Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

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.

FaNDOM: Fast nested distance-based seeding of optical maps

Optical mapping (OM) provides single-molecule readouts of fluorescently labeled sequence motifs on long fragments of DNA, resolved to nucleotide-level coordinates. With the advent of microfluidic technologies for analysis of DNA molecules, it is possible to inexpensively generate long OM data ( > 150 kbp) at high coverage. In addition to scaffolding for de novo assembly, OM data can be aligned to a reference genome for identification of genomic structural variants. We introduce FaNDOM (Fast Nested Distance Seeding of Optical Maps)-an optical map alignment tool that greatly reduces the search space of the alignment process. On four benchmark human datasets, FaNDOM was significantly (4-14×) faster than competing tools while maintaining comparable sensitivity and specificity. We used FaNDOM to map variants in three cancer cell lines and identified many biologically interesting structural variants, including deletions, duplications, gene fusions and gene-disrupting rearrangements. FaNDOM is publicly available at https://github.com/jluebeck/FaNDOM.

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.

Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

3D Printing-Enabled DNA Extraction for Long-Read Genomics

Long-read genomics technologies such as nanopore sequencing and genome mapping in nanochannels extract genomic information in the kilobase to megabase pair range from single DNA molecules, thereby overcoming read-length limitations in next-generation DNA sequencing. Long-read technologies start with long DNA molecules as the input and thus benefit from universal sample preparation methods that are fast and shear-free and present a scope of automation and direct upstream integration. We describe a 3D printing-assisted poly(dimethylysiloxane)-based DNA sample preparation device, where diffusive chemical lysis followed by electrophoresis produces circa 100 ng of long DNA directly from cells with less than 5 min of labor. Assessment of the product DNA by confinement in nanochannels reveals that the DNA sizes are commensurate with the requirements for long-read single-molecule technologies. Microfluidics not only expedites sample preparation, but also offers the opportunity for integration with genomics technologies to eliminate DNA fragmentation and loss during transfer to the genomic device.

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.

Conformation of Flexible and Semiflexible Chains Confined in Nanoposts Array of Various Geometries

The conformation and distribution of a flexible and semiflexible chain confined in an array of nanoposts arranged in parallel way in a square-lattice projection of their cross-section was investigated using coarse-grained molecular dynamics simulations. The geometry of the nanopost array was varied at the constant post diameter dp and the ensuing modifications of the chain conformation were compared with the structural behavior of the chain in the series of nanopost arrays with the constant post separation Sp as well as with the constant distance between two adjacent post walls (passage width) wp. The free energy arguments based on an approximation of the array of nanopost to a composite of quasi-channels of diameter dc and quasi-slits of height wp provide semiqualitative explanations for the observed structural behavior of both chains. At constant post separation and passage width, the occupation number displays a monotonic decrease with the increasing geometry ratio dc/wp or volume fraction of posts, while a maximum is observed at constant post diameter. The latter finding is attributed to a relaxed conformation of the chains at small dc/wp ratio, which results from a combination of wide interstitial volumes and wide passage apertures. This maximum is approximately positioned at the same dc/wp value for both flexible and semiflexible chains. The chain expansion from a single interstitial volume into more interstitial volumes also starts at the same value of dc/wp ratio for both chains. The dependence of the axial chain extension on the dc/wp ratio turns out to be controlled by the diameter of the interstitial space and by the number of monomers in the individual interstitial volumes. If these two factors act in the same way on the axial extension of chain fragments in interstitial volumes the monotonic increase of the axial chain extension with the dc/wp in the nanopost arrays is observed. At constant wp, however, these two factors act in opposite way and the axial chain extension plotted against the dc/wp ratio exhibits a maximum. In the case of constant post diameter, the characteristic hump in the single chain structure factor whose position correlates with the post separation is found only in the structure factor of the flexible chain confined in the nanopost array of certain value of Sp. The structure factor of the flexible chain contains more information on the monomer organization and mutual correlations than the structure factor of the semiflexible chain. The stiffer chain confined in the nanopost array is composed of low number of statistical segments important for the presence of respective hierarchical regimes in the structure factor.

