Dynamic mechanisms of cell rigidity sensing: insights from a computational model of actomyosin networks

Mechanical deformation and death of circulating tumor cells in the bloodstream

The circulation of tumor cells through the bloodstream is a significant step in tumor metastasis. To better understand the metastatic process, circulating tumor cell (CTC) survival in the circulation must be explored. While immune interactions with CTCs in recent decades have been examined, research has yet to sufficiently explain some CTC behaviors in blood flow. Studies related to CTC mechanical responses in the bloodstream have recently been conducted to further study conditions under which CTCs might die. While experimental methods can assess the mechanical properties and death of CTCs, increasingly sophisticated computational models are being built to simulate the blood flow and CTC mechanical deformation under fluid shear stresses (FSS) in the bloodstream.Several factors contribute to the mechanical deformation and death of CTCs as they circulate. While FSS can damage CTC structure, diverse interactions between CTCs and blood components may either promote or hinder the next metastatic step-extravasation at a remote site. Overall understanding of how these factors influence the deformation and death of CTCs could serve as a basis for future experiments and simulations, enabling researchers to predict CTC death more accurately. Ultimately, these efforts can lead to improved metastasis-specific therapeutics and diagnostics specific in the future.

Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions

Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.

Mechanics of cell-cell junctions

Tissue cells in epithelial or endothelial monolayers are connected through cell-cell junctions, which are stabilized by transmembrane E-cadherin bonds and intracellular actin filaments. These bonds and junctions play a crucial role in maintaining the barrier function of epithelia and endothelia and are believed to transmit forces between cells. Additionally, E-cadherin bonds can impact the shape of cell-cell junctions. In this study, we develop a continuum mechanical model of the cell-cell junction by explicitly incorporating the cell membrane, distributions of E-cadherin bonds, cytoplasmic fluid pressure, and F-actin dynamics. The static force-balanced version of the model is able to analyze the influences of cell cortical tension, actin dynamics, and cytoplasmic pressure on the junction shape and E-cadherin bonds. Furthermore, an extended model that incorporates fluid flow, across the cell boundary as well as around the cell, is also examined. This model can couple cell-shape changes with cell cortical tension and fluid flow, and predicts the additional effect of fluid motion on cell-cell junction mechanics. Taken together, our models serve as an intermediate link between molecular-scale models of cell-junction molecules and cell-scale models of tissue and epithelia.

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

Unravelling cell migration: defining movement from the cell surface

Cell motility is essential for life and development. Unfortunately, cell migration is also linked to several pathological processes, such as cancer metastasis. Cells' ability to migrate relies on many actors. Cells change their migratory strategy based on their phenotype and the properties of the surrounding microenvironment. Cell migration is, therefore, an extremely complex phenomenon. Researchers have investigated cell motility for more than a century. Recent discoveries have uncovered some of the mysteries associated with the mechanisms involved in cell migration, such as intracellular signaling and cell mechanics. These findings involve different players, including transmembrane receptors, adhesive complexes, cytoskeletal components , the nucleus, and the extracellular matrix. This review aims to give a global overview of our current understanding of cell migration.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Actin bundle architecture and mechanics regulate myosin II force generation

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

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

Self-organized cytoskeletal alignment during Drosophila mesoderm invagination

During tissue morphogenesis, mechanical forces are propagated across tissues, resulting in tissue shape changes. These forces in turn can influence cell behaviour, leading to a feedback process that can be described as self-organizing. Here, I discuss cytoskeletal self-organization and point to evidence that suggests its role in directing force during morphogenesis. During Drosophila mesoderm invagination, the shape of the region of cells that initiates constriction creates a mechanical pattern that in turn aligns the cytoskeleton with the axis of greatest resistance to contraction. The wild-type direction of the force controls the shape and orientation of the invaginating mesoderm. Given the ability of the actomyosin cytoskeleton to self-organize, these types of feedback mechanisms are likely to play important roles in a range of different morphogenetic events. This article is part of the discussion meeting issue 'Contemporary morphogenesis'.

