Phase Segregation of Passive Advective Particles in an Active Medium

Self-diffusion is temperature independent on active membranes

Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling. Temperature variations in thermal equilibrium rapidly change molecular transport properties. The coefficient of lipid self-diffusion increases exponentially with temperature in thermal equilibrium, for example. Hence, maintaining cellular homeostasis through molecular transport is hard in thermal equilibrium in the noisy cellular environment, where temperatures can fluctuate widely due to local heat generation. In this paper, using both molecular and lattice-based modeling of membrane transport, we show that the presence of active transport originating from the cell's cytoskeleton can make the self-diffusion of the molecules on the membrane robust to temperature fluctuations. The resultant temperature-independence of self-diffusion keeps the precision of cellular signaling invariant over a broad range of ambient temperatures, allowing cells to make robust decisions. We have also found that the Kawasaki algorithm, the widely used model of lipid transport on lattices, predicts incorrect temperature dependence of lipid self-diffusion in equilibrium. We propose a new algorithm that correctly captures the equilibrium properties of lipid self-diffusion and reproduces experimental observations.

Clustering of lipids driven by integrin

Integrin is an important transmembrane receptor protein which remodels the actin network and anchors the cell membrane towards the extracellular matrix via mechanochemical pathways. The clustering of specific lipids and lipid-anchored proteins, which is essential for a certain type of endocytosis process, is facilitated at integrin-mediated active regions. To study this, we propose a minimal exactly solvable model which includes the interplay of stochastic shuttling between integrin on and off states with the intrinsic dynamics of the membrane. We propose a two-step mechanism in which the integrin induces an aster-like arrangement in the actin network, followed by clustering of lipids in that region. We obtain an analytic expression for the deformation and local membrane velocity, and thereby the evolution of clustering mediated by a single integrin. The deformation evolves nonmonotonically and its dependence on the stochastic shuttling timescales and membrane properties is elucidated. Our estimates of the area of the deformed region and the number of lipids in it indicate strong clustering.

Active emulsions in living cell membranes driven by contractile stresses and transbilayer coupling

The spatiotemporal organization of proteins and lipids on the cell surface has direct functional consequences for signaling, sorting, and endocytosis. Earlier studies have shown that multiple types of membrane proteins, including transmembrane proteins that have cytoplasmic actin binding capacity and lipid-tethered glycosylphosphatidylinositol-anchored proteins (GPI-APs), form nanoscale clusters driven by active contractile flows generated by the actin cortex. To gain insight into the role of lipids in organizing membrane domains in living cells, we study the molecular interactions that promote the actively generated nanoclusters of GPI-APs and transmembrane proteins. This motivates a theoretical description, wherein a combination of active contractile stresses and transbilayer coupling drives the creation of active emulsions, mesoscale liquid order (lo) domains of the GPI-APs and lipids, at temperatures greater than equilibrium lipid phase segregation. To test these ideas, we use spatial imaging of molecular clustering combined with local membrane order, and we demonstrate that mesoscopic domains enriched in nanoclusters of GPI-APs are maintained by cortical actin activity and transbilayer interactions and exhibit significant lipid order, consistent with predictions of the active composite model.

Effective single component description of steady state structures of passive particles in an active bath

We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are the two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters, viz., homogeneous structures, disordered cluster, ordered cluster, and crystalline structure. The change in structure is dictated by the change in nature of the effective interaction. We further confirm the four structures using a full microscopic simulation of active and passive mixture. Our study is useful to understand the different collective behavior in non-equilibrium systems.

Clustering and phase separation in mixtures of dipolar and active particles

The self-assembly of colloidal particles in dynamic environments has become an important field of study because of potential applications in fabricating out-of-equilibrium materials. We investigate the phase behavior of mixtures of passive dipolar colloids and active soft spheres using Brownian dynamics simulations in two dimensions. The phase behaviors exhibited include dipolar percolated network, dipolar string-fluid, isotropic fluid, and a phase-separated state. We find that the clustering of dipolar colloids is enhanced in the presence of slow-moving active particles compared to the clustering of dipolar particles mixed with passive particles. When the active particle motility is high, the chains of dipolar particles are either broken into short chains or pushed into dense clusters. Motility-induced phase separation into dense and dilute phases is also present. The area fraction of particles in the dilute phase increases as the fraction of active particles in the system decreases, while the area fraction of particles in the dense phase remains constant. Our findings are relevant to the development of reconfigurable self-assembled materials.

