Forces generated during actin-based propulsion: a direct measurement by micromanipulation

Mechanosensitive Conjugated Oligoelectrolytes for Visualizing Temporal Changes in Live Cells

Membrane-intercalating conjugated oligoelectrolytes (COEs) are lipid-bilayer-spanning molecules that serve as fluorescent dyes for bioimaging. However, COE emission has thus far only been capable of visualizing dye location and their preferential accumulation in different membrane-bound intracellular compartments. Herein, we report the first example of environmentally sensitive COEs for visualizing temporal changes in live cells, providing information on the physical properties of intracellular lipid bilayer membranes. The new COE-BY series is designed around a BODIPY central unit with a membrane-spanning topology and six cationic pendant groups ensuring solubility in aqueous media. These reporters feature high two-photon absorption cross section, NIR-II excitation capabilities under multiphoton excitation, and high dye brightness; all highly desirable photophysical features for bioimaging. The emission lifetime of the probes was sensitive to changes to both the lipid composition of model vesicle systems and membrane tension within cells, induced by either mechanical or osmotic stress. Using two-photon fluorescence lifetime imaging microscopy, it is possible to use the most efficient emitter, namely, COE-BYPhOC4, to image changes in the mechanical properties of intracellular membranes. We show that these COEs remain stably vesicle-bound within the endolysosomal pathway over extended periods, allowing for long-term monitoring of the associated biophysical changes of these vesicles over time.

On the generation of force required for actin-based motility

The fundamental question of how forces are generated in a motile cell, a lamellipodium, and a comet tail is the subject of this note. It is now well established that cellular motility results from the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone around the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed, departing from the well-known theory of Larché-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.

Molecular simulation approaches to probing the effects of mechanical forces in the actin cytoskeleton

In this article we give our perspective on the successes and promise of various molecular and coarse-grained simulation approaches to probing the effect of mechanical forces in the actin cytoskeleton.

Composite branched and linear F-actin maximize myosin-induced membrane shape changes in a biomimetic cell model

The architecture of the actin cortex determines the generation and transmission of stresses, during key events from cell division to migration. However, its impact on myosin-induced cell shape changes remains unclear. Here, we reconstitute a minimal model of the actomyosin cortex with branched or linear F-actin architecture within giant unilamellar vesicles (GUVs, liposomes). Upon light activation of myosin, neither the branched nor linear F-actin architecture alone induces significant liposome shape changes. The branched F-actin network forms an integrated, membrane-bound "no-slip boundary" -like cortex that attenuates actomyosin contractility. By contrast, the linear F-actin network forms an unintegrated "slip boundary" -like cortex, where actin asters form without inducing membrane deformations. Notably, liposomes undergo significant deformations at an optimized balance of branched and linear F-actin networks. Our findings highlight the pivotal roles of branched F-actin in force transmission and linear F-actin in force generation to yield membrane shape changes.

Myosin-independent stiffness sensing by fibroblasts is regulated by the viscoelasticity of flowing actin

The stiffness of the extracellular matrix induces differential tension within integrin-based adhesions, triggering differential mechanoresponses. However, it has been unclear if the stiffness-dependent differential tension is induced solely by myosin activity. Here, we report that in the absence of myosin contractility, 3T3 fibroblasts still transmit stiffness-dependent differential levels of traction. This myosin-independent differential traction is regulated by polymerizing actin assisted by actin nucleators Arp2/3 and formin where formin has a stronger contribution than Arp2/3 to both traction and actin flow. Intriguingly, despite only slight changes in F-actin flow speed observed in cells with the combined inhibition of Arp2/3 and myosin compared to cells with sole myosin inhibition, they show a 4-times reduction in traction than cells with myosin-only inhibition. Our analyses indicate that traditional models based on rigid F-actin are inadequate for capturing such dramatic force reduction with similar actin flow. Instead, incorporating the F-actin network's viscoelastic properties is crucial. Our new model including the F-actin viscoelasticity reveals that Arp2/3 and formin enhance stiffness sensitivity by mechanically reinforcing the F-actin network, thereby facilitating more effective transmission of flow-induced forces. This model is validated by cell stiffness measurement with atomic force microscopy and experimental observation of model-predicted stiffness-dependent actin flow fluctuation.

Biophysics in tumor growth and progression: from single mechano-sensitive molecules to mechanomedicine

Evidence from physical sciences in oncology increasingly suggests that the interplay between the biophysical tumor microenvironment and genetic regulation has significant impact on tumor progression. Especially, tumor cells and the associated stromal cells not only alter their own cytoskeleton and physical properties but also remodel the microenvironment with anomalous physical properties. Together, these altered mechano-omics of tumor tissues and their constituents fundamentally shift the mechanotransduction paradigms in tumorous and stromal cells and activate oncogenic signaling within the neoplastic niche to facilitate tumor progression. However, current findings on tumor biophysics are limited, scattered, and often contradictory in multiple contexts. Systematic understanding of how biophysical cues influence tumor pathophysiology is still lacking. This review discusses recent different schools of findings in tumor biophysics that have arisen from multi-scale mechanobiology and the cutting-edge technologies. These findings range from the molecular and cellular to the whole tissue level and feature functional crosstalk between mechanotransduction and oncogenic signaling. We highlight the potential of these anomalous physical alterations as new therapeutic targets for cancer mechanomedicine. This framework reconciles opposing opinions in the field, proposes new directions for future cancer research, and conceptualizes novel mechanomedicine landscape to overcome the inherent shortcomings of conventional cancer diagnosis and therapies.