Stratification relieves constraints from steric hindrance in the generation of compact actomyosin asters at the membrane cortex

Recent in vivo studies reveal that several membrane proteins are driven to form nanoclusters by active contractile flows arising from localized dynamic patterning of F-actin and myosin at the cortex. Since myosin-II assemble as minifilaments with tens of myosin heads, one might worry that steric considerations would obstruct the emergence of nanoclustering. Using coarse-grained, agent-based simulations that account for steric constraints, we find that the patterns exhibited by actomyosin in two dimensions, do not resemble the steady-state patterns in our in vitro reconstitution of actomyosin on a supported bilayer. We perform simulations in a thin rectangular slab, separating the layer of actin filaments from myosin-II minifilaments. This recapitulates the observed features of in vitro patterning. Using super resolution microscopy, we find evidence for such stratification in our in vitro system. Our study suggests that molecular stratification may be an important organizing feature of the cortical cytoskeleton in vivo.

A mesoscopic theory to describe the flexibility regulation in F-actin networks: An approach of phase transitions with nonlinear elasticity

The synthetic actin network arouses great interest as bio-material due to its soft and wet nature that mimics many biological scaffolding structures. Inside the cell, the actin network is regulated by tens of actin-binding proteins (ABP's), which make for a highly complex system with several emergent behaviors. In particular, calponin is an ABP that was identified as an actin stabiliser, but whose mechanism is still poorly understood. Recent experiments using an in vitro model system of cross-linked actin with calponin and large deformation bulk rheology, found that networks with exhibited a delayed onset and were able to withstand a higher maximal strain before softening. In this work, we show that at network scale the actin network with calponin furthermore the reduction of the persistence length allows: (i) The reduction in the network pre-strain. (ii) The increment of the crosslinks adhesion energy. We verify these effects theoretically using nonlinear continuum mechanics for the semiflexible and crosslinked network. In addition, the alterations over the microstructure are described by the definition of an interaction parameter Γ according the formalism of Landau for phase transitions. According to this model we demonstrates that the interaction parameter can describe the experimental observations following a scaling exponent as Γ~|c-c_cr|^1/2, where c is the ratio between concentration of calponin and actin. This result provides interesting feedback to improve our understanding of several mechano-biological pathways.

Utilization of the Theory of Small on Large Deformation for Studying Mechanosensitive Cellular Behaviors

Recent studies suggest that cells routinely probe their mechanical environments and that this mechanosensitive behavior regulates some of their cellular activities. The finite elasticity theory of small-on-large deformation (SoL) has been shown to be effective in interpreting the mechanosensitive behavior of cells on a substrate that has been subjected to a prior large static stretch before the culturing of the cells. Small on large deformation is the superposition of a small deformation onto a prior large deformation that serves as the new reference configuration. This article aims to refine SoL theory to develop a theoretical framework for improved physical interpretation of mechanosensing. Given the initial large deformation in SoL, the stress generated by the small deformation is linearized, and the linearized elasticity tensor is taken to be a significant factor facilitating prediction of cellular behavior. The pre-stretch is shown to produce direction-based, effective elastic moduli for cellular mechanosensing. The utility of this SoL theory is illustrated by culturing of two different cell types grown on uniaxially pre-stretched surfaces that induce changes to the cell orientation and behavior.

Multiscale model of integrin adhesion assembly

The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. The assembly of adhesions is mediated by several types of integrins. These integrins differ in physical properties, including rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, the way in which nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we therefore develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. Organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total amount of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both structural and dynamic properties of adhesions.

