The polymer physics of single DNA confined in nanochannels

Techniques for assessing telomere length: A methodological review

Telomeres are located at the ends of chromosomes and have specific sequences with a distinctive structure that safeguards genes. They possess capping structures that protect chromosome ends from fusion events and ensure chromosome stability. Telomeres shorten in length during each cycle of cell division. When this length reaches a certain threshold, it can lead to genomic instability, thus being implicated in various diseases, including cancer and neurodegenerative disorders. The possibility of telomeres serving as a biomarker for aging and age-related disease is being explored, and their significance is still under study. This is because post-mitotic cells, which are mature cells that do not undergo mitosis, do not experience telomere shortening due to age. Instead, other causes, for example, exposure to oxidative stress, can directly damage the telomeres, causing genomic instability. Nonetheless, a general agreement has been established that measuring telomere length offers valuable insights and forms a crucial foundation for analyzing gene expression and epigenetic data. Numerous approaches have been developed to accurately measure telomere lengths. In this review, we summarize various methods and their advantages and limitations for assessing telomere length.

Unravelled proteins form blobs during translocation across nanopores

The electroosmotic-driven transport of unravelled proteins across nanopores is an important biological process that is now under investigation for the rapid analysis and sequencing of proteins. For this approach to work, however, it is crucial that the polymer is threaded in single file. Here we found that, contrary to the electrophoretic transport of charged polymers such as DNA, during polypeptide translocation blob-like structures typically form inside nanopores. Comparisons between different nanopore sizes, shapes and surface chemistries showed that under electroosmotic-dominated regimes single-file transport of polypeptides can be achieved using nanopores that simultaneously have an entry and an internal diameter that is smaller than the persistence length of the polymer, have a uniform non-sticky ( i . e . non-aromatic) nanopore inner surface, and using moderate translocation velocities.

An optically fabricated gradient nanochannel array to access the translocation dynamics of T4-phage DNA through nanoconfinement

It has been widely recognized that nanostructures in natural biological materials play important roles in regulating life machinery. Even though nanofabrication techniques such as two-photon polymerization (TPP) provide sub-100 nm fabrication resolution, it remains technologically challenging to produce 3D nanoscale features modeling the complexity in vivo. We herein demonstrate that a nanochannel array carrying different sizes and nanostructures with gradually transitioning dimensions can be easily produced on a slightly tilted nano-stage. Using the gradient nanochannel array, we systematically investigate the factors affecting the dynamics of DNA translocation through nanoconfinement, including the size of biomolecules and geometrical features of the physical environment, which resembles the selectivity of nanopores in the cell membrane. It is observed that T4-phage DNA shows distinctive conformational transition dynamics during translocation through nanochannels driven by electric field or flow, and the deformation energy required for DNA to enter the nanochannels depends on both chemical environmental conditions, i.e., the ionic strength regulating DNA persistence length and nanochannel dimension. In the electric field, DNA repeatedly gets stretched and compressed during its migration through the nanochannel, reflected by elevated fluctuation in extension, which is substantially greater than the thermal fluctuation. However, driven by flow, DNA remains stretched during translocation through nanochannels, and shows variances in extension of merely a few hundred nanometers. These results indicate that the optically fabricated gradient nanochannel array is a suitable platform for optimizing the experimental conditions for biomedical applications such as gene mapping, and verify that production of complex three dimensional (3D) nanostructures can be greatly simplified by including slight inclination during TPP fabrication.

A model for ribosome translocation based on the alternated displacement of its subunits

A meaningful dilemma in ribosome translocation arising from experimental facts is that, although the ribosome-mRNA interaction force always has a significant magnitude, the ribosome still moves to the next codon on the mRNA. How does the ribosome move to the next codon in the sequence while holding the mRNA tightly? The hypothesis proposed here is that ribosome subunits alternate the grip of the ribosome on the mRNA, freeing the other subunit of such interaction for a while, thus allowing its motion to the following codon. Based on this assumption, a single-loop cycle of ribosome configurations involving the relative position of its subunits is elaborated. When its dynamic is modeled as a Markov network, it gives expressions for the average ribosome translocation speed and stall force as functions of the equilibrium constants among the proposed ribosome configurations. The calculations have a reasonable agreement with experimental results, and the succession of molecular events considered here is consistent with current biomolecular concepts of the ribosome translocation process. Thus, the alternative displacements hypothesis developed in the present work suggests a feasible explanation of ribosome translocation.

