Insights into aggregation dynamics of NACore peptides from coarse-grained simulations.

Alpha(α)-synuclein is closely related to the pathogenesis of Parkinson's disease (PD). The NACore, a fragment of α-synuclein, is considered to be the key region of α-synuclein that causes PD. The aggregation dynamics of NACores are studied via coarse-grained molecular dynamics simulations. We find that NACores can self-assemble into a large cluster at high concentrations. The aggregation dynamics can be divided into three stages. The growth kinetics for the first and second stages follows the power law, Smax ~ tγ , with the second stage faster than the first one. The characteristic lifetime for the high concentration is 40 times larger than that for the low concentration, implying the low fluidity. Understanding the aggregation dynamics of NACores is helpful to develop drugs for therapeutic prevention and intervention.

Configuration and dynamics of a self-propelled diblock copolymer chain.

Active polymers are slender or chain-like self-propelled objects. Synthetic chains of self-propelled colloidal particles are one of the examples, which provide a potential way to develop varied active polymers. Here, we study the configuration and dynamics of an active diblock copolymer chain. Our focus is on the competition and the cooperation between the equilibrium self-assembly due to chain heterogeneity and the dynamic self-assembly due to propulsion. Simulations show that an active diblock copolymer chain can form the spiral(+)/tadpole(+) states under forward propulsion and the spiral(-)/tadpole(-)/bean states under backward propulsion. Interestingly, it is easier for the backward-propelled chain to form a spiral. The transitions between the states can be analyzed in terms of work and energy. For forward propulsion, we found a key quantity, i.e. the chirality of the packed self-attractive A block, which determines the configuration of the whole chain and the dynamics. However, no such quantity is found for the backward propulsion. Our results set the foundation for further study of the self-assembly of multiple active copolymer chains and provide a reference for the design and application of polymeric active materials.

Scaling behavior for the detachment of a self-propelling filament from an attractive surface.

Desorption of a self-propelling filament from an attractive surface is studied by computer simulations and the influence of activity, chain length, and chain rigidity is explored. For the flexible filament, we find three scaling regimes of desorption time vs activity with various scaling exponents. At low activity, the scaling law results from the spiral-like detachment kinetics. And at high activity, by theoretical analysis, the desorption is reminiscent of the escaping mechanism of a super-diffusive blob from a potential well at a short time scale. Additionally, the desorption time decreases first and then increases with chain length at low activity, since it is hard to form a spiral for short filaments due to the limited volume repulsion. For high activities, the desorption time approximately scales with chain length, with a scaling exponent ∼0.5, which can be explained by the theory and numerically fitting scaling law between the end-to-end distance of the "globule-like" filament and chain length. Furthermore, a non-monotonic behavior is observed between the desorption time and the chain stiffness. Desorption time slightly decreases first and then rapidly increases with stiffness due to the opposed effects of increasing rigidity on headiing-up time and leaving-away time. In contrast to traditional polymers, the scaling behavior suggests unique desorption characteristics of active polymers.

Structure and dynamics of an active polymer adsorbed on the surface of a cylinder.

The structure and dynamics of an active polymer on a smooth cylindrical surface are studied by Brownian dynamics simulations. The effect of an active force on the polymer adsorption behavior and the combined effect of chain mobility, length N, rigidity κ, and cylinder radius, R, on the phase diagrams are systemically investigated. We find that complete adsorption is replaced by the irregular alternative adsorption/desorption process at a large driving force. Three typical (spiral, helix-like, and rod-like) conformations of the active polymer are observed, dependent on N, κ, and R. Dynamically, the polymer shows rotational motion in the spiral state, snake-like motion in the intermediate state, and straight translational motion without turning back in the rod-like state. In the spiral state, we find that the rotation velocity ω and the chain length follow a power-law relation ω ∼ N-0.42, consistent with the torque-balance theory of general Archimedean spirals. And the polymer shows super-diffusive behavior along the cylinder for a long time in the helix-like and rod-like states. Our results highlight that the mobility, rigidity, and curvature of surface can be used to regulate the polymer behavior.

