Dynamical mechanism for sharp orientation tuning in an integrate-and-fire model of a cortical hypercolumn.
preprintposted on 15.02.2006, 10:29 authored by P.C. Bressloff, N.W. Bressloff, J.D. Cowan
Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous state to a non-phase-locked state whose spike trains are characterized by clustered but irregular fluctuations of the inter-spike intervals (ISIs). The separation of these clusters in phase space results in a localized peak of activity as measured by the time-averaged firing rate of the neurons. This generates a sharp orientation tuning curve that can lock to a slowly rotating, weakly tuned external stimulus. Under certain conditions the peak can slowly rotate even to a fixed external stimulus. The ring also exhibits hysteresis due to the subcritical nature of the bifurcation to sharp orientation tuning. Such behavior is shown to be consistent with a corresponding analog version of the IF model in the limit of slow synpatic interactions. For fast synapses, the deterministic fluctuations of the ISIs associated with the tuning curve can support a coefficient of variation (CV) of order unity.
- Mathematical Sciences