Role of mechanical flow for actin network organization

The major cytoskeletal protein actin forms complex networks to provide structural support and perform vital functions in cells. In vitro studies have revealed that the structure of the higher-order actin network is determined primarily by the type of actin binding protein (ABP). By comparison, there are far fewer studies about the role of the mechanical environment for the organization of the actin network. In particular, the duration over which cells reorganize their shape in response to functional demands is relatively short compared to the in vitro protein polymerization time, suggesting that such changes can influence the actin network formation. We hypothesize that mechanical flows in the cytoplasm generated by exogenous and endogenous stimulation play a key role in the spatiotemporal regulation of the actin architecture. To mimic cytoplasmic streaming, we generated a circulating flow using surface acoustic wave in a microfluidic channel and investigated its effect on the formation of networks by actin and ABPs. We found that the mechanical flow affected the orientation and thickness of actin bundles, depending on the type and concentration of ABPs. Our computational model shows that the extent of alignment and thickness of actin bundle are determined by the balance between flow-induced drag forces and the tendency of ABPs to crosslink actin filaments at given angles. These results suggest that local intracellular flows can affect the assembly dynamics and morphology of the actin cytoskeleton. STATEMENT OF SIGNIFICANCE: Spatiotemporal regulation of actin cytoskeleton structure is essential in many cellular functions. It has been shown that mechanical cues including an applied force and geometric boundary can alter the structural characteristics of actin network. However, even though the cytoplasm accounts for a large portion of the cell volume, the effect of the cytoplasmic streaming flow produced during cell dynamics on actin network organization has not been reported. In this study, we demonstrated that the mechanical flow exerted during actin network organization play an important role in determining the orientation and dimension of actin bundle network. Our result will be beneficial in understanding the mechanism of the actin network reorganization occurred during physiological and pathological processes.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

Emergent mechanics of actomyosin drive punctuated contractions and shape network morphology in the cell cortex

Filamentous actin (F-actin) and non-muscle myosin II motors drive cell motility and cell shape changes that guide large scale tissue movements during embryonic morphogenesis. To gain a better understanding of the role of actomyosin in vivo, we have developed a two-dimensional (2D) computational model to study emergent phenomena of dynamic unbranched actomyosin arrays in the cell cortex. These phenomena include actomyosin punctuated contractions, or "actin asters" that form within quiescent F-actin networks. Punctuated contractions involve both formation of high intensity aster-like structures and disassembly of those same structures. Our 2D model allows us to explore the kinematics of filament polarity sorting, segregation of motors, and morphology of F-actin arrays that emerge as the model structure and biophysical properties are varied. Our model demonstrates the complex, emergent feedback between filament reorganization and motor transport that generate as well as disassemble actin asters. Since intracellular actomyosin dynamics are thought to be controlled by localization of scaffold proteins that bind F-actin or their myosin motors we also apply our 2D model to recapitulate in vitro studies that have revealed complex patterns of actomyosin that assemble from patterning filaments and motor complexes with microcontact printing. Although we use a minimal representation of filament, motor, and cross-linker biophysics, our model establishes a framework for investigating the role of other actin binding proteins, how they might alter actomyosin dynamics, and makes predictions that can be tested experimentally within live cells as well as within in vitro models.

Recent genetic and mechanical studies of embryonic development reveal a critical role for intracellular scaffolds in generating the shape of the embryo and constructing internal organs. In this paper we developed computer simulations of these scaffolds, composed of filamentous actin (F-actin), a rod-like protein polymer, and mini-thick filaments, composed of non-muscle myosin II, forming a two headed spring-like complex of motor proteins that can walk on, and remodel F-actin networks. Using simulations of these dynamic interactions, we can carry out virtual experiments where we change the physics and chemistry of F-actin polymers, their associated myosin motors, and cross-linkers and observe the changes in scaffolds that emerge. For example, by modulating the motor stiffness of the myosin motors in our model we can observe the formation or loss of large aster-like structures. Such fine-grained control over the physical properties of motors or filaments within simulations are not currently possible with biological experiments, even where mutant proteins or small molecule inhibitors can be targeted to specific sites on filaments or motors. Our approach reflects a growing adoption of simulation methods to investigate microscopic features that shape actomyosin arrays and the mesoscale effects of molecular scale processes. We expect predictions from these models will drive more refined experimental approaches to expose the many roles of actomyosin in development.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

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.

Tension, contraction and tissue morphogenesis

D'Arcy Thompson was a proponent of applying mathematical and physical principles to biological systems, an approach that is becoming increasingly common in developmental biology. Indeed, the recent integration of quantitative experimental data, force measurements and mathematical modeling has changed our understanding of morphogenesis - the shaping of an organism during development. Emerging evidence suggests that the subcellular organization of contractile cytoskeletal networks plays a key role in force generation, while on the tissue level the spatial organization of forces determines the morphogenetic output. Inspired by D'Arcy Thompson's On Growth and Form, we review our current understanding of how biological forms are created and maintained by the generation and organization of contractile forces at the cell and tissue levels. We focus on recent advances in our understanding of how cells actively sculpt tissues and how forces are involved in specific morphogenetic processes.

