Active biological materials

Metareview: a survey of active matter reviews

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 1000 reviews on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles and books on active matter. Thereby, this article provides a useful starting point for finding literature about a specific topic.

Atomic Force Microscopy for the Study of Cell Mechanics in Pharmaceutics

Cell mechanics is gaining attraction in drug screening, but the applicable methods have not yet become part of the standardized norm. This review presents the current state of the art for atomic force microscopy, which is the most widely available method. The field is first motivated as a new way of tracking pharmaceutical effects, followed by a basic introduction targeted at pharmacists on how to measure cellular stiffness. The review then moves on to the current state of the knowledge in terms of experimental results and supplementary methods such as fluorescence microscopy that can give relevant additional information. Finally, rheological approaches as well as the theoretical interpretations are presented before ending on additional methods and outlooks.

A passive star polymer in a dense active bath: insights from computer simulations

Using computer simulations in two dimensions (2D), we explore the structure and dynamics of a star polymer with three arms made of passive monomers immersed in a bath of active Brownian particles (ABPs). We analyze the conformational and dynamical changes of the polymer as a function of activity and packing fraction. We also study the process of motility induced phase separation (MIPS) in the presence of a star polymer, which acts as a mobile nucleation center. The presence of the polymer increases the growth rate of the clusters in comparison to a bath without the polymer. In particular, for low packing fraction, both nucleation and cluster growth are affected by the inclusion of the star polymer. Clusters grow in the vicinity of the star polymer, resulting in the star polymer experiencing a caged motion similar to a tagged ABP in the dense phase. Due to the topological constraints of the star polymers and clustering nearby, the conformational changes of the star polymer lead to interesting observations. Inter alia, we observe the shrinking of the arm with increasing activity along with a short-lived hairpin structure of one arm formed. We also see the transient pairing of two arms of the star polymer, while the third is largely separated at high activity. We hope our findings will help in understanding the behavior of active-passive mixtures, including biopolymers of complex topology in dense active suspensions.

Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

Waste-Free Fully Electrically Fueled Dissipative Self-Assembly System

The importance and prevalence of energy-fueled active materials in living systems have inspired the design of synthetic active materials using various fuels. However, several major limitations of current designs remain to be addressed, such as the accumulation of chemical wastes during the process, unsustainable active behavior, and the lack of precise spatiotemporal control. Here, we demonstrate a fully electrically fueled (e-fueled) active self-assembly material that can overcome the aforementioned limitations. Using an electrochemical setup with dual electrocatalysts, the anodic oxidation of one electrocatalyst (ferrocyanide, [Fe(CN)₆]^4-) creates a positive fuel to activate the self-assembly, while simultaneously, the cathodic reduction of the other electrocatalyst (methyl viologen, [MV]²⁺) generates a negative fuel triggering fiber disassembly. Due to the fully catalytic nature for the reaction networks, this fully e-fueled active material system does not generate any chemical waste, can sustain active behavior for an extended period when the electrical potential is maintained, and provides spatiotemporal control.

From predicting to learning dissipation from pair correlations of active liquids

Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. Towards designing such materials, an important challenge is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on these challenges. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations which, unlike most existing approaches, is applicable even for strongly interacting particles and far from equilibrium, to predict dissipation in these systems. Based on this theory, we reveal analytically a robust relation between dissipation and structure which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out-of-equilibrium.

Chromatographic separation of active polymer-like worm mixtures by contour length and activity

The convective transport rate of polymers through confined geometries depends on their size, allowing for size-based separation of polymer mixtures (chromatography). Here, we investigate whether mixtures of active polymers can be separated in a similar manner based on their activity. We use thin, living Tubifex tubifex worms as a model system for active polymers and study the transport of these worms by an imposed flow through a channel filled with a hexagonal pillar array. The transport rate through the channel depends strongly on the degree of activity, an effect that we assign to the different distribution of conformations sampled by the worms depending on their activity. Our results demonstrate a unique way to sort mixtures of active polymers based on their activity and provide a versatile and convenient experimental system to investigate the hydrodynamics of active polymers.

