Sequence dependent circularization of DNAs: a physical model to predict the DNA sequence dependent propensity to circularization and its changes in the presence of protein-induced bending.

A simple physical model based on statistical thermodynamics is proposed to predict the DNA sequence dependent propensity to circularization, even in the presence of bend inducing proteins. Assuming the first order elasticity and an uniform force field in solution, the model requires the evaluation of the ground state energy difference between circular and linear forms as well as the difference of their canonical ensemble average energy on account of curvature and twisting fluctuations. These quantities are analytically obtained using the Parseval equality in the Fourier space and adopting a DNA curvature model previously proposed by us. The circularization propensity as defined by the J factor is obtained in terms of the intrinsic curvature, the persistence length, and the torsional constant. The comparison with the experimental data is very satisfactory in a range of DNA length between 100 and 10000 bp. The model can also be extended to evaluate the sequence dependent energy cost of looping deformation of a DNA tract also in the presence of CAP or other regulatory proteins, repressors, and operators, as in the first step of the transcription mechanism as well as to evaluate "allosteric" effects in protein binding on topologically constrained DNAs.