Active gels as a description of the actin-myosin cytoskeleton

Catch bond kinetics are instrumental to cohesion of fire ant rafts under load

Dynamic networks composed of constituents that break and reform bonds reversibly are ubiquitous in nature owing to their modular architectures that enable functions like energy dissipation, self-healing, and even activity. While bond breaking depends only on the current configuration of attachment in these networks, reattachment depends also on the proximity of constituents. Therefore, dynamic networks composed of macroscale constituents (not benefited by the secondary interactions cohering analogous networks composed of molecular-scale constituents) must rely on primary bonds for cohesion and self-repair. Toward understanding how such macroscale networks might adaptively achieve this, we explore the uniaxial tensile response of 2D rafts composed of interlinked fire ants (S. invicta). Through experiments and discrete numerical modeling, we find that ant rafts adaptively stabilize their bonded ant-to-ant interactions in response to tensile strains, indicating catch bond dynamics. Consequently, low-strain rates that should theoretically induce creep mechanics of these rafts instead induce elastic-like response. Our results suggest that this force-stabilization delays dissolution of the rafts and improves toughness. Nevertheless, above 35[Formula: see text] strain low cohesion and stress localization cause nucleation and growth of voids whose coalescence patterns result from force-stabilization. These voids mitigate structural repair until initial raft densities are restored and ants can reconnect across defects. However mechanical recovery of ant rafts during cyclic loading suggests that-even upon reinstatement of initial densities-ants exhibit slower repair kinetics if they were recently loaded at faster strain rates. These results exemplify fire ants' status as active agents capable of memory-driven, stimuli-response for potential inspiration of adaptive structural materials.

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

Evidence that tissue recoil in the early Drosophila embryo is a passive not active process

Understanding tissue morphogenesis is impossible without knowing the mechanical properties of the tissue being shaped. Although techniques for measuring tissue material properties are continually being developed, methods for determining how individual proteins contribute to mechanical properties are very limited. Here, we developed two complementary techniques for the acute inactivation of spaghetti squash (the Drosophila myosin regulatory light chain), one based on the recently introduced (auxin-inducible degron 2 (AID2) system, and the other based on a novel method for conditional protein aggregation that results in nearly instantaneous protein inactivation. Combining these techniques with rheological measurements, we show that passive material properties of the cellularization-stage Drosophila embryo are essentially unaffected by myosin activity. These results suggest that this tissue is elastic, not predominantly viscous, on the developmentally relevant timescale.

Thinking about the action potential: the nerve signal as a window to the physical principles guiding neuronal excitability

Ever since the work of Edgar Adrian, the neuronal action potential has been considered as an electric signal, modeled and interpreted using concepts and theories lent from electronic engineering. Accordingly, the electric action potential, as the prime manifestation of neuronal excitability, serving processing and reliable "long distance" communication of the information contained in the signal, was defined as a non-linear, self-propagating, regenerative, wave of electrical activity that travels along the surface of nerve cells. Thus, in the ground-breaking theory and mathematical model of Hodgkin and Huxley (HH), linking Nernst's treatment of the electrochemistry of semi-permeable membranes to the physical laws of electricity and Kelvin's cable theory, the electrical characteristics of the action potential are presented as the result of the depolarization-induced, voltage- and time-dependent opening and closure of ion channels in the membrane allowing the passive flow of charge, particularly in the form of Na+ and K+ -ions, into and out of the neuronal cytoplasm along the respective electrochemical ion gradient. In the model, which treats the membrane as a capacitor and ion channels as resistors, these changes in ionic conductance across the membrane cause a sudden and transient alteration of the transmembrane potential, i.e., the action potential, which is then carried forward and spreads over long(er) distances by means of both active and passive conduction dependent on local current flow by diffusion of Na+ ion in the neuronal cytoplasm. However, although highly successful in predicting and explaining many of the electric characteristics of the action potential, the HH model, nevertheless cannot accommodate the various non-electrical physical manifestations (mechanical, thermal and optical changes) that accompany action potential propagation, and for which there is ample experimental evidence. As such, the electrical conception of neuronal excitability appears to be incomplete and alternatives, aiming to improve, extend or even replace it, have been sought for. Commonly misunderstood as to their basic premises and the physical principles they are built on, and mistakenly perceived as a threat to the generally acknowledged explanatory power of the "classical" HH framework, these attempts to present a more complete picture of neuronal physiology, have met with fierce opposition from mainstream neuroscience and, as a consequence, currently remain underdeveloped and insufficiently tested. Here we present our perspective that this may be an unfortunate state of affairs as these different biophysics-informed approaches to incorporate also non-electrical signs of the action potential into the modeling and explanation of the nerve signal, in our view, are well suited to foster a new, more complete and better integrated understanding of the (multi)physical nature of neuronal excitability and signal transport and, hence, of neuronal function. In doing so, we will emphasize attempts to derive the different physical manifestations of the action potential from one common, macroscopic thermodynamics-based, framework treating the multiphysics of the nerve signal as the inevitable result of the collective material, i.e., physico-chemical, properties of the lipid bilayer neuronal membrane (in particular, the axolemma) and/or the so-called ectoplasm or membrane skeleton consisting of cytoskeletal protein polymers, in particular, actin fibrils. Potential consequences for our view of action potential physiology and role in neuronal function are identified and discussed.

