Modeling the Primary Visual Cortex

Transcription

1 Modeling the Primary Visual Cortex David W. McLaughlin Courant Institute & Center for Neural Science New York University Ohio - MBI Oct 02

2 Input Layer of Primary Visual Cortex (V1) for Macaque Monkey Modeled at : Courant Institute of Math. Sciences & Center for Neural Science, NYU In collaboration with: Robert Shapley (Neural Sci) Michael Shelley Louis Tao Jacob Wielaard But today, I ll describe work in collaboration with David Cai David Lorentz Louis Tao

3 Today, I ll Briefly set the background for our modeling study; Jump to a description of some of my current focus; (Bob and Mike will summarize our current results.)

4 We re studying the front end of the visual system -- the primary visual cortex

5 Visual Pathway: Retina --> LGN --> V1 --> Beyond

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8 Elementary Feature Detectors Individual neurons in V1 respond preferentially to elementary features of the visual scene (color, direction of motion, speed of motion, spatial wave-length). Two important features: Spatial phase φ (relative to receptive field center) Orientation θ of edges.

9 Grating Stimuli Standing & Drifting Two Angles: Angle of orientation -- θ Angle of spatial phase -- φ (relevant for standing gratings)

10 Orientation Tuning Curves (Firing Rates Vs Angle of Orientation) Spikes/sec Terminology: Orientation Preference Orientation Selectivity Measured by Half-Widths or Peak-to-Trough

11 Cortical Map of Orientation Preference Optical Imaging Blasdel, 1992 Outer layers (2/3) of V µ ---- Color coded for angle of orientation preference right eye left eye

12 Our Model A detailed, fine scale model of a local patch of input layer of Primary Visual Cortex; Realistically constrained by experimental data; Refs: McLaughlin, Shapley, Shelley & Wielaard --- PNAS (July, 2000) --- J Neural Science (July, 2001) --- J Comp Neural Sci (2002) --- J Comp Neural Sci (2002) ---

13 Two Extreme Classes: Classes of Models I. Feed forward filtering -- Hubel & Wiesel ( 62) II. Recurrent networks -- with strong excitatory feedback, and nonlinear attractor states Our model is in the middle -- recurrent network filtering with cortico-cortical inhibition dominating for simple (linear) cells, and with cortico-cortical excitation more dominant for complex (nonlinear) cells

14 Pinwheel Centers

15 Equations of the Model v j σ -- membrane potential -- σ = Exc, Inhib -- j = 2 dim label of location on cortical layer neurons per sq mm (12000 Exc, 4000 Inh) σ = E,I V E & V I -- Exc & Inh Reversal Potentials (Constants) Integrate & Fire, with voltage reset at spiking

16 Ordered and Disordered Maps Convergent LGN input confer the maps of orientation & spatial phase preference (Reid & Alonso, 1995) Regular Map of Orientation in Pinwheels (Optical Imaging: Bonhoeffer & Grinvald, 1991; Blasdel, 1992; Maldonado et al., 1997 Random Map of Spatial Phase (DeAngelis et al., 1999)

17 -- excitation -- inhibition Circles of Influence (Monosynaptic coupling)

18 Characteristic Features of our Recurrent Network Model Local (< 500 µm) lateral connectivity -- nonspecific & isotropic Ordered map of orientation preference Disordered map of spatial phase preference Dominance of cortico-cortical inhibition for simple cells Stronger cortico-cortical excitation for complex cells Each of which supported by experimental measurements

19 But remember, our model only local

20 Pinwheel Centers

21 Lateral Connections and Orientation -- Tree Shrew Bosking, Zhang, Schofield & Fitzpatrick J. Neuroscience, 1997

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23 Coarse-Grained Representations Using the spatial regularity of cortical maps (such as orientation preference), we coarse grain the cortical layer into local cells or placquets.

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26 Coarse-grained Representations: V1 Average firing rate models (Shelley & McLaughlin) m σ (x,t), σ = E,I PDF representations ( Cai, Tao & McLaughlin) ρ σ (v,g; x,t), σ = E,I Sub-network of embedded point neurons -- in a coarse-grained, dynamical background (Cai & McLaughlin)

27 Outline of Rest of Talk I. NMDA Behavior & Integrate and Fire Modeling II. Within a coarse-grained cell (or plaquet) IIa. NMDA & Oscillations and Synchrony IIb. Embedded point neurons

28 I. NMDA --Background In our network, slow excitation reduces synchrony and lessens oscillations. NMDA is a primary cause of slow excitation in V1; it is prevalent throughout the cortex, including V1 and layer 4c. NMDA channels can be blocked by Mg ions, leading to a voltage dependent conductance as mapped by Jahr & Stevens, How does this voltage dependence effect I&F modeling? Equation : I NMDA g t V Trans Volt = ( ) ( ) NMDA NMDA g [ V E ] NMDA

29 Realistic Voltage Behavior A basis for comparison. By X.J. Wang, Based upon Pinsky & Rinzel, Compartments: Soma and Dendrite. A number of ion channels, with Hodgkin-Huxley type mechanics: g Na,g K,g Ca, and g K AHP. AMPA-only synaptic makeup has been replaced by NMDA+AMPA. Significant g K AHP, slowdecaying. Potential (mv) Time (msec) Dendritic Potential Somatic Potential

