Complex self-propelled rings: a minimal model for cell motility

Chemo-mechanical model of cell polarization initiated by structural polarity

Cell polarization is crucial in most physiological functions. Living cells at the extracellular matrix (ECM) actively coordinate a polarized morphology to target the preferred signals. In particular, the initial heterogeneity of subcellular components, termed as structural polarity, has been discovered to mediate the early attachment and transmigration of cells in tumour metastasis. However, how heterogeneous cells initiate the early polarization remains incompletely discovered. Here, we establish a multiscale model of a cell to explore the chemo-mechanical mechanisms of cell polarization initiated by structural polarity. The two-dimensional vertex model of the cell is built with the main mechanical components of eukaryotic cells. The initial structural polarity of the modeled cell is introduced by seeding heterogeneous actin filaments at the cell cortex and quantified by the ratio of the filamentous forces at the vertices. Then, the structural polarity is integrated in the reaction-diffusion system of Rho GTPase (Cdc42) at the cell cortex to obtain the traction forces at the leading vertices. Finally, the modeled cell is actuated to spread under the traction forces and discovered to develop into a characteristic polarized morphology. The results indicate that the cell polarization is initiated and dynamically developed by structural polarity through the reaction-diffusion system of Cdc42. In addition, the bistability of Cdc42 activation at the cell cortex is defined and discovered to dominate the polarization status of the cell. Furthermore, biphasic (i.e., positive and negative) durotaxis of the cell is successfully modeled at an ECM with a stiffness gradient, and concluded to be codetermined by the chemo-mechanical coupling of the initial structural polarity and ECM stiffness gradient. The proposed multiscale model provides a quantitative way to probe cell polarization coupled with mechanical stimuli, biochemical reaction and cytoskeletal reorganization, and holds the potential to guide studies of cell polarization under multiple stimuli.

Deformation-induced phase separation of active vesicles

Many active materials, such as bacteria and cells, are deformable. Deformability significantly affects their collective behaviors and movements in complex environments. Here, we introduce a two-dimensional deformable active vesicle (DAV) model to emulate cell-like deformable active matter, wherein the deformability can be continuously adjusted. We find that changes in deformability can induce phase separation of DAVs. The system can transition between a homogeneous gas state, a coexistence of gas and liquid, and a coexistence of gas and solid. The occurrence of deformation-induced phase separation is accompanied by nonmonotonic changes in effective concentration, particle size and shape. Moreover, the degree of deformability also impacts the motility and stress within the dense phase following phase separation. Our results offer new insights into the role of deformability in the collective behavior of active matter.

Controlling the transport of the mixture involving active and passive rods in confined channel

The transport of the binary mixture of self-propelled rods (SPRs) and passive rods in the asymmetric conjugate periodic channel is studied by dissipative particle dynamics (DPD) simulations. It is found that the autonomous pumping of the binary mixture of active and passive rods can be achieved by either the individual or collective behaviour of SPRs. More specifically, the transport of passive rods can be driven through the individual, collective jostlement of the active rods, and crowding out effect. The strength of self-propulsion, rod length, rod concentration, and geometric feature of the channel determines the mechanism of pumping. In addition, the drift of the binary mixture can be in the positive and negative directions of the channel or the currents of SPRs and passive rods in opposite directions and relies on the geometric feature of the channel and concentration of the two species. Overall, our simulation study offers an efficient approach of flow control for both species.

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.

Lipid-mediated prestin organization in outer hair cell membranes and its implications in sound amplification

Prestin is a high-density motor protein in the outer hair cells (OHCs), whose conformational response to acoustic signals alters the shape of the cell, thereby playing a major role in sound amplification by the cochlea. Despite recent structures, prestin's intimate interactions with the membrane, which are central to its function remained unresolved. Here, employing a large set (collectively, more than 0.5 ms) of coarse-grained molecular dynamics simulations, we demonstrate the impact of prestin's lipid-protein interactions on its organization at densities relevant to the OHCs and its effectiveness in reshaping OHCs. Prestin causes anisotropic membrane deformation, which mediates a preferential membrane organization of prestin where deformation patterns by neighboring copies are aligned constructively. The resulting reduced membrane rigidity is hypothesized to maximize the impact of prestin on OHC reshaping. These results demonstrate a clear case of protein-protein cooperative communication in membrane, purely mediated by interactions with lipids.

