Diffusion of DNA in Nanoslits

Electrical Transport and Dynamics of Confined DNA through Highly Conductive 2D Graphene Nanochannels

Confining DNA in nanochannels is an important approach to studying its structure and transportation dynamics. Graphene nanochannels are particularly attractive for studying DNA confinement due to their atomic flatness, precise height control, and excellent mechanical strength. Here, using femtosecond laser etching and wetting transfer, we fabricate graphene nanochannels down to less than 4.3 nm in height, with the length-to-height ratios up to 103. These channels exhibit high stability, low noise, and self-cleaning ability during the long-term ionic current recording. We report a clear linear relationship between DNA length and the residence time in the channel and further utilize this relationship to differentiate DNA fragments based on their lengths, ranging widely from 200 bps to 48.5 kbps. The graphene nanochannel presented here provides a potential platform for label-free analyses and reveals fundamental insights into the conformational dynamics of DNA and proteins in confined space.

Diffusion of Short Semiflexible DNA Polymer Chains in Strong and Moderate Confinement

In many technological applications, DNA is confined within nanoenvironments that are smaller than the size of the unconfined polymer in solution. However, the dependence of the diffusion coefficient on molecular weight and characteristic confinement dimension remains poorly understood in this regime. Here, convex lens-induced confinement (CLiC) was leveraged to examine how the diffusion of short DNA fragments varied as a function of slit height by using single-molecule fluorescence tracking microscopy. The diffusion coefficient followed approximate power law behavior versus confinement height, with exponents of 0.27 ± 0.01, 0.32 ± 0.02, and 0.42 ± 0.06 for 692, 1343, and 2686 base pair chains, respectively. The weak dependence on slit height suggests that shorter semiflexible chains may adopt increasingly rodlike conformations and therefore experience weaker excluded-volume interactions as the confinement dimension is reduced. The diffusion coefficient versus molecular weight also exhibited apparent power law behavior, with exponents that varied slightly (from -0.89 to -0.85) with slit height, consistent with hydrodynamic interactions intermediate between Rouse and Zimm model predictions.

Probing the organization and dynamics of two DNA chains trapped in a nanofluidic cavity

Here we present a pneumatically-actuated nanofluidic platform that has the capability of dynamically controlling the confinement environment of macromolecules in solution. Using a principle familiar from classic devices based on soft-lithography, the system uses pneumatic pressure to deflect a thin nitride lid into a nanoslit, confining molecules in an array of cavities embedded in the slit. We use this system to quantify the interactions of multiple confined DNA chains, a key problem in polymer physics with important implications for nanofluidic device performance and DNA partitioning/organization in bacteria and the eukaryotes. In particular, we focus on the problem of two-chain confinement, using differential staining of the chains to independently assess the chain conformation, determine the degree of partitioning/mixing in the cavities and assess coupled diffusion of the chain center-of-mass positions. We find that confinement of more than one chain in the cavity can have a drastic impact on the polymer dynamics and conformation.

Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels

We have measured the diffusivity of λ-DNA molecules in approximately square nanochannels with effective sizes ranging from 117 nm to 260 nm at moderate ionic strength. The experimental results do not agree with the non-draining scaling predicted by blob theory. Rather, the data are consistent with the predictions of previous simulations of the Kirkwood diffusivity of a discrete wormlike chain model, without the need for any fitting parameters.

Nanoconfinement greatly speeds up the nucleation and the annealing in single-DNA collapse

Manipulating and measuring single-molecule dynamics and reactions in nanofluidics is a rapidly growing field with broad applications in developing new biotechnologies, understanding nanoconfinement effects in vivo, and exploring new phenomena in confinement. In this work, we investigate the kinetics of DNA collapse in nanoslits using single T4-DNA (165.6 kbp) and λ-DNA (48.5 kbp), with particular focus on the measurement of the nucleation and annealing times. Fixing the ethanol concentration at 35% and varying the slit height from 2000 to 31 nm, the nucleation time dramatically decreases from more than 1 hour to a few minutes or less. The increased collapsed rate results from the larger free energy experienced by coiled DNA in confinement relative to compacted DNA. Our results also shed light on other conformational transitions in confinement, such as protein folding.

