Cell shape dynamics reveal balance of elasticity and contractility in peripheral arcs

Apical constriction requires patterned apical surface remodeling to synchronize cellular deformation

Apical constriction is a basic mechanism for epithelial morphogenesis, making columnar cells into wedge shape and bending a flat cell sheet. It has long been thought that an apically localized myosin generates a contractile force and drives the cell deformation. However, when we tested the increased apical surface contractility in a cellular Potts model simulation, the constriction increased pressure inside the cell and pushed its lateral surface outward, making the cells adopt a drop shape instead of the expected wedge shape. To keep the lateral surface straight, we considered an alternative model in which the cell shape was determined by cell membrane elasticity and endocytosis, and the increased pressure is balanced among the cells. The cellular Potts model simulation succeeded in reproducing the apical constriction, and it also suggested that a too strong apical surface tension might prevent the tissue invagination.

Decisive role of mDia-family formins in cell cortex function of highly adherent cells

Cortical formins, pivotal for the assembly of linear actin filaments beneath the membrane, exert only minor effects on unconfined cell migration of weakly and moderately adherent cells. However, their impact on migration and mechanostability of highly adherent cells remains poorly understood. Here, we demonstrate that loss of cortical actin filaments generated by the formins mDia1 and mDia3 drastically compromises cell migration and mechanics in highly adherent fibroblasts. Biophysical analysis of the mechanical properties of the mutant cells revealed a markedly softened cell cortex in the poorly adherent state. Unexpectedly, in the highly adherent state, associated with a hyperstretched morphology with exaggerated focal adhesions and prominent high-strain stress fibers, they exhibited even higher cortical tension compared to control. Notably, misguidance of intracellular forces, frequently accompanied by stress-fiber rupture, culminated in the formation of tension- and contractility-induced macroapertures, which was instantly followed by excessive lamellipodial protrusion at the periphery, providing critical insights into mechanotransduction of mechanically stressed and highly adherent cells.

Diffusion model predicts the geometry of actin cytoskeleton from cell morphology

Cells exhibit various morphological characteristics due to their physiological activities, and changes in cell morphology are inherently accompanied by the assembly and disassembly of the actin cytoskeleton. Stress fibers are a prominent component of the actin-based intracellular structure and are highly involved in numerous physiological processes, e.g., mechanotransduction and maintenance of cell morphology. Although it is widely accepted that variations in cell morphology interact with the distribution and localization of stress fibers, it remains unclear if there are underlying geometric principles between the cell morphology and actin cytoskeleton. Here, we present a machine learning system that uses the diffusion model to convert the cell shape to the distribution and alignment of stress fibers. By training with corresponding cell shape and stress fibers datasets, our system learns the conversion to generate the stress fiber images from its corresponding cell shape. The predicted stress fiber distribution agrees well with the experimental data. With this conversion relation, our system allows for performing virtual experiments that provide a visual map showing the probability of stress fiber distribution from the virtual cell shape. Our system potentially provides a powerful approach to seek further hidden geometric principles regarding how the configuration of subcellular structures is determined by the boundary of the cell structure; for example, we found that the stress fibers of cells with small aspect ratios tend to localize at the cell edge while cells with large aspect ratios have homogenous distributions.

Polarized focal adhesion kinase activity within a focal adhesion during cell migration

Focal adhesion kinase (FAK) relays integrin signaling from outside to inside cells and contributes to cell adhesion and motility. However, the spatiotemporal dynamics of FAK activity in single FAs is unclear due to the lack of a robust FAK reporter, which limits our understanding of these essential biological processes. Here we have engineered a genetically encoded FAK activity sensor, dubbed FAK-separation of phases-based activity reporter of kinase (SPARK), which visualizes endogenous FAK activity in living cells and vertebrates. Our work reveals temporal dynamics of FAK activity during FA turnover. Most importantly, our study unveils polarized FAK activity at the distal tip of newly formed single FAs in the leading edge of a migrating cell. By combining FAK-SPARK with DNA tension probes, we show that tensions applied to FAs precede FAK activation and that FAK activity is proportional to the strength of tension. These results suggest tension-induced polarized FAK activity in single FAs, advancing the mechanistic understanding of cell migration.

