A nanofluidic knot factory based on compression of single DNA in nanochannels

Folding a Molecular Strand into a Trefoil Knot of Single Handedness with Co(II)/Co(III) Chaperones

We report the synthesis of a right-handed (Δ-stereochemistry of strand crossings) trefoil knot from a single molecular strand containing three pyrazine-2,5-dicarboxamide units adjacent to point-chiral centers and six pyridine moieties. The oligomeric ligand strand folds into an overhand (open-trefoil) knot through the assistance of coordinatively dynamic Co(II) "chaperones" that drive the formation of a three-metal-ion circular helicate. The entangled structure is kinetically locked by oxidation to Co(III) and covalently captured by ring-closing olefin metathesis to generate a trefoil knot of single topological handedness. The stereochemistry of the strand crossings in the metal-coordinated overhand knot is governed by the stereochemistry of the point-chiral carbon centers in the ligand strand. The overhand and trefoil knots were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography. Removal of the metal ions from the knot, followed by hydrogenation of the alkene, yielded the wholly organic trefoil knot. The metal-free knot and parent ligand were investigated by circular dichroism (CD) spectroscopy. The CD spectra indicate that the topological stereochemistry of the knot has a greater effect on the asymmetry of the chromophore environment than do the point-chiral centers of the strand.

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.

Transient physics in the compression and mixing dynamics of two nanochannel-confined polymer chains

We use molecular dynamics (MD) simulation and nanofluidic experiments to probe the non-equilibrium transient physics of two nanochannel-confined polymers driven against a permeable barrier in a flow field. For chains with a persistence length P smaller than the channel diameter D, both simulation and experiment with dsDNA reveal nonuniform mixing of the two chains, with one chain dominating locally in what we term "aggregates." Aggregates undergo stochastic dynamics, persisting for a limited time, then disappearing and reforming. Whereas aggregate-prone mixing occurs immediately at sufficiently high flow speeds, chains stay segregated at intermediate flow for some time, often attempting to mix multiple times, before suddenly successfully mixing. Observation of successful mixing nucleation events in nanofluidic experiments reveal that they arise through a peculiar "back-propagation" mechanism whereby the upstream chain, closest to the barrier, penetrates and passes through the downstream chain (farthest from the barrier) moving against the flow direction. Simulations suggest that the observed back-propagation nucleation mechanism is favored at intermediate flow speeds and arises from a special configuration where the upstream chain exhibits one or more folds facing the downstream chain, while the downstream chain has an unfolded chain end facing upstream.

Knot Formation on DNA Pushed Inside Chiral Nanochannels

We performed coarse-grained molecular dynamics simulations of DNA polymers pushed inside infinite open chiral and achiral channels. We investigated the behavior of the polymer metrics in terms of span, monomer distributions and changes of topological state of the polymer in the channels. We also compared the regime of pushing a polymer inside the infinite channel to the case of polymer compression in finite channels of knot factories investigated in earlier works. We observed that the compression in the open channels affects the polymer metrics to different extents in chiral and achiral channels. We also observed that the chiral channels give rise to the formation of equichiral knots with the same handedness as the handedness of the chiral channels.

Mixing and demixing arising from compression of two semiflexible polymer chains in nanochannels

We use molecular dynamics simulation to probe the non-equilibrium physics of two nanochannel-confined semiflexible polymers in a homogeneous flow field. We find that for sufficiently stiff chains the internal organization of the two chains takes the form of interwoven folds and circular coils. This organization can lead to mixing or demixing depending on chain stiffness and flow speed. At low and intermediate flow, the two chains adopt a folded configuration, which favours mixing. At high flow, the two chains adopt a predominantly coiled configuration. The coiled configuration results in demixing when the chains are compressed from an initially demixed condition and mixing when the chains are compressed from an initially mixed condition. We find that the mixing/demixing behaviour is governed by the ratio of the number of folded segments of one chain relative to the other at low flow and by the degree of coiling in both chains at high flow. For decreasing stiffness, the chains start to aggregate locally instead of mixing smoothly at low and intermediate flow. In the limit of completely flexible chains, the two chains either completely segregate at low flow, or adopt a locally demixed configuration consisting of large aggregates of one chain relative to the other that undergo complex stochastic dynamics, diffusing, disintegrating, and reforming at intermediate flow. The transition from complete segregation to the aggregate-dominated configuration occurs when the linear intra-chain ordering breaks down.

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.

