Conformation and dynamics of DNA confined in slitlike nanofluidic channels

Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers

We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.

Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets

Dynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients Deff decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems.

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DNA diffusion measured in cell-sized droplets with differential dynamic microscopy

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Combination of crowding and confinement leads to subdiffusion and slowing

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Diffusion coefficients of DNA decrease strongly with decreasing droplet size

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Polymer scaling theories and depletion effects predict observed dynamics

Confinement anisotropy drives polar organization of two DNA molecules interacting in a nanoscale cavity

There is growing appreciation for the role phase transition based phenomena play in biological systems. In particular, self-avoiding polymer chains are predicted to undergo a unique confinement dependent demixing transition as the anisotropy of the confined space is increased. This phenomenon may be relevant for understanding how interactions between multiple dsDNA molecules can induce self-organized structure in prokaryotes. While recent in vivo experiments and Monte Carlo simulations have delivered essential insights into this phenomenon and its relation to bacteria, there are fundamental questions remaining concerning how segregated polymer states arise, the role of confinement anisotropy and the nature of the dynamics in the segregated states. To address these questions, we introduce an artificial nanofluidic model to quantify the interactions of multiple dsDNA molecules in cavities with controlled anisotropy. We find that two dsDNA molecules of equal size confined in an elliptical cavity will spontaneously demix and orient along the cavity poles as cavity eccentricity is increased; the two chains will then swap pole positions with a frequency that decreases with increasing cavity eccentricity. In addition, we explore a system consisting of a large dsDNA molecule and a plasmid molecule. We find that the plasmid is excluded from the larger molecule and will exhibit a preference for the ellipse poles, giving rise to a non-uniform spatial distribution in the cavity that may help explain the non-uniform plasmid distribution observed during in vivo imaging of high-copy number plasmids in bacteria.

Melting of confined DNA: static and dynamic properties

We study dsDNA (double strand DNA) melting in detail within varying strip-like confinement in a two-dimensional lattice model. The interplay between reduced configurational entropy and attractive base-pairing energy results in a non-monotonic melting profile of DNA. Structural transitions associated with confined DNA melting reveal a stretched or extended state for very strong confinement. By using the exact enumeration method, we investigate the emergence of a local denatured zone e.g. bubbles during DNA melting. The survival time of a single bubble within varying strip width is studied from the Fokker-Planck formalism by considering the bubble size as a reaction co-ordinate. We show that a simple lattice model can capture the sequence heterogeneity effect on DNA melting and bubble dynamics within the strip. Different time scales of bubble zipping for different DNA sequences are found, which may have potential applications in denaturation mapping.

In Situ Monitoring of DNA-Hg2+ Binding Reaction within Confined Nanospace of Metamaterial Nanochannel by Plasmon-Enhanced Raman Scattering

Nanochannel-based plasmon-enhanced Raman scattering (PERS) substrates can simulate biological environments, revealing the recognition and conformation information on biomolecules in confined spaces. In this work, a metamaterial nanochannel-based PERS platform was constructed for highly sensitive analysis of DNA recognition to Hg²⁺ with the lowest Hg²⁺ concentration down to 1.0 pM. The established platform enables in situ monitoring of the thermodynamics and kinetics of DNA-Hg²⁺ recognition reaction in a confined nanospace. The recognition reaction in a nanospace shows good reversibility and specificity, and the isotherm follows well the Freundlich adsorption model. Compared to its folding on a rough Au nanofilm, the folding time of ssDNA-Rox decorated in nanochannels is remarkably increased, and the folding process can be tuned through varying the pore size and ionic strength. The presented PERS platform is promising for studying biomolecule-ion binding events and biomolecule conformation change under nanochannel-confined conditions.

Scanning Probe Lithography: State-of-the-Art and Future Perspectives

High-throughput and high-accuracy nanofabrication methods are required for the ever-increasing demand for nanoelectronics, high-density data storage devices, nanophotonics, quantum computing, molecular circuitry, and scaffolds in bioengineering used for cell proliferation applications. The scanning probe lithography (SPL) nanofabrication technique is a critical nanofabrication method with great potential to evolve into a disruptive atomic-scale fabrication technology to meet these demands. Through this timely review, we aspire to provide an overview of the SPL fabrication mechanism and the state-the-art research in this area, and detail the applications and characteristics of this technique, including the effects of thermal aspects and chemical aspects, and the influence of electric and magnetic fields in governing the mechanics of the functionalized tip interacting with the substrate during SPL. Alongside this, the review also sheds light on comparing various fabrication capabilities, throughput, and attainable resolution. Finally, the paper alludes to the fact that a majority of the reported literature suggests that SPL has yet to achieve its full commercial potential and is currently largely a laboratory-based nanofabrication technique used for prototyping of nanostructures and nanodevices.

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.

