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Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green's functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method. [ABSTRACT FROM AUTHOR]

Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly. [ABSTRACT FROM AUTHOR]

Recent experiments with super-resolution live cell microscopy revealed that nonmuscle myosin II minifilaments are much more dynamic than formerly appreciated, often showing plastic processes such as splitting, concatenation and stacking. Here we combine sequence information, electrostatics and elasticity theory to demonstrate that the parallel staggers at 14.3, 43.2 and 72 nm have a strong tendency to splay their heads away from the minifilament, thus potentially initiating the diverse processes seen in live cells. In contrast, the straight antiparallel stagger with an overlap of 43 nm is very stable and likely initiates minifilament nucleation. Using stochastic dynamics in a newly defined energy landscape, we predict that the optimal parallel staggers between the myosin rods are obtained by a trial-and-error process in which two rods attach and re-attach at different staggers by rolling and zipping motion. The experimentally observed staggers emerge as the configurations with the largest contact times. We find that contact times increase from isoforms C to B to A, that A-B-heterodimers are surprisingly stable and that myosin 18A should incorporate into mixed filaments with a small stagger. Our findings suggest that nonmuscle myosin II minifilaments in the cell are first formed by isoform A and then convert to mixed A-B-filaments, as observed experimentally. Author summary: Nonmuscle myosin II (NM2) is a non-processive molecular motor that assembles into minifilaments with a typical size of 300 nm to generate force and motion in the actin cytoskeleton. This process is essential for many cellular processes such as adhesion, migration, division and mechanosensing. Due to their small size below the resolution limit, minifilaments are a challenge for imaging with traditional light microscopy. With the advent of super-resolution microscopy, however, it has become apparent that the formation of NM2-minifilaments is much more dynamic than formerly appreciated. Modeling the electrostatic interaction between the rigid rods of the myosin monomers has confirmed the main staggers observed in experiments, but cannot explain these high dynamics. Here we complement electrostatics by elasticity theory and stochastic dynamics to show that the parallel staggers are likely to splay away from the main axis of the minifilament and that monomers attach and deattach with rolling and zipping motions. Based on the sequences of the different NM2-isoforms, we predict that isoform A forms the most stable homofilaments and that A-B-heterofilaments are also very stable. [ABSTRACT FROM AUTHOR]

Gliding motilityproceeds with little changes in cell shape and often results from actively driven surface flows of adhesins binding to the extracellular environment. It allows for fast movement over surfaces or through tissue, especially for the eukaryotic parasites from the phylum apicomplexa, which includes the causative agents of the widespread diseases malaria and toxoplasmosis. We have developed a fully three-dimensional active particle theory which connects the self-organized, actively driven surface flow over a fixed cell shape to the resulting global motility patterns. Our analytical solutions and numerical simulations show that straight motion without rotation is unstable for simple shapes and that straight cell shapes tend to lead to pure rotations. This suggests that the curved shapes of Plasmodium sporozoites and Toxoplasma tachyzoites are evolutionary adaptations to avoid rotations without translation. Gliding motility is also used by certain myxo- or flavobacteria, which predominantly move on flat external surfaces and with higher control of cell surface flow through internal tracks. We extend our theory for these cases. We again find a competition between rotation and translation and predict the effect of internal track geometry on overall forward speed. While specific mechanisms might vary across species, in general, our geometrical theory predicts and explains the rotational, circular, and helical trajectories which are commonly observed for microgliders. Our theory could also be used to design synthetic microgliders. [ABSTRACT FROM AUTHOR]

Single receptor-ligand bonds have finite lifetimes, so that biological systems can dynamically react to changes in their environment. In cell adhesion, adhesion bonds usually act cooperatively in adhesion clusters. Outside the cellular context, adhesion clusters can be probed quantitatively by attaching receptors and ligands to opposing surfaces. Here we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds under shared constant loading and with rebinding. Analytical solutions for the appropriate one-step master equation are presented for special cases, while the general case is treated with exact stochastic simulations. If the completely dissociated state is modeled as an absorbing boundary, mean cluster lifetime is finite and can be calculated exactly. We also present a detailed analysis of fluctuation effects and discuss various approximations to the full stochastic description.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Centrosome positioning is essential for many processes in animal cells, in particular during development and migration. A new study using quantitative analysis of enucleated cells plated on adhesive micropatterns reveals that microtubules position the centrosome in the geometric center of the intracellular space defined by the actin cytoskeleton. [ABSTRACT FROM AUTHOR]