ActuAtor, a Listeria-inspired molecular tool for physical manipulation of intracellular organizations through de novo actin polymerization

Form and function are often interdependent throughout biology. Inside cells, mitochondria have particularly attracted attention since both their morphology and functionality are altered under pathophysiological conditions. However, directly assessing their causal relationship has been beyond reach due to the limitations of manipulating mitochondrial morphology in a physiologically relevant manner. By engineering a bacterial actin regulator, ActA, we developed tools termed "ActuAtor" that inducibly trigger actin polymerization at arbitrary subcellular locations. The ActuAtor-mediated actin polymerization drives striking deformation and/or movement of target organelles, including mitochondria, Golgi apparatus, and nucleus. Notably, ActuAtor operation also disperses non-membrane-bound entities such as stress granules. We then implemented ActuAtor in functional assays, uncovering the physically fragmented mitochondria being slightly more susceptible to degradation, while none of the organelle functions tested are morphology dependent. The modular and genetically encoded features of ActuAtor should enable its application in studies of the form-function interplay in various intracellular contexts.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Integrative experimental/computational approach establishes active cellular protrusion as the primary driving force of phagocytic spreading by immune cells

The dynamic interplay between cell adhesion and protrusion is a critical determinant of many forms of cell motility. When modeling cell spreading on adhesive surfaces, traditional mathematical treatments often consider passive cell adhesion as the primary, if not exclusive, mechanistic driving force of this cellular motion. To better assess the contribution of active cytoskeletal protrusion to immune-cell spreading during phagocytosis, we here develop a computational framework that allows us to optionally investigate both purely adhesive spreading ("Brownian zipper hypothesis") as well as protrusion-dominated spreading ("protrusive zipper hypothesis"). We model the cell as an axisymmetric body of highly viscous fluid surrounded by a cortex with uniform surface tension and incorporate as potential driving forces of cell spreading an attractive stress due to receptor-ligand binding and an outward normal stress representing cytoskeletal protrusion, both acting on the cell boundary. We leverage various model predictions against the results of a directly related experimental companion study of human neutrophil phagocytic spreading on substrates coated with different densities of antibodies. We find that the concept of adhesion-driven spreading is incompatible with experimental results such as the independence of the cell-spreading speed on the density of immobilized antibodies. In contrast, the protrusive zipper model agrees well with experimental findings and, when adapted to simulate cell spreading on discrete adhesion sites, it also reproduces the observed positive correlation between antibody density and maximum cell-substrate contact area. Together, our integrative experimental/computational approach shows that phagocytic spreading is driven by cellular protrusion, and that the extent of spreading is limited by the density of adhesion sites.

Elasticity of podosome actin networks produces nanonewton protrusive forces

Actin filaments assemble into force-generating systems involved in diverse cellular functions, including cell motility, adhesion, contractility and division. It remains unclear how networks of actin filaments, which individually generate piconewton forces, can produce forces reaching tens of nanonewtons. Here we use in situ cryo-electron tomography to unveil how the nanoscale architecture of macrophage podosomes enables basal membrane protrusion. We show that the sum of the actin polymerization forces at the membrane is not sufficient to explain podosome protrusive forces. Quantitative analysis of podosome organization demonstrates that the core is composed of a dense network of bent actin filaments storing elastic energy. Theoretical modelling of the network as a spring-loaded elastic material reveals that it exerts forces of a few tens of nanonewtons, in a range similar to that evaluated experimentally. Thus, taking into account not only the interface with the membrane but also the bulk of the network, is crucial to understand force generation by actin machineries. Our integrative approach sheds light on the elastic behavior of dense actin networks and opens new avenues to understand force production inside cells.

The molecular mechanism of load adaptation by branched actin networks

Branched actin networks are self-assembling molecular motors that move biological membranes and drive many important cellular processes, including phagocytosis, endocytosis, and pseudopod protrusion. When confronted with opposing forces, the growth rate of these networks slows and their density increases, but the stoichiometry of key components does not change. The molecular mechanisms governing this force response are not well understood, so we used single-molecule imaging and AFM cantilever deflection to measure how applied forces affect each step in branched actin network assembly. Although load forces are observed to increase the density of growing filaments, we find that they actually decrease the rate of filament nucleation due to inhibitory interactions between actin filament ends and nucleation promoting factors. The force-induced increase in network density turns out to result from an exponential drop in the rate constant that governs filament capping. The force dependence of filament capping matches that of filament elongation and can be explained by expanding Brownian Ratchet theory to cover both processes. We tested a key prediction of this expanded theory by measuring the force-dependent activity of engineered capping protein variants and found that increasing the size of the capping protein increases its sensitivity to applied forces. In summary, we find that Brownian Ratchets underlie not only the ability of growing actin filaments to generate force but also the ability of branched actin networks to adapt their architecture to changing loads.

Connecting conformational stiffness of the protein with energy landscape by a single experiment

The structure-function dynamics of a protein as a flexible polymer is essential to describe its biological functions. Here, using single-molecule magnetic tweezers, we have studied the effect of ionic strength on the folding mechanics of protein L, and probed its folding-associated physical properties by re-measuring the same protein in a range of ammonium sulfate concentrations from 150 mM to 650 mM. We observed an electrolyte-dependent conformational dynamics and folding landscape of the protein in a single experiment. Salt increases the refolding kinetics, while decreasing the unfolding kinetics under force, which in turn modifies the barrier heights towards the folded state. Additionally, salt enhances the molecular compaction by decreasing the Kuhn length of the protein polymer from 1.18 nm to 0.58 nm, which we have explained by modifying the freely jointed chain model. Finally, we correlated polymer chain physics to the folding dynamics, and thus provided an analytical framework for understanding compaction-induced folding mechanics across a range of ionic strengths from a single experiment.

