  The time for a DNA sequence to find its homologous depends on a long random
search process inside the cell nucleus. Using polymer models, we model and
compute here the mean first encounter time (MFET) between two sites located on
two different polymer chains and confined by potential wells. We find that
reducing the potential (tethering) forces results in a local polymer
decondensation near the loci and numerical simulations of the polymer model
show that these changes are associated with a reduction of the MFET by several
orders of magnitude. We derive here new asymptotic formula for the MFET,
confirmed by Brownian simulations. We conclude that the acceleration of the
search process after local chromatin decondensation can be used to analyze the
local search step during homology search.