Wall depletion length of a channel-confined polymer

Numerous experiments have taken advantage of DNA as a model system to test theories for a channel-confined polymer. A tacit assumption in analyzing these data is the existence of a well-defined depletion length characterizing DNA-wall interactions such that the experimental system (a polyelectrolyte in a channel with charged walls) can be mapped to the theoretical model (a neutral polymer with hard walls). We test this assumption using pruned-enriched Rosenbluth method (PERM) simulations of a DNA-like semiflexible polymer confined in a tube. The polymer-wall interactions are modeled by augmenting a hard wall interaction with an exponentially decaying, repulsive soft potential. The free energy, mean span, and variance in the mean span obtained in the presence of a soft wall potential are compared to equivalent simulations in the absence of the soft wall potential to determine the depletion length. We find that the mean span and variance about the mean span have the same depletion length for all soft potentials we tested. In contrast, the depletion length for the confinement free energy approaches that for the mean span only when depletion length no longer depends on channel size. The results have implications for the interpretation of DNA confinement experiments under low ionic strengths.

Giant Acceleration of DNA Diffusion in an Array of Entropic Barriers

We investigate with experiments and computer simulations the nonequilibrium dynamics of DNA polymers crossing arrays of entropic barriers in nanofluidic devices in a pressure-driven flow. With increasing driving pressure, the effective diffusivity of DNA rises and then peaks at a value that is many times higher than the equilibrium diffusivity. This is an entropic manifestation of "giant acceleration of diffusion." The phenomenon is sensitive to the effective energy landscape; thus, it offers a unique probe of entropic barriers in a system driven away from equilibrium.

Force-Extension for DNA in a Nanoslit: Mapping between the 3D and 2D Limits

The force-extension relation for a semiflexible polymer confined in a nanoslit is investigated. Both the effective correlation length and force-extension relation change as the chain goes from 3D (large slit heights) to 2D (tight confinement). At low forces, correlations along the polymer give an effective dimensionality. The strong force limit can be interpolated with the weak force limit for two regimes: when confinement dominates over extensile force and vice versa. These interpolations give good agreement with simulations for all slit heights and forces. We thus generalize the Marko-Siggia force-extension relation for DNA and other semiflexible biopolymers in nanoconfinement.

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.

Fluctuations of DNA mobility in nanofluidic entropic traps

We studied the mobility of DNA molecules driven by an electric field through a nanofluidic device containing a periodic array of deep and shallow regions termed entropic traps. The mobility of a group of DNA molecules was measured by fluorescent video microscopy. Since the depth of a shallow region is smaller than the DNA equilibrium size, DNA molecules are trapped for a characteristic time and must compress themselves to traverse the boundary between deep and shallow regions. Consistent with previous experimental results, we observed a nonlinear relationship between the mobility and electric field strength, and that longer DNA molecules have larger mobility. In repeated measurements under seemingly identical conditions, we measured fluctuations in the mobility significantly larger than expected from statistical variation. The variation was more pronounced for lower electric field strengths where the trapping time is considerable relative to the drift time. To determine the origin of these fluctuations, we investigated the dependence of the mobility on several variables: DNA concentration, ionic strength of the solvent, fluorescent dye staining ratio, electroosmotic flow, and electric field strength. The mobility fluctuations were moderately enhanced in conditions of reduced ionic strength and electroosmotic flow.

Precision platform for convex lens-induced confinement microscopy

We present the conception, fabrication, and demonstration of a versatile, computer-controlled microscopy device which transforms a standard inverted fluorescence microscope into a precision single-molecule imaging station. The device uses the principle of convex lens-induced confinement [S. R. Leslie, A. P. Fields, and A. E. Cohen, Anal. Chem. 82, 6224 (2010)], which employs a tunable imaging chamber to enhance background rejection and extend diffusion-limited observation periods. Using nanopositioning stages, this device achieves repeatable and dynamic control over the geometry of the sample chamber on scales as small as the size of individual molecules, enabling regulation of their configurations and dynamics. Using microfluidics, this device enables serial insertion as well as sample recovery, facilitating temporally controlled, high-throughput measurements of multiple reagents. We report on the simulation and experimental characterization of this tunable chamber geometry, and its influence upon the diffusion and conformations of DNA molecules over extended observation periods. This new microscopy platform has the potential to capture, probe, and influence the configurations of single molecules, with dramatically improved imaging conditions in comparison to existing technologies. These capabilities are of immediate interest to a wide range of research and industry sectors in biotechnology, biophysics, materials, and chemistry.