Diffusion of knots in nanochannel-confined DNA molecules

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Pressure of Linear and Ring Polymers Confined in a Cavity

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Influence of ionic conditions on knotting in a coarse-grained model for DNA

We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and can be used for guiding future experiments on DNA knots.

Knot Factories with Helical Geometry Enhance Knotting and Induce Handedness to Knots

We performed molecular dynamics simulations of DNA polymer chains confined in helical nano-channels under compression in order to explore the potential of knot-factories with helical geometry to produce knots with a preferred handedness. In our simulations, we explore mutual effect of the confinement strength and compressive forces in a range covering weak, intermediate and strong confinement together with weak and strong compressive forces. The results find that while the common metrics of polymer chain in cylindrical and helical channels are very similar, the DNA in helical channels exhibits greatly different topology in terms of chain knottedness, writhe and handedness of knots. The results show that knots with a preferred chirality in terms of average writhe can be produced by using channels with a chosen handedness.

Organized states arising from compression of single semiflexible polymer chains in nanochannels

We use molecular dynamics simulation to probe the nonequilibrium physics of single nanochannel-confined semiflexible polymers in a homogeneous flow field. The flow field compresses the polymer against the end of the nanochannel, simulating an experiment of a nanochannel confined chain compressed against a slit barrier. The flow-based compression gives rise to a packing of the chain against the channel end that possesses a striking organization, consisting of interweaving of folds and circular coils. For stiff chains at low flow, we find that the organization is dominated by repeated hairpin folds. For stiff chains at higher flow, we observe that circular coils arise along with the folds, with folding and coiling domains becoming interwoven at the highest flow speeds. Chain organization is retained even when the chain persistence length is on order of the channel width. We show that the global polymer organization, consisting of a number of defined folds and coiled loops, arises from the minimization of the total chain free energy.

Knot formation of dsDNA pushed inside a nanochannel

Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.

Quantifying the effects of slit confinement on polymer knots using the tube model

Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

Interactions between two knots in nanochannel-confined DNA molecules

Experimental data on the interaction between two knots in deoxyribonucleic acid (DNA) confined in nanochannels produced two particular behaviors of knot pairs along the DNA molecules: (i) widely separated knots experience an attractive interaction but only remain in close proximity for several seconds and (ii) knots tend to remain separated until one of the knots unravels at the chain end. The associated free energy profile of the knot-knot separation distance for an ensemble of DNA knots exhibits a global minimum when knots are separated, indicating that the separated knot state is more stable than the intertwined knot state, with dynamics in the separated knot state that are consistent with independent diffusion. The experimental observations of knot-knot interactions under nanochannel confinement are inconsistent with previous simulation-based and experimental results for stretched polymers under tension wherein the knots attract and then stay close to each other. This inconsistency is postulated to result from a weaker fluctuation-induced attractive force between knots under confinement when compared to the knots under tension, the latter of which experience larger fluctuations in transverse directions.

DNA Knot Malleability in Single-Digit Nanopores

Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.

Aptamer-Gated Ion Channel for Ultrasensitive Mucin 1 Detection

Detection of cancer markers is important for early diagnosis and timely treatment of cancer. In this study, we fabricated a tailorable gold nanofilm-anodized aluminum oxide (Au-AAO) ion channel through nanoparticle self-assembly and proposed a highly sensitive and selective Mucin 1 (MUC1) detection method. By engineering the optimal layers of the Au-AAO ion channel and encoding the aptamer between the interlayers, a highly controllable ion rectification phenomenon was observed. From this, the relationship between the rectification ratio (RR) and the concentration of MUC1 was established and the highly sensitive detection of MUC1 is achieved. We found that the aptamer-modified Au-AAO ion channel has a good linear range within the MUC1 concentration of 1-10⁴ fg mL^-1 and the limit of detection (LOD) was as low as 0.0364 fg mL^-1 (0.0025 aM). Thus, this research opens a new horizon for fabricating multi-functional ion channels as well as developing ultrasensitive detection technologies.

