Southern Federal University
     A.B.Kogan Research Institute for Neurocybernetics
             Laboratory of neuroinforma...
Previous lecture in a nutshell
1. There is brain in head of human and animal. We use it for thinking.
2. Brain is research...
Previous lecture in a nutshell
8. Instead of detailed description of each ion channel by energy function
   we may use its...
Phenomenological models of neuron
Is it possible to model only phenomena of neuronal activity
       without detailed cons...
Hodjkin-Huxley style models




                              Reduction of base equations or/and number of compartments
  ...
FitzHugh-Nagumo's model
    R. FitzHugh
    «Impulses and physiological states in models of nerve membrane»
    Biophys. J...
Izhikevich's model
Eugene M. Izhikevich
«Which Model to Use for Cortical Spiking Neurons?»
IEEE TRANSACTIONS ON NEURAL NET...
Izhikevich's model
Integrate-and-Fire model
            Simple integrator:
                                  du
                             ...
Integrate-and-Fire model
            Simple integrator:
                                  du
                             ...
Modified Integrate-and-Fire model
Master and slave integrators
  dut           r                                        ...
Modified Integrate-and-Fire model
Modified Integrate-and-Fire model
omparative characteristics of
neuron models by Izhikevich
Synapses: chemical and electrical
Synapses: chemical and electrical
Chemical synapse models (ion model)
                       g s t =g s t s −t               Phenomenological models
  ...
Chemical synapse models
              (Phenomenological models)




                                                      ...
Learning, memory and neural networks
        Gerald M. Edelman
          The Group-Selective
         Theory of Higher Bra...
Learning, memory and neural networks



Sporns O.,     Tononi    G.,
Edelman G.M.

Theoretical  Neuroanatomy:
Relationg An...
Learning, memory and neural networks
 Gerald M. Edelman – Brain Based Device (BBD)




                   Krichmar J.L., E...
Learning, memory and neural networks
 Gerald M. Edelman – Brain Based Device (BBD)

                              McKinstr...
Learning, memory and single neuron
    Donald O. Hebb
Learning, memory and single neuron
                                                 Guo-qiang Bi and Mu-ming Poo

        ...
Learning, memory and single neuron
          Gerald M. Edelman – Experimental research




Vanderklish P.W., Krushel L.A.,...
Learning and local calcium dynamics
Feldman D.E.

Timing-Based LTP and LTD at
Vertical Inputs
to Layer II/III Pyramidal Ce...
Learning and local calcium dynamics
Shouval H.Z., Bear
M.F.,Cooper L.N.

A unified model of NMDA
receptor-dependent
bidire...
Learning and local calcium dynamics
                   Mizuno T., KanazawaI., Sakurai M.

                                ...
Learning and local calcium dynamics
Learning and local calcium dynamics

Urakubo H., Honda M., Froemke R.C., Kuroda S.

Requirement of an Allosteric Kinetics ...
Learning and local calcium dynamics




Letzkus J.J., Kampa B.M., Stuart
G.J.

Learning Rules for Spike Timing-
Dependent ...
Learning and local calcium dynamics




Letzkus J.J., Kampa B.M., Stuart
G.J.

Learning Rules for Spike Timing-
Dependent ...
Learning and Memory
                     Open issues
Frey & Morris, 1997
Learning and Memory
    Open issues




              from: Frankland & Bontempi (2005)
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Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 2

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AACIMP 2009 Summer School lecture by Ruben Tikidji-Hamburyan. "Neuromodelling" course. 4th hour.

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Introduction to Modern Methods and Tools for Biologically Plausible Modelling of Neural Structures of Brain. Part 2