Mean-field theory for the structure of strongly interacting active liquids

Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path towards such a goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools from liquid-state theories to approach this challenge for a classic minimal isotropic active matter model. First, we construct a nonequilibrium mean-field framework which can predict the structure of systems of weakly interacting particles. Second, motivated by equilibrium solvation theories, we modify this theory to extend it with surprisingly high accuracy to strongly interacting particles, distinguishing it from most existing similarly tractable approaches. Our results provide insight into spatial organization in strongly interacting out-of-equilibrium systems and strategies to control them.

Electrically Fueled Active Supramolecular Materials

Fuel-driven dissipative self-assemblies play essential roles in living systems, contributing both to their complex, dynamic structures and emergent functions. Several dissipative supramolecular materials have been created using chemicals or light as fuel. However, electrical energy, one of the most common energy sources, has remained unexplored for such purposes. Here, we demonstrate a new platform for creating active supramolecular materials using electrically fueled dissipative self-assembly. Through an electrochemical redox reaction network, a transient and highly active supramolecular assembly is achieved with rapid kinetics, directionality, and precise spatiotemporal control. As electronic signals are the default information carriers in modern technology, the described approach offers a potential opportunity to integrate active materials into electronic devices for bioelectronic applications.

Memory effects in spiral diffusion of rotary self-propellers

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)10.1103/PhysRevE.94.030601] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Unified analysis of topological defects in 2D systems of active and passive disks

We provide a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. We show that, both in and out-of-equilibrium, the passage from the solid to the hexatic is driven by the unbinding of dislocations, in quantitative agreement with the KTHNY singularity. Instead, extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate in the liquid phase very close to the hexatic-liquid transition, both for continuous and discontinuous transitions, in the homogeneous liquid regime. At critical percolation the clusters of defects are fractal with statistical and geometric properties that are independent of the activity and compatible with the universality class of uncorrelated critical percolation. We also characterize the spatial organization of point-like defects and we show that the disclinations are not free, but rather always very near more complex defect structures. At high activity, the bulk of the dense phase generated by Motility-Induced Phase Separation is characterized by a density of point-like defects, and statistics and morphology of defect clusters, set by the amount of activity and not the packing fraction. Hexatic domains within the dense phase are separated by grain-boundaries along which a finite network of topological defects resides, interrupted by gas bubbles in cavitation. This structure is dynamic in the sense that the defect network allows for an unzipping mechanism that leaves free space for gas bubbles to appear, close, and even be released into the dilute phase.

Active bath-induced localization and collapse of passive semiflexible polymers

The conformational and dynamical properties of a passive polymer embedded in a bath of active Brownian particles (ABPs) are studied by Langevin dynamics simulations. Various activities and ABP concentrations below and above the critical values for motility-induced phase separation (MIPS) are considered. In a homogeneous ABP fluid, the embedded polymer swells with increasing bath activity, with stronger swelling for larger densities. The polymer dynamics is enhanced, with the diffusion coefficient increasing by a power-law with increasing activity, where the exponent depends on the ABP concentration. For ABP concentrations in the MIPS regime, we observe a localization of the polymer in the low-density ABP phase associated with polymer collapse for moderate activities and a reswelling for high activities accompanied by a preferred localization in the high-density ABP phase. Localization and reswelling are independent of the polymer stiffness, with stiff polymers behaving similarly to flexible polymers. The polymer collapse is associated with a slowdown of its dynamics and a significantly smaller center-of-mass diffusion coefficient. In general, the polymer dynamics can only partially be described by an effective (bath) temperature. Moreover, the properties of a polymer embedded in a homogeneous active bath deviate quantitatively from those of a polymer composed of active monomers, i.e., linear chains of ABPs; however, such a polymer exhibits qualitatively similar activity-dependent features.

