Actin dynamics: from nanoscale to microscale

Calponin-homology domain of GAS2L1 promotes formation of stress fibers and focal adhesions

Growth arrest-specific 2-like 1 protein (GAS2L1) binds both actin and microtubules through its unique structural domains: a calponin-homology (CH) domain for actin binding and a GAS2-related (GAR) domain for microtubule interaction. In this study, we demonstrate that GAS2L1 promotes stress fiber assembly, enhances focal adhesion formation, and stabilizes cytoskeletal networks against mechanical perturbation through its CH domain. Remarkably, we show that the CH domain dimerizes and induces actin filament bundling and stabilization both in cells and in vitro. The CH and GAR domains interact to form an autoinhibitory module, wherein the GAR domain suppresses CH domain dimerization and actin-bundling activity. Our findings provide novel insights into the regulatory mechanisms of GAS2L1's autoinhibition and identify the CH domain as a critical actin-bundling factor that contributes to the organization of stress fibers and focal adhesions.

Macroscopic creep behavior of spheroids derived from mesenchymal stem cells under compression

Spheroid culture, where cells are aggregated three-dimensionally, is expected to have applications as a model that better recapitulates invivo environment beyond two-dimensional environments. When human mesenchymal stem cells are subjected to spheroid culture in the presence of osteogenesis supplements, the gene expression of osteocyte differentiation marker is greatly increased within a short period compared to two-dimensional culture. However, how such alterations may be reflected to mechanical properties of the spheroid remains unknown. In this study, using a uniaxial compression system, we evaluated the macroscopic mechanical properties of human mesenchymal stem cell-derived spheroids including viscoelastic behavior. The Young's modulus of spheroids cultured for 2 days was about 18 kPa, whereas that of individual cells is around 1-10 kPa. We also found that creep behavior of the spheroid was greater in 50% strain compression beyond 10 or 30% strain, indicating that they are viscoelastic materials. Upon release from compression, the spheroids tended to revert to their original shape through elastic deformation. However, spheroids in which actin filament formation was inhibited exhibited a remarkably greater plastic deformation, suggesting that the actin filaments play a crucial role in the elastic behavior of spheroids. By understanding the mechanical properties and behavior of spheroids, it provides a framework for predicting and manipulating the development of tissues and organs in the field of morphogenesis.

Cytoskeleton adaptation to stretchable surface relaxation improves adherent cryopreservation of human mesenchymal stem cells

Adherent cell systems are usually dissociated before being cryopreserved, as standard protocols are established for cells in suspension. The application of standard procedures to more complex systems, sensitive to dissociation, such as adherent monolayers, especially comprising mature cell types or tissues remains unsatisfactory. Uncontrolled cell detachment due to intracellular tensile stress, membrane ruptures and damages of adhesion proteins are common during freezing and thawing of cell monolayers. However, many therapeutically relevant cell systems grow adherently to develop their native morphology and functionality, but lose their integrity after dissociation. The hypothesis is that cells on stretchable substrates have a more adaptable cytoskeleton and membrane, reducing cryopreservation-induced stress. Our studies investigate the influence of stretchable surfaces on the cryopreservation of adherent cells to avoid harmful dissociation and expedite post-thawing cultivation of functional cells. A stretching apparatus for defined radial stretching, consisting of silicone vessels and films with specific surface textures for cell culture, was developed. Adherent human umbilical cord mesenchymal stem cells (hUC-MSCs) were cultivated on a stretched silicone film within the vessel, forming a monolayer that was compressed by relaxation, while remaining attached to the relaxed film. Compressed hUC-MSCs, which were cryopreserved adherently showed higher viability and less detachment after thawing compared to control cells without compression. Within three to seven days post-thawing, the hUC-MSCs recovered, and the monolayer reformed. These experiments support the hypothesis that cryopreservation success of adherent cell systems is enhanced by improved adaptability of the cytoskeleton and cell membrane, opening up new approaches in cryobiotechnology.

A continuum mechanical model of cell motion driven by a biphasic traction stress

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel et al. (Gardel et al. 2008 J. Cell Biol. 183, 999-1005 (doi:10.1083/jcb.200810060)), include a biphasic velocity-dependent traction stress acting on the actin network. While we chose certain specific models for each of these, in part to allow for an analytical solution, the generality of the framework allows one to readily introduce different constitutive laws to describe these phenomena as might be needed, for example, to study some different type of cells. As described in §5, the predictions of the model compare well with observations such as the magnitude of the very different actin retrograde speeds in the lamellum and lamellipodium including their jump at the interface, the magnitude of the cell speed, and the relative lengths of the lamellipodium and lamellum.