Coarsening dynamics in the Vicsek model of active matter

We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as [Formula: see text] (with [Formula: see text] , while the velocity length scale grows much faster, viz., [Formula: see text] (with [Formula: see text] . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively.

Light driven guided and self-organized motion of mesoporous colloidal particles

We report on guided and self-organized motion of ensembles of mesoporous colloidal particles that can undergo dynamic aggregation or separation upon exposure to light. The forces on particles involve the phenomenon of light-driven diffusioosmosis (LDDO) and are hydrodynamic in nature. They can be made to act passively on the ensemble as a whole but also used to establish a mutual interaction between particles. The latter scenario requires a porous colloid morphology such that the particle can act as a source or sink of a photosensitive surfactant, which drives the LDDO process. The interplay between the two modes of operation leads to fascinating possibilities of dynamical organization and manipulation of colloidal ensembles adsorbed at solid-liquid interfaces. While the passive mode can be thought of to allow for a coarse structuring of a cloud of colloids, the inter-particle mode may be used to impose a fine structure on a 2D particle grid. Local flow is used to impose and tailor interparticle interactions allowing for much larger interaction distances that can be achieved with, e.g., DLVO type of forces, and is much more versatile.

Phase behaviour and dynamical features of a two-dimensional binary mixture of active/passive spherical particles

In this work we have characterized the phase behaviour and the dynamics of bidimensional mixtures of active and passive Brownian particles. We have evaluated state diagrams at several concentrations of the passive components finding that, while passive agents tend to hinder phase separation, active agents force crystal-like structures on passive colloids. In order to study how passive particles affect the dynamics of the mixture, we have computed the long-time diffusion coefficient of each species, concluding that active particles induce activity and super-diffusive behaviour on passive ones. Interestingly, at the density at which the system enters a MIPS state the active particles' diffusivity shows an inflection point and the passive particles' one goes through a maximum, due to the change in the dynamics of the active components, as shown in the displacement's probability distribution function.

Mechanical Heterogeneity in Tissues Promotes Rigidity and Controls Cellular Invasion

We study the influence of cell-level mechanical heterogeneity in epithelial tissues using a vertex-based model. Heterogeneity is introduced into the cell shape index (p_{0}) that tunes the stiffness at a single-cell level. The addition of heterogeneity can always enhance the mechanical rigidity of the epithelial layer by increasing its shear modulus, hence making it more rigid. There is an excellent scaling collapse of our data as a function of a single scaling variable f_{r}, which accounts for the overall fraction of rigid cells. We identify a universal threshold f_{r}^{*} that demarcates fluid versus solid tissues. Furthermore, this rigidity onset is far below the contact percolation threshold of rigid cells. These results give rise to a separation of rigidity and contact percolation processes that leads to distinct types of solid states. We also investigate the influence of heterogeneity on tumor invasion dynamics. There is an overall impedance of invasion as the tissue becomes more rigid. Invasion can also occur in an intermediate heterogeneous solid state that is characterized by significant spatial-temporal intermittency.

Statistical mechanics of a single active slider on a fluctuating interface

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random environment, which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponents to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2, whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.

From Chaos to Order: Evaporative Assembly and Collective Behavior in Drying Liquid Crystal Droplets

The emergence of dynamic assembly and collective motion in living systems are marvels of nature that suggest universal principles for governing self-organization. By drying a drop of surfactant-stabilized liquid crystal emulsions, we present a simple form of evaporative assembly and collective motion in colloidal droplets. Driven by local evaporation flux distribution and capillary force, the dynamic mode in these swimming liquid crystal droplets highly depends on their intrinsic configurations, exhibiting a macroscopic transition from chaotic to well-organized. The combination of collective behavior, speed distribution, interparticle interaction, formation of topological defects and dislocations in a swarm of hexagonal ordered liquid crystal droplets produced a myriad of dynamical states, which suggest a means of mimicking the nonequilibrium state of living matter with controlled properties.