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.

Intrachain dynamics of large dsDNA confined to slitlike channels

Exploration of intrachain hydrodynamics of dsDNA within channels has been limited to indirect analysis of global coil dynamics. In this Letter, we isolate hydrodynamic interactions within single molecules of dsDNA confined to slitlike channels by making use of density covariance measurements. We show that the strength of hydrodynamic interactions in DNA is dependent on the intrachain correlation length and that screening by symmetry in slitlike confinement results in a screening length that is proportional channel height. Moreover, we directly show the partial draining nature of the blobs formed by dsDNA in slits and predict under what conditions a dsDNA blob should obey nondraining Zimm behavior.

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.

Electrokinetically-driven transport of DNA through focused ion beam milled nanofluidic channels

The electrophoretically driven transport of double-stranded λ-phage DNA through focused ion beam (FIB) milled nanochannels is described. Nanochannels were fabricated having critical dimensions (width and depth) corresponding to 0.5×, 1×, and 2× the DNA persistence length, or 25 nm, 50 nm, and 100 nm, respectively. The threshold field strength required to drive transport, the threading mobility, and the transport mobility were measured as a function of nanochannel size. As the nanochannel dimensions decreased, the entropic barrier to translocation increased and transport became more constrained. Equilibrium models of confinement provide a framework in which to understand the observed trends, although the dynamic nature of the experiments resulted in significant deviations from theory. It was also demonstrated that the use of dynamic wall coatings for the purpose of electroosmotic flow suppression can have a significant impact on transport dynamics that may obfuscate entropic contributions. The nonintermittent DNA transport through the FIB milled nanochannels demonstrates that they are well suited for use in nanofluidic devices. We expect that an understanding of the dynamic transport properties reported here will facilitate the incorporation of FIB-milled nanochannels in devices for single molecule and ensemble analyses.

A device for performing lateral conductance measurements on individual double-stranded DNA molecules

A nanofluidic device is described that is capable of electrically monitoring the driven translocation of DNA molecules through a nanochannel. This is achieved by intersecting a long transport channel with a shorter orthogonal nanochannel. The ionic conductance of this transverse nanochannel is monitored while DNA is electrokinetically driven through the transport channel. When DNA passes the intersection, the transverse conductance is altered, resulting in a transient current response. In 1 M KCl solutions, this was found to be a current enhancement of 5-25%, relative to the baseline transverse ionic current. Two different device geometries were investigated. In one device, the DNA was detected after it was fully inserted into and translocating through the transport nanochannel. In the other device, the DNA was detected while it was in the process of entering the nanochannel. It was found that these two conditions are characterized by different transport dynamics. Simultaneous optical and electrical monitoring of DNA translocation confirmed that the transient events originated from DNA transport through the nanochannel intersection.

DNA molecules descending a nanofluidic staircase by entropophoresis

A complex entropy gradient for confined DNA molecules was engineered for the first time. Following the second law of thermodynamics, this enabled the directed self-transport and self-concentration of DNA molecules. This new nanofluidic method is termed entropophoresis. As implemented in experiments, long DNA molecules were dyed with cyanine dimers, dispersed in a high ionic strength buffer, and confined by a nanofluidic channel with a depth profile approximated by a staircase function. The staircase step depths spanned the transition from strong to moderate confinement. The diffusion of DNA molecules across slitlike steps was ratcheted by entropic forces applied at step edges, so that DNA molecules descended and collected at the bottom of the staircase, as observed by fluorescence microscopy. Different DNA morphologies, lengths, and stoichiometric base pair to dye molecule ratios were tested and determined to influence the rate of transport by entropophoresis. A model of ratcheted diffusion was used to interpret a shifting balance of forces applied to linear DNA molecules of standard length in a complex free energy landscape. Related metrics for the overall and optimum performance of entropophoresis were developed. The device and method reported here transcend current limitations in nanofluidics and present new possibilities in polymer physics, biophysics, separation science, and lab-on-a-chip technology.

