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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

.

Program

Poster PS46A
Ernest Ho
University of Toronto; Toronto Western Research Institute
Title Slow population rhythms emerge in noisy inhibitory network models
Abstract The hippocampus is a brain region chiefly responsible for memory consolidation. Its functions are thought to be associated with neuronal population activities of various frequencies. Of the different types of neuronal networks, inhibitory interneuronal networks are known to underlie high-frequency population oscillations (~40 Hz).However, recent experiments on rodent hippocampal slices demonstrate that these same networks can exhibit robust spontaneous slow rhythms (0.5-4Hz) [1-2]. While we have gathered a relatively rich knowledge about the mechanism underlying high-frequency oscillations, a mechanistic understanding of the corresponding slow population activities is still absent. With a smaller circuitry, these in vitro slow rhythms provide an ideal platform for us to gain insight into similar but behaviourally significant in vivo slow rhythms such as neocortical UP and DOWN state transitions and large irregular activities in the hippocampus. Since the majority of hippocampal interneurons fire at a high frequency without adaptation, how is it possible for a network to exhibit slow oscillations when there is no slow time scale at the individual neuron level? We address this question from a mathematical and computer simulation standpoint.

Through simulations,we show that slow rhythms can emerge without any explicit slow time scale on the part of individual neurons and synapses.However, two crucial prerequisites are required for their occurrence.First,the network should possess a suitable amount of synaptic background activity,and second, the network should consist fast spiking constituent interneurons. From our simulations we have determined that the optimal rate of spike onset of constituent interneurons should be approximately ten times the rate of the commonly used Wang-Buzsaki model [3]. Furthermore, in order to understand why a fast onset of spiking is required for slow oscillations, we have mathematically analyzed the network equations in terms of firing rates of individual neurons. Results of our analysis indicate that a rapid onset of spike initiation of individual interneurons is necessary for the network to exhibit multi-stability. Slow oscillations occur as a result of the network with suitable synaptic background activity switching from one stable state to another. Our novel results underscore, for the first time, the importance of the fast-spiking character of interneurons in slow rhythms. It is possible that the `fast-spiking'-ness of interneurons may be a generic requirement for the occurrence of many slow population activities of which the mechanisms are yet unknown.

[1] Papatheodoropoulos and Kostopoulos 2002.
[2] Wu et al 2005.
[3] Wang and Buzsaki 1996.
CoauthorsLiang Zhang, Frances Skinner
LocationWoodward Lobby (Monday-Tuesday)