24 A. Vologodskii
are homogeneous, thin, and long. They can be easy converted from linear
to circular form. Circular DNA molecules in different topological states can
be separated by gel electrophoresis and, thus, the distributions of topological
states can be studied experimentally. The methods of experimental manip-
ulation with DNA molecules, developed in the last few decades, allows one
to easily perform many things that are beyond the imagination of traditional
polymer chemistry and physics. These features of DNA molecules can be used
to study general properties of polymer chains, and our ability to simulate
these properties with high accuracy helps greatly in such studies. The compu-
tational methods, which allow one to simulate large-scale statistical properties
of DNA, are a subject of this review. Major attention is paid to the simula-
tions to topological properties of circular DNA. Therefore we begin the review
with a brief description of the basic concepts related to DNA topology. Then
we illustrate, by comparison with the experimental data, how well conforma-
tional properties of circular DNA can be computed. Detailed description of
the computational methods will follow the analysis of the basic DNA model.
The review is restricted by Monte Carlo simulation of the equilibrium DNA
properties, which has a wider use than the dynamic simulation based on the
Brownian dynamics method [20–23], for example).
3.2 Circular DNA and Supercoiling
The circular form of DNA is widespread in nature. In this form each of the two
strands that make up the DNA molecule is closed in on itself. A diagrammatic
view of closed circular DNA is presented in Fig. 3.1.
The two strands of the double helix in closed circular DNA are linked. In
topological terms, the links between the strands of the double helix belong to
Fig. 3.1.Diagram of closed circular DNA. Two strands of the double helix are
shown together with the base pairs which are perpendicular to the helix axis. The
linking number of the complementary strands, Lk, equals 20