Analytical and numerical studies of sequence dependence of passage times for translocation of heterobiopolymers through nanopores

We consider chaperone-assisted translocation of biopolymers with two distinct monomers or bases $A$ and $B$⁠, with the size of the chaperones being $λσ$⁠, where $σ$ is a monomer’s size. The probability that $A$ and $B$ are neighbors in the biopolymer is $PAB$⁠. A master equation is used, together with the detailed-balanced condition, in order to derive analytical results for the statistics of the first-passage times of the biopolymer as a function of $PAB$⁠, $λ$⁠, and the biopolymer’s configuration. Monte Carlo simulations have also been carried out in order to compute the same quantities for biopolymers with 100–900 monomers and several $λ$⁠. The results indicate nontrivial dependence of the variance of the translocation times on the biopolymer’s composition. It is also shown that measurements of the first two moments of the biopolymer’s first-passage time distribution provide information on its length and ordering. Moreover, the probability density function $Q(t)$ of the first-passage times is almost Gaussian for small chaperone size $λ$⁠, but becomes non-Gaussian as $λ$ increases. At large times, $Q(t)$ decays exponentially.