Effect of confinement on DNA dynamics in microfluidic devices

Modulation of DNA conformation in electrolytic nanodroplets

The behavior of deoxyribonucleic acid (DNA) molecules in confinement is of profound importance in various bioengineering and medical applications. In the present study, all-atom molecular dynamics simulation is utilized to investigate the transition of the double-strand DNA (dsDNA) conformation in the electrolytic nanodroplet. Three typical conformations, i.e., C-shaped, folded S-shaped, and double C-shaped, are observed for different droplet sizes and ionic concentrations. To reveal the physics underlying this phenomenon, the characteristics of the dsDNA molecules, such as the overcharging intensity, the end-to-end distance, the radius of gyration, etc. are analyzed in detail based on the numerical results. It is found that the transition can be ascribed to the buckling of the polymer molecules under the compression due to the confinement of the nanodroplet, and it can be modulated by the ionic concentration in the electrolyte. Generally, nanoscale confinement dominates dsDNA behavior over the electrostatic effects in smaller nanodroplets, while the latter becomes more important for larger nanodroplets. This competition results in the persistence length increasing with the nanodroplet radii. Based on these discussions, a non-dimensional elasto-capillary number μ is proposed to classify the dsDNA conformations into three regions.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement

A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.

Modelling DNA extension and fragmentation in contractive microfluidic devices: a Brownian dynamics and computational fluid dynamics approach

Fragmenting DNA into short pieces is an essential manipulation in many biological studies, ranging from genome sequencing to molecular diagnosis. Among various DNA fragmentation methods, microfluidic hydrodynamic DNA fragmentation has huge advantages especially in terms of handling small-volume samples and being integrated into automatic and all-in-one DNA analysis equipment. Despite the fast progress in experimental studies and applications, a systematic understanding of how DNA molecules are distributed, stretched and fragmented in a confined microfluidic field is still lacking. In this work, we investigate the extension and fragmentation of DNA in a typical contractive microfluidic field, which consists of a shear flow-dominated area and an elongational flow-dominated area, using the Brownian dynamics-computational fluid dynamics method. Our results show that the shear flow at the straight part of the microfluidic channel and the elongational flow at the contractive bottleneck together determine the performance of DNA fragmentation. The average fragment size of DNA decreases with the increase of the strain rate of the elongational flow, and the upstream shear flow can significantly precondition the conformation of DNA to produce shorter and more uniform fragments. A systematic study of the dynamics of DNA fragmentation shows that DNA tends to break at the mid-point when the strain rate of elongational flow is small, and the breakage point largely deviates from the midpoint as the strain rate increases. Our simulation of the thorough DNA fragmentation process in a realistic microfluidic field agrees well with experimental results. We expect that our study can shed new light on the development of future microfluidic devices for DNA fragmentation and integrated DNA analysis devices.

Relaxation of surface-tethered polymers under moderate confinement

We study the relaxation of surface-tethered polymers in microchannels under moderate confinement (i.e. h ∼ Rg, where h is the channel height and Rg is the radius of gyration of the polymer) by experiments with fluorescence-marked DNA molecules and coupled lattice-Boltzmann/molecular dynamics simulations. The determined scaling exponent suggests that the relaxation is dominated by Zimm-dynamics with significant intra-chain hydrodynamic interactions. The relaxation of the DNA molecules is slower in shallower channels, indicating a pronounced effect of confinement on the longest relaxation time. An experimental correlation is obtained for the longest relaxation time as a function of the molecular contour length and the channel height. Good agreement between the experimental and the simulation results is found.

