DNA dynamics in a microchannel

Cross-streamline migration and near-wall depletion of elastic fibers in micro-channel flows

The complex dynamics of elastic fibers in viscous fluids are central to many biological and industrial systems. Fluid-structure interactions underlying these dynamics govern the shape and transport of flexible fibers, and understanding these interactions can help tune flow properties in applications such as microfluidic separation, printing and clogging. In this work, we use slender-body theory to study micromechanical dynamics that arise from the coupling between the elastic backbone of a fiber and the local straining flow that contributes to filament flipping and cross-streamline migration. The resulting transverse drift is unbiased in either direction in simple shear flow. However, a non-uniform shear rate results in bias towards regions of high shear, which we connect to the shape transitions during flips. We discover a depletion layer that forms near the boundaries of pressure-driven channel flow due to the competition between such a cross-streamline drift and steric exclusion from the walls. Finally, we develop scaling laws for the curvature of filaments during flip events, demonstrating the origin of the drift bias in non-uniform flows, and confirm this behavior from our simulations. Put together, these results shed light on the role of a local and dominant coupling between elasticity and viscous resistance in dictating long-term dynamics and transport of elastic fibers in confined flows.

Compression of a confined semiflexible polymer under direct and oscillating fields

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Two-fluid kinetic theory for dilute polymer solutions

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasiequilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equations for the polymer-solvent mixture. The proposed kinetic scheme leads to a numerical algorithm which is along the lines of the lattice Boltzmann method. Finally, the algorithm is applied to describe the evolution of a perturbed Kolmogorov flow profile, whereby we recover the major elastic effect exhibited by a polymer solution, specifically, the suppression of the original inertial instability.

Dynamical and Structural Properties of Comb Long-Chain Branched Polymer in Shear Flow

Using hybrid multi-particle collision dynamics (MPCD) and a molecular dynamics (MD) method, we investigate the effect of arms and shear flow on dynamical and structural properties of the comb long-chain branched (LCB) polymer with dense arms. Firstly, we analyze dynamical properties of the LCB polymer by tracking the temporal changes on the end-to-end distance of both backbones and arms as well as the orientations of the backbone in the flow-gradient plane. Simultaneously, the rotation and tumbling behaviors with stable frequencies are observed. In other words, the LCB polymer undergoes a process of periodic stretched–folded–stretched state transition and rotation, whose period is obtained by fitting temporal changes on the orientation to a periodic function. In addition, the impact induced by random and fast motions of arms and the backbone will descend as the shear rate increases. By analyzing the period of rotation behavior of LCB polymers, we find that arms have a function in keeping the LCB polymer’s motion stable. Meanwhile, we find that the rotation period of the LCB polymer is mainly determined by the conformational distribution and the non-shrinkable state of the structure along the velocity-gradient direction. Secondly, structural properties are numerically characterized by the average gyration tensor of the LCB polymer. The changes in gyration are in accordance with the LCB polymer rolling when varying the shear rate. By analyzing the alignment of the LCB polymer and comparing with its linear and star counterparts, we find that the LCB polymer with very long arms, like the corresponding linear chain, has a high speed to reach its configuration expansion limit in the flow direction. However, the comb polymer with shorter arms has stronger resistance on configuration expansion against the imposed flow field. Moreover, with increasing arm length, the comb polymer in shear flow follows change from linear-polymer-like to capsule-like behavior.

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

Real-time temperature measurement in stochastic rotation dynamics

Many physical and chemical processes involve energy change with rates that depend sensitively on local temperature. Important examples include heterogeneously catalyzed reactions and activated desorption. Because of the multiscale nature of such systems, it is desirable to connect the macroscopic world of continuous hydrodynamic and temperature fields to mesoscopic particle-based simulations with discrete particle events. In this work we show how to achieve real-time measurement of the local temperature in stochastic rotation dynamics (SRD), a mesoscale method particularly well suited for problems involving hydrodynamic flows with thermal fluctuations. We employ ensemble averaging to achieve local temperature measurement in dynamically changing environments. After validation by heat diffusion between two isothermal plates, heating of walls by a hot strip, and by temperature programed desorption, we apply the method to a case of a model flow reactor with temperature-sensitive heterogeneously catalyzed reactions on solid spherical catalysts. In this model, adsorption, chemical reactions, and desorption are explicitly tracked on the catalyst surface. This work opens the door for future projects where SRD is used to couple hydrodynamic flows and thermal fluctuations to solids with complex temperature-dependent surface mechanisms.