Migration of an active colloidal cell in inhomogeneous environments

Living cells on a substrate with mechanical inhomogeneities often migrate along or against the mechanical gradient, i.e., mechanotaxis, which inspires us to ask how biomimetic cells without biochemical signaling processes respond to environmental inhomogeneity. Here, we perform computer simulations to study the migration of a 2D active colloidal cell (ACC), which consists of active particles enclosed by a passive vesicle, in a heterogeneous environment composed of two adjoining uniform regions with different attributes (influencing the persistent length of the active particle). We find that the ACC can migrate unidirectionally across the interface separating the heterogeneous region and behave tactically. Interestingly, the tactic motion of the ACC is qualitatively different from that of the constituent active particles themselves. In addition, the ACC may also experience a directed drift along the interface of the heterogeneous environment. The tactic behavior of the ACC can be explained by analyzing the pressure distribution on the cell membrane exerted by the enclosed active particles. The findings provide insights into understanding the taxis of biological cells and designing biomimetic cells with environment-sensitive capabilities.

Membrane Mixer: A Toolkit for Efficient Shuffling of Lipids in Heterogeneous Biological Membranes

Molecular dynamics (MD) simulations of biological membranes have achieved such levels of sophistication that are commonly used to predict unresolved structures and various properties of lipids and to substantiate experimental data. While achieving sufficient sampling of lipid dynamics remains a major challenge, a commonly used method to improve lipid sampling, e.g., in terms of specific interactions with membrane-associated proteins, is to randomize the initial arrangement of lipid constituents in multiple replicas of simulations, without changing the overall lipid composition of the membrane of interest. Here, we introduce a method that can rapidly generate multiple replicas of lipid bilayers with different spatial and conformational configurations for any given lipid composition. The underlying algorithm, which allows one to shuffle lipids at any desired level, relies on the application of an external potential, here referred to as the "carving potential", that removes clashes/entanglements before lipid positions are exchanged (shuffled), thereby minimizing the energy penalty due to abrupt lipid repositioning. The method is implemented as "Membrane Mixer Plugin (MMP) 1.0" in VMD, with a convenient graphical user interface that guides the user in setting various options and parameters. The plugin is fully automated and generates new membrane replicas more rapidly and conveniently than other analogous tools. The plugin and its capabilities introduced here can be extended to include additional features in future versions.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

During immunosurveillance, lymphocytes patrol through tissues to interact with cancer cells, other immune cells, and pathogens. The efficiency of this process depends on the kinds of trajectories taken, ranging from simple Brownian walks to Lévy walks. The composition of the extracellular matrix (ECM), a network of macromolecules, affects the formation of cell-matrix adhesions, thus strongly influencing the way lymphocytes move. Here, we present a model of lymphocyte motility driven by adhesions that grow, shrink and rupture in response to the ECM and cellular forces. Compared to other models, our model is computationally light making it suitable for generating long term cell track data, while still capturing actin dynamics and adhesion turnover. Our model suggests that cell motility is affected by the force required to break adhesions and the rate at which new adhesions form. Adhesions can promote cell protrusion by inhibiting retrograde actin flow. After introducing this effect into the model, we found that it reduces the cellular diffusivity and that it promotes stick-slip behaviour. Furthermore, location and size of adhesion clusters determined cell persistence. Overall, our model explains the plasticity of lymphocyte behaviour in response to the ECM.

