Probabilistic model of the chain-like structures' translocation through the pore in membrane

The paper is devoted to the analysis of the translocation of the chain-like structures (CLS) through the pore in membrane. It focuses on the so-called passage time and the principal aim is to propose a proper probabilistic model for its distribution. The article starts with some preliminary results concerning stochastic processes. Next, an approximate analytic solution of the considered problem that was received in literature is presented. It is known that the resulting probability distribution of the passage time manifests some important shortcomings. Thus it is important to find a reasonable alternative. It is argued here that the beta Moyal probability distribution can be a good candidate for approximation of the theoretical distribution in various interesting situations. In this paper, two different problems connected with CLS translocation are considered. For both problems the theoretical distributions are known from literature and in both situations the beta Moyal approximations turn out to be very satisfactory.