A Review of the Methods of Modeling Multi-Phase Flows within Different Microchannels Shapes and Their Applications

In industrial processes, the microtechnology concept refers to the operation of small devices that integrate the elements of operational and reaction units to save energy and space. The advancement of knowledge in the field of microfluidics has resulted in fabricating devices with different applications in micro and nanoscales. Micro- and nano-devices can provide energy-efficient systems due to their high thermal performance. Fluid flow in microchannels and microstructures has been widely considered by researchers in the last two decades. In this paper, a review study on fluid flow within microstructures is performed. The present study aims to present the results obtained in previous studies on this type of system. First, different types of flows in microchannels are examined. The present article will then review previous articles and present a general summary in each section. Then, the multi-phase flows inside the microchannels are discussed, and the flows inside the micropumps, microturbines, and micromixers are evaluated. According to the literature review, it is found that the use of microstructures enhances energy efficiency. The results of previous investigations revealed that the use of nanofluids as a working fluid in microstructures improves energy efficiency. Previous studies have demonstrated special attention to the design aspects of microchannels and micro-devices compared to other design strategies to improve their performance. Finally, general concluding remarks are presented, and the existing challenges in the use of these devices and suggestions for future investigations are presented.

Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor

Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that rotation is necessary for the accumulation of DNA writhe and for the chiral organization of the genome. We observe that although in the initial steps of the packaging reaction, the torsional strain of the genome is released by rotation of the molecule, in the later stages, it is released by the accumulation of writhe. We suggest that the molecular motor plays a key role in determining the final structure of the encapsidated genome in bacteriophages.

Depletion layer dynamics of polyelectrolyte solutions under Poiseuille flow

The interfacial physics of complex liquids under flow remains a long-standing problem in fluid mechanics that is important for fields ranging from lubrication to nanofluidics. Liquids containing small amounts of high-molecular weight polymers are found to flow through channels faster than expected, a phenomenon attributed to the formation of boundary depletion layers that relaxes the no-slip boundary condition and allows the bulk of the fluid to slip past the walls. This work provides the most direct measurement to date of the dimension and composition of depletion layers of a polymer solution under flow. We anticipate extending this approach to help understand fluid dynamics in different regimes, such as flow in nanoconfinement and turbulence.

Complex liquids flow through channels faster than expected, an effect attributed to the formation of low-viscosity depletion layers at the boundaries. Characterization of depletion layer length scale, concentration, and dynamics has remained elusive due in large part to the lack of suitable real-space experimental techniques. The short length scales associated with depletion layers have traditionally prohibited direct imaging. By overcoming this limitation via adaptations of stimulated emission depletion (STED) microscopy, we directly measure the concentration profile of polymer solutions at a nonadsorbing wall under Poiseuille flow. Using this approach, we 1) confirm the theoretically predicted concentration profile governed by entropically driven depletion, 2) observe depletion layer narrowing at low to intermediate shear rates, and 3) report depletion layer composition that approaches pure solvent at unexpectedly low shear rates.

Conformation and Dynamics of Long-Chain End-Tethered Polymers in Microchannels

Polyelectrolytes constitute an important group of materials, used for such different purposes as the stabilization of emulsions and suspensions or oil recovery. They are also studied and utilized in the field of microfluidics. With respect to the latter, a part of the interest in polyelectrolytes inside microchannels stems from genetic analysis, considering that deoxyribonucleic acid (DNA) molecules are polyelectrolytes. This review summarizes the single-molecule experimental and molecular dynamics simulation-based studies of end-tethered polyelectrolytes, especially addressing their relaxation dynamics and deformation characteristics under various external forces in micro-confined environments. In most of these studies, DNA is considered as a model polyelectrolyte. Apart from summarizing the results obtained in that area, the most important experimental and simulation techniques are explained.

