Langevin Dynamics Simulations Research Articles

Multivalent binding proteins can drive collapse and reswelling of chromatin in confinement.

Collapsed conformations of chromatin have been long suspected of being mediated by interactions with multivalent binding proteins, which can bring together distant sections of the chromatin fiber. In this study, we use Langevin dynamics simulation of a coarse grained chromatin polymer to show that the role of binding proteins can be more nuanced than previously suspected. In particular, for chromatin polymer in confinement, entropic forces can drive reswelling of collapsed chromatin with increasing binder concentrations, and this reswelling transition happens at physiologically relevant binder concentrations. Both the extent of collapse, and also of reswelling depends on the strength of confinement. We also study the kinetics of collapse and reswelling and show that both processes occur in similar timescales. We characterise this reswelling of chromatin in biologically relevant regimes and discuss the non-trivial role of multivalent binding proteins in mediating the spatial organisation of the genome.

Phase separation phenomenon in mixed system composed of low- and high-inertia active particles

Active matter refers to a class of substance capable of autonomously moving by harnessing energy from its surrounding environment. The substance exhibits unique non-equilibrium phenomenon, and hence has attracted great attention in the scientific community. Many active matters, such as bacteria, cells, micro-swimmers, and self-propelled colloidal particles, operate in viscous environments and their motions are described usually by using overdamped models. Examples include overdamped active Brownian particle (ABP) model for self-propelled colloidal particles in solution and run-and-tumble (RTP) model for swimming bacteria. In recent years, increasing studies focus on the influence of inertia on the behavior of active matter. Vibrating robots, runners, flying insects, and micro-fliers are typical of active systems under the underdamped condition. The motions of these active matters can be modelled by underdamped Langevin equation, known as the active inertial particle (AIP) model. Previous studies have demonstrated that like the scenarios in ABP systems, motility-induced phase separation (MIPS) phenomena also happen in AIP systems under certain density conditions. However, due to the strong collision-and-rebound effect, aggregation of AIP particles and hence the MIPS are impeded. In complex living/application environments, mixture of different active agents is often seen. Some studies on mixed systems of active matter show that the composition is an important quantity, which influences the phase separation phenomena. In this paper, we study the phase separation phenomena in a mixed system composed of low- and high-inertia active particles by underdamped Langevin dynamics simulations. We find that compared with single-component system, the mixed system is unexpectedly favorable for the occurrence of phase separation at a moderate overall concentration and a certain range of component fraction, while unfavorable for phase separation at a high overall concentration. The underlying mechanism is that the presence of a small number of the high-inertia particles could accelerate the motion of the low-inertia particles, thus facilitating their aggregation and promoting the phase separation. However, when the fraction of the high-inertia particles is large, frequent elastic collisions would disturb the aggregation of the low-inertia particles and suppress the occurrence of phase separation. Our results provide a new insight into the collective behavior of active materials and also a reference for their design and applications.

Free and enclosed inertial active gas.

In this work, the free expansion of an inertial active gas in three dimensions made of spherical non-interactive active Brownian particles with both translational and rotational inertia (IABPs) is studied. After elucidating the active particles' orientational correlation in three dimensions by employing a Fokker-Planck formalism, the diffusion, mean-square speed, persistence length, reorientation time, Swim and Reynolds pressures and total pressure of this system, are obtained theoretically and corroborated by performing Langevin dynamics simulations. Afterwards, a numerical study on particles' distribution and the mechanical pressure exerted by the active gas enclosed in a cubic box and its dependence on inertia is also carried out. This experiment highlights two important observations: first, as inertia in the system grows while fixing activity, a more uniform particle distribution within the box is achieved. In other words, the classical accumulation of active particles at the walls is seen to be suppressed by inertia. Second, an active gas with translational and rotational inertiae and made of spherical particles still has a state equation which is offered here. This is supported by the fact that both the mechanical pressure definition and the bulk pressure definition as the trace of the swim and Reynolds stress tensors, coincide in the thermodynamic limit.

Expansion of Single Chains Released from a Spherical Cavity

A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.

Collective behavior of soft self-propelled disks with rotational inertia

We investigate collective properties of a large system of soft self-propelled inertial disks with active Langevin dynamics simulation in two dimensions. Rotational inertia of the disks is found to favor motility induced phase separation (MIPS), due to increased effective persistence of the disks. The MIPS phase diagram in the parameter space of rotational inertia and disk softness is reported over a range of values of translation inertia and self-propulsion strength of the disks. Our analytical prediction of the phase boundary between the homogeneous (no-MIPS) and MIPS state in the limit of small and large rotational inertia is found to agree with the numerical data over a large range of translational inertia. Shape of the high density MIPS phase is found to change from circular to rectangular one as the system moves away from the phase boundary. Structural and dynamical properties of the system, measured by several physical quantities, are found to be invariant in the central region of the high density MIPS phase, whereas they are found to vary gradually near the peripheral region of the high density phase. Importantly, the width of the peripheral region near the phase boundary is much larger compared to the narrow peripheral region far away from the phase boundary. Rich dynamics of the disks inside the high density MIPS phase is addressed. Spatial correlation of velocity of the disks is found to increase with rotational inertia and disk hardness. However, temporal correlation of the disks’ velocity is found to be a function of rotational inertia, while it is independent of disk softness.

