Attractive crowding effect on passive and active polymer looping kinetics.

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

Self-assembly of rigid amphiphilic graft cyclic-brush copolymers to nanochannels using dissipative particle dynamics simulation.

The synthesis of specific artificial nanochannels remains a formidable challenge in the field of nanomaterials and synthetic chemistry. In particular, the preparation of artificial nanochannels using amphiphilic graft cyclic-brush copolymers (AGCCs) as monomers has garnered substantial attention. Nevertheless, because of the constrained time and length scales inherent in traditional molecular dynamics simulations, a comprehensive theoretical understanding of the morphological regulation mechanism governing the self-assembly of AGCCs into nanochannels remains elusive. In this study, we employed the dissipative particle dynamics (DPD) method to explore the self-assembly mechanism considering factors such as the DPD interaction parameters, concentrations, and sizes of AGCCs. By calculating the phase diagrams, we predicted the emergence of four distinct nanochannel types: short independent, long independent, parallel, and disordered channels. Importantly, the formation of these nanochannels is highly contingent on specific environmental conditions. Furthermore, we extensively discussed self-assembly processes that lead to different types of nanochannels. The self-assembly of AGCCs is revealed as a multistep process primarily influenced by the interaction parameters. However, while the monomer size and concentration do not introduce novel self-assembly morphologies, they do influence the final aggregation state. The elucidation of the self-assembly mechanism presented in this study deepens our understanding of AGCC nanochannel formation. Consequently, this is a valuable guide for the preparation of copolymer materials with specific functionalities, offering insights into targeted copolymer material design.

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.

Translocation Dynamics of an Active Filament through a Long-Length Scale Channel.

Active filament translocation through a confined space is crucial for diverse biological processes. By using Langevin dynamics simulations, we investigate the translocation dynamics of an axially self-propelled chain through a channel. First, results show a suggestive reciprocal scaling of translocation time versus active force. Second, in the case of a long channel, we demonstrate a very intriguing nonmonotonic change of translocation time with increasing channel width. The driving force shows a similar trend, providing a consistent picture to understand the unexpected channel width effect. In particular, in a moderately broad channel, the disordered chain conformation results in a loss of driving force and thus inhibits translocation dynamics. Chain adsorption might occur in a wide channel, which accounts for a facilitated translocation. Lastly, we connect the translocation process to tension propagation (TP). A modified TP picture is proposed to interpret the waiting time distribution. Our work highlights the new phenomenology owing to the crucial interplay of activity and spacial confinement, which drives the translocation dynamics, going beyond the traditional entropic barrier scenario.

Conformation and dynamics of an active filament in crowded media.

The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.

Collective behavior of chiral active particles with anisotropic interactions in a confined space.

Extensive studies so far have indicated that chirality, anisotropic interactions and spatial confinement play important roles in collective dynamics in active matter systems. However, how the overall interplay of these crucial factors affects the novel phases and macroscopic properties remains less explored. Here, using Langevin dynamics simulations, we investigate the self-organization of a chiral active system composed of amphiphilic Janus particles, where the embedded anisotropic interaction orientation is assumed to be either the same or just opposite to the direction of active force. A wealth of dynamic phases are observed including formation of phase separation, clustering state, homogeneous state, spiral vortex flow, swarm and spatiotemporal oscillation. By tuning self-propelled angular speed and anisotropic interaction strength, we identify the non-equilibrium phase diagrams, and reveal the very non-trivial modulation of both vortex and swarm patterns. Intriguingly, we find that strong chirality-alignment-confinement coupling yields a self-driven spatial and temporal organization periodically oscillating between a counterclockwise vortex and a clockwise one. Our work provides a new understanding of the novel self-assembly arising in such a confined system and enables new strategies for achieving ordered dynamic structures.

Biased-angle effect on diffusion dynamics and phase separation in anisotropic active particle system.

