Machine learning interpretable models of cell mechanics from protein images.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.

Forcing cells into shape: the mechanics of actomyosin contractility.

Actomyosin-mediated contractility is a highly conserved mechanism for generating mechanical stress in animal cells and underlies muscle contraction, cell migration, cell division and tissue morphogenesis. Whereas actomyosin-mediated contractility in striated muscle is well understood, the regulation of such contractility in non-muscle and smooth muscle cells is less certain. Our increased understanding of the mechanics of actomyosin arrays that lack sarcomeric organization has revealed novel modes of regulation and force transmission. This work also provides an example of how diverse mechanical behaviours at cellular scales can arise from common molecular components, underscoring the need for experiments and theories to bridge the molecular to cellular length scales.

Learning to learn by using nonequilibrium training protocols for adaptable materials.

Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.

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.

Cracked actin filaments as mechanosensitive receptors.

Actin filament networks are exposed to mechanical stimuli, but the effect of strain on actin filament structure has not been well established in molecular detail. This is a critical gap in understanding because the activity of a variety of actin-binding proteins has recently been determined to be altered by actin filament strain. We therefore used all-atom molecular dynamics simulations to apply tensile strains to actin filaments and find that changes in actin subunit organization are minimal in mechanically strained, but intact, actin filaments. However, a conformational change disrupts the critical D-loop to W-loop connection between longitudinal neighboring subunits, which leads to a metastable cracked conformation of the actin filament whereby one protofilament is broken prior to filament severing. We propose that the metastable crack presents a force-activated binding site for actin regulatory factors that specifically associate with strained actin filaments. Through protein-protein docking simulations, we find that 43 evolutionarily diverse members of the dual zinc-finger-containing LIM-domain family, which localize to mechanically strained actin filaments, recognize two binding sites exposed at the cracked interface. Furthermore, through its interactions with the crack, LIM domains increase the length of time damaged filaments remain stable. Our findings propose a new molecular model for mechanosensitive binding to actin filaments.

Limiting pool and actin architecture controls myosin cluster sizes in adherent cells.

The actomyosin cytoskeleton generates mechanical forces that power important cellular processes, such as cell migration, cell division, and mechanosensing. Actomyosin self-assembles into contractile networks and bundles that underlie force generation and transmission in cells. A central step is the assembly of the myosin II filament from myosin monomers, regulation of which has been extensively studied. However, myosin filaments are almost always found as clusters within the cell cortex. While recent studies characterized cluster nucleation dynamics at the cell periphery, how myosin clusters grow on stress fibers remains poorly characterized. Here, we utilize a U2OS osteosarcoma cell line with endogenously tagged myosin II to measure the myosin cluster size distribution in the lamella of adherent cells. We find that myosin clusters can grow with Rho-kinase (ROCK) activity alone in the absence of myosin motor activity. Time-lapse imaging reveals that myosin clusters grow via increased myosin association to existing clusters, which is potentiated by ROCK-dependent myosin filament assembly. Enabling myosin motor activity allows further myosin cluster growth through myosin association that is dependent on F-actin architecture. Using a toy model, we show that myosin self-affinity is sufficient to recapitulate the experimentally observed myosin cluster size distribution, and that myosin cluster sizes are determined by the pool of myosin available for cluster growth. Together, our findings provide new insights into the regulation of myosin cluster sizes within the lamellar actomyosin cytoskeleton.

Highly flexible PEG-LifeAct constructs act as tunable biomimetic actin crosslinkers.

In vitro studies of actin filament networks crosslinked with dynamic actin binding proteins provide critical insights into cytoskeletal mechanics as well as inspiration for new adaptive materials design. However, discontinuous variance in the physiochemical properties of actin binding proteins impedes holistic relationships between crosslinker molecular parameters, network structure, and mechanics. Bio-synthetic constructs composed of synthetic polymer backbones and actin binding motifs would enable crosslinkers with engineered physiochemical properties to directly target the desired structure-property relationships. As a proof of concept, bio-synthetic crosslinkers composed of highly flexible polyethylene glycol (PEG) polymers functionalized with the actin binding peptide LifeAct, are explored as actin crosslinkers. Using bulk rheology and fluorescence microscopy, these constructs are shown to modulate actin filament network structure and mechanics in a contour length dependent manner, while maintaining the stress-stiffening behavior inherent to actin filament networks. These results encourage the design of more diverse and complex peptide-polymer crosslinkers to interrogate and control semi-flexible polymer networks.

Motor crosslinking augments elasticity in active nematics.

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Mechanical integration of actin and adhesion dynamics in cell migration.