Annotation-free learning of a spatio-temporal manifold of the cell life cycle

The cell cycle is a complex biological phenomenon, which plays an important role in many cell biological processes and disease states. Machine learning is emerging to be a pivotal technique for the study of the cell cycle, resulting in a number of available tools and models for the analysis of the cell cycle. Most, however, heavily rely on expert annotations, prior knowledge of mechanisms, and imaging with several fluorescent markers to train their models. Many are also limited to processing only the spatial information in the cell images. In this work, we describe a different approach based on representation learning to construct a manifold of the cell life cycle. We trained our model such that the representations are learned without exhaustive annotations nor assumptions. Moreover, our model uses microscopy images derived from a single fluorescence channel and utilizes both the spatial and temporal information in these images. We show that even with fewer channels and self-supervision, information relevant to cell cycle analysis such as staging and estimation of cycle duration can still be extracted, which demonstrates the potential of our approach to aid future cell cycle studies and in discovery cell biology to probe and understand novel dynamic systems.

Crawling, waving, inch worming, dilating, and pivoting mechanics of migrating cells: Lessons from Ken Jacobson

Research on the locomotion of single cells on hard, flat surfaces brought insight into the mechanisms of leading-edge protrusion, spatially graded adhesion, front-rear coordination, and how intracellular and traction forces are harnessed to execute various maneuvers. Here, we highlight how, by studying a variety of cell types, shapes, and movements, Ken Jacobson and his collaborators made several discoveries that triggered the mechanistic understanding of cell motility. We then review the recent advancements and current perspectives in this field.

SFAlab: image-based quantification of mechano-active ventral actin stress fibers in adherent cells

Ventral actin stress fibers (SFs) are a subset of actin SFs that begin and terminate at focal adhesion (FA) complexes. Ventral SFs can transmit forces from and to the extracellular matrix and serve as a prominent mechanosensing and mechanotransduction machinery for cells. Therefore, quantitative analysis of ventral SFs can lead to deeper understanding of the dynamic mechanical interplay between cells and their extracellular matrix (mechanoreciprocity). However, the dynamic nature and organization of ventral SFs challenge their quantification, and current quantification tools mainly focus on all SFs present in cells and cannot discriminate between subsets. Here we present an image analysis-based computational toolbox, called SFAlab, to quantify the number of ventral SFs and the number of ventral SFs per FA, and provide spatial information about the locations of the identified ventral SFs. SFAlab is built as an all-in-one toolbox that besides analyzing ventral SFs also enables the identification and quantification of (the shape descriptors of) nuclei, cells, and FAs. We validated SFAlab for the quantification of ventral SFs in human fetal cardiac fibroblasts and demonstrated that SFAlab analysis i) yields accurate ventral SF detection in the presence of image imperfections often found in typical fluorescence microscopy images, and ii) is robust against user subjectivity and potential experimental artifacts. To demonstrate the usefulness of SFAlab in mechanobiology research, we modulated actin polymerization and showed that inhibition of Rho kinase led to a significant decrease in ventral SF formation and the number of ventral SFs per FA, shedding light on the importance of the RhoA pathway specifically in ventral SF formation. We present SFAlab as a powerful open source, easy to use image-based analytical tool to increase our understanding of mechanoreciprocity in adherent cells.

Force propagation between epithelial cells depends on active coupling and mechano-structural polarization

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.

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

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

Profiling DNA damage in 3D Histology Samples

The morphology of individual cells can reveal much about the underlying states and mechanisms in biology. In tumor environments, the interplay among different cell morphologies in local neighborhoods can further improve this characterization. In this paper, we present an approach based on representation learning to capture similarities and subtle differences in cells positive for γH2AX, a common marker for DNA damage. We demonstrate that texture representations using GLCM and VAE-GAN enable profiling of cells in both singular and local neighborhood contexts. Additionally, we investigate a possible quantification of immune and DNA damage response interplay by enumerating CD8+ and γH2AX+ on different scales. Using our profiling approach, regions in treated tissues can be differentiated from control tissue regions, demonstrating its potential in aiding quantitative measurements of DNA damage and repair in tumor contexts.

Deconstructing the role of myosin contractility in force fluctuations within focal adhesions

Force fluctuations exhibited in focal adhesions that connect a cell to its extracellular environment point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space, that the system goes from decaying oscillations to stable limit cycle oscillations through a supercritical Hopf bifurcation. As a function of the motor activity and the number of clutches, the system exhibits a rich array of dynamical states. We corroborate our analytical results with stochastic simulations of the motor-clutch system. We obtain limit cycle oscillations in the parameter regime as predicted by our model. The frequency range of oscillations in the average clutch and motor deformation compares well with experimental results.

