Topology in Molecular Biology

40 A. Vologodskii

refers to the coordinates that define the mutual geometry of the specific sites.
AlthoughU(x) can greatly increase the probability of the site juxtaposition,
it does not disturb the conditional distribution sinceU(x) has the same value
for all conformations where the sites are juxtaposed (x=x 0 ). Indeed, the
statistical weights of all conformations with the juxtaposed sites will be mul-
tiplied by the same factor, exp(−U(x 0 )/kT). The efficiency of the approach,
which is called Umbrella method, depends on proper choice of the potential
U(x). The method was recently applied for the simulation of the juxtaposition
of specific sites in supercoiled DNA [54].

Acknowledgment

The author thanks the Max Plank Institute of Physics of the Complex Systems
for their hospitality during the workshop on “Topology in Condensed Matter”
Dresden 2002.

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