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Is it possible to extract the size and structure of chromosomal territories (confined domain) from the encounter frequencies of chromosomal loci? To answer this question, we estimate the mean time for two monomers located on the same polymer to encounter, which we call the mean first encounter time in a confined microdomain (MFETC). We approximate the confined domain geometry by a harmonic potential well and obtain an asymptotic expression that agrees with Brownian simulations for the MFETC as a function of the polymer length, the radius of the confined domain, and the activation distance radius e at which the two searching monomers meet. We illustrate the present approach using chromosome capture data for the encounter rate distribution of two loci depending on their distances along the DNA. We estimate the domain size that restricts the motion of one of these loci for chromosome II in yeast.

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).