A deep understanding for collective behavior in an active matter system with complex interactions has far-reaching impact in biology. In the present work, we adopt Langevin dynamics simulations to investigate diffusion dynamics and phase separation in an anisotropic active particle system with a tunable biased angle α defined as the deviation between the active force direction and anisotropic orientation. Our results demonstrate that the biased angle can induce super-rotational diffusion dynamics characterized by a power-law relationship between the mean square angle displacement (MSAD) and the time interval Δt in the form of MSAD ∼ Δtß with ß > 1 and also result in non-trivial phase separation kinetics. As activity is dominant, nucleation time shows a non-monotonic dependence on the biased angle. Moreover, there arises a distinct transition of phase separation, from spinodal decomposition without apparent nucleation time to binodal decomposition with prominent nucleation delay. A significant inhibition effect occurs at right and obtuse angles, where the remarkable super-rotational diffusion prevents particle aggregation, leading to a slow nucleation process. As active force is competitive to anisotropic interactions, the system is almost homogeneous, while, intriguingly, we observe a re-entrant phase separation as a small acute angle is introduced. The prominent super-rotational diffusion under small angles provides an optimum condition for particle adsorption and cluster growth and, thus, accounts for the re-entrance of phase separation. A consistent scenario for the physical mechanism of our observations is achieved by properly considering the modulation of the biased angle on the interplay between activity and anisotropic interactions.

Passive and active tracer dynamics in polymer solutions with isotropic-to-nematic phase transition.

Macromolecular crowding plays a crucial role in determining the dynamics in a living cell. We adopt Langevin dynamics simulations to investigate the anomalous diffusion dynamics of passive and active particles in a solution of polymer chains with tunable stiffness. The solution's anisotropic feature is modulated by changing both the polymer stiffness and volume fraction, where isotropic-to-nematic phase transition is involved. Our results demonstrate the significant impact of polymer flexibility on the dynamics of both passive and active probes. The distinct diffusion mechanism for an active particle is clarified by the interplay between polymer stiffness, crowdedness and activity. Polymer stiffness leads to a global inhibition effect on passive particle diffusion. The diffusion coefficient exhibits an intriguing non-monotonic variation at increasing polymer stiffness, which is due to the fact that the alignment of polymer chains is beneficial for diffusion along the nematic direction but unfavorable for that in the direction perpendicular to it. In sharp contrast, polymer stiffness plays a dominant role in facilitating active particle diffusion. Self-propulsion of the particle can utilize stiffness-induced elastic interactions more efficiently, which promotes its mobility in both directions. Meanwhile, an active particle might have a stronger ability to take advantage of the polymer alignment, contributing substantially enhanced diffusivity. In addition, the diffusion coefficient of an active particle is subject to a tendency of degeneration against varying volume fraction. This counter-intuitive behavior is due to the contrasting factors that increasing crowdedness induces a lower particle speed but a longer persistent motion time.

Polymer looping kinetics in active heterogeneous environments.

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Comparative study of polymer looping kinetics in passive and active environments.

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

Tunable depletion force in active and crowded environments.

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Effects of active crowder size and activity-crowding coupling on polymer translocation.

Polymer translocation in complex environments is crucially important to many biological processes in life. In the present work, we adopted two-dimensional Langevin dynamics simulations to study the forced and unbiased polymer translocation dynamics in active and crowded media. The translocation time and probability are analyzed in terms of active force Fa, volume fraction φ and also the crowder size. The non-trivial active crowder size effect and activity-crowding coupling effect as well as the novel mechanism of unbiased translocation between two active environments with different active particle sizes are clarified. Firstly, for forced translocation, we reveal an intriguing non-monotonic dependence of the translocation time on the crowder size in the case of large activity. In particular, crowders of intermediate size similar to the polymer segment are proven to be the most favorable for translocation. Moreover, a facilitation-inhibition crossover of the translocation time with increasing volume fraction is observed, indicating a crucial activity-crowding coupling effect. Secondly, for unbiased translocation driven by different active crowder sizes, the translocation probability demonstrates a novel turnover phenomenon, implying the appearance of an opposite directional preference as the active force exceeds a critical value. The translocation time in both directions decreases monotonically with the active force. The asymmetric activity effect together with the entropic driving scenario provides a reasonable picture for the peculiar behavior observed in unbiased translocation.