Directed cell migration is a physical process that requires dramatic changes in cell shape and adhesion to the extracellular matrix. For efficient movement, these processes must be spatiotemporally coordinated. To a large degree, the morphological changes and physical forces that occur during migration are generated by a dynamic filamentous actin (F-actin) cytoskeleton. Adhesion is regulated by dynamic assemblies of structural and signaling proteins that couple the F-actin cytoskeleton to the extracellular matrix. Here, we review current knowledge of the dynamic organization of the F-actin cytoskeleton in cell migration and the regulation of focal adhesion assembly and disassembly with an emphasis on how mechanical and biochemical signaling between these two systems regulate the coordination of physical processes in cell migration.

Cell cycle-dependent active stress drives epithelia remodeling.

Epithelia have distinct cellular architectures which are established in development, reestablished after wounding, and maintained during tissue homeostasis despite cell turnover and mechanical perturbations. In turn, cell shape also controls tissue function as a regulator of cell differentiation, proliferation, and motility. Here, we investigate cell shape changes in a model epithelial monolayer. After the onset of confluence, cells continue to proliferate and change shape over time, eventually leading to a final architecture characterized by arrested motion and more regular cell shapes. Such monolayer remodeling is robust, with qualitatively similar evolution in cell shape and dynamics observed across disparate perturbations. Here, we quantify differences in monolayer remodeling guided by the active vertex model to identify underlying order parameters controlling epithelial architecture. When monolayers are formed atop an extracellular matrix with varied stiffness, we find the cell density at which motion arrests varies significantly, but the cell shape remains constant, consistent with the onset of tissue rigidity. In contrast, pharmacological perturbations can significantly alter the cell shape at which tissue dynamics are arrested, consistent with varied amounts of active stress within the tissue. Across all experimental conditions, the final cell shape is well correlated to the cell proliferation rate, and cell cycle inhibition immediately arrests cell motility. Finally, we demonstrate cell cycle variation in junctional tension as a source of active stress within the monolayer. Thus, the architecture and mechanics of epithelial tissue can arise from an interplay between cell mechanics and stresses arising from cell cycle dynamics.

Machine learning active-nematic hydrodynamics.

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Evolutionarily diverse LIM domain-containing proteins bind stressed actin filaments through a conserved mechanism.

The actin cytoskeleton assembles into diverse load-bearing networks, including stress fibers (SFs), muscle sarcomeres, and the cytokinetic ring to both generate and sense mechanical forces. The LIM (Lin11, Isl- 1, and Mec-3) domain family is functionally diverse, but most members can associate with the actin cytoskeleton with apparent force sensitivity. Zyxin rapidly localizes via its LIM domains to failing SFs in cells, known as strain sites, to initiate SF repair and maintain mechanical homeostasis. The mechanism by which these LIM domains associate with stress fiber strain sites (SFSS) is not known. Additionally, it is unknown how widespread strain sensing is within the LIM protein family. We identify that the LIM domain-containing region of 18 proteins from the Zyxin, Paxillin, Tes, and Enigma proteins accumulate to SFSS. Moreover, the LIM domain region from the fission yeast protein paxillin like 1 (Pxl1) also localizes to SFSS in mammalian cells, suggesting that the strain sensing mechanism is ancient and highly conserved. We then used sequence and domain analysis to demonstrate that tandem LIM domains contribute additively, for SFSS localization. Employing in vitro reconstitution, we show that the LIM domain-containing region from mammalian zyxin and fission yeast Pxl1 binds to mechanically stressed F-actin networks but does not associate with relaxed actin filaments. We propose that tandem LIM domains recognize an F-actin conformation that is rare in the relaxed state but is enriched in the presence of mechanical stress.

High throughput discovery of functional protein modifications by Hotspot Thermal Profiling.

Mass spectrometry enables global analysis of posttranslationally modified proteoforms from biological samples, yet we still lack methods to systematically predict, or even prioritize, which modification sites may perturb protein function. Here we describe a proteomic method, Hotspot Thermal Profiling, to detect the effects of site-specific protein phosphorylation on the thermal stability of thousands of native proteins in live cells. This massively parallel biophysical assay unveiled shifts in overall protein stability in response to site-specific phosphorylation sites, as well as trends related to protein function and structure. This method can detect intrinsic changes to protein structure as well as extrinsic changes to protein-protein and protein-metabolite interactions resulting from phosphorylation. Finally, we show that functional 'hotspot' protein modification sites can be discovered and prioritized for study in a high-throughput and unbiased fashion. This approach is applicable to diverse organisms, cell types and posttranslational modifications.