Pattern formation, localized and running pulsation on active spherical membranes

Active force generation by an actin-myosin cortex coupled to a cell membrane allows the cell to deform, respond to the environment, and mediate cell motility and division. Several membrane-bound activator proteins move along it and couple to the membrane curvature. Besides, they can act as nucleating sites for the growth of filamentous actin. Actin polymerization can generate a local outward push on the membrane. Inward pull from the contractile actomyosin cortex can propagate along the membrane via actin filaments. We use coupled evolution of fields to perform linear stability analysis and numerical calculations. As activity overcomes the stabilizing factors such as surface tension and bending rigidity, the spherical membrane shows instability towards pattern formation, localized pulsation, and running pulsation between poles. We present our results in terms of phase diagrams and evolutions of the coupled fields. They have relevance for living cells and can be verified in experiments on artificial cell-like constructs.

Pinching the cortex of live cells reveals thickness instabilities caused by myosin II motors

The cell cortex is a contractile actin meshwork, which determines cell shape and is essential for cell mechanics, migration, and division. Because its thickness is below optical resolution, there is a tendency to consider the cortex as a thin uniform two-dimensional layer. Using two mutually attracted magnetic beads, one inside the cell and the other in the extracellular medium, we pinch the cortex of dendritic cells and provide an accurate and time-resolved measure of its thickness. Our observations draw a new picture of the cell cortex as a highly dynamic layer, harboring large fluctuations in its third dimension because of actomyosin contractility. We propose that the cortex dynamics might be responsible for the fast shape-changing capacity of highly contractile cells that use amoeboid-like migration.

Leukocyte transmigration and longitudinal forward-thrusting force in a microfluidic Transwell device

Transmigration of leukocytes across blood vessels walls is a critical step of the immune response. Transwell assays examine transmigration properties in vitro by counting cells passages through a membrane; however, the difficulty of in situ imaging hampers a clear disentanglement of the roles of adhesion, chemokinesis, and chemotaxis. We used here microfluidic Transwells to image the cells' transition from 2D migration on a surface to 3D migration in a confining microchannel and measure cells longitudinal forward-thrusting force in microchannels. Primary human effector T lymphocytes adhering with integrins LFA-1 (α_Lβ₂) had a marked propensity to transmigrate in Transwells without chemotactic cue. Both adhesion and contractility were important to overcome the critical step of nucleus penetration but were remarkably dispensable for 3D migration in smooth microchannels deprived of topographic features. Transmigration in smooth channels was qualitatively consistent with a propulsion by treadmilling of cell envelope and squeezing of cell trailing edge. Stalling conditions of 3D migration were then assessed by imposing pressure drops across microchannels. Without specific adhesion, the cells slid backward with subnanonewton forces, showing that 3D migration under stress is strongly limited by a lack of adhesion and friction with channels. With specific LFA-1 mediated adhesion, stalling occurred at around 3 and 6 nN in 2 × 4 and 4 × 4 μm² channels, respectively, supporting that stalling of adherent cells was under pressure control rather than force control. The stall pressure of 4 mbar is consistent with the pressure of actin filament polymerization that mediates lamellipod growth. The arrest of adherent cells under stress therefore seems controlled by the compression of the cell leading edge, which perturbs cells front-rear polarization and triggers adhesion failure or polarization reversal. Although stalling assays in microfluidic Transwells do not mimic in vivo transmigration, they provide a powerful tool to scrutinize 2D and 3D migration, barotaxis, and chemotaxis.

Influence of external forces on actin-dependent T cell protrusions during immune synapse formation

BACKGROUND INFORMATION

We have previously observed that in response to antigenic activation, T cells produce actin-rich protrusions that generate forces involved in T cell activation. These forces are influenced by the mechanical properties of antigen-presenting cells (APCs). However, how external forces, which can be produced by APCs, influence the dynamic of the actin protrusion remains unknown. In this study, we quantitatively characterised the effects of external forces in the dynamic of the protrusion grown by activated T cells.

RESULTS

Using a micropipette force probe, we applied controlled compressive or pulling forces on primary T lymphocytes activated by an antibody-covered microbead, and measured the effects of these forces on the protrusion generated by T lymphocytes. We found that the application of compressive forces slightly decreased the length, the time at which the protrusion stops growing and retracts and the velocity of the protrusion formation, whereas pulling forces strongly increased these parameters. In both cases, the applied forces did not alter the time required for the T cells to start growing the protrusion (delay). Exploring the molecular events controlling the dynamic of the protrusion, we showed that inhibition of the Arp2/3 complex impaired the dynamic of the protrusion by reducing both its maximum length and its growth speed and increasing the delay to start growing. Finally, T cells developed similar protrusions in more physiological conditions, that is, when activated by an APC instead of an activating microbead.

CONCLUSIONS

Our results suggest that the formation of the force-generating protrusion by T cells is set by an intracellular constant time and that its dynamic is sensitive to external forces. They also show that actin assembly mediated by actin-related protein Arp2/3 complex is involved in the formation and dynamic of the protrusion.

