AACIMP 2011 Summer School. Neuroscience stream. Lecture by Anton Chizhov.

1. Model of visual cortex Preferred direction Null direction V G E G I Experiments : Université Rene Descartes , Paris ( rats and cats, visual cortex neurons , in-vivo, dynamic clamp) : Anton V. Chizhov Ioffe Physico-Technical Institute of RAS, St.-Petersburg

2. Introduction

3. Experiment . Thalamic neuron responses on 3 trials of visual stimulation by movie.

4. F. Chavane, D. Sharon, D. Jancke, O.Marre, Y. Frégnac and A. Grinvald // Frontiers in Systems Neuroscience , v.5, article 4 , 1-26, 2011. Local interactions in visual cortex

5. 1 mm Hypercolumn Retinotopic projection Orientation-tuned patchy connections Ocular dominance Зрительная кора Experiment . Responses of a neuron selective to direction of stimulus movement. Experiment . Orientation map .

6. Model. Response of 1 mm 2 -area of the cortex on a change of orientation of visual stimulus-bar . Model. Responses of 2 neurons preferring orthogonal orientations. Simulation

8. Computational costs for simulation of 1 mm 2 of cortex Monte-Carlo simulation ( 1 0 1 -10 2 ODEs for 1 neuron + 2-10 4 ODEs for synapses ) X 2- 10 synaptic types X 10 2 neurons 1 one column X 10 1 -10 2 columns in 1 hypercolumn X 10 1 hypercolumns in 1 mm 2 X 10 2 -10 3 stimulation trials Total : 10 7 -10 12 ODEs . CBRD continual model ( 1 0 1 PDEs for 1 neuron X 2- 10 types of neurons X 10 1 - 10 2 discretization points in t*- space + 10 1 ODEs for synapses ) X ( 10 1 -10 2 ) 2 discretization points in (x,y)-space Total : 10 5 -10 8 PDEs .

9. Boundary conditions: Firing rate: -- Hazard function [Chizhov, Graham // PRE 2007,2008] CBRD model of inhibitory population [Chizhov et al. // Neurocomputing 2006]

10. Boundary conditions: Firing rate: CBRD model of excitatory adaptive neuron population 2- comp. model [ Чижов // Биофизика 2004]

11. preferred orientation: pinwheel centers: g S t d f w Synaptic inputs Synaptic kinetics Synaptic morphology Intracortical connections: Thalamic input:

12. Connections Potential connectivity matrix [Binzegger 2004 ] Electrophysiological estimations [Thomson 2002, 2007] I->I I->E E->E E->I [Bannister, Thomson 2007] [Tamas 1997] [Lubke,Feldmeyer 2007] [ Yoshimura , Callaway 2005] 740 66 3540 2400 1440 X/Y L2/3 L4+5+6 E->E 38 1300 280 1720 720 X/Y L2/3 L4+5+6 E->I 420 46 80 800 L2/3 L4+5+6 I->E 28 220 33 490 L2/3 L4+5+6 I->I X/Y L2/3 L4 2.7 1.2 2 . 0 2.8 X/Y L2/3 L4 1.7 2.7 0.6 7. 1 9.8 L2/3 L4 2.7 9 2.3 L2/3 L4 10 12

13. Analysis of the model

14. CBRD ring model for HH-neurons with synaptic kinetics RDA-based ring model for LIF-neurons with synaptic kinetics Kolmogorov-Fokker-Planck (KFP)-based ring model for LIF-neurons with synaptic kinetics 2-d CBRD model for Hodgkin-Huxley (HH)-neurons with synaptic kinetics KFP-based ring model for LIF-neurons with instantaneous synaptic currents Firing-Rate (FR) ring model with instantaneous synaptic currents = Hierarchy of models

15. Canonical firing-rate ring model [Ben Yishai 1995] [Hansel , Sompolinsky , 1996 ] V irtual rotation effect Contrast invariance effect

16. Map 2-d geometry to a ring

17. Threshold-linear approximation of steady-state firing rate of LIF noisy neuron

18. Map CBRD-ring to FR-ring Assumptions:

19. Canonical firing-rate ring model with shunt

20. Fokker-Planck-based ring model

21. 2-d CBRD FR-shunt ring FP-shunt ring CBRD ring, cos-profile CBRD ring, exp-profile canonical FR ring model CBRD ring, nonadapt. CBRD ring, 2-comp. LIF CBRD ring, 1-comp. LIF

22. Stationary solutions and the effect of Contrast Invariance No adaptation + adaptation + adaptation + NMDA

23. Comparison with experiments

24. Рис . Согласование модели двух-компонентного нейрона (кружки) с экспериментальными данными (сплошные линии) по одновременным регистрациям на соме и дендрите [ Pouille , Scanziani 2004]. A , ответы на стимуляцию в alveus в режиме фиксации тока показаны слева, ответ с фиксацией потенциала на соме -- справа. B , в другой клетке получены ответы на подачу тормозящей проводимости ( gin амплитудой 5 nS и временной зависимостью, показанной зеленой линией) в режиме dynamic - clamp . [F.Pouille, M.Scanziani // Nature , 2004] Passive properties of 2-compartment neuron Рис. Модель и эксперимент [Karnup, Stelzer 1999] C V d V d V d V d V s V s I s I s g=I d /(V d -V rev ) B A

25. Spiking of single neuron E X P E R I M E N T M O D E L

26. Lower Point Upper Point M O D E L E X P E R I M E N T

27. [Myme et al. 2003] AMPA- and NMDA-EPSCs [Dong et al. 2004] Synaptic currents EPSCs and IPSCs E X P E R I M E N T M O D E L

28. Spatiotemporal patterns generated by an electrical stimulus reveal clusters of activity . Scale bars in the experiments are 220μm. E X P E R I M E N T Activity patterns in visual cortex slices M O D E L 3.5 ms 6.5 ms [Tucker & Katz, 2003] 3.5 ms 6.5 ms

29. [Tucker & Katz, 2003] PSPs Responses on electrical stimulation E X P E R I M E N T M O D E L PSPs

30. Stimulation of the diffuse zone and optical claster 2 stimulating electrodes E X P E R I M E N T M O D E L S1 S 2 [Tucker & Katz, 2003]

31. E X P E R I M E N T M O D E L S1 S 2 [Tucker & Katz, 2003] Stimulation of two diffuse zones 2 stimulating electrodes

32. Excitatory neurons Interneurons Experiment Model

33. Stimulus Visual cortex 1 mm E X P E R I M E N T M O D E L E X P E R I M E N T Visual stimulation

35. Explanation: Model Visual illusion (tilt after-effect)

36. Hypothetic effect of depression of the “background” image by binocular vision

37. Thanks to colleagues: Lyle Graham Adrien Schramm Erez Persi Elena Smirnova Anatoly Buchin Andrey Turbin