DNA Confined in a Nanodroplet: A Molecular Dynamics Study

As a major genetic material, the configuration and the mechanical properties of a double-stranded DNA (dsDNA) molecule in confinement are crucial for the application of nanotechnology and biological engineering. In the present paper, molecular dynamics simulation is utilized to study the configuration of dsDNA in a nanodroplet on a graphene substrate. The results show that the semiflexible dsDNA molecule changes its configuration with radius of gyration ( R_g) of a few nanometers because of the confined space, that is, the R_g of the dsDNA molecule decreases with the reduction of the nanodroplet size. In comparison, the dsDNA in the bulk usually has a persistent length of tens of nanometers. Especially, if the nanodroplet is small enough, the dsDNA molecule might form a loop structure inside. The dsDNA molecule affects the wetting properties of the graphene substrate. It is found that the graphene becomes more hydrophilic in smaller systems containing the dsDNA molecule, whereas for larger droplets, the changes of the contact angles are not significant with the presence of dsDNA. Moreover, the results indicate that for larger droplets, the line tension of the droplet containing DNA is positive and greater than that without DNA; for smaller droplets, the line tension becomes negative because the dsDNA is compressed and bent in the confinement, and has the potential to expand outwards. The worm-like chain model is used to study the bending energy of a dsDNA molecule in a droplet. The results address that the bending energy of the non-loop-structured dsDNA decreases as the droplet becomes larger, and it is larger than that of loop-structured dsDNA, as the loop structure efficiently prevents the DNA from bending in the vertical direction.

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.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

The effect of wall depletion and hydrodynamic interactions on stress-gradient-induced polymer migration

We generalize our recent continuum theory for the stress-gradient-induced migration of polymers [Zhu et al., J. Rheol., 2016, 60, 327-343] by incorporating the effect of solid boundaries on concentration variations. For a model flow in a channel with periodic slip wall velocity, which can in principle be produced by an electric field in the presence of a sinusoidal wall charge, we obtain theoretical results for the steady-state distribution of dilute solutions of polymer dumbbells using a systematic perturbation analysis in Weissenberg number Wi. We find that the presence of a thin wall depletion zone changes the lowest order solution from second to first in Wi and drastically affects the concentration field far from the depletion layer, due both to a coupling of the second derivative of the velocity field to the concentration gradient, and to convection of the polymer-depleted fluid in this layer into the bulk of the fluid. Additional effects induced by wall hydrodynamic interaction (HI) are assessed by incorporating polymer flux from the wall-HI migration theory of Ma and Graham into our continuum theory. We establish the range of validity of our theory by comparing the theoretical results with Brownian dynamics (BD) simulations: excellent agreement is achieved for relatively small molecules, while the theory breaks down when the Gradient number Gd is greater than 0.5, where Gd is the ratio of polymer coil size to the length scale over which the velocity gradient changes. The BD simulations are also extended to the case of long Hookean chains with numbers of springs per chain ranging from 1 to 32, where it is found that for fixed Gd and Wi, the results are nearly identical, showing that all important phenomena are captured by a simple dumbbell model, thus supporting the continuum theory which was derived for the case of dumbbells. In addition, the Stochastic Rotation Dynamics (SRD) method is employed to evaluate the role of HI on the migration pattern, producing effects consistent with the continuum theory incorporating the wall-migration flux. In general, we demonstrate that the polymer concentrates in drastically different regions of the channel depending on Gd and Wi.

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.

Dimensional reduction of duplex DNA under confinement to nanofluidic slits

There has been much interest in the dimensional properties of double-stranded DNA (dsDNA) confined to nanoscale environments as a problem of fundamental importance in both biological and technological fields. This has led to a series of measurements by fluorescence microscopy of single dsDNA molecules under confinement to nanofluidic slits. Despite the efforts expended on such experiments and the corresponding theory and simulations of confined polymers, a consistent description of changes of the radius of gyration of dsDNA under strong confinement has not yet emerged. Here, we perform molecular dynamics (MD) simulations to identify relevant factors that might account for this inconsistency. Our simulations indicate a significant amplification of excluded volume interactions under confinement at the nanoscale due to the reduction of the effective dimensionality of the system. Thus, any factor influencing the excluded volume interaction of dsDNA, such as ionic strength, solution chemistry, and even fluorescent labels, can greatly influence the dsDNA size under strong confinement. These factors, which are normally less important in bulk solutions of dsDNA at moderate ionic strengths because of the relative weakness of the excluded volume interaction, must therefore be under tight control to achieve reproducible measurements of dsDNA under conditions of dimensional reduction. By simulating semi-flexible polymers over a range of parameter values relevant to the experimental systems and exploiting past theoretical treatments of the dimensional variation of swelling exponents and prefactors, we have developed a novel predictive relationship for the in-plane radius of gyration of long semi-flexible polymers under slit-like confinement. Importantly, these analytic expressions allow us to estimate the properties of dsDNA for the experimentally and biologically relevant range of contour lengths that is not currently accessible by state-of-the-art MD simulations.