Quantitative Methodologies to Dissect Immune Cell Mechanobiology

Mechanobiology seeks to understand how cells integrate their biomechanics into their function and behavior. Unravelling the mechanisms underlying these mechanobiological processes is particularly important for immune cells in the context of the dynamic and complex tissue microenvironment. However, it remains largely unknown how cellular mechanical force generation and mechanical properties are regulated and integrated by immune cells, primarily due to a profound lack of technologies with sufficient sensitivity to quantify immune cell mechanics. In this review, we discuss the biological significance of mechanics for immune cells across length and time scales, and highlight several experimental methodologies for quantifying the mechanics of immune cells. Finally, we discuss the importance of quantifying the appropriate mechanical readout to accelerate insights into the mechanobiology of the immune response.

Learning the non-equilibrium dynamics of Brownian movies

Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.

Is the plant nucleus a mechanical rheostat?

Beyond its biochemical nature, the nucleus is also a physical object. There is accumulating evidence that its mechanics plays a key role in gene expression, cytoskeleton organization, and more generally in cell and developmental biology. Building on data mainly obtained from the animal literature, we show how nuclear mechanics may orchestrate development and gene expression. In other words, the nucleus may play the additional role of a mechanical rheostat. Although data from plant systems are still scarce, we pinpoint recent advances and highlight some differences with animal systems. Building on this survey, we propose a list of prospects for future research in plant nuclear mechanotransduction and development.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems

We study the stationary dynamics of an active interacting Brownian particle system. We measure the violations of the fluctuation dissipation theorem, and the corresponding effective temperature, in a locally resolved way. Quite naturally, in the homogeneous phases the diffusive properties and effective temperature are also homogeneous. Instead, in the inhomogeneous phases (close to equilibrium and within the MIPS sector) the particles can be separated in two groups with different diffusion properties and effective temperatures. Notably, at fixed activity strength the effective temperatures in the two phases remain distinct and approximately constant within the MIPS region, with values corresponding to the ones of the whole system at the boundaries of this sector of the phase diagram. We complement the study of the globally averaged properties with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases. We also distinguish the behavior of the (time-delayed) effective temperature from the (instantaneous) kinetic temperature, showing that the former is independent of the friction coefficient.

The Actin Cytoskeleton as an Active Adaptive Material

Actin is the main protein used by biological cells to adapt their structure and mechanics to their needs. Cellular adaptation is made possible by molecular processes that strongly depend on mechanics. The actin cytoskeleton is also an active material that continuously consumes energy. This allows for dynamical processes that are possible only out of equilibrium and opens up the possibility for multiple layers of control that have evolved around this single protein.Here we discuss the actin cytoskeleton from the viewpoint of physics as an active adaptive material that can build structures superior to man-made soft matter systems. Not only can actin be used to build different network architectures on demand and in an adaptive manner, but it also exhibits the dynamical properties of feedback systems, like excitability, bistability, or oscillations. Therefore, it is a prime example of how biology couples physical structure and information flow and a role model for biology-inspired metamaterials.

Cooperative ordering of treadmilling filaments in cytoskeletal networks of FtsZ and its crosslinker ZapA

During bacterial cell division, the tubulin-homolog FtsZ forms a ring-like structure at the center of the cell. This Z-ring not only organizes the division machinery, but treadmilling of FtsZ filaments was also found to play a key role in distributing proteins at the division site. What regulates the architecture, dynamics and stability of the Z-ring is currently unknown, but FtsZ-associated proteins are known to play an important role. Here, using an in vitro reconstitution approach, we studied how the well-conserved protein ZapA affects FtsZ treadmilling and filament organization into large-scale patterns. Using high-resolution fluorescence microscopy and quantitative image analysis, we found that ZapA cooperatively increases the spatial order of the filament network, but binds only transiently to FtsZ filaments and has no effect on filament length and treadmilling velocity. Together, our data provides a model for how FtsZ-associated proteins can increase the precision and stability of the bacterial cell division machinery in a switch-like manner.

The Z-ring, constituted of the tubulin homolog FtsZ protein, plays an essential role for bacterial cell division. Here the authors use an in vitro reconstitution approach to determine how the regulatory protein ZapA affects FtsZ treadmilling and filament organization into large-scale patterns.