Obstacle-induced giant jammed aggregation of active semiflexible filaments.

Filaments driven by bound motor proteins and chains of self-propelled colloidal particles are a typical example of active polymers (APs). Due to deformability, APs exhibit very rich dynamic behaviors and collective assembling structures. Here, we are concerned with a basic question: how APs behave near a single obstacle? We find that, in the presence of a big single obstacle, the assembly of APs becomes a two-state system, i.e. APs either gather nearly completely together into a giant jammed aggregate (GJA) on the surface of the obstacle or distribute freely in space. No partial aggregation is observed. Such a complete aggregation/collection is unexpected since it happens on a smooth convex surface instead of, e.g., a concave wedge. We find that the formation of a GJA experiences a process of nucleation and the curves of the transition between the GJA and the non-aggregate state form hysteresis-like loops. Statistical analysis of massive data on the growing time, chirality and angular velocity of both the GJAs and the corresponding nuclei shows the strong random nature of the phenomenon. Our results provide new insights into the behavior of APs in contact with porous media and also a reference for the design and application of polymeric active materials.

Absorption of self-propelled particles into a dense porous medium.

We study the absorption of self-propelled particles into a finite-size dense porous medium, which is mimicked by an obstacle array. We find that, depending on the competition of the propelling strength versus the repulsive barrier formed by obstacles and the contrast between the characteristic time scales of permeation and propelling persistence, the absorption process exhibits three distinct types of behavior. In Type I and II behavior, the propelling strength is not large enough to surmount the barrier, and hence particles transport in the medium by barrier-hopping dynamics. The initial permeation of particles toward the medium center is phenomenologically similar to a normal slow diffusion process. But, surprisingly, after the initial permeation process, a concentrated nucleus of particle aggregates forms and grows at the medium center in Type I, due to the long propelling persistence. Such an abnormal "nucleation" phenomenon does not appear in Type II, in which the propelling persistence is low. When the propelling strength is very high (Type III), particles transport smoothly in the medium, hence the initial slow diffusion process disappears and small particle clusters form and merge randomly in the medium. Our results provide a foundation for applications of active objects in a complex environment and also suggest the possible usage of a porous medium, for example, in the selection or sorting of active matter.

Extracting free energies of counterion binding to polyelectrolytes by molecular dynamics simulations.

We use all-atom molecular dynamics simulations to extract ΔGeff, the free energy of binding of potassium ions K+ to the partially charged polyelectrolyte poly(acrylic acid), or PAA, in dilute regimes. Upon increasing the charge fraction of PAA, the chains adopt more extended conformations, and simultaneously, potassium ions bind more strongly (i.e., with more negative ΔGeff) to the highly charged chains to relieve electrostatic repulsions between charged monomers along the chains. We compare the simulation results with the predictions of a model that describes potassium binding to PAA chains as a reversible reaction whose binding free energy (ΔGeff) is adjusted from its intrinsic value (ΔG) by electrostatic correlations, captured by a random phase approximation. The bare or intrinsic binding free energy ΔG, which is an input in the model, depends on the binding species and is obtained from the radial distribution function of K+ around the charged monomer of a singly charged, short PAA chain in dilute solutions. We find that the model yields semi-quantitative predictions for ΔGeff and the degree of potassium binding to PAA chains, α, as a function of PAA charge fraction without using fitting parameters.

Vortex formation of spherical self-propelled particles around a circular obstacle.

A vortex is a common ratchet phenomenon in active systems. The spatial symmetry is usually broken by introducing asymmetric shapes or spontaneously by collective motion in the presence of hydrodynamic interactions or other alignment effects. Unexpectedly, we observe, by simulations, the formation of a vortex in the simplest model of a circular obstacle immersed in a bath of spherical self-propelled particles. No symmetry-breaking factors mentioned above are included in this model. The vortex forms only when the particle activity is high, i.e. large persistence. The obstacle size is also a key factor and the vortex only forms in a limited range of obstacle sizes. The sustainment of the vortex originates from the bias of the rotating particle cluster around the obstacle in accepting the incoming particles based on their propelling directions. Our results provide new understanding of and insights into the spontaneous symmetry-breaking and ratchet phenomena in active matter.

