Ratcheting Charged Polymers through Symmetric Nanopores Using Pulsed Fields: Designing a Low Pass Filter for Concentrating Polyelectrolytes.

We present a new concept for the separation of DNA molecules by contour length that combines a nanofluidic ratchet, nanopore translocation, and pulsed fields. Using Langevin dynamics simulations, we show that it is possible to design pulsed field sequences to ratchet captured semiflexible molecules in such a way that only short chains successfully translocate, effectively transforming the nanopore process into a low pass molecular filter. We also show that asymmetric pulses can significantly enhance the device efficiency. The process itself can be performed with many pores in parallel, and it should be possible to integrate it directly into nanopore sequencing devices, increasing its potential utility.

Capture and translocation of a rod-like molecule by a nanopore: orientation, charge distribution and hydrodynamics.

We investigate the translocation of rods with different charge distributions using hybrid Langevin dynamics and lattice Boltzmann (LD-LB) simulations. Electrostatic interactions are added to the system using the P3M algorithm to model the electrohydrodynamic interactions (EHI). We first examine the free-solution electrophoretic properties of rods with various charge distributions. Our translocation simulation results suggest that the order parameter is asymmetric during the capture and escape processes despite the symmetric electric field lines, while the impacts of the charge distribution on rod orientation are more significant during the capture process. The capture/threading/escape times are under the combined effects of charge screening, rod orientation, and charge distributions. We also show that the mean capture time of a rod is shorter when it is launched near the wall because rods tend to align along the wall and hence with the local field lines. Remarkably, the orientational capture radius we proposed previously for uniformly charged rods is still valid in the presence of EHI.

An efficient kinetic Monte Carlo to study analyte capture by a nanopore: transients, boundary conditions and time-dependent fields.

To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically symmetric system onto the 1D biased random walk. Our algorithm recovers the steady-state analytical solution and allows us to study time-dependent processes such as transients. Simulation results show that the steady-state depletion zone near pore is barely larger than the pore radius and narrows at higher field intensities; as a result, the time to reach steady-state is much smaller than the time required to empty a zone of the size of the capture radius λe. When the sample reservoir has a finite size, a second depletion region propagates inward from the outer wall, and the capture rate starts decreasing when it reaches the capture radius λe. We also note that the flatness of the electric field near the pore, which is often neglected, induces a traffic jam that can increase the transient time by several orders of magnitude. Finally, we propose a new proof-of-concept scheme to separate two analytes of the same mobility but different diffusion coefficients using time-varying fields.

Electrophoretic ratcheting of spherical particles in well/channel microfluidic devices: Making particles move against the net field.

We examine the electrophoresis of spherical particles in microfluidic devices made of alternating wells and narrow channels, including a system previously used to separate DNA molecules. Our computer simulations predict that such systems can be used to separate spherical particles of different sizes that share the same free-solution mobility. Interestingly, the electrophoretic velocity shows an inversion as the field intensity is increased: while small particles have higher velocities at low field, the situation is reversed at high fields with the larger particles then moving faster. The resulting nonlinearity suggests that asymmetric pulsed electric fields could be used to build separation ratchets: particles then have a net size-dependent velocity in the presence of a zero-mean external field. Exploiting the inversion mentioned above, we show how to design pulsed field sequences that make particles move against the mean field (an example of negative mobility). Finally, we demonstrate that it is possible to use pulsed fields to make particles of different sizes move in opposite directions, even though their charge have the same sign.

Capture of rod-like molecules by a nanopore: Defining an "orientational capture radius".

Both the translational diffusion coefficient D and the electrophoretic mobility µ of a short rod-like molecule (such as dsDNA) that is being pulled toward a nanopore by an electric field should depend on its orientation. Since a charged rod-like molecule tends to orient in the presence of an inhomogeneous electric field, D and µ will change as the molecule approaches the nanopore, and this will impact the capture process. We present a simplified study of this problem using theoretical arguments and Langevin dynamics simulations. In particular, we introduce a new orientational capture radius, which we compare to the capture radius for the equivalent point-like particle, and we discuss the different physical regimes of orientation during capture and the impact of initial orientations on the capture time.

Voltage-driven translocation: Defining a capture radius.

Analyte translocation involves three phases: (i) diffusion in the loading solution, (ii) capture by the pore, and (iii) threading. The capture process remains poorly characterized because it cannot easily be visualized or inferred from indirect measurements. The capture performance of a device is often described by a capture radius generally defined as the radial distance R* at which diffusion-dominated dynamics cross over to field-induced drift. However, this definition is rather ambiguous and the related models are usually oversimplified and studied in the steady-state limit. We investigate different approaches to defining and estimating R* for a charged particle diffusing in a liquid and attracted to the nanopore by the electric field. We present a theoretical analysis of the Péclet number as well as Monte Carlo simulations with different simulation protocols. Our analysis shows that the boundary conditions, pore size, and finite experimental times all matter in the interpretation and calculation of R*.