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.

Extension distribution for DNA confined in a nanochannel near the Odijk regime

DNA confinement in a nanochannel typically is understood via mapping to the confinement of an equivalent neutral polymer by hard walls. This model has proven to be effective for confinement in relatively large channels where hairpin formation is frequent. An analysis of existing experimental data for Escherichia coli DNA extension in channels smaller than the persistence length, combined with an additional dataset for λ-DNA confined in a 34 nm wide channel, reveals a breakdown in this approach as the channel size approaches the Odijk regime of strong confinement. In particular, the predicted extension distribution obtained from the asymptotic solution to the weakly correlated telegraph model for a confined wormlike chain deviates significantly from the experimental distribution obtained for DNA confinement in the 34 nm channel, and the discrepancy cannot be resolved by treating the alignment fluctuations or the effective channel size as fitting parameters. We posit that the DNA-wall electrostatic interactions, which are sensible throughout a significant fraction of the channel cross section in the Odijk regime, are the source of the disagreement between theory and experiment. Dimensional analysis of the wormlike chain propagator in channel confinement reveals the importance of a dimensionless parameter, reflecting the magnitude of the DNA-wall electrostatic interactions relative to thermal energy, which has not been considered explicitly in the prevailing theories for DNA confinement in a nanochannel.

Simulations corroborate telegraph model predictions for the extension distributions of nanochannel confined DNA

Hairpins in the conformation of DNA confined in nanochannels close to their persistence length cause the distribution of their fractional extensions to be heavily left skewed. A recent theory rationalizes these skewed distributions using a correlated telegraph process, which can be solved exactly in the asymptotic limit of small but frequent hairpin formation. Pruned-enriched Rosenbluth method simulations of the fractional extension distribution for a channel-confined wormlike chain confirm the predictions of the telegraph model. Remarkably, the asymptotic result of the telegraph model remains robust well outside the asymptotic limit. As a result, the approximations in the theory required to map it to the polymer model and solve it in the asymptotic limit are not the source of discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA during genome mapping. The agreement between theory and simulations motivates future work to determine the source of the remaining discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA in nanochannels used for genome mapping.

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.

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.

Measuring the wall depletion length of nanoconfined DNA

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

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.

OMBlast: alignment tool for optical mapping using a seed-and-extend approach

Motivation

Optical mapping is a technique for capturing fluorescent signal patterns of long DNA molecules (in the range of 0.1–1 Mbp). Recently, it has been complementing the widely used short-read sequencing technology by assisting with scaffolding and detecting large and complex structural variations (SVs). Here, we introduce a fast, robust and accurate tool called OMBlast for aligning optical maps, the set of signal locations on the molecules generated from optical mapping. Our method is based on the seed-and-extend approach from sequence alignment, with modifications specific to optical mapping.

Results

Experiments with both synthetic and our real data demonstrate that OMBlast has higher accuracy and faster mapping speed than existing alignment methods. Our tool also shows significant improvement when aligning data with SVs.

Availability and Implementation

OMBlast is implemented for Java 1.7 and is released under a GPL license. OMBlast can be downloaded from https://github.com/aldenleung/OMBlast and run directly on machines equipped with a Java virtual machine.

Supplementary information

Supplementary data are available at Bioinformatics online

Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior

Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.

Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels

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

Stretching and compression of DNA by external forces under nanochannel confinement

Mechanical deformation of dsDNA molecules inside square nanochannels is investigated using simulations based on a coarse-grained model of DNA. The combined action of confinement and weak external forces is explored in a variety of confinement regimes, including the transition zone relevant to nanofluidic experiments. The computed free energy and force profiles are markedly affected by the channel size. Effective elastic softening of confined DNA molecules relative to the bulk DNA is observed in the channels of intermediate widths. The extension of DNA from its bulk equilibrium length in nanofluidic devices is resolved into contributions from the passive extension due to confinement and from the active stretching induced by force. Potential implications of the very different energy costs computed for the two extension modes (extension by confinement takes much more free energy than stretching by force) for behavior of DNA in nanofluidic chips are indicated.

