Entropy production rate is maximized in non-contractile actomyosin

Filament transport supports contractile steady states of actin networks

In all eukaryotic cells, the actin cytoskeleton is maintained in a dynamic steady-state. Actin filaments are continuously displaced from cell periphery, where they assemble, towards the cell's center, where they disassemble. Despite this constant flow and turnover, cellular networks maintain their overall architecture constant. How such a flow of material can support dynamic yet steady cellular architectures remains an open question. To investigate the role of myosin-based forces in contractile steady-states of actin networks, we used a reconstituted in vitro system based on a minimal set of purified proteins, namely actin, myosin and actin regulators. We found that, contrary to previous bulk experiments, when confined in microwells, the actin network could self-organize into ordered arrangements of contractile bundles, flowing continuously without collapsing. This was supported by three-dimensional fluxes of actin filaments, spatially separated yet balancing each other. Unexpectedly, maintaining these fluxes did not depend on filament nucleation or elongation, but solely on filament transport. Ablation of the contractile bundles abolished the flux balance and led to network collapse. These findings demonstrate that the dynamic steady state of actin networks can be sustained by filament displacement and recirculation, independently of filament assembly and disassembly.

Entropy Production in a System of Janus Particles

Entropy production is a key descriptor of out-of-equilibrium behavior in active matter systems, providing insights into both single-particle dynamics and emergent collective phenomena. It helps determine transport coefficients and phoretic velocities and serves as a crucial tool for understanding collective phenomena such as structural transitions, regime shifts, clustering, and self-organization. This study investigates the role of entropy production for individual active (catalytic Janus) particles and in systems of active particles interacting with one another and their environment. We employ a multiscale framework to bridge microscopic particle dynamics and macroscopic behavior, offering a thermodynamic perspective on active matter. These findings enhance our understanding of the fundamental principles governing active particle systems and create new opportunities for addressing unresolved questions in non-equilibrium thermodynamics.

F-actin architecture determines the conversion of chemical energy into mechanical work

Mechanical work serves as the foundation for dynamic cellular processes, ranging from cell division to migration. A fundamental driver of cellular mechanical work is the actin cytoskeleton, composed of filamentous actin (F-actin) and myosin motors, where force generation relies on adenosine triphosphate (ATP) hydrolysis. F-actin architectures, whether bundled by crosslinkers or branched via nucleators, have emerged as pivotal regulators of myosin II force generation. However, it remains unclear how distinct F-actin architectures impact the conversion of chemical energy to mechanical work. Here, we employ in vitro reconstitution of distinct F-actin architectures with purified components to investigate their influence on myosin ATP hydrolysis (consumption). We find that F-actin bundles composed of mixed polarity F-actin hinder network contraction compared to non-crosslinked network and dramatically decelerate ATP consumption rates. Conversely, linear-nucleated networks allow network contraction despite reducing ATP consumption rates. Surprisingly, branched-nucleated networks facilitate high ATP consumption without significant network contraction, suggesting that the branched network dissipates energy without performing work. This study establishes a link between F-actin architecture and myosin energy consumption, elucidating the energetic principles underlying F-actin structure formation and the performance of mechanical work.

Measuring response functions of active materials from data

From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so-called active systems generally aim to extract important length or time scales from experimental fields. Because such methods focus on extracting scalar values, they do not wring maximal information from experimental data. We introduce a method to overcome these limitations. We extend the framework of correlation functions by taking into account the internal headings of displacement fields. The functions we construct represent the material response to specific types of active perturbation within the system. Utilizing these response functions we query the material response of disparate active systems composed of actin filaments and myosin motors, from model fluids to living cells. We show we can extract critical length scales from the turbulent flows of an active nematic, anticipate contractility in an active gel, distinguish viscous from viscoelastic dissipation, and even differentiate modes of contractility in living cells. These examples underscore the vast utility of this method which measures response functions from experimental observations of complex active systems.