Reconstitution of actin-based cellular processes: Why encapsulation changes the rules

While in vitro reconstitution of cellular processes is progressing rapidly, the encapsulation of biomimetic systems to reproduce the cellular environment is a major challenge. Here we review the difficulties, using reconstitution of processes dependent on actin polymerization as an example. Some of the problems are purely technical, due to the need for engineering strategies to encapsulate concentrated solutions in micrometer-sized compartments. However, other significant issues arise from the reduction of experimental volumes, which alters the chemical evolution of these non-equilibrium systems. Important parameters to consider for successful reconstitutions are the amount of each component, their consumption and renewal rates to guarantee their continuous availability.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

The nonlinear motion of cells subject to external forces

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop.

Uncovering the universality of self-replication in protein aggregation and its link to disease

Fibrillar protein aggregates are a hallmark of a range of human disorders, from prion diseases to dementias, but are also encountered in several functional contexts. Yet, the fundamental links between protein assembly mechanisms and their functional or pathological roles have remained elusive. Here, we analyze the aggregation kinetics of a large set of proteins that self-assemble by a nucleated-growth mechanism, from those associated with disease, over those whose aggregates fulfill functional roles in biology, to those that aggregate only under artificial conditions. We find that, essentially, all such systems, regardless of their biological role, are capable of self-replication. However, for aggregates that have evolved to fulfill a structural role, the rate of self-replication is too low to be significant on the biologically relevant time scale. By contrast, all disease-related proteins are able to self-replicate quickly compared to the time scale of the associated disease. Our findings establish the ubiquity of self-replication and point to its potential importance across aggregation-related disorders.

A mechanism with severing near barbed ends andannealing explains structure and dynamics of dendriticactin networks

Single molecule imaging has shown that part of actin disassembles within a few seconds after incorporation into the dendritic filament network in lamellipodia, suggestive of frequent destabilization near barbed ends. To investigate the mechanisms behind network remodeling, we created a stochastic model with polymerization, depolymerization, branching, capping, uncapping, severing, oligomer diffusion, annealing, and debranching. We find that filament severing, enhanced near barbed ends, can explain the single molecule actin lifetime distribution, if oligomer fragments reanneal to free ends with rate constants comparable to in vitro measurements. The same mechanism leads to actin networks consistent with measured filament, end, and branch concentrations. These networks undergo structural remodeling, leading to longer filaments away from the leading edge, at the +/- 35𝑜 orientation pattern. Imaging of actin speckle lifetimes at sub-second resolution verifies frequent disassembly of newly-assembled actin. We thus propose a unified mechanism that fits a diverse set of basic lamellipodia phenomenology.

Fluid shear stress-induced mechanotransduction in myoblasts: Does it depend on the glycocalyx?

Muscle stem cells (MuSCs) are involved in muscle maintenance and regeneration. Mechanically loaded MuSCs within their native niche undergo tensile and shear deformations, but how MuSCs sense mechanical stimuli and translate these into biochemical signals regulating function and fate is still poorly understood. We aimed to investigate whether the glycocalyx is involved in the MuSC mechanoresponse, and whether MuSC morphology affects mechanical loading-induced pressure, shear stress, and fluid velocity distribution. FSS-induced deformation of active proliferating MuSCs (myoblasts) with intact or degraded glycocalyx was assessed by live-cell imaging. Glycocalyx-degradation did not significantly affect nitric oxide production, but reduced FSS-induced myoblast deformation and modulated gene expression. Finite-element analysis revealed that the distribution of FSS-induced pressure, shear stress, and fluid velocity on myoblasts was non-uniform, and the magnitude depended on myoblast morphology and apex-height. In conclusion, our results suggest that the glycocalyx does not play a role in NO production in myoblasts but might impact mechanotransduction and gene expression, which needs further investigation. Future studies will unravel the underlying mechanism by which the glycocalyx affects FSS-induced myoblast deformation, which might be related to increased drag forces. Moreover, MuSCs with varying apex-height experience different levels of FSS-induced pressure, shear stress, and fluid velocity, suggesting differential responsiveness to fluid shear forces.