Odijk excluded volume interactions during the unfolding of DNA confined in a nanochannel

We report experimental data on the unfolding of human and E. coli genomic DNA molecules shortly after injection into a 45 nm nanochannel. The unfolding dynamics are deterministic, consistent with previous experiments and modeling in larger channels, and do not depend on the biological origin of the DNA. The measured entropic unfolding force per friction per unit contour length agrees with that predicted by combining the Odijk excluded volume with numerical calculations of the Kirkwood diffusivity of confined DNA. The time scale emerging from our analysis has implications for genome mapping in nanochannels, especially as the technology moves towards longer DNA, by setting a lower bound for the delay time before making a measurement.

One-Parameter Scaling Theory for DNA Extension in a Nanochannel

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.

Sequence-Dependent Persistence Length of Long DNA

Using a high-throughput genome-mapping approach, we obtained circa 50 million measurements of the extension of internal human DNA segments in a 41  nm×41  nm nanochannel. The underlying DNA sequences, obtained by mapping to the reference human genome, are 2.5-393 kilobase pairs long and contain percent GC contents between 32.5% and 60%. Using Odijk's theory for a channel-confined wormlike chain, these data reveal that the DNA persistence length increases by almost 20% as the percent GC content increases. The increased persistence length is rationalized by a model, containing no adjustable parameters, that treats the DNA as a statistical terpolymer with a sequence-dependent intrinsic persistence length and a sequence-independent electrostatic persistence length.

Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

Non-monotonic knotting probability and knot length of semiflexible rings: the competing roles of entropy and bending energy

We consider self-avoiding rings of up to 1000 beads and study, by Monte Carlo techniques, how their equilibrium knotting properties depend on the bending rigidity. When the rings are taken from the rigid to fully-flexible limit, their average compactness increases, as expected. However, this progressive compactification is not parallelled by a steady increase of the abundance of knots. In fact the knotting probability, P_k, has a prominent maximum when the persistence length is a few times larger than the bead size. At similar bending rigidities, the knot length has, instead, a minimum. We show that the observed non-monotonicity of P_k arises from the competition between two effects. The first one is the entropic cost of introducing a knot. The second one is the gain in bending energy due to the presence of essential crossings. These, in fact, constrain the knotted region and keep it less bent than average. The two competing effects make knots maximally abundant when the persistence length is 5-10 times larger than the bead size. At such intermediate bending rigidities, knots in the chains of 500 and 1000 beads are 40 times more likely than in the fully-flexible limit.

Simulations of knotting of DNA during genome mapping

Genome mapping involves the confinement of long DNA molecules, in excess of 150 kilobase pairs, in nanochannels near the circa 50 nm persistence length of DNA. The fidelity of the map relies on the assumption that the DNA is linearized by channel confinement, which assumes the absence of knots. We have computed the probability of forming different knot types and the size of these knots for long chains (approximately 164 kilobase pairs) via pruned-enriched Rosenbluth method simulations of a discrete wormlike chain model of DNA in channel sizes ranging from 35 nm to 60 nm. Compared to prior simulations of short DNA in similar confinement, these long molecules exhibit both complex knots, with up to seven crossings, and multiple knots per chain. The knotting probability is a very strong function of channel size, ranging from 0.3% to 60%, and rationalized in the context of Odijk's theory for confined semiflexible chains. Overall, the knotting probability and knot size obtained from these equilibrium measurements are not consistent with experimental measurements of the properties of anomalously bright regions along the DNA backbone during genome mapping experiments. This result suggests that these events in experiments are either knots formed during the processing of the DNA prior to injection into the nanochannel or regions of locally high DNA concentration without a topological constraint. If so, knots during genome mapping are not an intrinsic problem for genome mapping technology.