Cytoskeletal and Actin-Based Polymerization Motors and Their Role in Minimal Cell Design

Life implies motion. In cells, protein-based active molecular machines drive cell locomotion and intracellular transport, control cell shape, segregate genetic material, and split a cell in two parts. Key players among molecular machines driving these various cell functions are the cytoskeleton and motor proteins that convert chemical bound energy into mechanical work. Findings over the last decades in the field of in vitro reconstitutions of cytoskeletal and motor proteins have elucidated mechanistic details of these active protein systems. For example, a complex spatial and temporal interplay between the cytoskeleton and motor proteins is responsible for the translation of chemically bound energy into (directed) movement and force generation, which eventually governs the emergence of complex cellular functions. Understanding these mechanisms and the design principles of the cytoskeleton and motor proteins builds the basis for mimicking fundamental life processes. Here, a brief overview of actin, prokaryotic actin analogs, and motor proteins and their potential role in the design of a minimal cell from the bottom-up is provided.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Axonal Transport, Phase-Separated Compartments, and Neuron Mechanics - A New Approach to Investigate Neurodegenerative Diseases

Many molecular and cellular pathogenic mechanisms of neurodegenerative diseases have been revealed. However, it is unclear what role a putatively impaired neuronal transport with respect to altered mechanical properties of neurons play in the initiation and progression of such diseases. The biochemical aspects of intracellular axonal transport, which is important for molecular movements through the cytoplasm, e.g., mitochondrial movement, has already been studied. Interestingly, transport deficiencies are associated with the emergence of the affliction and potentially linked to disease transmission. Transport along the axon depends on the normal function of the neuronal cytoskeleton, which is also a major contributor to neuronal mechanical properties. By contrast, little attention has been paid to the mechanical properties of neurons and axons impaired by neurodegeneration, and of membraneless, phase-separated organelles such as stress granules (SGs) within neurons. Mechanical changes may indicate cytoskeleton reorganization and function, and thus give information about the transport and other system impairment. Nowadays, several techniques to investigate cellular mechanical properties are available. In this review, we discuss how select biophysical methods to probe material properties could contribute to the general understanding of mechanisms underlying neurodegenerative diseases.

Emergence of coexisting ordered states in active matter systems

Active systems can produce a far greater variety of ordered patterns than conventional equilibrium systems. In particular, transitions between disorder and either polar- or nematically ordered phases have been predicted and observed in two-dimensional active systems. However, coexistence between phases of different types of order has not been reported. We demonstrate the emergence of dynamic coexistence of ordered states with fluctuating nematic and polar symmetry in an actomyosin motility assay. Combining experiments with agent-based simulations, we identify sufficiently weak interactions that lack a clear alignment symmetry as a prerequisite for coexistence. Thus, the symmetry of macroscopic order becomes an emergent and dynamic property of the active system. These results provide a pathway by which living systems can express different types of order by using identical building blocks.

Layered Structure and Complex Mechanochemistry Underlie Strength and Versatility in a Bacterial Adhesive