Actin Dynamics as a Multiscale Integrator of Cellular Guidance Cues

Migrating cells must integrate multiple, competing external guidance cues. However, it is not well understood how cells prioritize among these cues. We investigate external cue integration by monitoring the response of wave-like, actin-polymerization dynamics, the driver of cell motility, to combinations of nanotopographies and electric fields in neutrophil-like cells. The electric fields provide a global guidance cue, and approximate conditions at wound sites in vivo. The nanotopographies have dimensions similar to those of collagen fibers, and act as a local esotactic guidance cue. We find that cells prioritize guidance cues, with electric fields dominating long-term motility by introducing a unidirectional bias in the locations at which actin waves nucleate. That bias competes successfully with the wave guidance provided by the bidirectional nanotopographies.

A coarse-grained approach to model the dynamics of the actomyosin cortex

Background

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions.

Results

Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin.

Conclusions

We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-022-01279-2).

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Nuclear Actin Dynamics in Gene Expression, DNA Repair, and Cancer

Actin is a highly conserved protein in mammals. The actin dynamics is regulated by actin-binding proteins and actin-related proteins. Nuclear actin and these regulatory proteins participate in multiple nuclear processes, including chromosome architecture organization, chromatin remodeling, transcription machinery regulation, and DNA repair. It is well known that the dysfunctions of these processes contribute to the development of cancer. Moreover, emerging evidence has shown that the deregulated actin dynamics is also related to cancer. This chapter discusses how the deregulation of nuclear actin dynamics contributes to tumorigenesis via such various nuclear events.

Droplet-based vitrification of adherent human induced pluripotent stem cells on alginate microcarrier influenced by adhesion time and matrix elasticity

The gold standard in cryopreservation is still conventional slow freezing of single cells or small aggregates in suspension, although major cell loss and limitation to non-specialised cell types in stem cell technology are known drawbacks. The requirement for rapidly available therapeutic and diagnostic cell types is increasing constantly. In the case of human induced pluripotent stem cells (hiPSCs) or their derivates, more sophisticated cryopreservation protocols are needed to address this demand. These should allow a preservation in their physiological, adherent state, an efficient re-cultivation and upscaling upon thawing towards high-throughput applications in cell therapies or disease modelling in drug discovery. Here, we present a novel vitrification-based method for adherent hiPSCs, designed for automated handling by microfluidic approaches and with ready-to-use potential e.g. in suspension-based bioreactors after thawing. Modifiable alginate microcarriers serve as a growth surface for adherent hiPSCs that were cultured in a suspension-based bioreactor and subsequently cryopreserved via droplet-based vitrification in comparison to conventional slow freezing. Soft (0.35%) versus stiff (0.65%) alginate microcarriers in concert with adhesion time variation have been examined. Findings revealed specific optimal conditions leading to an adhesion time and growth surface (matrix) elasticity dependent hypothesis on cryo-induced damaging regimes for adherent cell types. Deviations from the found optimum parameters give rise to membrane ruptures assessed via SEM and major cell loss after adherent vitrification. Applying the optimal conditions, droplet-based vitrification was superior to conventional slow freezing. A decreased microcarrier stiffness was found to outperform stiffer material regarding cell recovery, whereas the stemness characteristics of rewarmed hiPSCs were preserved.

Force-mediated cellular anisotropy and plasticity dictate the elongation dynamics of embryos

We developed a unified dynamic model to explain how cellular anisotropy and plasticity, induced by alignment and severing/rebundling of actin filaments, dictate the elongation dynamics of Caenorhabditis elegans embryos. It was found that the gradual alignment of F-actins must be synchronized with the development of intracellular forces for the embryo to elongate, which is then further sustained by muscle contraction-triggered plastic deformation of cells. In addition, we showed that preestablished anisotropy is essential for the proper onset of the process while defects in the integrity or bundling kinetics of actin bundles result in abnormal embryo elongation, all in good agreement with experimental observations.

Microfluidic channel integrated with a lattice lightsheet microscopic system for continuous cell imaging

In this study, a continuous cell-imaging system with subcellular resolution was developed by integrating a microfluidic platform with lattice lightsheet microscopy (LLSM). To reduce aberrations of the lightsheet propagating into the device, a microfluidic channel sealed with a water refractive index-matched thin film was fabricated. When the lightsheet emerged from the water-immersed objectives and penetrated through the water refractive-matched thin film into the microfluidic channel at an incident angle, less light scattering and fewer aberrations were found. Suspended cells flowed across the lattice lightsheet, and an imaging system with the image plane perpendicular to the lightsheet was used to sequentially acquire cell images. By applying a thinner lattice lightsheet, higher-resolution, higher-contrast images were obtained. Furthermore, three-dimensional cell images could be achieved by reconstructing sequential two-dimensional cell images.

