Brownian Dynamics Simulations Research Articles

Brownian dynamics simulation of the structural evolution in monodisperse hard-sphere suspensions during drying and sedimentation processes.

The drying behavior of monodisperse colloidal films, with a focus on the influence of process variables on film microstructures, is explored via Brownian dynamics (BD) simulations. In our model, hard-sphere colloidal particles are dispersed in a Newtonian liquid with an initial particle volume fraction of 0.1. The effects of the drying rate and sedimentation on the evolving microstructures are systematically investigated using two dimensionless numbers: the Péclet number (Pe), which represents the competition between evaporation and diffusion, and the sedimentation number (Ns), which reflects the relative influence of sedimentation on evaporation. First, we analyze the local particle volume fraction and film structure at various Pe and Ns. As Pe increases, particle accumulation occurs near the liquid-gas interface, whereas a high Ns promotes dense packing near the substrate owing to sedimentation. The BD simulation results, viz. the local volume fraction profiles and drying regime maps, are in good agreement with those of the continuum model proposed by Wang and Brady. Structural analysis of the dried films reveals that at a low Pe (Pe = 0.1), a face-centered cubic (FCC) structure dominates, primarily independent of the sedimentation effects. In contrast, a high Pe leads to hexagonal close-packed or amorphous structure formation. Notably, at intermediate drying rates (Pe = 10), an increase in Ns promotes additional FCC ordering in the final film structure. Our study provides new insights into the hitherto underexplored role of sedimentation in the structural evolution of drying colloidal films, revealing the mechanisms of drying-induced assembly in colloidal systems.

Self-Generated Ions Modify the Pair Interaction and the Phase Separation of Chemically Active Colloids.

Chemically active colloids that release/consume ions are an important class of active matter, and exhibit interesting collective behaviors such as phase separation, swarming, and waves. Key to these behaviors is the pair-wise interactions mediated by the concentration gradient of self-generated ions. This interaction is often simplified as a pair-wise force decaying at 1/r2, where r is the interparticle distance. Here, we show that this simplification fails for isotropic and immotile active colloids with net ion production, such as Ag colloids in H2O2. Specifically, the production of ions on the surface of the Ag colloids increases the local ion concentration, c, and attenuates the pair-wise interaction force that scales with ∇c/c. As a result, the attractive force between an Ag colloid and its neighbor (active or passive) decays at 1/r or 1/r2 for small or large r, respectively. In a population, the attraction of a colloid by a growing cluster also scales with ∇c/c, so that medium-sized clusters grow fastest, and that the cluster coarsening slows with time. These results, supported by finite element and Brownian dynamic simulations, highlight the important role of self-generated ions in shaping the collective behavior of chemically active colloids.

Coupled dynamics in binary mixtures of model colloidal Yukawa systems.

The dynamical behavior of binary mixtures consisting of highly charged colloidal particles is studied by means of Brownian dynamics simulations. We investigate differently sized, but identically charged particles with nearly identical interactions between all species in highly dilute suspensions. Different short-time self-diffusion coefficients induce, mediated by electrostatic interactions, a coupling of both self and collective dynamics of differently sized particles: the long-time self-diffusion coefficients of a larger species are increased by the presence of a more mobile, smaller species and vice versa. Similar coupling effects are observed in collective dynamics where both time constant and functional form of intermediate scattering functions' initial decay are influenced by the presence of a differently sized species. We provide a systematic analysis of coupling effects in dependence on the ratio of sizes, number densities, and the strength of electrostatic interactions.

Regulating transport efficiency through the nuclear pore complex: The role of binding affinity with FG-Nups.

Macromolecules are transported through the nuclear pore complex (NPC) via a series of transient binding and unbinding events with FG-Nups, which are intrinsically disordered proteins anchored to the pore's inner wall. Prior studies suggest that the weak and transient nature of this binding is crucial for maintaining the transported molecules' diffusivity. In this study, we explored the relationship between binding kinetics and transport efficiency using Brownian dynamics simulations. Our results indicate that the duration of binding is a critical factor in regulating transport efficiency. Specifically, excessively short binding durations insufficiently facilitate transport, while overly long durations impede molecular movement. We calculated the optimal binding duration for efficient molecular transport and found that it aligns with other theoretical predictions. Additionally, the calculated value is comparable to experimental measurements of the association timescale between nuclear transport receptors and FG-Nups at a single binding site. Our study provides a quantitative framework that bridges local molecular interactions with overall transport dynamics through the NPC, offering valuable insights into the mechanisms governing selective molecular transport.