Advanced quantification for single-cell adhesion by variable-angle TIRF nanoscopy

Over the last decades, several techniques have been developed to study cell adhesion; however, they present significant shortcomings. Such techniques mostly focus on strong adhesion related to specific protein-protein associations, such as ligand-receptor binding in focal adhesions. Therefore, weak adhesion, related to less specific or nonspecific cell-substrate interactions, are rarely addressed. Hence, we propose in this work a complete investigation of cell adhesion, from highly specific to nonspecific adhesiveness, using variable-angle total internal reflection fluorescence (vaTIRF) nanoscopy. This technique allows us to map in real time cell topography with a nanometric axial resolution, along with cell cortex refractive index. These two key parameters allow us to distinguish high and low adhesive cell-substrate contacts. Furthermore, vaTIRF provides cell-substrate binding energy, thus revealing a correlation between cell contractility and cell-substrate binding energy. Here, we highlight the quantitative measurements achieved by vaTIRF on U87MG glioma cells expressing different amounts of α ₅ integrins and distinct motility on fibronectin. Regarding integrin expression level, data extracted from vaTIRF measurements, such as the number and size of high adhesive contacts per cell, corroborate the adhesiveness of U87MG cells as intended. Interestingly enough, we found that cells overexpressing α ₅ integrins present a higher contractility and lower adhesion energy.

Distinct roles of nonmuscle myosin II isoforms for establishing tension and elasticity during cell morphodynamics

Nonmuscle myosin II (NM II) is an integral part of essential cellular processes, including adhesion and migration. Mammalian cells express up to three isoforms termed NM IIA, B, and C. We used U2OS cells to create CRISPR/Cas9-based knockouts of all three isoforms and analyzed the phenotypes on homogenously coated surfaces, in collagen gels, and on micropatterned substrates. In contrast to homogenously coated surfaces, a structured environment supports a cellular phenotype with invaginated actin arcs even in the absence of NM IIA-induced contractility. A quantitative shape analysis of cells on micropatterns combined with a scale-bridging mathematical model reveals that NM IIA is essential to build up cellular tension during initial stages of force generation, while NM IIB is necessary to elastically stabilize NM IIA-generated tension. A dynamic cell stretch/release experiment in a three-dimensional scaffold confirms these conclusions and in addition reveals a novel role for NM IIC, namely the ability to establish tensional homeostasis.

Extracellular Matrix Geometry and Initial Adhesive Position Determine Stress Fiber Network Organization during Cell Spreading

Three-dimensional matrices often contain highly structured adhesive tracks that require cells to turn corners and bridge non-adhesive areas. Here, we investigate these complex processes using micropatterned cell adhesive frames. Spreading kinetics on these matrices depend strongly on initial adhesive position and are predicted by a cellular Potts model (CPM), which reflects a balance between adhesion and intracellular tension. As cells spread, new stress fibers (SFs) assemble periodically and parallel to the leading edge, with spatial intervals of ∼2.5 μm, temporal intervals of ∼15 min, and characteristic lifetimes of ∼50 min. By incorporating these rules into the CPM, we can successfully predict SF network architecture. Moreover, we observe broadly similar behavior when we culture cells on arrays of discrete collagen fibers. Our findings show that ECM geometry and initial cell position strongly determine cell spreading and that cells encode a memory of their spreading history through SF network organization.

On the mechanical response of the actomyosin cortex during cell indentations

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

A Micropatterning Strategy to Study Nuclear Mechanotransduction in Cells

Micropatterning techniques have been widely used in biology, particularly in studies involving cell adhesion and proliferation on different substrates. Cell micropatterning approaches are also increasingly employed as in vitro tools to investigate intracellular mechanotransduction processes. In this report, we examined how modulating cellular shapes on two-dimensional rectangular fibronectin micropatterns of different widths influences nuclear mechanotransduction mediated by emerin, a nuclear envelope protein implicated in Emery-Dreifuss muscular dystrophy (EDMD). Fibronectin microcontact printing was tested onto glass coverslips functionalized with three different silane reagents (hexamethyldisilazane (HMDS), (3-Aminopropyl)triethoxysilane (APTES) and (3-Glycidyloxypropyl)trimethoxysilane (GPTMS)) using a vapor-phase deposition method. We observed that HMDS provides the most reliable printing surface for cell micropatterning, notably because it forms a hydrophobic organosilane monolayer that favors the retainment of surface antifouling agents on the coverslips. We showed that, under specific mechanical cues, emerin-null human skin fibroblasts display a significantly more deformed nucleus than skin fibroblasts expressing wild type emerin, indicating that emerin plays a crucial role in nuclear adaptability to mechanical stresses. We further showed that proper nuclear responses to forces involve a significant relocation of emerin from the inner nuclear envelope towards the outer nuclear envelope and the endoplasmic reticulum membrane network. Cell micropatterning by fibronectin microcontact printing directly on HMDS-treated glass represents a simple approach to apply steady-state biophysical cues to cells and study their specific mechanobiology responses in vitro.

