MATHEMATICAL BIOLOGY SEMINAR

        There is great interest in how the brain can maintain the persistent neural activity encoding recent stimuli that is thought to be the basis of working memory. At least three theoretical mechanisms for the maintenance of persistent activity have been described, including local recurrent feedback, intrinsic persistent activity on a single-cell basis, and nonlocal recurrence. Of these, recurrent excitation at the local circuit level has received the most attention, from Hopfield models through elaborated conductance unit networks. At the same time, there is now renewed interest in the concept that individual neurons might have some inherent ability to sustain persistent activity without recurrence. The remarkable finding by Egorov et al. that individual cortical neurons can sustain graded persistent activity is the perhaps most striking experimental example to date. At the intersection of these ideas is a model by Camperi and Wang, which explores the idea of bistability in individual neurons within an Amari/Wilson-Cowan-type continuous integrodifferential network model. The central insight from this work was that intrinsic bistability on the single unit level provides robustness against noise and distracters as compared with the Amari type model. We have explored the Camperi-Wang (C-W) model in more detail, with the expectation that the combination of nonlocal kernels and intrinsic bistability might yield further interesting properties. Indeed, our computational experiments suggest that the C-W model can admit multiple stable bump states that are stimulus (or initial condition) dependent, and that these multiple stable states are complicated when the connection kernel is multiply periodic as might be the case in the patch-gap-patch cortical architecture. In addition, the interaction of bistability and the weight kernel can result in transient network behavior with transient dynamics on a much longer timescale than the intrinsic time constant of the individual cells. I will give an introduction to the neurobiology of persistent activity, compare the Camperi-Wang model to other theoretical treatments of persistent activity, present our explorations and extensions of the Camperi-Wang model and suggest future directions.