Topology in Molecular Biology

3 Monte Carlo Simulation of DNA Topological Properties 29

agree extremely well over the whole range ofσand NaCl concentrations stud-
ied, even though the range ofBvalues exceeds two orders of magnitude. The
data make it clear that conformations of supercoiled DNA vary greatly over
this range of sodium ion concentrations. This work convincingly proved that
the simulation is capable of accurately predicing conformational properties of

10.3.2 Formula Cˇalugˇareanu and Supercoiled DNA

3.4 DNA Model................................................

The DNA model represents a discrete analog of the wormlike chain that also
accounts for DNA torsional rigidity, excluded volume, and intersegment elec-
trostatic interaction [8, 30–32]. A DNA molecule composed ofnKuhn statis-
tical lengths is modeled as a closed chain consisting ofnrigid segments that
are cylinders of equal length wherekis a computational parameter of our
choice (Fig. 3.6).
The bending elastic energy of the chain,n, is computed as

Eb=kBTg

∑kn

i=1

θ^2 i, (3.8)

where the summation extends over all the joints between the elementary seg-
ments,

Eb=

g

2

∑kn

i=1

θ^2 i

is the angular displacement of segment

Eb=

g

2

∑kn

i=1

θ^2 i

relative to segment

Eb=

g

2

∑kn

i=1

θ^2 i,

Fig. 3.6.The model of double-stranded DNA. The length of the cylinders can vary,
although it usually equals 30 base pairs of the double helix (1/5 of the persistence
length)