  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 II Ruben A. Tikidji – Hamburyan rth@nisms.krinc.ru
  2. 2. Previous lecture in a nutshell 1. There is brain in head of human and animal. We use it for thinking. 2. Brain is researched at different levels. However physiological methods is constrained. To avoid this limitations mathematical modeling is widely used. 3. The brain is a huge network of connected cells. Cells are called neurons, connections - synapses. 4. It is assumed that information processes in neurons take place at membrane level. These processes are electrical activity of neuron. 5. Neuron electrical activity is based upon potentials generated by selective channels and difference of ion concentration in- and outside of cell. 6. Dynamics of membrane potential is defined by change of conductances of different ion channels. 7. The biological modeling finishes and physico-chemical one begins at the level of singel ion channel modeling.
  3. 3. Previous lecture in a nutshell 8. Instead of detailed description of each ion channel by energy function we may use its phenomenological representation in terms of dynamic system. This first representation for Na and K channels of giant squid axon was supposed by Hodjkin&Huxley in 1952. 9. However, the H&H model has not key properties of neuronal activity. To avoid this disadvantage, this model may be widened by additional ion channels. Moreover, the cell body may be divided into compartments. 10.Using the cable model for description of dendrite arbor had blocked the researches of distal synapse influence for ten years up to 80s and allows to model cell activity in dependence of its geometry. 11.There are many types of neuronal activity and different classifications. 12.The most of accuracy classification methods use pure mathematical formalizations. 13.Identification of network environment is complicated experimental problem that was resolved just recently. The simple example shows that one connection can dramatically change the pattern of neuron output.
  4. 4. Phenomenological models of neuron Is it possible to model only phenomena of neuronal activity without detailed consideration of electrical genesis?
  5. 5. Hodjkin-Huxley style models Reduction of base equations or/and number of compartments or/and simplification of equations for currents Speed up and dimension of network Accuracy neuron description Simplification Sophistication Description of neuron dynamics by formal function Integrate-and-Fire style models
  6. 6. FitzHugh-Nagumo's model R. FitzHugh «Impulses and physiological states in models of nerve membrane» Biophys. J., vol. 1, pp. 445-466, 1961. 2 3 v '=ab vc v d v −u u' =  e v−u 
  7. 7. Izhikevich's model Eugene M. Izhikevich «Which Model to Use for Cortical Spiking Neurons?» IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 15, NO. 5, SEPTEMBER 2004 2 v ' =0.04 v 5 v140−u u ' =ab v−u where a,b,c,d – model parameters if v30 then v=c ,u=ud
  8. 8. Izhikevich's model
  9. 9. Integrate-and-Fire model Simple integrator: du  = ∑ I syn−ut  ⌠ dt │dt ⌡ Threshold function – short circuit of membrane: if u then u=0
  10. 10. Integrate-and-Fire model Simple integrator: du  = ∑ I syn−ut  ⌠ dt │dt ⌡ Threshold function – short circuit of membrane: if u then u=0
  11. 11. Modified Integrate-and-Fire model Master and slave integrators dut  r du ap 1  =rI t  uap t −ut  −ut ap =  u t −uap t  dt r ap dt ap Adaptive threshold { a dui t  r  ut −ui t  if utui t  = =ui t cth dt a f  ut−ui t if ut ui t  Pulse generator:  du (t ) 1 u ap (t ) − u (t ) u (t ) 2U s τ fire  = I (t ) + − + если t − t ' < dt C CRap τs τ fire 2   du (t ) 1  u ap (t ) − u (t ) u (t ) 2U s τ fire  = I (t ) + − − если < t − t ' < τ fire dt C CRap τs τ fire 2   du (t ) 1 u ap (t ) − u (t ) u (t )  = I (t ) + − во всех остальных случаях  dt  C CRap τ
  12. 12. Modified Integrate-and-Fire model
  13. 13. Modified Integrate-and-Fire model
  14. 14. omparative characteristics of neuron models by Izhikevich