SIGNIFICANCE

Actin-rich protrusions developed by T cells are sensory organelles that serve as actuators of immune surveillance. Our study shows that forces experienced by this organelle modify their dynamic suggesting that they might modify immune responses. Moreover, the quantitative aspects of our analysis should help to get insight into the molecular mechanisms involved in the formation of the protrusion.

Actin-Membrane Release Initiates Cell Protrusions

Despite the well-established role of actin polymerization as a driving mechanism for cell protrusion, upregulated actin polymerization alone does not initiate protrusions. Using a combination of theoretical modeling and quantitative live-cell imaging experiments, we show that local depletion of actin-membrane links is needed for protrusion initiation. Specifically, we show that the actin-membrane linker ezrin is depleted prior to protrusion onset and that perturbation of ezrin's affinity for actin modulates protrusion frequency and efficiency. We also show how actin-membrane release works in concert with actin polymerization, leading to a comprehensive model for actin-driven shape changes. Actin-membrane release plays a similar role in protrusions driven by intracellular pressure. Thus, our findings suggest that protrusion initiation might be governed by a universal regulatory mechanism, whereas the mechanism of force generation determines the shape and expansion properties of the protrusion.

A continuum model for the growth of dendritic actin networks

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here, we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore, a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.

Force generation by a propagating wave of supramolecular nanofibers

Dynamic spatiotemporal patterns that arise from out-of-equilibrium biochemical reactions generate forces in living cells. Despite considerable recent efforts, rational design of spatiotemporal patterns in artificial molecular systems remains at an early stage of development. Here, we describe force generation by a propagating wave of supramolecular nanofibers. Inspired by actin dynamics, a reaction network is designed to control the formation and degradation of nanofibers by two chemically orthogonal stimuli. Real-time fluorescent imaging successfully visualizes the propagating wave based on spatiotemporally coupled generation and collapse of nanofibers. Numerical simulation indicates that the concentration gradient of degradation stimulus and the smaller diffusion coefficient of the nanofiber are critical for wave emergence. Moreover, the force (0.005 pN) generated by chemophoresis and/or depletion force of this propagating wave can move nanobeads along the wave direction.

Actin modulates shape and mechanics of tubular membranes

The actin cytoskeleton shapes cells and also organizes internal membranous compartments. In particular, it interacts with membranes for intracellular transport of material in mammalian cells, yeast, or plant cells. Tubular membrane intermediates, pulled along microtubule tracks, are formed during this process and destabilize into vesicles. While the role of actin in tubule destabilization through scission is suggested, literature also provides examples of actin-mediated stabilization of membranous structures. To directly address this apparent contradiction, we mimic the geometry of tubular intermediates with preformed membrane tubes. The growth of an actin sleeve at the tube surface is monitored spatiotemporally. Depending on network cohesiveness, actin is able to entirely stabilize or locally maintain membrane tubes under pulling. On a single tube, thicker portions correlate with the presence of actin. These structures relax over several minutes and may provide enough time and curvature geometries for other proteins to act on tube stability.

Cytoskeleton Force Exertion in Bulk Cytoplasm

The microtubule and actin cytoskeletons generate forces essential to position centrosomes, nuclei, and spindles for division plane specification. While the largest body of work has documented force exertion at, or close to the cell surface, mounting evidence suggests that cytoskeletal polymers can also produce significant forces directly from within the cytoplasm. Molecular motors such as kinesin or dynein may for instance displace cargos and endomembranes in the viscous cytoplasm yielding friction forces that pull or push microtubules. Similarly, the dynamics of bulk actin assembly/disassembly or myosin-dependent contractions produce cytoplasmic forces which influence the spatial organization of cells in a variety of processes. We here review the molecular and physical mechanisms supporting bulk cytoplasmic force generation by the cytoskeleton, their limits and relevance to organelle positioning, with a particular focus on cell division.

Pulling-force generation by ensembles of polymerizing actin filaments

The process by which actin polymerization generates pulling forces in cellular processes such as endocytosis is less well understood than pushing-force generation. To clarify the basic mechanisms of pulling-force generation, we perform stochastic polymerization simulations for a square array of polymerizing semiflexible actin filaments, having different interactions with the membrane. The filaments near the array center have a strong attractive component. Filament bending and actin-network elasticity are treated explicitly. We find that the outer filaments push on the membrane and the inner filaments pull, with a net balance of forces. The total calculated pulling force is maximized when the central filaments have a very deep potential well, and the outer filaments have no well. The steady-state force is unaffected by the gel rigidity, but equilibration takes longer for softer gels. The force distributions are flat over the pulling and pushing regions. Actin polymerization is enhanced by softening the gel or reducing the filament binding to the membrane. Filament-membrane detachment can occur for softer gels, even if the total binding energy of the filaments to the membrane is 100 [Formula: see text] or more. It propagates via a stress-concentration mechanism similar to that of a brittle crack in a solid, and the breaking stress is determined by a criterion similar to that of the 'Griffith' theory of crack propagation.

Actin shells control buckling and wrinkling of biomembranes

Global changes of cell shape under mechanical or osmotic external stresses are mostly controlled by the mechanics of the cortical actin cytoskeleton underlying the cell membrane. Some aspects of this process can be recapitulated in vitro on reconstituted actin-and-membrane systems. In this paper, we investigate how the mechanical properties of a branched actin network shell, polymerized at the surface of a liposome, control membrane shape when the volume is reduced. We observe a variety of membrane shapes depending on the actin thickness. Thin shells undergo buckling, characterized by a cup-shape deformation of the membrane that coincides with the one of the actin network. Thick shells produce membrane wrinkles, but do not deform their outer layer. For intermediate micrometer-thick shells, wrinkling of the membrane is observed, and the actin layer is slightly deformed. Confronting our experimental results with a theoretical description, we determine the transition between buckling and wrinkling, which depends on the thickness of the actin shell and the size of the liposome. We thus unveil the generic mechanism by which biomembranes are able to accommodate their shape against mechanical compression, through thickness adaptation of their cortical cytoskeleton.