Characteristic time for the end monomers of a spherically confined polymer to find a nano-pore

Translocation of a polymer through a nano-pore is relevant in a variety of contexts such as passage of RNAs through a nuclear pore and transportation of proteins across a membrane. An essential step in polymer translocation is for the end monomers to search the pore. This process requires a characteristic time, referred to as the "attempt time" in this work. Here, we study the attempt time τ of a confined polymer inside a spherical surface by combining a scaling approach and Langevin dynamics simulations. For a moderately to strongly confined polymer, our results suggest that τ ∼ R^3.67 for R > P and τ ∼ R^2.67 for R < P, where R is the radius of the spherical surface and P is the persistence length of the polymer. All simulation data obtained for an intermediate range of the volume fraction of monomers ϕ(≲ 0.2) tend to collapse onto each other. This implies that τ does not explicitly depend on ϕ, in agreement with the theoretical predictions. These results will be useful for interpreting translocation as a two-step process: the initial attempt to find the pore and eventual pore crossing.

Transport of neutral and charged nanorods across varying-section channels

We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods with diverse lengths, aspect ratios and charge. Our analysis shows that the dynamics of charged rods is sensitive to the geometry of the channel and that their transport can be controlled by tuning both the shape of the confining walls and the charge of the rod. Interestingly, we find that the channel permeability does not depend monotonically on the charge of the rod. This opens the possibility of a novel mechanism to separate charged rods.

Translocation of DNA through Ultrathin Nanoslits

2D nanoslit devices, where two crystals with atomically flat surfaces are separated by only a few nanometers, have attracted considerable attention because their tunable control over the confinement allows for the discovery of unusual transport behavior of gas, water, and ions. Here, the passage of double-stranded DNA molecules is studied through nanoslits fabricated from exfoliated 2D materials, such as graphene or hexagonal boron nitride, and the DNA polymer behavior is examined in this tight confinement. Two types of events are observed in the ionic current: long current blockades that signal DNA translocation and short spikes where DNA enters the slits but withdraws. DNA translocation events exhibit three distinct phases in their current-blockade traces-loading, translation, and exit. Coarse-grained molecular dynamics simulation allows the different polymer configurations of these phases to be identified. DNA molecules, including folds and knots in their polymer structure, are observed to slide through the slits with near-uniform velocity without noticeable frictional interactions of DNA with the confining graphene surfaces. It is anticipated that this new class of 2D-nanoslit devices will provide unique ways to study polymer physics and enable lab-on-a-chip biotechnology.

Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers

It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.

Calculated Terahertz Spectra of Glycine Oligopeptide Solutions Confined in Carbon Nanotubes

To reduce the intense terahertz (THz) wave absorption of water and increase the signal-to-noise ratio, the THz spectroscopy detection of biomolecules usually operates using the nanofluidic channel technologies in practice. The effects of confinement due to the existence of nanofluidic channels on the conformation and dynamics of biomolecules are well known. However, studies of confinement effects on the THz spectra of biomolecules are still not clear. In this work, extensive all-atom molecular dynamics simulations are performed to investigate the THz spectra of the glycine oligopeptide solutions in free and confined environments. THz spectra of the oligopeptide solutions confined in carbon nanotubes (CNTs) with different radii are calculated and compared. Results indicate that with the increase of the degree of confinement (the reverse of the radius of CNT), the THz absorption coefficient decreases monotonically. By analyzing the diffusion coefficient and dielectric relaxation dynamics, the hydrogen bond life, and the vibration density of the state of the water molecules in free solution and in CNTs, we conclude that the confinement effects on the THz spectra of biomolecule solutions are mainly to slow down the dynamics of water molecules and hence to reduce the THz absorption of the whole solution in confined environments.

Confinement-Induced Ordering and Self-Folding of Cellulose Nanofibrils

Cellulose is a pervasive polymer, displaying hierarchical lengthscales and exceptional strength and stiffness. Cellulose's complex organization, however, also hinders the detailed understanding of the assembly, mesoscopic properties, and structure of individual cellulose building blocks. This study combines nanolithography with atomic force microscopy to unveil the properties and structure of single cellulose nanofibrils under weak geometrical confinement. By statistical analysis of the fibril morphology, it emerges that confinement induces both orientational ordering and self-folding of the fibrils. Excluded volume simulations reveal that this effect does not arise from a fibril population bias applied by the confining slit, but rather that the fibril conformation itself changes under confinement, with self-folding favoring fibril's free volume entropy. Moreover, a nonstochastics angular bending probability of the fibril kinks is measured, ruling out alternating amorphous-crystalline regions. These findings push forward the understanding of cellulose nanofibrils and may inspire the design of functional materials based on fibrous templates.

DNA size in confined environments

For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders.

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.