Self-consistent description of electrokinetic phenomena in particle-based simulations

A new computational method is presented for study suspensions of charged particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins, and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism that is applicable to any geometry and that can be extended to deformable objects. The convection-diffusion equation for the continuum ions is solved simultaneously considering Nernst-Planck diffusion. The method can be applied to systems at equilibrium and far from equilibrium. Its applicability is demonstrated in the context of electrokinetic motion, where it is shown that the ionic clouds associated with individual particles can be severely altered by the flow and concentration, leading to intriguing cooperative effects.

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.

Hydrodynamics of DNA confined in nanoslits and nanochannels

Modeling the dynamics of a confined, semi exible polymer is a challenging problem, owing to the complicated interplay between the configurations of the chain, which are strongly affected by the length scale for the confinement relative to the persistence length of the chain, and the polymer-wall hydrodynamic interactions. At the same time, understanding these dynamics are crucial to the advancement of emerging genomic technologies that use confinement to stretch out DNA and "read" a genomic signature. In this mini-review, we begin by considering what is known experimentally and theoretically about the friction of a wormlike chain such as DNA confined in a slit or a channel. We then discuss how to estimate the friction coefficient of such a chain, either with dynamic simulations or via Monte Carlo sampling and the Kirk-wood pre-averaging approximation. We then review our recent work on computing the diffusivity of DNA in nanoslits and nanochannels, and conclude with some promising avenues for future work and caveats about our approach.

DNA Duplex Formation with a Coarse-Grained Model

A middle-resolution coarse-grained model of DNA is proposed. The DNA chain is built of spherical and planar rigid bodies connected by elastic virtual bonds. The bonded part of the potential energy function is fit to potentials of mean force of model systems. The rigid bodies are sets of neutral, charged, and dipolar beads. Electrostatic and van der Waals interactions are parametrized by our recently developed procedure [Maciejczyk, M.; Spasic, A.; Liwo, A.; Scheraga, H.A. J. Comp. Chem.2010, 31, 1644]. Interactions with the solvent and an ionic cloud are approximated by a multipole-multipole Debye-Hückel model. A very efficient R-RATTLE algorithm, for integrating the movement of rigid bodies, is implemented. It is the first coarse-grained model, in which both bonded and nonbonded interactions were parametrized ab initio and which folds stable double helices from separated complementary strands, with the final conformation close to the geometry of experimentally determined structures.

Influence of internal viscoelastic modes on the Brownian motion of a λ-DNA coated colloid

We study the influence of grafted polymers on the diffusive behaviour of a colloidal particle. Our work demonstrates how such additional degrees of freedom influence the Brownian motion of the particle, focusing on internal viscoelastic coupling between the polymer and colloid. Specifically, we study the mean-squared displacements (MSDs) of λ-DNA grafted colloids using Brownian dynamics simulation. Our simulations reveal the non-trivial effect of internal modes, which gives rise to a crossover from the short-time viscoelastic to long-time diffusional behaviour. We also show that basic features can be captured by a simple theoretical model considering the relative motion of a colloid to a part of the polymer corona. This model describes well a MSD calculated from an extremely long trajectory of a single λ-DNA coated colloid from experiment and allows characterisation of the λ-DNA hairs. Our study suggests that the access to the internal relaxation modes via the colloid trajectory offers a novel method for the characterisation of soft attachments to a colloid.