Phase separation in binary mixtures of active and passive particles

We study binary mixtures of small active and big passive athermal particles interacting via soft repulsive forces on a frictional substrate. Athermal self propelled particles are known to phase separate into a dense aggregate and a dilute gas-like phase at fairly low packing fractions. Known as motility induced phase separation, this phenomenon governs the behaviour of binary mixtures for small to intermediate size ratios of the particle species. An effective attraction between passive particles, due to the surrounding active medium, leads to true phase separation for large size ratios and volume fractions of active particles. The effective interaction between active and passive particles can be attractive or repulsive at short range depending on the size ratio and volume fractions of the particles. This affects the clustering of passive particles. We find three distinct phases based on the spatial distribution of passive particles. The cluster size distribution of passive particles decays exponentially in the homogeneous phase. It decays as a power law with an exponential cutoff in the clustered phase and tends to a power law as the system approaches the transition to the phase separated state. We present a phase diagram in the plane defined by the size ratio and volume fraction of passive particles.

Time evolution of intermittency in the passive slider problem

How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing length scale which governs scaling properties. A simple model of sticky sliders suggests scaling forms for the time-dependent flatness and hyperflatness, both measures of intermittency and these are confirmed numerically for passive sliders driven by a Kardar-Parisi-Zhang surface. Aging properties are studied via a two-time flatness. We predict and verify numerically that the time-dependent flatness is, remarkably, a nonmonotonic function of time with different scaling forms at short and long times. The scaling description remains valid when clustering is more diffuse as for passive sliders evolving through Edwards-Wilkinson driving or under antiadvection, although exponents and scaling functions differ substantially.

Effective equilibrium states in mixtures of active particles driven by colored noise

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

Ordered phases in coupled nonequilibrium systems: Static properties

We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in different ways. As a result of this two-way coupling between the landscape and the particles, the system shows interesting new phases, characterized by different sorts of long-ranged order in the particles and in the landscape. In all these ordered phases, the two particle species phase separate completely from each other, but the underlying landscape may either show complete ordering, with macroscopic regions with distinct average slopes, or may show coexistence of ordered and disordered regions, depending on the differential nature of effect produced by the particle species on the landscape. We discuss several aspects of static properties of these phases in this paper, and we discuss the dynamics of these phases in the sequel.

Emergent Structures in an Active Polar Fluid: Dynamics of Shape, Scattering, and Merger

Spatially localized defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar "actin" filaments and "myosin" motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile-we derive effective equations of motion for these "extended particles" and analyze their shape, kinetics, interactions, and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger. Our results are relevant for the dynamics of actomyosin-dense structures at the cell cortex, reconstituted actomyosin complexes, and 2D active colloidal gels.

Large compact clusters and fast dynamics in coupled nonequilibrium systems

We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle densities and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains.

Actomyosin dynamics drive local membrane component organization in an in vitro active composite layer

The surface of a living cell provides a platform for receptor signaling, protein sorting, transport, and endocytosis, whose regulation requires the local control of membrane organization. Previous work has revealed a role for dynamic actomyosin in membrane protein and lipid organization, suggesting that the cell surface behaves as an active composite composed of a fluid bilayer and a thin film of active actomyosin. We reconstitute an analogous system in vitro that consists of a fluid lipid bilayer coupled via membrane-associated actin-binding proteins to dynamic actin filaments and myosin motors. Upon complete consumption of ATP, this system settles into distinct phases of actin organization, namely bundled filaments, linked apolar asters, and a lattice of polar asters. These depend on actin concentration, filament length, and actin/myosin ratio. During formation of the polar aster phase, advection of the self-organizing actomyosin network drives transient clustering of actin-associated membrane components. Regeneration of ATP supports a constitutively remodeling actomyosin state, which in turn drives active fluctuations of coupled membrane components, resembling those observed at the cell surface. In a multicomponent membrane bilayer, this remodeling actomyosin layer contributes to changes in the extent and dynamics of phase-segregating domains. These results show how local membrane composition can be driven by active processes arising from actomyosin, highlighting the fundamental basis of the active composite model of the cell surface, and indicate its relevance to the study of membrane organization.