  15. 15. Synapses: chemical and electrical
  16. 16. Synapses: chemical and electrical
  17. 17. Chemical synapse models (ion model) g s t =g s t s −t  Phenomenological models I s =g s  u−E s  g s t =g s u ps ,t  g s t =g s u ps ,t ,[ Ma2 + ]o , u ps , t= P u ps , t  ps 1 u , t=1− 1exp  u ps −   ps 1 ps 2+ ps u , t=1− u , t ,[ Ma ]o =u ,t  g ∞ 1exp  u ps t− t−     g ∞= 1exp  u[ Ma ]o  2+ −1 
  18. 18. Chemical synapse models (Phenomenological models) { if tt s { 0 if tt s 0 { s 0 if tt t s −t t s −t I s = t −t e s if other I s=  t s −t   exp 1− t s −t   if other I s=  e 1 −e 1−2 2 if other { m s mi − if t−t sr dmi t  r  f I s = mi t = dt mi − if t−t sr f
  19. 19. Learning, memory and neural networks Gerald M. Edelman The Group-Selective Theory of Higher Brain Function The brain is hierarchy of non-degenerate neural group
  20. 20. Learning, memory and neural networks Sporns O., Tononi G., Edelman G.M. Theoretical Neuroanatomy: Relationg Anatomical and Functional Connectivity in Graphs and Cortical Connection Matrices Cerebral Cortex, Feb 2000; 10: 127 - 141
  21. 21. Learning, memory and neural networks Gerald M. Edelman – Brain Based Device (BBD) Krichmar J.L., Edelman G.M. Machine Psychology: Autonomous Behavior, Perceptual Categorization and Conditioning in a Brain-based Device Cerebral Cortex Aug. 2002; v12: n8 818-830
  22. 22. Learning, memory and neural networks Gerald M. Edelman – Brain Based Device (BBD) McKinstry J.L., Edelman G.M., Krichmar J.K. An Embodied Cerebellar Model for Predictive Motor Control Using Delayed Eligibility Traces Computational Neurosci. Conf. 2006
  23. 23. Learning, memory and single neuron Donald O. Hebb
  24. 24. Learning, memory and single neuron Guo-qiang Bi and Mu-ming Poo Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type The Journal of Neuroscience, 1998, 18(24):10464–1047 Long Term Depression Long-Term Potentiation Spike Time-Dependent Plasticity (LTD) (LTP) (STDP)
  25. 25. Learning, memory and single neuron Gerald M. Edelman – Experimental research Vanderklish P.W., Krushel L.A., Holst B.H., Gally J. A., Crossin K.L., Edelman G.M. Marking synaptic activity in dendritic spines with a calpain substrate exhibiting fluorescence resonance energy transfer PNAS, February 29, 2000, vol. 97, no. 5, p.2253 2258
  26. 26. Learning and local calcium dynamics Feldman D.E. Timing-Based LTP and LTD at Vertical Inputs to Layer II/III Pyramidal Cells in Rat Barrel Cortex Neuron, Vol. 27, 45–56, (2000)
  27. 27. Learning and local calcium dynamics Shouval H.Z., Bear M.F.,Cooper L.N. A unified model of NMDA receptor-dependent bidirectional synaptic plasticity PNAS August 6, 2002 vol. 99 no. 16 10831–10836
  28. 28. Learning and local calcium dynamics Mizuno T., KanazawaI., Sakurai M. Differential induction of LTP and LTD is not determined solely by instantaneous calcium concentration: an essential involvement of a temporal factor European Journal of Neuroscience, Vol. 14, pp. 701-708, 2001 Kitajima T., Hara K. A generalized Hebbian rule for activity- dependent synaptic modification Neural Network, 13(2000) 445 - 454
  29. 29. Learning and local calcium dynamics
  30. 30. Learning and local calcium dynamics Urakubo H., Honda M., Froemke R.C., Kuroda S. Requirement of an Allosteric Kinetics of NMDA Receptors for Spike Timing-Dependent Plasticity The Journal of Neuroscience, March 26, 2008 v. 28(13):3310 –3323
  31. 31. Learning and local calcium dynamics Letzkus J.J., Kampa B.M., Stuart G.J. Learning Rules for Spike Timing- Dependent Plasticity Depend on Dendritic Synapse Location The Journal of Neuroscience, 2006 26(41):10420 –1042
  32. 32. Learning and local calcium dynamics Letzkus J.J., Kampa B.M., Stuart G.J. Learning Rules for Spike Timing- Dependent Plasticity Depend on Dendritic Synapse Location The Journal of Neuroscience, 2006 26(41):10420 –1042
  33. 33. Learning and Memory Open issues Frey & Morris, 1997
  34. 34. Learning and Memory Open issues from: Frankland & Bontempi (2005)
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