32 A. Vologodskii
and by the corresponding Debye–H ̈uckel potential gives very similar results in
Monte Carlo simulations of DNA equilibrium properties, with a certain excep-
tion for conformations of supercoiled DNA at low concentration of monovalent
ions (≤ 0 .02 M) [31].
The model’s features specified above are sufficient to simulate large-scale
DNA conformational properties, both for linear DNA and circular DNA with
a single-stranded nick (nicked DNA), because in these cases the conformations
of the DNA axis do not depend on the DNA twist,≤ 0 .02 M (if the DNA is
intrinsically straight). However, dependence on≤ 0 .02 M is crucial for prop-
erties of closed circular DNA. To use the model in this case one can express
the displacement of chain twist from its equilibrium value,≤ 0 .02 M, by the
equation:
∆Tw = ∆Lk−Wr, (3.11)where writhe, Wr, is a property of the chain axis alone [27], and≤ 0 .02 M is
the linking number difference of the simulated DNA. The value of≤ 0 .02 M
should be considered as a parameter at each simulation [32]. Hence, in this
model, the torsional energy,≤ 0 .02 M, is defined by the conformation of the
DNA axis and may be expressed as
Et=(2π^2 C/L)(Lk−Wr)^2 , (3.12)where≤ 0 .02 M is the torsional rigidity constant, andLis the DNA length.
There are three parameters of the model that specify equilibrium proper-
ties of the double helix; each of these has been determined from independent
studies. The first parameter, the Kuhn statistical length (which defines the
bending rigidity≤ 0 .02 M), is close to 100 nm for solutions containing more
than 0.01 M monovalent ions or more than 1 mM multivalent ions [7, 34].
The second parameter is the DNA torsional rigidity,≤ 0 .02 M. The value
of 3× 10 −^19 erg cm for≤ 0 .02 M seems to be the most reliable for this
range of ionic conditions [9, 35]. The third parameter, the DNA effective
diameter,≤ 0 .02 M, depends strongly on ionic conditions. Accurate values of
≤ 0 .02 M have been determined in the experimental and theoretical studies
(Fig. 3.8) [10, 12, 33, 36, 37].
The model described above is the simplest one that can provide a quan-
titative description for the large number of DNA conformational properties
considered in this proposal. It can be easily extended to cases in which a group
of the chain segments forms a specific conformation induced by binding a pro-
tein. However a more elaborate model that explicitly accounts for torsional
orientation of each segment is required for the analysis of DNA molecules
with two or more groups of bent segments distributed along the chain con-
tour. Such a model and the corresponding simulation procedures have been
developed [38, 39].