Effects of dust particle number on the structure and dynamics in a binary complex plasma system by Langevin dynamics simulation

In this paper, Langevin dynamics simulation is used to study the influence of particle number on the structures and dynamics of a binary complex plasma, in which two kinds of particles with different masses are considered. The structures of the binary system are characterized by particle distribution, nearest-neighbor, and pair correlation function. The dynamics of the system are characterized by the evolution of average speed and kinetic energy as time, the mean square displacement (MSD) and self-diffusion coefficient of the binary particles. The lattice structures and the dynamics evolution of binary particles versus the particle number are investigated in detail in this paper. The space distribution shows that the binary particles easily fully separate themselves for a small particle number. The dynamics evolutions indicate that small particles reach the system center first, and then are pushed out by the later reached large particles. As the number of particles increases, the system becomes more ordered and the kinetic energy difference between the two kinds of particles becomes smaller. This study shows that the structure and dynamics of a binary complex plasma can be affected by dust particle number.

Coupling Effects of Electrostatic Interactions and Salt Concentration Gradient in Polymer Translocation through a Nanopore: A Coarse-Grained Molecular Dynamics Simulations Study.

We study the influence of polymer pore interactions and focus on the role played by the concentration gradient of salt in the translocation of polyelectrolytes (PE) through nanopores explicitly using coarse-grained Langevin dynamics simulations. The mean translocation time is calculated by varying the applied voltage, the pH, and the salt concentration gradient. Changing the pH can alter the electrostatic interaction between the protein pore and the polyelectrolyte chain. The polymer pore interaction is weakened by the increase in the strength of the externally applied electric field that drives translocation. Additionally, the screening effect of the salt can reduce the strong charge-charge repulsion between the PE beads which can make translocation faster. The simulation results show there can be antagonistic or synergistic coupling between the salt concentration-induced screening effect and the drift force originating from the salt concentration gradient thereby affecting the translocation time. Our simulation results are explained qualitatively with free energy calculations.

Persistence of an active asymmetric rigid Brownian particle in two dimensions.

We have studied the persistence probability p(t) of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability of a stochastic variable that has not changed its signin a given fixed time interval. We have investigated two cases: (1) diffusion of a free active particle and (2) that of a harmonically trapped particle. In our earlier work, by Ghosh et al. [J. Chem. Phys. 152, 174901 (2020)], we had shown that p(t) can be used to determine the translational and rotational diffusion constant of an asymmetrically shaped particle. The method has the advantage that the measurement of the rotational motion of the anisotropic particle is not required. In this paper, we extend the study to an active anisotropic particle and show how the persistence probability of an anisotropic particle is modified in the presence of a propulsion velocity. Furthermore, we validate our analytical expression against the measured persistence probability from the numerical simulations of single particle Langevin dynamics and test whether the method proposed in our earlier work can help distinguish between active and passive anisotropic particles.

Langevin dynamic simulations of magnetic hyperthermia in rotating fields

The effect of a rotating magnetic field on heat dissipation due to magnetic hyperthermia is investigated numerically. A robust and validated in-house code based on Langevin Dynamics is used. High order asymptotic solutions of the temperature rate are used to validate the numerical approach. Comparisons between a rotating and an oscillatory excitation indicate a nonlinear response of the magnetic suspension with respect to the amplitude and frequency of the field. The relaxation time and volume fraction of particles also play a relevant role in this dynamics. A complete analysis on the effect of these parameters on the thermal response of the system is presented. The timescales of the problem and geometric features of the suspension micro-structure are used to interpret the results. Hysteresis curves and the real and imaginary components of the complex susceptibility are also presented in order to provide a clear physical description of the problem.

Langevin Dynamics Simulation on the Diffusivity of Polymers in Crowded Environments with Immobile Nanoparticles

Langevin Dynamics Simulation on the Diffusivity of Polymers in Crowded Environments with Immobile Nanoparticles

Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise.