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

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

Changes in nanomechanical properties of single neuroblastoma cells as a model for oxygen and glucose deprivation (OGD)

Although complex, the biological processes underlying ischemic stroke are better known than those related to biomechanical alterations of single cells. Mechanisms of biomechanical changes and their relations to the molecular processes are crucial for understanding the function and dysfunction of the brain. In our study, we applied atomic force microscopy (AFM) to quantify the alterations in biomechanical properties in neuroblastoma SH-SY5Y cells subjected to oxygen and glucose deprivation (OGD) and reoxygenation (RO). Obtained results reveal several characteristics. Cell viability remained at the same level, regardless of the OGD and RO conditions, but, in parallel, the metabolic activity of cells decreased with OGD duration. 24 h RO did not recover the metabolic activity fully. Cells subjected to OGD appeared softer than control cells. Cell softening was strongly present in cells after 1 h of OGD and with longer OGD duration, and in RO conditions, cells recovered their mechanical properties. Changes in the nanomechanical properties of cells were attributed to the remodelling of actin filaments, which was related to cofilin-based regulation and impaired metabolic activity of cells. The presented study shows the importance of nanomechanics in research on ischemic-related pathological processes such as stroke.

Partitioning of ribonucleoprotein complexes from the cellular actin cortex

The cell cortex plays a crucial role in cell mechanics, signaling, and development. However, little is known about the influence of the cortical meshwork on the spatial distribution of cytoplasmic biomolecules. Here, we describe a fluorescence microscopy method with the capacity to infer the intracellular distribution of labeled biomolecules with subresolution accuracy. Unexpectedly, we find that RNA binding proteins are partially excluded from the cytoplasmic volume adjacent to the plasma membrane that corresponds to the actin cortex. Complementary diffusion measurements of RNA-protein complexes suggest that a rudimentary model based on excluded volume interactions can explain this partitioning effect. Our results suggest the actin cortex meshwork may play a role in regulating the biomolecular content of the volume immediately adjacent to the plasma membrane.

Catapulting of topological defects through elasticity bands in active nematics

Active materials are those in which individual, uncoordinated local stresses drive the material out of equilibrium on a global scale. Examples of such assemblies can be seen across scales from schools of fish to the cellular cytoskeleton and underpin many important biological processes. Synthetic experiments that recapitulate the essential features of such active systems have been the object of study for decades as their simple rules allow us to elucidate the physical underpinnings of collective motion. One system of particular interest has been active nematic liquid crystals (LCs). Because of their well understood passive physics, LCs provide a rich platform to interrogate the effects of active stress. The flows and steady state structures that emerge in an active LCs have been understood to result from a competition between nematic elasticity and the local activity. However most investigations of such phenomena consider only the magnitude of the elastic resistance and not its peculiarities. Here we investigate a nematic liquid crystal and selectively change the ratio of the material's splay and bend elasticities. We show that increases in the nematic's bend elasticity specifically drives the material into an exotic steady state where elongated regions of acute bend distortion or "elasticity bands" dominate the structure and dynamics. We show that these bands strongly influence defect dynamics, including the rapid motion or "catapulting" along the disintegration of one of these bands thus converting bend distortion into defect transport. Thus, we report a novel dynamical state resultant from the competition between nematic elasticity and active stress.

