David Sean

Modeling the separation of macromolecules: a review of current computer simulation methods.

Theory and numerical simulations play a major role in the development of improved and novel separation methods. In some cases, computer simulations predict counterintuitive effects that must be taken into account in order to properly optimize a device. In other cases, simulations allow the scientist to focus on a subset of important system parameters. Occasionally, simulations even generate entirely new separation ideas! In this article, we review the main simulation methods that are currently being used to model separation techniques of interest to the readers of Electrophoresis. In the first part of the article, we provide a brief description of the numerical models themselves, starting with molecular methods and then moving towards more efficient coarse‐grained approaches. In the second part, we briefly examine nine separation problems and some of the methods used to model them. We conclude with a short discussion of some notoriously hard‐to‐model separation problems and a description of some of the available simulation software packages.

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.

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 tubes 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.

Electrophoretic mobility of partially denatured DNA in a gel: qualitative and semiquantitative differences between bubbles and split ends.

Partially melted DNA is known to exhibit an abrupt decrease of electrophoretic mobility in a gel. Although this is the main phenomenon exploited in TGGE/DGGE (temperature gradient gel electrophoresis/denaturing gradient gel electrophoresis), not much is known about the physical processes responsible for the blocking. While there is a commonly used formula for the reduced mobility based on the theory of branched polymers, it does not discriminate between denatured domains bounded on one (split end) or two sides (bubble). To better understand how the blocking occurs in both of these cases, a coarse‐grained model of DNA gel electrophoresis is simulated using Langevin Dynamics. The simulations reveal that the low‐field mobility is much more sensitive to denatured domains located at the ends of a DNA fragment. A denatured domain occurring at the center of a fragment indeed reduces the mobility, but at a much lower rate.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A− + H+. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant Ka. These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge—both monomer and ionic—is distributed inside the nanogel. Our findings reveal that, depending on the value of Ka, added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Physical confinement signals regulate the organization of stem cells in three dimensions

During embryogenesis, the spherical inner cell mass (ICM) proliferates in the confined environment of a blastocyst. Embryonic stem cells (ESCs) are derived from the ICM, and mimicking embryogenesis in vitro, mouse ESCs (mESCs) are often cultured in hanging droplets. This promotes the formation of a spheroid as the cells sediment and aggregate owing to increased physical confinement and cell–cell interactions. In contrast, mESCs form two-dimensional monolayers on flat substrates and it remains unclear if the difference in organization is owing to a lack of physical confinement or increased cell–substrate versus cell–cell interactions. Employing microfabricated substrates, we demonstrate that a single geometric degree of physical confinement on a surface can also initiate spherogenesis. Experiment and computation reveal that a balance between cell–cell and cell–substrate interactions finely controls the morphology and organization of mESC aggregates. Physical confinement is thus an important regulatory cue in the three-dimensional organization and morphogenesis of developing cells.

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.

Rotation-Induced Macromolecular Spooling of DNA

Genetic information is stored in a linear sequence of base-pairs; however, thermal fluctuations and complex DNA conformations such as folds and loops make it challenging to order genomic material for in vitro analysis. In this work, we discover that rotation-induced macromolecular spooling of DNA around a rotating microwire can monotonically order genomic bases, overcoming this challenge. We use single-molecule fluorescence microscopy to directly visualize long DNA strands deforming and elongating in shear flow near a rotating microwire, in agreement with numerical simulations. While untethered DNA is observed to elongate substantially, in agreement with our theory and numerical simulations, strong extension of DNA becomes possible by introducing tethering. For the case of tethered polymers, we show that increasing the rotation rate can deterministically spool a substantial portion of the chain into a fully stretched, single-file conformation. When applied to DNA, the fraction of genetic information sequentially ordered on the microwire surface will increase with the contour length, despite the increased entropy. This ability to handle long strands of DNA is in contrast to modern DNA sample preparation technologies for sequencing and mapping, which are typically restricted to comparatively short strands resulting in challenges in reconstructing the genome. Thus, in addition to discovering new rotation-induced macromolecular dynamics, this work inspires new approaches to handling genomic-length DNA strands.

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.

Langevin dynamcis simulations of driven polymer translocation into a crosslinked 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.