Transport of self-propelled particles across a porous medium: trapping, clogging, and the Matthew effect.

We study the transport of self-propelled particles from one free chamber to another across two stripe-like areas of dense porous medium. The medium is mimicked by arrays of obstacles. We find that active motion could greatly speed up the transport of particles. However, more and more particles become trapped in the obstacle arrays with the enhancement of activity. At high persistence (low rotational diffusion rate) and moderate particle concentration, we observe the Matthew effect in the aggregation of particles in the two obstacle arrays. This effect is weakened by introduction of randomness or deformability into the obstacle arrays. Moreover, the dependence on deformability shows the characteristics of first-order phase transition. In rare situations, the system could be stuck in a dynamic unstable state, e.g. the particles alternatively gather more in one of the two obstacle arrays, exhibiting oscillation of particle number between the arrays. Our results reveal new features in the transport of active objects in a complex medium and have implications for manipulating their collective assembly.

Assembly structures and dynamics of active colloidal cells.

Many types of active matter are deformable, such as epithelial cells and bacteria. To mimic the feature of deformability, we built a model called an active colloidal cell (ACC), i.e. a vesicle enclosed with self-propelled particles (SPPs), which as a whole can move actively. Based on the model, we then study the role of deformability in the assembly structures and dynamics of ACCs by Langevin dynamics simulation. We find that deformability weakens the self-trapping effect and hence suppresses the clustering and phase separation of the deformable soft ACCs (sACCs). Instead of forming a large compact cluster like ordinary SPPs, sACCs pack into a loose network or porous structure in the phase-separation region. The condensed phase is liquid-like, in which sACCs are strongly compressed and deformed but still keep high motility. The interface between the gas and the condensed phases is blurry and unstable, and the effective interfacial energy is very low. Our work gives new insights into the role of deformability in the assembly of active matter and also provides a reference for further studies on different types of deformable active matter.

Globule-stretch transition of a self-attracting chain in the repulsive active particle bath.

Folding and unfolding of a chain structure are often manipulated in experiments by tuning the pH, temperature, single-molecule forces or shear fields. Here, we carry out Brownian dynamics simulations to explore the behavior of a single self-attracting chain in a suspension of self-propelling particles (SPPs). As the propelling force increases, the globule-stretch (G-S) transition of the chain occurs due to the enhanced disturbance from the SPPs. Two distinct mechanisms of the transition in the limits of low and high rotational diffusion rates of SPPs have been observed: shear-induced stretching at a low rate and collision-induced melting at a high rate. The G-S and S-G (stretch-globule) curves form a hysteresis loop at the low rate, while they merge at the high rate. Besides, we find that two competing effects result in a non-monotonic dependence of the G-S transition on SPP density at the low rate. Our results suggest an alternative approach to manipulating the folding and unfolding of (bio)polymers by utilizing active agents.

Unfolding of a diblock chain and its anomalous diffusion induced by active particles.

We study the structural and dynamical behavior of an A-B diblock chain in the bath of active Brownian particles (ABPs) by Brownian dynamics simulations in two dimensions. We are interested in the situation that the effective interaction between the A segments is attractive, while that between the B segments is repulsive. Therefore, in thermal (nonactive) equilibrium, the A block "folds" into a compact globule, while the B block is in the expanded coil state. Interestingly, we find that the A block could "unfold" sequentially like unknitting a sweater, driven by the surrounding ABPs when the propelling strength on them is beyond a certain value. This threshold value decreases and then levels off as the length of the B block increases. We also find a simple power-law relation between the unfolding time of the A block and the self-propelling strength and an exponential relation between the unfolding time and the length of the B block. Finally, we probe the translational and rotational diffusion of the chain and find that both of them show "super-diffusivity" in a large time window, especially when the self-propelling strength is small and the A block is in the folded state. Such super-diffusivity is due to the strong asymmetric distribution of ABPs around the chain. Our work provides new insights into the behavior of a polymer chain in the environment of active objects.