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before. [ABSTRACT FROM AUTHOR]

The measurement of cellular traction forces on soft elastic substrates has become a standard tool for many labs working on mechanobiology. Here we review the basic principles and different variants of this approach. In general, the extraction of the substrate displacement field from image data and the reconstruction procedure for the forces are closely linked to each other and limited by the presence of experimental noise. We discuss different strategies to reconstruct cellular forces as they follow from the foundations of elasticity theory, including two- versus three-dimensional, inverse versus direct and linear versus non-linear approaches. We also discuss how biophysical models can improve force reconstruction and comment on practical issues like substrate preparation, image processing and the availability of software for traction force microscopy. This article is part of a Special Issue entitled: Mechanobiology. [ABSTRACT FROM AUTHOR]

In this pedagogical review, we discuss the physical constraints that pathogens experience when they move in their host environment. Due to their small size, pathogens are living in a low Reynolds number world dominated by viscosity. For swimming pathogens, the so-called scallop theorem determines which kinds of shape changes can lead to productive motility. For crawling or gliding cells, the main resistance to movement comes from protein friction at the cell–environment interface. Viruses and pathogenic bacteria can also exploit intracellular host processes such as actin polymerization and motor-based transport, if they present the appropriate factors on their surfaces. Similar to cancer cells that also tend to cross various barriers, pathogens often combine several of these strategies in order to increase their motility and therefore their chances to replicate and spread. [ABSTRACT FROM AUTHOR]

Background: Focal adhesions are integrin-based cell-matrix contacts that transduce and integrate mechanical and biochemical cues from the environment. They develop from smaller and more numerous focal complexes under the influence of mechanical force and are key elements for many physiological and disease-related processes, including wound healing and metastasis. More than 150 different proteins localize to focal adhesions and have been systematically classified in the adhesome project (www.adhesome.org). First RNAi-screens have been performed for focal adhesions and the effect of knockdown of many of these components on the number, size, shape and location of focal adhesions has been reported. Results: We have developed a kinetic model for RNA interference of focal adhesions which represents some of its main elements: a spatially layered structure, signaling through the small GTPases Rac and Rho, and maturation from focal complexes to focal adhesions under force. The response to force is described by two complementary scenarios corresponding to slip and catch bond behavior, respectively. Using estimated and literature values for the model parameters, three time scales of the dynamics of RNAi-influenced focal adhesions are identified: a sub-minute time scale for the assembly of focal complexes, a sub-hour time scale for the maturation to focal adhesions, and a time scale of days that controls the siRNA-mediated knockdown. Our model shows bistability between states dominated by focal complexes and focal adhesions, respectively. Catch bonding strongly extends the range of stability of the state dominated by focal adhesions. A sensitivity analysis predicts that knockdown of focal adhesion components is more efficient for focal adhesions with slip bonds or if the system is in a state dominated by focal complexes. Knockdown of Rho leads to an increase of focal complexes. Conclusions: The suggested model provides a kinetic description of the effect of RNA-interference of focal adhesions. Its predictions are in good agreement with known experimental results and can now guide the design of RNAi-experiments. In the future, it can be extended to include more components of the adhesome. It also could be extended by spatial aspects, for example by the differential activation of the Rac- and Rho-pathways in different parts of the cell [ABSTRACT FROM AUTHOR]

Propulsion by growing actin networks is a universal mechanism used in many different biological systems, ranging from the sheet-like lamellipodium of crawling animal cells to the actin comet tails induced by certain bacteria and viruses in order to move within their host cells. Although the core molecular machinery for actin network growth is well preserved in all of these cases, the geometry of the propelled obstacle varies considerably. During recent years, filament orientation distribution has emerged as an important observable characterizing the structure and dynamical state of the growing network. Here we derive several continuum equations for the orientation distribution of filaments growing behind stiff obstacles of various shapes and validate the predicted steady state orientation patterns by stochastic computer simulations based on discrete filaments. We use an ordinary differential equation approach to demonstrate that for flat obstacles of finite size, two fundamentally different orientation patterns peaked at either ±35° or +70°/0°/-70° exhibit mutually exclusive stability, in agreement with earlier results for flat obstacles of very large lateral extension. We calculate and validate phase diagrams as a function of model parameters and show how this approach can be extended to obstacles with piecewise straight contours. For curved obstacles, we arrive at a partial differential equation in the continuum limit, which again is in good agreement with the computer simulations. In all cases, we can identify the same two fundamentally different orientation patterns, but only within an appropriate reference frame, which is adjusted to the local orientation of the obstacle contour. Our results suggest that two fundamentally different network architectures compete with each other in growing actin networks, irrespective of obstacle geometry, and clarify how simulated and electron tomography data have to be analyzed for non-flat obstacle geometries. [ABSTRACT FROM AUTHOR]