Actin Stress Fibers Response and Adaptation under Stretch

One of the many effects of soft tissues under mechanical solicitation in the cellular damage produced by highly localized strain. Here, we study the response of peripheral stress fibers (SFs) to external stretch in mammalian cells, plated onto deformable micropatterned substrates. A local fluorescence analysis reveals that an adaptation response is observed at the vicinity of the focal adhesion sites (FAs) due to its mechanosensor function. The response depends on the type of mechanical stress, from a Maxwell-type material in compression to a complex scenario in extension, where a mechanotransduction and a self-healing process takes place in order to prevent the induced severing of the SF. A model is proposed to take into account the effect of the applied stretch on the mechanics of the SF, from which relevant parameters of the healing process are obtained. In contrast, the repair of the actin bundle occurs at the weak point of the SF and depends on the amount of applied strain. As a result, the SFs display strain-softening features due to the incorporation of new actin material into the bundle. In contrast, the response under compression shows a reorganization with a constant actin material suggesting a gliding process of the SFs by the myosin II motors.

Spontaneous flow created by active topological defects

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.

Geometrical characterization of active contraction pulses in epithelial cells using the two-dimensional vertex model

Several models have been proposed to describe the dynamics of epithelial tissues undergoing morphogenetic changes driven by apical constriction pulses, which differ in where the constriction is applied, either at the perimeter or in the medial regions. To help discriminate between these models, we analyse the impact of where constriction is applied on the final geometry of the active contracted cell, using the two-dimensional vertex model. We find that medial activity, characterized by a reduction in the reference area, generates anisotropic cell shapes, whereas isotropic cell shapes are produced when the reference perimeter is reduced. When plasticity is included, sufficiently slow processes of medial contractile activity, compared with the characteristic times of elasticity and plasticity, cells can achieve less elongated shapes. Similarly, for perimeter activity, the highest level of contraction is achieved. Finally, we apply the model to describe the apical contractile pulses observed within the epithelial enveloping cell layer during the pre-epiboly of the annual killifish Austrolebias nigripinnis. The analysis of the cell shape changes allowed a global fit of all parameters of the vertex model, with the pulses being quantitatively captured using perimeter activity and area plasticity.

Dissecting Organismal Morphogenesis by Bridging Genetics and Biophysics

Multicellular organisms develop complex shapes from much simpler, single-celled zygotes through a process commonly called morphogenesis. Morphogenesis involves an interplay between several factors, ranging from the gene regulatory networks determining cell fate and differentiation to the mechanical processes underlying cell and tissue shape changes. Thus, the study of morphogenesis has historically been based on multidisciplinary approaches at the interface of biology with physics and mathematics. Recent technological advances have further improved our ability to study morphogenesis by bridging the gap between the genetic and biophysical factors through the development of new tools for visualizing, analyzing, and perturbing these factors and their biochemical intermediaries. Here, we review how a combination of genetic, microscopic, biophysical, and biochemical approaches has aided our attempts to understand morphogenesis and discuss potential approaches that may be beneficial to such an inquiry in the future. Expected final online publication date for the Annual Review of Genetics, Volume 55 is November 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Electroactive macromolecular motors as model materials of ectotherm muscles

The electrochemical reaction in liquid electrolytes of conducting polymers, carbon nanotubes, graphenes, among other materials, replicates the active components (macromolecular electro-chemical motors, ions and solvent) and volume variation of the sarcomere in any natural muscles during actuation, allowing the development of electro-chemo-mechanical artificial muscles. Materials, reactions and artificial muscles have been used as model materials, model reactions and model devices of the muscles from ectotherm animals. We present in this perspective the experimental results and a quantitative description of the thermal influence on the reaction extension and energetic achievements of those muscular models using different experimental methodologies. By raising the temperature for 40 °C keeping the extension of the muscular movement the cooperative actuation of the macromolecular motors harvest, saving chemical energy, up to 60% of the reaction energy from the thermal environment. The synergic thermal influence on either, the reaction rate (Arrhenius), the conformational movement rates of the motors (ESCR model) and the diffusion coefficients of ions across polymer matrix (WLF equation) can support the physical chemical foundations for the selection by nature of ectotherm muscles. Macromolecular motors act, simultaneously, as electro-chemo-mechanical and thermo-mechanical transducers. Technological and biological perspectives are presented.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Soft channel formation and symmetry breaking in exotic active emulsions