30 Significant K-AHP conductance 0.2 g K AHP Other Conductances Conductance (ms) Time (msec) Can be approximated in an IF model by an Adaptive Conductance step function. 350

31 Integrate-and-Fire (IF) Modeling A neuron s voltage threshold can be found experimentally. An all or none event, the action potential (AP) or spike occurs if and only if V Th is crossed. IF modeling truncates spikes instead of modeling them, only recording spike times. Potential (mv) Dendritic Potential Somatic Potential V Th Time (msec)

32 1 NMDA Voltage-Dependence g NMDA Volt (Normalized) V Th E NMDA V Peak Jahr and Stevens, V R Voltage (mv) A Problem for IF Modeling: Superthreshold potential, the majority of the voltagedependence curve, is truncated in IF models.

33 Pasting Spikes I Everything is integrated as usual. NMDA behavior is determined by a pasted-in spike, added to the standard IF potential, following threshold crossing. Equation : Trans Volt NMDA= g () t g ( V+ V ) NMDA NMDA Paste [ V+ V E ] Paste NMDA Potential (mv) V + V Paste V Spike Times Time (msec)

34 40 Detail of Pasted Spikes Potential (mv) Time (msec) Potential (mv) Detail Time (msec) This model encourages overexcitation: there is no refractoriness.

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36 Comparison of Firing Statistics

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38 40 20 ISI Distributions: Light Stimulus (mean input ISI = 5 msec) Wang Model IF Model without Pasted Spike IF Model with Pasted Spike Miller Model with O riginal Parameterization

39 Why so little effect from spikes?

40 I NMDA = g NMDA (v - E NMDA )

41 Effects of Spike Height Spike Width

42 Result: Pasting Spike has little effect. Voltage (mv) Voltage (mv) Spikes 8 Spikes 9 Spikes Time (msec) Time (msec) 8 Spikes With Pasted Spike Without Pasted Spike: Identical Spike Rate Causes: (i) Reversal of current at reversal potential crossing; (ii) Short duration of each spike. Insensitivity of NMDA conductance to spikes also shown, very convincingly, by clipping spikes in Wang model

43 40 20 Regular-Spiking Model: 20 Spikes With NMDA at all times Potential (mv) Potential (mv) Time (ms) No NMDA when V D >= Spikes Time (ms)

44 Effective Reversal Potential & NMDA Modeling An alternative approach, using an effective reversal or shadow potential Krukowski & Miller (Nature Neuroscience 01; To describe this approach, we begin from the concept of an effective reversal potential (Shelley, McLaughlin, Shapley & Wielaard; J. Comp. Neurosci 02)

45 Conductance Based Model dv/dt = - g T (t) [ v - V Eff (t) ], σ = E,I where g T (t) denotes the total conductance, gj T (t) = g T + g j σe (t) + g j σi (t), and V Eff (t) = [V E g EE (t) - V I g EI (t) ] [g T (t)] -1 If [g T (t)] -1 << τ syn v V Eff (t)

46 Active Cortex - Causes High Conductances, which in turn cause Sub-threshold membrane potential ``instantaneously tracks conductances on the synaptic time scale. V(t) ~ V Eff (t) = [V E g EE (t) - V I g EI (t) ] [g T (t)] -1 where g T (t) denotes the total conductance

47 Active Background High Conductances in Active Cortex Membrane Potential Tracks Instantaneously Effective Reversal Potential

48 Effective Reversal Potential & NMDA Wang s Model Krukowski & Millers Original Model Reparameterized Model [Mg] = 1.0 mm & Stronger KAHP

49 gkahp

50 Can we linearize g NV? (Normalized) volt g NMDA NMDA Voltage Dependence Voltage (mv) (Normalized) volt g NMDA Jahr Equation Linearized Voltage (mv) This yields nearly identical behavior.

51 Can we make g NV constant? A good constant (horizontal) value can be chosen computationally, to fit typical stimulation intensities. However, the actual value of the constant must be fit for each different numerical run (change of intensity of stimulus, etc.) Probably best to use linear representation

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53 Conclusions (for this NMDA part of the talk) NMDA s can be realistically incorporated into traditional IF models of regularly spiking neurons, with no special modifications (pasted spike, shadow potential) necessary. That is, spikes themselves have little effect. The voltage dependence can be linearized to fit the subthreshold region. A few remarks:

54 Remark 1: Calcium Transport While voltage and spiking (for regularly firing neurons) not affected by the nonlinearity of the NMDA conductance, Not so for calcium transport because the calcium current does not average to zero over a spike. Could be important for longer time effects, such as plasticity, LTP, etc for which calcium plays a major role.

55 Remark 2: Bursting Neurons The nonlinearity could be more important for bursting neurons, which fire on top of a voltage plateau.