Many essential cellular functions in health and disease are closely linked to the ability of cells to respond to mechanical forces. In the context of cell adhesion to the extracellular matrix, the forces that are generated within the actin cytoskeleton and transmitted through integrin-based focal adhesions are essential for the cellular response to environmental clues, such as the spatial distribution of adhesive ligands or matrix stiffness. Whereas substantial progress has been made in identifying mechanosensitive molecules that can transduce mechanical force into biochemical signals, much less is known about the nature of cytoskeletal force generation and transmission that regulates the magnitude, duration and spatial distribution of forces imposed on these mechanosensitive complexes. By focusing on cell-matrix adhesion to flat elastic substrates, on which traction forces can be measured with high temporal and spatial resolution, we discuss our current understanding of the physical mechanisms that integrate a large range of molecular mechanotransduction events on cellular scales. Physical limits of stability emerge as one important element of the cellular response that complements the structural changes affected by regulatory systems in response to mechanical processes. [ABSTRACT FROM AUTHOR]

Forces in the actin cytoskeleton are generated by small groups of nonprocessive myosin II motors for which stochastic effects are highly relevant. Using a cross-bridge model with the assumptions of fast power-stroke kinetics and equal load sharing between equivalent states, we derive a one-step master equation for the activity of a finite-sized ensemble of mechanically coupled myosin II motors. For constant external load, this approach yields analytical results for duty ratio and force-velocity relation as a function of ensemble size. We find that stochastic effects cannot be neglected for ensemble sizes below 15. The one-step master equation can be used also for efficient computer simulations with linear elastic external load and reveals the sequence of buildup of force and ensemble rupture that is characteristic for reconstituted actomyosin contractility. [ABSTRACT FROM AUTHOR]

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance, and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions. We also show that anisotropic extracellular stiffness can lead to force localization in the stiffer direction, as observed experimentally. [ABSTRACT FROM AUTHOR]

The lamellipodium of migrating animal cells protrudes by directed polymerization of a branched actin network. The underlying mechanisms of filament growth, branching, and capping can be studied in in vitro assays. However, conflicting results have been reported for the force-velocity relation of such actin networks. namely both convex and concave shapes as well as history dependencies. Here we model branching as a reaction that is independent of the number of existing filaments, in contrast to capping, which is assumed to be proportional to the number of existing filaments. Using both stochastic network simulations and deterministic rate equations, we show that such a description naturally leads to the stability of two qualitatively different stationary states of the system, namely a ±35° and a +70/0/ 70° orientation pattern. Changes in network growth velocity induce a transition between these two patterns. For sufficiently different protrusion efficiency of the two network architectures, this leads to hysteresis in the growth velocity of actin networks under force. Dependent on the history of the system, convex and concave regimes are obtained for the force-velocity relation. Thus a simple generic model can explain the experimentally observed anomalies, with far reaching consequences for cell migration. [ABSTRACT FROM AUTHOR]

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here, we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings. [ABSTRACT FROM AUTHOR]

Abstract: Adhesion-dependent cells actively sense the mechanical properties of their environment through mechanotransductory processes at focal adhesions, which are integrin-based contacts connecting the extracellular matrix to the cytoskeleton. Here we present first steps towards a quantitative understanding of focal adhesions as mechanosensors. It has been shown experimentally that high levels of force are related to growth of and signaling at focal adhesions. In particular, activation of the small GTPase Rho through focal adhesions leads to the formation of stress fibers. Here we discuss one way in which force might regulate the internal state of focal adhesions, namely by modulating the internal rupture dynamics of focal adhesions. A simple two-spring model shows that the stiffer the environment, the more efficient cellular force is built up at focal adhesions by molecular motors interacting with the actin filaments. [Copyright &y& Elsevier]