Langevin dynamcis simulations of driven polymer translocation into a cross-linked gel.

We investigate the dynamics of driving a polyelectrolyte such as DNA through a nanopore and into a cross-linked gel. Placing the gel on the trans-side of the nanopore can increase the translocation time while not negatively affecting the capture rates. Thus, this setup combines the mechanics of gel electrophoresis with nanopore translocation. However, contrary to typical gel electrophoresis scenarios, the effect of the field is localized in the immediate vicinity of the nanopore and becomes negligible inside the gel matrix. Thus, we investigate the process by which a semiflexible polymer can be pushed into a gel matrix via a localized field and we describe how the dynamics of gel penetration depends upon the field intensity, polymer stiffness, and gel pore size. Our simulation results show that a semiflexible polymer enters the gel region with two distinct mechanisms depending upon the ratio between the bending length scale and the gel pore size. In both regimes, the gel fibers cause a net increase in the mean translocation time. Interestingly, the translocation rate is found to be constant (a potentially useful feature for many applications) during the predominant part of the translocation process when the polymer is stiff over a length scale comparable to the gel pore size.

Highly driven polymer translocation from a cylindrical cavity with a finite length.

We present a computer simulation study of polymer translocation in a situation where the chain is initially confined to a closed cylindrical cavity in order to reduce the impact of conformational diversity on the translocation times. In particular, we investigate how the coefficient of variation of the distribution of translocation times can be minimized by optimizing both the volume and the aspect ratio of the cavity. Interestingly, this type of confinement sometimes increases the number and impact of hairpin conformations such that the fluctuations in the translocation process do not follow a power law in time (for instance, these fluctuations can even vary non-monotonically with time). We develop a tension-propagation model for a polymer compressed into such a confining volume and find that its predictions are in good agreement with our simulation results in the experimentally relevant strongly driven limit. Both the theoretical calculations and the simulation data yield a minimum in the coefficient of variation of the distribution of translocation times for a cylindrical cavity with an aspect ratio that makes it similar to a hemisphere. This provides guidance for the design of new devices based on the preconfinement of the target polymer into cavities.

Simulating the entropic collapse of coarse-grained chromosomes.

Depletion forces play a role in the compaction and decompaction of chromosomal material in simple cells, but it has remained debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics simulations, which reveal that depletion-induced attraction is sufficient to cause the collapse of a flexible chain of large structural monomers immersed in a bath of smaller depletants. These simulations use an explicit coarse-grained computational model that treats both the supercoiled DNA structural monomers and the smaller protein crowding agents as combinatorial, truncated Lennard-Jones spheres. By presenting a simple theoretical model, we quantitatively cast the action of depletants on supercoiled bacterial DNA as an effective solvent quality. The rapid collapse of the simulated flexible chromosome at the predicted volume fraction of depletants is a continuous phase transition. Additional physical effects to such simple chromosome models, such as enthalpic interactions between structural monomers or chain rigidity, are required if the collapse is to be a first-order phase transition.

Translocation of a polymer through a nanopore starting from a confining nanotube.

In this manuscript, Langevin Dynamics simulations and Tension-Propagation theory are used to investigate the forced translocation of a polymer from a confining tube through a nanopore situated at one of the tube's ends. The diameter of the tube allows for a control over the polymer conformations: decreasing the tube diameter reduces the number of conformations available to the polymer chain both before and during translocation. As the tube diameter is decreased, the translocation time is observed to increase. Interestingly, while the width of the distribution of translocation times is reduced if the chain starts in a tube, it reaches a maximum for weakly confining tubes. A Tension-Propagation approach is developed for the tube-nanopore setup in the strongly driven limit. Good agreement between the simulations and the theory allows for an exploration of the underlying physical mechanisms, including the calculation of an effective pore friction and the assessing of the impact of monomer crowding on the trans side.

Interfacing solid-state nanopores with gel media to slow DNA translocations.

We demonstrate the ability to slow DNA translocations through solid-state nanopores by interfacing the trans side of the membrane with gel media. In this work, we focus on two reptation regimes: when the DNA molecule is flexible on the length scale of a gel pore, and when the DNA behaves as persistent segments in tight gel pores. The first regime is investigated using agarose gels, which produce a very wide distribution of translocation times for 5 kbp dsDNA fragments, spanning over three orders of magnitude. The second regime is attained with polyacrylamide gels, which can maintain a tight spread and produce a shift in the distribution of the translocation times by an order of magnitude for 100 bp dsDNA fragments, if intermolecular crowding on the trans side is avoided. While previous approaches have proven successful at slowing DNA passage, they have generally been detrimental to the S/N, capture rate, or experimental simplicity. These results establish that by controlling the regime of DNA movement exiting a nanopore interfaced with a gel medium, it is possible to address the issue of rapid biomolecule translocations through nanopores-presently one of the largest hurdles facing nanopore-based analysis-without affecting the signal quality or capture efficiency.