While designing synthetic adhesives that perform in aqueous environments has proven challenging, microorganisms commonly produce bioadhesives that efficiently attach to a variety of substrates, including wet surfaces. The aquatic bacterium Caulobacter crescentus uses a discrete polysaccharide complex, the holdfast, to strongly attach to surfaces and resist flow. The holdfast is extremely versatile and has impressive adhesive strength. Here, we used atomic force microscopy in conjunction with superresolution microscopy and enzymatic assays to unravel the complex structure of the holdfast and to characterize its chemical constituents and their role in adhesion. Our data support a model whereby the holdfast is a heterogeneous material organized as two layers: a stiffer nanoscopic core layer wrapped into a sparse, far-reaching, flexible brush layer. Moreover, we found that the elastic response of the holdfast evolves after surface contact from initially heterogeneous to more homogeneous. From a composition point of view, besides N-acetyl-d-glucosamine (NAG), the only component that had been identified to date, our data show that the holdfast contains peptides and DNA. We hypothesize that, while polypeptides are the most important components for adhesive force, the presence of DNA mainly impacts the brush layer and the strength of initial adhesion, with NAG playing a primarily structural role within the core. The unanticipated complexity of both the structure and composition of the holdfast likely underlies its versatility as a wet adhesive and its distinctive strength. Continued improvements in understanding of the mechanochemistry of this bioadhesive could provide new insights into how bacteria attach to surfaces and could inform the development of new adhesives.IMPORTANCE There is an urgent need for strong, biocompatible bioadhesives that perform underwater. To strongly adhere to surfaces and resist flow underwater, the bacterium Caulobacter crescentus produces an adhesive called the holdfast, the mechanochemistry of which remains undefined. We show that the holdfast is a layered structure with a stiff core layer and a polymeric brush layer and consists of polysaccharides, polypeptides, and DNA. The DNA appears to play a role in the structure of the brush layer and initial adhesion, the peptides in adhesive strength, and the polysaccharides in the structure of the core. The complex, multilayer organization and diverse chemistry described here underlie the distinctive adhesive properties of the holdfast and will provide important insights into the mechanisms of bacterial adhesion and bioadhesive applications.

Phase Coexistence in Two-Dimensional Passive and Active Dumbbell Systems

We demonstrate that there is a macroscopic coexistence between regions with hexatic order and regions in the liquid or gas phase over a finite interval of packing fractions in active dumbbell systems with repulsive power-law interactions in two dimensions. In the passive limit, this interval remains finite, similar to what has been found in two-dimensional systems of hard and soft disks. We did not find discontinuous behavior upon increasing activity from the passive limit.

Rapid dynamics of cell-shape recovery in response to local deformations

It is vital that cells respond rapidly to mechanical cues within their microenvironment through changes in cell shape and volume, which rely upon the mechanical properties of cells' highly interconnected cytoskeletal networks and intracellular fluid redistributions. While previous research has largely investigated deformation mechanics, we now focus on the immediate cell-shape recovery response following mechanical perturbation by inducing large, local, and reproducible cellular deformations using AFM. By continuous imaging within the plane of deformation, we characterize the membrane and cortical response of HeLa cells to unloading, and model the recovery via overdamped viscoelastic dynamics. Importantly, the majority (90%) of HeLa cells recover their cell shape in <1 s. Despite actin remodelling on this time scale, we show that cell-shape recovery time is not affected by load duration, nor magnitude for untreated cells. To further explore this rapid recovery response, we expose cells to cytoskeletal destabilizers and osmotic shock conditions, which uncovers the interplay between actin and osmotic pressure. We show that the rapid dynamics of recovery depend crucially on intracellular pressure, and provide strong evidence that cortical actin is the key regulator in the cell-shape recovery processes, in both cancerous and non-cancerous epithelial cells.

Force fluctuations in three-dimensional suspended fibroblasts

Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. To test quantitatively forces generated by cells not attached to a substrate, we used a dual optical trap to suspend 3T3 fibroblasts between two fibronectin-coated beads. In this simple geometry, we measured both the cells' elastic properties and the force fluctuations they generate with high bandwidth. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. We show that cortical forces generated by non-muscle myosin II deform the cell from its rounded shape in the frequency regime from 0.1 to 10 Hz. The amplitudes of these forces were strongly reduced by blebbistatin and serum starvation, but were unaffected by depolymerization of microtubules. Force fluctuations show a spectrum that is characteristic for an elastic network activated by random sustained stresses with abrupt transitions.

Emergent mechanics of biological structures

Mechanical force organizes life at all scales, from molecules to cells and tissues. Although we have made remarkable progress unraveling the mechanics of life's individual building blocks, our understanding of how they give rise to the mechanics of larger-scale biological structures is still poor. Unlike the engineered macroscopic structures that we commonly build, biological structures are dynamic and self-organize: they sculpt themselves and change their own architecture, and they have structural building blocks that generate force and constantly come on and off. A description of such structures defies current traditional mechanical frameworks. It requires approaches that account for active force-generating parts and for the formation of spatial and temporal patterns utilizing a diverse array of building blocks. In this Perspective, we term this framework “emergent mechanics.” Through examples at molecular, cellular, and tissue scales, we highlight challenges and opportunities in quantitatively understanding the emergent mechanics of biological structures and the need for new conceptual frameworks and experimental tools on the way ahead.