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.

Crowding-Induced Spatial Organization of Gene Expression in Cell-Sized Vesicles

Cell-free protein synthesis is an important tool for studying gene expression and harnessing it for applications. In cells, gene expression is regulated in part by the spatial organization of transcription and translation. Unfortunately, current cell-free approaches are unable to control the organization of molecular components needed for gene expression, which limits the ability to probe and utilize its effects. Here, we show, using complementary computational and experimental approaches, that macromolecular crowding can be used to control the spatial organization and translational efficiency of gene expression in cell-sized vesicles. Computer simulations and imaging experiments reveal that, as crowding is increased, DNA plasmids become localized at the inner surface of vesicles. Ribosomes, in contrast, remain uniformly distributed, demonstrating that crowding can be used to differentially organize components of gene expression. We further carried out cell-free protein synthesis reactions in cell-sized vesicles and quantified mRNA and protein abundance. At sufficiently high levels of crowding, we observed localization of mRNA near vesicle surfaces, a decrease in translational efficiency and protein abundance, and anomalous scaling of protein abundance as a function of vesicle size. These results are consistent with high levels of crowding causing altered spatial organization and slower diffusion. Our work demonstrates a straightforward way to control the organization of gene expression in cell-sized vesicles and provides insight into the spatial regulation of gene expression in cells.

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.

Confinement free energy for a polymer chain: Corrections to scaling

Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D^-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D^-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ D^y/N^Δ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).

Entropic force of cone-tethered polymers interacting with a planar surface

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched Rosenbluth method Monte Carlo simulations are used to calculate the variation of the conformational free energy F of a hard-sphere polymer with respect to the cone-tip-to-surface distance h from which the variation of the entropic force f≡|dF/dh| with h is determined. We consider the following cases: a single freely jointed tethered chain, a single semiflexible tethered chain, and several freely jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. [Maghrebi et al., Europhys. Lett. 96, 66002 (2011)0295-507510.1209/0295-5075/96/66002; Phys. Rev. E 86, 061801 (2012)1539-375510.1103/PhysRevE.86.061801] that f∝(γ_{∞}-γ_{0})h^{-1}, where γ_{0} and γ_{∞} are universal scaling exponents for the partition function of the tethered polymer for h=0 and h=∞, respectively. The measured functions f(h) are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.

Nonlinear electrophoretic velocity of DNA in slitlike confinement

We have applied zero-time-averaged alternating electric fields to DNA molecules in a cross-shaped nanofluidic slit. We observed a net drift of DNA molecules, the magnitude of which depends on the square of the electric field amplitude. From the rate of accumulation of DNA at the center of the device, we derive an estimate for the second-order electrophoretic mobility, μ_{2}. We observe that focusing is absent at a dipole rotation frequency >20 Hz, which suggests that μ_{2} depends on the frequency of the alternating fields. The observation of a nonzero μ_{2} raises the possibility of frequency-dependent electrophoretic DNA separation by length achievable in the absence of a sieving matrix.

Mobility of Bacterial Protein Hfq on dsDNA: Role of C-Terminus-Mediated Transient Binding

The mobility of protein is fundamental in the machinery of life. Here, we have investigated the effect of DNA binding in conjunction with DNA segmental fluctuation (internal motion) of the bacterial Hfq master regulator devoid of its amyloid C-terminus domain. Hfq is one of the most abundant nucleoid associated proteins that shape the bacterial chromosome and is involved in several aspects of nucleic acid metabolism. Fluorescence microscopy has been used to track a C-terminus domain lacking mutant form of Hfq on double-stranded DNA, which is stretched by confinement to a rectangular nanofluidic channel. The mobility of the mutant is strongly accelerated with respect to the wild-type variant. Furthermore, it shows a reverse dependence on the internal motion of DNA, in that slower motion results in slower protein diffusion. The results demonstrate the subtle role of DNA internal motion in controlling the mobility of a nucleoid associated protein, and, in particular, the importance of transient binding and moving DNA strands out of the way.

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.

