Evaluation of the Kirkwood approximation for the diffusivity of channel-confined DNA chains in the de Gennes regime

Abstract

We use Brownian dynamics with hydrodynamic interactions to calculate both the Kirkwood (short-time) diffusivity and the long-time diffusivity of DNA chains from free solution down to channel confinement in the de Gennes regime. The Kirkwood diffusivity in confinement is always higher than the diffusivity obtained from the mean-squared displacement of the center-of-mass, as is the case in free solution. Moreover, the divergence of the local diffusion tensor, which is non-zero in confinement, makes a negligible contribution to the latter diffusivity in confinement. The maximum error in the Kirkwood approximation in our simulations is about 2% for experimentally relevant simulation times. The error decreases with increasing confinement, consistent with arguments from blob theory and the molecular-weight dependence of the error in free solution. In light of the typical experimental errors in measuring the properties of channel-confined DNA, our results suggest that the Kirkwood approximation is sufficiently accurate to model experimental data. V C 2015 AIP Publishing LLC. [http://dx

Modeling the relaxation of internal DNA segments during genome mapping in nanochannels

“…Each bead also has a hydrodynamic radius a that is generally not equal to the effective width and, for DNA, conveniently satisfies the inequality a < w. 66 The standard PERM simulations for a confined chain 27 furnish the average extension of the chain in the axial direction, X, and the variance about the mean, dX 2 , as a function of L. We also use PERM simulations to compute a Kirkwood diffusivity D K in the axial direction, 44 using a grid-based method to obtain the hydrodynamic interactions between segments and between the DNA and the walls. 45 We have recently shown that the Kirkwood approximation improves as confinement increases, 67 and we obtained a good agreement between experiments and simulations for the relaxation time of the entire DNA chain by invoking the Kirkwood approximation. 42 For our purposes here, it proves convenient to recast the Kirkwood diffusivity as an axial friction coefficient f P , where the superscript denotes a quantity obtained from PERM simulations.…”

Kirkwood Diffusivity of Long Semiflexible Chains in Nanochannel Confinement

“…However, recent work from our group indicates that the deviation in the value of the Kirkwood diffusivity from the “long-time” diffusivity given by Einstein’s theory is suppressed in channel confinement. 34 This result is encouraging in hindsight, as the Kirk-wood approximation has been used extensively in scaling theories for polymer diffusion in confinement. 1,6,8,22 …”

“…We account for the effect of HI through the pre-averaging approximation in Kirkwood-Riseman theory, 33 which has recently been shown to provide reliable estimates of diffusivity in channel confinement. 34 By computing the diffusivity for asymptotically long chains for several values of l p / w , we show that the blob theory proposed by Brochard and de Gennes 8 is valid in the classic de Gennes regime. We further develop a modified blob theory inspired by the work of Dai et al 22 for the scaling of diffusivity in the extended de Gennes regime, and demonstrate that this theory captures the deviation of our simulation data from blob theory in this regime.…”

Odijk Excluded Volume Interactions during the Unfolding of DNA Confined in a Nanochannel

“…While the Kirkwood approximation does not account for certain correlations in the hydrodynamics, simulations indicate that the Kirkwood approximation is increasingly more accurate as the confinement increases. 58 The hydrodynamic simulations begin to deviate from Eq. 10 near α = 0.8, where α can refer to either the folded or unfolded region.…”