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