Double Mpemba effect in the cooling of trapped colloids.

The Mpemba effect describes the phenomenon that a system at hot initial temperature cools faster than at an initial warm temperature in the same environment. Such an anomalous cooling has recently been predicted and realized for trapped colloids. Here, we investigate the freezing behavior of a passive colloidal particle by employing numerical Brownian dynamics simulations and theoretical calculations with a model that can be directly tested in experiments. During the cooling process, the colloidal particle exhibits multiple non-monotonic regimes in cooling rates, with the cooling time decreasing twice as a function of the initial temperature-an unexpected phenomenon we refer to as the Double Mpemba effect. In addition, we demonstrate that both the Mpemba and Double Mpemba effects can be predicted by various machine-learning methods, which expedite the analysis of complex, computationally intensive systems.

Mechanical unfolding of RNA molecules using a knowledge-based model.

We revisit a coarse-grained model to study the dynamics of ribonucleic acid (RNA). In our model, each nucleotide is replaced by an interaction center located at the center of mass. The interaction between nucleotides is carried out by a series of effective pair potentials obtained from the statistical analysis of 501 RNA molecules of high molecular weight from the Protein Data Bank. In addition to the Watson-Crick interactions, we also include non-canonical interactions, which provide stability to the three-dimensional (3D) structure of the molecule. The resulting knowledge-based interactions for the nucleotides (KIN) model allow us to perform efficient Brownian dynamics simulations under different conditions. First, we simulate the stretch of a set of hairpins at a loading rate similar to the values employed in unfolding experiments near equilibrium using optical tweezers. Additionally, we explore unfolding a set of pseudoknots under conditions farther from equilibrium, namely, at loading rates higher than the experimental equilibrium values. The results of our simulations are compared with those obtained from experimental measurements and theoretical models intended to estimate transition states and activation energies. Our KIN model is able to reproduce the intermediate states observed during mechanical unfolding experiments. Moreover, the results of the KIN model are in good agreement with the measured data.

Immersed boundary method for dynamic simulation of polarizable colloids of arbitrary shape in explicit ion electrolytes.

We develop a computational method for modeling electrostatic interactions of arbitrarily shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion electrolytes and nonionic solvents. Our method computes the nonuniform polarization charge distribution induced in a colloidal particle by both externally applied electric fields and local electric fields arising from other charged objects in the dispersion. This leads to expressions for electrostatic energies, forces, and torques that enable efficient molecular dynamics and Brownian dynamics simulations of colloidal dispersions in electrolytes, which can be harnessed to accurately predict structural and transport properties. We describe an implementation in which colloidal particles are modeled as rigid composites of small spherical beads that tessellate the surface of the particle. The electrostatics calculations are accelerated using a spectrally accurate particle-mesh-Ewald technique implemented on a graphics processing unit and regularized such that the electrostatic calculations are well-defined even for overlapping bodies. We illustrate the effectiveness of this approach with a comprehensive set of calculations: the induced dipole moments and forces for individual, paired, and lattice configurations of spherical colloids in an electric field; the induced dipole moment and torque for anisotropic particles subjected to an electric field; the equilibrium ion distribution in the double layer surrounding charged colloids; the dynamics of charged colloids; and the behavior of ions in the double layer of a polarizable colloid under the influence of an electric field.

Structures of the First Epitaxial Layer Created in Colloidal Heteroepitaxy.

Brownian dynamics simulations have been performed to investigate the structural dependence of the first epitaxial layer in colloidal heteroepitaxy. When the epitaxial particles were larger than the substrate particles and the interactions were dominated by the depletion force, a hexagonal structure formed on a closely packed hexagonal substrate. The orientation of this hexagonal structure varied with the size ratio of the epitaxial to substrate particles to make the interaction between the substrate and epitaxial particles strong. When the sizes of the substrate and epitaxial particles were similar, long-period structures formed instead of hexagonal structures to strengthen the interaction between the substrate and epitaxial layer at the expense of the interaction between particles in the first epitaxial layer.

