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:, CV Which model is favored?

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

3. Oscillator Models for Directly Competing Populations w/ N Rubin, A Shpiro, R Curtu Two mutually inhibitory populations, corresponding to each percept. Firing rate model: r 1 (t), r 2 (t) Slow negative feedback: adaptation or synaptic depression. Wilson 2003; Laing and Chow 2003 r1r1 Slow adaptation, a 1 (t) r1r1 r2r2 r2r2 r1r1 No recurrent excitation …half-center oscillator τ dr 1 /dt = -r 1 + f(-βr 2 - g a 1 + I 1 ) τ a da 1 /dt = -a 1 + r 1 τ dr 2 /dt = -r 2 + f(-βr 1 - g a 2 + I 2 ) τ a da 2 /dt = -a 2 + r 2 τ a >> τ, f(u)=1/(1+exp[(θ-u)/k]) u f f Shpiro et al, J Neurophys 2007

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

5. Fast-Slow dissection: r 1, r 2 fast variables a 1, a 2 slow variables r 1 - nullcline r 2 - nullcline r 1 = f(-βr 2 - g a 1 + I 1 ) r 2 = f(-βr 1 - g a 2 + I 2 ) Analysis of Dynamics a 1, a 2 frozen r1r1 r2r2

6. r 1 -r 2 phase plane, slowly drifting nullclines a1a1 a2a2 Switching occurs when a 1 -a 2 traj reaches a curve of SNs (knees) At a switch: saddle-node in fast dynamics. dominant r is high while system rides near “threshold” of suppressed populn’s nullcline  ESCAPE. β =0.9, I 1 =I 2 =1.4 r 1 - nullcline r 2 - nullcline r1r1 r2r2

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

8. Noise leads to random dominance durations and eliminates WTA behavior. Added to stimulus I 1,2 s.d., σ = 0.03, τ n = 10 Model with synaptic depression τ dr i /dt = -r i + f(-βr j - g a i + I i + n i ) τ a da i /dt = -a i + r i

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. g A = g B activity r A =r B WTA OSC Compare dynamical skeletons: “oscillator” and attractor-based models

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

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

14. Best fit distribution depends on parameter values. I 1, I 2 = 0.6 Noise dominated Adaptation dominated

15. SUMMARY Experimentally: Monotonic vs I 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 I 1, I 2 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 vs I. Swartz Foundation and NIH. w/ N Rubin, A Shpiro, R Curtu, R Moreno