Entropic depletion of DNA in triangular nanochannels

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.

Crowding-induced polymer trapping in a channel

In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ϕ^{*}, which scales as ϕ^{*}∼(a_{c}/L_{p})^{1/3} for a_{c}≫a_{m} and ϕ^{*}∼(a_{c}/L_{p})^{1/3}(a_{c}/a_{m})^{1/2} for a_{c}≪a_{m}, where a_{c} is the crowder diameter, a_{m} is the monomer diameter, and L_{p} is the polymer persistence length. For DNA, ϕ^{*} is estimated to be around 0.25 for crowders with a_{c}=2nm. We find that ϕ^{*} also strongly depends on the shape of the channel cross section, and ϕ^{*} is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy

Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to N=601 monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area A for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-A and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio ≥1.

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.

Tunable Confinement for Bridging Single-Cell Manipulation and Single-Molecule DNA Linearization

DNA linearization by nanoconfinement has offered a new avenue toward large-scale genome mapping. The ability to smoothly interface the widely different length scales from cell manipulation to DNA linearization is critical to the development of single-cell genomic mapping or sequencing technologies. Conventional nanochannel technologies for DNA analysis suffer from complex fabrication procedures, DNA stacking at the nanochannel entrance, and inefficient solution exchange. In this work, a dynamic and tunable confinement strategy is developed to manipulate and linearize genomic-length DNA molecules from a single cell. By leveraging pneumatic microvalve control and elastomeric collapse, an array of nanochannels with confining dimension down to 20 nm and length up to sub-millimeter is created and can be dynamically tuned in size. The curved edges of the microvalve form gradual transitions from microscale to nanoscale confinement, smoothly facilitating DNA entry into the nanochannels. A unified micro/nanofluidic device that integrates single-cell trapping and lysis, DNA extraction, purification, labeling, and linearization is developed based on dynamically controllable nanochannels. Mbp-long DNA molecules are extracted directly from a single cell and in situ linearized in the nanochannels. The device provides a facile and promising platform to achieve the ultimate goal of single-cell, single-genome analysis.

Dynamic simulations show repeated narrowing maximizes DNA linearization in elastomeric nanochannels

This paper uses computer simulations to reveal unprecedented details about linearization of deoxyribonucleic acid (DNA) inside dynamic nanochannels that can be repeatedly widened and narrowed. We first analyze the effect of rate of channel narrowing on DNA linearization dynamics. Quick (∼0.1 s) narrowing of nanoscale channels results in rapid overstretching of the semi-flexible chain followed by a slower (∼0.1-10 s) relaxation to an equilibrium extension. Two phenomena that induce linearization during channel narrowing, namely, elongational-flow and confinement, occur simultaneously, regardless of narrowing speed. Interestingly, although elongational flow is a minimum at the mid-point of the channel and increases towards the two ends, neither the linearization dynamics nor the degree of DNA extension varies significantly with the center-of-mass of the polymer projected on the channel axis. We also noticed that there was a significant difference in time to reach the equilibrium length, as well as the degree of DNA linearization at short times, depending on the initial conformation of the biopolymer. Based on these observations, we tested a novel linearization protocol where the channels are narrowed and widened repeatedly, allowing DNA to explore multiple conformations. Repeated narrowing and widening, something uniquely enabled by the elastomeric nanochannels, significantly decrease the time to reach the equilibrium-level of stretch when performed within periods comparable to the chain relaxation time and more effectively untangle chains into more linearized biopolymers.

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.

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.

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.

Stretching of DNA confined in nanochannels with charged walls

There is currently a growing interest in control of stretching of DNA inside nanoconfined regions due to the possibility to analyze and manipulate single biomolecules for applications such as DNA mapping and barcoding, which are based on stretching the DNA in a linear fashion. In the present work, we couple Finite Element Methods and Monte Carlo simulations in order to study the conformation of DNA molecules confined in nanofluidic channels with neutral and charged walls. We find that the electrostatic forces become more and more important when lowering the ionic strength of the solution. The influence of the nanochannel cross section geometry is also studied by evaluating the DNA elongation in square, rectangular, and triangular channels. We demonstrate that coupling electrostatically interacting walls with a triangular geometry is an efficient way to stretch DNA molecules at the scale of hundreds of nanometers. The paper reports experimental observations of λ-DNA molecules in poly(dimethylsiloxane) nanochannels filled with solutions of different ionic strength. The results are in good agreement with the theoretical predictions, confirming the crucial role of the electrostatic repulsion of the constraining walls on the molecule stretching.

Ultra-high-aspect-orthogonal and tunable three dimensional polymeric nanochannel stack array for BioMEMS applications

Nanofabrication technologies have been a strong advocator for new scientific fundamentals that have never been described by traditional theory, and have played a seed role in ground-breaking nano-engineering applications. In this study, we fabricated ultra-high-aspect (∼10(6) with O(100) nm nanochannel opening and O(100) mm length) orthogonal nanochannel array using only polymeric materials. Vertically aligned nanochannel arrays in parallel can be stacked to form a dense nano-structure. Due to the flexibility and stretchability of the material, one can tune the size and shape of the nanochannel using elongation and even roll the stack array to form a radial-uniformly distributed nanochannel array. The roll can be cut at discretionary lengths for incorporation with a micro/nanofluidic device. As examples, we demonstrated ion concentration polarization with the device for Ohmic-limiting/overlimiting current-voltage characteristics and preconcentrated charged species. The density of the nanochannel array was lower than conventional nanoporous membranes, such as anodic aluminum oxide membranes (AAO). However, accurate controllability over the nanochannel array dimensions enabled multiplexed one microstructure-on-one nanostructure interfacing for valuable biological/biomedical microelectromechanical system (BioMEMS) platforms, such as nano-electroporation.

Interplay between chain stiffness and excluded volume of semiflexible polymers confined in nanochannels

The properties of channel-confined semiflexible polymers are determined by a complicated interplay of chain stiffness and excluded volume effects. Using Pruned-Enriched Rosenbluth Method (PERM) simulations, we study the equilibrium properties of channel-confined polymers by systematically controlling chain stiffness and excluded volume. Our calculations of chain extension and confinement free energy for freely jointed chains with and without excluded volume show excellent agreement with theoretical predictions. For ideal wormlike chains, the extension is seen to crossover from Odijk behavior in strong confinement to zero-stretching, bulk-like behavior in weak confinement. In contrast, for self-avoiding wormlike chains, we always observe that the linear scaling of the extension with the contour length is valid in the long-chain limit irrespective of the regime of confinement, owing to the coexistence of stiffness and excluded volume effects. We further propose that the long-chain limit for the extension corresponds to chain lengths wherein the projection of the end-to-end distance along the axis of the channel is nearly equal to the mean span parallel to the axis. For DNA in nanochannels, this limit was identified using PERM simulations out to molecular weights of more than 1 megabase pairs; the molecular weight of λ-DNA is found to exhibit nearly asymptotic fractional extension for channels sizes used commonly in experiments.

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.

Entropic depletion of DNA in triangular nanochannels

Using Monte Carlo simulations of a touching-bead model of double-stranded DNA, we show that DNA extension is enhanced in isosceles triangular nanochannels (relative to a circular nanochannel of the same effective size) due to entropic depletion in the channel corners. The extent of the enhanced extension depends non-monotonically on both the accessible area of the nanochannel and the apex angle of the triangle. We also develop a metric to quantify the extent of entropic depletion, thereby collapsing the extension data for circular, square, and various triangular nanochannels onto a single master curve for channel sizes in the transition between the Odijk and de Gennes regimes.