arXiv subjects

Gary W. Slater

Publications and source records attributed to Gary W. Slater.

At least 19 recordsLinked to original sources

arXiv2025

Polymer (imperfect) single-file diffusion: A phase diagram

We use Langevin dynamics (LD) simulations to investigate single-file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube with periodic boundary conditions (a torus). The transition from SFD, where the time (t) dependence of the mean-square displacement scales like $\langle x^2\rangle \sim t^{1/2}$, to normal diffusion with $\langle x^2 \rangle \sim t$, is studied as a function of the system parameters, such as the size and concentration of the polymer chains and the width of the tube. We propose a phase diagram describing different diffusion regimes. In particular, we highlight the fact that there are two different pathways to normal long-time diffusion. We also map this problem onto a one-dimensional Lattice Monte Carlo model where the diffusing object represents the polymer center of mass. Possible extensions of this work to polydisperse polymer solutions, one-dimensional electrophoresis and DNA mapping are discussed.

cond-mat.soft↗

arXiv2023

Ratcheting charged polymers through symmetric nanopores using pulsed fields: Designing a low pass filter for concentrating DNA

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.

cond-mat.soft↗

arXiv2022

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 $P^3M$ 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 \textit{orientational capture radius} we proposed previously for uniformly charged rods is still valid in the presence of EHI.

cond-mat.soft↗

arXiv2022

An empirical method to characterize displacement distribution functions for anomalous and transient diffusion

We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a colloidal particle diffusing between two walls using Langevin Dynamics (LD) simulations of a raspberry particle coupled to a lattice Boltzmann (LB) fluid. We also test the function with a simple model of anomalous diffusion on a square lattice with obstacles. In both cases, the fitting parameters provide more physical information than just the Kurtosis (which is often the method used to quantify the degree of anomaly of the dynamics), including a length scale that marks where the tails of the DispD begin. In all cases, the fitting parameters smoothly converge to Gaussian values as the systems become less anomalous.

cond-mat.soft↗

arXiv2021

Estimating the Steady State Diffusion Coefficient Using Data from the Transient Anomalous Regime

When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common to characterize this transient regime using the concept of anomalous (sub)diffusion with the scaling law $\left< r^2 \right> \sim t^α$, where the corresponding exponent $α<1$. We propose a new method to estimate the critical time $t^*$ that marks the transition between these two regimes. The method uses short-time data from the transient regime to estimate $t^*$, which can then be used to estimate the steady-state diffusion coefficient $D$. In other words, we propose a procedure that makes it possible to estimate the steady state diffusion coefficient without reaching the steady-state. We test the procedure with various two-dimensional lattice systems.

physics.bio-ph↗

arXiv2021

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 $λ_e$. 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 $λ_e$. 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.

physics.bio-ph↗

arXiv2020

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 towards 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 \textit{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.

physics.bio-ph↗

arXiv2019

Voltage-Driven Translocation: Defining a Capture Radius

Analyte translocation involves three phases: (i) diffusion in the loading solution; (ii) capture by the pore; (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 \textit{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 over-simplified 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 $R^*$.

physics.bio-ph↗

arXiv2019

Random walk on a lattice in the presence of obstacles: The short-time transient regime, anomalous diffusion and crowding

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the motion is Fickian with a diffusion coefficient $D$ that depends on the concentration and type of obstacles present in the system. For intermediate times, the mean-square displacement of the particle often increases approximately as $~t^α$, with $α<1$, typical of what is generally called anomalous diffusion. However, it is not clear how one can identify or choose a time or displacement interval that would give a reliable estimate of $α$. In this paper, we use two exact numerical approaches to obtain diffusion data for a simple Lattice Monte Carlo model in both time limits. This allows us to propose an objective definition of the transient regime and a unique value for $α$. Furthermore, our methodology directly gives us the length scale over which the transient regime switches to the steady-state regime. We test our proposed approach using several types of obstacle systems, and we introduce the novel concept of excess diffusion lengths. Finally, we show that the values of the parameters describing the anomalous transient regime depend on the Monte Carlo moves used to describe the dynamics of the particle, and we propose a new algorithm that correctly models the short time diffusion of a particle on a lattice.

physics.bio-ph↗

arXiv2018

Reducing the variance in the translocation times by pre-stretching the polymer

Langevin Dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the \textit{trans}-side. Under the influence of pre-stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields a reduced variation in translocations times relative to the mean translocation time. This effect is explored for different ratios of the amplitude of thermal fluctuations to driving forces to control for the relative influence of the thermal path sampled by the polymer. Since the variance in translocation times is due to contributions coming from sampling both thermal noise and initial conformations, our simulations offer independent control over the two main sources of noise, and allow us to shed light on how they both contribute to translocation dynamics. Experimentally relevant conditions are highlighted and shown to correspond to a significant decrease in the spread of translocation times, thus indicating that stretching DNA prior to translocation could assist in nanopore-based sequencing and sizing applications.

cond-mat.soft↗

arXiv2017

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.

cond-mat.soft↗

arXiv2015

Electrophoretic Mobility of Polyelectrolytes within a Confining Well

We present a numerical study of polyelectrolytes electrophoresing in free solution while squeezed by an axisymmetric confinement force transverse to their net displacement. Hybrid multi-particle collision dynamics and molecular dynamics simulations with mean-field finite Debye layers show that even though the polyelectrolyte chains remain "free-draining", their electrophoretic mobility increases with confinement in nanoconfining potential wells. The primary mechanism leading to the increase in mobility above the free-solution value, despite long-range hydrodynamic screening by counterion layers, is the orientation of polymer segments within Debye layers. The observed length-dependence of the electrophoretic mobility arises due to secondary effects of counterion condensation related to confinement compactification.