Probing eukaryotic cell mechanics via mesoscopic simulations

Cell mechanics has proven to be important in many biological processes. Although there is a number of experimental techniques which allow us to study mechanical properties of cell, there is still a lack of understanding of the role each sub-cellular component plays during cell deformations. We present a new mesoscopic particle-based eukaryotic cell model which explicitly describes cell membrane, nucleus and cytoskeleton. We employ Dissipative Particle Dynamics (DPD) method that provides us with the unified framework for modeling of a cell and its interactions in the flow. Data from micropipette aspiration experiments were used to define model parameters. The model was validated using data from microfluidic experiments. The validated model was then applied to study the impact of the sub-cellular components on the cell viscoelastic response in micropipette aspiration and microfluidic experiments.

Spontaneous Formation of a Globally Connected Contractile Network in a Microtubule-Motor System

Microtubule (MT) networks play key roles in cell division, intracellular transport, and cell motility. These functions of MT networks occur through interactions between MTs and various associated proteins, notably motor proteins that bundle and slide MTs. Our objective in this study was to address the question of how motors determine the nature of MT networks. We conducted in vitro assays using homotetrameric kinesin Eg5, a motor protein involved in the formation and maintenance of the mitotic spindle. The mixing of Eg5 and MTs produced a range of spatiotemporal dynamics depending on the motor/filament ratio. Low motor/filament ratios produced globally connected static MT networks with sparsely distributed contractile active nodes (motor-accumulating points with radially extending MTs). Increasing the motor/filament ratio facilitated the linking of contractile active nodes and led to a global contraction of the network. When the motor/filament ratio was further increased, densely distributed active nodes formed local clusters and segmented the network into pieces with their strong contractile forces. Altering the properties of the motor through the use of chimeric Eg5, which has kinesin-1 heads, resulted in the generation of many isolated asters. These results suggest that the spatial distribution of contractile active nodes determines the dynamics of MT-motor networks. We then developed a coarse-grained model of MT-motor networks and identified two essential features for reproducing the experimentally observed patterns: an accumulation of motors that form the active nodes necessary to generate contractile forces, and a nonlinear dependency of contractile force on motor densities. Our model also enabled us to characterize the mechanical properties of the contractile network. Our study provides insight into how local motor-MT interactions generate the spatiotemporal dynamics of macroscopic network structures.

Actomyosin meshwork mechanosensing enables tissue shape to orient cell force

Sculpting organism shape requires that cells produce forces with proper directionality. Thus, it is critical to understand how cells orient the cytoskeleton to produce forces that deform tissues. During Drosophila gastrulation, actomyosin contraction in ventral cells generates a long, narrow epithelial furrow, termed the ventral furrow, in which actomyosin fibres and tension are directed along the length of the furrow. Using a combination of genetic and mechanical perturbations that alter tissue shape, we demonstrate that geometrical and mechanical constraints act as cues to orient the cytoskeleton and tension during ventral furrow formation. We developed an in silico model of two-dimensional actomyosin meshwork contraction, demonstrating that actomyosin meshworks exhibit an inherent force orienting mechanism in response to mechanical constraints. Together, our in vivo and in silico data provide a framework for understanding how cells orient force generation, establishing a role for geometrical and mechanical patterning of force production in tissues.

Large-scale tissue reorganization requires the generation of directional tension, which requires orientation of the cytoskeleton. Here Chanet et al. alter tissue shape and tension in the Drosophila embryo to show that geometric and mechanical constraints act as cues to orient the cytoskeleton and tension.

Regulatory Roles of Fluctuation-Driven Mechanotransduction in Cell Function

Cells in the body are exposed to irregular mechanical stimuli. Here, we review the so-called fluctuation-driven mechanotransduction in which stresses stretching cells vary on a cycle-by-cycle basis. We argue that such mechanotransduction is an emergent network phenomenon and offer several potential mechanisms of how it regulates cell function. Several examples from the vasculature, the lung, and tissue engineering are discussed. We conclude with a list of important open questions.

