Langevin Dynamics Simulations Research Articles

Field-driven polyelectrolyte-polymer collisions in nanochannels.

Even though dilute (unentangled) polymer solutions cannot act as gel-like sieving media, it has been shown that they can be used to separate DNA molecules in capillary electrophoresis. The separation then comes from sporadic, independent DNA-polymer collisions. We study polymer-polymer collisions in nanochannels (i.e., channels that are smaller than the normal size of the polymers), a situation where a polyelectrolyte is forced to migrate "through" isolated uncharged molecules during electrophoresis. We use Langevin dynamics simulations to explore the nature of these collisions and their effect on the net motion of the two polymer chains. We identify several types of collisions, including some that are unique to nanochannels. When the uncharged polymer is much larger than the polyelectrolyte, the system is reminiscent of gel electrophoresis, and we propose a modified empirical reptation model to explain the data, with an orientation factor that depends on the tube diameter. We also observe that the duration of a collision is a non-monotonic function of the polymer size ratio when the two chains are of comparable size, a surprising resonance-like phenomenon, which, combined with the asymmetric nature of molecular conformations during collision, suggests possible ratchet-like mechanisms that could be used to sort polyelectrolytes in nanodevices.

Revisiting the Second Vassiliev (In)variant for polymer knots

Abstract Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulations of open knotted polymer chains, often parameterized to DNA, typically perform a closure operation and calculate the Alexander polynomial to assign a knot topology. This is limited in scenarios where the topology is less well-defined, for example when the chain is in the process of untying or is strongly confined. Here, we use a discretized version of the Second Vassiliev Invariant for open chains to analyze Langevin Dynamics simulations of untying and strongly confined polymer chains. We demonstrate that the Vassiliev parameter can accurately and efficiently characterize the knotted state of polymers, providing additional information not captured by a single-closure Alexander calculation. We discuss its relative strengths and weaknesses compared to standard techniques, and argue that it is a useful and powerful tool for analyzing polymer knot simulations.

Translocation of two-dimensional active polymers through nanopores using Langevin dynamics simulations.

The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs-1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process.

Effect of Counterion Size on Knotted Polyelectrolyte Conformations.

Using Langevin dynamics simulations and a coarse-grained primitive model of electrolytes, we show that the behavior of knotted circular strong polyelectrolytes (PEs) in diluted aqueous solution is largely affected by the diameter of the counterions (CIs), σCI. Indeed, we observe that both gyration radius and knot length vary nonmonotonically with σCI, with both small and bulky CIs favoring knot localization, while medium-sized ones promote delocalized knots. We also show that the conformational change from delocalized to tight knots occurs via the progressive coalescence of the knot's essential crossings. The emerging conformers correspond to the minima of the free energy landscape profiled as a function of the knot length or PE size. We demonstrate that different conformational states can coexist, the transition between them appearing first-order-like and controlled by the enthalpic and entropic trade-off of the amount of CIs condensed on the PE. Such balance can be further altered by varying CI concentrations, thus providing an additional and more convenient tuning parameter for the system properties. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and shape by choosing the nature of its CIs. Thus, they offer new intriguing possibilities for designing novel PE-based materials that are capable of responding to changes in ionic solution properties.

Removal of Pseudomonas type IV pili by a small RNA virus.

The retractile type IV pilus (T4P) is important for virulence of the opportunistic human pathogen Pseudomonas aeruginosa. The single-stranded RNA (ssRNA) phage PP7 binds to T4P and is brought to the cell surface through pilus retraction. Using fluorescence microscopy, we discovered that PP7 detaches T4P, which impairs cell motility and restricts the pathogen's virulence. Using cryo-electron microscopy, mutagenesis, optical trapping, and Langevin dynamics simulation, we resolved the structure of PP7, T4P, and the PP7/T4P complex and showed that T4P detachment is driven by the affinity between the phage maturation protein and its bound pilin, plus the pilus retraction force and speed, and pilus bending. Pilus detachment may be widespread among other ssRNA phages and their retractile pilus systems and offers new prospects for antibacterial prophylaxis and therapeutics.