Rotational and translational diffusion in an interacting active dumbbell system

We study the dynamical properties of a two-dimensional ensemble of self-propelled dumbbells with only repulsive interactions. This model undergoes a phase transition between a homogeneous and a segregated phase and we focus on the former. We analyze the translational and rotational mean-square displacements in terms of the Péclet number, describing the relative role of active forces and thermal fluctuations, and of particle density. We find that the four distinct regimes of the translational mean-square displacement of the single active dumbbell survive at finite density for parameters that lead to a separation of time scales. We establish the Péclet number and density dependence of the diffusion constant in the last diffusive regime. We prove that the ratio between the diffusion constant and its value for the single dumbbell depends on temperature and active force only through the Péclet number at all densities explored. We also study the rotational mean-square displacement proving the existence of a rich behavior with intermediate regimes only appearing at finite density. The ratio of the rotational late-time diffusion constant and its vanishing density limit depends on the Péclet number and density only. At low Péclet number it is a monotonically decreasing function of density. At high Péclet number it first increases to reach a maximum and then decreases as a function of density. We interpret the latter result advocating the presence of large-scale fluctuations close to the transition, at large-enough density, that favor coherent rotation inhibiting, however, rotational motion for even larger packing fractions.

Investigating cell mechanics with atomic force microscopy

Transmission of mechanical force is crucial for normal cell development and functioning. However, the process of mechanotransduction cannot be studied in isolation from cell mechanics. Thus, in order to understand how cells 'feel', we must first understand how they deform and recover from physical perturbations. Owing to its versatility, atomic force microscopy (AFM) has become a popular tool to study intrinsic cellular mechanical properties. Used to directly manipulate and examine whole and subcellular reactions, AFM allows for top-down and reconstitutive approaches to mechanical characterization. These studies show that the responses of cells and their components are complex, and largely depend on the magnitude and time scale of loading. In this review, we generally describe the mechanotransductive process through discussion of well-known mechanosensors. We then focus on discussion of recent examples where AFM is used to specifically probe the elastic and inelastic responses of single cells undergoing deformation. We present a brief overview of classical and current models often used to characterize observed cellular phenomena in response to force. Both simple mechanistic models and complex nonlinear models have been used to describe the observed cellular behaviours, however a unifying description of cell mechanics has not yet been resolved.

Extracting the dynamic correlation length of actin networks from microrheology experiments

The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle pairs, it is possible to extract viscoelastic properties at different length scales. In a recent study, a crossover between intermediate and bulk response of complex fluids was discovered in microrheology measurements of reconstituted actin networks. This crossover length was related to structural and mechanical properties of the networks, such as their mesh size and dynamic correlation length. Here we capitalize on this result giving a detailed description of our analysis scheme, and demonstrating how this relation can be used to extract the dynamic correlation length of a polymer network. We further study the relation between the dynamic correlation length and the structure of the network, by introducing a new length scale, the average filament length, without altering the network's mesh size. Contrary to the prevailing assumption, that the dynamic correlation length is equivalent to the mesh size of the network, we find that the dynamic correlation length increases once the filament length is reduced below the crossover distance.