Mechanical stiffness of reconstituted actin patches correlates tightly with endocytosis efficiency

Clathrin-mediated endocytosis involves the sequential assembly of more than 60 proteins at the plasma membrane. An important fraction of these proteins regulates the assembly of an actin-related protein 2/3 (Arp2/3)-branched actin network, which is essential to generate the force during membrane invagination. We performed, on wild-type (WT) yeast and mutant strains lacking putative actin crosslinkers, a side-by-side comparison of in vivo endocytic phenotypes and in vitro rigidity measurements of reconstituted actin patches. We found a clear correlation between softer actin networks and a decreased efficiency of endocytosis. Our observations support a chain-of-consequences model in which loss of actin crosslinking softens Arp2/3-branched actin networks, directly limiting the transmission of the force. Additionally, the lifetime of failed endocytic patches increases, leading to a larger number of patches and a reduced pool of polymerizable actin, which slows down actin assembly and further impairs endocytosis.

This study uses in vitro reconstitution of endocytic actin patches and mechanical measurements with chains of superparamagnetic microbeads to reveal a tight correlation between the stiffness of actin networks and the efficiency of endocytosis in yeast.

Interplay between surface and bending energy helps membrane protrusion formation

We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.

Micropipette force sensors for in vivo force measurements on single cells and multicellular microorganisms

Measuring forces from the piconewton to millinewton range is of great importance for the study of living systems from a biophysical perspective. The use of flexible micropipettes as highly sensitive force probes has become established in the biophysical community, advancing our understanding of cellular processes and microbial behavior. The micropipette force sensor (MFS) technique relies on measurement of the forces acting on a force-calibrated, hollow glass micropipette by optically detecting its deflections. The MFS technique covers a wide micro- and mesoscopic regime of detectable forces (tens of piconewtons to millinewtons) and sample sizes (micrometers to millimeters), does not require gluing of the sample to the cantilever, and allows simultaneous optical imaging of the sample throughout the experiment. Here, we provide a detailed protocol describing how to manufacture and calibrate the micropipettes, as well as how to successfully design, perform, and troubleshoot MFS experiments. We exemplify our approach using the model nematode Caenorhabditis elegans, but by following this protocol, a wide variety of living samples, ranging from single cells to multicellular aggregates and millimeter-sized organisms, can be studied in vivo, with a force resolution as low as 10 pN. A skilled (under)graduate student can master the technique in ~1-2 months. The whole protocol takes ~1-2 d to finish.

Macropinocytosis Overcomes Directional Bias in Dendritic Cells Due to Hydraulic Resistance and Facilitates Space Exploration

The migration of immune cells can be guided by physical cues imposed by the environment, such as geometry, rigidity, or hydraulic resistance (HR). Neutrophils preferentially follow paths of least HR in vitro, a phenomenon known as barotaxis. The mechanisms and physiological relevance of barotaxis remain unclear. We show that barotaxis results from the amplification of a small force imbalance by the actomyosin cytoskeleton, resulting in biased directional choices. In immature dendritic cells (DCs), actomyosin is recruited to the cell front to build macropinosomes. These cells are therefore insensitive to HR, as macropinocytosis allows fluid transport across these cells. This may enhance their space exploration capacity in vivo. Conversely, mature DCs down-regulate macropinocytosis and are thus barotactic. Modeling suggests that HR may help guide these cells to lymph nodes where they initiate immune responses. Hence, DCs can either overcome or capitalize on the physical obstacles they encounter, helping their immune-surveillance function.

Actin filaments pushing against a barrier: Comparison between two force generation mechanisms

To theoretically understand force generation properties of actin filaments, many models consider growing filaments pushing against a movable obstacle or barrier. In order to grow, the filaments need space and hence it is necessary to move the barrier. Two different mechanisms for this growth are widely considered in the literature. In one class of models (type A , the filaments can directly push the barrier and move it, thereby performing some work in the process. In another type of models (type B , the filaments wait till thermal fluctuations of the barrier position create enough space between the filament tip and the barrier, and then they grow by inserting one monomer in that gap. The difference between these two types of growth seems microscopic and rather a matter of modelling details. However, we find that this difference has an important effect on many qualitative features of the models. In particular, how the relative time-scale between the barrier dynamics and filament dynamics influences the force generation properties is significantly different for type A and B models. We illustrate these differences for three types of barrier: a rigid wall-like barrier, an elastic barrier and a barrier with Kardar-Parisi-Zhang dynamics. Our numerical simulations match well with our analytical calculations. Our study highlights the importance of taking the details of the filament-barrier interaction into account while modelling the force generation properties of actin filaments.

Building a dendritic actin filament network branch by branch: models of filament orientation pattern and force generation in lamellipodia

We review mathematical and computational models of the structure, dynamics, and force generation properties of dendritic actin networks. These models have been motivated by the dendritic nucleation model, which provided a mechanistic picture of how the actin cytoskeleton system powers cell motility. We describe how they aimed to explain the self-organization of the branched network into a bimodal distribution of filament orientations peaked at 35° and - 35° with respect to the direction of membrane protrusion, as well as other patterns. Concave and convex force-velocity relationships were derived, depending on network organization, filament, and membrane elasticity and accounting for actin polymerization at the barbed end as a Brownian ratchet. This review also describes models that considered the kinetics and transport of actin and diffuse regulators and mechanical coupling to a substrate, together with explicit modeling of dendritic networks.