Kinetics of actin networks formation measured by time resolved particle-tracking microrheology

Actin is one of the most studied cytoskeleton proteins showing a very rich span of structures and functions. For example, adenosine triphosphate (ATP)-assisted polymerization of actin is used to push protrusions forward in a mechanism that enables cells to crawl on a substrate. In this process, the chemical energy released from the hydrolysis of ATP is what enables force generation. We study a minimal model system comprised of actin monomers in an excess of ATP concentration. In such a system polymerization proceeds in three stages: nucleation of actin filaments, elongation, and network formation. While the kinetics of filament growth was characterized previously, not much is known about the kinetics of network formation and the evolution of networks towards a steady-state structure. In particular, it is not clear how the non-equilibrium nature of this ATP-assisted polymerization manifests itself in the kinetics of self-assembly. Here, we use time-resolved microrheology to follow the kinetics of the three stages of self-assembly as a function of initial actin monomer concentration. Surprisingly, we find that at high enough initial monomer concentrations the effective elastic modulus of the forming actin networks overshoots and then relaxes with a -2/5 power law. We attribute the overshoot to the non-equilibrium nature of the polymerization and the relaxation to rearrangements of the network into a steady-state structure.

Coronin 2B regulates dendrite outgrowth by modulating actin dynamics

Cytoskeletal remodeling is indispensable for the development and maintenance of neuronal structures and functions. However, the molecular machinery that controls the balance between actin polymerization and depolymerization during these processes is incompletely understood. Here, we report that coronin 2B, a conserved actin-binding protein, is concentrated at the tips of developing dendrites and that knockdown of coronin 2B inhibits the growth of dendrites. Importantly, coronin 2B interacts with actin and reduces the F-actin/G-actin ratio. Furthermore, the coiled-coil domain of coronin 2B is required for its oligomerization, thus confining coronin 2B to neurite tips. Our findings collectively suggest that coronin 2B is important for promoting dendrite outgrowth by limiting the speed of actin polymerization at growth cones.

Adjustable viscoelasticity allows for efficient collective cell migration

Cell migration is essential for a wide range of biological processes such as embryo morphogenesis, wound healing, regeneration, and also in pathological conditions, such as cancer. In such contexts, cells are required to migrate as individual entities or as highly coordinated collectives, both of which requiring cells to respond to molecular and mechanical cues from their environment. However, whilst the function of chemical cues in cell migration is comparatively well understood, the role of tissue mechanics on cell migration is just starting to be studied. Recent studies suggest that the dynamic tuning of the viscoelasticity within a migratory cluster of cells, and the adequate elastic properties of its surrounding tissues, are essential to allow efficient collective cell migration in vivo. In this review we focus on the role of viscoelasticity in the control of collective cell migration in various cellular systems, mentioning briefly some aspects of single cell migration. We aim to provide details on how viscoelasticity of collectively migrating groups of cells and their surroundings is adjusted to ensure correct morphogenesis, wound healing, and metastasis. Finally, we attempt to show that environmental viscoelasticity triggers molecular changes within migrating clusters and that these new molecular setups modify clusters' viscoelasticity, ultimately allowing them to migrate across the challenging geometries of their microenvironment.

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.

Biomechanical properties of red blood cells infected by Plasmodium berghei ANKA

Malaria is a pathogenic disease in mammal species and typically causes destruction of red blood cells (RBCs). The malaria-infected RBCs undergoes alterations in morphology and its rheological properties, and the altered rheological properties of RBCs have a significant impact on disease pathophysiology. In this study, we investigated detailed topological and biomechanical properties of RBCs infected with malaria Plasmodium berghei ANKA using atomic force microscopy. Mouse (BALB/c) RBCs were obtained on Days 4, 10, and 14 after infection. We found that malaria-infected RBCs changed significantly in shape. The RBCs maintained a biconcave disk shape until Day 4 after infection and then became lopsided on Day 7 after infection. The central region of RBCs began to swell beginning on Day 10 after infection. More schizont stages were present on Days 10 and 14 compared with on Day 4. The malaria-infected RBCs also showed changes in mechanical properties and the cytoskeleton. The stiffness of infected RBCs increased 4.4-4.6-fold and their cytoskeletal F-actin level increased 18.99-67.85% compared with the control cells. The increase in F-actin depending on infection time was in good agreement with the increased stiffness of infected RBCs. Because more schizont stages were found at a late period of infection at Days 10 and 14, the significant changes in biomechanical properties might contribute to the destruction of RBCs, possibly resulting in the release of merozoites into the blood circulation.

