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

AACIMP 2009 Summer School lecture by Ruben Tikidji-Hamburyan. "Neuromodelling" course. 1st hour.

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  • 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. 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. Cellular and subcellular levels Ramon-y-Cajal's paradigm. Camillo Santiago Golgi Ramon-y-Cajal 1885 1888 – 1891
  • 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. Neuron as alive biological cell
  • 13. Spike generation. Afterpolarization Synapse Potential impulse «Action Potential» or Spike threshold Afterpolarization
  • 14. Formal description = Σ
  • 15. Formal description = ⌠ │Σ │dt dt ⌡
  • 16. Formal description = Σ ⌠ │Σ dt ⌡
  • 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. 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. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  • 20. Membrane level organization of neuron Sirs A. L. Hodgkin, A. F. Huxley and squid with its own giant axon
  • 21. Ion currents blockage. Spike generation Current of capacitance When K+ is blocked. Na+ current. When Na+ is blocked. K+ current.
  • 22. Ion currents blockage. Spike generation
  • 23. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  • 24. Gate currents and method Patch-Clamp Erwin Neher and Bert Sakmann
  • 25. Molecular level. The last outpost of biologically plausible modeling. E - - + x
  • 26. Molecular level. The last outpost of biologically plausible modeling.
  • 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. 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. Non-plausibility of the most biologically plausible model! Threshold is depended upon speed of potential raising Threshold adaptation under prolongated polarization.
  • 30. Non-plausibility of the most biologically plausible model!
  • 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. 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. Compartment model of neuron du C =∑i g i u− E i  dt g m u− E m  g A u−u'  I
  • 34. Compartment model of neuron
  • 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. 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. 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. Cell geometry and activity
  • 39. Neuron types by Nowak et. al. 2003
  • 40. Neuron types by Nowak et. al. 2003
  • 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. 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. 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. 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. Properties of single neuron in network and network with such elements
  • 46. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005
  • 47. Autoinhibition as nontrivial example Dodla R., Rinzel J., Recurrent inhibition can enhance spontaneous neuronal firing // CNS 2005

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