0
Southern Federal University
     A.B.Kogan Research Institute for Neurocybernetics
             Laboratory of neuroinforma...
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 combine...
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...
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 u−E K g Na u− E Na  g L u− E...
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»
       ...
Compartment model of neuron




                      du
                   C     =∑i g i u− E i 
                     ...
Compartment model of neuron
Cable equation
                                R L i  xdx =u t , xdx −ut , x 
                                 i ...
Cell geometry and activity
                            ∂
  i  xdx −i  x =C         u t , x ∑ [ g i t , uu t , ...
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




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




 Somogyi P., Tamas G., Lujan R., Buhl E.H.
 Salient features ...
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...
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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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AACIMP 2009 Summer School lecture by Ruben Tikidji-Hamburyan. "Neuromodelling" course. 1st hour.

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Transcript of "Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 1"

  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. 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. Cellular and subcellular levels Ramon-y-Cajal's paradigm. Camillo Santiago Golgi Ramon-y-Cajal 1885 1888 – 1891
  11. 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
  12. 12. Neuron as alive biological cell
  13. 13. Spike generation. Afterpolarization Synapse Potential impulse «Action Potential» or Spike threshold Afterpolarization
  14. 14. Formal description = Σ
  15. 15. Formal description = ⌠ │Σ │dt dt ⌡
  16. 16. Formal description = Σ ⌠ │Σ dt ⌡
  17. 17. Ions Uin neuron. Reversal potential NaCl NaCl C1=1.5 mM/L C2=1.0 mM/L C1 c = RT ln C2 Na+ Na+ e = zF U Na+ e =c RT C 1 U= ln zF C 2
  18. 18. 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
  19. 19. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  20. 20. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  21. 21. Ion currents blockage. Spike generation Current of capacitance When K+ is blocked. Na+ current. When Na+ is blocked. K+ current.
  22. 22. Ion currents blockage. Spike generation
  23. 23. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  24. 24. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  25. 25. Molecular level. The last outpost of biologically plausible modeling. E - - + x
  26. 26. Molecular level. The last outpost of biologically plausible modeling.
  27. 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. 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. 29. Non-plausibility of the most biologically plausible model! Threshold is depended upon speed of potential raising Threshold adaptation under prolongated polarization.
  30. 30. Non-plausibility of the most biologically plausible model!
  31. 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. 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. 33. Compartment model of neuron du C =∑i g i u− E i  dt g m u− E m  g A u−u'  I
  34. 34. Compartment model of neuron
  35. 35. Cable equation R L i  xdx =u t , xdx −ut , x  i  xdx −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 ut , x =c r L ut , 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 ut , x − 2 ut , x i ext t , x  ∂t ∂x
  36. 36. Cell geometry and activity ∂ i  xdx −i  x =C u t , x ∑ [ g i t , uu t , x −E i  ] −I ext t , x  ∂t i 2 ∂ ∂ ut , x =c r L ut , x r L ∑ [ g i t , uu 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. 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)
  38. 38. Cell geometry and activity
  39. 39. Neuron types by Nowak et. al. 2003
  40. 40. Neuron types by Nowak et. al. 2003
  41. 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. 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. 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. 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
  45. 45. Properties of single neuron in network and network with such elements
  46. 46. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
  47. 47. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
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