Active fluids display spontaneous turbulentlike flows known as active turbulence. Recent work revealed that these flows have universal features, independent of the material properties and of the presence of topological defects. However, the differences between defect-laden and defect-free active turbulence remain largely unexplored. Here, by means of large-scale numerical simulations, we show that defect-free active nematic turbulence can undergo dynamical arrest. This state is characterized by an emergent network of nematic domain walls that channels coherent streams and suppresses chaotic flows. As the system evolves, the branched wall network produces a large-scale pattern with treelike topological properties. We find that flow alignment—the tendency of nematics to reorient under shear—enhances large-scale chaotic jets in contractile rodlike systems while promoting dynamical arrest in extensile systems. We further show that dynamical arrest arises regardless of whether defects are prohibited by construction or simply fail to form due to a high energy cost of defect cores. Taken together, our findings reveal a striking pattern-formation mechanism, with labyrinths emerging from active turbulence, and illuminate the rich transitional regime between defect-free and defect-laden dynamics. These behaviors call for the experimental realization of active nematics at vanishing or low defect densities, and underscore that, in extensile rodlike nematics, topological defects enable turbulence by preventing dynamical arrest.

To migrate, cells exert traction forces on the extracellular matrix (ECM) – a biopolymer network that often exhibits nonlinear strain-stiffening elasticity. Cellular tractions can therefore stiffen the ECM. At the same time, cells exert stronger tractions on stiffer ECM. Here, we show theoretically that this traction-stiffness feedback can produce traction bistability and hysteresis. As a result, increasing either the ECM's nonlinear elasticity or cellular contractility leads to a discontinuous transition from low to high tractions. This traction jump might trigger collective cell migration as the ECM stiffens, for example during development and tumor progression. Moreover, the bistable behavior might provide robustness to cellular traction forces when cells migrate through mechanically heterogeneous environments.

The collective migration of epithelial groups of cells plays a central role in processes such as embryo development, wound healing, and cancer invasion. While finite cell clusters are known to collectively migrate in response to external gradients, the competing effect of possible endogenous cues is largely unknown.Here, we demonstrate that the polarization of peripheral cells that pull the cluster's edge outward is sufficient to induce and sustain the collective migration of confluent clusters. We use a general continuum model to show that the underlying shape-sensing mechanism is purely mechanical, relying on long-range hydrodynamic interactions and cell-cell alignment forces. As a proof-of-concept, we validate our findings with experiments on monolayer clusters from various cell lines, where we control initial shapes and sizes. The mechanism operates independently of external signals and will generally interfere with them. Specifically, we predict and observe experimentally that it can override collective durotaxis, reversing the direction of migration. Together, our results offer a physical framework for understanding how cell interactions govern the interplay between global shape and collective motion and afford engineering principles for optimal control and manipulation of cell cluster shape and motion.

Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly-aligned quiescent state. Here we show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. Through a weakly nonlinear analysis and a numerical study, we trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. We predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. Our predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions.

The efficient transport of fluids through disordered media requires a thorough understanding of how the driving rate affects two-phase interface propagation. Despite our understanding of front dynamics in homogeneous environments, as well as how medium heterogeneities shape fluid interfaces at rest, little is known about the effects of localized topographical variations on large-scale interface dynamics. To gain physical insights into this problem, we study here oil-air displacements through an "imperfect" Hele-Shaw cell. Combining experiments, numerical simulations, and theory, we show that the flow rate dramatically alters the interface response to a porous constriction as one approaches the Saffman-Taylor instability, strictly under stable conditions. This gives rise to asymmetric imbibition-drainage hysteresis cycles that feature divergent extensions and nonlocal effects, all of which are aptly captured and explained by a minimal free boundary model.