Enhancing directed collective motion of self-propelled particles in confined channel

The collective transport of the self-propelled rods (SPRs) is studied by dissipative particle dynamics simulations. Two types of channels (channel I and channel II) are taken into account for various rod concentrations. It is found that in channel I-the asymmetric corrugated channel with periodically varying width, some SPRs are trapped at the corners and form the hedgehog clusters. Other SPRs aggregate at the bottleneck and lead to a traffic jam. Consequently, channel I is inefficient for the directional SPR transport in the case of finite concentration. To achieve efficient collective particle transport, channel II-the channel with constant width and arrays of asymmetric obstacles within it, which can avoid the traffic clogging and hedgehog aggregate is suggested. It is found that the swimmer-obstacle interaction gives rise to the directional motion, the spacing between obstacles can avoid the formation of the hedgehog clusters. The high-efficiency directional collective motion of the SPRs is acquired in channel II. Overall, our simulation study offers an efficient approach for directional collective motion of SPRs.

A single active ring model with velocity self-alignment

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

Defect dynamics in clusters of self-propelled rods in circular confinement

Rod-shaped active micro/nano-particles, such as bacterial and bipolar metallic micro/nano-motors, demonstrate novel collective phenomena far from the equilibrium state compared to passive particles. We apply a simulation approach --dissipative particle dynamics (DPD)-- to explore the collectively ordered states of self-propelled rods (SPRs). The SPRs are confined in a finite circular zone and repel each other when two rods touch each other. It is found that for a long enough rods system, the global vortex patterns, dynamic pattern oscillation between hedgehog pattern and vortex pattern, and hedgehog patterns are observed successively with increasing active force F_a. For the vortex pattern, the total interaction energy between the rods U is linear with active force F_a, i.e., U ∼ F_a . While the relation U ∼ F_a² is obtained for the hedgehog structure. It is observed that a new hedgehog pattern with one defect core is created by two ejections of polar cluster in opposite directions from the original hedgehog pattern, and then merges into one through the diffusion of the two aggregates, i.e., the creation and annihilation of topological charges.

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.

Collective behavior of self-propelled rods with quorum sensing

Active agents-like phoretic particles, bacteria, sperm, and cytoskeletal filaments in motility assays-show a large variety of motility-induced collective behaviors, such as aggregation, clustering, and phase separation. The behavior of dense suspensions of engineered phoretic particles and of bacteria during biofilm formation is determined by two qualitatively different physical mechanisms: (i) volume exclusion (short-range steric repulsion) and (ii) quorum sensing (longer-range reduced propulsion due to alteration of the local chemical environment). To systematically characterize such systems, we study semi-penetrable self-propelled rods in two dimensions, with a propulsion force that decreases with increasing local rod density, by employing Brownian dynamics simulations. Volume exclusion and quorum sensing both lead to phase separation; however, the structure of the systems and the rod dynamics vastly differ. Quorum sensing enhances the polarity of the clusters, induces perpendicularity of rods at the cluster borders, and enhances cluster formation. For systems where the rods essentially become passive at high densities, formation of asters and stripes is observed. Systems of rods with larger aspect ratios show more ordered structures compared to those with smaller aspect ratios, due to their stronger alignment, with almost circular asters for strongly density-dependent propulsion force. With increasing range of the quorum-sensing interaction, the local density decreases, asters become less stable, and polar hedgehog clusters and clusters with domains appear.

Hierarchical collective motion of a mixture of active dipolar Janus particles and passive charged colloids in two dimensions

We use computer simulations to study the behavior of a mixture of large passive charged colloids in a suspension of smaller active dipolar Janus particles. We find that when a single charged colloid is present in solution, it acquires a rotational or translational motion depending on how the active dipoles self-assemble on its surface to form active complexes. The collective behavior of these complexes is quite remarkable, and includes swarming behavior and coherent macroscopic motion. We detail how the variety of different phenomenologies emerging in this system can ultimately be controlled by the strength of the active forces and the relative concentration of the two species.