Morphological Transformation and Force Generation of Active Cytoskeletal Networks

Cells assemble numerous types of actomyosin bundles that generate contractile forces for biological processes, such as cytokinesis and cell migration. One example of contractile bundles is a transverse arc that forms via actomyosin-driven condensation of actin filaments in the lamellipodia of migrating cells and exerts significant forces on the surrounding environments. Structural reorganization of a network into a bundle facilitated by actomyosin contractility is a physiologically relevant and biophysically interesting process. Nevertheless, it remains elusive how actin filaments are reoriented, buckled, and bundled as well as undergo tension buildup during the structural reorganization. In this study, using an agent-based computational model, we demonstrated how the interplay between the density of myosin motors and cross-linking proteins and the rigidity, initial orientation, and turnover of actin filaments regulates the morphological transformation of a cross-linked actomyosin network into a bundle and the buildup of tension occurring during the transformation.

Modeling cytokinesis of eukaryotic cells driven by the actomyosin contractile ring

A three-dimensional (3D) hydrodynamic model for cytokinesis of eukaryotic cells is developed, in which we model dynamics of actomyosins in the cell cortex, in particular, along the cytokinetic ring formed in the cortex and in the neighborhood of the cell's division plane explicitly. Specifically, the active force actuated by the actomyosin's activity along the cytokinetic ring is modeled by a surface force whose strength is proportional to the actomyosin concentration while the cell morphology is tracked by a phase field model. The model is then solved in 3D space and time using a finite difference method on graphic processing units. Dynamical morphological patterns of eukaryotic cells during cytokinesis are numerically simulated with the model. These simulated morphological patterns agree quantitatively with experimental observations. Copyright © 2016 John Wiley & Sons, Ltd.

Homeostatic maintenance via degradation and repair of elastic fibers under tension

Cellular maintenance of the extracellular matrix requires an effective regulation that balances enzymatic degradation with the repair of collagen fibrils and fibers. Here, we investigate the long-term maintenance of elastic fibers under tension combined with diffusion of general degradative and regenerative particles associated with digestion and repair processes. Computational results show that homeostatic fiber stiffness can be achieved by assuming that cells periodically probe fiber stiffness to adjust the production and release of degradative and regenerative particles. However, this mechanism is unable to maintain a homogeneous fiber. To account for axial homogeneity, we introduce a robust control mechanism that is locally governed by how the binding affinity of particles is modulated by mechanical forces applied to the ends of the fiber. This model predicts diameter variations along the fiber that are in agreement with the axial distribution of collagen fibril diameters obtained from scanning electron microscopic images of normal rat thoracic aorta. The model predictions match the experiments only when the applied force on the fiber is in the range where the variance of local stiffness along the fiber takes a minimum value. Our model thus predicts that the biophysical properties of the fibers play an important role in the long-term regulatory maintenance of these fibers.

Three-Dimensional Characterization of Mechanical Interactions between Endothelial Cells and Extracellular Matrix during Angiogenic Sprouting

We studied the three-dimensional cell-extracellular matrix interactions of endothelial cells that form multicellular structures called sprouts. We analyzed the data collected in-situ from angiogenic sprouting experiments and identified the differentiated interaction behavior exhibited by the tip and stalk cells. Moreover, our analysis of the tip cell lamellipodia revealed the diversity in their interaction behavior under certain conditions (e.g., when the heading of a sprout is switched approximately between the long-axis direction of two different lamellipodia). This study marks the first time that new characteristics of such interactions have been identified with shape changes in the sprouts and the associated rearrangements of collagen fibers. Clear illustrations of such changes are depicted in three-dimensional views.