Simulations of DNA stretching by flow field in microchannels with complex geometry

Recently, we have reported the experimental results of DNA stretching by flow field in three microchannels (C. H. Lee and C. C. Hsieh, Biomicrofluidics 7(1), 014109 (2013)) designed specifically for the purpose of preconditioning DNA conformation for easier stretching. The experimental results do not only demonstrate the superiority of the new devices but also provides detailed observation of DNA behavior in complex flow field that was not available before. In this study, we use Brownian dynamics-finite element method (BD-FEM) to simulate DNA behavior in these microchannels, and compare the results against the experiments. Although the hydrodynamic interaction (HI) between DNA segments and between DNA and the device boundaries was not included in the simulations, the simulation results are in fairly good agreement with the experimental data from either the aspect of the single molecule behavior or from the aspect of ensemble averaged properties. The discrepancy between the simulation and the experimental results can be explained by the neglect of HI effect in the simulations. Considering the huge savings on the computational cost from neglecting HI, we conclude that BD-FEM can be used as an efficient and economic designing tool for developing new microfluidic device for DNA manipulation.

Modeling the relaxation time of DNA confined in a nanochannel

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping.

Is DNA a Good Model Polymer?

The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit "ideal" scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.

Presentation of large DNA molecules for analysis as nanoconfined dumbbells

The analysis of very large DNA molecules intrinsically supports long-range, phased sequence information, but requires new approaches for their effective presentation as part of any genome analysis platform. Using a multi-pronged approach that marshaled molecular confinement, ionic environment, and DNA elastic properties-but tressed by molecular simulations-we have developed an efficient and scalable approach for presentation of large DNA molecules within nanoscale slits. Our approach relies on the formation of DNA dumbbells, where large segments of the molecules remain outside the nanoslits used to confine them. The low ionic environment, synergizing other features of our approach, enables DNA molecules to adopt a fully stretched conformation, comparable to the contour length, thereby facilitating analysis by optical microscopy. Accordingly, a molecular model is proposed to describe the conformation and dynamics of the DNA molecules within the nanoslits; a Langevin description of the polymer dynamics is adopted in which hydrodynamic effects are included through a Green's function formalism. Our simulations reveal that a delicate balance between electrostatic and hydrodynamic interactions is responsible for the observed molecular conformations. We demonstrate and further confirm that the "Odijk regime" does indeed start when the confinement dimensions size are of the same order of magnitude as the persistence length of the molecule. We also summarize current theories concerning dumbbell dynamics.

The diffusion and relaxation of Gaussian chains in narrow rectangular slits

The confinement of a polymer to volumes whose characteristic linear dimensions are comparable to or smaller than its bulk radius of gyration R(G,bulk) can produce significant changes in its static and dynamic properties, with important implications for the understanding of single-molecule processes in biology and chemistry. In this paper, we present calculations of the effects of a narrow rectangular slit of thickness d on the scaling behavior of the diffusivity D and relaxation time τr of a Gaussian chain of polymerization index N and persistence length l0. The calculations are based on the Rouse-Zimm model of chain dynamics, with the pre-averaged hydrodynamic interaction being obtained from the solutions to Stokes equations for an incompressible fluid in a parallel plate geometry in the limit of small d. They go beyond de Gennes' purely phenomenological analysis of the problem based on blobs, which has so far been the only analytical route to the determination of chain scaling behavior for this particular geometry. The present model predicts that D ∼ dN(-1)ln (N∕d(2)) and τr ∼ N(2)d(-1)[ln (N∕d(2))](-1) in the regime of moderate confinement, where l0 ≪ d < R(G,bulk). The corresponding results for the blob model have exactly the same power law behavior, but contain no logarithmic corrections; the difference suggests that segments within a blob may actually be partially draining and not non-draining as generally assumed.