Nanoplumbing with 2D Metamaterials

Complex manipulations of DNA in a nanofluidic device require channels with branches and junctions. However, the dynamic response of DNA in such nanofluidic networks is relatively unexplored. Here, the transport of DNA in a 2D metamaterial made by arrays of nanochannel junctions is investigated. The mechanism of transport is explained as Brownian motion through an energy landscape formed by the combination of the confinement free energy of DNA and the effective potential of hydrodynamic flow, which both can be tuned independently within the device. For the quantitative understanding of DNA transport, a dynamic mean-field model of DNA at a nanochannel junction is proposed. It is shown that the dynamics of DNA in a nanofluidic device with branched channels and junctions is well described by the model.

Polymer margination in uniform shear flows

We address the issue of polymer margination (migration towards surfaces) in uniform shear flows through extensive LBMD (lattice-Boltzmann molecular dynamics) simulations. In particular we consider the effect of monomer size, a on the chain's overall margination tendency for chains of length N = 16, 32 monomers in flows at multiple shear rates [small gamma, Greek, dot above]. We observed higher margination of chains with larger radii monomers in comparison to smaller radii monomer chains of the same length N. We quantify this effect by considering various measures such as the distribution of the maximum extent of the chain into the channel bulk, zm, distribution of its center of mass in the direction normal to the surface, zc and the distributions of the chain's radius of gyration in directions parallel and perpendicular to the surface i.e. Rx, Ry and Rz respectively.

The role of near-wall drag effects in the dynamics of tethered DNA under shear flow

We utilized single-molecule tethered particle motion (TPM) tracking, optimized for studying the behavior of short (0.922 μm) dsDNA molecules under shear flow conditions, in the proximity of a wall (surface). These experiments track the individual trajectories through a gold nanobead (40 nm in radius), attached to the loose end of the DNA molecules. Under such circumstances, local interactions with the wall become more pronounced, manifested through hydrodynamic interactions. To elucidate the mechanical mechanism that affects the statistics of the molecular trajectories of the tethered molecules, we estimate the resting diffusion coefficient of our system. Using this value and our measured data, we calculate the orthogonal distance of the extended DNA molecules from the surface. This calculation considers the hydrodynamic drag effect that emerges from the proximity of the molecule to the surface, using the Faxén correction factors. Our finding enables the construction of a scenario according to which the tension along the chain builds up with the applied shear force, driving the loose end of the DNA molecule away from the wall. With the extension from the wall, the characteristic times of the system decrease by three orders of magnitude, while the drag coefficients decay to a plateau value that indicates that the molecule still experiences hydrodynamic effects due to its proximity to the wall.

Electroosmosis of Viscoelastic Fluids: Role of Wall Depletion Layer

We investigate electroosmotic flow of two immiscible viscoelastic fluids in a parallel plate microchannel. Contrary to traditional analysis, the effect of the depletion layer is incorporated near the walls, thereby capturing the complex coupling between rheology and electrokinetics. Toward ensuring realistic prediction, we show the dependence of electroosmotic flow rate on the solution pH and polymer concentration of the complex fluid. In order to assess our theoretical predictions, we have further performed experiments on electroosmosis of an aqueous solution of polyacrylamide (PAAm). Our analysis reveals that neglecting the existence of a depletion layer would result in grossly incorrect predictions of the electroosmotic transport of such fluids. These findings are likely to be of importance in understanding electroosmotically driven transport of complex fluids, including biological fluids, in confined microfluidic environments.

Stretching of surface-tethered polymers in pressure-driven flow under confinement

We study the effect of pressure-driven flow on a single surface-tethered DNA molecule confined between parallel surfaces. The influence of flow and channel parameters as well as the length of the molecules on their extension and orientation is explored. In the experiments the chain conformations are imaged by laser scanning confocal microscopy. We find that the fractional extension of the tethered DNA molecules mainly depends on the wall shear stress, with effects of confinement being very weak. Experiments performed with molecules of different contour length show that the fractional extension is a universal function of the product of the wall shear stress and the contour length, a result that can be obtained from a simple scaling relation. The experimental results are in good agreement with results from coarse-grained molecular dynamics/Lattice-Boltzmann simulations.