Contribution of myosin II activity to cell spreading dynamics

Myosin II activity and actin polymerization at the leading edge of the cell are known to be essential sources of cellular stress. However, a quantitative account of their separate contributions is still lacking; so is the influence of the coupling between the two phenomena on cell spreading dynamics. We present a simple analytic elastic theory of cell spreading dynamics that quantitatively demonstrates how actin polymerization and myosin activity cooperate in the generation of cellular stress during spreading. Consistent with experiments, myosin activity is assumed to polarize in response to the stresses generated during spreading. The characteristic response time and the overall spreading time are predicted to determine different evolution profiles of cell spreading dynamics. These include, a (regular) monotonic increase of cell projected area with time, a non-monotonic (overshooting) profile with a maximum, and damped oscillatory modes. In addition, two populations of myosin II motors are distinguished based on their location in the lamella; those located above the major adhesion zone at the cell periphery are shown to facilitate spreading whereas those in deeper regions of the lamella are shown to oppose spreading. We demonstrate that the attenuation of myosin activity in the two regions may result in reciprocal effects on spreading. These findings provide important new insight into the function of myosin II motors in the course of spreading.

Interplay of active processes modulates tension and drives phase transition in self-renewing, motor-driven cytoskeletal networks

The actin cytoskeleton--a complex, nonequilibrium network consisting of filaments, actin-crosslinking proteins (ACPs) and motors--confers cell structure and functionality, from migration to morphogenesis. While the core components are recognized, much less is understood about the behaviour of the integrated, disordered and internally active system with interdependent mechano-chemical component properties. Here we use a Brownian dynamics model that incorporates key and realistic features--specifically actin turnover, ACP (un)binding and motor walking--to reveal the nature and underlying regulatory mechanisms of overarching cytoskeletal states. We generate multi-dimensional maps that show the ratio in activity of these microscopic elements determines diverse global stress profiles and the induction of nonequilibrium morphological phase transition from homogeneous to aggregated networks. In particular, actin turnover dynamics plays a prominent role in tuning stress levels and stabilizing homogeneous morphologies in crosslinked, motor-driven networks. The consequence is versatile functionality, from dynamic steady-state prestress to large, pulsed constrictions.

Tensional homeostasis in single fibroblasts

Adherent cells generate forces through acto-myosin contraction to move, change shape, and sense the mechanical properties of their environment. They are thought to maintain defined levels of tension with their surroundings despite mechanical perturbations that could change tension, a concept known as tensional homeostasis. Misregulation of tensional homeostasis has been proposed to drive disorganization of tissues and promote progression of diseases such as cancer. However, whether tensional homeostasis operates at the single cell level is unclear. Here, we directly test the ability of single fibroblast cells to regulate tension when subjected to mechanical displacements in the absence of changes to spread area or substrate elasticity. We use a feedback-controlled atomic force microscope to measure and modulate forces and displacements of individual contracting cells as they spread on a fibronectin-patterned atomic-force microscope cantilever and coverslip. We find that the cells reach a steady-state contraction force and height that is insensitive to stiffness changes as they fill the micropatterned areas. Rather than maintaining a constant tension, the fibroblasts altered their contraction force in response to mechanical displacement in a strain-rate-dependent manner, leading to a new and stable steady-state force and height. This response is influenced by overexpression of the actin crosslinker α-actinin, and rheology measurements reveal that changes in cell elasticity are also strain- rate-dependent. Our finding of tensional buffering, rather than homeostasis, allows cells to transition between different tensional states depending on how they are displaced, permitting distinct responses to slow deformations during tissue growth and rapid deformations associated with injury.

Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.

Isoforms Confer Characteristic Force Generation and Mechanosensation by Myosin II Filaments

Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) arrays to generate contractile forces in muscle and nonmuscle cells. How myosin II force production is shaped by isoform-specific motor properties and environmental stiffness remains poorly understood. Here, we used computer simulations to analyze force production by an ensemble of myosin motors against an elastically tethered actin filament. We found that force output depends on two timescales: the duration of F-actin attachment, which varies sharply with the ensemble size, motor duty ratio, and external load; and the time to build force, which scales with the ensemble stall force, gliding speed, and environmental stiffness. Although force-dependent kinetics were not required to sense changes in stiffness, the myosin catch bond produced positive feedback between the attachment time and force to trigger switch-like transitions from transient attachments, generating small forces, to high-force-generating runs. Using parameters representative of skeletal muscle myosin, nonmuscle myosin IIB, and nonmuscle myosin IIA revealed three distinct regimes of behavior, respectively: 1) large assemblies of fast, low-duty ratio motors rapidly build stable forces over a large range of environmental stiffness; 2) ensembles of slow, high-duty ratio motors serve as high-affinity cross-links with force buildup times that exceed physiological timescales; and 3) small assemblies of low-duty ratio motors operating at intermediate speeds are poised to respond sharply to changes in mechanical context-at low force or stiffness, they serve as low-affinity cross-links, but they can transition to force production via the positive-feedback mechanism described above. Together, these results reveal how myosin isoform properties may be tuned to produce force and respond to mechanical cues in their environment.