Entropy-driven single molecule tug-of-war of DNA at micro-nanofluidic interfaces

Entropy-driven polymer dynamics at the nanoscale is fundamentally important in biological systems but the dependence of the entropic force on the nanoconfinement remains elusive. Here, we established an entropy-driven single molecule tug-of-war (TOW) at two micro-nanofluidic interfaces bridged by a nanoslit, performed the force analysis from a modified wormlike chain in the TOW scenario and the entropic recoiling process, and determined the associated scalings on the nanoconfinement. Our results provide a direct experimental evidence that the entropic forces in these two regimes, though unequal, are essentially constant at defined slit heights, irrespective of the slit lengths and the DNA segments within. Our findings have the implications to polymer transport at the nanoscale, device design for single molecule analysis, and biotechnological applications.

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.

Gated and near-surface diffusion of charged fullerenes in nanochannels

Nanoparticles and their derivatives have engendered significant recent interest. Despite considerable advances in nanofluidic physics, control over nanoparticle diffusive transport, requisite for a host of innovative applications, has yet to be demonstrated. In this study, we performed diffusion experiments for negatively and positively charged fullerene derivatives (dendritic fullerene-1, DF-1, and amino fullerene, AC60) in 5.7 and 13 nm silicon nanochannels in solutions with different ionic strengths. With DF-1, we demonstrated a gated diffusion whereby precise and reproducible control of the dynamics of the release profile was achieved by tuning the gradient of the ionic strength within the nanochannels. With AC60, we observed a near-surface diffusive transport that produced release rates that were independent of the size of the nanochannels within the range of our experiments. Finally, through theoretical analysis we were able to elucidate the relative importance of physical nanoconfinement, electrostatic interactions, and ionic strength heterogeneity with respect to these gated and near-surface diffusive transport phenomena. These results are significant for multiple applications, including the controlled administration of targeted nanovectors for therapeutics.

Partial hydrodynamic screening of confined linear and circular double-stranded DNA dynamics

We performed experiments and simulations to investigate the influence of hydrodynamic interaction on the diffusion dynamics of circular and linear λ-DNA confined in nanoslits. Contrary to the common assumption that intrachain hydrodynamic interaction (HI) is completely screened when polymers are confined in channels with height h smaller than the radius of gyration R(g), it is found that the HI is partially screened and approaches complete screening only for R(g)≪h. For λ-DNA, the HI becomes nearly completely screened only when the channel height is smaller than the Kuhn length. In addition, the dynamics of linear and circular λ-DNA in very strong confinement is shown to be independent of the chain topology.

Crossover behavior in static and dynamic properties of a single DNA molecule from three to quasi-two dimensions

We studied the conformation and dynamics of a single DNA molecule in a thin slit by a fluorescent microscope. In a slit thinner than the Flory radius in three dimensions, the length of the major axis, the translational self-diffusion coefficient and the rotational relaxation time in a dilute solution show the apparent dependence on the thickness of the slit. The observed dependence is in agreement with that predicted by blob theory, despite the number of blobs is very small. The radial distribution of the segments around the center of mass of a single molecule was also studied and compared with that calculated for a Gaussian and an excluded volume chain. The influence of the polymer concentration on the geometrical confinement by slits was also studied in a semidilute solution near the overlap concentration c∗. The confinement effect is found to be not so serious near c∗ and is only significant in the so-called "two-dimensional pancake" region.

Nanofluidic structures with complex three-dimensional surfaces

Nanofluidic devices have typically explored a design space of patterns limited by a single nanoscale structure depth. A method is presented here for fabricating nanofluidic structures with complex three-dimensional (3D) surfaces, utilizing a single layer of grayscale photolithography and standard integrated circuit manufacturing tools. This method is applied to construct nanofluidic devices with numerous (30) structure depths controlled from approximately 10 to approximately 620 nm with an average standard deviation of <10 nm over distances of >1 cm. A prototype 3D nanofluidic device is demonstrated that implements size exclusion of rigid nanoparticles and variable nanoscale confinement and deformation of biomolecules.