Effects of turn-structure on folding and entanglement in artificial molecular overhand knots

The length and constitution of spacers linking three 2,6-pyridinedicarboxamide units in a molecular strand influence the tightness of the resulting overhand (open-trefoil) knot that the strand folds into in the presence of lanthanide(iii) ions. The use of β-hairpin forming motifs as linkers enables a metal-coordinated pseudopeptide with a knotted tertiary structure to be generated. The resulting pseudopeptide knot has one of the highest backbone-to-crossing ratios (BCR)—a measure of knot tightness (a high value corresponding to looseness)—for a synthetic molecular knot to date. Preorganization in the crossing-free turn section of the knot affects aromatic stacking interactions close to the crossing region. The metal-coordinated pseudopeptide knot is compared to overhand knots with other linkers of varying tightness and turn preorganization, and the entangled architectures characterized by NMR spectroscopy, ESI-MS, CD spectroscopy and, in one case, X-ray crystallography. The results show how it is possible to program specific conformational properties into different key regions of synthetic molecular knots, opening the way to systems where knotting can be systematically incorporated into peptide-like chains through design.

Spacers linking 2,6-pyridinedicarboxamide units influence the tightness of the corresponding lanthanide-coordinated overhand knot. β-Hairpin forming motifs generate a metal-coordinated pseudopeptide with a knotted tertiary structure.

Topological Disentanglement of Linear Polymers under Tension

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semiflexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain Our theory is extensively benchmarked with corresponding molecular dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.

Free energy of a knotted polymer confined to narrow cylindrical and conical channels

Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.

Tying different knots in a molecular strand

The properties of knots are exploited in a range of applications, from shoelaces to the knots used for climbing, fishing and sailing¹. Although knots are found in DNA and proteins², and form randomly in other long polymer chains^3,4, methods for tying⁵ different sorts of knots in a synthetic nanoscale strand are lacking. Molecular knots of high symmetry have previously been synthesized by using non-covalent interactions to assemble and entangle molecular chains^6-15, but in such instances the template and/or strand structure intrinsically determines topology, which means that only one type of knot is usually possible. Here we show that interspersing coordination sites for different metal ions within an artificial molecular strand enables it to be tied into multiple knots. Three topoisomers-an unknot (0₁) macrocycle, a trefoil (3₁) knot^6-15, and a three-twist (5₂) knot-were each selectively prepared from the same molecular strand by using transition-metal and lanthanide ions to guide chain folding in a manner reminiscent of the action of protein chaperones¹⁶. We find that the metal-ion-induced folding can proceed with stereoinduction: in the case of one knot, a lanthanide(III)-coordinated crossing pattern formed only with a copper(I)-coordinated crossing of particular handedness. In an unanticipated finding, metal-ion coordination was also found to translocate an entanglement from one region of a knotted molecular structure to another, resulting in an increase in writhe (topological strain) in the new knotted conformation. The knot topology affects the chemical properties of the strand: whereas the tighter 5₂ knot can bind two different metal ions simultaneously, the looser 3₁ isomer can bind only either one copper(I) ion or one lutetium(III) ion. The ability to tie nanoscale chains into different knots offers opportunities to explore the modification of the structure and properties of synthetic oligomers, polymers and supramolecules.

Separation of Geometrical and Topological Entanglement in Confined Polymers Driven out of Equilibrium

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nanochannels and under periodic compression. By introducing suitable observables, we can distinguish two main forms of entanglement that we term geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression-elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.

Loop-closure kinetics reveal a stable, right-handed DNA intermediate in Cre recombination

In Cre site-specific recombination, the synaptic intermediate is a recombinase homotetramer containing a pair of loxP DNA target sites. The enzyme system's strand-exchange mechanism proceeds via a Holliday-junction (HJ) intermediate; however, the geometry of DNA segments in the synapse has remained highly controversial. In particular, all crystallographic structures are consistent with an achiral, planar Holliday-junction (HJ) structure, whereas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-handed chiral junction. We use the kinetics of loop closure involving closely spaced (131-151 bp) loxP sites to investigate the in-aqueo ensemble of conformations for the longest-lived looped DNA intermediate. Fitting the experimental site-spacing dependence of the loop-closure probability, J, to a statistical-mechanical theory of DNA looping provides evidence for substantial out-of-plane HJ distortion, which unequivocally stands in contrast to the square-planar intermediate geometry from Cre-loxP crystal structures and those of other int-superfamily recombinases. J measurements for an HJ-isomerization-deficient Cre mutant suggest that the apparent geometry of the wild-type complex is consistent with temporal averaging of right-handed and achiral structures. Our approach connects the static pictures provided by crystal structures and the natural dynamics of macromolecules in solution, thus advancing a more comprehensive dynamic analysis of large nucleoprotein structures and their mechanisms.

Identifying knot types of polymer conformations by machine learning

We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot. Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer conformations for five knot types: 0, 3_{1}, 4_{1}, 5_{1}, and 5_{2}, and we design various NN models for classification. Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest that deep learning may be used in specific applications of knot detection where some error is permissible. Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.