A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator

The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of the s-d exchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.

Na+-Mg2+ ion effects on conformation and translocation dynamics of single-stranded RNA: Cooperation and competition

The nanopore-based translocation of a single-stranded RNA (ssRNA) in mixed salt solution has garnered increasing interest for its biological and technological significance. However, it is challenging to comprehensively understand the effects of the mixed ion species on the translocation dynamics due to their cooperation and competition, which can be directly reflected by the ion screening and neutralizing effects, respectively. In this study, Langevin dynamics simulation is employed to investigate the properties of ssRNA conformation and translocation in mixed Na+-Mg2+ ion environments. Simulation results reveal that the ion screening effect dominates the change in the ssRNA conformational size, the ion neutralizing effect controls the capture rate of the ssRNA by the nanopore, and both of them take charge of the different changes in translocation time of the ssRNA under various mixed ion environments. Under high Na+ ion concentration, as Mg2+ concentration increases, the ion neutralizing effect strengthens, weakening the driving force inside the nanopore, leading to longer translocation time. Conversely, at low Na+ concentration, an increase in Mg2+ concentration enhances the ion screening effect, aiding in faster translocation. Furthermore, these simulation results will be explained by quantitative analysis, advancing a deeper understanding of the complicated effects of the mixed Na+-Mg2+ ions.

Diffusion of nanochannel-confined knot along a tensioned polymer* *The National Natural Science Foundation of China under Grant Nos. 11864006, 11874309, 12164007, and 12204118.

The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation. In this work, Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints. The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot. As a result, the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained. In the space without constraints or with weak constraints, the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours. On the contrary, for the knot with relatively small bending stiffness, the diffusion coefficients were monotonically reduced with increasing tension. However, in a space with strong constraints, all the curves showed one turnover behaviour regardless of the bending stiffness. The turnover behaviours divided the curves into different regimes, and the dominant diffusion mechanisms in the regimes, namely, knot-region breathing, self-reptation, and internal friction, were clearly identified. The effective friction coefficients ξ of the knots with 31, 41, 51 and 52 types as a function of the knot size N at a fixed tension were well fitted by the relation ξ ∝ N. The effective friction coefficients of the knots at relatively large tension f > 3 sharply increased with the knot complexity, which is not dependent on the spatial constraints. By contrast, the values of these coefficients at relatively small tension f ≤ 3 were remarkably dependent on the spatial constraints. Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot, but also highlights the single-molecule design for the manipulation of DNA knots in future.

Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers.

We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

Emergence of slip-ideal-slip behavior in tip-links serve as force filters of sound in hearing

Tip-links in the inner ear convey force from sound and trigger mechanotransduction. Here, we present evidence that tip-links (collectively as heterotetrameric complexes of cadherins) function as force filters during mechanotransduction. Our force-clamp experiments reveal that the tip-link complexes show slip-ideal-slip bond dynamics. At low forces, the lifetime of the tip-link complex drops monotonically, indicating slip-bond dynamics. The ideal bond, rare in nature, is seen in an intermediate force regime where the survival of the complex remains constant over a wide range. At large forces, tip-links follow a slip bond and dissociate entirely to cut-off force transmission. In contrast, the individual tip-links (heterodimers) display slip-catch-slip bonds to the applied forces. While with a phenotypic mutant, we showed the importance of the slip-catch-slip bonds in uninterrupted hearing, our coarse-grained Langevin dynamics simulations demonstrated that the slip-ideal-slip bonds emerge as a collective feature from the slip-catch-slip bonds of individual tip-links.