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.

Single Molecule Hydrodynamic Separation Allows Sensitive and Quantitative Analysis of DNA Conformation and Binding Interactions in Free Solution

Limited tools exist that are capable of monitoring nucleic acid conformations, fluctuations, and distributions in free solution environments. Single molecule free solution hydrodynamic separation enables the unique ability to quantitatively analyze nucleic acid biophysics in free solution. Single molecule fluorescent burst data and separation chromatograms can give layered insight into global DNA conformation, binding interactions, and molecular distributions. First, we show that global conformation of individual DNA molecules can be directly visualized by examining single molecule fluorescent burst shapes and that DNA exists in a dynamic equilibrium of fluctuating conformations as it is driven by Poiseuille flow through micron-sized channels. We then show that this dynamic equilibrium of DNA conformations is reflected as shifts in hydrodynamic mobility that can be perturbed using salt and ionic strength to affect packing density. Next, we demonstrate that these shifts in hydrodynamic mobility can be used to investigate hybridization thermodynamics and binding interactions. We distinguish and classify multiple interactions within a single sample, and demonstrate quantification amidst large concentration differences for the detection of rare species. Finally, we demonstrate that these differences can resolve perfect complement, 2 bp mismatched, and 3 bp mismatched sequences. Such a system can be used to garner diverse information about DNA conformation and structure, and potentially be extended to other molecules and mixed-species interactions, such as between nucleic acids and proteins or synthetic polymers.

Mesoscopic simulation of single DNA dynamics in rotational flows

In this numerical study, the transport and dynamics of an isolated DNA in rotational flow generated in a microchannel have been investigated using dissipative particle dynamics. Often, inertial flow through microchannels with a sudden change in surface structure facilitates a re-circulation or vortex region. The conformation and mobility of the bio-polymer under the influence of such rotating fluid inside a square cavity of the microchannel is analyzed. The flexible polymer chain is found to migrate towards the rotating region and follows the vortex streamline. The orientation, size and tumbling period of polymer strands are affected by the strength of the microvortex. At elevated flow rates, the macromolecule prefers to remain inside the vortex and a hydrodynamic trap is formed. Moreover, residence time of the single molecule in the microcavity is significantly influenced by the chain length and flow strength. Further, it has been demonstrated that, such entrapment duration can be strategically altered by modifying the hydrophobicity of the microchannel.

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.

Separation of DNA by length in rotational flow: Lattice-Boltzmann-based simulations

We use a lattice-Boltzmann based Brownian dynamics simulation to investigate the separation of different lengths of DNA through the combination of a trapping force and the microflow created by counter-rotating vortices. We can separate most long DNA molecules from shorter chains that have lengths differing by as little as 30%. The sensitivity of this technique is determined by the flow rate, size of the trapping region, and the trapping strength. We expect that this technique can be used in microfluidic devices to separate long DNA fragments that result from techniques such as restriction enzyme digests of genomic DNA.

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.

Molecular-scale simulation of cross-flow migration in polymer melts

The first ever molecular-scale simulation of cross-flow migration effects in dense polymer melts is presented; simulations for both unentangled and entangled chains are presented. At quiescence a small depletion next to the wall for the segmental densities of longer chains is present, a corresponding excess exists about one-half a radii of gyration away from the wall, and uniform values are observed further from the wall. In shear flow the melts exhibit similar behavior as the quiescent case; a constant shear rate across the gap does not induce chain length based migration. In contradistinction, parabolic flow (where gradients in shear rate are present) causes profound migration for both unentangled and entangled melts. Mapping onto polyethylene and calculating stress shows the system is far below the stress required to break chains. Accordingly, our findings are consistent with flow induced migration mechanisms predominating over competing chain degradation mechanisms thus resolving a 40 year old controversy.

