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Introduction to modern methods and tools for biologically plausible modeling of neurons and neural networks (2)

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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 …

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 2.
More info at http://summerschool.ssa.org.ua

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  • 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 II Ruben A. Tikidji – Hamburyan rth@nisms.krinc.ru 2010
  • 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. 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. Phenomenological models of neuron Is it possible to model only phenomena of neuronal activity without detailed consideration of electrical genesis?
  • 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. 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. 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. Izhikevich's model
  • 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. 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. Modified Integrate-and-Fire model Master and slave integrators dut  r duap 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 CR ap 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 CR ap τs τ fire 2   du (t ) 1 u ap (t ) − u (t ) u (t )  = I (t ) + − во всех остальных случаях  dt  C CR ap τ
  • 12. Modified Integrate-and-Fire model
  • 13. Modified Integrate-and-Fire model
  • 14. Comparative characteristics o neuron models by Izhikevich
  • 15. Synapses: chemical and electrical
  • 16. Synapses: chemical and electrical
  • 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[ Ma ]o e  2+ − u −1 
  • 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. 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. 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. 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. 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. Learning, memory and single neuron Donald O. Hebb
  • 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. 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. 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. 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. 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. Learning and local calcium dynamics
  • 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. 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. 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. Learning and Memory Frey & Morris, 1997 Open issues
  • 34. Learning and Memory Open issues from: Frankland & Bontempi (2005)
  • 35. Tools for biologically plausible modeling Simulator Publicat Versi First Latest Primary License MS Mac OS X Linux Other Active Language ions on release release author Windows Community Emergent (formerly AisaMin 4.0 1986 2008 Dr. Randy GNU GPL XP, 2003, Intel, PPC Any, Any Unix emergent- C++ PDP++ and PDP) gusORei O'Reilly Vista Fedora, users list, lly07 Ubuntu Wiki GENESIS (the GEneral Beeman 2.3 1988 2007 Dr. James GNU GPL Cygwin Intel, PPC Yes Any Unix SourceForge C NEural SImulation EtAl07 Bower & list System) Dr. Dave Beeman NEURON (originally Hines93 6.2 1986 2008 Dr. Michael GNU GPL 95+ Intel, PPC Debian Any Unix NEURON C, C++ CABLE) HinesCa Hines Forum rnevale9 7 HinesEt Al06 SNNAP (Simulator for Unknow 8.1 2001 2007 Dr. John Proprietary Java Java Java Java Available Java Neural Networks and n Byrne & Dr. but defunct Action Potentials) Douglas Baxter Catacomb2 (Components Unknow 2.111 2001 2003 Robert GNU GPL Java Java Java Java No Java And Tools for Accessible n Cannon COmputer Modeling in Biology Topographica Neural BednarE 0.9.4 1998 2008 Dr. James A. GNU GPL Vista, XP, Build from Build from Build from Mailing list, Python/C++ Map Simulator tAl04 Bednar NT source source source boards NEST (NEural Diesman 2.0 2004 2006 Unknown Proprietary Unknown Unknown Unknown Any Unix, NEST-users Unknown Simulation Tool) nEtAl95 build from list Diesman source nGewalti g02 Gewaltig EtAl02D jurfeldt0 8 http://grey.colorado.edu/emergent/index.php/Comparison_of_Neural_Network_Simulators
