Correlation anisotropy and stiffness of DNA molecules confined in nanochannels

Compression and Stretching of Single DNA Molecules under Channel Confinement

We study the compression and extension response of single dsDNA (double-stranded DNA) molecules confined in cylindrical channels by means of Monte Carlo simulations. The elastic response of micrometer-sized DNA to the external force acting through the chain ends or through the piston is markedly affected by the size of the channel. The interpretation of the force (f)-displacement (R) functions under quasi-one-dimensional confinement is facilitated by resolving the overall change of displacement ΔR into the confinement contribution ΔR_D and the force contribution ΔR_f. The external stretching of confined DNA results in a characteristic pattern of f-R functions involving their shift to the larger extensions due to the channel-induced pre-stretching ΔR_D. A smooth end-chain compression into loop-like conformations observed in moderately confined DNA can be accounted for by the relationship valid for a Gaussian chain in bulk. In narrow channels, the considerably pre-stretched DNA molecules abruptly buckle on compression by the backfolding into hairpins. On the contrary, the piston compression of DNA is characterized by a gradual reduction of the chain span S and by smooth f-S functions in the whole spatial range from the 3d near to 1d limits. The observed discrepancy between the shape of the f-R and f-S functions from two compression methods can be important for designing nanopiston experiments of compaction and knotting of single DNA in nanochannels.

Force-displacement relations at compression of dsDNA macromolecules

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

Twist-bend coupling and the statistical mechanics of the twistable wormlike-chain model of DNA: Perturbation theory and beyond

The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling G between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here the effect of G on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness C_{eff} for small twist-bend coupling. We find that the "bare" G is "screened" by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with G=0 but with long-wavelength bending and twisting rigidities that are shifted by G-dependent amounts. Using results for torsional and bending rigidities for freely fluctuating DNA, we show how our perturbative results can be extended to a nonperturbative regime. These results are in excellent agreement with numerical calculations for Monte Carlo "triad" and molecular dynamics "oxDNA" models, characterized by different degrees of coarse graining, validating the perturbative and nonperturbative analyses. While our theory is in generally good quantitative agreement with experiment, the predicted torsional stiffness does systematically deviate from experimental data, suggesting that there are as-yet-uncharacterized aspects of DNA twisting-stretching mechanics relevant to low-force, long-molecule mechanical response, which are not captured by widely used coarse-grained models.