Force-extension and longitudinal response of wormlike chains with single cross-link

Certain important biopolymers, such as actin filaments, are known to have cross-links at their interfaces, which significantly influence their mechanical properties. To explore these effects, the force-extension and longitudinal response of wormlike chains (WLCs) with a single cross-link under tension in two-dimension are examined using both analytical methods and Brownian dynamics simulations. The cross-link is modeled as a spring in the analytical method, and mode analysis is used to calculate the path integrals associated with the partition function. These theoretical results are then validated through Brownian dynamics simulations. Final results indicate that the simulation results are consistent with the theoretical predictions, particularly for situations involving large tensile force and short chain, which are prerequisites for the application of the weak bending approximation.

Macrotransport of active particles in periodic channels and fields: Rectification and dispersion.

Transport and dispersion of active particles in structured environments, such as corrugated channels and porous media, are important for the understanding of both natural and engineered active systems. Owing to their continuous self-propulsion, active particles exhibit rectified transport under spatially asymmetric confinement. While progress has been made in experiments and particle-based simulations, a theoretical understanding of the effective long-time transport dynamics in spatially periodic geometries remains less developed. In this paper, we apply generalized Taylor dispersion theory to analyze the long-time effective transport dynamics of active Brownian particles (ABPs) in periodic channels and fields. We show that the long-time transport behavior is governed by an effective advection-diffusion equation. The derived macrotransport equations allow us to characterize the average drift and effective dispersion coefficient. For the case of ABPs subject to a no-flux boundary condition at the channel wall, we show that regardless of activity, the average drift is given by the net diffusive flux along the channel. For ABPs, their activity is the driving mechanism that sustains a density gradient, which ultimately leads to rectified motion along the channel. Our continuum theory is validated against direct Brownian dynamics simulations of the Langevin equations governing the motion of each ABP.

Channel-facilitated transport under resetting dynamics.

The transport of particles through channels holds immense significance in physics, chemistry, and biological sciences. For instance, the motion of solutes through biological membranes is facilitated by specialized proteins that create water-filled channels. Valuable insights can be obtained by studying the transition paths of particles through a channel and gathering information on their lifetimes inside the channel as well as their exit probabilities. In a similar vein, we consider a one-dimensional model of channel-facilitated transport where a diffusive particle is subject to attractive interactions with the walls of the channel. We study the statistics of conditional and unconditional escape times in the presence of resetting-an intermittent dynamics that brings the particle back to its initial coordinate stochastically. We determine analytically the physical conditions under which such a resetting mechanism becomes beneficial for the faster escape of the particles from the channel, thus enhancing transport. Our theory has been verified with the aid of Brownian dynamics simulations for various interaction strengths and extents. The overall results presented herein highlight the scope of resetting-based strategies to be universally promising for complex transport processes of single or long molecules through biological membranes.

Scaling Relationships of the Structural and Rheological Behavior of Tadpole Polymer Chains in Dilute Solution Systems Using Brownian Dynamics Simulations.

Tadpole polymers, also known as lasso polymers, feature molecular structures that combine a single ring with a single linear side branch, leading to distinct conformational, dynamical, and rheological characteristics compared to their corresponding counterparts, particularly pure linear and pure ring polymers. To elucidate the mechanisms underlying these distinctive behaviors, comprehensive mesoscopic Brownian dynamics (BD) simulations of dilute solution systems of tadpole polymers were conducted using a bead-rod chain model under both equilibrium and flow conditions. Three types of tadpole polymer chains were prepared by varying the ring-to-linear ratio within the tadpole chain and comparing them with the corresponding linear and ring chains. Depending on this ratio, tadpole polymer chains exhibit entirely different structural properties and rotational dynamics, both in equilibrium and under shear flow. As the linear proportion within the tadpole chain increased, the structural, dynamic, and rheological properties of the tadpole polymer chains became more similar to those of pure linear polymers. Conversely, with an increasing ring proportion, these properties began to resemble those of pure ring polymers. Based on these observed tendencies, a simple general scaling expression is proposed for tadpole polymer properties that integrates scaling expressions for both pure linear and pure ring polymers. Our results indicate that the conformational, dynamic, and rheological properties of tadpole polymers, as predicted by these simple scaling expressions, are in good agreement with the simulated values, a result we consider statistically significant.