We use computer simulations to study the morphology and rheological properties of a bidimensional emulsion resulting from a mixture of a passive isotropic fluid and an active contractile polar gel, in the presence of a surfactant that favours the emulsification of the two phases. By varying the intensity of the contractile activity and of an externally imposed shear flow, we find three possible morphologies. For low shear rates, a simple lamellar state is obtained. For intermediate activity and shear rate, an asymmetric state emerges, which is characterized by shear and concentration banding at the polar/isotropic interface. A further increment in the active forcing leads to the self-assembly of a soft channel where an isotropic fluid flows between two layers of active material. We characterize the stability of this state by performing a dynamical test varying the intensity of the active forcing and shear rate. Finally, we address the rheological properties of the system by measuring the effective shear viscosity, finding that this increases as active forcing is increased-so that the fluid thickens with activity.

A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells

Here we report on the viscosity of eukaryotic living cells, as a function of time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblast cells are investigated using an active microrheological technique, where the magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1-10 s and 100-200 s, not previously disclosed. The shorter time is found to be related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and the statistical results from a mathematical finance approach. The current approach could be exploited to reveal hidden features from biological complex systems or to determine new biomarkers of cellular metabolism.

Thin-film modeling of resting and moving active droplets

We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energy for a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This gives a consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of living cells on solid substrates. As example, we analyze the dynamics of two-dimensional active drops (i.e., ridges) and demonstrate how active forces compete with passive surface forces to shape droplets and drive their motion. In our simple two-dimensional scenario we find that defect structures within the polarization profile drastically influence the shape and motility of active droplets. Thus, we can observe a transition from resting to motile droplets via the elimination of defects in the polarization profile. Furthermore, droplet motility is modulated by strong active stresses. Contractile stresses even lead to topological changes, i.e., drop splitting, which is naturally encoded in the evolution equations.

Thermodynamically consistent treatment of the growth of a biopolymer in the presence of a smooth obstacle interaction potential

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force, as previous work has often done, is thermodynamically inconsistent and can overestimate the stall force, sometimes by more than a factor of two. We perform simulations and analytic calculations of the force-velocity relation satisfying the thermodynamic relationship. The force-velocity relation can deviate strongly from the Brownian-Ratchet predictions. For shallow potential wells of depth ∼5k_{B}T, which might correspond to transient filament-membrane attachments, the velocity drops more rapidly than predicted by the Brownian-Ratchet model, in some cases by as much as a factor of 50 at an opposing force of only 1 pN. On the other hand, the zero-force velocity is much less affected than would be expected from naive use of the Boltzmann factor. Furthermore, the growth velocity has a surprisingly strong dependence on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing but only if the attractive well is relatively flat over a region comparable to or greater than the monomer size. For double-well potentials, which have such a flat region, the slowing of polymerization by external pushing force is almost linear up to the stall force in some parameter ranges.

The Poisson Ratio of the Cellular Actin Cortex Is Frequency Dependent

Cell shape changes are vital for many physiological processes such as cell proliferation, cell migration, and morphogenesis. They emerge from an orchestrated interplay of active cellular force generation and passive cellular force response, both crucially influenced by the actin cytoskeleton. To model cellular force response and deformation, cell mechanical models commonly describe the actin cytoskeleton as a contractile isotropic incompressible material. However, in particular at slow frequencies, there is no compelling reason to assume incompressibility because the water content of the cytoskeleton may change. Here, we challenge the assumption of incompressibility by comparing computer simulations of an isotropic actin cortex with tunable Poisson ratio to measured cellular force response. Comparing simulation results and experimental data, we determine the Poisson ratio of the cortex in a frequency-dependent manner. We find that the Poisson ratio of the cortex decreases in the measured frequency regime analogous to trends reported for the Poisson ratio of glassy materials. Our results therefore indicate that actin cortex compression or dilation is possible in response to acting forces at sufficiently fast timescales. This finding has important implications for the parameterization in active gel theories that describe actin cytoskeletal dynamics.