Crowding-induced polymer trapping in a channel

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

Compression and Stretching of Confined Linear and Ring Polymers by Applying Force

We use Langevin dynamics to study the deformations of linear and ring polymers in different confinements by applying compression and stretching forces on their two sides. Our results show that the compression deformations are the results of an interplay among of polymer rigidity, degree of confinement, and force applied. When the applied force is beyond the threshold required for the buckling transition, the semiflexible chain under the strong confinement firstly buckles; then comes helical deformation. However, under the same force loading, the semiflexible chain under the weaker confinement exhibits buckling instability and shrinks from the folded ends/sides until it becomes three-folded structures. This happens because the strong confinement not only strongly reduces the buckling wavelength, but also increases the critical buckling force threshold. For the weakly confined polymers, in compression process, the flexible linear polymer collapses into condensed states under a small external force, whereas the ring polymer only shows slight shrinkage, due to the excluded volume interactions of two strands in the crowded states. These results are essential for understanding the deformations of the ring biomacromolecules and polymer chains in mechanical compression or driven transport.

Fabrication of Ultranarrow Nanochannels with Ultrasmall Nanocomponents in Glass Substrates

Nanofluidics is supposed to take advantage of a variety of new physical phenomena and unusual effects at nanoscales typically below 100 nm. However, the current chip-based nanofluidic applications are mostly based on the use of nanochannels with linewidths above 100 nm, due to the restricted ability of the efficient fabrication of nanochannels with narrow linewidths in glass substrates. In this study, we established the fabrication of nanofluidic structures in glass substrates with narrow linewidths of several tens of nanometers by optimizing a nanofabrication process composed of electron-beam lithography and plasma dry etching. Using the optimized process, we achieved the efficient fabrication of fine glass nanochannels with sub-40 nm linewidths, uniform lateral features, and smooth morphologies, in an accurate and precise way. Furthermore, the use of the process allowed the integration of similar or dissimilar material-based ultrasmall nanocomponents in the ultranarrow nanochannels, including arrays of pockets with volumes as less as 42 zeptoliters (zL, 10⁻²¹ L) and well-defined gold nanogaps as narrow as 19 nm. We believe that the established nanofabrication process will be very useful for expanding fundamental research and in further improving the applications of nanofluidic devices.

Equilibrium organization, conformation, and dynamics of two polymers under box-like confinement

Motivated by recent nanofluidics experiments, we use Brownian dynamics and Monte Carlo simulations to study the conformation, organization and dynamics of two polymer chains confined to a single box-like cavity. The polymers are modeled as flexible bead-spring chains, and the box has a square cross-section of side length L and a height that is small enough to compress the polymers in that dimension. For sufficiently large L, the system behaviour approaches that of an isolated polymer in a slit. However, the combined effects of crowding and confinement on the polymer organization, conformation and equilibrium dynamics become significant when where is the transverse radius of gyration for a slit geometry. In this regime, the centre-of-mass probability distribution in the transverse plane exhibits a depletion zone near the centre of the cavity (except at very small L) and a 4-fold symmetry with quasi-discrete positions. Reduction in polymer size with decreasing L arises principally from confinement rather than inter-polymer crowding. By contrast, polymer diffusion and internal motion are strongly affected by inter-polymer crowding. The two polymers tend to occupy opposite positions relative to the box centre, about which they diffuse relatively freely. Qualitatively, this static and dynamical behaviour differs significantly from that previously observed for confinement of two polymers to a narrow channel. The simulation results for a suitably chosen box width are qualitatively consistent with results from a recent experimental study of two λ-DNA chains confined to a nanofluidic cavity.

Single-molecule optical genome mapping in nanochannels: multidisciplinarity at the nanoscale

The human genome contains multiple layers of information that extend beyond the genetic sequence. In fact, identical genetics do not necessarily yield identical phenotypes as evident for the case of two different cell types in the human body. The great variation in structure and function displayed by cells with identical genetic background is attributed to additional genomic information content. This includes large-scale genetic aberrations, as well as diverse epigenetic patterns that are crucial for regulating specific cell functions. These genetic and epigenetic patterns operate in concert in order to maintain specific cellular functions in health and disease. Single-molecule optical genome mapping is a high-throughput genome analysis method that is based on imaging long chromosomal fragments stretched in nanochannel arrays. The access to long DNA molecules coupled with fluorescent tagging of various genomic information presents a unique opportunity to study genetic and epigenetic patterns in the genome at a single-molecule level over large genomic distances. Optical mapping entwines synergistically chemical, physical, and computational advancements, to uncover invaluable biological insights, inaccessible by sequencing technologies. Here we describe the method's basic principles of operation, and review the various available mechanisms to fluorescently tag genomic information. We present some of the recent biological and clinical impact enabled by optical mapping and present recent approaches for increasing the method's resolution and accuracy. Finally, we discuss how multiple layers of genomic information may be mapped simultaneously on the same DNA molecule, thus paving the way for characterizing multiple genomic observables on individual DNA molecules.

