Dependence of
j-factors on the length of DNA fragments. The
j-factor values were measured for intact DNA fragments (○) and for same fragments with a 4-nt-long gap (•). The sequence of the fragments is shown in Fig. 2 except for a few point mutations/deletions that were introduced to change the fragment length. The straight line corresponds to the theoretical
j-factor values calculated for the fragments with gaps. The gap bending rigidity, g
gap, was adjusted to yield the best fit between the theoretical curve and experiment (
solid line). To illustrate the sensitivity of the theoretical dependence to g
gap, we performed the computations for two more values of g
gap(
dotted lines),

and

where

is the best-fit value. The computation assumes that all torsional orientations of the fragment ends are equally probable (see Materials and Methods for details). The experimental data for intact fragments (
without gaps) were approximated by the theoretical dependence (Shimada and Yamakawa, 1984) by adjusting the values of three parameters,
a,
γ, and
C. The best fit (
solid line) corresponds to
a = 48.5 nm,
γ = 10.49 bp/(helix turn), and
C = 2.4 × 10
−19 erg × cm.