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

Tissue Regeneration from Mechanical Stretching of Cell-Cell Adhesion

Cell-cell adhesion complexes are macromolecular adhesive organelles that integrate cells into tissues. This mechanochemical coupling in cell-cell adhesion is required for a large number of cell behaviors, and perturbations of the cell-cell adhesion structure or related mechanotransduction pathways can lead to critical pathological conditions such as skin and heart diseases, arthritis, and cancer. Mechanical stretching has been a widely used method to stimulate the mechanotransduction process originating from the cell-cell adhesion and cell-extracellular matrix (ECM) complexes. These studies aimed to reveal the biophysical processes governing cell proliferation, wound healing, gene expression regulation, and cell differentiation in various tissues, including cardiac, muscle, vascular, and bone. This review explores techniques in mechanical stretching in two-dimensional settings with different stretching regimens on different cell types. The mechanotransduction responses from these different cell types will be discussed with an emphasis on their biophysical transformations during mechanical stretching and the cross talk between the cell-cell and cell-ECM adhesion complexes. Therapeutic aspects of mechanical stretching are reviewed considering these cellular responses after the application of mechanical forces, with a focus on wound healing and tissue regeneration. Impact Statement Mechanical stretching has been proposed as a therapeutic option for tissue regeneration and wound healing. It has been accepted that mechanotransduction processes elicited by mechanical stretching govern cellular response and behavior, and these studies have predominantly focused on the cell-extracellular matrix (ECM) sites. This review serves the mechanobiology community by shifting the focus of mechanical stretching effects from cell-ECM adhesions to the less examined cell-cell adhesions, which we believe play an equally important role in orchestrating the response pathways.

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.

Rheology of active polar emulsions: from linear to unidirectional and inviscid flow, and intermittent viscosity

The rheological behaviour of an emulsion made of an active polar component and an isotropic passive fluid is studied by lattice Boltzmann methods. Different flow regimes are found by varying the values of the shear rate and extensile activity (occurring, e.g., in microtubule-motor suspensions). By increasing the activity, a first transition occurs from the linear flow regime to spontaneous persistent unidirectional macro-scale flow, followed by another transition either to a (low shear) intermittent flow regime with the coexistence of states with positive, negative, and vanishing apparent viscosity, or to a (high shear) symmetric shear thinning regime. The different behaviours can be explained in terms of the dynamics of the polarization field close to the walls. A maximum entropy production principle selects the most likely states in the intermittent regime.

Tensile Forces and Mechanotransduction at Cell-Cell Junctions

Cell-cell junctions are specializations of the plasma membrane responsible for physically integrating cells into tissues. We are now beginning to appreciate the diverse impacts that mechanical forces exert upon the integrity and function of these junctions. Currently, this is best understood for cadherin-based adherens junctions in epithelia and endothelia, where cell-cell adhesion couples the contractile cytoskeletons of cells together to generate tissue-scale tension. Junctional tension participates in morphogenesis and tissue homeostasis. Changes in tension can also be detected by mechanotransduction pathways that allow cells to communicate with each other. In this review, we discuss progress in characterising the forces present at junctions in physiological conditions; the cellular mechanisms that generate intrinsic tension and detect changes in tension; and, finally, we consider how tissue integrity is maintained in the face of junctional stresses.

Active poroelastic two-phase model for the motion of physarum microplasmodia

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 μm. Both predictions are in line with recent experimental observations.

Cell spread area and traction forces determine myosin-II-based cortex thickness regulation

Actomyosin network under the plasma membrane of cells forms a cortical layer that regulates cellular deformations during different processes. What regulates the cortex? Characterized by its thickness, it is believed to be regulated by actin dynamics, filament-length regulators and myosin motor proteins. However, its regulation by cellular morphology (e.g. cell spread area) or mechanical microenvironment (e.g. substrate stiffness) has remained largely unexplored. In this study, super- and high-resolution imaging of actin in CHO cells demonstrates that at high spread areas (>450 μm²), the cortex is thinner, better separated as layers, and sensitive to deactivation of myosin II motors or reduction of substrate stiffness (and traction forces). In less spread cells (<400 μm²) such perturbations do not elicit a response. Myosin IIA's mechanosensing is limited here due to its lowered actin-bound fraction and higher turnover rate. Cofilin, in line with its competitive inhibitory role, is found to be overexpressed in these cells. To establish the causal relation, we initiate a spread area drop by de-adhesion and find enhanced actin dynamics and fragmentation along with oscillations and increase in thickness. This is more correlated to the reduction of traction forces than the endocytosis-based reduction in cell volume. Cortex thickness control by spread area is also found be true during differentiation of THP-1 monocytes to macrophages. Thus, we propose that spread area regulates cortex and its thickness by traction-based mechanosensing of myosin II.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.