Dissipation and energy propagation across scales in an active cytoskeletal material

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Bioinspired Membrane Interfaces: Controlling Actomyosin Architecture and Contractility

The creation of biologically inspired artificial lipid bilayers on planar supports provides a unique platform to study membrane-confined processes in a well-controlled setting. At the plasma membrane of mammalian cells, the linkage of the filamentous (F)-actin network is of pivotal importance leading to cell-specific and dynamic F-actin architectures, which are essential for the cell's shape, mechanical resilience, and biological function. These networks are established through the coordinated action of diverse actin-binding proteins and the presence of the plasma membrane. Here, we established phosphatidylinositol-4,5-bisphosphate (PtdIns[4,5]P₂)-doped supported planar lipid bilayers to which contractile actomyosin networks were bound via the membrane-actin linker ezrin. This membrane system, amenable to high-resolution fluorescence microscopy, enabled us to analyze the connectivity and contractility of the actomyosin network. We found that the network architecture and dynamics are not only a function of the PtdIns[4,5]P₂ concentration but also depend on the presence of negatively charged phosphatidylserine (PS). PS drives the attached network into a regime, where low but physiologically relevant connectivity to the membrane results in strong contractility of the actomyosin network, emphasizing the importance of the lipid composition of the membrane interface.

Toward droplets displaying life-like interaction behaviors

Developments in synthetic biology usually bring the conception of individual artificial cells. A key feature of living systems is, however, the interaction between individuals, in which living units can interact autonomously and display a role differentiation such as the case of entities chasing each other. On the other hand, droplets have become a very useful and exciting medium for modern microengineering and biomedical technologies. In this Perspective, we show a brief discussion-outlook of different approaches to recreate predator-prey interactions in both swimmer and crawling droplet systems toward a new generation of synthetic life with impact in both fundamental insights and relevant applications.

Fluctuations of entropy production of a run-and-tumble particle

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.

F-actin architecture determines constraints on myosin thick filament motion

Active stresses are generated and transmitted throughout diverse F-actin architectures within the cell cytoskeleton, and drive essential behaviors of the cell, from cell division to migration. However, while the impact of F-actin architecture on the transmission of stress is well studied, the role of architecture on the ab initio generation of stresses remains less understood. Here, we assemble F-actin networks in vitro, whose architectures are varied from branched to bundled through F-actin nucleation via Arp2/3 and the formin mDia1. Within these architectures, we track the motions of embedded myosin thick filaments and connect them to the extent of F-actin network deformation. While mDia1-nucleated networks facilitate the accumulation of stress and drive contractility through enhanced actomyosin sliding, branched networks prevent stress accumulation through the inhibited processivity of thick filaments. The reduction in processivity is due to a decrease in translational and rotational motions constrained by the local density and geometry of F-actin.

Nonequilibrium thermodynamics of Janus particle self-assembly

We compute the energetic cost of formation of Janus particle structures. Using an approach that couples particle dynamics to the evolution of fuel concentration in the medium, which we consider to be initially inhomogeneous, we show the different types of emerging structures. The energy dissipated in the formation of such structures is obtained from the entropy production rate, which is a non-monotonic function of the fraction of assembled particles and, thus, different in each self-assembly regime. An analysis of the free energy of these particles allows us to establish a thermodynamic criterion of structure formation based on the behavior of chemical potential as a function of the fraction of assembled particles.

Actin-microtubule dynamic composite forms responsive active matter with memory

Active cytoskeletal materials in vitro demonstrate self-organizing properties similar to those observed in their counterparts in cells. However, the search to emulate phenomena observed in living matter has fallen short of producing a cytoskeletal network that would be structurally stable yet possess adaptive plasticity. Here, we address this challenge by combining cytoskeletal polymers in a composite where self-assembling microtubules and actin filaments collectively self-organize due to the activity of microtubule-percolating molecular motors. We demonstrate that microtubules spatially organize actin filaments that in turn guide microtubules. The two networks align in an ordered fashion using this feedback loop. In this composite, actin filaments can act as structural memory and, depending on the concentration of the components, microtubules either write this memory or get guided by it. The system is sensitive to external stimuli, suggesting possible autoregulatory behavior in changing mechanochemical environments. We thus establish an artificial active actin-microtubule composite as a system demonstrating architectural stability and plasticity.