Rotational Taylor dispersion in linear flows

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

Molecular mechanics studies of factors affecting overall rate in cascade reactions: Multi-enzyme colocalization and environment.

Millions of years of evolution have optimized many biosynthetic pathways by use of multi-step catalysis. In addition, multi-step metabolic pathways are commonly found in and on membrane-bound organelles in eukaryotic biochemistry. The fundamental mechanisms that facilitate these reaction processes provide strategies to bioengineer metabolic pathways in synthetic chemistry. Using Brownian dynamics simulations, here we modeled intermediate substrate transportation of colocalized yeast-ester biosynthesis enzymes on the membrane. The substrate acetate ion traveled from the pocket of aldehyde dehydrogenase to its target enzyme acetyl-CoA synthetase, then the substrate acetyl CoA diffused from Acs1 to the active site of the next enzyme, alcohol-O-acetyltransferase. Arranging two enzymes with the smallest inter-enzyme distance of 60 Å had the fastest average substrate association time as compared with anchoring enzymes with larger inter-enzyme distances. When the off-target side reactions were turned on, most substrates were lost, which suggests that native localization is necessary for efficient final product synthesis. We also evaluated the effects of intermolecular interactions, local substrate concentrations, and membrane environment to bring mechanistic insights into the colocalization pathways. The computation work demonstrates that creating spatially organized multi-enzymes on membranes can be an effective strategy to increase final product synthesis in bioengineering systems.

Accurate drift-invariant single-molecule force calibration using the Hadamard variance

Single-molecule force spectroscopy (SMFS) techniques play a pivotal role in unraveling the mechanics and conformational transitions of biological macromolecules under external forces. Among these techniques, multiplexed magnetic tweezers (MT) are particularly well suited to probe very small forces, ≤1 pN, critical for studying noncovalent interactions and regulatory conformational changes at the single-molecule level. However, to apply and measure such small forces, a reliable and accurate force-calibration procedure is crucial. Here, we introduce a new approach to calibrate MT based on thermal motion using the Hadamard variance (HV). To test our method, we perform bead-tether Brownian dynamics simulations that mimic our experimental system and compare the performance of the HV method against two established techniques: power spectral density (PSD) and Allan variance (AV) analyses. Our analysis includes an assessment of each method’s ability to mitigate common sources of additive noise, such as white and pink noise, as well as drift, which often complicate experimental data analysis. We find that the HV method exhibits overall similar or higher precision and accuracy, yielding lower force estimation errors across a wide range of signal/noise ratios (SNRs) and drift speeds compared with the PSD and AV methods. Notably, the HV method remains robust against drift, maintaining consistent uncertainty levels across the entire studied SNR and drift speed spectrum. We also explore the HV method using experimental MT data, where we find overall smaller force estimation errors compared with PSD and AV approaches. Overall, the HV method offers a robust method for achieving sub-pN resolution and precision in multiplexed MT measurements. Its potential extends to other SMFS techniques, presenting exciting opportunities for advancing our understanding of mechanosensitivity and force generation in biological systems. To make our methods widely accessible to the research community, we provide a well-documented Python implementation of the HV method as an extension to the Tweezepy package.

Transcribing RNA polymerases: Dynamics of twin supercoiled domains

Gene transcription by an RNA polymerase (RNAP) enzyme requires that double-stranded DNA be locally and transiently opened, which results in an increase of DNA supercoiling downstream of the RNAP and a decrease of supercoiling upstream of it. When the DNA is initially torsionally relaxed and the RNAP experiences sufficiently large rotational drag, these variations lead to positively supercoiled plectonemes ahead of the RNAPs and negatively supercoiled ones behind it, a feature known as “twin supercoiled domain” (TSD). This work aims at deciphering into some more detail the torsional dynamics of circular DNA molecules being transcribed by RNAP enzymes. To this end, we performed Brownian dynamics simulations with a specially designed coarse-grained model. Depending on the superhelical density of the DNA molecule and the ratio of RNAP’s twist injection rate and rotational relaxation speed, simulations reveal a rich panel of behaviors, which sometimes differ markedly from the crude TSD picture. In particular, for sufficiently slow rotational relaxation speed, positively supercoiled plectonemes never form ahead of an RNAP that transcribes a DNA molecule with physiological negative supercoiling. Rather, negatively supercoiled plectonemes form almost periodically at the upstream side of the RNAP and grow up to a certain length before detaching from the RNAP and destabilizing rapidly. The extent to which topological barriers hinder the dynamics of TSDs is also discussed.

