neher
     and
Bert Sakmann
Molecular level. The last outpost of
 biologically plausible modeling.




                              E
               ...
Molecular level. The last outpost of
 biologically plausible modeling.
Hodjkin-Huxley equations
Dynamics of gate variables
            du
        C      = g K  E K  Na  E Na  L  E L 
    ...
First activation and inactivation
                         functions.
                                                    ...
Non-plausibility of the most biologically
          plausible model!
 Threshold is depended upon speed of potential raisin...
Non-plausibility of the most biologically
          plausible model!
The Zoo of Ion Channels
     Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
       ...
The Zoo of Ion Channels
     Gerstner and Kistler «Spiking Neuron Models. Single Neurons, Populations, Plasticity»
       ...
The Zoo of Ion Channels

Regular Spiking (RS)          Fast Spiking (FS) cell
cell (Na, K, M)               (Na, K)




In...
Compartment model of neuron




                     du
                  C     = ∑ i gi  E i
                          ...
Compartment model of neuron
Cable equation
                                RL i 
                                     xdx  u , xdx  u, x 
    ...
Fist modeling fault

John Carew Eccles




                    Wilfrid Rall
Cell geometry and activity
                         ∂
  i xdx  i  C
             − x =          u , x  ∑ [g i , u...
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...
Cell geometry and activity
Neuron types by Nowak et. al. 2003
Neuron types by Nowak et. al. 2003
How to identify the neurons and
         connections.




    Bannister A.P.
    Inter- and intra-laminar connections of
 ...
How to identify the neurons and
                connections.




D. Schubert, R. Kotter, H.J. Luhmann, J.F. Staiger
Morpho...
Neurodynamics and circuit of cortex
         connections




 Somogyi P., Tamas G., Lujan R., Buhl E.H.
 Salient features ...
Neurodynamics and circuit of cortex
         connections




               West D.C., Mercer A., Kirchhecker S., Morris O...
Neurodynamics and circuit of cortex
         connections




           Thomson A.M., Lamy C. 2007
Properties of single neuron in network
   and network with such elements
Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // C...
Autoinhibition as nontrivial example
Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // C...
If the brain were so simple we could understand it,
 we would be so simple we couldn't




                       Lyall Wa...
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Introduction to modern methods and tools for biologically plausible modeling of neurons and neural networks (1)

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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

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Introduction to modern methods and tools for biologically plausible modeling of neurons and neural networks (1)

  1. 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. 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. 3. System level Reception (sense) functions: vision, hearing, touch, ... Perception. Cognitive functions: attention, memory, emotions, speech, thinking ... Methods: EEG, PET, MRT, ...
  4. 4. System level Mathematical Modeling: Population models based on collective dynamics Oscillating networks Formal neural networks, fuzzy logic
  5. 5. Structure level Anatomical Functional Methods of research and modeling use and combine methods of both system and population levels
  6. 6. Populations, modules and ensembles Research methods: Focal macroelectrode records from intact brain Marking by selective dyes Specific morphological methods
  7. 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. 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. 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. 10. Is a brain a set of cells or syncytium? Single Cell OR Syncytium Muscle Cells Liver Cells Heart Cells v v
  11. 11. Cellular and subcellular levels Ramon-y-Cajal's paradigm. Camillo Santiago Golgi Ramon-y-Cajal 1885 1888 – 1891
  12. 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. 13. Neuron as alive biological cell
  14. 14. Spike generation. Afterpolarization Synapse Potential impulse «Action Potential» or Spike threshold Afterpolarization
  15. 15. Formal description = Σ
  16. 16. Formal description = ⌠ │Σ │dt dt ⌡
  17. 17. Formal description = Σ ⌠ │Σ dt ⌡
  18. 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. 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. 20. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  21. 21. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  22. 22. Ion currents blockage. Spike generation Current of capacitance When K+ is blocked. Na+ current. When Na+ is blocked. K+ current.
  23. 23. Ion currents blockage. Spike generation
  24. 24. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  25. 25. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  26. 26. Molecular level. The last outpost of biologically plausible modeling. E - - + x
  27. 27. Molecular level. The last outpost of biologically plausible modeling.
  28. 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. 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. 30. Non-plausibility of the most biologically plausible model! Threshold is depended upon speed of potential raising Threshold adaptation under prolongated polarization.
  31. 31. Non-plausibility of the most biologically plausible model!
  32. 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. 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. 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. 35. Compartment model of neuron du C = ∑ i gi  E i u−  dt g m  E m  A  u'  u− g u− I
  36. 36. Compartment model of neuron
  37. 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. 38. Fist modeling fault John Carew Eccles Wilfrid Rall
  39. 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. 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. 41. Cell geometry and activity
  42. 42. Neuron types by Nowak et. al. 2003
  43. 43. Neuron types by Nowak et. al. 2003
  44. 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. 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. 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. 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. 48. Neurodynamics and circuit of cortex connections Thomson A.M., Lamy C. 2007
  49. 49. Properties of single neuron in network and network with such elements
  50. 50. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
  51. 51. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
  52. 52. If the brain were so simple we could understand it, we would be so simple we couldn't Lyall Watson

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