Abstract: Cell adhesion is an integral part of many physiological processes in tissues, including development, tissue maintenance, angiogenesis, and wound healing. Recent advances in materials science (including microcontact printing, soft lithography, microfluidics, and nanotechnology) have led to strongly improved control of extracellular ligand distribution and of the properties of the micromechanical environment. As a result, the investigation of cellular response to the physical properties of adhesive surfaces has become a very active area of research. Sophisticated use of elastic substrates has revealed that cell organization in soft media is determined by active mechanosensing at cell-matrix adhesions. In order to determine the underlying mechanisms, quantification and biophysical modelling are essential. In tissue engineering, theory might help to design new environments for cells. [Copyright &y& Elsevier]

L-selectin-mediated tethers result in leukocyte rolling only above a threshold in shear. Here we present biophysical modeling based on recently published data from flow chamber experiments, which supports the interpretation that 1-selectin-mediated tethers below the shear threshold correspond to single L-selectin carbohydrate bonds dissociating on the time scale of milliseconds, whereas 1-selectin-mediated tethers above the shear threshold are stabilized by multiple bonds and fast rebinding of broken bonds, resulting in tether lifetimes on the time scale of 10-1 seconds. Our calculations for cluster dissociation suggest that the single molecule rebinding rate is of the order of 104 Hz. A similar estimate results if increased tether dissociation for tail-truncated L-selectin mutants above the shear threshold is modeled as diffusive escape of single receptors from the rebinding region due to increased mobility. Using computer simulations, we show that our model yields first-order dissociation kinetics and exponential dependence of tether dissociation rates on shear stress. Our results suggest that multiple contacts, cytoskeletal anchorage of L-selectin, and local rebinding of ligand play important roles in L-selectin tether stabilization and progression of tethers into persistent rolling on endothelial surfaces. [ABSTRACT FROM AUTHOR]

Mechanical forces play a major role in the regulation of cell adhesion and cytoskeletal organization. In order to explore the molecular mechanism underlying this regulation, we have investigated the relationship between local force applied by the cell to the substrate and the assembly of focal adhesions. A novel approach was developed for real-time, high-resolution measurements of forces applied by cells at single adhesion sites. This method combines micropatterning of elastomer substrates and fluorescence imaging of focal adhesions in live cells expressing GFP-tagged vinculin. Local forces are correlated with the orientation, total fluorescence intensity and area of the focal adhesions, indicating a constant stress of 5.5 ± 2 nNμm-2. The dynamics of the force-dependent modulation of focal adhesions were characterized by blocking actomyosin contractility and were found to be on a time scale of seconds. The results put clear constraints on the possible molecular mechanisms for the mechanosensory response of focal adhesions to applied force. [ABSTRACT FROM AUTHOR]

Liquid crystalline (LC) materials are especially suited for the preparation of active three-dimensional (3D) and 4D microstructures using two-photon laser printing. To achieve the desired actuation, the alignment of the LCs has to be controlled during the printing process. In most cases studied before, the alignment relied on surface modifications and complex alignment patterns and concomitant actuation were not possible. Here, we introduce a strategy for spatially aligning LC domains in three-dimensional space by using 3D-printed polydimethylsiloxane-based microscaffolds as confinement barriers, which induce the desired director field. The director field resulting from the boundary conditions is calculated with Landau de Gennes theory and validated by comparing experimentally measured and theoretically predicted birefringence patterns. We demonstrate our procedures for structures of varying complexity and then employed them to fabricate 4D microstructures that show the desired actuation. Overall, we obtain excellent agreement between theory and experiment. This opens the door for rational design of functional materials for 4D (micro)printing in the future. [ABSTRACT FROM AUTHOR]

Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells. [ABSTRACT FROM AUTHOR]

