J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain end boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length (N) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.