Rhythmicity and waves in the cortex of single cells

Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information.

This article is part of the theme issue ‘Self-organization in cell biology’.

The Mechanobiology of the Actin Cytoskeleton in Stem Cells during Differentiation and Interaction with Biomaterials

An understanding of the cytoskeleton's importance in stem cells is essential for their manipulation and further clinical application. The cytoskeleton is crucial in stem cell biology and depends on physical and chemicals signals to define its structure. Additionally, cell culture conditions will be important in the proper maintenance of stemness, lineage commitment, and differentiation. This review focuses on the following areas: the role of the actin cytoskeleton of stem cells during differentiation, the significance of cellular morphology, signaling pathways involved in cytoskeletal rearrangement in stem cells, and the mechanobiology and mechanotransduction processes implicated in the interactions of stem cells with different surfaces of biomaterials, such as nanotopography, which is a physical cue influencing the differentiation of stem cells. Also, cancer stem cells are included since it is necessary to understand the role of their mechanical properties to develop new strategies to treat cancer. In this context, to study the stem cells requires integrated disciplines, including molecular and cellular biology, chemistry, physics, and immunology, as well as mechanobiology. Finally, since one of the purposes of studying stem cells is for their application in regenerative medicine, the deepest understanding is necessary in order to establish safety protocols and effective cell-based therapies.

PI(4,5)P2 forms dynamic cortical structures and directs actin distribution as well as polarity in Caenorhabditis elegans embryos

Asymmetric division is crucial for embryonic development and stem cell lineages. In the one-cell Caenorhabditis elegans embryo, a contractile cortical actomyosin network contributes to asymmetric division by segregating partitioning-defective (PAR) proteins to discrete cortical domains. In the current study, we found that the plasma membrane lipid phosphatidylinositol 4,5-bisphosphate (PIP₂) localizes to polarized dynamic structures in C. elegans zygotes, distributing in a PAR-dependent manner along the anterior-posterior (A-P) embryonic axis. PIP₂ cortical structures overlap with F-actin, and coincide with the actin regulators RHO-1 and CDC-42, as well as ECT-2. Particle image velocimetry analysis revealed that PIP₂ and F-actin cortical movements are coupled, with PIP₂ structures moving slightly ahead of F-actin. Importantly, we established that PIP₂ cortical structure formation and movement is actin dependent. Moreover, we found that decreasing or increasing the level of PIP₂ resulted in severe F-actin disorganization, revealing interdependence between these components. Furthermore, we determined that PIP₂ and F-actin regulate the sizing of PAR cortical domains, including during the maintenance phase of polarization. Overall, our work establishes that a lipid membrane component, PIP₂, modulates actin organization and cell polarity in C. elegans embryos.

Activity-dependent self-regulation of viscous length scales in biological systems

The cellular cortex, which is a highly viscous thin cytoplasmic layer just below the cell membrane, controls the cell's mechanical properties, which can be characterized by a hydrodynamic length scale ℓ. Cells actively regulate ℓ via the activity of force-generating molecules, such as myosin II. Here we develop a general theory for such systems through a coarse-grained hydrodynamic approach including activity in the static description of the system providing an experimentally accessible parameter and elucidate the detailed mechanism of how a living system can actively self-regulate its hydrodynamic length scale, controlling the rigidity of the system. Remarkably, we find that ℓ, as a function of activity, behaves universally and roughly inversely proportional to the activity of the system. Our theory rationalizes a number of experimental findings on diverse systems, and comparison of our theory with existing experimental data shows good agreement.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

Load Adaptation of Lamellipodial Actin Networks

Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated. In a steady state, migrating cell filaments assume the canonical dendritic geometry, defined by Arp2/3-generated 70° branch points. Increased tension triggers a dense network with a broadened range of angles, whereas decreased tension causes a shift to a sparse configuration dominated by filaments growing perpendicularly to the plasma membrane. We show that these responses emerge from the geometry of branched actin: when load per filament decreases, elongation speed increases and perpendicular filaments gradually outcompete others because they polymerize the shortest distance to the membrane, where they are protected from capping. This network-intrinsic geometrical adaptation mechanism tunes protrusive force in response to mechanical load.

