Extension of nanoconfined DNA: Quantitative comparison between experiment and theory

Fluorescence Microscopy of Nanochannel-Confined DNA

Stretching of DNA in nanoscale confinement allows for several important studies. The genetic contents of the DNA can be visualized on the single DNA molecule level, and the polymer physics of confined DNA and also DNA/protein and other DNA/DNA-binding molecule interactions can be explored. This chapter describes the basic steps to fabricate the nanostructures, perform the experiments, and analyze the data.

Continuous-flow macromolecular sieving in slanted nanofilter array: stochastic model and coupling effect of electrostatic and steric hindrance

Microfabricated slanted nanofilter arrays are a promising technology for integrated biomolecule analysis systems such as online monitoring and point-of-care quality validation, due to their continuous-flow and one-step operation capability. However, an incomplete understanding of the system limits the performance and wider applications of slanted nanofilter arrays. In this paper, we present rigorous theoretical and experimental studies on macromolecule sieving in a slanted nanofilter array. From both stochastic and kinetic models, an explicit theoretical solution describing size-dependent molecule sieving was derived, which was validated using experimental sieving results obtained for various sieving conditions. Our results not only detail the relationship between sieving conditions and sieving efficiency but also demonstrate that sieving is affected by multiple hindrance effects (electrostatic hindrance), not steric hindrance alone. There is an optimal sieving condition for achieving the greatest separation efficiency for DNAs of a certain size range. Small DNA has great size selectivity in small nanofilters and in weak electric fields, whereas large DNA is present in large nanofilters and in strong electric fields. This study provides insights into designing a slanted nanofilter array for particular target applications and understanding the sieving principles in the nanofilter array.

High-Throughput Separation of Long DNA in Deterministic Lateral Displacement Arrays

Length-based separation of DNA remains as relevant today as when gel electrophoresis was introduced almost 100 years ago. While new, long-read genomics technologies have revolutionised accessibility to powerful genomic data, the preparation of samples has not proceeded at the same pace, with sample preparation often constituting a considerable bottleneck, both in time and difficulty. Microfluidics holds great potential for automated, sample-to-answer analysis via the integration of preparatory and analytical steps, but for this to be fully realised, more versatile, powerful and integrable unit operations, such as separation, are essential. We demonstrate the displacement and separation of DNA with a throughput that is one to five orders of magnitude greater than other microfluidic techniques. Using a device with a small footprint (23 mm × 0.5 mm), and with feature sizes in the micrometre range, it is considerably easier to fabricate than parallelized nano-array-based approaches. We show the separation of 48.5 kbp and 166 kbp DNA strands achieving a significantly improved throughput of 760 ng/h, compared to previous work and the separation of low concentrations of 48.5 kbp DNA molecules from a massive background of sub 10 kbp fragments. We show that the extension of DNA molecules at high flow velocities, generally believed to make the length-based separation of long DNA difficult, does not place the ultimate limitation on our method. Instead, we explore the effects of polymer rotations and intermolecular interactions at extremely high DNA concentrations and postulate that these may have both negative and positive influences on the separation depending on the detailed experimental conditions.

A Parallelized Nanofluidic Device for High-Throughput Optical DNA Mapping of Bacterial Plasmids

Optical DNA mapping (ODM) has developed into an important technique for DNA analysis, where single DNA molecules are sequence-specifically labeled and stretched, for example, in nanofluidic channels. We have developed an ODM assay to analyze bacterial plasmids-circular extrachromosomal DNA that often carry genes that make bacteria resistant to antibiotics. As for most techniques, the next important step is to increase throughput and automation. In this work, we designed and fabricated a nanofluidic device that, together with a simple automation routine, allows parallel analysis of up to 10 samples at the same time. Using plasmids encoding extended-spectrum beta-lactamases (ESBL), isolated from Escherichiacoli and Klebsiellapneumoniae, we demonstrate the multiplexing capabilities of the device when it comes to both many samples in parallel and different resistance genes. As a final example, we combined the device with a novel protocol for rapid cultivation and extraction of plasmids from fecal samples collected from patients. This combined protocol will make it possible to analyze many patient samples in one device already on the day the sample is collected, which is an important step forward for the ODM analysis of plasmids in clinical diagnostics.

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.

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.

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.

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.

Motor-like DNA motion due to an ATP-hydrolyzing protein under nanoconfinement

We report that long double-stranded DNA confined to quasi-1D nanochannels undergoes superdiffusive motion under the action of the enzyme T4 DNA ligase in the presence of necessary co-factors. Inside the confined environment of the nanochannel, double-stranded DNA molecules stretch out due to self-avoiding interactions. In absence of a catalytically active enzyme, we see classical diffusion of the center of mass. However, cooperative interactions of proteins with the DNA can lead to directed motion of DNA molecules inside the nanochannel. Here we show directed motion in this configuration for three different proteins (T4 DNA ligase, MutS, E. coli DNA ligase) in the presence of their energetic co-factors (ATP, NAD⁺).

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.

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

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

The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics

The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.

Fluorescence Microscopy of Nanochannel-Confined DNA

Stretching of DNA in nanoscale confinement allows for several important studies. The genetic contents of the DNA can be visualized on the single DNA molecule level and both the polymer physics of confined DNA and also DNA/protein and other DNA/DNA-binding molecule interactions can be explored. This chapter describes the basic steps to fabricate the nanostructures, perform the experiments and analyze the data.

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.

Noise reduction in single time frame optical DNA maps

In optical DNA mapping technologies sequence-specific intensity variations (DNA barcodes) along stretched and stained DNA molecules are produced. These “fingerprints” of the underlying DNA sequence have a resolution of the order one kilobasepairs and the stretching of the DNA molecules are performed by surface adsorption or nano-channel setups. A post-processing challenge for nano-channel based methods, due to local and global random movement of the DNA molecule during imaging, is how to align different time frames in order to produce reproducible time-averaged DNA barcodes. The current solutions to this challenge are computationally rather slow. With high-throughput applications in mind, we here introduce a parameter-free method for filtering a single time frame noisy barcode (snap-shot optical map), measured in a fraction of a second. By using only a single time frame barcode we circumvent the need for post-processing alignment. We demonstrate that our method is successful at providing filtered barcodes which are less noisy and more similar to time averaged barcodes. The method is based on the application of a low-pass filter on a single noisy barcode using the width of the Point Spread Function of the system as a unique, and known, filtering parameter. We find that after applying our method, the Pearson correlation coefficient (a real number in the range from -1 to 1) between the single time-frame barcode and the time average of the aligned kymograph increases significantly, roughly by 0.2 on average. By comparing to a database of more than 3000 theoretical plasmid barcodes we show that the capabilities to identify plasmids is improved by filtering single time-frame barcodes compared to the unfiltered analogues. Since snap-shot experiments and computational time using our method both are less than a second, this study opens up for high throughput optical DNA mapping with improved reproducibility.

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.

Sorting ring polymers by knot type with modulated nanochannels

In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.

Exploring DNA–protein interactions on the single DNA molecule level using nanofluidic tools

This review highlights the use of nanofluidic channels for studying DNA–protein interactions on the single DNA molecule level.

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.

Finite-size corrections for confined polymers in the extended de Gennes regime

Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favorably with pruned-enriched Rosenbluth method (PERM) simulations of a three-dimensional discrete wormlike chain model of DNA confined in a nanochannel. We discuss the implications for experimental studies of linear λ-DNA confined to nanochannels at the high ionic strengths used in many experiments.