Global dust density in two-dimensional complex plasma

The driven-dissipative Langevin dynamics simulation is used to produce a two-dimensional (2D) dense cloud, which is composed of charged dust particles trapped in a quadratic potential. A 2D mesh grid is built to analyze the center-to-wall dust density. It is found that the local dust density in the outer region relative to that of the inner region is more nonuniform, being consistent with the feature of quadratic potential. The dependences of the global dust density on equilibrium temperature, particle size, confinement strength, and confinement shape are investigated. It is found that the particle size, the confinement strength, and the confinement shape strongly affect the global dust density, while the equilibrium temperature plays a minor effect on it. In the direction where there is a stronger confinement, the dust density gradient is bigger.

Physical Limit of Nonlinear Brownian Oscillators in Quantum Trap.

Quantum trap, a quantum and thermal fluctuations-induced nonmonotonous potential, offers a chance to build up microscopic mechanical systems completely dominated by fluctuations. Here, we explore the physical limit of the effective damping ratio of the nonlinear Brownian oscillator in a quantum trap, set by the finite separation for avoiding molecular-scale effects on the trap potential and the surface confinement effect-induced diverging damping and random forces. The quasiharmonic approximations and Langevin dynamics simulations show that the lowest effective damping ratios of the suspended Au plate and Au sphere upon a Teflon coating of 10 nm can be ∼210 and ∼145, respectively, at room temperature. Perforation is proposed as an effective route to reduce the damping ratio (down to 6.4) by attenuating the surface confinement effect. An unexpected result due to the temperature dependences of dielectric function and viscosity of ethanol is a further reduced damping ratio at 400 K (1.3). The nonlinear Brownian oscillator in the quantum trap shows promise of probing near-boundary hydrodynamics at nanoscale.

Emergent clustering due to quorum sensing interactions in active matter

Many organisms in nature use local interactions to generate global cooperative phenomena. To unravel how the behavior of individuals generates effective interactions within a group, we introduce a simple model, wherein each agent senses the presence of others nearby and changes its physical motion accordingly. This generates non-physical, or virtual interactions between agents. We study the radial distribution function and the cluster size distribution to quantify the emergent interactions for both social and anti-social behavior; We identify social behavior as when an agent exhibits a tendency to remain in the vicinity of other agents, whereas anti-social behavior as when it displays a tendency to escape from the vicinity of others. Using Langevin dynamics simulations in two and three spatial dimensions, we discover that under certain conditions, positive correlations, which indicate attraction can emerge even in the case of anti-social behavior. Our results are potentially useful for designing robotic swimmers that can swim collectively only based on sensing the distance to their neighbors, without measuring any orientational information.

Adsorption of active polymers on attractive nanoparticles.

The adsorption of active polymers on an attractive nanoparticle (NP) is studied using Langevin dynamics simulations. The active polymers consist of an active Brownian particle (ABP) at the head and a subsequent passive polymer chain. The ABP experiences an active force of magnitude Fa. The interactions between the active polymer and NP are modeled as Lennard-Jones potential with a strength εpn. We find the critical adsorption point εpn* increases with increasing the active force Fa. The increment of εpn*, denoted as Δεpn*, due to Fa can be expressed approximately as Δεpn* ∝ Fa2.5 for the restricted rotating active polymer (RRAP) where the rotation of the head ABP is restricted and Δεpn* ∝ Fa1.7 for the freely rotating active polymer (FRAP) where the ABP rotates freely. Meanwhile, the conformation of the adsorbed polymer, such as adsorbed trains on NP and the tail near the ABP, are also dependent on Fa. When the tail near the ABP is short, the adsorption is significantly affected by the active force. However, when the tail is long, the whole polymer can be viewed as a long tail stretched by the active force and unperturbed adsorption monomers. Simulation results show that the active force has a direct and significant effect on εpn* and the structure of the adsorbed active polymers.

Polymer translocation: effects of periodically driven confinement.