Revisiting blob theory for DNA diffusivity in slitlike confinement

Blob theory has been widely applied to describe polymer conformations and dynamics in nanoconfinement. In slit confinement, blob theory predicts a scaling exponent of 2/3 for polymer diffusivity as a function of slit height, yet a large body of experimental studies using DNA produce a scaling exponent significantly less than 2/3. In this work, we develop a theory that predicts that this discrepancy occurs because the segment correlation function for a semiflexible chain such as DNA does not follow the Flory exponent for length scales smaller than the persistence length. We show that these short length scale effects contribute significantly to the scaling for the DNA diffusivity, but do not appreciably affect the scalings for static properties. Our theory is fully supported by Monte Carlo simulations, quantitative agreement with DNA experiments, and the results reconcile this outstanding problem for confined polymers.

Electro-entropic excluded volume effects on DNA looping and relaxation in nanochannels

We investigate the fluctuation-relaxation dynamics of entropically restricted DNA molecules in square nanochannels ranging from 0.09 to 19.9 times the persistence length. In nanochannels smaller than the persistence length, the chain relaxation time is found to have cubic dependence on the channel size. It is found that the effective polymer width significantly alter the chain conformation and relaxation time in strong confinement. For thinner chains, looped chain configurations are found in channels with height comparable to the persistence length, with very slow relaxation compared to un-looped chains. Larger effective chain widths inhibit the formation of hairpin loops.

DNA confinement in nanochannels: physics and biological applications

DNA is the central storage molecule of genetic information in the cell, and reading that information is a central problem in biology. While sequencing technology has made enormous advances over the past decade, there is growing interest in platforms that can readout genetic information directly from long single DNA molecules, with the ultimate goal of single-cell, single-genome analysis. Such a capability would obviate the need for ensemble averaging over heterogeneous cellular populations and eliminate uncertainties introduced by cloning and molecular amplification steps (thus enabling direct assessment of the genome in its native state). In this review, we will discuss how the information contained in genomic-length single DNA molecules can be accessed via physical confinement in nanochannels. Due to self-avoidance interactions, DNA molecules will stretch out when confined in nanochannels, creating a linear unscrolling of the genome along the channel for analysis. We will first review the fundamental physics of DNA nanochannel confinement--including the effect of varying ionic strength--and then discuss recent applications of these systems to genomic mapping. Apart from the intense biological interest in extracting linear sequence information from elongated DNA molecules, from a physics view these systems are fascinating as they enable probing of single-molecule conformation in environments with dimensions that intersect key physical length-scales in the 1 nm to 100 µm range.

Mobility of a semiflexible chain confined in a nanochannel

The classic results of de Gennes and Odijk describe the mobility of a semiflexible chain confined in a nanochannel only in the limits of very weak and very strong confinement, respectively. Using Monte Carlo sampling of the Kirkwood diffusivity with full hydrodynamic interactions, we show that the mobility of a semiflexible chain exhibits a broad plateau as a function of extension before transitioning to an Odijk regime, and that the width of the plateau depends on the anisotropy of the monomers. For the particular case of DNA in a high ionic strength buffer, which has highly anisotropic monomers, we predict that this Rouse-like behavior will be observed over most of the measurable chain extensions seen in experiments.

Microfluidic systems for single DNA dynamics

Recent advances in microfluidics have enabled the molecular-level study of polymer dynamics using single DNA chains. Single polymer studies based on fluorescence microscopy allow for the direct observation of non-equilibrium polymer conformations and dynamical phenomena such as diffusion, relaxation, and molecular stretching pathways in flow. Microfluidic devices have enabled the precise control of model flow fields to study the non-equilibrium dynamics of soft materials, with device geometries including curved channels, cross-slots, and microfabricated obstacles and structures. This review explores recent microfluidic systems that have advanced the study of single polymer dynamics, while identifying new directions in the field that will further elucidate the relationship between polymer microstructure and bulk rheological properties.