Shape transformation and manipulation of a vesicle by active particles.

Langevin dynamics simulations are employed to study the shape transformation of a two-dimensional vesicle induced by active particles both inside and outside. We find that the shape of the vesicle changes from circle, to capsule, and eventually to dumbbell with the enhancement of the particle activity. Under the cooperation between the inside and the outside active particles, such significant shape transformation is realized by tuning the activity in a small range. And unexpectedly, the fluctuations of the capsule and the dumbbell shapes are not completely random but mostly along the direction of the short axis. In the situation of strong activity, the inside of the dumbbell vesicle is analogous to a system of two chambers, which are connected by a narrow channel. Intriguingly, we observe the vibration of the channel width, accompanied with the exchange of active particles between the two chambers. We also find that dynamical manipulation of the vesicle shape is possible through tuning the particle activity dynamically. This work provides new ideas to the control of the vesicle morphology and new insights into the dynamics in the vesicle's shape transformation.

Microrotor of a chain-grafted colloidal disk immersed in the active bath: The impact of particle concentration, grafting density, and chain rigidity.

In an earlier work, we discussed the possibility to realize a microrotor by immersing a chain-grafted colloidal disk in a thin film of active-particle suspension. Under certain conditions, the colloidal disk rotates unidirectionally driven by the bath active particles. Here we systematically study the role of active-particle concentration, grafting density, and chain rigidity in the phenomenon of the spontaneous symmetry breaking of the chain configurations and the unidirectional rotation of the disk. We find that high chain rigidity can help stabilize both the collective asymmetric chain configurations and the rotation of the disk, while it has a weak impact on the rotational speed/efficiency. Increasing the number of grafted chains can also stabilize the rotation but has a negative impact on the rotational speed/efficiency. Active particles power the rotation of the colloidal disk, yet their contribution saturates beyond a certain concentration. Our work provides new insights into the active systems with chain-structured objects and the design of soft/deformable micromachines.

Beating of grafted chains induced by active Brownian particles.

We study the interplay between active Brownian particles (ABPs) and a "hairy" surface in two-dimensional geometry. We find that the increase of propelling force leads to and enhances inhomogeneous accumulation of ABPs inside the brush region. Oscillation of chain bundles (beating like cilia) is found in company with the formation and disassembly of a dynamic cluster of ABPs at large propelling forces. Meanwhile chains are stretched and pushed down due to the effective shear force by ABPs. The decrease of the average brush thickness with propelling force reflects the growth of the beating amplitude of chain bundles. Furthermore, the beating phenomenon is investigated in a simple single-chain system. We find that the chain swings regularly with a major oscillatory period, which increases with chain length and decreases with the increase of propelling force. We build a theory to describe the phenomenon and the predictions on the relationship between the period and amplitude for various chain lengths, and propelling forces agree very well with simulation data.

Spontaneous symmetry breaking induced unidirectional rotation of a chain-grafted colloidal particle in the active bath.

Exploiting the energy of randomly moving active agents such as bacteria is a fascinating way to power a microdevice. Here we show, by simulations, that a chain-grafted disk-like colloidal particle can rotate unidirectionally and hence output work when immersed in a thin film of active particle suspension. The collective spontaneous symmetry breaking of chain configurations is the origin of the unidirectional rotation. Long persistence time, large propelling force and/or small rotating friction are keys to sustaining the collective broken symmetry and realizing the rotation. In the rotating state, we find very simple linear relations, e.g. between the mean angular speed and the propelling force. The time-evolving asymmetry of chain configurations reveals that there are two types of non-rotating state. The basic phenomena are also observed in the macroscopic granular experiments, implying the generic nature of these phenomena. Our findings provide new insights into the collective spontaneous symmetry breaking in active systems with flexible objects and also open the way to conceive new soft/deformable microdevices.

The unique role of bond length in the glassy dynamics of colloidal polymers.