We study the influence of confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore. Using the Langevin dynamics simulations, we calculate both the first attempt time and translocation time as a function of the position of the back wall and apex angle α. As the in vivo confining environment is inherently dynamic, we extended the present study to explore the consequences of a periodically driven back wall and apex angles on the translocation dynamics. Our findings reveal that the translocation time initially decreases as the driving frequency increases, but increases after a certain frequency. The frequency at which the translocation time is found to be minimum is referred to as the resonance activation. Analyzing the distribution of translocation times around this frequency renders interesting information about the translocation process. We further explore the translocation dynamics by calculating the residence time of individual monomers, shedding light on the microscopic aspects of the process.

Forced and spontaneous translocation dynamics of a semiflexible active polymer in two dimensions.

Polymer translocation is a fundamental topic in non-equilibrium physics and is crucially important to many biological processes in life. In the present work, we adopt two-dimensional Langevin dynamics simulations to study the forced and spontaneous translocation dynamics of an active filament. The influence of polymer stiffness on the underlying dynamics is explicitly analyzed. For the forced translocation, the results show a robust stiffness-induced inhibition, and the translocation time exhibits a dual-exponent scaling relationship with the bending modulus. Tension propagation (TP) is also examined, where we find prominent modifications in terms of both activity and stiffness. For spontaneous translocation into a pure solvent, the translocation time is almost independent of the polymer stiffness. However, when the polymer is translocated into a porous medium, an intriguing non-monotonic alteration of translocation time with increasing chain stiffness is demonstrated. The semiflexible chain is beneficial for translocation while the rigid chain is not conducive. Stiffness regulation on the diffusion dynamics of the polymer in porous media shows a consistent scenario. The interplay of activity, stiffness, and porous crowding provides a new mechanism for understanding the non-trivial translocation dynamics of an active filament in complex environments.

The effects of asymmetry in active noises on the efficiency of single colloidal Stirling engines with active noises.

Molecular machines, which operate in highly fluctuating environments far from equilibrium, may benefit from their non-equilibrium environments. It is, however, a topic of controversy how the efficiency of the microscopic engines can be enhanced. Recent experiments showed that microscopic Stirling engines in bacterial reservoirs could show high performance beyond the equilibrium thermodynamics. In this work, we perform overdamped Langevin dynamics simulations for microscopic Stirling heat engines in bacterial reservoirs and show that the temperature dependence of the magnitude of active noises should be responsible for such high efficiency. Only when we introduce temperature-dependent active noises, the efficiency of the microscopic Stirling engines is enhanced significantly as in experiments.

Identification of the melting line in the two-dimensional complex plasmas using an unsupervised machine learning method

Machine learning methods have been widely used in the investigations of the complex plasmas. In this paper, we demonstrate that the unsupervised convolutional neural network can be applied to obtain the melting line in the two-dimensional complex plasmas based on the Langevin dynamics simulation results. The training samples do not need to be labeled. The resulting melting line coincides with those obtained by the analysis of hexatic order parameter and supervised machine learning method.

Enzymatic metabolons dramatically enhance metabolic fluxes of low-efficiency biochemical reactions

In this work, we investigate how spatial proximity of enzymes belonging to the same pathway (metabolon) affects metabolic flux. Using off-lattice Langevin dynamics simulations in tandem with a stochastic reaction-diffusion protocol and a semi-analytical reaction-diffusion model, we systematically explored how strength of protein-protein interactions, catalytic efficiency, and protein-ligand interactions affect metabolic flux through the metabolon. Formation of a metabolon leads to a greater speedup for longer pathways and especially for reaction-limited enzymes, whereas, for fully optimized diffusion-limited enzymes, the effect is negligible. Notably, specific cluster architectures are not a prerequisite for enhancing reaction flux. Simulations uncover the crucial role of optimal nonspecific protein-ligand interactions in enhancing catalytic efficiency of a metabolon. Our theory implies, and bioinformatics analysis confirms, that longer catalytic pathways are enriched in less optimal enzymes, whereas most diffusion-limited enzymes populate shorter pathways. Our findings point toward a plausible evolutionary strategy where enzymes compensate for less-than-optimal efficiency by increasing their local concentration in the clustered state.