Functional Epithelium Remodeling in Response to Applied Stress under In Vitro Conditions

Mathematical modeling is often used in tissue engineering in order to overcome one of its major challenges: transformation of complex biological and rheological behaviors of cells and tissue in a mathematically predictive and physically manipulative engineering process. The successive accomplishment of this task will greatly help in quantifying and optimizing clinical application of the tissue engineering products. One of the problems emerging in this area is the relation between resting and migrating cell groups, as well as between different configurations of migrating cells and viscoelasticity. A deeper comprehension of the relation between various configurations of migrating cells and viscoelasticity at the supracellular level represents the prerequisite for optimization of the performance of the artificial epithelium. Since resting and migrating cell groups have a considerable difference in stiffness, a change in their mutual volume ratio and distribution may affect the viscoelasticity of multicellular surfaces. If those cell groups are treated as different phases, then an analogous model may be applied to represent such systems. In this work, a two-step Eyring model is developed in order to demonstrate the main mechanical and biochemical factors that influence configurations of migrating cells. This model could be also used for considering the long-time cell rearrangement under various types of applied stress. The results of this theoretical analysis point out the cause-consequence relationship between the configuration of migrating cells and rheological behavior of multicellular surfaces. Configuration of migrating cells is influenced by mechanical and biochemical perturbations, difficult to measure experimentally, which lead to uncorrelated motility. Uncorrelated motility results in (1) decrease of the volume fraction of migrating cells, (2) change of their configuration, and (3) softening of multicellular surfaces.

Bulk Actin Dynamics Drive Phase Segregation in Zebrafish Oocytes

Segregation of maternal determinants within the oocyte constitutes the first step in embryo patterning. In zebrafish oocytes, extensive ooplasmic streaming leads to the segregation of ooplasm from yolk granules along the animal-vegetal axis of the oocyte. Here, we show that this process does not rely on cortical actin reorganization, as previously thought, but instead on a cell-cycle-dependent bulk actin polymerization wave traveling from the animal to the vegetal pole of the oocyte. This wave functions in segregation by both pulling ooplasm animally and pushing yolk granules vegetally. Using biophysical experimentation and theory, we show that ooplasm pulling is mediated by bulk actin network flows exerting friction forces on the ooplasm, while yolk granule pushing is achieved by a mechanism closely resembling actin comet formation on yolk granules. Our study defines a novel role of cell-cycle-controlled bulk actin polymerization waves in oocyte polarization via ooplasmic segregation.

Entropic Forces Drive Cellular Contact Guidance

Contact guidance-the widely known phenomenon of cell alignment induced by anisotropic environmental features-is an essential step in the organization of adherent cells, but the mechanisms by which cells achieve this orientational ordering remain unclear. Here, we seeded myofibroblasts on substrates micropatterned with stripes of fibronectin and observed that contact guidance emerges at stripe widths much greater than the cell size. To understand the origins of this surprising observation, we combined morphometric analysis of cells and their subcellular components with a, to our knowledge, novel statistical framework for modeling nonthermal fluctuations of living cells. This modeling framework is shown to predict not only the trends but also the statistical variability of a wide range of biological observables, including cell (and nucleus) shapes, sizes, and orientations, as well as stress-fiber arrangements within the cells with remarkable fidelity with a single set of cell parameters. By comparing observations and theory, we identified two regimes of contact guidance: 1) guidance on stripe widths smaller than the cell size (w ≤ 160 μm), which is accompanied by biochemical changes within the cells, including increasing stress-fiber polarization and cell elongation; and 2) entropic guidance on larger stripe widths, which is governed by fluctuations in the cell morphology. Overall, our findings suggest an entropy-mediated mechanism for contact guidance associated with the tendency of cells to maximize their morphological entropy through shape fluctuations.