Wall depletion length of a channel-confined polymer

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

Super-Resolution Genome Mapping in Silicon Nanochannels

Optical genome mapping in nanochannels is a powerful genetic analysis method, complementary to deoxyribonucleic acid (DNA) sequencing. The method is based on detecting a pattern of fluorescent labels attached along individual DNA molecules. When such molecules are extended in nanochannels, the labels create a fluorescent genetic barcode that is used for mapping the DNA molecule to its genomic locus and identifying large-scale variation from the genome reference. Mapping resolution is currently limited by two main factors: the optical diffraction limit and the thermal fluctuations of DNA molecules suspended in the nanochannels. Here, we utilize single-molecule tracking and super-resolution localization in order to improve the mapping accuracy and resolving power of this genome mapping technique and achieve a 15-fold increase in resolving power compared to currently practiced methods. We took advantage of a naturally occurring genetic repeat array and labeled each repeat with custom-designed Trolox conjugated fluorophores for enhanced photostability. This model system allowed us to acquire extremely long image sequences of the equally spaced fluorescent markers along DNA molecules, enabling detailed characterization of nanoconfined DNA dynamics and quantitative comparison to the Odijk theory for confined polymer chains. We present a simple method to overcome the thermal fluctuations in the nanochannels and exploit single-step photobleaching to resolve subdiffraction spaced fluorescent markers along fluctuating DNA molecules with ∼100 bp resolution. In addition, we show how time-averaging over just ∼50 frames of 40 ms enhances mapping accuracy, improves mapping P-value scores by 3 orders of magnitude compared to nonaveraged alignment, and provides a significant advantage for analyzing structural variations between DNA molecules with similar sequence composition.

Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel

The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

Modeling the relaxation of internal DNA segments during genome mapping in nanochannels

We have developed a multi-scale model describing the dynamics of internal segments of DNA in nanochannels used for genome mapping. In addition to the channel geometry, the model takes as its inputs the DNA properties in free solution (persistence length, effective width, molecular weight, and segmental hydrodynamic radius) and buffer properties (temperature and viscosity). Using pruned-enriched Rosenbluth simulations of a discrete wormlike chain model with circa 10 base pair resolution and a numerical solution for the hydrodynamic interactions in confinement, we convert these experimentally available inputs into the necessary parameters for a one-dimensional, Rouse-like model of the confined chain. The resulting coarse-grained model resolves the DNA at a length scale of approximately 6 kilobase pairs in the absence of any global hairpin folds, and is readily studied using a normal-mode analysis or Brownian dynamics simulations. The Rouse-like model successfully reproduces both the trends and order of magnitude of the relaxation time of the distance between labeled segments of DNA obtained in experiments. The model also provides insights that are not readily accessible from experiments, such as the role of the molecular weight of the DNA and location of the labeled segments that impact the statistical models used to construct genome maps from data acquired in nanochannels. The multi-scale approach used here, while focused towards a technologically relevant scenario, is readily adapted to other channel sizes and polymers.

The polymer physics of single DNA confined in nanochannels

In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.

Pore Translocation of Knotted Polymer Chains: How Friction Depends on Knot Complexity

Knots can affect the capability of polymers to translocate through narrow pores in complex and counterintuitive ways that are still relatively unexplored. We report here on a systematic theoretical and computational investigation of the driven translocation of flexible chains accommodating a large repertoire of knots trapped at the pore entrance. These include composite knots, which are the most common form of spontaneous entanglement in long polymers. Two unexpected results emerge from this study. First, the high force translocation compliance does not decrease systematically with knot complexity. Second, the response of composite knots is so dependent on the order of their factor knots, that their hindrance can even be lower than some of their prime components. We show that the resulting rich and seemingly disparate phenomenology can be captured in a seamless framework based on the mechanism by which the tractive force is propagated along and past the knots. The quantitative scheme can be viably used for predictive purposes and, hence, ought to be useful in applicative contexts, too.

