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Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here we surprisingly observed that knotting can be very effectively produced in active polymers. When one end of an actively reptative polymer is anchored, it can undergo continual self-knotting as a result of intermittent giant conformation fluctuations and the outward reptative motion. Once a knot is formed, it migrates to the anchored point due to a non-equilibrium ratchet effect. Moreover, when the active polymer is grafted on the end of a passive polymer, it can function as a self-propelling soft needle to either transfer its own knots to the passive polymer or directly braid knots on the passive polymer. We further show that these active needles can create inter-molecular bridging knots between two passive polymers. Our finding highlights the non-equilibrium effects in modifying the dynamic pathways of polymer systems, which have potential applications in macromolecular topology engineering, e.g., manipulating topological states of proteins and nucleic acids, as well as macromolecular braiding.

Cells not only can have self-motility by crawling, but also are capable of other types of active motions like periodic contraction or pulsation. In this work, by using the Voronoi cell model, we show how this non-motility activity affects the structure, dynamic and density fluctuations of cellular monolayers. We found that random cell pulsation can fluidize solid epithelial tissues, resulting in a \emph{hyperuniform} fluid state, while pulsation synchronization inhibits the fluidity, causes a reversed solidification. We prove this solidification is BKT-type transition, characterized by strong density/dynamic heterogeneity arising from the creation of topological defects in the pulsating phase space. The magnitude and length scale of density heterogeneity diverge as the pulsating period increases, resulting in an opposite \emph{giant} density fluctuation. Our findings accord with recent experimental observations and can be quantitatively explained by a proposed fluctuating hydrodynamic theory., Comment: 7pages, 3 figures

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field (MF) theories, which fail to address the problem of whether the long-range time crystalline order exists in noisy, spatially extended systems without the protection of all-to-all couplings. Here, we propose a new kind of CTC realized in a quantum contact model through self-organized bistability (SOB). The exotic CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions (APTs) and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of quantum synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time diverging with system size, thus also constituting a boundary time crystal (BTC). Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems., Comment: 6 pages, 4 figures

Colloidal particles can spontaneously self-assemble into ordered structures, which not only can manipulate the propagation of light, but also vibration or phonons. Using Monte Carlo simulation, we study the self-assembly of perfectly aligned segment rod particles with lateral flat cutting. Under the help of surface attractions, we find that particles with different cutting degree can self-assemble into different crystal phases characterized by bond coordination z that varies from 3 to 6. Importantly, we identify a transformable super-isostatic structures with pgg symmetry and redundant bonds (z=5). We find that this structure can support either the soft bulk model or soft edge model depending on its Poisson's ratio which can be tuned from positive to negative by a uniform soft deformation. Importantly, the bulk soft modes are associated with states of self-stress along the direction of zero strain during the uniform soft deformation. This self-assembled transformable super-isostatic structure may act as mechanical metamaterials with potential application in micro-mechanical engineering., Comment: 12 pages,6 figures

Thermodynamic behavior of polymer chains out of equilibrium is a fundamental problem in both polymer physics and biological physics. By using molecular dynamics simulation, we discover a general non-equilibrium mechanism that controls the conformation and dynamics of polar active polymer, i.e., head activity commands the overall chain activity, resulting in re-entrant swelling of active chains and non-monotonic variation of Flory exponent $\nu$. These intriguing phenomena lie in the head-controlled railway motion of polar active polymer, from which two oppose non-equilibrium effects emerge, i.e., dynamic chain rigidity and the involution of chain conformation characterized by the negative bond vector correlation. The competition between these two effects determines the polymer configuration. Moreover, we identify several generic dynamic features of polar active polymers, i.e., linear decay of the end-to-end vector correlation function, polymer-size dependent crossover from ballistic to diffusive dynamics, and a polymer-length independent diffusion coefficient that is sensitive to head activity. A simple dynamic theory is proposed to faithfully explain these interesting dynamic phenomena. This sensitive structural and dynamical response of active polymer to its head activity provides us a practical way to control active-agents with applications in biomedical engineering., Comment: 9 pages, 5 figures

Recently, a new type of duality was reported in some deformable mechanical networks which exhibit Kramers-like degeneracy in phononic spectrum at the self-dual point. In this work, we clarify the origin of this duality and propose a design principle of 2D self-dual structures with arbitrary complexity. We find that this duality originates from the (PCI) symmetry of the hinge, which belongs to a more general end-fixed scaling transformation. This symmetry gives the structure an extra degree of freedom without modifying its dynamics. This results in , i.e., dissimilar 2D mechanical structures, either periodic or aperiodic, having identical dynamic modes, based on which we demonstrate a new type of wave-guide without reflection or loss. Moreover, the PCI symmetry allows us to design various 2D periodic isostatic networks with hinge duality. At last, by further studying a 2D non-mechanical magnonic system, we show that the duality and the associated hidden symmetry should exist in a broad range of Hamiltonian systems., Comment: 6 pages, 4 figures