Simulation of DNA Extension in Nanochannels

We have used a realistic model for double stranded DNA and Monte Carlo simulations to compute the extension (mean span) of a DNA molecule confined in a nanochannel over the full range of confinement in a high ionic strength buffer. The simulation data for square nanochannels resolve the apparent contradiction between prior simulation studies and the predictions from Flory theory, demonstrating the existence of two transition regimes between weak confinement (the de Gennes regime) and strong confinement (the Odijk regime). The simulation data for rectangular nanochannels support the use of the geometric mean for mapping data obtained in rectangular channels onto models developed for cylinders. The comparison of our results with experimental data illuminates the challenges in applying models for confined, neutral polymers to polyelectrolytes. Using a Flory-type approach, we also provide an improved scaling result for the relaxation time in the transition regime close to that found in experiments.

Efficient lattice Boltzmann algorithm for Brownian suspensions

A lattice Boltzmann (LB)-based hybrid method is developed to simulate suspensions of Brownian particles. The method uses conventional LB discretization (without fluid- level fluctuations) for suspending fluid, and treats Brownian particles as point masses with a stochastic thermal noise. LB equations are used to compute the velocity perturbations induced by the particle motion. It is shown that this method correctly reproduces the short-time and long-time diffusive behaviour of a Brownian particle. Unlike the earlier hybrid methods that use thermal fluctuations in the fluid, this method correctly reproduces the temperature of the particle and does not require an empirical rescaling of the bare friction coefficient to obtain the correct diffusive behaviour. It is observed that the present method is at least twice as fast as the earlier method. This method is best suited for flows of polymers and Brownian suspensions in microfluidic devices.

Confined dynamics of a single DNA molecule

The effect of a slit-like confinement on the relaxation dynamics of DNA is studied via a mesoscale model in which a bead and spring model for the polymer is coupled to a particle-based Navier-Stokes solver (multi-particle collision dynamics). The confinement is found to affect the equilibrium stretch of the chain when the bulk gyration radius is comparable to or smaller than the channel height and our data are in agreement with the (R(g,bulk)/h)(1/4) scaling of the polymer extension in the wall tangential direction. Relaxation simulation at different confinements indicates that, while the overall behaviour of the relaxation dynamics is similar for low and strong confinements, a small, but significant, slowing of the far-equilibrium relaxation is found as the confinement increases.

Nanochannel confinement: DNA stretch approaching full contour length

Fully stretched DNA molecules are becoming a fundamental component of new systems for comprehensive genome analysis. Among a number of approaches for elongating DNA molecules, nanofluidic molecular confinement has received enormous attentions from physical and biological communities for the last several years. Here we demonstrate a well-optimized condition that a DNA molecule can stretch almost to its full contour length: the average stretch is 19.1 µm ± 1.1 µm for YOYO-1 stained λ DNA (21.8 µm contour length) in 250 nm × 400 nm channel, which is the longest stretch value ever reported in any nanochannels or nanoslits. In addition, based on Odijk's polymer physics theory, we interpret our experimental findings as a function of channel dimensions and ionic strengths. Furthermore, we develop a Monte Carlo simulation approach using a primitive model for the rigorous understanding of DNA confinement effects. Collectively, we present a more complete understanding of nanochannel confined DNA stretching via the comparisons to computer simulation results and Odijk's polymer physics theory.

Semiflexible polymer conformation, distribution and migration in microcapillary flows

The flow behavior of a semiflexible polymer in microchannels is studied using multiparticle collision dynamics, a particle-based hydrodynamic simulation technique. Conformations, distributions, and radial cross-streamline migration are investigated for various bending rigidities, with persistence lengths L(p) in the range 0.5 ≤ L(p)/L(r) ≤ 30. The flow behavior is governed by the competition between a hydrodynamic lift force and steric repulsion from the wall, which lead to migration away from the wall, and a locally varying flow induced orientation, which drives the polymer away from the channel center and towards the wall. The different dependences of these effects on the polymer bending rigidity and the flow velocity results in a complex dynamical behavior. However, a generic effect is the appearance of a maximum in the monomer and the center-of-mass distributions, which occurs at the channel center for small flow velocities, but moves off-center at higher velocities.