A continuum rod model of sequence-dependent DNA structure

Abstract

Experimentally motivated parameters from a base-pair-level discrete DNA model are averaged to yield parameters for a continuum elastic rod with a curved unstressed shape reflecting the local DNA geometry. The continuum model permits computations with discretization lengths longer than the intrinsic discretization of the base-pair model, and, for this and other reasons, yields an efficient computational formulation. Obtaining continuum stiffnesses is straightforward, but obtaining a continuum unstressed shape is hindered by the ‘‘noisy’’ small-scale structure and rapid helix twist of the discrete unstressed shape. Filtering of the discrete data and an analytic transformation from the true normal-vector field to a natural (untwisted) frame allows a stable continuum fit. Equilibrium energies of closed rings predicted by the continuum model are found to match the energies of the underlying discrete model to within 0.5%. The model is applied to a set of 11 short DNA molecules (≊ 150 bp) and properly distinguishes their cyclization probabilities (J factors) when compared both to experimental cyclization rates and to Monte Carlo simulations. The continuum model does not include entropic contributions to the free energy. However, because of its rapid and accurate computation of internal energy, the continuum model should, when combined with further work on entropic effects, be a useful method for computing experimental DNA free energies.

Flexibility and Control of Protein–dna Loops

“…Sequence-dependent DNA bending was described by a scaled wedge angle model. 39,40 The DNA helical repeat (hr), torsional modulus (C), and persistence length Each set of flexibility parameters required 88 individual simulations corresponding to combinations of inner and outer loop, hinge angles, and loop types. Eight molecules were simulated, but the total number of simulations required was reduced because molecules with the same sticky ends (BssH II or BsaH I) have the same outer loop for any inner loop at a given hinge angle, inner loop structure (for 7C16, 9C14, or 11C12) is the same for any outer loop, and length variant results were derived from the parent 9C14.…”

Statistical mechanics of triangulated ribbons

“…Together with the parameter setû i (s), which determines whether the stressfree reference configuration includes spontaneous curvature and twist, the elastic part of the Hamiltonian is usually defined by quadratic terms in u i (s) −û i (s) [11,12,13,14,15,16,17,18,19,20,24].…”

“…The model mostly used to interpret recent experimental data of micromechanical manipulations of single DNA chains [3,4,5,6,7,8] is that of the Kratky-Porod wormlike chain in which the polymer flexibility is determined by a single length, the persistence length l p . Generalizations account for the chain helicity and coupling terms between bending, stretching, and twisting allowed by symmetry [9,10,11,12,13,14,15,16,17,18,19,20]. All these continuum models of DNA neglect the doublestranded structure of DNA and one may ask, if this feature could not cause qualitative different behavior.…”

Molecular simulations of cellular processes

“…Because of the aggressive simplifications, mesoscale models are typically suitable to explore genome organization or macromolecular diffusion over timescales longer than the ones of internal fluctuations. Continuous models are based on equations for the probability of observing a target quantity and they can access the longest timescales, being computationally very convenient (Manning et al 1996;Argudo et al 2016).…”