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Summer Program Seminars 2006

Tuesday, June 27, 2006 @ 10:00AM
Cullimore Hall, Room 611
New Jersey Institute of Technology

The Geometry of Neuronal Recruitment

Amit Bose

Department of Mathematical Sciences

New Jersey Institute of Technology

Newark, New Jersey

ABSTRACT

We address the question of whether or not a periodic train of excitatory synaptic inputs recruits an excitable cell, such that it fires repeatedly, or does not recruit a cell, such that it fails to fire, possibly after some transient.  In particular, we study the scenarios of one or two inputs per period; in the latter case, the degree of synchrony of the inputs is a crucial factor in recruitment.  We establish rigorous geometric conditions that pinpoint the transition between recruitment and non-recruitment as the degree of synchrony between input pairs, or other input parameters, is varied.  These conditions can be used to determine whether a particular temporal relation between periodic input pairs leads to recruitment or not and to prove, in certain parameter regimes, that recruitment can only occur when the inputs are sufficiently closely synchronized.  These results are discussed in the context of recruitment of cells into localized activity patterns.