Cell-Matrix Elastocapillary Interactions Drive Pressure-based Wetting of Cell Aggregates

Cell-matrix interfacial energies and the energies of matrix deformations may be comparable on cellular length-scales, yet how capillary effects influence tis sue shape and motion are unknown. In this work, we induce wetting (spreading and migration) of cell aggregates, as models of active droplets onto adhesive substrates of varying elasticity and correlate the dynamics of wetting to the balance of interfacial tensions. Upon wetting rigid substrates, cell-substrate tension drives outward expansion of the monolayer. By contrast, upon wetting compliant substrates, cell substrate tension is attenuated and aggregate capillary forces contribute to internal pressures that drive expansion. Thus, we show by experiments, data-driven modeling and computational simulations that myosin-driven 'active elasto-capillary' effects enable adaptation of wetting mechanisms to substrate rigidity and introduce a novel, pressure-based mechanism for guiding collective cell motion.

Droplets in underlying chemical communication recreate cell interaction behaviors

The sensory-motor interaction is a hallmark of living systems. However, developing inanimate systems with “recognize and attack” abilities remains challenging. On the other hand, controlling the inter-droplet dynamics on surfaces is key in microengineering and biomedical applications. We show here that a pair of droplets can become intelligently interactive (chemospecific stimulus-response inter-droplet autonomous operation) when placed on a nanoporous thin film surface. We find an attacker-victim-like non-reciprocal interaction between spatially separated droplets leading to an only-in-one shape instability that triggers a drop projection to selectively couple, resembling cellular phenomenologies such as pseudopod emission and phagocytic-like functions. The nanopore-driven underlying communication and associated chemical activity are the main physical ingredients behind the observed behavior. Our results reveal that basic features found in many living cell types can emerge from a simple two-droplet framework. This work is a promising step towards the design of microfluidic smart robotics and for origin-of-life protocell models.

While a hallmark of living systems, developing sensory-motor interactions in inanimate systems remains challenging. Here, authors show that nanoporous surfaces can be used to create stimuli-responsive droplet interplay with shape transformation and complex behaviours reminiscent of living cell actions.

Active Regulation of Pressure and Volume Defines an Energetic Constraint on the Size of Cell Aggregates

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the F-actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

Microfluidic investigation of the effect of graphene oxide on mechanical properties of cell and actin cytoskeleton networks: experimental and theoretical approaches

Biomechanical and morphological analysis of the cells is a novel approach for monitoring the environmental features, drugs, and toxic compounds’ effects on cells. Graphene oxide (GO) has a broad range of medical applications such as tissue engineering and drug delivery. However, the effects of GO nanosheets on biological systems have not been completely understood. In this study, we focused on the biophysical characteristics of cells and their changes resulting from the effect of GO nanosheets. The biophysical properties of the cell population were characterized as follows: cell stiffness was calculated by atomic force microscopy, cell motility and invasive properties were characterized in the microfluidic chip in which the cells are able to visualize cell migration at a single-cell level. Intracellular actin was stained to establish a quantitative picture of the intracellular cytoskeleton. In addition, to understand the molecular interaction of GO nanosheets and actin filaments, coarse-grained (CG) molecular dynamics (MD) simulations were carried out. Our results showed that GO nanosheets can reduce cell stiffness in MCF7 cells and MDA-MB-231 cell lines and highly inhibited cell migration (39.2%) in MCF-7 and (38.6%) in MDA-MB-231 cell lines through the GO nanosheets-mediated disruption of the intracellular cytoskeleton. In the presence of GO nanosheets, the cell migration of both cell lines, as well as the cell stiffness, significantly decreased. Moreover, after GO nanosheets treatment, the cell actin network dramatically changed. The experimental and theoretical approaches established a quantitative picture of changes in these networks. Our results showed the reduction of the order parameter in actin filaments was 23% in the MCF7 cell line and 20.4% in the MDA-MB-231 cell line. The theoretical studies also showed that the GO nanosheet–actin filaments have stable interaction during MD simulation. Moreover, the 2D free energy plot indicated the GO nanosheet can induce conformational changes in actin filaments. Our findings showed that the GO nanosheets can increase the distance of actin-actin subunits from 3.22 to 3.5 nm and in addition disrupt native contacts between two subunits which lead to separate actin subunits from each other in actin filaments. In this study, the biomechanical characteristics were used to explain the effect of GO nanosheets on cells which presents a novel view of how GO nanosheets can affect the biological properties of cells without cell death. These findings have the potential to be applied in different biomedical applications.

Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics

We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive limit, we show that, as the friction is increased, memory effects become more prominent and +1/2 topological defects leave increasingly persistent trails in the director field as they pass. The trails are preferential sites for defect formation and they tend to impose polar order on any new +1/2 defects. In the absence of noise and for high friction, it becomes very difficult to create defects, but trails formed by any defects present at the beginning of the simulations persist and organise into parallel arch-like patterns in the director field. We show aligned arches of equal width are approximate steady state solutions of the equations of motion which co-exist with the nematic state. We compare our results to other models in the literature, in particular dry systems with no hydrodynamics, where trails, arches and polar defect ordering have also been observed.

Irreversibility in dynamical phases and transitions

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a measure of irreversibility we term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales. We use this scalar, dimensionless function to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We measure the total energetic cost of establishing synchronized biochemical oscillations while simultaneously quantifying the distribution of irreversibility across spatiotemporal frequencies.

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.

Actin and microtubule crosslinkers tune mobility and control co-localization in a composite cytoskeletal network

Actin and microtubule filaments, with their auxiliary proteins, enable the cytoskeleton to carry out vital processes in the cell by tuning the organizational and mechanical properties of the network. Despite their critical importance and interactions in cells, we are only beginning to uncover information about the composite network. The challenge is due to the high complexity of combining actin, microtubules, and their hundreds of known associated proteins. Here, we use fluorescence microscopy, fluctuation, and cross-correlation analysis to examine the role of actin and microtubules in the presence of an antiparallel microtubule crosslinker, MAP65, and a generic, strong actin crosslinker, biotin-NeutrAvidin. For a fixed ratio of actin and microtubule filaments, we vary the amount of each crosslinker and measure the organization and fluctuations of the filaments. We find that the microtubule crosslinker plays the principle role in the organization of the system, while, actin crosslinking dictates the mobility of the filaments. We have previously demonstrated that the fluctuations of filaments are related to the mechanics, implying that actin crosslinking controls the mechanical properties of the network, independent of the microtubule-driven re-organization.

Quantifying the non-equilibrium activity of an active colloid

Active matter systems exhibit rich emergent behavior due to constant injection and dissipation of energy at the level of individual agents. Since these systems are far from equilibrium, their dynamics and energetics cannot be understood using the framework of equilibrium statistical mechanics. Recent developments in stochastic thermodynamics extend classical concepts of work, heat, and energy dissipation to fluctuating non-equilibrium systems. We use recent advances in experiment and theory to study the non-thermal dissipation of individual light-activated self-propelled colloidal particles. We focus on characterizing the transition from thermal to non-thermal fluctuations and show that energy dissipation rates on the order of ∼kBT s-1 are measurable from finite time series data.

Estimating entropy production by machine learning of short-time fluctuating currents

Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the stochastic dynamics, it would be promising to apply the TURs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics. Here we investigate a theoretical framework for estimation of the entropy production rate using the TURs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics. Specifically, we derive a TUR for the short-time region and prove that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen. This formulation naturally includes a generalization of the TURs with the partial entropy production of subsystems under autonomous interaction, which reveals the hierarchical structure of the estimation. We then construct estimators on the basis of the short-time TUR and machine learning techniques such as the gradient ascent. By performing numerical experiments, we demonstrate that our learning protocol performs well even in nonlinear Langevin dynamics. We also discuss the case of Markov jump processes, where the exact estimation is shown to be impossible in general. Our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium, including biological systems.