From cell shape to cell fate via the cytoskeleton - Insights from the epidermis

Animal cells exhibit a wide range of shapes that reflect their diverse functions. Cell shape is determined by a balance between internal and external forces and therefore involves the cytoskeleton and its associated adhesion structures. Cell shape dynamics during development and homeostasis are tightly regulated and closely coordinated with cell fate determination. Defects in cell shape are a hallmark of many pathological conditions including cancer and skin diseases. This review highlights the links between cell shape and cell fate in the epidermis, which have been studied for over 40 years both in vitro and in vivo. Briefly discussing seminal experiments showing the strong coupling between keratinocyte cell shape and their fate we primarily focus on recent studies uncovering novel cellular and molecular mechanisms linking epidermal cell shape with cell growth, differentiation, asymmetric division, and delamination.

Stress-dependent amplification of active forces in nonlinear elastic media

The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a continuum elastic medium prone to buckling subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium. Inserting these relations into popular "active gel" descriptions of living tissues and the cytoskeleton will enable investigations into nonlinear regimes previously inaccessible due to the phenomenological nature of these theories.

Increasing complexity: Mechanical guidance and feedback loops as a basis for self-organization in morphogenesis

The article is devoted to physical views on embryo development as a combination of structurally stable dynamics and symmetry-breaking events in the general process of self-organization. The first corresponds to the deterministic aspect of embryo development. The second type of processes is associated with sudden increase of variability in the periods of symmetry-breaking, which manifests unstable dynamics. The biological basis under these considerations includes chemokinetics (a system of inductors, repressors, and interaction with their next surrounding) and morphomechanics (i.e. mechanotransduction, mechanosensing, and related feedback loops). Although the latter research area is evolving rapidly, up to this time the role of mechanical properties of embryonic tissues and mechano-dependent processes in them are integrated in the general picture of embryo development to a lesser extent than biochemical signaling. For this reason, the present article is mostly devoted to experimental data on morphomechanics in the process of embryo development, also including analysis of its limitations and possible contradictions. The general system of feedback-loops and system dynamics delineated in this review is in large part a repetition of the views of Lev Beloussov, who was one of the founders of the whole areas of morphomechanics and morphodynamics, and to whose memory this article is dedicated.

Getting in shape and swimming: the role of cortical forces and membrane heterogeneity in eukaryotic cells

Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves-crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highly-simplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to a number of different characteristic cell shapes, and our first objective is to understand how different distributions of membrane tension influence the shape of cells in an inviscid quiescent fluid. We then analyze the effects of spatial variation in other membrane properties, and how they interact with tension gradients to determine the shape. We also study the effect of fluid-cell interactions and show how tension leads to cell movement, how the balance between tension gradients and a variable bending modulus determine the shape and direction of movement, and how the efficiency of movement depends on the properties of the fluid and the distribution of tension and bending modulus in the membrane.

On the relation between filament density, force generation, and protrusion rate in mesenchymal cell motility

Lamellipodia are flat membrane protrusions formed during mesenchymal motion. Polymerization at the leading edge assembles the actin filament network and generates protrusion force. How this force is supported by the network and how the assembly rate is shared between protrusion and network retrograde flow determines the protrusion rate. We use mathematical modeling to understand experiments changing the F-actin density in lamellipodia of B16-F1 melanoma cells by modulation of Arp2/3 complex activity or knockout of the formins FMNL2 and FMNL3. Cells respond to a reduction of density with a decrease of protrusion velocity, an increase in the ratio of force to filament number, but constant network assembly rate. The relation between protrusion force and tension gradient in the F-actin network and the density dependency of friction, elasticity, and viscosity of the network explain the experimental observations. The formins act as filament nucleators and elongators with differential rates. Modulation of their activity suggests an effect on network assembly rate. Contrary to these expectations, the effect of changes in elongator composition is much weaker than the consequences of the density change. We conclude that the force acting on the leading edge membrane is the force required to drive F-actin network retrograde flow.