Comparison of [corrected] actin- and glass-supported phospholipid bilayer diffusion coefficients

The formation of biomimetic lipid membranes has the potential to provide insights into cellular lipid membrane dynamics. The construction of such membranes necessitates not only the utilization of appropriate lipids, but also physiologically relevant substrate/support materials. The substrate materials employed have been shown to have demonstrable effects on the behavior of the overlying lipid membrane, and thus must be studied before use as a model cushion support. To our knowledge, we report the formation and investigation of a novel actin protein-supported lipid membrane. Specifically, inner leaflet lateral mobility of globular actin-supported DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) bilayers, deposited via the Langmuir-Blodgett/Langmuir Schaefer methodology, was investigated by z-scan fluorescence correlation spectroscopy across a temperature range of 20-44°C. The actin substrate was found to decrease the diffusion coefficient when compared to an identical membrane supported on glass. The depression of the diffusion coefficient occurred across all measured temperatures. These results indicated that the actin substrate exerted a direct effect on the fluidity of the lipid membrane and highlighted the fact that the choice of substrate/support is critical in studies of model lipid membranes.

Accessible Synthetic Probes for Staining Actin inside Platelets and Megakaryocytes by Employing Lifeact Peptide

Lifeact is a 17-residue peptide that can be employed in cell microscopy as a probe for F-actin when fused to fluorescent proteins, but therefore is not suitable for all cell types. We have conjugated fluorescently labelled Lifeact to three different cell-penetrating systems (a myristoylated carrier (myr), the pH low insertion peptide (pHLIP) and the cationic peptide TAT) as a strategy to deliver Lifeact into cells and developed new tools for actin staining with improved synthetic accessibility and low toxicity, focusing on their suitability in platelets and megakaryocytes. Using confocal microscopy, we characterised the cell distribution of the new hybrids in fixed cells, and found that both myr– and pHLIP–Lifeact conjugates provide efficient actin staining upon cleavage of Lifeact from the carriers, without affecting cell spreading. This new approach could facilitate the design of new tools for actin visualisation.

The cytoskeleton and neurite initiation

Neurons begin their life as simple spheres, but can ultimately assume an elaborate morphology with numerous, highly arborized dendrites, and long axons. This is achieved via an astounding developmental progression which is dependent upon regulated assembly and dynamics of the cellular cytoskeleton. As neurites emerge out of the soma, neurons break their spherical symmetry and begin to acquire the morphological features that define their structure and function. Neurons regulate their cytoskeleton to achieve changes in cell shape, velocity, and direction as they migrate, extend neurites, and polarize. Of particular importance, the organization and dynamics of actin and microtubules directs the migration and morphogenesis of neurons. This review focuses on the regulation of intrinsic properties of the actin and microtubule cytoskeletons and how specific cytoskeletal structures and dynamics are associated with the earliest phase of neuronal morphogenesis—neuritogenesis.

A mechano-chemiosmotic model for the coupling of electron and proton transfer to ATP synthesis in energy-transforming membranes: a personal perspective

ATP is synthesized using ATP synthase by utilizing energy either from the oxidation of organic compounds, or from light, via redox reactions (oxidative- or photo phosphorylation), in energy-transforming membranes of mitochondria, chloroplasts, and bacteria. ATP synthase undergoes several changes during its functioning. The generally accepted model for ATP synthesis is the well-known rotatory model (see e.g., Junge et al., Nature 459:364-370, 2009; Junge and Müller, Science 333:704-705, 2011). Here, we present an alternative modified model for the coupling of electron and proton transfer to ATP synthesis, which was initially developed by Albert Lester Lehninger (1917-1986). Details of the molecular mechanism of ATP synthesis are described here that involves cyclic low-amplitude shrinkage and swelling of mitochondria. A comparison of the well-known current model and the mechano-chemiosmotic model is also presented. Based on structural, and other data, we suggest that ATP synthase is a Ca(2+)/H(+)-K(+) Cl(-)-pump-pore-enzyme complex, in which γ-subunit rotates 360° in steps of 30°, and 90° due to the binding of phosphate ions to positively charged amino acid residues in the N-terminal γ-subunit, while in the electric field. The coiled coil b 2-subunits are suggested to act as ropes that are shortened by binding of phosphate ions to positively charged lysines or arginines; this process is suggested to pull the α 3 β 3-hexamer to the membrane during the energization process. ATP is then synthesized during the reverse rotation of the γ-subunit by destabilizing the phosphated N-terminal γ-subunit and b 2-subunits under the influence of Ca(2+) ions, which are pumped over from storage-intermembrane space into the matrix, during swelling of intermembrane space. In the process of ATP synthesis, energy is first, predominantly, used in the delivery of phosphate ions and protons to the α 3 β 3-hexamer against the energy barrier with the help of C-terminal alpha-helix of γ-subunit that acts as a lift; then, in the formation of phosphoryl group; and lastly, in the release of ATP molecules from the active center of the enzyme and the loading of ADP. We are aware that our model is not an accepted model for ATP synthesis, but it is presented here for further examination and test.