Morphological Transition between Patterns Formed by Threads of Magnetic Beads

Magnetic beads attract each other, forming chains. We push such chains into an inclined Hele-Shaw cell and discover that they spontaneously form self-similar patterns. Depending on the angle of inclination of the cell, two completely different situations emerge; namely, above the static friction angle the patterns resemble the stacking of a rope and below they look similar to a fortress from above. Moreover, locally the first pattern forms a square lattice, while the second pattern exhibits triangular symmetry. For both patterns, the size distributions of enclosed areas follow power laws. We characterize the morphological transition between the two patterns experimentally and numerically and explain the change in polarization as a competition between friction-induced buckling and gravity.

Internal Motion of Chromatin Fibers Is Governed by Dynamics of Uncompressed Linker Strands

Chromatin compaction and internal motion are fundamental aspects of gene expression regulation. Here, we have investigated chromatin fibers comprising recombinant histone octamers reconstituted with double-stranded bacteriophage T4-DNA. The size of the fibers approaches the typical size of genomic topologically associated domains. Atomic force and fluorescence (correlation) microscopy have been used to assess the structural organization, histone-induced compaction, and internal motion. In particular, the fibers are stretched on arrays of nanochannels, each channel with a diameter of 60 or 125 nm. Major intrafiber segregation and fast internal fluctuations are observed. Full compaction was only achieved by triggering an attractive nucleosome interaction through the addition of magnesium cations. Besides compaction, histone complexation results in a dramatic decrease in the fiber's relaxation time. The relaxation times are similar to those of naked DNA with a comparable stretch, which indicates that internal motion is governed by the dynamics of uncompressed linker strands. Furthermore, the main reorganization process is association-dissociation of individually compacted regions. We surmise that the modulation of chromatin's internal motion by histone complexation might have implications for transcriptional bursting.

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.

Role of Internal DNA Motion on the Mobility of a Nucleoid-Associated Protein

Protein transport on DNA is at the core of the machinery of life. Here we investigated the influence of DNA internal motion on the mobility of Hfq, which is involved in several aspects of nucleic acid metabolism and is one of the nucleoid-associated proteins that shape the bacterial chromosome. Fluorescence microscopy was used to follow Hfq on double-stranded DNA that was stretched by confinement to a channel with a diameter of 125 nm. The protein mobility shows a strong dependence on the internal motion of DNA in that slower motion results in faster protein diffusion. A model of released diffusion is proposed that is based on three-dimensional diffusion through the interior of the DNA coil interspersed by periods in which the protein is immobilized in a bound state. We surmise that the coupling between DNA internal motion and protein mobility has important implications for DNA metabolism and protein-binding-related regulation of gene expression.

Effect of Confinement in Nanopores on RNA Interactions with Functionalized Mesoporous Silica Nanoparticles

Amine-functionalized mesoporous silica nanoparticles (MSNPAs) are ideal carriers for oligonucleotides for gene delivery and RNA interference. This investigation examines the thermodynamic driving force of interactions of double-stranded (ds) RNA with MSNPAs as a function of RNA length (84 and 282 base pair) and particle pore diameter (nonporous, 2.7, 4.3, and 8.1 nm) using isothermal titration calorimetry, extending knowledge of solution-based nucleic acid-polycation interactions to RNA confined in nanopores. Adsorption of RNA follows a two-step process: endothermic interactions driven by entropic contribution from counterion (and water) release and an exothermic regime dominated by short-range interactions within the pores. Evidence of hindered pore loading of the longer RNA and pore size-dependent confinement of RNA in the MSPAs is provided from the relative contributions of the endothermic and exothermic regimes. Reduction of endothermic and exothermic enthalpies in both regimes in the presence of salt for both lengths of RNA indicates the significant contribution of short-range electrostatic interactions, whereas ΔH and ΔG values are consistent with conformation changes and desolvation of nucleic acids upon binding with polycations. Knowledge of the interactions between RNA and functionalized porous nanoparticles will aid in porous nanocarrier design suitable for functional RNA delivery.