Recent studies reported that adenosine triphosphate (ATP) could inhibit as well as enhance the phase separation in prion-like proteins. The molecular mechanism underlying such a puzzling phenomenon remains elusive. Here, taking the fused in sarcoma (FUS) solution as an example, we comprehensively reveal the underlying mechanism by which ATP regulates phase separation by combining the semiempirical quantum mechanical method, mean-field theory, and molecular simulation. At the microscopic level, ATP acts as a bivalent or trivalent binder; at the macroscopic level, the reentrant phase separation indeed occurs in dilute FUS solutions, resulting from the ATP-concentration--dependent binding ability under different conditions. Importantly, the ATP concentration for dissolving the protein condensates is about 10 mM, agreeing with experimental results. Furthermore, from a dynamic point of view, the effect of ATP on phase separation is also non-monotonic. This work provides a clear physical description of the microscopic interaction and macroscopic phase diagram of the ATP-modulated phase separation., Comment: 24 pages, 5 figures

The outbreak of the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has become a worldwide public health crisis. When the SARS-CoV-2 enters the biological fluids in the human body, different types of biomolecules (in particular proteins) may adsorb on its surface and alter its infection ability. Although great efforts have recently been devoted to the interaction of the specific antibodies with the SARS-CoV-2, it still remains largely unknown how the other serum proteins affect the infection of the SARS-CoV-2. In this work, we systematically investigate the interaction of serum proteins with the SARS-CoV-2 RBD by the molecular docking and the all-atom molecular dynamics simulations. It is found that the non-specific immunoglobulin (Ig) indeed cannot effectively bind to the SARS-CoV-2 RBD while the human serum albumin (HSA) may have some potential of blocking its infection (to ACE2). More importantly, we find that the RBD can cause the significant structural change of the Apolipoprotein E (ApoE), by which SARS-CoV-2 may hijack the metabolic pathway of the ApoE to facilitate its cell entry. The present study enhances the understanding of the role of protein corona in the bio-behaviors of SARS-CoV-2, which may aid the more precise and personalized treatment for COVID-19 infection in the clinic., Comment: 18 pages, 7 figures

The spread of the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has become a global health crisis. The binding affinity of SARS-CoV-2 (in particular the receptor binding domain, RBD) to its receptor angiotensin converting enzyme 2 (ACE2) and the antibodies is of great importance in understanding the infectivity of COVID-19 and evaluating the candidate therapeutic for COVID-19. In this work, we propose a new method based on molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) to accurately calculate the free energy of SARS-CoV-2 RBD binding to ACE2 and antibodies. The calculated binding free energy of SARS-CoV-2 RBD to ACE2 is -13.3 kcal/mol, and that of SARS-CoV RBD to ACE2 is -11.4 kcal/mol, which agrees well with experimental result (-11.3 kcal/mol and -10.1 kcal/mol, respectively). Moreover, we take two recently reported antibodies as the example, and calculate the free energy of antibodies binding to SARS-CoV-2 RBD, which is also consistent with the experimental findings. Further, within the framework of the modified MM/PBSA, we determine the key residues and the main driving forces for the SARS-CoV-2 RBD/CB6 interaction by the computational alanine scanning method. The present study offers a computationally efficient and numerically reliable method to evaluate the free energy of SARS-CoV-2 binding to other proteins, which may stimulate the development of the therapeutics against the COVID-19 disease in real applications., Comment: 18 pages, 5 figures

We show that spatial quenched disorder affects polar active matter in ways more complex and far-reaching than believed heretofore. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order., Comment: 6 pages, 5 figures, comments are welcome

Steady structures originating from dynamic self-assembly have begun to show their advantages in new generation materials, and pose challenges to equilibrium self-assembly. In view of the important role of confinement in self-assembly, here, we propose a new type of confinement leading to dynamic steady structures, which opens a new window for the conventional confinement. In our model, we consider the self-assembly of ellipsoids in 2D circular confinement via the boundary performing periodically stretching and contracting oscillation. Langevin dynamics simulations reveal the achievement of non-equilibrium steady structures under appropriate boundary motions, which are novel smectic structures with stable topological defects. Different from the confinement with a static boundary, ellipsoids close to the boundary have variable orientations depending on the boundary motion. Order-order structural transitions, accompanied by the symmetry change and varied defect number, occur with the change of oscillating amplitude and/or frequency of the boundary. Slow and fast dynamics are distinguished according to whether structural rearrangements and energetic adjustment happen or not. The collective motion of confined ellipsoids, aroused by the work performed on the system, is the key factor determining both the structure and dynamics of the self-assembly. Our results not only achieve novel textures of circular confined liquid crystals, but also inspire us to reconsider the self-assembly within the living organisms.