A model of protein association based on their hydrophobic and electric interactions

The propensity of many proteins to oligomerize and associate to form complex structures from their constituent monomers, is analyzed in terms of their hydrophobic (H), and electric pseudo-dipole (D) moment vectors. In both cases these vectors are defined as the product of the distance between their positive and negative centroids, times the total hydrophobicity or total positive charge of the protein. Changes in the magnitudes and directions of H and D are studied as monomers associate to form larger complexes. We use these descriptors to study similarities and differences in two groups of associations: a) open associations such as polymers with an undefined number of monomers (i.e. actin polymerization, amyloid and HIV capsid assemblies); b) closed symmetrical associations of finite size, like spherical virus capsids and protein cages. The tendency of the hydrophobic moments of the monomers in an association is to align in parallel arrangements following a pattern similar to those of phospholipids in a membrane. Conversely, electric dipole moments of monomers tend to align in antiparallel associations. The final conformation of a given assembly is a fine-tuned combination of these forces, limited by steric constraints. This determines whether the association will be open (indetermined number of monomers) or closed (fixed number of monomers). Any kinetic, binding or molecular peculiarities that characterize a protein assembly, comply with the vector rules laid down in this paper. These findings are also independent of protein size and shape.

The association of myosin IB with actin waves in dictyostelium requires both the plasma membrane-binding site and actin-binding region in the myosin tail

F-actin structures and their distribution are important determinants of the dynamic shapes and functions of eukaryotic cells. Actin waves are F-actin formations that move along the ventral cell membrane driven by actin polymerization. Dictyostelium myosin IB is associated with actin waves but its role in the wave is unknown. Myosin IB is a monomeric, non-filamentous myosin with a globular head that binds to F-actin and has motor activity, and a non-helical tail comprising a basic region, a glycine-proline-glutamine-rich region and an SH3-domain. The basic region binds to acidic phospholipids in the plasma membrane through a short basic-hydrophobic site and the Gly-Pro-Gln region binds F-actin. In the current work we found that both the basic-hydrophobic site in the basic region and the Gly-Pro-Gln region of the tail are required for the association of myosin IB with actin waves. This is the first evidence that the Gly-Pro-Gln region is required for localization of myosin IB to a specific actin structure in situ. The head is not required for myosin IB association with actin waves but binding of the head to F-actin strengthens the association of myosin IB with waves and stabilizes waves. Neither the SH3-domain nor motor activity is required for association of myosin IB with actin waves. We conclude that myosin IB contributes to anchoring actin waves to the plasma membranes by binding of the basic-hydrophobic site to acidic phospholipids in the plasma membrane and binding of the Gly-Pro-Gln region to F-actin in the wave.

Continuum descriptions of cytoskeletal dynamics

This tutorial presents an introduction into continuum descriptions of cytoskeletal dynamics. In contrast to discrete models in which each molecule keeps its identity, such descriptions are given in terms of averaged quantities per unit volume like the number density of a certain molecule. Starting with a discrete description for the assembly dynamics of cytoskeletal filaments, we derive the continuity equation, which serves as the basis of many continuum theories. We illustrate the use of this approach with an investigation of spontaneous cytoskeletal polymerization waves. Such waves have by now been observed in various cell types and might help to orchestrate cytoskeletal dynamics during cell spreading and locomotion. Our analysis shows how processes at the scale of single molecules, namely, the nucleation of new filaments and filament treadmilling, can lead to the spontaneous appearance of coherent traveling waves on scales spanning many filament lengths. For readers less familiar with calculus, we include an informal introduction to the Taylor expansion.

A model for intracellular actin waves explored by nonlinear local perturbation analysis

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.