Visualization and Phospholipid Identification (VaLID): online integrated search engine capable of identifying and visualizing glycerophospholipids with given mass.

MOTIVATION: Establishing phospholipid identities in large lipidomic datasets is a labour-intensive process. Where genomics and proteomics capitalize on sequence-based signatures, glycerophospholipids lack easily definable molecular fingerprints. Carbon chain length, degree of unsaturation, linkage, and polar head group identity must be calculated from mass to charge (m/z) ratios under defined mass spectrometry (MS) conditions. Given increasing MS sensitivity, many m/z values are not represented in existing prediction engines. To address this need, Visualization and Phospholipid Identification is a web-based application that returns all theoretically possible phospholipids for any m/z value and MS condition. Visualization algorithms produce multiple chemical structure files for each species. Curated lipids detected by the Canadian Institutes of Health Research Training Program in Neurodegenerative Lipidomics are provided as high-resolution structures. AVAILABILITY: VaLID is available through the Canadian Institutes of Health Research Training Program in Neurodegenerative Lipidomics resources web site at https://www.med.uottawa.ca/lipidomics/resources.html. CONTACTS: lipawrd@uottawa.ca SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Theory of end-labeled free-solution electrophoresis: is the end effect important?

In the theory of free-solution electrophoresis of a polyelectrolyte (such as the DNA) conjugated with a "drag-tag," the conjugate is divided into segments of equal hydrodynamic friction and its electrophoretic mobility is calculated as a weighted average of the mobilities of individual segments. If all the weights are assumed equal, then for an electrically neutral drag-tag, the elution time t is predicted to depend linearly on the inverse DNA length 1/M. While it is well-known that the equal-weights assumption is approximate and in reality the weights increase toward the ends, this "end effect" has been assumed to be small, since in experiments the t(1/M) dependence seems to be nearly perfectly linear. We challenge this assumption pointing out that some experimental linear fits do not extrapolate to the free (i.e. untagged) DNA elution time in the limit 1/M→0, indicating nonlinearity outside the fitting range. We show that a theory for a flexible polymer taking the end effect into account produces a nonlinear curve that, however, can be fitted with a straight line over a limited range of 1/M typical of experiments, but with a "wrong" intercept, which explains the experimental results without additional assumptions. We also study the influence of the flexibilities of the charged and neutral parts.

Can gel concentration gradients improve two-dimensional DNA displays?

The abrupt reduction in gel electrophoretic mobility that is observed when a dsDNA fragment is partially denatured has recently been predicted to exhibit a dependence upon the gel pore size. Using theoretical modeling, we demonstrate that this dependence can be exploited and used to improve the performance of 2D display of DNA. We report experimental evidence of this dependence and propose a new separation system in which a gel porosity gradient is utilized in a way analogous to temperature or denaturant gradients in traditional 2D display. Such gel porosity gradients can also be used in conjunction with denaturant gradients to improve 2D display results. We test these new ideas by modeling the fragment mobilities and computing the final fragment positions to find optimal 2D separation conditions.

Diffusing diffusivity: a model for anomalous, yet Brownian, diffusion.

Wang et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 15160 (2009)] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution G(x,t), with roughly exponential tails at short times, a situation they termed "anomalous yet Brownian" diffusion. The diversity of systems in which this is observed calls for a generic model. We present such a model where there is diffusivity memory but no direction memory in the particle trajectory, and we show that it leads to both a linear MSD and a non-Gaussian G(x,t) at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression "diffusing diffusivity". G(x,t) is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.

Coarse-grained molecular dynamics simulations of depletion-induced interactions for soft matter systems.

Given the ubiquity of depletion effects in biological and other soft matter systems, it is desirable to have coarse-grained Molecular Dynamics (MD) simulation approaches appropriate for the study of complex systems. This paper examines the use of two common truncated Lennard-Jones (Weeks-Chandler-Andersen (WCA)) potentials to describe a pair of colloidal particles in a thermal bath of depletants. The shifted-WCA model is the steeper of the two repulsive potentials considered, while the combinatorial-WCA model is the softer. It is found that the depletion-induced well depth for the combinatorial-WCA model is significantly deeper than the shifted-WCA model because the resulting overlap of the colloids yields extra accessible volume for depletants. For both shifted- and combinatorial-WCA simulations, the second virial coefficients and pair potentials between colloids are demonstrated to be well approximated by the Morphometric Thermodynamics (MT) model. This agreement suggests that the presence of depletants can be accurately modelled in MD simulations by implicitly including them through simple, analytical MT forms for depletion-induced interactions. Although both WCA potentials are found to be effective generic coarse-grained simulation approaches for studying depletion effects in complicated soft matter systems, combinatorial-WCA is the more efficient approach as depletion effects are enhanced at lower depletant densities. The findings indicate that for soft matter systems that are better modelled by potentials with some compressibility, predictions from hard-sphere systems could greatly underestimate the magnitude of depletion effects at a given depletant density.