Systematic Approach toward Accurate and Efficient DNA Sequencing via Nanoconfinement

Coarse-grained modeling tools are employed to simulate the mechanics of DNA loading within a nanoscale confinement and predict semiflexible polymer conformations within the confinement, providing design recommendations for DNA-sequencing devices. A workflow is developed to quantify competing requirements of efficiency and accuracy and extract metrics that guide design optimization. The mean first-passage time for DNA loading is calculated as a function of the nanochannel geometry and the applied electric field. We analyze the interplay between the free energy of confinement and the electric potential energy in achieving high-throughput, base-pair detection. The single-read probability is investigated as informative metrics for sequencing accuracy and for sensing-strategy design. High cost, low throughput, and low accuracy have so far limited the adoption of nanochannel analysis and other long-read technologies. Our work directly addresses these limitations with a systematic approach that is scalable to long molecules and complex geometries.

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.

Equilibrium structure and deformation response of 2D kinetoplast sheets

The considerable interest in two-dimensional (2D) materials and complex molecular topologies calls for a robust experimental system for single-molecule studies. In this work, we study the equilibrium properties and deformation response of a complex DNA structure called a kinetoplast, a 2D network of thousands of linked rings akin to molecular chainmail. Examined in good solvent conditions, kinetoplasts appear as a wrinkled hemispherical sheet. The conformation of each kinetoplast is dictated by its network topology, giving it a unique shape, which undergoes small-amplitude thermal fluctuations at subsecond timescales, with a wide separation between fluctuation and diffusion timescales. They deform elastically when weakly confined and swell to their equilibrium dimensions when the confinement is released. We hope that, in the same way that linear DNA became a canonical model system on the first investigations of its polymer-like behavior, kinetoplasts can serve that role for 2D and catenated polymer systems.

Limitations of the equivalent neutral polymer assumption for theories describing nanochannel-confined DNA

The prevailing theories describing DNA confinement in a nanochannel are predicated on the assumption that wall-DNA electrostatic interactions are sufficiently short-ranged such that the problem can be mapped to an equivalent neutral polymer confined by hard walls with an appropriately reduced effective channel size. To determine when this hypothesis is valid, we leveraged a recently reported experimental data set for the fractional extension of DNA molecules in a 250-nm-wide poly(dimethyl siloxane) (PDMS) nanochannel with buffer ionic strengths between 0.075 and 48 mM. Evaluating these data in the context of the weakly correlated telegraph model of DNA confinement reveals that, at ionic strengths greater than 0.3 mM, the average fractional extension of the DNA molecules agree with theoretical predictions with a mean absolute error of 0.04. In contrast, experiments at ionic strengths below 0.3 mM produce average fractional extensions that are systematically smaller than the theoretical predictions with a larger mean absolute error of 0.15. The deviations between experiment and theory display a correlation coefficient of 0.82 with the decay length for the DNA-wall electrostatics, linking the deviations with a breakdown in approximating the DNA with an equivalent neutral polymer.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

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

Sculpturing wafer-scale nanofluidic devices for DNA single molecule analysis

We present micro- and nanofluidic devices with 3D structures and nanochannels with multiple depths for the analysis of single molecules of DNA. Interfacing the nanochannels with graded and 3D inlets allows the improvement of the flow and controls not only the translocation speed of the DNA but also its conformation inside the nanochannels. The complex, multilevel, multiscale fluidic circuits are patterned in a simple, two-minute imprinting step. The stamp, the key of the technology, is directly milled by focused ion beam, which allows patterning nanochannels with different cross sections and depths, together with 3D transient inlets, all at once. Having such a variety of structures integrated in the same sample allows studying, optimizing and directly comparing their effect on the DNA flow. Here, DNA translocation is studied in long (160 µm) and short (5-40 µm) nanochannels. We study the homogeneity of the stretched molecules in long, meander nanochannels made with this technology. In addition, we analyze the effect of the different types of inlet structures interfacing short nanochannels. We observe pre-stretching and an optimal flow, and no hairpin formation, when the inlets have gradually decreasing widths and depths. In contrast, when the nanochannels are faced with an abrupt transition, we observe clogging and hairpin formation. In addition, 3D inlets strongly decrease the DNA molecules' speed before they enter the nanochannels, and help capturing more DNA molecules. The robustness and versatility of this technology and DNA testing results evidence the potential of imprinted devices in biomedical applications as low cost, disposable lab-on-a-chip devices.