Compression and Stretching of Single DNA Molecules under Channel Confinement

We study the compression and extension response of single dsDNA (double-stranded DNA) molecules confined in cylindrical channels by means of Monte Carlo simulations. The elastic response of micrometer-sized DNA to the external force acting through the chain ends or through the piston is markedly affected by the size of the channel. The interpretation of the force (f)-displacement (R) functions under quasi-one-dimensional confinement is facilitated by resolving the overall change of displacement ΔR into the confinement contribution ΔR_D and the force contribution ΔR_f. The external stretching of confined DNA results in a characteristic pattern of f-R functions involving their shift to the larger extensions due to the channel-induced pre-stretching ΔR_D. A smooth end-chain compression into loop-like conformations observed in moderately confined DNA can be accounted for by the relationship valid for a Gaussian chain in bulk. In narrow channels, the considerably pre-stretched DNA molecules abruptly buckle on compression by the backfolding into hairpins. On the contrary, the piston compression of DNA is characterized by a gradual reduction of the chain span S and by smooth f-S functions in the whole spatial range from the 3d near to 1d limits. The observed discrepancy between the shape of the f-R and f-S functions from two compression methods can be important for designing nanopiston experiments of compaction and knotting of single DNA in nanochannels.

Complex DNA knots detected with a nanopore sensor

Equilibrium knots are common in biological polymers-their prevalence, size distribution, structure, and dynamics have been extensively studied, with implications to fundamental biological processes and DNA sequencing technologies. Nanopore microscopy is a high-throughput single-molecule technique capable of detecting the shape of biopolymers, including DNA knots. Here we demonstrate nanopore sensors that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding. We show the occurrence of both tight and loose knots, reconciling previous contradictory results from different experimental techniques. We evidence the occurrence of two quantitatively different modes of knot translocation through the nanopores, involving very different tension forces. With large statistics, we explore the complex knots and, for the first time, reveal the existence of rare composite knots. We use parametrized complexity, in concert with simulations, to test the theoretical assumptions of the models, further asserting the relevance of nanopores in future investigation of knots.

Long-Lived Self-Entanglements in Ring Polymers

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

Force-displacement relations at compression of dsDNA macromolecules

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

Directly Accessible and Transferrable Nanofluidic Systems for Biomolecule Manipulation

Molecular detection and manipulation via nanofluidic systems offers new routes for single-molecule analysis to study epigenetic mechanisms and genetic mutation of disease. For detection of single biological molecule, many types of nanomicrofluidic systems have been utilized. Typically, mechanical tethering, fluidic pressure, chemical interactions, or electrical forces allow controllable attraction, enrichment, confinement, and elongation of target molecules. The currently available methods, however, are unable to offer both molecular manipulation and direct and concurrent assessment of target molecules in the system due to the nature of enclosed channels and associated fluidic components. Here, we introduce a wafer-scale nanofluidic system that incorporates an array of accessible open nanochannels and nano-microtrappers to enrich and elongate target molecules (DNA) via the combination of an electric field and hydrodynamic force. The open nanofluidic system allows easy access, direct observation, and manipulation of molecules in the nanochannels. The presence of a stretched single DNA and the efficacy of the nanofluidic system are studied by fluorescence microscopy and atomic force microscopy. Hybrid integration of the nanodevice fabrication with a material transfer printing technique enables to design a highly flexible and transferrable nanofluidic system after molecular concentration.

Topological Disentanglement Dynamics of Torus Knots on Open Linear Polymers

We simulate and study the topological disentanglement occurring when torus knots reach the ends of a semiflexible open polymer (decay into simpler knots or unknotting). Through a rescaling procedure and the application of appropriate boundary conditions, we show that the full unknotting process can be understood in terms of point-like particles representing essential crossings, diffusing on the support [0, 1]. We address the bending and configurational free energy drives on the diffusion process, together with the scaling properties of the effective diffusion and friction coefficients. Agreement with simulations suggests universal features for these two model parameters.