It is a long‐standing challenge to exploit cellular uptake mechanisms to deliver desired cargo into cells, for example, specific drugs or gene editing techniques. This study introduces a bioinspired material approach where nanoparticles are presented at the ventral side of cells adhering to engineered extracellular matrices. The effect of matrix stiffness on cell adhesion and mechanics, as well as on particle internalization by clathrin‐mediated endocytosis (CME), is investigated for varying particle size and surface functionalization. The results presented here show that substrate stiffness affects both cell adhesion and particle internalization, with softer substrates promoting higher levels of particle uptake. However, the activation of the CME pathway, either mechanically by particle size or functionally by receptor binding, regulates the sensitivity of cellular particle uptake to matrix stiffness. Finally, adeno‐associated viruses as the leading platform for therapeutic gene delivery are used as model cargo to showcase the importance of considering multiple components when designing delivery systems. These findings indicate that particle uptake is a multifaceted process that can be improved by the appropriate combination of extracellular environment mechanics and cargo properties. [ABSTRACT FROM AUTHOR]

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry. [ABSTRACT FROM AUTHOR]

With the advent of mechanobiology, cell shape and forces have emerged as essential elements of cell behavior and fate, in addition to biochemical factors such as growth factors. Cell shape and forces are intrinsically linked to the physical properties of the environment. Extracellular stiffness guides migration of single cells and collectives as well as differentiation and developmental processes. In confined environments, cell division patterns are altered, cell death or extrusion might be initiated, and other modes of cell migration become possible. Tools from materials science such as adhesive micropatterning of soft elastic substrates or direct laser writing of 3D scaffolds have been established to control and quantify cell shape and forces in structured environments. Herein, a review is given on recent experimental and modeling advances in this field, which currently moves from single cells to cell collectives and tissue. A very exciting avenue is the combination of organoids with structured environments, because this will allow one to achieve organotypic function in a controlled setting well suited for long‐term and high‐throughput culture. [ABSTRACT FROM AUTHOR]

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments. Author summary: Cell shape and forces have emerged as important determinants of cell function and thus their prediction is essential to describe and control the behaviour of cells in complex environments. While there exist well-established models for the two-dimensional shape of cells on flat substrates, it is less clear how cell shape should be modeled in three dimensions. Different from the philosophy of the vertex model often used for epithelial sheets, we find that models based only on cortical tension as a constant geometrical surface tension are not sufficient to describe the shape of single cells in 3D. Therefore, we employ different variants of the cellular Potts model, where either a target area is prescribed by an elastic constraint or the area energy is described with a linear surface tension. By comparing the simulated shapes to experimental images of cells in 3D scaffolds, we can identify parameters that accurately model 3D cell shape. [ABSTRACT FROM AUTHOR]

The article focuses on different researchers conducted to understand the molecular mechanism undertaken by actin cytoskeleton during response to changes caused by mechanical loading in cells. The article mentions that actin cytoskeleton is not mechanosensitive due to single mechanotransduction process but due to a complex network of integrated mechanosensitive processes with different signals forming a complex response.

Cell-generated forces play a major role in coordinating the large-scale behavior of cell assemblies, in particular during development, wound healing, and cancer. Mechanical signals propagate faster than biochemical signals, but can have similar effects, especially in epithelial tissues with strong cell-cell adhesion. However, a quantitative description of the transmission chain from force generation in a sender cell, force propagation across cell-cell boundaries, and the concomitant response of receiver cells is missing. For a quantitative analysis of this important situation, here we propose a minimal model system of two epithelial cells on an H-pattern ('cell doublet'). After optogenetically activating RhoA, a major regulator of cell contractility, in the sender cell, we measure the mechanical response of the receiver cell by traction force and monolayer stress microscopies. In general, we find that the receiver cells show an active response so that the cell doublet forms a coherent unit. However, force propagation and response of the receiver cell also strongly depend on the mechano-structural polarization in the cell assembly, which is controlled by cell-matrix adhesion to the adhesive micropattern. We find that the response of the receiver cell is stronger when the mechano-structural polarization axis is oriented perpendicular to the direction of force propagation, reminiscent of the Poisson effect in passive materials. We finally show that the same effects are at work in small tissues. Our work demonstrates that cellular organization and active mechanical response of a tissue are key to maintain signal strength and lead to the emergence of elasticity, which means that signals are not dissipated like in a viscous system, but can propagate over large distances. [ABSTRACT FROM AUTHOR]

