Control of reaction rate by asymmetric two-state noise

Focusing in multiwell potentials: applications to ion channels

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

Resonant activation in the presence of nonequilibrated baths

We study the generic problem of the escape of a classical particle over a fluctuating barrier under the influence of non-Gaussian noise mimicking the effects of nonequilibrated bath. The model system is described by a Langevin equation with two independent noise sources, one of which stands for the dichotomous process and the other describes external driving by alpha-stable noise. Our attention focuses on the effect of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation. Possible physical interpretation of the occurrence of Lévy noises and the relevance of the model for chemical kinetics is briefly discussed.

Influence of the barrier shape on resonant activation

The escape of a Brownian particle over a dichotomously fluctuating barrier is investigated for various shapes of the barrier. The problem of resonant activation is revisited with the attention on the effect of the barrier shape on optimal value of the mean escape time in the system. The characteristic features of resonant behavior are analyzed for situations when the barrier switches either between different heights representing erection of a barrier and formation of a well, respectively, or it proceeds through "on" and "off" positions.