Dynamical mechanism for sharp orientation tuning in an integrate-and-fire model of a cortical hypercolumn

Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neuro ns is analyzed in terms of spontaneous pattern formation. It is shown how t he ring bifurcates from a synchronous state to a non-phase-locked state who se spike trains are characterized by clustered but irregular fluctuations o f the interspike intervals (ISIs). The separation of these clusters in phas e space results in a localized peak of activity as measured by the time-ave raged 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 extern al stimulus. The ring also exhibits hysteresis due to the subcritical natur e 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 l imit of slow synaptic interactions. For fast synapses, the deterministic fl uctuations of the ISIs associated with the tuning curve can support a coeff icient of variation of order unity.