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

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

Multi-scale ordering in highly stretchable polymer semiconducting films

Stretchable semiconducting polymers have been developed as a key component to enable skin-like wearable electronics, but their electrical performance must be improved to enable more advanced functionalities. Here, we report a solution processing approach that can achieve multi-scale ordering and alignment of conjugated polymers in stretchable semiconductors to substantially improve their charge carrier mobility. Using solution shearing with a patterned microtrench coating blade, macroscale alignment of conjugated-polymer nanostructures was achieved along the charge transport direction. In conjunction, the nanoscale spatial confinement aligns chain conformation and promotes short-range π-π ordering, substantially reducing the energetic barrier for charge carrier transport. As a result, the mobilities of stretchable conjugated-polymer films have been enhanced up to threefold and maintained under a strain up to 100%. This method may also serve as the basis for large-area manufacturing of stretchable semiconducting films, as demonstrated by the roll-to-roll coating of metre-scale films.

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.

Stochastic unfolding of nanoconfined DNA: Experiments, model and Bayesian analysis

Nanochannels provide a means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. Here we introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force and the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory-type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement. We provide publically available software for performing the required image and Bayesian analysis.

Clog and Release, and Reverse Motions of DNA in a Nanopore

Motions of circular and linear DNA molecules of various lengths near a nanopore of 100 or 200 nm diameter were experimentally observed and investigated by fluorescence microscopy. The movement of DNA molecules through nanopores, known as translocation, is mainly driven by electric fields near and inside the pores. We found significant clogging of nanopores by DNA molecules, particularly by circular DNA and linear T4 DNA (165.65 kbp). Here, the probabilities of DNA clogging events, depending on the DNA length and shape—linear or circular—were determined. Furthermore, two distinct DNA motions were observed: clog and release by linear T4 DNA, and a reverse direction motion at the pore entrance by circular DNA, after which both molecules moved away from the pore. Finite element method-based numerical simulations were performed. The results indicated that DNA molecules with pores 100–200 nm in diameter were strongly influenced by opposing hydrodynamic streaming flow, which was further enhanced by bulky DNA configurations.

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.

Nanoplumbing with 2D Metamaterials

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

Single-Molecule Study of Peptide Gel Dynamics Reveals States of Prestress

De novo peptide surfactant (I₃K) gels provide an ideal system to study the complex dynamics of lightly cross-linked semiflexible fibers because of their large contour lengths, simple chemistry, and slow dynamics. We used single-molecule fluorescence microscopy to record individual fibers and Fourier decomposition of the fiber dynamics to separate thermal contributions to the persistence length from compressive states of prestress (SPS). Our results show that SPS in the network depend strongly on peptide concentration, buffer, and pH and that the fibril energies in SPS follow a Lévy distribution. The presence of SPS in the network imply that collective states of self-stress are also present. Therefore, semiflexible polymer gels need to be considered as complex load-bearing structures and the mean field models for polymer gel elasticity and dynamics often applied to them will not be fully representative of the behavior at the nanoscale. We quantify the impact of cross-links on reptation tube dynamics, which provides a second population of tube fluctuations in addition to those expected for uncross-linked entangled solutions.

Block Copolymer of Flexible and Semi-Flexible Block Confined in Nanopost Array

Coarse-grained molecular dynamics simulations of a diblock copolymer consisting of a flexible and semi-flexible block in a dense array of parallel nanoposts with a square lattice packing were performed. The mutual interactions between the two blocks of the confined diblock chain were investigated through a comparison of their size, structure, and penetration among nanoposts with the corresponding separate chains. The geometry of a nanopost array was varied at constant post separation or at constant width of the passage between nanoposts. The size of a single interstitial volume was comparable to or smaller than the size of the diblock chain. A comparison of the blocks with their separate analogous chains revealed that the mutual interactions between the blocks were shielded by the nanoposts and, thus, the blocks behaved independently. At constant passage width, competitive effects of the axial chain extension in interstitial volumes and the lateral chain expansion among interstitial volumes led to a nonmonotonic behavior of the axial span. The position of the maximum in the span plotted against the filling fraction for a diblock chain was dictated by the semi-flexible block. The semi-flexible block penetrates among the nanoposts more readily and the expansion of the whole diblock copolymer is governed by the semiflexible block. The main findings were explained using the free energy arguments when an interstitial volume was approximated by a channel geometry and a passage aperture by a slit geometry. Detail knowledge of controlled conformational behavior in a compartmentalized environment can contribute to new processes in the storage and retrieval of information.

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.