Actin polymerization negatively regulates p53 function by impairing its nuclear import in response to DNA damage

Actin, one of the most evolutionarily conservative proteins in eukaryotes, is distributed both in the cytoplasm and the nucleus, and its dynamics plays important roles in numerous cellular processes. Previous evidence has shown that actin interacts with p53 and this interaction increases in the process of p53 responding to DNA damage, but the physiological significance of their interaction remains elusive. Here, we show that DNA damage induces both actin polymerization and p53 accumulation. To further understand the implication of actin polymerization in p53 function, cells were treated with actin aggregation agent. We find that the protein level of p53 decrease. The change in p53 is a consequence of the polymeric actin anchoring p53 in the cytoplasm, thus impairing p53 nuclear import. Analysis of phosphorylation and ubiquitination of p53 reveals that actin polymerization promotes the p53 phosphorylation at Ser315 and reduces the stabilization of p53 by recruiting Aurora kinase A. Taken together, our results suggest that the actin polymerization serves as a negative modulator leading to the impairment of nuclear import and destabilization of p53. On the basis of our results, we propose that actin polymerization might be a factor participating in the process of orchestrating p53 function in response to DNA damage.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour

Patterns of waves, patches, and peaks of actin are observed experimentally in many living cells. Models of this phenomenon have been based on the interplay between filamentous actin (F-actin) and its nucleation promoting factors (NPFs) that activate the Arp2/3 complex. Here we present an alternative biologically-motivated model for F-actin-NPF interaction based on properties of GTPases acting as NPFs. GTPases (such as Cdc42, Rac) are known to promote actin nucleation, and to have active membrane-bound and inactive cytosolic forms. The model is a natural extension of a previous mathematical mini-model of small GTPases that generates static cell polarization. Like other modellers, we assume that F-actin negative feedback shapes the observed patterns by suppressing the trailing edge of NPF-generated wave-fronts, hence localizing the activity spatially. We find that our NPF-actin model generates a rich set of behaviours, spanning a transition from static polarization to single pulses, reflecting waves, wave trains, and oscillations localized at the cell edge. The model is developed with simplicity in mind to investigate the interaction between nucleation promoting factor kinetics and negative feedback. It explains distinct types of pattern initiation mechanisms, and identifies parameter regimes corresponding to distinct behaviours. We show that weak actin feedback yields static patterning, moderate feedback yields dynamical behaviour such as travelling waves, and strong feedback can lead to wave trains or total suppression of patterning. We use a recently introduced nonlinear bifurcation analysis to explore the parameter space of this model and predict its behaviour with simulations validating those results.

Physical microscopic model of proteins under force

Nature has evolved proteins to counteract forces applied on living cells, and has designed proteins that can sense forces. One can appreciate Nature's ingenuity in evolving these proteins to be highly sensitive to force and to have a high dynamic force range at which they operate. To achieve this level of sensitivity, many of these proteins are composed of multiple domains and linking peptides connecting these domains, each of them having their own force response regimes. Here, using a simple model of a protein, we address the question of how each individual domain responds to force. We also ask how multidomain proteins respond to forces. We find that the end-to-end distance of individual domains under force scales linearly with force. In multidomain proteins, we find that the force response has a rich range: at low force, extension is predominantly governed by "weaker" linking peptides or domain intermediates, while at higher force, the extension is governed by unfolding of individual domains. Overall, the force extension curve comprises multiple sigmoidal transitions governed by unfolding of linking peptides and domains. Our study provides a basic framework for the understanding of protein response to force, and allows for interpretation experiments in which force is used to study the mechanical properties of multidomain proteins.

A review of models of fluctuating protrusion and retraction patterns at the leading edge of motile cells

A characteristic feature of motile cells as they undergo a change in motile behavior is the development of fluctuating exploratory motions of the leading edge, driven by actin polymerization. We review quantitative models of these protrusion and retraction phenomena. Theoretical studies have been motivated by advances in experimental and computational methods that allow controlled perturbations, single molecule imaging, and analysis of spatiotemporal correlations in microscopic images. To explain oscillations and waves of the leading edge, most theoretical models propose nonlinear interactions and feedback mechanisms among different components of the actin cytoskeleton system. These mechanisms include curvature-sensing membrane proteins, myosin contraction, and autocatalytic biochemical reaction kinetics. We discuss how the combination of experimental studies with modeling promises to quantify the relative importance of these biochemical and biophysical processes at the leading edge and to evaluate their generality across cell types and extracellular environments.