Bond length is generally not considered as a controllable variable for molecular polymers. Hence, no experimental, simulation or theoretical research, to our knowledge, has examined the influence of bond length on the glassy dynamics of polymers. Recently, a new class of assembling materials called "colloidal polymers" has been synthesized. These colloidal polymers have advantages over molecular polymers in the visibility and flexibility of tuning, for example, the size and shape of the "monomers", the interaction, and the bond length. Dense suspension of colloidal polymers will become a very promising ideal model system for exploring the fundamental problems in the glass transition of chain "molecules". Here, we study the static structure and activated dynamics of hard-sphere colloidal polymers by generalizing the colloidal nonlinear Langevin equation theory to colloidal polymers. Surprisingly, we find that the bond length plays a critical and unique role in many aspects. For instance, the universal relations of the characteristic local lengths and the activated barrier versus the "degree of supercooling", and the structural relaxation versus local vibrational motion are found to be dependent on bond length and independent of chain length and rigidity. We hope that our findings inspire future experimental and simulation research studies on the glassy dynamics of colloidal polymers.

Glassy dynamics of model colloidal polymers: The effect of "monomer" size.

In recent years, attempts have been made to assemble colloidal particles into chains, which are termed "colloidal polymers." An apparent difference between molecular and colloidal polymers is the "monomer" size. Here, we propose a model to represent the variation from molecular polymer to colloidal polymer and study the quantitative differences in their glassy dynamics. For chains, two incompatible local length scales, i.e., monomer size and bond length, are manifested in the radial distribution function and intramolecular correlation function. The mean square displacement of monomers exhibits Rouse-like sub-diffusion at intermediate time/length scale and the corresponding exponent depends on the volume fraction and the monomer size. We find that the threshold volume fraction at which the caging regime emerges can be used as a rescaling unit so that the data of localization length versus volume fraction for different monomer sizes can gather close to an exponential curve. The increase of monomer size effectively increases the hardness of monomers and thus makes the colloidal polymers vitrify at lower volume fraction. Static and dynamic equivalences between colloidal polymers of different monomer sizes have been discussed. In the case of having the same peak time of the non-Gaussian parameter, the motion of monomers of larger size is much less non-Gaussian. The mode-coupling critical exponents for colloidal polymers are in agreement with that of flexible bead-spring chains.

Polydispersity and gelation in concentrated colloids with competing interactions.

In colloids with competing short-range attractions and long-range repulsions, microcrystalline gels are experimentally formed under conditions where computer simulations point to a lamellar phase as the ground state. Here, upon applying a low-frequency alternating electric field, we bring the system from an initial gel state to a columnar-like state. While molecular dynamics simulations on monodisperse colloids reveal that a columnar structure spontaneously evolves towards a lamellar phase, the columnar-like state in experiments relaxes back to the initial disordered gel state once the electric field is switched off. Similarly, a columnar phase in molecular dynamics simulations decomposes into finite-size crystalline clusters as the relative polydispersity of the colloids is around 1.0%. We conclude that the experimentally observed melting of the columnar structure is driven by polydispersity. Moreover, further simulations reveal that the critical polydispersity required to destabilize a long-range ordered structure increases with the attraction range, pointing to the possibility of observing periodic structures in experiments if the attraction range is sufficiently long compared to the polydispersity of the colloids.

Brush in the bath of active particles: Anomalous stretching of chains and distribution of particles.

The interaction between polymer brush and colloidal particles has been intensively studied in the last two decades. Here, we consider a flat chain-grafted substrate immersed in a bath of active particles. Simulations show that an increase in the self-propelling force causes an increase in the number of particles that penetrate into the brush. Anomalously, the particle density inside the main body of the brush eventually becomes higher than that outside the brush at very large self-propelling force. The grafted chains are further stretched due to the steric repulsion from the intruded particles. Upon the increase of the self-propelling force, distinct stretching behaviors of the chains were observed for low and high grafting densities. Surprisingly, we find a weak descent of the average end-to-end distance of chains at high grafting density and very large force which is reminiscent of the compression effect of a chain in the active bath.