We show that the dominant mode of alignment plays an important role in dry active nematics,leading to two dynamical sub-classes defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the break-up of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level., Comment: 5 pages, 4 figures. Supplementary and movies are available upon request

We study the structural and dynamical behaviors of a diblock copolymer chain in a bath of active Brownian particles (ABPs) by extensive Brownian dynamics simulation in a two-dimensional model system. Specifically, the A block of chain is self-attractive, while the B block is self-repulsive. We find, beyond a threshold, the A block unfolds with a pattern like extracting a woolen string from a ball. The critical force decreases with the increase of the B block length,NB, for short cases, then keeps a constant with further increase of NB. In addition, we find a power law exists between the unfolding time of chain and active force, Fa, as well as NB. Finally, we focus on the translational and rotational diffusion of chain, and find that both of them remain supper-diffusive at the long time limit for small active forces due to an asymmetry distribution of ABPs. Our results open new routes for manipulating polymer's behaviors with ABPs., Comment: 11 pages, 7 figures

Folding and unfolding of biopolymers are often manipulated in experiment by tuning pH, temperature, single-molecule force or shear field. Here we carry out Brownian dynamics simulations to explore the behavior of a single self-attracting chain in the suspension of self-propelling particles (SPPs). As the propelling force increases, globule-stretch (G-S) transition of the chain happens due to the enhanced disturbance from SPPs. Two distinct mechanisms of the transition in the limits of low and high rotational diffusion rates of SPPs have been observed: shear effect at low rate and collision-induced melting at high rate. The G-S and S-G (stretch-globule) curves form hysteresis loop at low rate, while they merge at high rate. Besides, we find two competing effects result in the non-monotonic dependence of the G-S transition on the SPP density at low rate. Our results suggest an alternative approach to manipulating the folding and unfolding of (bio)polymers by utilizing active agents., Comment: 7pages, 4figures

We show that fore-aft asymmetry, a generic feature of living organisms and some active matter systems, can have a strong influence on the collective properties of even the simplest flocking models. Specifically, an arbitrarily weak asymmetry favoring front neighbors changes qualitatively the phase diagram of the Vicsek model. A region where many sharp traveling band solutions coexist is present at low noise strength, below the Toner-Tu liquid, at odds with the phase-separation scenario well describing the usual isotropic model. Inside this region, a `banded liquid' phase with algebraic density distribution coexists with band solutions. Linear stability analysis at the hydrodynamic level suggests that these results are generic and not specific to the Vicsek model., Comment: 6 pages, 5 figures

Chiral crystals consisting of micro-helices have many optical properties while presently available fabrication processes limit their large-scale applications in photonic devices. Here, by using a simplified simulation method, we investigate a bottom-up self-assembly route to build up helical crystals from the smectic monolayer of colloidal helices racemate. With increasing the density, the system undergoes an entropy-driven co-crystallization by forming crystals of various symmetries with different helical shapes. In particular, we identify two crystals of helices arranged in the binary honeycomb and square lattices, which are essentially composed by two sets of opposite-handed chiral crystal. Photonic calculations show that these chiral structures can have large complete photonic bandgaps. In addition, in the self-assembled chiral square crystal, we also find dual polarization bandgaps that selectively forbid the propagation of circularly polarized lights of a specific handedness along the helical axis direction. The self-assembly process in our proposed system is robust, suggesting possibilities of using chiral colloids to assemble photonic metamaterials., Comment: Accepted in ACS Nano

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 colloid can rotate unidirectionally when immersed in a thin film of active particle suspension. The 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 keeping the broken symmetry and realizing the rotation. In the rotating state, we find very simple linear relations, e.g. between mean angular speed and propelling force. The time-evolving asymmetry of chain configurations reveals that there are two types of non-rotating state. Our findings provide new insights into the phenomena of spontaneous symmetry breaking in active systems with flexible objects and also open the way to conceive new soft/deformable microdevices., Comment: 14 pages (single column, double spaced), 5 figures

We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two typical stages in the variation of the morphology with the increase of active force. One is at small force characterized by radially inhomogeneous redistribution of particles and suppression of local fluctuations of the boundary. The other is at large force featured by angularly redistribution of particles and global shape deformation of the boundary. The last two processes are strongly cooperative. We also find different mechanisms in the particle redistribution and opposite force-dependences of the rate of the shape variation at low and high particle concentrations., Comment: 11 pages, 6 figures

We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density, magnitude of nematic order, and nematic director is crucial for the long-wave-length instability and the emergence of seemingly fluctuated collective motions. Ordered nematic domains can absorb particles, grow and divide endlessly. The present finding extends our understanding of the large-scale and seemingly fluctuated organization in active fluids., Comment: 5 pages, 3 figures