Fabrication of polydimethylsiloxane nanofluidic chips under AFM tip-based nanomilling process

In current research realm, polydimethylsiloxane (PDMS)-based nanofluidic devices are widely used in medical, chemical, and biological applications. In the present paper, a novel nanomilling technique (consisting of an AFM system and a piezoelectric actuator) was proposed to fabricate nanochannels (with controllable sizes) on PDMS chips, and nanochannel size was controlled by the driving voltage and frequency inputted to the piezoelectric actuator. Moreover, microchannel and nanochannel molds were respectively fabricated by UV lithography and AFM tip-based nanomilling, and finally, PDMS slabs with micro/nanochannels were obtained by transfer process. The influences of PDMS weight ratio on nanochannel size were also investigated. The bonding process of microchannel and nanochannel slabs was conducted on a homemade alignment system consisted of an optical monocular microscope and precision stages. Furthermore, the effects of nanochannel size on electrical characteristics of KCl solution (concentration of 1 mM) were analyzed. Therefore, it can be concluded that PDMS nanofluidic devices with multiple nanochannels of sub-100-nm depth can be efficiently and economically fabricated by the proposed method.

Topologically Linked Chains in Confinement

We examine how channel confinement affects the equilibrium properties of topologically linked ring polymers and, by contrast, of equivalent unlinked rings, too. By performing extensive simulations of semiflexible rings of different chain length, N, and channel diameter, D, we discover three notable properties purely due to linking. First, upon entering the weak confinement regime, the length of the physically linked portion, lLKThe, becomes independent of chain length. Next, even when confinement is strong enough to pull apart and segregate unlinked rings, lLK stays much larger than in the highly stretched limit. Finally, at fixed N, lLK varies approximately as D^0.5, and we provide a simple scaling argument for this power-law behavior. These properties, which may hold for different link topologies, can be tested by current experimental setups on DNA rings confined in microchannels. Moreover, they could be relevant for the efficient in vivo unlinking of newly replicated bacterial chromosomes.

Nanochannel-Confined TAMRA-Polypyrrole Stained DNA Stretching by Varying the Ionic Strength from Micromolar to Millimolar Concentrations

Large DNA molecules have been utilized as a model system to investigate polymer physics. However, DNA visualization via intercalating dyes has generated equivocal results due to dye-induced structural deformation, particularly unwanted unwinding of the double helix. Thus, the contour length increases and the persistence length changes so unpredictably that there has been a controversy. In this paper, we used TAMRA-polypyrrole to stain single DNA molecules. Since this staining did not change the contour length of B-form DNA, we utilized TAMRA-polypyrrole stained DNA as a tool to measure the persistence length by changing the ionic strength. Then, we investigated DNA stretching in nanochannels by varying the ionic strength from 0.06 mM to 47 mM to evaluate several polymer physics theories proposed by Odijk, de Gennes and recent papers to deal with these regimes.

Miniaturized flow cell with pneumatically-actuated vertical nanoconfinement for single-molecule imaging and manipulation

Convex Lens-induced Confinement (CLiC) is a single-molecule imaging technique that uses a deformable glass flow cell to gently trap, manipulate, and visualize single molecules within micro- and nano-structures, to enable a wide range of applications. Here, we miniaturize the CLiC flow cell, from 25 × 25 to 3 × 3 mm 2 and introduce pneumatic control of the confinement. Miniaturization of the flow cell improves fabrication throughput by almost two orders of magnitude and, advantageous for pharmaceutical and diagnostic applications where samples are precious, significantly lowers the internal volume from microliters to nanoliters. Pneumatic control of the device reduces the confinement gradient and improves mechanical stability while maintaining low autofluorescence and refractive index-matching with oil-immersion objectives. To demonstrate our "mini CLiC" system, we confine and image DNA in sub-50 nm nanogrooves, with high DNA extension consistent with the Odijk confinement regime.

Correlation anisotropy and stiffness of DNA molecules confined in nanochannels

The anisotropy of orientational correlations in DNA molecules confined in cylindrical channels is explored by Monte Carlo simulations using a coarse-grained model of double-stranded (ds) DNA. We find that the correlation function ⟨C(s)⟩_⊥ in the transverse (confined) dimension exhibits a region of negative values in the whole range of channel sizes. Such a clear-cut sign of the opposite orientation of chain segments represents a microscopic validation of the Odijk deflection mechanism in narrow channels. At moderate-to-weak confinement, the negative ⟨C(s)⟩_⊥ correlations imply a preference of DNA segments for transverse looping. The inclination for looping can explain a reduction of stiffness as well as the enhanced knotting of confined DNA relative to that detected earlier in bulk at some channel sizes. Furthermore, it is shown that the orientational persistence length P_or fails to convey the apparent stiffness of DNA molecules in channels. Instead, correlation lengths P_∥ and P_⊥ in the axial and transverse directions, respectively, encompass the channel-induced modifications of DNA stiffness.