Inferring Entropy Production from Short Experiments

We provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in nonequilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite-time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines.

Myosin II Filament Dynamics in Actin Networks Revealed with Interferometric Scattering Microscopy

The plasma membrane and the underlying cytoskeletal cortex constitute active platforms for a variety of cellular processes. Recent work has shown that the remodeling acto-myosin network modifies local membrane organization, but the molecular details are only partly understood because of difficulties with experimentally accessing the relevant time and length scales. Here, we use interferometric scattering microscopy to investigate a minimal acto-myosin network linked to a supported lipid bilayer membrane. Using the magnitude of the interferometric contrast, which is proportional to molecular mass, and fast acquisition rates, we detect and image individual membrane-attached actin filaments diffusing within the acto-myosin network and follow individual myosin II filament dynamics. We quantify myosin II filament dwell times and processivity as functions of ATP concentration, providing experimental evidence for the predicted ensemble behavior of myosin head domains. Our results show how decreasing ATP concentrations lead to both increasing dwell times of individual myosin II filaments and a global change from a remodeling to a contractile state of the acto-myosin network.

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.

Gibbs free energy change of a discrete chemical reaction event

In modeling the interior of cells by simulating a reaction-diffusion master equation over a grid of compartments, one employs the assumption that the copy numbers of various chemical species are small, discrete quantities. We show that, in this case, textbook expressions for the change in Gibbs free energy accompanying a chemical reaction or diffusion between adjacent compartments are inaccurate. We derive exact expressions for these free energy changes for the case of discrete copy numbers and show how these expressions reduce to traditional expressions under a series of successive approximations leveraging the relative sizes of the stoichiometric coefficients and the copy numbers of the solutes and solvent. Numerical results are presented to corroborate the claim that if the copy numbers are treated as discrete quantities, then only these more accurate expressions lead to correct behavior. Thus, the newly derived expressions are critical for correctly computing entropy production in mesoscopic simulations based on the reaction-diffusion master equation formalism.

Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving

Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine the non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here, we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.

Nonequilibrium dynamics of isostatic spring networks

Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be actively driven, but it is unclear how their critical nature affects their nonequilibrium dynamics. Here, we study the influence of isostaticity on the nonequilibrium dynamics of active spring networks. In our model, heterogeneously distributed white or colored, motorlike noise drives the system into a nonequilibrium steady state. We quantify the nonequilibrium dynamics of pairs of network nodes by the characteristic cycling frequency ω-an experimentally accessible measure of the circulation of the associated phase space currents. The distribution of these cycling frequencies exhibits critical scaling, which we approximately capture by a mean-field theory. Finally, we show that the scaling behavior of ω with distance is controlled by a diverging length scale. Overall, we provide a theoretical approach to elucidate the role of marginality in active disordered systems.

Scaling behavior of nonequilibrium measures in internally driven elastic assemblies

Detecting and quantifying nonequilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a noninvasive approach of measuring nonequilibrium behavior based on the breaking of detailed balance. We focus on "cycling frequencies"-the average frequency with which the trajectories of pairs of degrees of freedom revolve in phase space-and explain their connection with other nonequilibrium measures, including the area enclosing rate and the entropy production rate. We test our approach on simple toy models composed of elastic networks immersed in a viscous fluid with site-dependent internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the tracked degrees of freedom. Importantly, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. The mapping we use in our analytical approach thus offers a convenient framework for predicting the behavior of two-point nonequilibrium measures for a given activity distribution in the network.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks

The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force "plucks" the fiber and induces a nonlinear tension. In stiff and densely connected networks, this tension results in large network-wide tensile stresses that far exceed the expectation drawn from a linear elastic theory. This amplification mechanism competes with a recently characterized network-level amplification due to fiber buckling, suggesting that that fiber networks provide several distinct pathways for living systems to amplify their molecular forces.