The tendency for relatively short (<500 base-pair) DNA molecules to circularize in the presence of DNA ligase is a sensitive function of both the lateral and torsional flexibilities of the molecules being studied. This tendency is reflected in a quantity known as the j-factor, which is determined experimentally by measuring the relative rates of circle and linear dimer formation at a specified concentration of linear monomer. Shimada & Yamakawa have provided an analytical representation j that takes account of DNA molecules whose ends are not torsionally aligned. Their approach, however, assumes that contributions from helix writhe are small. Using a Monte Carlo approach for the determination of j, thereby avoiding any assumptions regarding writhe, we demonstrate that the computed, torsion angle-averaged quantity, 〈j〉, is exactly reproduced by the corresponding Shimada & Yamakawa quantity for all lengths examined. However, for DNA molecules having lengths that are substantially greater than the persistence length, P, the analysis of experimental ring-closure data using j (Shimada & Yamakawa) may lead to underestimates for the torsional elastic constant C. We demonstrate that no single set of values for P, C and the helical repeat (hR) can produce a reasonable fit of the computed j curve to the experimental values of Shore et al. This observation suggests that P, C and/or hR vary within the set of DNA molecules studied by those authors. The current computational analysis considers the effects on j of single or multiple bends in the helix axis. For single, centrally located bends, the shift in the distribution of end-to-end separations to smaller values is nearly offset by the less favorable polar alignment of the ends of the chain; the net effect being a modest change in j that is not a monotonic function of the bend angle. In contrast, polar alignment, and hence j, can be enhanced dramatically for molecules containing multiple, phased bends. However, for studies of the distribution of circle sizes formed from ligation of bend-containing DNA oligomers, the DNA lengths giving rise to maximal j values are smaller than predicted on the basis of the number of bends and the per-bend angle. This last result suggests that such studies may yield apparent bend angles that are too large.
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