Spatiotemporal control of liquid crystal structure and dynamics through activity patterning.

Active materials are capable of converting free energy into mechanical work to produce autonomous motion, and exhibit striking collective dynamics that biology relies on for essential functions. Controlling those dynamics and transport in synthetic systems has been particularly challenging. Here, we introduce the concept of spatially structured activity as a means of controlling and manipulating transport in active nematic liquid crystals consisting of actin filaments and light-sensitive myosin motors. Simulations and experiments are used to demonstrate that topological defects can be generated at will and then constrained to move along specified trajectories by inducing local stresses in an otherwise passive material. These results provide a foundation for the design of autonomous and reconfigurable microfluidic systems where transport is controlled by modulating activity with light.

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.

Self-organizing motors divide active liquid droplets.

The cytoskeleton is a collection of protein assemblies that dynamically impose spatial structure in cells and coordinate processes such as cell division and mechanical regulation. Biopolymer filaments, cross-linking proteins, and enzymatically active motor proteins collectively self-organize into various precise cytoskeletal assemblies critical for specific biological functions. An outstanding question is how the precise spatial organization arises from the component macromolecules. We develop a system to investigate simple physical mechanisms of self-organization in biological assemblies. Using a minimal set of purified proteins, we create droplets of cross-linked biopolymer filaments. Through the addition of enzymatically active motor proteins, we construct composite assemblies, evocative of cellular structures such as spindles, where the inherent anisotropy drives motor self-organization, droplet deformation, and division into two droplets. These results suggest that simple physical principles underlie self-organization in complex biological assemblies and inform bioinspired materials design.

Cofilin drives rapid turnover and fluidization of entangled F-actin.

The shape of most animal cells is controlled by the actin cortex, a thin network of dynamic actin filaments (F-actin) situated just beneath the plasma membrane. The cortex is held far from equilibrium by both active stresses and polymer turnover: Molecular motors drive deformations required for cell morphogenesis, while actin-filament disassembly dynamics relax stress and facilitate cortical remodeling. While many aspects of actin-cortex mechanics are well characterized, a mechanistic understanding of how nonequilibrium actin turnover contributes to stress relaxation is still lacking. To address this, we developed a reconstituted in vitro system of entangled F-actin, wherein the steady-state length and turnover rate of F-actin are controlled by the actin regulatory proteins cofilin, profilin, and formin, which sever, recycle, and assemble filaments, respectively. Cofilin-mediated severing accelerates the turnover and spatial reorganization of F-actin, without significant changes to filament length. We demonstrate that cofilin-mediated severing is a single-timescale mode of stress relaxation that tunes the low-frequency viscosity over two orders of magnitude. These findings serve as the foundation for understanding the mechanics of more physiological F-actin networks with turnover and inform an updated microscopic model of single-filament turnover. They also demonstrate that polymer activity, in the form of ATP hydrolysis on F-actin coupled to nucleotide-dependent cofilin binding, is sufficient to generate a form of active matter wherein asymmetric filament disassembly preserves filament number despite sustained severing.

Actin bundle architecture and mechanics regulate myosin II force generation.

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

Actin filament alignment causes mechanical hysteresis in cross-linked networks.

Cells dynamically control their material properties through remodeling of the actin cytoskeleton, an assembly of cross-linked networks and bundles formed from the biopolymer actin. We recently found that cross-linked networks of actin filaments reconstituted in vitro can exhibit adaptive behavior and thus serve as a model system to understand the underlying mechanisms of mechanical adaptation of the cytoskeleton. In these networks, training, in the form of applied shear stress, can induce asymmetry in the nonlinear elasticity. Here, we explore control over this mechanical hysteresis by tuning the concentration and mechanical properties of cross-linking proteins in both experimental and simulated networks. We find that this effect depends on two conditions: the initial network must exhibit nonlinear strain stiffening, and filaments in the network must be able to reorient during training. Hysteresis depends strongly and non-monotonically on cross-linker concentration, with a peak at moderate concentrations. In contrast, at low concentrations, where the network does not strain stiffen, or at high concentrations, where filaments are less able to rearrange, there is little response to training. Additionally, we investigate the effect of changing cross-linker properties and find that longer or more flexible cross-linkers enhance hysteresis. Remarkably plotting hysteresis against alignment after training yields a single curve regardless of the physical properties or concentration of the cross-linkers.

Interplay of structure, elasticity, and dynamics in actin-based nematic materials.

Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with [Formula: see text] topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U shape into a V shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal's elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.