Actin filaments growing against an elastic membrane: Effect of membrane tension

We study the force generation by a set of parallel actin filaments growing against an elastic membrane. The elastic membrane tries to stay flat and any deformation from this flat state, either caused by thermal fluctuations or due to protrusive polymerization force exerted by the filaments, costs energy. We study two lattice models to describe the membrane dynamics. In one case, the energy cost is assumed to be proportional to the absolute magnitude of the height gradient (gradient model) and in the other case it is proportional to the square of the height gradient (Gaussian model). For the gradient model we find that the membrane velocity is a nonmonotonic function of the elastic constant μ and reaches a peak at μ=μ^{*}. For μ<μ^{*} the system fails to reach a steady state and the membrane energy keeps increasing with time. For the Gaussian model, the system always reaches a steady state and the membrane velocity decreases monotonically with the elastic constant ν for all nonzero values of ν. Multiple filaments give rise to protrusions at different regions of the membrane and the elasticity of the membrane induces an effective attraction between the two protrusions in the Gaussian model which causes the protrusions to merge and a single wide protrusion is present in the system. In both the models, the relative time scale between the membrane and filament dynamics plays an important role in deciding whether the shape of elasticity-velocity curve is concave or convex. Our numerical simulations agree reasonably well with our analytical calculations.

Mechanotransduction by the Actin Cytoskeleton: Converting Mechanical Stimuli into Biochemical Signals

Force transmission through the actin cytoskeleton plays a central role in cell movements, shape change, and internal organization. Dynamic reorganization of actin filaments by an array of specialized binding proteins creates biochemically and architecturally distinct structures, many of which are finely tuned to exert or resist mechanical loads. The molecular complexity of the actin cytoskeleton continues to be revealed by detailed biochemical assays, and the architectural diversity and dynamics of actin structures are being uncovered by advances in super-resolution fluorescence microscopy and electron microscopy. However, our understanding of how mechanical forces feed back on cytoskeletal architecture and actin-binding protein organization is comparatively limited. In this review, we discuss recent work investigating how mechanical forces applied to cytoskeletal proteins are transduced into biochemical signals. We explore multiple mechanisms for mechanical signal transduction, including the mechanosensitive behavior of actin-binding proteins, the effect of mechanical force on actin filament dynamics, and the influence of mechanical forces on the structure of single actin filaments. The emerging picture is one in which the actin cytoskeleton is defined not only by the set of proteins that constitute a network but also by the constant interplay of mechanical forces and biochemistry.

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.

Quantitative Deformability Cytometry: Rapid, Calibrated Measurements of Cell Mechanical Properties

Advances in methods that determine cell mechanical phenotype, or mechanotype, have demonstrated the utility of biophysical markers in clinical and research applications ranging from cancer diagnosis to stem cell enrichment. Here, we introduce quantitative deformability cytometry (q-DC), a method for rapid, calibrated, single-cell mechanotyping. We track changes in cell shape as cells deform into microfluidic constrictions, and we calibrate the mechanical stresses using gel beads. We observe that time-dependent strain follows power-law rheology, enabling single-cell measurements of apparent elastic modulus, E_a, and power-law exponent, β. To validate our method, we mechanotype human promyelocytic leukemia (HL-60) cells and thereby confirm q-DC measurements of E_a = 0.53 ± 0.04 kPa. We also demonstrate that q-DC is sensitive to pharmacological perturbations of the cytoskeleton as well as differences in the mechanotype of human breast cancer cell lines (E_a = 2.1 ± 0.1 and 0.80 ± 0.19 kPa for MCF-7 and MDA-MB-231 cells). To establish an operational framework for q-DC, we investigate the effects of applied stress and cell/pore-size ratio on mechanotype measurements. We show that E_a increases with applied stress, which is consistent with stress stiffening behavior of cells. We also find that E_a increases for larger cell/pore-size ratios, even when the same applied stress is maintained; these results indicate strain stiffening and/or dependence of mechanotype on deformation depth. Taken together, the calibrated measurements enabled by q-DC should advance applications of cell mechanotype in basic research and clinical settings.

A new method to measure mechanics and dynamic assembly of branched actin networks

We measured mechanical properties and dynamic assembly of actin networks with a new method based on magnetic microscopic cylinders. Dense actin networks are grown from the cylinders’ surfaces using the biochemical Arp2/3-machinery at play in the lamellipodium extension and other force-generating processes in the cell. Under a homogenous magnetic field the magnetic cylinders self-assemble into chains in which forces are attractive and depend on the intensity of the magnetic field. We show that these forces, from piconewtons to nanonewtons, are large enough to slow down the assembly of dense actin networks and controlled enough to access to their non linear mechanical responses. Deformations are measured with nanometer-resolution, well below the optical resolution. Self-assembly of the magnetic particles into chains simplifies experiments and allows for parallel measurements. The combination of accuracy and good throughput of measurements results in a method with high potential for cell and cytoskeleton mechanics. Using this method, we observed in particular a strong non linear mechanical behavior of dense branched actin networks at low forces that has not been reported previously.

