1. V1 Dynamics and Sparsity and Multiple Feature Maps Michael Shelley – Courant Institute/CNS, NYU Collaborators: Bob Shapley – CNS/CIMS David Cai -- CIMS Dave McLaughlin – CIMS/CNS Louis Tao -- NJIT Wei Zhu -- CNS/CIMS

2. I E I E LGN Simple Complex Inhibitory Excitatory V1 Important Features: Nonspecific and Isotropic (egalitarian) cortical coupling (I&II) (monosynaptic inhibition of shorter length-scale) Fitzpatrick et al 85, Lund 87, Callaway & Wiser 96 LGN imparts random preferred spatial phase (I&II) De Angelis et al (1999) Combined AMPA and NMDA excitation (II) Total (LGN + cortical) excitation on a cell is (approx) constant (II) Miller 96, Royer & Pare 02 NYU V1 models I & II

3. Drifting Grating & Modulation Ratio Simple Complex • Isotropic coupling & random phase: (DG) cortical conductances unmodulated • Standard Characterization of Responses: Modulation Ratio F1/F0 F1/F0 = 1.7 F1/F0 = 0.05 Drifting Grating Stimulus and S/C characterization m m

4. Simple Complex Ringach, Shapley & Hawken JNS 2002 extracellular modulation ratio intracellular modulation ratio Priebe et al, Nat. Neuro. 2004

5. But … complex cells poorly tuned increasing self-excitation led to bistability & high firing rates marked near/far from pinwheel tuning differences (Sur ’ s lab: intracellular differences, but little extracellular) Our previous work suggested that recurrent excitation could be stabilized and graded by intrinsic fluctuations in the local circuit. Cai et al, PNAS 2004 Approach here: Probabilistically sparsify the network and simultaneously boost efficacy of active connections (psp ’ s are fewer and bigger). Numerology: Mason, Nicoll, Stratford 1991 Thomson et al 2002 suggests O(10 2 ) presynaptic cortical cells give drive

7. tuned complex cells small near/far diffs statistically contrast invariant experiment Shapley et al

8. complex simple near pinwheel centeriso-orientation domain intracellular conductances somewhat more broadly tuned or diverse at p.w. centers Well-tuned complex cells both near and far from p.w. centers.

9. What underlies the tuning and the stability? Fluctuations. In V1 model, histogram of diff. in spike count on increment and decrement of slowly modulated contrast. Hysteresis in excitatory complex cell network Firing Rate Simple, homogeneously coupled model network fashioned after V1 model. 50% receive external excitatory drive (simple) 50% receive strong cortical excitation (complex) Existence of critical gain point we call fluctuation controlled criticality hysteric loop graded response critical gain Ex.C.

10. or How about “ functional ” sparsity? Many visual neurons are silent except when driven by near-optimal stimuli, e.g. optimal orientation & spatial frequency (w. Shapley & W. Zhu) tuning curves for orientation and spatial frequency. Xing, Ringach, Shapley, Hawken ‘ 04 s.f. 0 2π2π 10 1 0.1 firing rate No observed relation between preferred orientation and spatial frequency. In our previous models, LGN drive has single preferred s.f. cycles/deg 

11. 89 cells layer 4Ca But, strong relation between degree of selectivity for orientation and s.f. peak s.f.

12. Spatial frequency mapping remains contentious … Hubener, Shoham, Grinvald, Bonhoeffer ’ 97 Everson et al 1998 Issa, Trepel, Stryker 2000 orientation map of high spatial freq. response orientation map of low spatial freq. response high low Sirovich & Uglesich 2004 Suggests the spatial frequency is not a well-structured map, consistent with electrophysiology.

13. Modification of NYU-II: Add diversity in preferred spatial frequency of LGN drive to V1. Keep # of LGN cells independent of pref. s.f. 50% “ even ”, 50% “ odd ” structure. or odd even

14. Some results F1/F0 preferred s.f. % of cells # of cells

15. CV[firing rate] LSFV s.f.orientation As with expt., find correlation between tuning of orientation and tuning of s.f. Two sample cells still working on complex cell tuning …

16. Thanks & Thanks to Jerry