The directed migration of cellular clusters enables morphogenesis, wound healing and collective cancer invasion. Gradients of substrate stiffness direct the migration of cellular clusters in a process called collective durotaxis, but the underlying mechanisms remain unclear. Here we unveil a connection between collective durotaxis and the wetting properties of cellular clusters. We show that clusters of cancer cells dewet soft substrates and wet stiff ones. At intermediate stiffness—at the crossover from low to high wettability—clusters on uniform-stiffness substrates become maximally motile, and clusters on stiffness gradients exhibit optimal durotaxis. Durotactic velocity increases with cluster size, stiffness gradient and actomyosin activity. We demonstrate this behaviour on substrates coated with the cell–cell adhesion protein E-cadherin and then establish its generality on substrates coated with extracellular matrix. We develop an active wetting model that explains collective durotaxis in terms of a balance between in-plane active traction and tissue contractility and out-of-plane surface tension. Finally, we show that the distribution of cluster displacements has a heavy tail, with infrequent but large cellular hops that contribute to durotactic migration. Our study demonstrates a physical mechanism of collective durotaxis, through both cell–cell and cell–substrate adhesion ligands, based on the wetting properties of active droplets. Substrate stiffness influences cellular cluster migration through collective durotaxis. Now, the underlying mechanism of this process is explained by considering the wetting dynamics of the clusters.

Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the absence of inertia, chaotic active flows are reminiscent of inertial turbulence, and hence they are known as active turbulence. Here, we survey the field, providing a unified perspective over different classes of active turbulence. To this end, we divide our review in sections for systems with either polar or nematic order, and with or without momentum conservation (wet/dry). Comparing to inertial turbulence, we highlight the emergence of power-law scaling with either universal or non-universal exponents. We also contrast scenarios for the transition from steady to chaotic flows, and we discuss the absence of energy cascades. We link this feature to both the existence of intrinsic length scales and the self-organized nature of energy injection in active turbulence, which are fundamental differences with inertial turbulence. We close by outlining the emerging picture, remaining challenges, and future directions.

Active fluids exhibit complex turbulentlike flows at low Reynolds number. Recent predicted that 2D active nematic turbulence follows scaling laws with universal exponents. However, experimentally testing these predictions is conditioned by the coupling to the 3D environment. Here, we measure the spectrum of the kinetic energy E ð q Þ in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes E ð q Þ ∼ q − 4 and E ð q Þ ∼ q − 1 , respectively, in agreement with the theoretical prediction for 2D active nematics. At large scales, however, we find a new scaling E ð q Þ ∼ q , which emerges when the dissipation is dominated by the 3D oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of scaling laws with universal exponents in active turbulence, and it establishes how the spectrum is affected by external dissipation.

Recent experiments have shown that the spontaneous activity of developing dissociated neuronal cultures can be described as a process of highly inhomogeneous nucleation and front propagation due to the localization of noise activity, i.e. , noise focusing. However, the basic understanding of the mechanisms of noise build-up leading to the nucleation remains an open fundamental problem. Here we present a minimal dynamical model called stochastic quorum percolation that can account for the observed phenomena, while providing a robust theoretical framework. The model reproduces the first- and second-order phase transitions of bursting dynamics and neuronal avalanches, respectively, and captures the profound effect metric correlations in the network topology can have on the dynamics. The application of our results to other systems such as in the propagation of infectious diseases and of rumors is discussed.

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model, the cell is driven out of equilibrium by an active cytsokeleton force that acts on the membrane. The cell cytoplasm, described as a viscous droplet in the Darcy flow regime, contains a diffusive solute that actively transduces the applied cytoskeleton force. While fairly simple and analytically tractable, this quasi-two-dimensional model predicts a range of compelling dynamic behaviours. A linear stability analysis of the system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.

A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov’s E(q) ~ q−5∕3 scaling of the kinetic energy spectrum of inertial turbulence with the wavevector q. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling E(q) ~ q−1 at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-range velocity correlations, which lead to the scaling behaviour. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number. Determining the properties that emerge from the equations that govern turbulent flow is a fundamental challenge in non-equilibrium physics. A hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number is now put forward, revealing a universal scaling behaviour for this class of systems.