A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment.

We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.

Exploring the Activation Mechanism of a Metabotropic Glutamate Receptor Homodimer via Molecular Dynamics Simulation.

Metabotropic glutamate receptors of class C GPCRs exist as constitutive dimers, which play important roles in activating excitatory synapses of the central nervous system. However, the activation mechanism induced by agonists has not been clarified in experiments. To address the problem, we used microsecond all-atom molecular dynamics (MD) simulation couple with protein structure network (PSN) to explore the glutamate-induced activation for the mGluR1 homodimer. The results indicate that glutamate binding stabilizes not only the closure of Venus flytrap domains but also the polar interaction of LB2-LB2, in turn keeping the extracelluar domain in the active state. The activation of the extracelluar domain drives transmembrane domains (TMDs) of the two protomers closer and induces asymmetric activation for the TMD domains of the two protomers. One protomer with lower binding affinity to the agonist is activated, while the other protomer with higher binding energy is still in the inactive state. The PSN analysis identifies the allosteric regulation pathway from the ligand-binding pocket in the extracellular domain to the G-protein binding site in the intracellular TMD region and further reveals that the asymmetric activation is attributed to a combination of trans-pathway and cis-pathway regulations from two glumatates, rather than a single activation pathway. These observations could provide valuable molecular information for understanding of the structure and the implications in drug efficacy for the class C GPCR dimers.

Activity-crowding coupling effect on the diffusion dynamics of a self-propelled particle in polymer solutions.

The anomalous diffusion dynamics of an active particle in polymer solutions is studied based on a Langevin Brownian dynamics simulation. Firstly, the mean-square displacement (MSD) is investigated under various system parameters of active force Fa, probe size σa, polymer volume fraction φ and polymer chain length N. A very novel transition between superdiffusion and subdiffusion is observed with varying Fa and φ, owing to the activity and crowding competition effect. The two anomalous diffusion regimes are identified in the parameter space diagram. The increment of the MSD under activity is examined on intermediate time scales, which manifests a power law relation with the particle's dynamical persistence length L, i.e., ΔMSD = 2Lm, where the exponent m decreases with φ. Secondly, we explicitly evaluate the long-time diffusion coefficients D in a pure solvent and Da in polymer solutions. The dependence of relative diffusivity Da/D on volume fraction φ reproduces the well-known Phillies' equation exp(-κφµ). The fitting parameters show µ≃ 1, but κ apparently increases with activity. More importantly, our simulation justifies a multi-length scaling relation in a very similar form to that for passive probes, depending on simple structural parameters of the probe-polymer system. With the aid of an activation energy model, we find a counterintuitive activity-crowding coupling effect: activity enhances the effective viscosity experienced by the probe and thus strengthens the crowding-induced slowing of diffusion.

Hydrogen-Bonding-Driven Ion-Pair Formation in Protic Ionic Liquid Aqueous Solution.

Protic ionic liquids (PILs) in solution especially in water have attracted more and more attention due to their unique properties. The solvation of PILs in water is important to their properties and applications. To explore the solvation of bio-based PILs in water, acidity of 49 [AA]X amino acid ionic liquids (AAILs) consisting of 7 different cations and 7 different anions was studied as a favorable probe. The pKa values for [AA]X PILs containing same cations were obtained and discussed. The acidity strength of the [AA]X PILs varies with both cation and anion which does not follow the conventional assumption that the acidity for PILs is independent of anions. The acidic discrepancy of [AA]X PILs aqueous solution is probably mediated by the formation of ion pairs according to a revised solvation model of PILs. Quantum-chemistry calculation was employed to unpuzzle anion's different effects on the acid balance of cations where cation-anion hydrogen bonds play an important role. Such difference in acidity allows us to understand the formation of solvated ion pairs. This work provides an insight into the fundamental solvation of PILs from acid perspective and their influence on acidity properties for the first time.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions.