56 1 NMDA Voltage-Dependence g NMDA Volt (Normalized) V Th E NMDA V Peak Jahr and Stevens, V R Voltage (mv)

57 Bursting Model: With NMDA at all times 20 Potential (mv) Spikes Time (ms) No NMDA when V D >= -50 Potential (mv) Spikes Time (ms)

58 40 20 Regular-Spiking Model: 20 Spikes With NMDA at all times Potential (mv) Potential (mv) Time (ms) No NMDA when V D >= Spikes Time (ms)

59 Outline I. NMDA Behavior & Integrate and Fire Modeling II. Within a coarse-grained cell (or plaquet) IIa. NMDA & Oscillations and Synchrony IIb. Embedded point neurons

60 II. Within One Coarse-Grained Cell IIa. NMDA s Effects

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62 Effects of NMDA Within CG Cell NMDA lessons oscillations and synchrony Increases firing rates With respect to removing synchrony, NMDA works in the same direction as synaptic failure -- as seen in an all AMPA network by (Cai, Tao & Shelley, 02) We illustrate these effects in a toy, all excitatory network

63 Driver frequency = 5Hz, no synaptic failure, 0% NMDA on Complex ps = S = 0.24, p = 1, efracs = 0., efracc = 0., n = 120 /NMDA5Hz1 Firing rate = 73/sec for SIMPLE 80 = 13/sec for Complex

64 Driver frequency = 5Hz, 1% synaptic failure, 0% NMDA on Complex ps = S = , p = 0.99, efracs = 0., efracc = 0., n = 120 /NMDA5Hz1.1 Firing rate = 74/sec for SIMPLE 80 = 14/sec for Complex

65 Driver frequency = 5Hz, no synaptic failure, 50% NMDA on Complex ps = S = 0.24, p = 1, efracs = 0., efracc = 0.5, n = 120 /NMDA5Hz2 Firing rate = 86/sec for SIMPLE 80 = 56/sec for Complex

66 Driver frequency = 5Hz, 1% synaptic failure, 50% NMDA on Complex ps = S = , p = 0.99, efracs = 0., efracc = 0.5, n = 120 /NMDA5Hz1.2 Firing rate = 88/sec for SIMPLE 80 = 65/sec for Complex

67 Driver frequency = 5Hz, no synaptic failure, 100% NMDA on Complex ps = 0.24 S = 0.24, p = 1, efracs = 0., efracc = 1., n = 120 /NMDA5Hz3 120 Firing rate = 110/sec for SIMPLE 100 = 122/sec for Complex 80 Note: Firing rate is higher for COMPLEX

68 A Realistic Network Within a CG Cell Two types of inhibition KAHP current AMPA & NMDA Very preliminary

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71 Outline I. NMDA Behavior & Integrate and Fire Modeling II. Within a coarse-grained cell (or plaquet) IIa. NMDA & Oscillations and Synchrony IIb. Embedded point neurons

72 IIb. Embedded Point Neurons Point neurons -- embedded in, and fully interacting with, coarse-grained firing rate representation For scale-up computer efficiency Yet maintaining firing properties of individual neurons -- for spike coding, coincidence detection, etc. Today, I ll show some preliminary consistency studies

73 Embedded Network All excitatory network both AMPA & NMDA; Within the CG cell 200 neurons (100 simple ; 100 complex ) Compared with embedded network, with 80 of the complex neurons replaced by a CG firing rate representation, leaving 20 embedded complex neurons; In the embedded network, CG firing rate drives 80 modulated Poisson spikers.

74 Mixed Representation, SIMPLE: 100 I&F, COMPLEX: 20 I&F + MF vs 100 SIMPLE I&F and 100 COMPLEX I&F Firing rate = /sec for SIMPLE; 45-75/sec for Complex All I&F: 120 efracs = 0, efracc = 0.2 /MF6.7 I&F COMPLEX: 20% NMDA, SIMPLE: all AMPA, INPUT: all AMPA

75 Mixed Representation, SIMPLE: 100 I&F, COMPLEX: 20 I&F + MF vs 100 SIMPLE I&F and 100 COMPLEX I&F Firing rate = /sec for SIMPLE; 45-75/sec for Complex Mixed: efracs = 0, efracc = 0.2 /MF6.6 MeanField Firing rate = 126/sec for SIMPLE = 66/sec for Complex COMPLEX: 20% NMDA, SIMPLE: all AMPA, INPUT: all AMPA

76 Membrane Potential of a representative COMPLEX neuron ( all I&F vs Mixed): Voltage vs time 1 I & F 0.8 Neuron in full network Same neuron, in embedded network Mean Field Mixed

77 Embedded Network Computational efficiency -- scales as N 2 where N = # of point neurons; (i.e. 100! 20 yields 10000!400)

78 Conclusion I. NMDA Behavior & Integrate and Fire Modeling [For regularly spiking neurons, NMDA nonlinearity (and spikes) have little effect.] II. Within a coarse-grained cell (or plaquet) IIa. NMDA & Oscillations and Synchrony [Lessoned by NMDA (and synaptic failure)] IIb. Embedded point neurons [Consistency, within 10%, easily achievable.]

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82 400 ISI Distributions: Heavy Stimulus (mean input ISI = 1.5 msec) Wang Model IF Model without Pasted Spike IF Model with Pasted Spike Miller Model with O riginal Parameterization