## A stochastic two-state signalling module with negative feedback

- Date: 11/09/2006

Peter Borowski (Max-Planck-Institute for the Physics of Complex Systems)

University of British Columbia

Motivated by the negative feedback calcium exerts on the gating

dynamics of a calcium-conducting ion channel in olfactory receptor

neurons, we develop an abstract two-state (open/closed) signalling

module with negative feedback. The coupling between the gating dynamics

of the channel and the conducted ion makes the effective dynamics of

the channel non-Markovian and difficult to treat in a

Langevin-approach. We make use of two different techniques to describe

the stochastic dynamics of the module. First, we calculate the steady

state probability distribution using a Master/Fokker-Planck-type

equation. Second, a path-integral formulation based on the temporal

statistics of the channel state-flips is developed to calculate

dynamical properties of the module. The feedback effect is built into

the model in a systematic way in the form of a weak perturbation.

Analytic results are obtained for the open probability of the channel

as well as the auto-correlation and response functions (both for the

discrete channel variable and the continuous calcium concentration).

Monte Carlo simulations are performed which support the analytical

predictions in the weak feedback limit and provide results beyond

linear perturbation theory.

MITACS Math Biology Seminar 2006