title: Computation of the mean first-encounter time between the ends of a polymer chain.
abstract: Using a novel theoretical approach, we study the mean first-encounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however, to incompatible results. We construct here for the first time a general theory that allows us to compute the MFET. The method is based on estimating the mean time for a Brownian particle to reach a narrow domain in the polymer configuration space. In dimension two and three, we find that the MFET depends mainly on the first eigenvalue of the associated Fokker-Planck operator and provide precise estimates that are confirmed by Brownian simulations. Interestingly, although many time scales are involved in the encounter process, its distribution can be well approximated by a single exponential, which has several consequences for modeling chromosome dynamics in the nucleus. Another application of our result is computing the mean time for a DNA molecule to form a closed loop (when its two ends meet for the first time).
authors.affiliation: Institute of Biology, Ecole Normale Supérieure, Paris, France.
authors.forename: A
authors.initials: A
authors.lastname: Amitai
authors.forename: I
authors.initials: I
authors.lastname: Kupka
authors.forename: D
authors.initials: D
authors.lastname: Holcman
mesh_terms: D008958:Models, Molecular; D009038:Motion; D011108:Polymers / Q000737:chemistry*; D011336:Probability; D013997:Time Factors
chemical_list: D011108:Polymers