Dynamics of a homogeneous active dumbbell system

We analyze the dynamics of a two-dimensional system of interacting active dumbbells. We characterize the mean-square displacement, linear response function, and deviation from the equilibrium fluctuation-dissipation theorem as a function of activity strength, packing fraction, and temperature for parameters such that the system is in its homogeneous phase. While the diffusion constant in the last diffusive regime naturally increases with activity and decreases with packing fraction, we exhibit an intriguing nonmonotonic dependence on the activity of the ratio between the finite-density and the single-particle diffusion constants. At fixed packing fraction, the time-integrated linear response function depends nonmonotonically on activity strength. The effective temperature extracted from the ratio between the integrated linear response and the mean-square displacement in the last diffusive regime is always higher than the ambient temperature, increases with increasing activity, and, for small active force, monotonically increases with density while for sufficiently high activity it first increases and next decreases with the packing fraction. We ascribe this peculiar effect to the existence of finite-size clusters for sufficiently high activity and density at the fixed (low) temperatures at which we worked. The crossover occurs at lower activity or density the lower the external temperature. The finite-density effective temperature is higher (lower) than the single dumbbell one below (above) a crossover value of the Péclet number.

Impact fragmentation of model flocks

Predicting the bulk material properties of active matter is challenging since these materials are far from equilibrium and standard statistical-mechanics approaches may fail. We report a computational study of the surface properties of a well known active matter system: aggregations of self-propelled particles that are coupled via an orientational interaction and that resemble bird flocks. By simulating the impact of these models flocks on an impermeable surface, we find that they fragment into subflocks with power-law mass distributions, similar to shattering brittle solids but not to splashing liquid drops. Thus, we find that despite the interparticle interactions, these model flocks do not possess an emergent surface tension.

The cytoplasm of living cells behaves as a poroelastic material

The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales.

Spontaneous motion in hierarchically assembled active matter

With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication¹. Besides their biological importance, such inherently non-equilibrium processes are an inspiration for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion^2–4. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit highly sought-after properties such as autonomous motility, internally generated flows and self-organized beating^5–7. Starting from extensile microtubule bundles, we hierarchically assemble active analogs of conventional polymer gels, liquid crystals and emulsions. At high enough concentration, microtubules form a percolating active network characterized by internally driven chaotic flows, hydrodynamic instabilities, enhanced transport and fluid mixing. When confined to emulsion droplets, 3D networks spontaneously adsorb onto the droplet surfaces to produce highly active 2D nematic liquid crystals whose streaming flows are controlled by internally generated fractures and self-healing, as well as unbinding and annihilation of oppositely charged disclination defects. The resulting active emulsions exhibit unexpected properties, such as autonomous motility, which are not observed in their passive analogues. Taken together, these observations exemplify how assemblages of animate microscopic objects exhibit collective biomimetic properties that are starkly different from those found in materials assembled from inanimate building blocks, challenging us to develop a theoretical framework that would allow for a systematic engineering of their far-from-equilibrium material properties.

Reverse engineering the euglenoid movement

Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.

Active compaction of crosslinked driven filament networks

The contractile ability of active materials relies on the interplay of force-exerting and force-bearing structures. However, the complexity of interactions and limited parameter control of many model systems are major obstacles in advancing our understanding of the underlying fundamental principles. To shed light on these principles we introduce and analyse a minimal reconstituted system, consisting of highly concentrated actin filaments that are crosslinked by α-actinin and actively transported in the two-dimensional geometry of a motility assay. This minimal system actively compacts and evolves into highly compact fibres that exceed the length of the individual filaments by two orders of magnitude. We identify the interplay between active transport and crosslinking to be responsible for the observed active compaction. This enables us to control the structure and the length scale of active compaction.

Structure formation in active networks

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells. Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of intracellular dynamics.

Patterned two-photon photoactivation illuminates spatial reorganization in live cells