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Crowding-Activity Coupling Effect on Conformational Change of a Semi-Flexible Polymer.

The behavior of a polymer in a passive crowded medium or in a very dilute active bath has been well studied, while a polymer immersed in an environment featured by both crowding and activity remains an open problem. In this paper, a systematic Langevin simulation is performed to investigate the conformational change of a semi-flexible chain in a concentrated solution packed with spherical active crowders. A very novel shrinkage-to-swelling transition is observed for a polymer with small rigidity. The underlying phase diagram is constructed in the parameter space of active force and crowder size. Moreover, the variation of the polymer gyration radius demonstrates a non-monotonic dependence on the dynamical persistence length of the active particle. Lastly, the activity-crowding coupling effect in different crowder size baths is clarified. In the case of small crowders, activity strengthens the crowding-induced shrinkage to the chain. As crowder size increases, activity turns out to be a contrasting factor to crowding, resulting in a competitive shrinkage and swelling. In the large size situation, the swelling effect arising from activity eventually becomes dominant. The present study provides a deeper understanding of the unusual behavior of a semi-flexible polymer in an active and crowded medium, associated with the nontrivial activity-crowding coupling and the cooperative crowder size effect.

Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems.

A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer. Dependence of probed chain compaction on both crowder size and concentration is investigated explicitly. Particular attention is paid to examining the significant discrepancy in collapse effect associated with the crowder structure. First, we find an opposite compaction behavior in the HS and flexible polymer systems, in consistence with previous simulation and experimental observations. Compaction decreases with HS size while it increases with flexible polymer chain length. The underlying mechanism for such a contradiction is unraveled in terms of a depletion effect. For the HS system, as the crowder size increases, the ability of accommodating the probed chain enhances with a negligible depletion effect and thus results in a reduced compaction, while a polymer crowder system introduces a local depletion effect, responsible for an intensified compaction effect with increasing polymer length. Secondly, we reveal that the anisotropic feature of the rod-like polymer is a crucial factor in compaction. A novel non-monotonous behavior against the polymer length is observed under rod-like polymer crowding, which can be ascribed to the competition between anisotropy-induced stretching and crowding-induced compaction. Lastly, we present a quantitative evaluation of the crowding-induced potential, which provides a scenario for understanding compaction from a microscopic viewpoint. The potential profiles with respect to crowder size demonstrate a consistent tendency with the corresponding collapse behavior. The study in the present work provides a deeper insight into the modeling structure and dynamics of macromolecules in crowded media.

Quantifying the protein-protein association rate in polymer solutions: crowding-induced diffusion and energy modifications.

A theoretical framework is developed to study protein-protein association in polymer solutions under diffusion-limited conditions. Starting from the basal association rate, two fundamental aspects concerning macromolecular crowding are particularly taken into account. One is the effect of microviscosity on protein diffusion. The length-scale dependent relations of translational and rotational diffusion coefficients are incorporated. Another is relevant to the crowding-induced effective interaction between the pair of proteins. The resultant energy modifications to the basal association rate are properly introduced, following an instructive classification with increasing crowder size: repulsive interaction dominant, repulsive and attractive interactions competitive, and attractive interaction prevailing. With specific energy modification terms, we are able to investigate the deviations of the association rate from the Stokes-Einstein (SE) behavior (i.e., the linear relationship with respect to the reciprocal of macroviscosity) in a quantitative manner. Our theory is applied to study the association of TEM1-ß-lactamase (TEM) and the ß-lactamase inhibitor protein (BLIP) in polyethylene glycol (PEG) solutions, with varying concentration and polymerization. We explicitly evaluate the relative association rate constant as a function of the solution macroviscosity. The theoretical results demonstrate very good agreement with the experimental data. Moreover, the complicated non-trivial deviations, either positive (slower than SE) or negative (faster than SE), are systematically rationalized. The precise role of energy modifications and the microviscosity effect on diffusion, in particular on rotational diffusion, are clearly unraveled.