Self-generated gradients steer collective migration on viscoelastic collagen networks.

Growing evidence suggests that the physical properties of the cellular microenvironment influence cell migration. However, it is not currently understood how active physical remodelling by cells affects migration dynamics. Here we report that cell clusters seeded on deformable collagen-I networks display persistent collective migration despite not showing any apparent intrinsic polarity. Clusters generate transient gradients in collagen density and alignment due to viscoelastic relaxation of the collagen networks. Combining theory and experiments, we show that crosslinking collagen networks or reducing cell cluster size results in reduced network deformation, shorter viscoelastic relaxation time and smaller gradients, leading to lower migration persistence. Traction force and Brillouin microscopy reveal asymmetries in force distributions and collagen stiffness during migration, providing evidence of mechanical cross-talk between cells and their substrate during migration. This physical model provides a mechanism for self-generated directional migration on viscoelastic substrates in the absence of internal biochemical polarity cues.

Erratum: Oriented Active Solids [Phys. Rev. Lett. 123, 238001 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.238001.

Incompressible Polar Active Fluids with Quenched Random Field Disorder in Dimensions d>2.

We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.

Packed Swarms on Dirt: Two-Dimensional Incompressible Flocks with Quenched and Annealed Disorder.

We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed disorder (i.e., time-dependent random white noise) only, which behave like equilibrium ferromagnets with long-range interactions, this robustness against quenched disorder is a fundamentally nonequilibrium phenomenon. The ordered state belongs to a new universality class, whose scaling laws we calculate using three different renormalization group schemes, which all give scaling exponents within 0.02 of each other, indicating that our results are quite accurate. Our predictions can be quantitatively tested in readily available artificial active systems and imply that biological systems such as cell layers can move coherently in vivo, where disorder is inevitable.

Crosslinking and depletion determine spatial instabilities in cytoskeletal active matter.

Active gels made of cytoskeletal proteins are valuable materials with attractive non-equilibrium properties such as spatial self-organization and self-propulsion. At least four typical routes to spatial patterning have been reported to date in different types of cytoskeletal active gels: bending and buckling instabilities in extensile systems, and global and local contraction instabilities in contractile gels. Here we report the observation of these four instabilities in a single type of active gel and we show that they are controlled by two parameters: the concentrations of ATP and depletion agent. We demonstrate that as the ATP concentration decreases, the concentration of passive motors increases until the gel undergoes a gelation transition. At this point, buckling is selected against bending, while global contraction is favored over local ones. Our observations are coherent with a hydrodynamic model of a viscoelastic active gel where the filaments are crosslinked with a characteristic time that diverges as the ATP concentration decreases. Our work thus provides a unified view of spatial instabilities in cytoskeletal active matter.

Tunable corrugated patterns in an active nematic sheet.

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

Layered Chiral Active Matter: Beyond Odd Elasticity.

In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this Letter, starting from active model H^{*}, the general hydrodynamics of a pseudoscalar in a momentum-conserving fluid, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active "odder" elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with an antiferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state-an array of lines on an incompressible, freestanding film of chiral active fluid with a preferred normal direction-is generically unstable. However, this instability can be tuned in easily realizable experimental settings when the film is either on a substrate or in an ambient fluid.

A nonequilibrium force can stabilize 2D active nematics.

Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial suspensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.

Enhanced Orientational Ordering Induced by an Active yet Isotropic Bath.

Can a bath of isotropic but active particles promote ordering of anisotropic but passive particles? In this Letter, we uncover a fluctuation-driven mechanism by which this is possible. Somewhat counterintuitively, we show that the passive particles tend to be more ordered upon increasing the noise strength of the active isotropic bath. We first demonstrate this in a general dynamical model for a nonconserved order parameter (model A) coupled to an active isotropic field and then concentrate on two examples: (i) a collection of polar rods on a substrate in an active isotropic bath and (ii) a passive apolar suspension in a momentum conserved, actively forced but isotropic fluid, which are relevant for current research in active systems. Our theory, which is relevant for understanding ordering transitions in out-of-equilibrium systems can be tested in experiments, for instance, by introducing a low concentration of passive rodlike objects in active isotropic fluids and, since it is applicable to any nonconserved dynamical field, may have applications far beyond active matter.

Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order.

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.

Oriented Active Solids.

We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.

Activating membranes.