Brownian ratchets are shown to feature a nontrivial vanishing-noise limit where the dynamics is reduced to a stochastic alternation between two deterministic circle maps (quasideterministic ratchets). Motivated by cooperative dynamics of molecular motors, here we solve exactly the problem of two interacting quasideterministic ratchets. We show that the dynamics can be described as a random walk on a graph that is specific to each set of parameters. We compute point by point the exact velocity-force V (f) function as a summation over all paths in the specific graph for each f, revealing a complex structure that features self-similarity and nontrivial continuity properties. From a general perspective, we unveil that the alternation of two simple piecewise linear circle maps unfolds a very rich variety of dynamical complexity, in particular the phenomenon of piecewise chaos, where chaos emerges from the combination of nonchaotic maps. We show convergence of the finite-noise case to our exact solution.

We design, construct, and test a device for controlled boiling by means of local vapor bubble formation in a cavity that injects vapor bubbles in a capillary crossflow. The outcome of the device is a regular slug flow of approximately monodisperse bubbles that can be used for a variety of applications. The setup is designed to be independent of gravity level and is tested succesfully both in normal gravity and in microgravity using drop tower experiments. The device is calibrated by a systematic study determining the size and frequency of bubble formation as a function of pressure and flow conditions. Results turn out to be virtually independent of gravity. Different regimes of operations are identified and described, and basic properties of the behavior of the bubbles inside the nucleation cavity are discussed. The slug flow downstream the crossflow is characterized and shows some differences depending on gravity. Finally, we illustrate the use of a controlled regular slug flow generated by our device by using it as an input of a serpentine heat exchanger. This emphasizes an important virtue of our method for practical applications, namely, the ability to separate the process of bubble formation from the actual heat exchange by phase transformation in the region of interest.

Active turbulence describes a flow regime that is erratic, and yet endowed with a characteristic length scale1. It arises in animate soft-matter systems as diverse as bacterial baths2, cell tissues3 and reconstituted cytoskeletal preparations4. However, the way that these turbulent dynamics emerge in active systems has so far evaded experimental scrutiny. Here, we unveil a direct route to active nematic turbulence by demonstrating that, for radially aligned unconfined textures, the characteristic length scale emerges at the early stages of the instability. We resolve two-dimensional distortions of a microtubule-based extensile system5 in space and time, and show that they can be characterized in terms of a growth rate that exhibits quadratic dependence on a dominant wavenumber. This wavelength selection mechanism is justified on the basis of a continuum model for an active nematic including viscous coupling to the adjacent fluid phase. Our findings are in line with the classical pattern-formation studies in non-active systems6, bettering our understanding of the principles of active self-organization, and providing potential perspectives for the control of biological fluids. Experiments on microtubule-based nematics, together with active gel theory, suggest that the length scale associated with active turbulence is selected at its onset—balancing activity with the stabilizing effects of nematic elasticity and geometry.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The kinesin-3 motor KIF1A is involved in long-ranged axonal transport in neurons. To ensure vesicular delivery, motors need to navigate the microtubule lattice and overcome possible roadblocks along the way. The single-headed form of KIF1A is a highly diffusive motor that has been shown to be a prototype of a Brownian motor by virtue of a weakly bound diffusive state to the microtubule. Recently, groups of single-headed KIF1A motors were found to be able to sidestep along the microtubule lattice, creating left-handed helical membrane tubes when pulling on giant unilamellar vesicles in vitro. A possible hypothesis is that the diffusive state enables the motor to explore the microtubule lattice and switch protofilaments, leading to a left-handed helical motion. Here, we study the longitudinal rotation of microtubules driven by single-headed KIF1A motors using fluorescence-interference contrast microscopy. We find an average rotational pitch of ≃1.5 μm, which is remarkably robust to changes in the gliding velocity, ATP concentration, microtubule length, and motor density. Our experimental results are compared to stochastic simulations of Brownian motors moving on a two-dimensional continuum ratchet potential, which quantitatively agree with the fluorescence-interference contrast experiments. We find that single-headed KIF1A sidestepping can be explained as a consequence of the intrinsic handedness and polarity of the microtubule lattice in combination with the diffusive mechanochemical cycle of the motor.

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.