Actin stress fiber dynamics in laterally confined cells

Multiple cellular processes are affected by spatial constraints from the extracellular matrix and neighboring cells. In vitro experiments using defined micro-patterning allow for in-depth analysis and a better understanding of how these constraints impact cellular behavior and functioning. Herein we focused on the analysis of actin cytoskeleton dynamics as a major determinant of mechanotransduction mechanisms in cells. We seeded primary human umbilical vein endothelial cells onto stripe-like cell-adhesive micro-patterns with varying widths and then monitored and quantified the dynamic reorganization of actin stress fibers, including fiber velocities, orientation and density, within these live cells using the cell permeable F-actin marker SiR-actin. Although characteristic parameters describing the overall stress fiber architecture (average orientation and density) were nearly constant throughout the observation time interval of 60 min, we observed permanent transport and turnover of individual actin stress fibers. Stress fibers were more strongly oriented along stripe direction with decreasing stripe width, (5° on 20 μm patterns and 10° on 40 μm patterns), together with an overall narrowing of the distribution of fiber orientation. Fiber dynamics was characterized by a directed movement from the cell edges towards the cell center, where fiber dissolution frequently took place. By kymograph analysis, we found median fiber velocities in the range of 0.2 μm/min with a weak dependence on pattern width. Taken together, these data suggest that cell geometry determines actin fiber orientation, while it also affects actin fiber transport and turnover.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Many studies in cell biology employ global shape descriptors to probe mechanisms of cell morphogenesis. Here, we implement a framework in this paper to profile cellular morphodynamics very locally. We employ the Hilbert-Huang transform (HHT) to extract along the entire cell edge spectra of instantaneous edge motion frequency and magnitude and use them to classify overall cell behavior as well as subcellular edge sectors of distinct dynamics. We find in fibroblast-like COS7 cells that the marked heterogeneity in mobility of an unstimulated population is fully captured by differences in the magnitude spectra, while the frequency spectra are conserved between cells. Using optogenetics to acutely inhibit morphogenetic signaling pathways we find that these molecular shifts are reflected by changes in the frequency spectra but not in the magnitude spectra. After clustering cell edge sectors with distinct morphodynamics we observe in cells expressing a Rac1 activity biosensor that the sectors with different frequency spectra associate with different signaling intensity and dynamics. Together, these observations let us conclude that the frequency spectrum encodes the wiring of the molecular circuitry that regulates edge movements, whereas the magnitude captures the activation level of the circuitry.

Balancing forces in migration

The integrated molecular interactions of proteins can create active biological networks whose material properties and actions can impact a variety of physiological processes. Chief among these is the ability to generate and respond to physical forces. The cytoskeleton plays a key role in this behavior, characterized by active self-reorganization to control a cell's shape and mediate its physical interactions. This review discusses our current understanding of how the material properties of the cytoskeleton and its physical interactions with the extracellular environment impact cell migration.

Cell-Shaping Micropatterns for Quantitative Super-Resolution Microscopy Imaging of Membrane Mechanosensing Proteins

