|M.Sc Student||Gilboa-Freedman Gail|
|Subject||History Dependent Multiple Time Scale Dynamics in a Single|
|Department||Department of Applied Mathematics||Supervisor||Professor Naama Brenner|
History dependent characteristic time scales in dynamics have been observed at several levels of organization in neural systems. Such dynamics can provide powerful means for computation and memory. At the level of the single neuron several microscopic mechanisms, including ion channel kinetics, can support multiple-time- scale dynamics. How the temporally complex channel kinetics give rise to dynamical properties of the neuron is not well understood. We here construct a model that captures some features of the connection between these two levels of organization. The model neuron exhibits history dependent multiple-time-scale dynamics in several effects: first, following stimulation the recovery time scale is related to the stimulation duration by a power-law scaling; second, temporal patterns of neural activity in response to ongoing stimulation are modulated over time; finally, the characteristic time scale for adaptation following a step change in stimulus depends on the duration of the preceding stimulus. All these effects have been observed experimentally and are not explained by current single neuron models. The model neuron here presented is composed of an ensemble of ion channels that can wander in a large pool of degenerate inactive states, and thus exhibits multiple-time-scale dynamics at the molecular level. Channel inactivation rate depends on recent neural activity, which in turn depends through modulations of the neural response function on the fraction of active channels. : the availability of channels determines neuronal excitability, which determines neuronal activity; activity, in turn, affects the availability of channels by enhancing inactivation. the availability of channels determines neuronal excitability, which determines neuronal activity; activity, in turn, affects the availability of channels by enhancing inactivation.the availability of channels determines neuronal excitability, which determines neuronal activity; activity, in turn, affects the availability of channels by enhancing inactivation.This construction produces a model that robustly exhibits non-exponential history-dependent dynamics, in qualitative agreement with experimental results.