Escape of an active ring from an attractive surface: Behaving like a self-propelled Brownian particle.

Escape of active agents from metastable states is of great interest in statistical and biological physics. In this paper, we investigate the escape of a flexible active ring, composed of active Brownian particles, from a flat attractive surface using Brownian dynamics simulations. To systematically explore the effects of activity, persistence time, and the shape of attractive potentials, we calculate escape time τ_{e} and effective temperature T_{eff}. We observe two distinct escape mechanisms: Kramers-like thermal activation at small persistence times, where ln(τ_{e})∼1/(k_{B}T_{eff}), and the maximal force problem at large persistence time, where τ_{e} is determined by persistence time. The escape time explicitly depends on the shape of the potential barrier at high activity and large persistence time. Moreover, when the propulsion force is biased along the ring's contour, escape becomes more difficult and is primarily driven by thermal noise. Our findings highlight that, despite its intricate configuration, the active ring can be effectively modeled as a self-propelled Brownian particle when studying its escape from a smooth surface.

Active string fluids and gels formed by dipolar active Brownian particles in 3D.

Self-propelled particles possessing permanent magnetic dipole moments occur naturally in magnetotactic bacteria and can be built into man-made systems such as active colloids or micro-robots. Yet, the interplay between self-propulsion and anisotropic dipole-dipole interactions on dynamic self-assembly in three dimensions (3D) remains poorly understood. We conduct Brownian dynamics simulations of active dipolar particles in 3D, focusing on the low-density regime, where dipolar hard spheres tend to form chain-like aggregates and percolated networks with increasing dipolar coupling strength. We find that strong active forces override dipolar attractions, effectively inhibiting chain-like aggregation and network formation. Conversely, activating particles with low to moderate forces results in a fluid composed of active chains and rings. At strong dipolar coupling strengths, this active fluid transitions into an active gel, consisting of a percolated network of active chains. Although the overall structure of the active gel remains interconnected, the network experiences more frequent configurational rearrangements due to the reduced bond lifetime of active dipolar particles. Consequently, particles exhibit enhanced translational and rotational diffusion within the active fluid of strings and active gels compared to their passive counterparts. We quantify the influence of activity on aggregate topology as they transition from branched structures to unconnected chains and rings. Our findings are summarized in a state diagram, delineating the impact of dipolar coupling strength and active force magnitude on the system.

Anti-matching effect in a two dimensional driven vortex lattice in the presence of periodic pinning

The dynamics of a driven superconducting vortex lattice in a two-dimensional (2D) periodic potential of square symmetry is studied using Brownian dynamics simulations. The range and strength of the vortex-substrate interaction are taken to be of the same order as that of the vortex-vortex interaction. The matching effect in a driven vortex lattice in the presence of a periodic array of pinning centers refers to the enhanced resistance to the vortex lattice motion when the ratio of the number of vortices to the number of pinning centers (called the filling fraction) takes simple fractional values. In particular, one expects a pronounced matching effect when the filling fraction is one. Contrary to this expectation, a drop in the vortex lattice mobility is observed as the filling fraction is increased from value one. This anti-matching effect can be understood in terms of the structural change in the vortex lattice as the filling fraction is varied. The dip observed in vortex mobility as a function of temperature when the filling fraction equals one (Joseph T 2020PhysicaA556124737), is studied for other values of filling above and below one. The behavior is found to persist for other fillings as well and is associated with the melting of the vortex lattice. The temperature at which the lattice melts is found to increase with drive and explains the shift in the temperature at which mobility is a minimum, locally.

Nonequilibrium relaxation of soft responsive colloids.

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.