Due to the stochastic nature of biochemical processes, the copy number of any given type of molecule inside a living cell often exhibits large temporal fluctuations. Here, we develop analytic methods to investigate how the noise arising from a bursting input is reshaped by a transport reaction which is either linear or of the Michaelis-Menten type. A slow transport rate smoothes out fluctuations at the output end and minimizes the impact of bursting on the downstream cellular activities. In the context of gene expression in eukaryotic cells, our results indicate that transcriptional bursting can be substantially attenuated by the transport of mRNA from nucleus to cytoplasm. Saturation of the transport mediators or nuclear pores contributes further to the noise reduction. We suggest that the mRNA transport should be taken into account in the interpretation of relevant experimental data on transcriptional bursting., Comment: 18 pages, 3 figures

Membrane organization is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is to understand the lateral heterogeneous structures in membranes and membrane fluidity in the presence of inclusions. Based on a considerable amount of experimental evidence for lateral organization of lipid membranes which share astonishingly similar features in the presence of different inclusions, we first present a general model system of bilayer membranes embedded by nanosized inclusions, and explain experimental findings. Here, the hydrophobic inclusions are simple models of intrinsic membrane proteins, cholesterol embedded in the membrane, hydrophobic drugs, or other nanoparticles for bio-medical applications. It is found that lipid/inclusion-rich raft domains are formed at moderate inclusion concentrations, and disappear with the increase of inclusions. At high inclusion content, chaining of inclusions occurs due to the effective attraction between inclusions mediated by lipids. Meanwhile, increasing inclusions can also cause thickening of the membrane, and the distribution of inclusions undergoes a layering transition from one-layer located in the bilayer midplane to two-layer structure arranged into the two leaflets of a bilayer. Our theoretical predictions address the complex interactions between membranes and inclusions, suggesting a unifying mechanism which reflects the competition between the conformational entropy of lipids favoring the formation of lipid-rich rafts and the steric repulsion of inclusions leading to the uniform dispersion., Comment: 11 pages, 5 figures

Using integral equation theory of liquids to a binary mixed fluid lipid membrane, we study the membrane-mediated interactions between the macroions and the redistribution of neutral and charged lipids due to binding macroions. We find that when the concentration of binding macroions is infinitely dilute, the main contribution to the attractive potential between macroions is the line tension between neutral and charged lipids of the membrane, and the bridging effect also contributes to the attraction. As the relative concentration of charged lipids is increased, we observe a repulsive - attractive - repulsive potential transition due to the competition between the line tension of lipids and screened electrostatic macroion-macroion interactions. For the finite concentration of macroions, the main feature of the attraction is similar to the infinite dilution case. However, due to the interplay of formation of charged lipid - macroion complexes, the line tension of redistributed binary lipids induced by single macroion is lowered in this case, and the maximum of attractive potential will shift toward the higher values of the charged lipid concentration.

We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensional arrangement of colloidal crystals and controlled layer-by-layer growth driven entropically by non-adsorbing polymer solvent with increasing the particles. The result indicates a possibility for the production of highly ordered and defect-free structures by simply using the grafted substrate instead of periodically patterned templates, under appropriate selection of colloidal size, effective depositing potential, and brush coverage density.

The organization of lipids in biological membranes is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is how to control lateral lipid composition in supported membranes which are crucial for the design of biosensors and investigation of cellular processes. Here, we undertake the first theoretical study of lateral organization of mixed lipids in bilayers induced by a geometrically patterned substrate, and examine the physical mechanism of patterned substrate-induced structural formation in the supported lipid bilayers. A rich variety of composition segregations of lipids are regulated, and the results can account well for most recent experimental works [Yoon, T. Y. et al. \textit{Nat. Mater.} \textbf{5}, 281(2006) and Parthasarathy, R. et al. \textit{Langmuir} \textbf{22}, 5095(2006)]. The present study provides a comprehensive understanding of mechanically controlling the spatial organization of membrane components by unifying these experimental evidences.

Using self-consistent field and density-functional theories, we first investigate colloidal self-assembling of colloid/polymer films confined between two soft surfaces grafted by polymers. With the increase of colloidal concentrations, the film undergoes a series of transitions from disordered liquid $\to$ sparse square $\to$ hexagonal (or mixed square-hexagonal) $\to$ dense square $\to$ cylindric structures in plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable regions of different in-layer ordering structures as the colloidal concentration is varied and layering transitions as the polymer-grafted density is decreased. Our results show a new control mechanism to stabilize the ordering of structures within the films.

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by use of self-consistent field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate an existence of repulsive energy barrier of several $k_{B}T$, which can be interpreted by separating the interaction energy into three parts: colloids-polymer interfacial energy, entropic contribution due to ``depletion zone" overlap of colloidal particles, and entropically elastic energy of grafted chains by compression of particles. The existence of repulsive barrier which is of entirely entropic origin, can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach to control the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.