Topology in Molecular Biology

30 A. Vologodskii

and

Eb=

g

2

∑kn

i=1

θ^2 i

is the bending rigidity constant,kBTis the Boltzmann temperature factor.
The bending constantkBTis defined so that the Kuhn statistical length cor-
responds tokBTrigid segments [30]:

k=

1+〈cosθ〉

1 −〈cosθ〉

, (3.9)

where

〈cosθ〉=

∫π

0 cosθsinθexp(−gθ

(^2) )dθ
∫π
0 sinθexp(−gθ
(^2) )dθ. (3.10)
The value
〈cosθ〉=
∫π
0 cosθsinθexp(−gθ
(^2) )dθ
∫π
0 sinθexp(−gθ
(^2) )dθ
can be found as by numerical solution of (3.10).
Replacement of the continuous wormlike chain with a discrete chain con-
sisting of
〈cosθ〉=
∫π
0 cosθsinθexp(−gθ
(^2) )dθ
∫π
0 sinθexp(−gθ
(^2) )dθ
hinged rigid segments is an approximation that improves as
〈cosθ〉=
∫π
0 cosθsinθexp(−gθ
(^2) )dθ
∫π
0 sinθexp(−gθ
(^2) )dθ
increases. The computer time needed for a simulation increases approximately
as
(
〈cosθ〉=
∫π
0 cosθsinθexp(−gθ
(^2) )dθ
∫π
0 sinθexp(−gθ
(^2) )dθ

) 2

.