Ebola viruses (EBOVs) assemble into filamentous virions, whose shape and stability are determined by the matrix viral protein 40 (VP40). Virus entry into host cells occurs via membrane fusion in late endosomes; however, the mechanism of how the remarkably long virions undergo uncoating, including virion disassembly and nucleocapsid release into the cytosol, remains unknown. Here, we investigate the structural architecture of EBOVs entering host cells and discover that the VP40 matrix disassembles prior to membrane fusion. We reveal that VP40 disassembly is caused by the weakening of VP40–lipid interactions driven by low endosomal pH that equilibrates passively across the viral envelope without a dedicated ion channel. We further show that viral membrane fusion depends on VP40 matrix integrity, and its disassembly reduces the energy barrier for fusion stalk formation. Thus, pH‐driven structural remodeling of the VP40 matrix acts as a molecular switch coupling viral matrix uncoating to membrane fusion during EBOV entry. Synopsis: Ebola viruses enter host cells via late endosomes and fuse their envelope with the endosomal membrane. Here, this step is shown to require the disassembly of the VP40 matrix as the first step of viral uncoating, which is triggered by the low endosomal pH. Low endosomal pH passively equilibrates across the endosomal membrane, independently of a dedicated viral ion channelLow pH inside the virus lumen disrupts electrostatic interactions between VP40 proteins and the viral membrane, leading to the disassembly of the VP40 matrixDisassembly of the VP40 matrix is pivotal in increasing the flexibility of the viral membrane and allowing membrane fusionDisassembly of the VP40 matrix precedes GP‐driven membrane fusion and release of the condensed nucleocapsid into the cytoplasm [ABSTRACT FROM AUTHOR]

Actomyosin stress fibers (SFs) play key roles in driving polarized motility and generating traction forces, yet little is known about how tension borne by an individual SF is governed by SF geometry and its connectivity to other cytoskeletal elements. We now address this question by combining single-cell micropatterning with subcellular laser ablation to probe the mechanics of single, geometrically defined SFs. The retraction length of geometrically isolated SFs after cutting depends strongly on SF length, demonstrating that longer SFs dissipate more energy upon incision. Furthermore,when cell geometry and adhesive spacing are fixed, cell-to-cell heterogeneities in SF dissipated elastic energy can be predicted from varying degrees of physical integration with the surrounding network. We apply genetic, pharmacological, and computational approaches to demonstrate a causal and quantitative relationship between SF connectivity and mechanics for patterned cells and show that similar relationships hold for nonpatterned cells allowed to form cell-cell contacts in monolayer culture. Remarkably, dissipation of a single SF within a monolayer induces cytoskeletal rearrangements in cells long distances away. Finally, stimulation of cell migration leads to characteristic changes in network connectivity that promote SF bundling at the cell rear. Our findings demonstrate that SFs influence and are influenced by the networks in which they reside. Such higher order network interactions contribute in unexpected ways to cell mechanics and motility. [ABSTRACT FROM AUTHOR]

Eukaryotic cells use clathrin-mediated endocytosis to take up a large range of extracellular cargo. During endocytosis, a clathrin coat forms on the plasma membrane, but it remains controversial when and how it is remodeled into a spherical vesicle. Here, we use 3D superresolution microscopy to determine the precise geometry of the clathrin coat at large numbers of endocytic sites. Through pseudo-temporal sorting, we determine the average trajectory of clathrin remodeling during endocytosis. We find that clathrin coats assemble first on flat membranes to 50% of the coat area before they become rapidly and continuously bent, and this mechanism is confirmed in three cell lines. We introduce the cooperative curvature model, which is based on positive feedback for curvature generation. It accurately describes the measured shapes and dynamics of the clathrin coat and could represent a general mechanism for clathrin coat remodeling on the plasma membrane. [ABSTRACT FROM AUTHOR]

Summary: Keeping cells separated in well-defined domains is essential for development. A new computational–experimental study elucidates the physical mechanisms that establish and maintain the dorsal-ventral compartment boundary in the Drosophila wing disc and demonstrates the increasing value of computer simulations in developmental biology. [ABSTRACT FROM AUTHOR]

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps. [ABSTRACT FROM AUTHOR]