Electrophoretic mobilities of counterions and a polymer in cylindrical pores

We have simulated the transport properties of a uniformly charged flexible polymer chain and its counterions confined inside cylindrical nanopores under an external electric field. The hydrodynamic interaction is treated by describing the solvent molecules explicitly with the multiparticle collision dynamics method. The chain consisting of charged monomers and the counterions interact electrostatically with themselves and with the external electric field. We find rich behavior of the counterions around the polymer under confinement in the presence of the external electric field. The mobility of the counterions is heterogeneous depending on their location relative to the polymer. The adsorption isotherm of the counterions on the polymer depends nonlinearly on the electric field. As a result, the effective charge of the polymer exhibits a sigmoidal dependence on the electric field. This in turn leads to a nascent nonlinearity in the chain stretching and electrophoretic mobility of the polymer in terms of their dependence on the electric field. The product of the electric field and the effective polymer charge is found to be the key variable to unify our simulation data for various polymer lengths. Chain extension and the electrophoretic mobility show sigmoidal dependence on the electric field, with crossovers from the linear response regime to the nonlinear regime and then to the saturation regime. The mobility of adsorbed counterions is nonmonotonic with the electric field. For weaker and moderate fields, the adsorbed counterions move with the polymer and at higher fields they move opposite to the polymer's direction. We find that the effective charge and the mobility of the polymer decrease with a decrease in the pore radius.

Transport of DNA in hydrophobic microchannels: a dissipative particle dynamics simulation

In this work, we numerically study a new means of manipulating single DNA chains in microchannels. The method is based on the effect of finite slip at hydrophobic walls on the hydrodynamics and, consequently, on the dynamics of the DNA in microchannels. We use dissipative particle dynamics to study DNA transport as a function of chain length and the Reynolds number in two dimensional parallel plate channels. We show how an asymmetric velocity profile in a channel with hydrophobic and hydrophilic walls can be used to manipulate the location of the DNA molecules. Using this effect, we propose a simple arrangement of hydrophobic and hydrophilic strips which can be exploited to separate long and short DNA chains.

Von Willlebrand adhesion to surfaces at high shear rates is controlled by long-lived bonds

Von Willebrand factor (vWF) adsorbs and immobilizes platelets at sites of injury under high-shear-rate conditions. It has been recently demonstrated that single vWF molecules only adsorb significantly to collagen above a threshold shear, and here we explain such counterintuitive behavior using a coarse-grained simulation and a phenomenological theory. We find that shear-induced adsorption only occurs if the vWF-surface bonds are slip-resistant such that force-induced unbinding is suppressed, which occurs in many biological bonds (i.e., catch bonds). Our results quantitatively match experimental observations and may be important to understand the activation and mechanical regulation of vWF activity during blood clotting.

Unfolding of collapsed polymers in shear flow: effects of colloid banding structures in confining channels

Using hydrodynamic simulations, we demonstrate that confined colloidal suspensions can greatly enhance the unfolding of collapsed single polymers in flow. When colloids come in direct contact with the polymers due to the flow, the collapsed chains become flattened or elongated on the surface of the colloids, increasing the probability of forming large chain protrusions that the flow can pull out to unfold the polymers. This phenomenon may be suppressed if the colloid size is commensurate with the confining channels, where the colloids form well-defined banding structures. Here, we analyze the colloid banding structures in detail and their relation to the chain unfolding. We find that for colloid volume fractions up to 30%, the confined colloids form simple cubic (sc), hexagonal (hex), or a mixture of sc + hex structures. By directly changing the heights of the confining channels, we show that the collapsed polymers unfold the most in the mixed sc + hex structures. The diffuse (not well-defined) bands in the mixed sc + hex structures provide the highest collision probability for the colloids and the polymers, thus enhancing unfolding the most. Without colloidal suspensions, we show that the confining channels alone do not have an observable effect on the unfolding of collapsed polymers. The well-defined colloid bands also suppress the unfolding of noncollapsed polymers. In fact, the average size for noncollapsed chains is even smaller in the well-defined bands than in a channel without any colloids. The appearance of well-defined bands in this case also indicates that lift forces experienced by the polymers in confinement are negligible compared to those exerted by the colloidal band structures. Our results may be important for understanding the dynamics of mixed colloid polymer solutions.

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.

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.