Patterning cells on microcontact-printed substrates is a powerful approach to control cell morphology and introduce specific mechanical cues on a cell's molecular organization. Although global changes in cellular architectures caused by micropatterns can easily be probed with diffraction-limited optical microscopy, studying molecular reorganizations at the nanoscale demands micropatterned substrates that accommodate the optical requirements of single molecule microscopy techniques. Here, we developed a simple micropatterning strategy that provides control of cellular architectures and is optimized for nanometer accuracy single molecule tracking and three-dimensional super-resolution imaging of plasma and nuclear membrane proteins in cells. This approach, based on fibronectin microcontact printing on hydrophobic organosilane monolayers, allows evanescent wave and light-sheet microscopy of cells whilst fulfilling the stringent optical demands of point reconstruction optical microscopy. By imposing steady-state mechanical cues on cells grown in these micropatterns, we reveal nanoscale remodeling in the dynamics and the structural organizations of the nuclear envelope mechanotransducing protein emerin and of the plasma membrane mechanosensing protein caveolin-1 using single particle tracking photoactivated localization microscopy and direct stochastic optical reconstruction microscopy imaging. In addition to allowing quantitative biophysical studies of mechanoresponsive membrane proteins, this approach provides an easy means to probe mechanical regulations in cellular membranes with high optical resolution and nanometer precision.

Tension and Elasticity Contribute to Fibroblast Cell Shape in Three Dimensions

The shape of animal cells is an important regulator for many essential processes such as cell migration or division. It is strongly determined by the organization of the actin cytoskeleton, which is also the main regulator of cell forces. Quantitative analysis of cell shape helps to reveal the physical processes underlying cell shape and forces, but it is notoriously difficult to conduct it in three dimensions. Here we use direct laser writing to create 3D open scaffolds for adhesion of connective tissue cells through well-defined adhesion platforms. Due to actomyosin contractility in the cell contour, characteristic invaginations lined by actin bundles form between adjacent adhesion sites. Using quantitative image processing and mathematical modeling, we demonstrate that the resulting shapes are determined not only by contractility, but also by elastic stress in the peripheral actin bundles. In this way, cells can generate higher forces than through contractility alone.

Dissipation of contractile forces: the missing piece in cell mechanics

Mechanical forces are key regulators of cell and tissue physiology. The basic molecular mechanism of fiber contraction by the sliding of actin filament upon myosin leading to conformational change has been known for decades. The regulation of force generation at the level of the cell, however, is still far from elucidated. Indeed, the magnitude of cell traction forces on the underlying extracellular matrix in culture is almost impossible to predict or experimentally control. The considerable variability in measurements of cell-traction forces indicates that they may not be the optimal readout to properly characterize cell contractile state and that a significant part of the contractile energy is not transferred to cell anchorage but instead is involved in actin network dynamics. Here we discuss the experimental, numerical, and biological parameters that may be responsible for the variability in traction force production. We argue that limiting these sources of variability and investigating the dissipation of mechanical work that occurs with structural rearrangements and the disengagement of force transmission is key for further understanding of cell mechanics.

The assembly and function of perinuclear actin cap in migrating cells

Stress fibers are actin bundles encompassing actin filaments, actin-crosslinking, and actin-associated proteins that represent the major contractile system in the cell. Different types of stress fibers assemble in adherent cells, and they are central to diverse cellular processes including establishment of the cell shape, morphogenesis, cell polarization, and migration. Stress fibers display specific cellular organization and localization, with ventral fibers present at the basal side, and dorsal fibers and transverse actin arcs rising at the cell front from the ventral to the dorsal side and toward the nucleus. Perinuclear actin cap fibers are a specific subtype of stress fibers that rise from the leading edge above the nucleus and terminate at the cell rear forming a dome-like structure. Perinuclear actin cap fibers are fixed at three points: both ends are anchored in focal adhesions, while the central part is physically attached to the nucleus and nuclear lamina through the linker of nucleoskeleton and cytoskeleton (LINC) complex. Here, we discuss recent work that provides new insights into the mechanism of assembly and the function of these actin stress fibers that directly link extracellular matrix and focal adhesions with the nuclear envelope.

Geometry and network connectivity govern the mechanics of stress fibers

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.

Prediction of traction forces of motile cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

Modeling cell shape and dynamics on micropatterns

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

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.

Microsurgery-aided in-situ force probing reveals extensibility and viscoelastic properties of individual stress fibers

Actin-myosin filament bundles (stress fibers) are critical for tension generation and cell shape, but their mechanical properties are difficult to access. Here we propose a novel approach to probe individual peripheral stress fibers in living cells through a microsurgically generated opening in the cytoplasm. By applying large deformations with a soft cantilever we were able to fully characterize the mechanical response of the fibers and evaluate their tension, extensibility, elastic and viscous properties.

Optimizing micropattern geometries for cell shape and migration with genetic algorithms

Adhesive micropatterns have become a standard tool to control cell shape and function in cell culture.