Extension of nanoconfined DNA: Quantitative comparison between experiment and theory

The extension of DNA confined to nanochannels has been studied intensively and in detail. However, quantitative comparisons between experiments and model calculations are difficult because most theoretical predictions involve undetermined prefactors, and because the model parameters (contour length, Kuhn length, effective width) are difficult to compute reliably, leading to substantial uncertainties. Here we use a recent asymptotically exact theory for the DNA extension in the "extended de Gennes regime" that allows us to compare experimental results with theory. For this purpose, we performed experiments measuring the mean DNA extension and its standard deviation while varying the channel geometry, dye intercalation ratio, and ionic strength of the buffer. The experimental results agree very well with theory at high ionic strengths, indicating that the model parameters are reliable. At low ionic strengths, the agreement is less good. We discuss possible reasons. In principle, our approach allows us to measure the Kuhn length and the effective width of a single DNA molecule and more generally of semiflexible polymers in solution.

Nanotechnologies for biomedical science and translational medicine

In 2000 the United States launched the National Nanotechnology Initiative and, along with it, a well-defined set of goals for nanomedicine. This Perspective looks back at the progress made toward those goals, within the context of the changing landscape in biomedicine that has occurred over the past 15 years, and considers advances that are likely to occur during the next decade. In particular, nanotechnologies for health-related genomics and single-cell biology, inorganic and organic nanoparticles for biomedicine, and wearable nanotechnologies for wellness monitoring are briefly covered.

Measurements of DNA barcode label separations in nanochannels from time-series data

We analyzed time-series data for fluctuations of intramolecular segments of barcoded E. coli genomic DNA molecules confined in nanochannels with sizes near the persistence length of DNA. These dynamic data allowed us to measure the probability distribution governing the distance between labels on the DNA backbone, which is a key input into the alignment methods used for genome mapping in nanochannels. Importantly, this dynamic method does not require alignment of the barcode to the reference genome, thereby removing a source of potential systematic error in a previous study of this type. The results thus obtained support previous evidence for a left-skewed probability density for the distance between labels, albeit at a lower magnitude of skewness. We further show that the majority of large fluctuations between labels are short-lived events, which sheds further light upon the success of the linearized DNA genome mapping technique. This time-resolved data analysis will improve existing genome map alignment algorithms, and the overall idea of using dynamic data could potentially improve the accuracy of genome mapping, especially for complex heterogeneous samples such as cancer cells.

Topological events in single molecules of E. coli DNA confined in nanochannels

We present experimental data concerning potential topological events such as folds, internal backfolds, and/or knots within long molecules of double-stranded DNA when they are stretched by confinement in a nanochannel. Genomic DNA from E. coli was labeled near the 'GCTCTTC' sequence with a fluorescently labeled dUTP analog and stained with the DNA intercalator YOYO. Individual long molecules of DNA were then linearized and imaged using methods based on the NanoChannel Array technology (Irys® System) available from BioNano Genomics. Data were collected on 189 153 molecules of length greater than 50 kilobases. A custom code was developed to search for abnormal intensity spikes in the YOYO backbone profile along the length of individual molecules. By correlating the YOYO intensity spikes with the aligned barcode pattern to the reference, we were able to correlate the bright intensity regions of YOYO with abnormal stretching in the molecule, which suggests these events were either a knot or a region of internal backfolding within the DNA. We interpret the results of our experiments involving molecules exceeding 50 kilobases in the context of existing simulation data for relatively short DNA, typically several kilobases. The frequency of these events is lower than the predictions from simulations, while the size of the events is larger than simulation predictions and often exceeds the molecular weight of the simulated molecules. We also identified DNA molecules that exhibit large, single folds as they enter the nanochannels. Overall, topological events occur at a low frequency (∼7% of all molecules) and pose an easily surmountable obstacle for the practice of genome mapping in nanochannels.

Scaling regimes of a semiflexible polymer in a rectangular channel

We derive scaling relations for the extension statistics and the confinement free energy for a semiflexible polymer confined to a channel with a rectangular cross section. Our motivation is recent numerical results [Gupta et al., J. Chem. Phys. 140, 214901 (2014)] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nanochannels, as many experiments are performed for rectangular channels with large aspect ratios, while theoretical and simulation results are usually obtained for square channels.