Cytoadhesion of Plasmodium falciparum-infected erythrocytes to the microvascular endothelial lining shares striking similarities to cytoadhesion of leukocytes. In both cases, adhesins are presented in structures that raise them above the cell surface. Another similarity is the enhancement of adhesion under physical force (catch bonding). Here, we review recent advances in our understanding of the molecular and biophysical mechanisms underlying cytoadherence in both cellular systems. We describe how imaging, flow chamber experiments, single-molecule measurements, and computational modeling have been used to decipher the relevant processes. We conclude that although the parasite seems to induce processes that resemble the cytoadherence of leukocytes, the mechanics of erythrocytes is such that the resulting behavior in shear flow is fundamentally different. [ABSTRACT FROM AUTHOR]

Cytoadhesion of Plasmodium falciparum-infected erythrocytes to the microvascular endothelial lining shares striking similarities to cytoadhesion of leukocytes. In both cases, adhesins are presented in structures that raise them above the cell surface. Another similarity is the enhancement of adhesion under physical force (catch bonding). Here, we review recent advances in our understanding of the molecular and biophysical mechanisms underlying cytoadherence in both cellular systems. We describe how imaging, flow chamber experiments, single-molecule measurements, and computational modeling have been used to decipher the relevant processes. We conclude that although the parasite seems to induce processes that resemble the cytoadherence of leukocytes, the mechanics of erythrocytes is such that the resulting behavior in shear flow is fundamentally different. [ABSTRACT FROM AUTHOR]

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 ( HIV-1) and hepatitis C virus ( HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps. [ABSTRACT FROM AUTHOR]

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments. Author summary: Malaria is one of the deadliest infectious diseases and its symptoms are related to the blood stage, when the parasite multiplies within red blood cells. In order to avoid clearance by the spleen, the parasite produces specific factors like the adhesion receptor PfEMP1 and the multifunctional protein KAHRP that lead to the formation of adhesive knobs on the surface of the red blood cells and thus increase residence time in the vasculature. We have developed a computational model for the parasite-induced remodelling of the actin-spectrin network to quantitatively predict the dynamical changes in the mechanical properties of the infected red blood cells and the spatial distribution of the different protein components of the membrane skeleton. Our simulations show that KAHRP can relocate to actin junctions due to dynamical changes in binding affinities, in good qualitative agreement with super-resolution imaging experiments. In the future, our simulation framework can be used to gain further mechanistic insight into the way malaria parasites attack the red blood cell cytoskeleton. [ABSTRACT FROM AUTHOR]

The article presents a study which explores the asynchronous nuclear cycles in multinucleated Plasmodium falciparum facilitate rapid proliferation. It mentions the findings of the study which suggest the existence of evolutionary pressure that selects for asynchronous DNA replication, balancing available resources with rapid pathogen proliferation.

Mammalian cells have evolved complex mechanical connections to their microenvironment, including focal adhesion clusters that physically connect the cytoskeleton and the extracellular matrix. This mechanical link is also part of the cellular machinery to transduce, sense and respond to external forces. Although methods to measure cell attachment and cellular traction forces are well established, these are not capable of quantifying force transmission through the cell body to adhesion sites. We here present a novel approach to quantify intracellular force transmission by combining microneedle shearing at the apical cell surface with traction force microscopy at the basal cell surface. The change of traction forces exerted by fibroblasts to underlying polyacrylamide substrates as a response to a known shear force exerted with a calibrated microneedle reveals that cells redistribute forces dynamically under external shearing and during sequential rupture of their adhesion sites. Our quantitative results demonstrate a transition from dipolar to monopolar traction patterns, an inhomogeneous distribution of the external shear force to the adhesion sites as well as dynamical changes in force loading prior to and after the rupture of single adhesion sites. Our strategy of combining traction force microscopy with external force application opens new perspectives for future studies of force transmission and mechanotransduction in cells. [ABSTRACT FROM AUTHOR]

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping, and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament numbers. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth-order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, these mechanisms allow cells to grow stable actin networks over a large range of different conditions. [ABSTRACT FROM AUTHOR]

