A new,computationally efficient Monte Carlo approach has been developed to estimate the ring-closure properties of short,realistically modeled DNA chains.The double helix is treated at the level of base-pair steps using an elastic potential that accounts for the sequence-dependent variability in the intrinsic structure and elastic moduli of the base-pair steps,including the known coupling of conformational variables.Rather than using traditional Metropolis-Monte Carlo techniques to generate representative configurations,a Gaussian sampling method is introduced to construct three-dimensional structures from linear combinations of the rigid-body parameters defining the relative orientation and displacement of successive base pairs.The computation of the J factor,the well-known ratio of the equilibrium constants for cyclization vs bimolecular association of a linear molecule,takes into account restrictions on the displacement and directions of the base pairs joined in ring closure,including the probability that the end-to-end vector is null and the terminal base pairs coincide.The increased sample sizes needed to assess the likelihood that very short chains satisfy these criteria are attained using the Alexandrowicz half-chain sampling enhancement technique in combination with selective linkage of the two-half-chain segments.The method is used to investigate the cyclization properties of arbitrary-length DNA with greatly enhanced sampling sizes,i.e.,0(10~(14))configurations,and to estimate J factors lower than 0.1 pM with high accuracy.The methodology has been checked against classic theoretical predictions of the cyclization properties of an ideal,inextensible,naturally straight,DNA elastic rod and then applied to investigate the extent to which one can account for the unexpectedly large J factors of short DNA chains without the need to invoke significant distortions of double helical structure.Several well-known structural features of DNA- including the presence of intrinsic curvature,roll-twist coupling,or enhanced pyrimidine-purine deformability-bring the computed Jfactors in line with the observed data.Moreover,periodically distributed roll-twist coupling reduces the magnitude of oscillations in J,seen in plots of J vs chain length,to the extent found experimentally.
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