cond-mat.soft↗

arXiv2014

Simulating the Entropic Collapse of Coarse-Grained Chromosomes

Depletion forces play a role in the compaction and de-compation of chromosomal material in simple cells but it remains 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 continous 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.

cond-mat.soft↗

arXiv2014

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 simulation approaches appropriate for the study of complex systems. This paper examines the use of two common truncated Lennard-Jones (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.

cond-mat.soft↗

arXiv2014

Using a Péclet Number for the Translocation of Polymer through a Nanopore to Tune Coarse-Grained Simulations to Experimental Conditions

Coarse-grained simulations are often employed to study the translocation of DNA through a nanopore. The majority of these studies investigate the translocation process in a relatively generic sense and do not endeavour to match any particular set of experimental conditions. In this manuscript, we use the concept of a Péclet number for translocation, $P_t$, to compare the drift-diffusion balance in a typical experiment vs a typical simulation. We find that the standard coarse-grained approach over-estimates diffusion effects by anywhere from a factor of 5 to 50 compared to experimental conditions using dsDNA. By defining a coarse-graining parameter, $λ$, we are able to correct this and tune the simulations to replicate the experimental $P_t$ (for dsDNA and other scenarios). To show the effect that a particular $P_t$ can have on the dynamics of translocation, we perform simulations across a wide range of $P_t$ values for two different types of driving forces: a force applied in the pore and a pulling force applied to the end of the polymer. As $P_t$ brings the system from a diffusion dominated to a drift dominated regime, a variety of effects are observed including a non-monotonic dependence of the translocation time $τ$ on $P_t$ and a steep rise in the probability of translocating. Comparing the two force cases illustrates the impact of the crowding effects that occur on the trans side: a non-monotonic dependence of the width of the $τ$ distributions is obtained for the in-pore force but not for the pulling force.

cond-mat.soft↗

arXiv2014

"Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion

Wang et al. [PNAS 106 (2009) 15160] 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 (DisD), 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 DisD at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression "diffusing diffusivity". The DisD is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit to the DisD for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.

cond-mat.stat-mech↗

arXiv2012

Translocation of a Polymer through a Nanopore across a Viscosity Gradient

The translocation of a polymer through a pore in a membrane separating fluids of different viscosities is studied via several computational approaches. Starting with the polymer halfway, we find that as a viscosity difference across the pore is introduced, translocation will predominately occur towards one side of the membrane. These results suggest an intrinsic pumping mechanism for translocation across cell walls which could arise whenever the fluid across the membrane is inhomogeneous. Somewhat surprisingly, the sign of the preferred direction of translocation is found to be strongly dependent on the simulation algorithm: for Langevin Dynamics (LD) simulations, a bias towards the low viscosity side is found while for Brownian Dynamics (BD), a bias towards the high viscosity is found. Examining the translocation dynamics in detail across a wide range of viscosity gradients and developing a simple force model to estimate the magnitude of the bias, the LD results are demonstrated to be more physically realistic. The LD results are also compared to those generated from a simple, one dimensional random walk model of translocation to investigate the role of the internal degrees of freedom of the polymer and the entropic barrier. To conclude, the scaling of the results across different polymer lengths demonstrates the saturation of the preferential direction with polymer length and the non-trivial location of the maximum in the exponent corresponding to the scaling of the translocation time with polymer length.

cond-mat.soft↗

arXiv2012

Monte Carlo Approaches for Simulating a Particle at a Diffusivity Interface and the "Ito--Stratonovich Dilemma"

The possibility of different interpretations of the stochastic term (or calculi) in the overdamped Langevin equation for the motion of a particle in an inhomogeneous medium is often referred to as the "Ito--Stratonovich dilemma," although there is, in fact, a continuum of choices. We introduce two Monte Carlo (MC) simulation approaches for studying such systems, with both approaches giving the choice between different calculi (in particular, Ito, Stratonovich, and "isothermal"). To demonstrate these approaches, we study the diffusion on a 1D interval of a particle released at an interface (in the middle of the system) between two media where this particle has different diffusivities (e.g., two fluids with different viscosities). For reflecting boundary conditions at the ends of the interval, a discontinuity at the interface in the stationary-state particle distribution is found, except for the isothermal case, as expected. We also study the first-passage problem using absorbing boundary conditions. Good agreement is found when comparing the MC approaches to theory as well as Brownian and Langevin dynamics simulations. Also, the results themselves turn out to be interesting. For instance: 1) for some calculi, there are more particles on the low-viscosity side (LVS) at earlier times and then fewer particles at later times; 2) there is no preference to end up on a particular wall for the Ito variant, but a bias towards the wall on the LVS in all other cases; 3) the mean first-passage time to the wall on the LVS grows as the viscosity on the other side is increased, except for the isothermal case where it approaches a constant; 4) when the viscosity ratio is high, the first-passage-time distribution for the wall on the LVS is much broader than for the other wall, with a power-law dependence of the former in a certain time interval whose exponent depends on the calculus.

cond-mat.stat-mech↗