Active mechanical coupling between the nucleus, cytoskeleton and the extracellular matrix, and the implications for perinuclear actomyosin organization

Experimental and theoretical studies have demonstrated that the polarization of actomyosin forces in the cytoskeleton of adherent cells is governed by local elastic stresses. Based on this phenomenon, and the established observation that the nucleus is mechanically connected to the extracellular matrix (ECM) via the cytoskeleton, we theoretically analyze here the active mechanical coupling between the nucleus, cytoskeleton and the ECM. The cell is modeled as an active spherical inclusion, containing a round nucleus at its center, and embedded in a 3D elastic matrix. We investigate three sources of cellular stress: spreading-induced stress, actomyosin contractility and chromatin entropic forces. Formulating the coupling of actomyosin contractility to the local stress we predict the consequences that the nucleus, cytoskeleton and ECM mechanical properties may have on the overall force-balance in the cell and the perinuclear acto-myosin polarization. We demonstrate that the presence of the nucleus induces symmetry breaking of the elastic stress that, we predict, elastically tends to orient actomyosin alignment tangentially around the nucleus; the softer the nucleus or the matrix, the stronger is the preference for tangential alignment. Spreading induced stresses may induce radial actomyosin alignment near stiff nuclei. In addition, we show that in regions of high actomyosin density myosin motors have an elastic tendency to orient tangentially as often occurs near the cell periphery. These conclusions highlight the role of the nucleus in the regulation of cytoskeleton organization and may provide new insight into the mechanics of stem cell differentiation involving few fold increase in nucleus stiffness.

Cells as liquid motors: mechanosensitivity emerges from collective dynamics of actomyosin cortex

Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodeling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerization at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn, regulates the cell length in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena, which are of the same nature as those taking place during the contraction of a whole muscle. This similarity explains the fact that single nonmuscle cell and whole-muscle contraction both follow a Hill-like force-velocity relationship.

Formation of contractile networks and fibers in the medial cell cortex through myosin-II turnover, contraction, and stress-stabilization

The morphology of adhered cells depends crucially on the formation of a contractile meshwork of parallel and cross-linked fibers along the contacting surface. The motor activity and minifilament assembly of non-muscle myosin-II is an important component of cortical cytoskeletal remodeling during mechanosensing. We used experiments and computational modeling to study cortical myosin-II dynamics in adhered cells. Confocal microscopy was used to image the medial cell cortex of HeLa cells stably expressing myosin regulatory light chain tagged with GFP (MRLC-GFP). The distribution of MRLC-GFP fibers and focal adhesions was classified into three types of network morphologies. Time-lapse movies show: myosin foci appearance and disappearance; aligning and contraction; stabilization upon alignment. Addition of blebbistatin, which perturbs myosin motor activity, leads to a reorganization of the cortical networks and to a reduction of contractile motions. We quantified the kinetics of contraction, disassembly and reassembly of myosin networks using spatio-temporal image correlation spectroscopy (STICS). Coarse-grained numerical simulations include bipolar minifilaments that contract and align through specified interactions as basic elements. After assuming that minifilament turnover decreases with increasing contractile stress, the simulations reproduce stress-dependent fiber formation in between focal adhesions above a threshold myosin concentration. The STICS correlation function in simulations matches the function measured in experiments. This study provides a framework to help interpret how different cortical myosin remodeling kinetics may contribute to different cell shape and rigidity depending on substrate stiffness.