We present a general dynamical theory of a membrane coupled to an actin cortex containing polymerizing filaments with active stresses and currents, and demonstrate that active membrane dynamics [S. Ramaswamy et al., Phys. Rev. Lett. 84, 3494 (2000)] and spontaneous shape oscillations emerge from this description. We also consider membrane instabilities and patterns induced by the presence of filaments with polar orientational correlations in the tangent plane of the membrane. The dynamical features we predict should be seen in a variety of cellular contexts involving the dynamics of the membrane-cytoskeleton composite and cytoskeletal extracts coupled to synthetic vesicles.

Dynamics of packed swarms: Time-displaced correlators of two-dimensional incompressible flocks.

We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the roughness exponent χ and anisotropy exponent ζ that are extremely near the known exact results. This implies our prediction for the previously unknown dynamic exponent z is likely to be quantitatively accurate.

Front speed and pattern selection of a propagating chemical front in an active fluid.

Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly understood in general. In this analytical and numerical paper, we study an experimentally motivated minimal model of coupling between reaction-diffusion and active matter: a propagating front of an autocatalytic and stress-generating species. In the absence of activity, the front is described by the well-studied Kolmogorov, Petrovsky, and Piskunov equation. We find that front propagation is maintained even in active systems, with crucial differences: an extensile stress increases the front speed beyond a critical magnitude of the stress, while a contractile stress has no effect on the front speed but can generate a periodic instability in the high-concentration region behind the front. We expect our results to be useful in interpreting pattern formation in active systems with mechanochemical coupling in vivo and in vitro.

Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder.

We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two d=(d_{c}-ε) expansions to O(ε), obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a "hard" continuation which has d_{c}=7/3, and a "soft" continuation with d_{c}=5/2. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.

Cell clusters adopt a collective amoeboid mode of migration in confined nonadhesive environments.

Cell migration is essential to living organisms and deregulated in cancer. Single cell's migration ranges from traction-dependent mesenchymal motility to contractility-driven propulsive amoeboid locomotion, but collective cell migration has only been described as a focal adhesion-dependent and traction-dependent process. Here, we show that cancer cell clusters, from patients and cell lines, migrate without focal adhesions when confined into nonadhesive microfabricated channels. Clusters coordinate and behave like giant super cells, mobilizing their actomyosin contractility at the rear to power their migration. This polarized cortex does not sustain persistent retrograde flows, of cells or actin, like in the other modes of migration but rather harnesses fluctuating cell deformations, or jiggling. Theoretical physical modeling shows this is sufficient to create a gradient of friction forces and trigger directed cluster motion. This collective amoeboid mode of migration could foster metastatic spread by enabling cells to cross a wide spectrum of environments.

Active uniaxially ordered suspensions on disordered substrates.

Multiple experiments on active systems consider oriented active suspensions on substrates or in chambers tightly confined along one direction. The theories of polar and apolar phases in such geometries were considered in A. Maitra et al. [Phys. Rev. Lett. 124, 028002 (2020)10.1103/PhysRevLett.124.028002] and A. Maitra et al. [Proc. Natl. Acad. Sci. USA 115, 6934 (2018)10.1073/pnas.1720607115], respectively. However, the presence of quenched random disorder due to the substrate cannot be completely eliminated in many experimental contexts possibly masking the predictions from those theories. In this paper, I consider the effect of quenched orientational disorder on the phase behavior of both polar and apolar suspensions on substrates. I show that polar suspensions have long-range order in two dimensions with anomalous number fluctuations, while their apolar counterparts have only short-range order, albeit with a correlation length that can increase with activity, and even more violent number fluctuations than active nematics without quenched disorder. These results should be of value in interpreting experiments on active suspensions on substrates with random disorder.

Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks.

As the constituent particles of a flock are polar and in a driven state, their interactions must, in general, be fore-aft asymmetric and nonreciprocal. Within a model that explicitly retains the classical spin angular momentum field of the particles we show that the resulting asymmetric contribution to interparticle torques, if large enough, leads to a buckling instability of the flock. More precisely, this asymmetry also yields a natural mechanism for a difference between the speed of advection of polarization information along the flock and the speed of the flock itself, concretely establishing that the absence of detailed balance, and not merely the breaking of Galilean invariance, is crucial for this distinction. To highlight this we construct a model of asymmetrically interacting spins fixed to lattice points and demonstrate that the speed of advection of polarization remains nonzero. We delineate the conditions on parameters and wave number for the existence of the buckling instability. Our theory should be consequential for interpreting the behavior of real animal groups as well as experimental studies of artificial flocks composed of polar motile rods on substrates.

Spontaneous rotation can stabilise ordered chiral active fluids.

Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present a complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation-which drives chaotic flows in non-rotating active fluids-is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilisation in active systems, which could be key in interpreting the collective behaviors of some biological tissues, cytoskeletal systems and collections of bacteria.