Dynamics of Perceptual Bistability J Rinzel, NYU

1. Dynamics of Perceptual Bistability J Rinzel, NYU w/ N Rubin, A Shpiro, R Curtu, R Moreno • Alternations in perception of ambiguous stimulus – irregular… • Oscillator models – mutual inhibition, switches due to adaptation • -- noise gives randomness to period • Attractor models – noise driven, no alternation w/o noise • Constraints from data: <T>, CV • Which model is favored?

2. IV: Levelt, 1968 Mutual inhibition with slow adaptation  alternating dominance and suppression

3. r1 r2 f r1 r2 Slow adaptation, a1(t) u τdr1/dt = -r1 + f(-βr2 - g a1+ I1) τa da1/dt = -a1 + r1 τ dr2/dt = -r2 + f(-βr1 - g a2+ I2) τa da2/dt = -a2 + r2 τa >> τ , f(u)=1/(1+exp[(θ-u)/k]) Oscillator Models for Directly Competing Populations Two mutually inhibitory populations, corresponding to each percept. Firing rate model: r1(t), r2(t) Slow negative feedback: adaptation or synaptic depression. f r1 No recurrent excitation …half-center oscillator w/ N Rubin, A Shpiro, R Curtu Wilson 2003; Laing and Chow 2003 Shpiro et al, J Neurophys 2007

4. IV Alternating firing rates Adaptation slowly grows/decays WTA or ATT regime adaptation LC model

5. Analysis of Dynamics r1- nullcline r2- nullcline r1 = f(-βr2 - g a1+ I1) r2 = f(-βr1 - g a2+ I2) r2 r1 Fast-Slow dissection: r1 , r2 fast variables a1 , a2 slow variables a1, a2 frozen

6. Switching occurs when a1-a2 traj reaches a curve of SNs (knees) r2 a2 r1 a1 r1-r2 phase plane, slowly drifting nullclines • At a switch: • saddle-node in fast dynamics. • dominant r is high while system rides • near “threshold” of suppressed populn’s • nullcline  ESCAPE. r1- nullcline r2- nullcline β =0.9, I1=I2=1.4

7. net input net input Small I, “release” input Large I, “escape” Dominant, a ↑ I – g a I + α a – g a θ θ Suppressed, a ↓ I – g a - β Recurrent excitation, secures “escape” Switching due to adaptation: release or escape mechanism f

8. Noise leads to random dominance durations and eliminates WTA behavior. τdri/dt = -ri+ f(-βrj - g ai+ Ii + ni) τa dai/dt = -ai + ri Added to stimulus I1,2 s.d., σ= 0.03, τn= 10 Model with synaptic depression

9. Noise-Driven Attractor Models w/ R Moreno, N Rubin J Neurophys, 2007 No oscillations if noise is absent. Kramers 1940

10. LP-IV in an attractor model

11. WTA activity rA=rB OSC gA= gB Compare dynamical skeletons: “oscillator” and attractor-based models

12. With noise 1 sec < mean T < 10 sec 0.4 < CV < 0.6 Noise-free Difficult to arrange low CV and high <T> in OSC regime. Observed variability and mean duration constrain the model.

13. With noise Favored: noise-driven attractor with weak adaptation – but not far from oscillator regime.

14. Best fit distribution depends on parameter values. Noise dominated Adaptationdominated I1 , I2 = 0.6

15. Swartz Foundation and NIH. SUMMARY • Experimentally: • Monotonic <T> vs I • <T> and CV as constraints • No correlation between successive cycles • Models, one framework – vary params. • Mutual, direct inhibition; w/o recurrent excitation • Non-monotonic dominance duration vs I1, I2 • Attractor regime, noise dominated • Better match w/ data. • Balance between noise level and adaptation strength. • Oscillator regime, adaptation dominated • Relatively smaller CV. • Relatively greater correlation between successive cycles. • Moreno model (J Neurophys 2007): local inhibition, strong recurrent excitation: monotonic <T> vs I. w/ N Rubin, A Shpiro, R Curtu, R Moreno