Impact of dimensionality and network disruption on microrheology of cancer cells in 3D environments

Dimensionality is a fundamental component that can have profound implications on the characteristics of physical systems. In cell biology, however, the majority of studies on cell physical properties, from rheology to force generation to migration, have been performed on 2D substrates, and it is not clear how a more realistic 3D environment influences cell properties. Here, we develop an integrated approach and demonstrate the combination of mitochondria-tracking microrheology, microfluidics, and Brownian dynamics simulations to explore the impact of dimensionality on intracellular mechanics and on the effects of intracellular disruption. Additionally, we consider both passive thermal and active motor-driven processes within the cell and demonstrate through modeling how active internal fluctuations are modulated via dimensionality. Our results demonstrate that metastatic breast cancer cells (MDA-MB-231) exhibit more solid-like internal motions in 3D compared to 2D, and actin network disruption via Cytochalasin D has a more pronounced effect on internal cell fluctuations in 2D. Our computational results and modeling show that motor-induced active stress fluctuations are enhanced in 2D, leading to increased local intracellular particle fluctuations and apparent fluid-like behavior.

Biomechanical properties at the cellular and subcellular levels are important in providing proper biological functions, from cell migratory capabilities to intracellular transport. Deregulation in these properties can lead to disease states such as cancer metastasis. We develop and demonstrate an integrated experimental and computational approach to study intracellular mechanics. We demonstrate that a key environmental factor, dimensionality, plays a significant role in modulating intracellular mechanical behavior. This is important as typical cell biology and mechanics experiments are performed on 2D substrates, which do not capture the physiological features of 3D matrices and may not induce physiologically accurate cell properties. We further develop an effective temperature model to describe how dimensionality changes intracellular particle motion by altering the activity of molecular motors.

Early-time dynamics of actomyosin polarization in cells of confined shape in elastic matrices

The cell shape and the rigidity of the extracellular matrix have been shown to play an important role in the regulation of cytoskeleton structure and force generation. Elastic stresses that develop by actomyosin contraction feedback on myosin activity and govern the anisotropic polarization of stress fibers in the cell. We theoretically study the consequences that the cell shape and matrix rigidity may have on the dynamics and steady state polarization of actomyosin forces in the cell. Actomyosin forces are assumed to polarize in accordance with the stresses that develop in the cytoskeleton. The theory examines this self-polarization process as a relaxation response determined by two distinct susceptibility factors and two characteristic times. These reveal two canonical polarization responses to local variations in the elastic stress: an isotropic response, in which actomyosin dipolar stress isotropically changes in magnitude, and an orientational response, in which actomyosin forces orient with no net change in magnitude. Actual polarization may show up as a superimposition of the two mechanisms yielding different phases in the polarization response as observed experimentally. The cell shape and elastic moduli of the surroundings are shown to govern both the dynamics of the process as well as the steady-state. We predict that in the steady-state, beyond a critical matrix rigidity, spherical cells exert maximal force, and below that rigidity, elongated or flattened cells exert more force. Similar behaviors are reflected in the rate of the polarization process. The theory is also applicable to study the elastic response of whole cell aggregates in a gel.

A cell-regulatory mechanism involving feedback between contraction and tissue formation guides wound healing progression

Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

A computational model of the response of adherent cells to stretch and changes in substrate stiffness

Cells in the body exist in a dynamic mechanical environment where they are subject to mechanical stretch as well as changes in composition and stiffness of the underlying extracellular matrix (ECM). However, the underlying mechanisms by which cells sense and adapt to their dynamic mechanical environment, in particular to stretch, are not well understood. In this study, we hypothesized that emergent phenomena at the level of the actin network arising from active structural rearrangements driven by nonmuscle myosin II molecular motors play a major role in the cellular response to both stretch and changes in ECM stiffness. To test this hypothesis, we introduce a simple network model of actin-myosin interactions that links active self-organization of the actin network to the stiffness of the network and the traction forces generated by the network. We demonstrate that such a network replicates not only the effect of changes in substrate stiffness on cellular traction and stiffness and the dependence of rate of force development by a cell on the stiffness of its substrate, but also explains the physical response of adherent cells to transient and cyclic stretch. Our results provide strong indication that network phenomena governed by the active reorganization of the actin-myosin structure plays an important role in cellular mechanosensing and response to both changes in ECM stiffness and externally applied mechanical stretch.

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behavior. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determines the mechano-sensing behavior of single cells.