Measuring the wall depletion length of nanoconfined DNA

Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomic DNA with contour length separations of at least 30 µm (88 325 base pairs) between nick pairs. Over 5 × 106 measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data.

Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement

We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.

Shape of a Stretched Polymer

The shape of a polymer plays an important role in its interactions with surrounding molecules. We characterize the shape and the orientational properties of a polymer chain under tension in a good solvent, a physical condition that is often realized both in single-molecule experiments and in vivo. Our findings reveal the existence of hitherto unobserved universal laws encompassing polymers with different rigidities and including the possible presence of excluded-volume effects, showing that both shape and orientation are solely determined by the force contribution to the free energy. In doing so, they also provide a simple way to retrieve these quantities from the knowledge of the force-versus-extension curve.

Spatial confinement induces hairpins in nicked circular DNA

In living cells, DNA is highly confined in space with the help of condensing agents, DNA binding proteins and high levels of supercoiling. Due to challenges associated with experimentally studying DNA under confinement, little is known about the impact of spatial confinement on the local structure of the DNA. Here, we have used well characterized slits of different sizes to collect high resolution atomic force microscopy images of confined circular DNA with the aim of assessing the impact of the spatial confinement on global and local conformational properties of DNA. Our findings, supported by numerical simulations, indicate that confinement imposes a large mechanical stress on the DNA as evidenced by a pronounced anisotropy and tangent-tangent correlation function with respect to non-constrained DNA. For the strongest confinement we observed nanometer sized hairpins and interwound structures associated with the nicked sites in the DNA sequence. Based on these findings, we propose that spatial DNA confinement in vivo can promote the formation of localized defects at mechanically weak sites that could be co-opted for biological regulatory functions.

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.

Dynamics of DNA Squeezed Inside a Nanochannel via a Sliding Gasket

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or "nanodozer". From our simulations we extract the nonequilibrim density profile c ( x , t ) of the squeezed molecule along the channel axis (x-coordinate) and then analyze the non-equilibrium profile using a recently introduced phenomenological Nonlinear Partial Differential Equation (NPDE) model. Since the NPDE approach also fits the experimental results well and is numerically efficient to implement, the combined BD + NPDE methods can be a powerful approach to analyze details of the confined molecular dynamics. In particular, the overall excellent agreement between the two complementary sets of data provides a strategy for carrying out large scale simulation on semi-flexible biopolymers in confinement at biologically relevant length scales.

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.

Flow of DNA in micro/nanofluidics: From fundamentals to applications

Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil-stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.

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.

Knotting dynamics of DNA chains of different length confined in nanochannels

Langevin dynamics simulations are used to characterize the typical mechanisms governing the spontaneous tying, untying and the dynamical evolution of knots in coarse-grained models of DNA chains confined in nanochannels. In particular we focus on how these mechanisms depend on the chain contour length, Lc, at a fixed channel width D = 56 nm corresponding to the onset of the Odijk scaling regime where chain backfoldings and hence knots are disfavoured but not suppressed altogether. We find that the lifetime of knots grows significantly with Lc, while that of unknots varies to a lesser extent. The underlying kinetic mechanisms are clarified by analysing the evolution of the knot position along the chain. At the considered confinement, in fact, knots are typically tied by local backfoldings of the chain termini where they are eventually untied after a stochastic motion along the chain. Consequently, the lifetime of unknots is mostly controlled by backfoldings events at the chain ends, which is largely independent of Lc. The lifetime of knots, instead, increases significantly with Lc because knots can, on average, travel farther along the chain before being untied. The observed interplay of knots and unknots lifetimes underpins the growth of the equilibrium knotting probability of longer and longer chains at fixed channel confinement.

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.

Accuracy of the blob model for single flexible polymers inside nanoslits that are a few monomer sizes wide

The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the confining geometry to be much larger than the monomer size. In this paper, the opposite limit of polymer in nanoslits with one to several monomers width is studied, using molecular dynamics simulations. Extension of the polymer inside nanoslits, confinement force on the plates, and the effective spring constant of the confined polymer are investigated. Despite the theoretical limitations of the blob model, the simulation results are explained with the blob model very well. The agreement is observed for the static properties and the dynamic spring constant of the polymer. A theoretical description of the conditions under which the dynamic spring constant of the polymer is independent of the small number of monomers inside blobs is given. Our results on the limit of applicability of the blob model can be useful in the design of nanotechnology devices.

Knotting and Unknotting Dynamics of DNA Strands in Nanochannels

The self-knotting dynamics of DNA strands confined in nanochannels is studied with Brownian simulations. The model DNA chains are several microns long and placed inside channels that are 50-300 nm wide. This width range covers the transition between different metric scaling regimes and the concomitant drop of DNA knotting probability for channel widths below ∼75 nm. We find that knots typically originate from deep looping and backfoldings of the chain ends. Upon lowering the channel width, backfoldings become shallower and rarer and the lifetime of knots decreases while that of unknots increases. This lifetimes interplay causes the dramatic reduction of knots incidence for increasing confinement. The results can aid the design of nanochannels capable of harnessing the self-knotting dynamics to quench or relax the DNA topological state as desired.

