2134/825 P.C. Bressloff P.C. Bressloff N.W. Bressloff N.W. Bressloff J.D. Cowan J.D. Cowan Dynamical mechanism for sharp orientation tuning in an integrate-and-fire model of a cortical hypercolumn. Loughborough University 2006 untagged Mathematical Sciences not elsewhere classified 2006-02-15 10:29:49 Preprint https://repository.lboro.ac.uk/articles/preprint/Dynamical_mechanism_for_sharp_orientation_tuning_in_an_integrate-and-fire_model_of_a_cortical_hypercolumn_/9384476 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.