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

Odijk excluded volume interactions during the unfolding of DNA confined in a nanochannel

We report experimental data on the unfolding of human and E. coli genomic DNA molecules shortly after injection into a 45 nm nanochannel. The unfolding dynamics are deterministic, consistent with previous experiments and modeling in larger channels, and do not depend on the biological origin of the DNA. The measured entropic unfolding force per friction per unit contour length agrees with that predicted by combining the Odijk excluded volume with numerical calculations of the Kirkwood diffusivity of confined DNA. The time scale emerging from our analysis has implications for genome mapping in nanochannels, especially as the technology moves towards longer DNA, by setting a lower bound for the delay time before making a measurement.

Effects of Polymer Length and Salt Concentration on the Transport of ssDNA in Nanofluidic Channels

Electrokinetic phenomena in micro/nanofluidic channels have attracted considerable attention because precise control of molecular transport in liquids is required to optically and electrically capture the behavior of single molecules. However, the detailed mechanisms of polymer transport influenced by electroosmotic flows and electric fields in micro/nanofluidic channels have not yet been elucidated. In this study, a Langevin dynamics simulation was used to investigate the electrokinetic transport of single-stranded DNA (ssDNA) in a cylindrical nanochannel, employing a coarse-grained bead-spring model that quantitatively reproduced the radius of gyration, diffusion coefficient, and electrophoretic mobility of the polymer. Using this practical scale model, transport regimes of ssDNA with respect to the ζ-potential of the channel wall, the ion concentration, and the polymer length were successfully characterized. It was found that the relationship between the radius of gyration of ssDNA and the channel radius is critical to the formation of deformation regimes in a narrow channel. We conclude that a combination of electroosmotic flow velocity gradients and electric fields due to electrically polarized channel surfaces affects the alignment of molecular conformations, such that the ssDNA is stretched/compressed at negative/positive ζ-potentials in comparatively low-concentration solutions. Furthermore, this work suggests the possibility of controlling the center-of-mass position by tuning the salt concentration. These results should be applicable to the design of molecular manipulation techniques based on liquid flows in micro/nanofluidic devices.

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pH-profile in the middle of the channel. Skew category Brownian motion and non-Gaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called "diffusing diffusivity." In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D.

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

We have developed a multi-scale model describing the dynamics of internal segments of DNA in nanochannels used for genome mapping. In addition to the channel geometry, the model takes as its inputs the DNA properties in free solution (persistence length, effective width, molecular weight, and segmental hydrodynamic radius) and buffer properties (temperature and viscosity). Using pruned-enriched Rosenbluth simulations of a discrete wormlike chain model with circa 10 base pair resolution and a numerical solution for the hydrodynamic interactions in confinement, we convert these experimentally available inputs into the necessary parameters for a one-dimensional, Rouse-like model of the confined chain. The resulting coarse-grained model resolves the DNA at a length scale of approximately 6 kilobase pairs in the absence of any global hairpin folds, and is readily studied using a normal-mode analysis or Brownian dynamics simulations. The Rouse-like model successfully reproduces both the trends and order of magnitude of the relaxation time of the distance between labeled segments of DNA obtained in experiments. The model also provides insights that are not readily accessible from experiments, such as the role of the molecular weight of the DNA and location of the labeled segments that impact the statistical models used to construct genome maps from data acquired in nanochannels. The multi-scale approach used here, while focused towards a technologically relevant scenario, is readily adapted to other channel sizes and polymers.

The polymer physics of single DNA confined in nanochannels

In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.

Kirkwood diffusivity of long semiflexible chains in nanochannel confinement

We compute the axial diffusivity of asymptotically long semiflexible polymers confined in square channels. Our calculations employ the Kirkwood approximation of the mobility tensor by combining computational fluid dynamics (CFD) calculations of the hydrodynamic tensor in channel confinement with pruned-enriched Rosenbluth method (PERM) simulations of a discrete wormlike chain model. Three key results emerge from our study. First, for the classic de Gennes regime, we confirm that Brochard and de Gennes' blob theory correctly predicts the scaling of the axial diffusivity, contrary to the conclusions of previous analyses. Second, for the extended de Gennes regime, we show that a modified blob theory, which has been used to incorporate the effect of local stiffness on DNA diffusion in nanoslits, explains the deviation from the prediction of classic blob theory for diffusion in nanochannels. Third, we provide a calculation similar to the modified blob theory to explain the relative insensitivity of the diffusivity to channel size for channels between the extended de Gennes regime and the Odijk regime, which is the most relevant regime for experiments and technological applications of DNA confinement in nanochannels. Our results are not only relevant to the dynamics of confined semiflexible polymers such as DNA, but also reveal interesting analogies between confinement in channels and slits.

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

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.