Nanoslit Confined DNA at Low Ionic Strengths

We present nanoslit confined DNA conformations at very low ionic strengths and a theory to explain most measurements for single DNA molecule size under strong nanoslit confinement. Very low ionic strength conditions not only increase the DNA persistence length dramatically, but also cause DNA molecules to swell to the extent that the effective diameter of DNA becomes larger than the nanoslit height. By accounting for these effects, our results and theory provide a reasonable clue for a current controversy regarding the dependence of the DNA conformation on slit height (h), persistence length (p), and effective diameter (w).

Direct optical mapping of transcription factor binding sites on field-stretched λ-DNA in nanofluidic devices

Mapping transcription factor (TF) binding sites along a DNA backbone is crucial in understanding the regulatory circuits that control cellular processes. Here, we deployed a method adopting bioconjugation, nanofluidic confinement and fluorescence single molecule imaging for direct mapping of TF (RNA polymerase) binding sites on field-stretched single DNA molecules. Using this method, we have mapped out five of the TF binding sites of E. coli RNA polymerase to bacteriophage λ-DNA, where two promoter sites and three pseudo-promoter sites are identified with the corresponding binding frequency of 45% and 30%, respectively. Our method is quick, robust and capable of resolving protein-binding locations with high accuracy (∼ 300 bp), making our system a complementary platform to the methods currently practiced. It is advantageous in parallel analysis and less prone to false positive results over other single molecule mapping techniques such as optical tweezers, atomic force microscopy and molecular combing, and could potentially be extended to general mapping of protein–DNA interaction sites.

Electroless deposition and nanolithography can control the formation of materials at the nano-scale for plasmonic applications

The new revolution in materials science is being driven by our ability to manipulate matter at the molecular level to create structures with novel functions and properties. The aim of this paper is to explore new strategies to obtain plasmonic metal nanostructures through the combination of a top down method, that is electron beam lithography, and a bottom up technique, that is the chemical electroless deposition. This technique allows a tight control over the shape and size of bi- and three-dimensional metal patterns at the nano scale. The resulting nanostructures can be used as constituents of Surface Enhanced Raman Spectroscopy (SERS) substrates, where the electromagnetic field is strongly amplified. Our results indicate that, in electroless growth, high quality metal nanostructures with sizes below 50 nm may be easily obtained. These findings were explained within the framework of a diffusion limited aggregation (DLA) model, that is a simulation model that makes it possible to decipher, at an atomic level, the rules governing the evolution of the growth front; moreover, we give a description of the physical mechanisms of growth at a basic level. In the discussion, we show how these findings can be utilized to fabricate dimers of silver nanospheres where the size and shape of those spheres is controlled with extreme precision and can be used for very large area SERS substrates and nano-optics, for single molecule detection.

Polymer escape from a confining potential

The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were calculated using the path integral hyperdynamics method to evaluate the escape rate. A minimum is found in the rate for self-avoiding polymers of intermediate length while the escape rate decreases monotonically with polymer length for ideal polymers. The increase in the rate for long, self-avoiding polymers is ascribed to crowding in the potential well which reduces the free energy escape barrier. An effective potential curve obtained using the centroid as an independent variable was evaluated by thermodynamic averaging and Kramers rate theory then applied to estimate the escape rate. While the qualitative features are well reproduced by this approach, it significantly overestimates the rate, especially for the longer polymers. The reason for this is illustrated by constructing a two-dimensional effective energy surface using the radius of gyration as well as the centroid as controlled variables. This shows that the description of a transition state dividing surface using only the centroid fails to confine the system to the region corresponding to the free energy barrier and this problem becomes more pronounced the longer the polymer is. A proper definition of a transition state for polymer escape needs to take into account the shape as well as the location of the polymer.

Tandem array of nanoelectronic readers embedded coplanar to a fluidic nanochannel for correlated single biopolymer analysis

We have developed a two-step electron-beam lithography process to fabricate a tandem array of three pairs of tip-like gold nanoelectronic detectors with electrode gap size as small as 9 nm, embedded in a coplanar fashion to 60 nm deep, 100 nm wide, and up to 150 μm long nanochannels coupled to a world-micro-nanofluidic interface for easy sample introduction. Experimental tests with a sealed device using DNA-protein complexes demonstrate the coplanarity of the nanoelectrodes to the nanochannel surface. Further, this device could improve transverse current detection by correlated time-of-flight measurements of translocating samples, and serve as an autocalibrated velocimeter and nanoscale tandem Coulter counters for single molecule analysis of heterogeneous samples.