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration - Multi-scale modeling considerations

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration depends on: (1) the volume fraction and configuration of migrating cells and the rate of its change, (2) the viscoelasticity of migrating cell groups, and (3) the viscoelasticity of surrounding resting cells. The key parameter that influences the viscoelasticity is the size, shape, and thickness of the biointerface between migrating and resting cell sub-populations. The multi-scale nature of the biointerface dynamics represents the product of: (1) the local changes of the size and shape of migrating cell groups, (2) the local accumulation of resistance stress within the core regions of migrating cell groups (internal effects), (3) the collision of the velocity fronts (external effects). The local changes of the size and shape of migrating cell groups induces additional energy dissipation. The accumulated stress could induce disordering of migrating cell groups and consequently migrating-to-resting cell state transition. The collision of the velocity fronts could lead to stagnant zone formation and local increase of the volume fraction of resting cells. Herein, an attempt is made to discuss and connect various modeling approaches from the stand point of thermodynamics and rheology obtained at: (1) cellular level, (2) biointerface between migrating cell group and surrounding resting cells, and (3) a part of multicellular surfaces. These complex phenomena are discussed on the model system such as cell aggregate rounding after uni-axial compression under in vitro conditions at characteristic times such as: (1) cell shape relaxation time under stretching/compression, (2) contact time between migrating cell group and surrounding resting cells, (3) cell persistence time, (4) the lifetime of migrating cell groups, (5) cell rearrangement time (i.e. the process time), and (6) the stress and strain relaxation times of perturbed multicellular surface parts. The results of this theoretical analysis point to the relationship between interfacial size, mechanical coupling mode and rheological behavior of multicellular surfaces. Multi scale dynamics at the biointerface is a key parameter which influences mechanical behavior of multicellular surfaces. Consequently, the shape of migrating cell groups and their distribution are not random characteristics of the multicellular surface but rather influenced by cause-consequence relations between biochemical processes at the cellular level and surface stiffness distribution at the mesoscopic level.

pH-Triggered self-assembly and hydrogelation of cyclic peptide nanotubes confined in water micro-droplets

The controlled one-dimensional supramolecular polymerization of synthetic building blocks in confined spaces constitutes a key challenge to simplify the understanding of the fundamental physical principles behind the behavior of more complex encapsulated polymer networks. Cyclic peptide nanotubes constitute an optimal scaffold for the fabrication of hierarchical one-dimensional self-assembled architectures. Herein we report the pH-controlled nanotube formation and fibrillation of supramolecular cyclic peptides in confined aqueous droplets. The externally triggered self-assembly of these peptides gave rise to viscoelastic hydrogels in which the one-dimensional molecular arrangement was perfectly preserved from the nano- to the micro-scale. The cyclic peptide building blocks were confined inside water microdroplets and the base-triggered supramolecular polymerization was externally triggered and followed by confocal microscopy showing that the confined fibrillation spanned and affected the shape of the droplet micro container.

Transient response of nonlinear polymer networks: A kinetic theory

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Maximal Fluctuations of Confined Actomyosin Gels: Dynamics of the Cell Nucleus

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in nonequilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus, and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)PNASA60027-842410.1073/pnas.1513189113].

Topological Edge Floppy Modes in Disordered Fiber Networks

Disordered fiber networks are ubiquitous in a broad range of natural (e.g., cytoskeleton) and manmade (e.g., aerogels) materials. In this Letter, we discuss the emergence of topological floppy edge modes in two-dimensional fiber networks as a result of deformation or active driving. It is known that a network of straight fibers exhibits bulk floppy modes which only bend the fibers without stretching them. We find that, interestingly, with a perturbation in geometry, these bulk modes evolve into edge modes. We introduce a topological index for these edge modes and discuss their implications in biology.

Dynamically generated patterns in dense suspensions of active filaments

We use Langevin dynamics simulations to study dynamical behavior of a dense planar layer of active semiflexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several nonequilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that, for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterized by strong density fluctuations. Furthermore, we identify an activity-driven crossover from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analog in systems of active particles without internal degrees of freedom.

Excess area dependent scaling behavior of nano-sized membrane tethers

Thermal fluctuations in cell membranes manifest as an excess area ([Formula: see text]) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate [Formula: see text] in live cells. We perform our simulations in two different thermodynamic ensembles: (i) the constant projected area and (ii) the constant frame tension ensembles and show the equivalence of our results in the two. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations performed in the initial tether formation regime (i.e. when the length of the tether is comparable to its radius) along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness κ, and membrane tension σ. We show that [Formula: see text] is an important determinant of the radius of the extracted tether, which is equal to the characteristic length [Formula: see text] for [Formula: see text], and is equal to [Formula: see text] for [Formula: see text]. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of [Formula: see text] for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.