28 A. Vologodskii
Fig. 3.4.Probability of linkage between two relaxed DNA molecules 7,000 and
10,000 base pairs in length as a function of the distance between the chains centers
of mass,R. The function strongly depends on solution ionic conditions.p(R) shown
in the figure corresponds to near physiological ionic conditions. For each value of
Ra fraction of conformations of two chains is forbidden because of overlap of one
chain with the other. Since this fraction increases sharply asRdiminishes, there is
a decrease ofp(R) at small values ofR
Fig. 3.5.Measured and simulated probabilities of catenation as a function of su-
percoiling [11]. The experimental values ofB(open symbols) are shown together
with calculated results (filled symbols) for NaCl concentrations of 0.02 M (U, P), ̈
0.2 M (E, J). The large changes of conformational properties of supercoiled DNA
with ionic conditions result, in good approximation, from the change of interseg-
ment electrostatic interactions, specified by the variation DNA effective diameter
(see below)
The value ofBdoes not depend on DNA concentration and reflects only
the properties of a particular circular DNA. It depends on the lengths of both
DNAs, the superhelix density, and on the ionic conditions, which change the
conformational properties of supercoiled DNA.
Figure 3.5 presents the measured and simulated values ofBfor solutions of
two different concentrations of NaCl (0.02 M, 0.2 M) as a function of the DNA
superhelical density [11]. Note that the simulated and measured values ofB