Field-flow fractionation and hydrodynamic chromatography on a microfluidic chip.

We present gravitational field-flow fractionation and hydrodynamic chromatography of colloids eluting through 18 µm microchannels. Using video microscopy and mesoscopic simulations, we investigate the average retention ratio of colloids with both a large specific weight and neutral buoyancy. We consider the entire range of colloid sizes, including particles that barely fit in the microchannel and nanoscopic particles. Ideal theory predicts four operational modes, from hydrodynamic chromatography to Faxén-mode field-flow fractionation. We experimentally demonstrate, for the first time, the existence of the Faxén-mode field-flow fractionation and the transition from hydrodynamic chromatography to normal-mode field-flow fractionation. Furthermore, video microscopy and simulations show that the retention ratios are largely reduced above the steric-inversion point, causing the variation of the retention ratio in the steric- and Faxén-mode regimes to be suppressed due to increased drag. We demonstrate that theory can accurately predict retention ratios if hydrodynamic interactions with the microchannel walls (wall drag) are added to the ideal theory. Rather than limiting the applicability, these effects allow the microfluidic channel size to be tuned to ensure high selectivity. Our findings indicate that particle velocimetry methods must account for the wall-induced lag when determining flow rates in highly confining systems.

Gel electrophoresis of DNA partially denatured at the ends: what are the dominant conformations?

Gel electrophoresis of a partially denatured dsDNA fragment is studied using Langevin Dynamics computer simulations. For simplicity, the denatured ssDNA sections are placed at the ends of the fragment in a symmetrical fashion. A squid-like conformation is found to sometimes cause the fragment to completely block in the gel. In fact, this conformation is the principal cause of the steep reduction in mobility observed in the simulations. As the field is increased, it is found that the occurrence of this conformation dominates the migration dynamics. Although the squid conformation seems to be more stable at high fields, the field can eventually force the fragments to thread through the gel pores regardless. We qualitatively explore the behavior of this squid-like conformation across a range of fields and degrees of denaturation, and we discuss the relevance of our findings for TGGE.

Translocation of "rod-coil" polymers: probing the structure of single molecules within nanopores.

Using simulation and analytical techniques, we demonstrate that it is possible to extract structural information about biological molecules by monitoring the dynamics as they translocate through nanopores. From Langevin dynamics simulations of polymers exhibiting discrete changes in flexibility (rod-coil polymers), distinct plateaus are observed in the progression towards complete translocation. Characterizing these dynamics via an incremental mean first passage approach, the large steps are shown to correspond to local barriers preventing the passage of the coils while the rods translocate relatively easily. Analytical replication of the results provides insight into the corrugated nature of the free energy landscape as well as the dependence of the effective barrier heights on the length of the coil sections. Narrowing the width of the pore or decreasing the charge on either the rod or the coil segments are both shown to enhance the resolution of structural details. The special case of a single rod confined within a nanopore is also studied. Here, sufficiently long flexible sections attached to either end are demonstrated to act as entropic anchors which can effectively trap the rod within the pore for an extended period of time. Both sets of results suggest new experimental approaches for the control and study of biological molecules within nanopores.

Structure of polyelectrolyte brushes subject to normal electric fields.

Molecular dynamic simulations of salt-free polyelectrolyte brushes subject to external fields applied normal to the grafting substrate reveal the three-dimensional monomer and counterion distributions. It is found that below a critical electric field, local electroneutrality holds for densely grafted brushes and the brush height remains independent of field intensity. Above this critical field (which scales as 1/3 with grafting density) brush height increases smoothly, and the fraction of condensed counterions decreases. The brush bifurcates into two subpopulations of stretched and collapsed chains when the grafting density is not low. At intermediate grafting densities, the majority of chains are stretched and the minority are nonstretched. At high grafting densities bifurcation and brush height growth occur consecutively. The majority of the chains are nonstretched at high grafting densities. Although not observed prior to overstretching of the chain model, it is predicted that the two subpopulations will re-merge to a single highly stretched phase when field intensity reaches a third critical value. The ability to control subpopulations of chains suggests that utilizing electric fields normal to polyelectrolyte brushes holds potential as controllable gates in microfluidic devices.