Elsen Tjhung

Spontaneous symmetry breaking in active droplets provides a generic route to motility

We explore a generic mechanism whereby a droplet of active matter acquires motility by the spontaneous breakdown of a discrete symmetry. The model we study offers a simple representation of a “cell extract” comprising, e.g., a droplet of actomyosin solution. (Such extracts are used experimentally to model the cytoskeleton). Actomyosin is an active gel whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes (‘treadmilling’), the gel’s dynamics arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. Adapting our model to wall-bound cells in two dimensions, we find that as wall friction is reduced, treadmilling-induced motility falls but SSB-mediated motility rises. The latter might therefore be crucial in three dimensions where frictional forces are likely to be modest. At a supracellular level, the same generic mechanism can impart motility to aggregates of nonmotile but active bacteria; we show that SSB in this (extensile) case leads generically to rotational as well as translational motion.

A minimal physical model captures the shapes of crawling cells

Cell motility in higher organisms (eukaryotes) is crucial to biological functions ranging from wound healing to immune response, and also implicated in diseases such as cancer. For cells crawling on hard surfaces, significant insights into motility have been gained from experiments replicating such motion in vitro. Such experiments show that crawling uses a combination of actin treadmilling (polymerization), which pushes the front of a cell forward, and myosin-induced stress (contractility), which retracts the rear. Here we present a simplified physical model of a crawling cell, consisting of a droplet of active polar fluid with contractility throughout, but treadmilling connected to a thin layer near the supporting wall. The model shows a variety of shapes and/or motility regimes, some closely resembling cases seen experimentally. Our work strongly supports the view that cellular motility exploits autonomous physical mechanisms whose operation does not need continuous regulatory effort.

Nonequilibrium steady states in polar active fluids

We study numerically the hydrodynamics of an active polar suspension, both in the absence and in the presence of an external shear. We focus on extensile fluids, which are models for bacterial suspensions and are well known to undergo a transition from a quiescent to a spontaneously flowing state, even in one dimension. We characterise the transition to spontaneous flow in a quasi-2-dimensional geometry. We find that it is continuous, and that the succession of steady states obtained for an extensile fluid are dramatically different when the orientation, or polarisation, field is fully two-dimensional or when it is allowed to move out of the plane. Shear slightly stabilises the passive phase and strongly affects the accessible steady states. The distinction between polar active fluids of ‘mover’ and ‘shaker’ particles (with and without self-advection, respectively) is addressed; we find that density inhomogeneities are greatly enhanced by self-advection.

Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibrium Character of Active Matter

Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wavevector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent, and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions

Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by the interfaces between these domains. At continuum level, the structure is defined by a composition field whose gradients which are steep near interfaces drive its diffusive current. These gradients also cause thermodynamic stresses which can drive fluid flow. Fluid flow in turn advects the composition field, while thermal noise creates additional random fluxes that allow the system to explore its configuration space and move towards the Boltzmann distribution. This article introduces continuum models of binary fluids, first covering some well-studied areas such as the thermodynamics and kinetics of phase separation, and emulsion stability. We then address cases where one of the fluid components has anisotropic structure at mesoscopic scales creating nematic (or polar) liquid-crystalline order; this can be described through an additional tensor (or vector) order parameter field. We conclude by outlining a thriving area of current research, namely active emulsions, in which one of the binary components consists of living or synthetic material that is continuously converting chemical energy into mechanical work.

Contractile and chiral activities codetermine the helicity of swimming droplet trajectories

Significance Active fluids include bacterial suspensions, biological tissues, and the cytoskeleton. They are far from equilibrium because the fluid is continuously stirred by constituent particles themselves. A model droplet of active fluid can show swimming or crawling motilities resembling those in real biological cells despite the simplifications entailed. Here, we consider the effects of microscopic chirality on the motility of these active droplets. We find a rich phase diagram including oscillatory dynamics, run and tumble, and helical swimming with either the same or opposite sign to the microscopic one. Active fluids are a class of nonequilibrium systems where energy is injected into the system continuously by the constituent particles themselves. Many examples, such as bacterial suspensions and actomyosin networks, are intrinsically chiral at a local scale, so that their activity involves torque dipoles alongside the force dipoles usually considered. Although many aspects of active fluids have been studied, the effects of chirality on them are much less known. Here, we study by computer simulation the dynamics of an unstructured droplet of chiral active fluid in three dimensions. Our model considers only the simplest possible combination of chiral and achiral active stresses, yet this leads to an unprecedented range of complex motilities, including oscillatory swimming, helical swimming, and run-and-tumble motion. Strikingly, whereas the chirality of helical swimming is the same as the microscopic chirality of torque dipoles in one regime, the two are opposite in another. Some of the features of these motility modes resemble those of some single-celled protozoa, suggesting that underlying mechanisms may be shared by some biological systems and synthetic active droplets.