Abstract
We present a theoretical study of the interaction between a protein (diffusing particle) with chromatin (polymer chain). Each monomer is a trap where a particle can transiently bind. We derive novel formulas for the transition rate between monomer sites, given a specific polymer configuration, and find that a particle is likely to rapidly rebind many times to its release site, before moving to another. The reattachment probability is larger when the local density around the release site is smaller. Interestingly, for an equilibrated polymer, the transition probability decays as a power-law for close monomer-to-monomer distances and reaches an asymptotic value for faraway ones. By computing the transition rate between monomers, we show that the problem of facilitated search by a protein can be mapped to a continuous time Markov chain, which we solve. Our findings suggest that proteins may be locally trapped for a time much longer than their dissociation time, while their overall motion is ergodic. Our results are corroborated by Brownian simulations.