Background: In order to replicate within their cellular host, many viruses have developed self-assembly strategies for their capsids which are sufficiently robust as to be reconstituted in vitro. Mathematical models for virus self-assembly usually assume that the bonds leading to cluster formation have constant reactivity over the time course of assembly (direct assembly). In some cases, however, binding sites between the capsomers have been reported to be activated during the self-assembly process (hierarchical assembly). Results: In order to study possible advantages of such hierarchical schemes for icosahedral virus capsid assembly, we use Brownian dynamics simulations of a patchy particle model that allows us to switch binding sites on and off during assembly. For T1 viruses, we implement a hierarchical assembly scheme where inter-capsomer bonds become active only if a complete pentamer has been assembled. We find direct assembly to be favorable for reversible bonds allowing for repeated structural reorganizations, while hierarchical assembly is favorable for strong bonds with small dissociation rate, as this situation is less prone to kinetic trapping. However, at the same time it is more vulnerable to monomer starvation during the final phase. Increasing the number of initial monomers does have only a weak effect on these general features. The differences between the two assembly schemes become more pronounced for more complex virus geometries, as shown here for T3 viruses, which assemble through homogeneous pentamers and heterogeneous hexamers in the hierarchical scheme. In order to complement the simulations for this more complicated case, we introduce a master equation approach that agrees well with the simulation results. Conclusions: Our analysis shows for which molecular parameters hierarchical assembly schemes can outperform direct ones and suggests that viruses with high bond stability might prefer hierarchical assembly schemes. These insights increase our physical understanding of an essential biological process, with many interesting potential applications in medicine and materials science. [ABSTRACT FROM AUTHOR]

Cells in tissues are mechanically coupled both to the ECM and neighboring cells, but the coordination and interdependency of forces sustained at cell-ECM and cell-cell adhesions are unknown. In this paper, we demonstrate that the endogenous force sustained at the cell-cell contact between a pair of epithelial cells is approximately 100 nN, directed perpendicular to the cell-cell interface and concentrated at the contact edges. This force is stably maintained over time despite significant fluctuations in cell-cell contact length and cell morphology. A direct relationship between the total cellular traction force on the ECM and the endogenous cell-cell force exists, indicating that the cell-cell tension is a constant fraction of the cell-ECM traction. Thus, modulation of ECM properties that impact cell-ECM traction alters cell-cell tension. Finally, we show in a minimal model of a tissue that all cells experience similar forces from the surrounding microenvironment, despite differences in the extent of cell-ECM and cell-cell adhesion. This interdependence of cell-cell and cell-ECM forces has significant implications for the maintenance of the mechanical integrity of tissues, mechanotransduction, and tumor mechanobiology. [ABSTRACT FROM AUTHOR]

The knob-associated histidine-rich protein (KAHRP) plays a pivotal role in the pathophysiology of Plasmodium falciparum malaria by forming membrane protrusions in infected erythrocytes, which anchor parasite- encoded adhesins to the membrane skeleton. The resulting sequestration of parasitized erythrocytes in the microvasculature leads to severe disease. Despite KAHRP being an important virulence factor, its physical location within the membrane skeleton is still debated, as is its function in knob formation. Here, we show by super-resolution microscopy that KAHRP initially associates with various skeletal components, including ankyrin bridges, but eventually colocalizes with remnant actin junctions. We further present a 35 Å map of the spiral scaffold underlying knobs and show that a KAHRP-targeting nanoprobe binds close to the spiral scaffold. Single-molecule localization microscopy detected ~60 KAHRP molecules/knob. We propose a dynamic model of KAHRP organization and a function of KAHRP in attaching other factors to the spiral scaffold. [ABSTRACT FROM AUTHOR]

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an informationtheoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands. [ABSTRACT FROM AUTHOR]

Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment. [ABSTRACT FROM AUTHOR]

Clathrin-mediated endocytosis is one of the major pathways by which cells internalise cargo molecules. Recently it has been shown that clathrin triskelia can first assemble as flat lattices before the membrane starts to bend. However, for fully assembled clathrin lattices high energetic and topological barriers exist for the flat-to-curved transition. Here we explore the possibility that flat clathrin lattices grow with vacancies that are not visible in traditional imaging techniques but would lower these barriers. We identify the Eden model for cluster growth as the most appropriate modeling framework and systematically derive the four possible variants that result from the specific architecture of the clathrin triskelion. Our computer simulations show that the different models lead to clear differences in the statistical distributions of cluster shapes and densities. Experimental results from electron microscopy and correlative light microscopy provide first indications for the model variants with a moderate level of lattice vacancies. [ABSTRACT FROM AUTHOR]

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time. [ABSTRACT FROM AUTHOR]