cgNA+min: computation of sequence-dependent dsDNA energy-minimizing minicircles

The recently developed cgNA+ model of double-stranded DNA (dsDNA) accurately predicts equilibrium distributions (in solution) of linear dsDNA fragments of arbitrary sequence, expressed in enhanced Curves+ internal coordinates. This article introduces cgNA+min, a computational framework built on the cgNA+ energy to compute sequence-dependent energy-minimizing configurations of topologically closed dsDNA minicircles with a range of linking numbers. We employ a chain rule to re-express the cgNA+ energy in absolute coordinates using quaternions, which drastically simplifies the minicircle looping constraint. Additionally, a semi-analytic method generates sequence-dependent, reasonably low-energy, initial guesses for minicircles of prescribed link, which enhances efficiency of our energy-minimizing algorithm. Leveraging this efficiency, we analyze 190K random DNA sequences with lengths from 88 to 106 base pairs, revealing multiplicities over different values of link, and of distinct energy minimizers at the same link. The length dependence of the sequence-average of cgNA+min predicted minicircle energies at prescribed link matches closely to the twisted worm-like chain model, while the variation of those energies with sequence at fixed length and link is shown to be comparatively large. For various specific sequence families, we verify that cgNA+min minicircle energies closely correlate with energies derived from experimentally measured cyclization $J$-factors.