Stability and response times in balanced networks
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Persistent neuronal activity is usually studied in the context of short-term memory localized in central cortical areas. Several recent studies have shown that early sensory areas also have persistent representations of stimuli which decay over the course of seconds. Traditional mechanisms of short-term memory cannot explain sensory persistence of this form for at least two reasons. (i) Most of those mechanisms are positive feedback models resulting in attractor dynamics, where a transient perturbation results in a quasi-permanent change of system state (attractor dynamics). In contrast, sensory systems respond to a transient by a prolonged return to the original state. (ii) In contrast to higher level areas, dynamics of excitatory connections in early sensory areas tend to be dominated by short-term depression. We develop a theory of short-term persistence in sensory areas by studying negative derivative feedback networks. These networks respond quickly and with high precision to their input. The stability of such networks is known to depend on balancing the strengths of positive and negative feedback. We show that a second condition is required for stability which depends on the relative strengths and time courses of fast (AMPA) and slow (NMDA) currents in the excitatory projections. This condition also determines the response time of the network. We also show that networks which respond quickly to an input are necessarily close to an oscillatory instability which resonates in the delta range and may explain the emergence of absence epilepsy. Persistent activity in early sensory areas operates with two vastly different time courses, showing a fast response during stimulus onset and a slow response after stimulus offset. We show that short-term depression, when acting differentially on positive and negative feedback projections, is capable of dynamically changing the time constant of the underlying network, thus allowing fast onset responses and slow offset responses. We also incorporate this network into grouping models of border ownership selectivity and show that it allows the border ownership signal to persist after the offset of a stimulus and, given appropriate network structure, remap its activity when a visual stimulus shifts its retinotopic position.