  • 36. Tools for biologically plausible modeling Simulator Publicat Vers First Latest Primary License MS Mac OS X Linux Other Active Language ions ion release release author Windows Community KInNeSS - KDE Gorchote 0.3.4 2004 2008 Dr. Anatoli GNU GPL No No KDE 3.1 No No C++ Integrated chnikov Gorchetchni required NeuroSimulation EtAl04G kov Software rossberg EtAl05 XNBC VibertAz 9.10 1988 2006 Dr. Jean- GNU GPL 9x, 2000, Build from RPM Tru 64, No C++ my92Vib -h François XP source (Fedora), Ultrix, AIX, ertEtAl9 VIBERT Build from SunOS, 7VibertE source HPux tAl01 PCSIM: A Parallel neural Unknow 0.5.0 2008 2008 Dr. Dejan GNU GPL No No Build from No No Python/C++ Circuit SIMulator n Pecevski source Dr. Thomas Natschlager NeuroCAD Unknow 0.00. 2003 2007 Dr. Ruben GNU GPL No No Yes Any Unix No C n 21a Tikidji - Hamburyan http://grey.colorado.edu/emergent/index.php/Comparison_of_Neural_Network_Simulators
  • 37. NeuroCAD – Problem definition To create a computer environment, combining flexibility and universality of script machines, with efficacy of monolithically compiled, high optimized application. It would be very nice, if found solution allows to perform computations in homogeneous, heterogeneous and SMP system. Thereby parallelism is included in background of NeuroCAD project.
  • 38. NeuroCAD – how to make model? Step I: Select and export required modules from modules data bases as c-code and compile it Modules (shared objects files *.so) Step V: Step II: Make modules runtime Link its by NeuroCAD Engine scheduler and run. Step III: Export variable blocks in shared memory of NeuroCAD Engine Step IV: Connect variables. Step IV: Connect variables. shared memory
  • 39. NeuroCAD Benchmarks NeuroCAD vs. GENESIS ~ 5 – 15 times NeuroCAD -normal NeuroCAD – tab Neuron – tab 0.2740 0.1955 1.1740 1 0.71 4.28NeuroCAD -normal 1 6.01 NeuroCAD – tab 1 Neuron – tab http://nisms.krinc.ru/neurocad.org rth@nisms.krinc.ru
  • 40. The big model of Purkinje Cell E. DeSchutter J.M. Bower «An Active Membrane Model of the Cerebellar Purkinje Cell» J. Neurophysiology Vol. 71, No. 1, January 1994. ● 1600 compartments ● 12 types of ion channels ● Ca2+ concentration dynamics ● Ca2+ dependent K+ channels ● Two synaptic types ● Three types of dendritic zones ● More than 60 tests and real data comparisons (runtime for some tests in 1994 was approximately two weeks)
  • 41. The big model of Purkinje Cell E. DeSchutter J.M. Bower «An Active Membrane Model of the Cerebellar Purkinje Cell» J. Neurophysiology Vol. 71, No. 1, January 1994.
  • 42. The big model of Purkinje Cell E. DeSchutter J.M. Bower «An Active Membrane Model of the Cerebellar Purkinje Cell» J. Neurophysiology Vol. 71, No. 1, January 1994.
  • 43. The big model of Purkinje Cell E. DeSchutter J.M. Bower «An Active Membrane Model of the Cerebellar Purkinje Cell» J. Neurophysiology Vol. 71, No. 1, January 1994.
  • 44. Detailed model of thalamo-cortical part of cat vision system S. Hill, G. Tononi «Modeling Sleep and Wakefulness in the Thalamocortical System» J. Neurophysiology Vol. 93, 1671-1698, 2005. ● approximately 65000 neurons ● approximately 1.5 million synapses ● ration number of neurons in model and average cat 1:9 ● Three cortex layers and two thalamus layers with modeling of primary and secondary zones of visual perception ● Neuron model – hybrid of H-H and IaF with 4 types of ion channels. ● 5 types of synapses. Synaptic model includes mediator waste effect. ● Predominant anisotropy of network with local formed ensembles.
  • 45. Detailed model of thalamo-cortical part of cat vision system
  • 46. ”I have all this data – cell types, firing properties, connectivity, dendritic excitability, synaptic dynamics, ..... But I don’t understand it. I need to model it” ”У меня есть все эти данные – типы клеток, условия их срабатывания, связи, возбудимость дендритов, динамика синапсов, ..... Но я не могу понять этого. Я вынужден это моделировать” Bert Sakmann, 2001, Jerusalem

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