Consequences of local inter-strand dehybridization for large-amplitude bending fluctuations of double-stranded DNA

The wormlike chain (WLC) model of DNA bending accurately reproduces single-molecule force-extension profiles of long (kilobase) chains. These bending statistics over large scales do not, however, establish a unique microscopic model for elasticity at the 1-10 bp scale, which holds particular interest in biological contexts. Here we examine a class of microscopic models which allow for disruption of base pairing (i.e., a melt' or kink’, generically an `excitation’) and consequently enhanced local flexibility. We first analyze the effect on the excitation free energy of integrating out the spatial degrees of freedom in a wormlike chain. Based on this analysis, we present a formulation of these models that ensures consistency with the well-established thermodynamics of melting in long chains. Using a new method to calculate cyclization statistics of short chains from enhanced-sampling Monte Carlo simulations, we compute J-factors of a meltable wormlike chain (MWLC) over a broad range of chain lengths, including very short molecules (30 bp) that have not yet been explored experimentally. For chains longer than about 120 bp, including most molecules studied to date in the laboratory, we find that melting excitations have little impact on cyclization kinetics. Strong signatures of melting, which might be resolved within typical experimental scatter, emerge only for shorter chains.

💡 Research Summary

This paper investigates how local inter‑strand dehybridization—commonly referred to as a “melt” or “kink”—affects the bending elasticity of double‑stranded DNA on the 1–10 bp scale, a regime that is biologically relevant but not uniquely constrained by the well‑validated wormlike chain (WLC) model. The authors begin by noting that while the WLC accurately reproduces force‑extension curves for kilobase‑length DNA and predicts cyclization rates for medium‑length fragments, it offers no guidance on the microscopic mechanics governing large‑amplitude bends in very short segments. To address this gap, they extend the WLC to a meltable wormlike chain (MWLC) in which each node can exist in either a hybridized (normal) state or a locally melted state. In the melted state the persistence length is dramatically reduced, and an additional free‑energy penalty Δµ(T) is incurred for breaking base pairs at zero curvature.

A key theoretical contribution is the analysis of how integrating out the spatial (curvature) degrees of freedom renormalizes the effective free energy of a melt. The authors show that the “bare” Δµ used in earlier formulations (e.g., Yan and Marko) underestimates the entropic stabilization provided by the additional configurational freedom of a melted segment. Consequently, the original parameterization double‑counts the entropic gain and becomes inconsistent with bulk DNA melting thermodynamics. By re‑parameterizing Δµ to match experimentally measured melting enthalpies and entropies of long DNA, the MWLC model becomes thermodynamically self‑consistent.

To test the impact of these excitations on cyclization kinetics, the authors develop an enhanced‑sampling Monte Carlo (MC) method that efficiently samples the rare, highly bent conformations required for loop closure. Traditional MC or analytical approaches become prohibitively expensive for short chains because the probability of the ends meeting with the correct orientation is vanishingly small. The new algorithm applies a bias to the end‑to‑end distance and the join angle, then reweights the sampled configurations to obtain unbiased estimates of the J‑factor, the equilibrium measure of cyclization propensity. This technique incurs essentially the same computational cost for both long (hundreds of base pairs) and short (as few as 30 bp) DNA fragments.

Simulation results reveal a clear length‑dependent effect of melting. For chains longer than roughly 120 bp—covering the majority of DNA fragments studied experimentally—the inclusion of melt excitations changes the J‑factor by less than the typical experimental scatter; the MWLC predictions collapse onto the standard WLC curve. Only when the contour length falls below ~120 bp does the presence of melts appreciably raise the J‑factor, with the most pronounced enhancement occurring for 60–80 bp fragments, where the J‑factor can be up to an order of magnitude larger than the WLC prediction. This increase, however, is far smaller than the 10⁵‑fold enhancement reported by Cloutier and Widom for ~100 bp DNA, indicating that melts alone cannot account for those anomalously high cyclization rates.

The authors discuss the broader implications of these findings. First, the bending elasticity of DNA on scales larger than the persistence length is robust against local melting; the effective persistence length of the MWLC remains close to that of the bare WLC once the correct thermodynamic penalty is applied. Second, while melts provide a plausible mechanism for modestly increased flexibility in very short DNA, additional factors—such as protein‑induced kinking, electrostatic interactions, or sequence‑dependent structural heterogeneity—must be invoked to explain the extreme cyclization efficiencies observed in some experiments. Finally, the work underscores the importance of correctly accounting for entropic contributions when coarse‑graining polymer models: neglecting the renormalization of excitation free energies can lead to double‑counting and erroneous predictions.

In summary, this study (i) formulates a thermodynamically consistent meltable wormlike chain model, (ii) demonstrates how integrating out spatial degrees of freedom lowers the effective melt free energy, (iii) introduces a versatile enhanced‑sampling MC method for computing J‑factors across a wide range of DNA lengths, and (iv) shows that, after proper parameterization, melts have negligible impact on cyclization for DNA longer than ~120 bp but can modestly boost cyclization of shorter fragments. The results provide a rigorous baseline for future investigations into DNA bending mechanics and suggest that additional, possibly protein‑mediated, mechanisms are required to reconcile theory with the most extreme experimental observations.