We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent Liouvillian is coarse-grained by means of a projection operator formalism. We show how to replace the deterministic fluctuating force in the generalized Langevin equation by a stochastic process, such that the distributions of the observables are reproduced up to moments of a given order. Thus, in combination with a method to extract the memory kernel from simulation data of the underlying microscopic model, the method introduced here allows us to construct and simulate a coarse-grained model for a driven process.

An investigation into oxidation-induced fragmentation of soot aggregates by Langevin dynamics simulations

The present work proposes a novel oxidation-induced fragmentation model for soot aggregates which is implemented as a submodel in Langevin dynamics (LD) simulations. The surface growth and particle aggregation are first simulated in the LD framework to generate a large number of aggregates with sufficient geometric diversities resembling realistic soot aggregates. The fragmentation of these aggregates induced by surface oxidation through reaction with molecular oxygen at high temperatures is then modelled. The probability density function (PDF) of a newly proposed fragmentation pattern factor is obtained from the statistical analysis of the fragment sizes. The probability of forming a monomer fragment and a remaining aggregate fragment (monomer fragmentation) is found to be two orders of magnitude higher than that of forming two fragments of similar size (equal-sized fragmentation). The relative importance of various aggregate characteristic parameters affecting the fragmentation pattern, i.e., splitting size ratio, is quantified by a Random Forest regression. It is found that the standard deviation of the overlapping coefficient is the most important parameter, followed by the global average overlapping coefficient, number of primary particles, fractal prefactor, and the fractal dimension. An exponential function is fitted to the PDF of the fragmentation pattern factor. The functional form is independent of the aggregate parameters and the fitted function shows good agreements with the statistics of the fragmentation pattern factor.

Conformation and dynamics of a tethered active polymer chain.

The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.

Effect of grafting density on the adsorption of end-grafted polymer chains

The critical adsorption temperature ( T CAP ) and adsorption process of end-grafted polymer chains with grafting density f on a homogeneous, attractive surface are studied using Langevin dynamics simulations. Results show that T CAP is roughly a constant at low f far below the critical grafting density f c which separates the polymer brush from the mushroom region, then it decreases with increasing f due to the inter-polymer repulsive interactions, and finally becomes a constant roughly independent of polymer length at f > f c because only the chain sections closest to the surface are involved in the adsorption process. However, T CAP is only estimated for f less than f limit = 1.5/ N where more than 50% of polymer monomers ( N ) per chain can be adsorbed at low temperature. The dynamic adsorption process for the polymer chains below f limit and T CAP shows that the adsorption time τ ads (for polymer chains from desorbed state to adsorbed state) changes non-monotonically with f and exhibits a maximum at f τ,max = 0.5 f limit . The increase of τ ads below f τ,max is due to the inter-polymer repulsive interactions which hinder the adsorption. Whereas the decrease of τ ads at high f is attributed to the decrease of the number of adsorbed monomers per chain. Our study reveals that the critical adsorption temperature and adsorption process of the end-grafted polymer chains are dependent on the grafting density. • Critical adsorption temperature of polymer is dependent on the grafting density. • Inter-polymer repulsive interactions decrease the critical adsorption temperature. • Critical adsorption temperature decreases fast near the critical grafting density. • Inter-polymer repulsive interactions increase the adsorption time of polymer. • Adsorption time decreases when the number of adsorbed monomers per chain decreases.

Effects of temperature on the structures and dynamics of a binary complex plasma

In the paper, the effects of temperature on the structure and dynamics of a binary complex plasma system are investigated through two-dimensional (2D) Langevin dynamics simulation. Two kinds of dust particles with different masses are considered in the binary complex system. The particle distribution, Voronoi structure diagram and pair correlation function are used to characterize the system structure. The evolution process of kinetic energy, speed and trajectories of binary particles as time under different system temperatures are used to study the dynamical characteristics of the system. It shows that binary particles with different masses have the trend to separately distribute themselves with a boundary, which is very clear at the lower temperature. There is an optimum temperature, which can produce the separation distribution with fewest small particles mixing in the region of large particles. The dynamical investigation shows that small particles firstly reach the system center and then they are pushed out by large particles. The kinetic energy has a radial distribution, showing a drastic change around the boundary of the binary particles. The investigations indicate that the structures and dynamics of the binary complex plasma can be affected by system temperature.

Superlubric-pinned transition of a two-dimensional solid dusty plasma under a periodic triangular substrate.

The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the 2D solid dusty plasma perfectly matches the triangular substrate, two distinctive pinned and moving ordered states are observed as the external uniform driving force gradually increases from zero. When there is a mismatch between the lattice structure and the triangular substrate, however, on shallow substrates, it is discovered that all of the particles can slide freely on the substrate even when the applied driving force is tiny. This is a typical example of superlubricity, which is caused by the competition between the substrate-particle and particle-particle interactions. If the substrate depth increases further, as the driving force increases from zero, there are three dynamical states consisting of the pinned state, the disordered plastic flow state, and the moving ordered state. In an underdense system, where there are fewer particles than potential well minima, it is found that the occurrence of the three different dynamical states is controlled by the depth of the substrate, which is quantitatively characterized using the average mobility.