Photoactivatable fluorescent proteins offer the possibility to optically tag and track the location of molecules in their bright state with high spatial and temporal resolution. Several reports of patterned photoactivation have emerged since the development of a photoactivatable variant of the green fluorescent protein (PaGFP) and the demonstration of two-photon activation of PaGFP. To date, however, there have been few methods developed to quantify the spatial reorganization of the photoactivated population. Here we report on the use of singular value decomposition (SVD) to track the time-dependent distribution of fluorophores after photoactivation. The method was used to describe live-cell actin cytoskeleton behavior in primary murine T-cells, in which a dynamic cytoskeleton is responsible for the reorganization of membrane proteins in response to antigen peptide recognition. The method was also used to observe immortalized simian kidney (Cos-7) cells, in which the cytoskeleton is more stable. Both cell types were transfected with PaGFP fused to the F-actin binding domain of utrophin (UtrCH). Photoactivation patterns were written in the samples with a pair of galvanometric scanning mirrors in circular patterns that were analyzed by transforming the images into a time series of radial distribution profiles. The time-evolution of the profiles was well-described by the first two SVD component states. For T-cells, we find that actin filaments are highly mobile. Inward transport from the photoactivation region was observed and occurred on a 1-2 s time scale, which is consistent with retrograde cycling. For Cos-7 cells, we find that the actin is relatively stationary and does not undergo significant centripetal flow as expected for a resting fibroblast. The combination of patterned photoactivation and SVD analysis offers a unique way to measure spatial redistribution dynamics within live cells.

Mechanical distortion of protein receptor decreases the lifetime of a receptor-ligand bond

Substantial experimental evidence indicates that the mechanical force applied to pull apart non-covalent molecular bonds (such as receptor-ligand pairs) can significantly decrease the bond lifetime. This evidence is often generated in single-molecule experiments that are designed to specifically test effects of pulling forces. However, the effect of compressive forces on the lifetime of receptor-ligand bonds remains largely unexplored. Here we extend the common usage of the atomic force microscopy technique to study whether compressive forces applied to bound streptavidin-biotin species can significantly accelerate the rate of dissociation. Presented experimental data indicate that compressive forces can substantially decrease the lifetime of the molecular bond. Surprisingly, the efficiency of accelerating dissociation by compressive forces sometimes exceeds the enhancement of the dissociation rate measured in pulling experiments, indicating that compressive forces applied to the bound species might be efficiently used to control the lifetime of adhesion bonds.

Molecular shuttles powered by motor proteins: loading and unloading stations for nanocargo integrated into one device

A central challenge on the way to engineer novel materials and nanodevices comprising active transport by nanomotors is the integration of cargo loading and unloading stations on one chip. Exploiting DNA hybridization in zipping and shearing geometries, we demonstrate spatially distinct cargo pick-up and unload by "molecular shuttles" in an integrated device. With this approach, applications can be realized where motor-driven processes are needed to enable transport and active sorting of analytes and nanosystems, or the reconfiguration or self-repair of materials and devices.

Domain-driven morphogenesis of cellular membranes

Cellular membrane systems delimit and organize the intracellular space. Most of the morphological rearrangements in cells involve the coordinated remodeling of the lipid bilayer, the core of the membranes. This process is generally thought to be initiated and coordinated by specialized protein machineries. Nevertheless, it has become increasingly evident that the most essential part of the geometric information and energy required for membrane remodeling is supplied via the cooperative and synergistic action of proteins and lipids, as cellular shapes are constructed using the intrinsic dynamics, plasticity and self-organizing capabilities provided by the lipid bilayer. Here, we analyze the essential role of proteo-lipid membrane domains in conducting and coordinating morphological remodeling in cells.

Mechanics of the F-actin cytoskeleton

Dynamic regulation of the filamentous actin (F-actin) cytoskeleton is critical to numerous physical cellular processes, including cell adhesion, migration and division. Each of these processes require precise regulation of cell shape and mechanical force generation which, to a large degree, is regulated by the dynamic mechanical behaviors of a diverse assortment of F-actin networks and bundles. In this review, we review the current understanding of the mechanics of F-actin networks and identify areas of further research needed to establish physical models. We first review our understanding of the mechanical behaviors of F-actin networks reconstituted in vitro, with a focus on the nonlinear mechanical response and behavior of "active" F-actin networks. We then explore the types of mechanical response measured of cytoskeletal F-actin networks and bundles formed in living cells and identify how these measurements correspond to those performed on reconstituted F-actin networks formed in vitro. Together, these approaches identify the challenges and opportunities in the study of living cytoskeletal matter.