Micropipette force probe to quantify single-cell force generation: application to T-cell activation

We describe the micropipette force probe, a novel technique that uses a micropipette as a flexible cantilever that aspirates a coated microbead and brings it into contact with a cell. We apply the technique to quantify mechanical and morphological events occurring during T-cell activation.

In response to engagement of surface molecules, cells generate active forces that regulate many cellular processes. Developing tools that permit gathering mechanical and morphological information on these forces is of the utmost importance. Here we describe a new technique, the micropipette force probe, that uses a micropipette as a flexible cantilever that can aspirate at its tip a bead that is coated with molecules of interest and is brought in contact with the cell. This technique simultaneously allows tracking the resulting changes in cell morphology and mechanics as well as measuring the forces generated by the cell. To illustrate the power of this technique, we applied it to the study of human primary T lymphocytes (T-cells). It allowed the fine monitoring of pushing and pulling forces generated by T-cells in response to various activating antibodies and bending stiffness of the micropipette. We further dissected the sequence of mechanical and morphological events occurring during T-cell activation to model force generation and to reveal heterogeneity in the cell population studied. We also report the first measurement of the changes in Young’s modulus of T-cells during their activation, showing that T-cells stiffen within the first minutes of the activation process.

Supported lipid bilayer platforms to probe cell mechanobiology

Mammalian and bacterial cells sense and exert mechanical forces through the process of mechanotransduction, which interconverts biochemical and physical signals. This is especially important in contact-dependent signaling, where ligand-receptor binding occurs at cell-cell or cell-ECM junctions. By virtue of occurring within these specialized junctions, receptors engaged in contact-dependent signaling undergo oligomerization and coupling with the cytoskeleton as part of their signaling mechanisms. While our ability to measure and map biochemical signaling within cell junctions has advanced over the past decades, physical cues remain difficult to map in space and time. Recently, supported lipid bilayer (SLB) technologies have emerged as a flexible platform to mimic and perturb cell-cell and cell-ECM junctions, allowing one to study membrane receptor mechanotransduction. Changing the lipid composition and underlying substrate tunes bilayer fluidity, and lipid and ligand micro- and nano-patterning spatially control positioning and clustering of receptors. Patterning metal gridlines within SLBs confines lipid mobility and introduces mechanical resistance. Here we review fundamental SLB mechanics and how SLBs can be engineered as tunable cell substrates for mechanotransduction studies. Finally, we highlight the impact of this work in understanding the biophysical mechanisms of cell adhesion. This article is part of a Special Issue entitled: Interactions between membrane receptors in cellular membranes edited by Kalina Hristova.

Usher syndrome type 1-associated cadherins shape the photoreceptor outer segment

Usher syndrome type 1 (USH1) causes combined hearing and sight defects, but USH1 protein function in the retina is unclear. Schietroma et al. use Xenopus to model the deficiency in two USH1 proteins—protocadherin-15 and cadherin-23—and identify crucial roles for these molecules in shaping the photoreceptor outer segment.

Usher syndrome type 1 (USH1) causes combined hearing and sight defects, but how mutations in USH1 genes lead to retinal dystrophy in patients remains elusive. The USH1 protein complex is associated with calyceal processes, which are microvilli of unknown function surrounding the base of the photoreceptor outer segment. We show that in Xenopus tropicalis, these processes are connected to the outer-segment membrane by links composed of protocadherin-15 (USH1F protein). Protocadherin-15 deficiency, obtained by a knockdown approach, leads to impaired photoreceptor function and abnormally shaped photoreceptor outer segments. Rod basal outer disks displayed excessive outgrowth, and cone outer segments were curved, with lamellae of heterogeneous sizes, defects also observed upon knockdown of Cdh23, encoding cadherin-23 (USH1D protein). The calyceal processes were virtually absent in cones and displayed markedly reduced F-actin content in rods, suggesting that protocadherin-15–containing links are essential for their development and/or maintenance. We propose that calyceal processes, together with their associated links, control the sizing of rod disks and cone lamellae throughout their daily renewal.

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

Local Arp2/3-dependent actin assembly modulates applied traction force during apCAM adhesion site maturation

In growth cones, local Arp 2/3-dependent actin assembly mechanically buffers apCAM adhesions from retrograde flow–associated traction forces. The resulting propulsive forces drive the exploratory motility of inductopodia. Increasing the stiffness of apCAM targets induces an extensive 3D actin cup to form at the adhesion during evoked growth responses.

Homophilic binding of immunoglobulin superfamily molecules such as the Aplysia cell adhesion molecule (apCAM) leads to actin filament assembly near nascent adhesion sites. Such actin assembly can generate significant localized forces that have not been characterized in the larger context of axon growth and guidance. We used apCAM-coated bead substrates applied to the surface of neuronal growth cones to characterize the development of forces evoked by varying stiffness of mechanical restraint. Unrestrained bead propulsion matched or exceeded rates of retrograde network flow and was dependent on Arp2/3 complex activity. Analysis of growth cone forces applied to beads at low stiffness of restraint revealed switching between two states: frictional coupling to retrograde flow and Arp2/3-dependent propulsion. Stiff mechanical restraint led to formation of an extensive actin cup matching the geometric profile of the bead target and forward growth cone translocation; pharmacological inhibition of the Arp2/3 complex or Rac attenuated F-actin assembly near bead binding sites, decreased the efficacy of growth responses, and blocked accumulation of signaling molecules associated with nascent adhesions. These studies introduce a new model for regulation of traction force in which local actin assembly forces buffer nascent adhesion sites from the mechanical effects of retrograde flow.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Cell-sized liposome doublets reveal active tension build-up driven by acto-myosin dynamics