Effect of anisotropy on the formation of active particle films.

Active colloids belong to a class of nonequilibrium systems where energy uptake, conversion, and dissipation occur at the level of individual colloidal particles, which can lead to particles' self-propelled motion and surprising collective behavior. Examples include coexistence of vapor- and liquid-like steady states for active particles with repulsive interactions only, phenomena known as motility-induced phase transitions. Similarly to motile unicellular organisms, active colloids tend to accumulate at confining surfaces forming dense adsorbed films. In this work, we study the structure and dynamics of aggregates of self-propelled particles near confining solid surfaces, focusing on the effects of the particle anisotropic interactions. We performed Langevin dynamics simulations of two complementary models for active particles: ellipsoidal particles interacting through the Gay-Berne potential and rodlike particles composed of several repulsive Lennard-Jones beads. We observe a nonmonotonic behavior of the structure of clusters formed along the confining surface as a function of the particle aspect ratio, with a film spreading when particles are near-spherical, compact clusters with hedgehog-like particle orientation for more elongated active particles, and a complex dynamical behavior for an intermediate aspect ratio. The stabilization time of cluster formation along the confining surface also displays a nonmonotonic dependence on the aspect ratio, with a local minimum at intermediate values. Additionally, we demonstrate that the hedgehog-like aggregates formed by Gay-Berne ellipsoids exhibit higher structural stability as compared to the ones formed by purely repulsive active rods, which are stable due to the particle activity only.

Tunability and Ordering in 2D Arrays of Magnetic Nanoparticles Assembled via Extreme Field Gradients

AbstractColloidal magnetite nanoparticles self‐assemble onto a disk drive medium as directed by magnetic field gradients created where the medium magnetic moment switches direction over single nanometer distances. Here, it is shown that for two such reversals or transitions that are closely spaced, the nanoparticles self‐assemble into a single feature centered between the transitions, rather than forming separate features at the transitions, and the resulting 2D assembly achieves hexatic ordering. Langevin dynamics simulations are used to explain these results, and it is found that the detailed magnetic properties of the medium play a critical role in determining assembly location. Slight changes to solvent polarity disrupt the hexatic ordering and push the nanoparticles toward the transitions, suggesting an alternate mechanism to precisely tune the self‐assembly process.

Active Diffusion of Self-Propelled Particles in Flexible Polymer Networks

Biopolymer networks having a meshwork topology, e.g., extracellular matrix and mucus gels, are ubiquitous. It is an open question to understand how self-propelled agents such as Janus colloidal particles diffuse through such a biopolymer network. Here, we computationally explore this issue in-depth by explicitly modeling three-dimensional biopolymer networks and performing Langevin dynamics simulations of active diffusion of the self-propelled tracers therein. We show that the active tracer performs distinct diffusion dynamics depending on the mesh-to-particle size and P\'eclet number (Pe). When the particle is smaller than the mesh size, it moves as if in free space with a decreased mobility depending on the polymer occupation density and Pe. However, when the particle size is increased to be comparable to the mesh size, the active particles explore the polymer network using the trapped-and-hopping mechanism. We study the trapped time distribution, flight length distribution, the mean-squared displacement, and the long-time diffusivity at varying Pe. If the particle is larger than the mesh, it captures the collective viscoelastic dynamics from the polymer network at short times and the simple diffusion of the total system at large times. Finally, we discuss the scaling behavior of the long-time diffusivity with Pe, where we find a range of Pe that yields a nontrivial power law. The latter turns out to arise from a large fluctuation of trapped, activated tracers in conjugation with responsive polymer networks.

Optimal searcher distribution for parallel random target searches.

We consider a problem of finding a target located in a finite d-dimensional domain, using N independent random walkers, when partial information about the target location is given as a probability distribution. When N is large, the first-passage time sensitively depends on the initial searcher distribution, which invokes the question of the optimal searcher distribution that minimizes the first-passage time. Here, we analytically derive the equationfor the optimal distribution and explore its limiting expressions. If the target volume can be ignored, the optimal distribution is proportional to the target distribution to the power of one third. If we consider a target of a finite volume and the probability of the initial overlapping of searchers with the target cannot be ignored in the large N limit, the optimal distribution has a weak dependence on the target distribution, with its variation being proportional to the logarithm of the target distribution. Using Langevin dynamics simulations, we numerically demonstrate our predictions in one and two dimensions.