Cells modulate their shape to fulfill specific functions, mediated by the cell cortex, a thin actin shell bound to the plasma membrane. Myosin motor activity, together with actin dynamics, contributes to cortical tension. Here, we examine the individual contributions of actin polymerization and myosin activity to tension increase with a non-invasive method. Cell-sized liposome doublets are covered with either a stabilized actin cortex of preformed actin filaments, or a dynamic branched actin network polymerizing at the membrane. The addition of myosin II minifilaments in both cases triggers a change in doublet shape that is unambiguously related to a tension increase. Preformed actin filaments allow us to evaluate the effect of myosin alone while, with dynamic actin cortices, we examine the synergy of actin polymerization and myosin motors in driving shape changes. Our assay paves the way for a quantification of tension changes triggered by various actin-associated proteins in a cell-sized system.

Actin filaments growing against a barrier with fluctuating shape

We study force generation by a set of parallel actin filaments growing against a nonrigid obstacle, in the presence of an external load. The filaments polymerize by either moving the whole obstacle, with a large energy cost, or by causing local distortion in its shape which costs much less energy. The nonrigid obstacle also has local thermal fluctuations due to which its shape can change with time and we describe this using fluctuations in the height profile of a one-dimensional interface with Kardar-Parisi-Zhang dynamics. We find the shape fluctuations of the barrier strongly affect the force generation mechanism. The qualitative nature of the force-velocity curve is crucially determined by the relative time scale of filament and barrier dynamics. The height profile of the barrier also shows interesting variation with the external load. Our analytical calculations within mean-field theory show reasonable agreement with our simulation results.

Force Feedback Controls Motor Activity and Mechanical Properties of Self-Assembling Branched Actin Networks

Branched actin networks--created by the Arp2/3 complex, capping protein, and a nucleation promoting factor--generate and transmit forces required for many cellular processes, but their response to force is poorly understood. To address this, we assembled branched actin networks in vitro from purified components and used simultaneous fluorescence and atomic force microscopy to quantify their molecular composition and material properties under various forces. Remarkably, mechanical loading of these self-assembling materials increases their density, power, and efficiency. Microscopically, increased density reflects increased filament number and altered geometry but no change in average length. Macroscopically, increased density enhances network stiffness and resistance to mechanical failure beyond those of isotropic actin networks. These effects endow branched actin networks with memory of their mechanical history that shapes their material properties and motor activity. This work reveals intrinsic force feedback mechanisms by which mechanical resistance makes self-assembling actin networks stiffer, stronger, and more powerful.

Toward the reconstitution of synthetic cell motility

Cellular motility is a fundamental process essential for embryonic development, wound healing, immune responses, and tissues development. Cells are mostly moving by crawling on external, or inside, substrates which can differ in their surface composition, geometry, and dimensionality. Cells can adopt different migration phenotypes, e.g., bleb-based and protrusion-based, depending on myosin contractility, surface adhesion, and cell confinement. In the few past decades, research on cell motility has focused on uncovering the major molecular players and their order of events. Despite major progresses, our ability to infer on the collective behavior from the molecular properties remains a major challenge, especially because cell migration integrates numerous chemical and mechanical processes that are coupled via feedbacks that span over large range of time and length scales. For this reason, reconstituted model systems were developed. These systems allow for full control of the molecular constituents and various system parameters, thereby providing insight into their individual roles and functions. In this review we describe the various reconstituted model systems that were developed in the past decades. Because of the multiple steps involved in cell motility and the complexity of the overall process, most of the model systems focus on very specific aspects of the individual steps of cell motility. Here we describe the main advancement in cell motility reconstitution and discuss the main challenges toward the realization of a synthetic motile cell.

Interplay of migratory and division forces as a generic mechanism for stem cell patterns

In many adult tissues, stem cells and differentiated cells are not homogeneously distributed: stem cells are arranged in periodic "niches," and differentiated cells are constantly produced and migrate out of these niches. In this article, we provide a general theoretical framework to study mixtures of dividing and actively migrating particles, which we apply to biological tissues. We show in particular that the interplay between the stresses arising from active cell migration and stem cell division give rise to robust stem cell patterns. The instability of the tissue leads to spatial patterns which are either steady or oscillating in time. The wavelength of the instability has an order of magnitude consistent with the biological observations. We also discuss the implications of these results for future in vitro and in vivo experiments.

Reconstituting the actin cytoskeleton at or near surfaces in vitro

Actin filament dynamics have been studied for decades in pure protein solutions or in cell extracts, but a breakthrough in the field occurred at the turn of the century when it became possible to reconstitute networks of actin filaments, growing in a controlled but physiological manner on surfaces, mimicking the actin assembly that occurs at the plasma membrane during cell protrusion and cell shape changes. The story begins with the bacteria Listeria monocytogenes, the study of which led to the reconstitution of cellular actin polymerization on a variety of supports including plastic beads. These studies made possible the development of liposome-type substrates for filament assembly and micropatterning of actin polymerization nucleation. Based on the accumulated expertise of the last 15 years, many exciting approaches are being developed, including the addition of myosin to biomimetic actin networks to study the interplay between actin structure and contractility. The field is now poised to make artificial cells with a physiological and dynamic actin cytoskeleton, and subsequently to put these cells together to make in vitro tissues. This article is part of a Special Issue entitled: Mechanobiology.