Traction force microscopy in Dictyostelium reveals distinct roles for myosin II motor and actin-crosslinking activity in polarized cell movement

Field Guide to Traction Force Microscopy

Introduction

Traction force microscopy (TFM) is a widely used technique to measure cell contractility on compliant substrates that mimic the stiffness of human tissues. For every step in a TFM workflow, users make choices which impact the quantitative results, yet many times the rationales and consequences for making these decisions are unclear. We have found few papers which show the complete experimental and mathematical steps of TFM, thus obfuscating the full effects of these decisions on the final output.

Methods

Therefore, we present this "Field Guide" with the goal to explain the mathematical basis of common TFM methods to practitioners in an accessible way. We specifically focus on how errors propagate in TFM workflows given specific experimental design and analytical choices.

Results

We cover important assumptions and considerations in TFM substrate manufacturing, substrate mechanical properties, imaging techniques, image processing methods, approaches and parameters used in calculating traction stress, and data-reporting strategies.

Conclusions

By presenting a conceptual review and analysis of TFM-focused research articles published over the last two decades, we provide researchers in the field with a better understanding of their options to make more informed choices when creating TFM workflows depending on the type of cell being studied. With this review, we aim to empower experimentalists to quantify cell contractility with confidence.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00801-6.

Hs27 fibroblast response to contact guidance cues

Contact guidance is the phenomena of how cells respond to the topography of their external environment. The morphological and dynamic cell responses are strongly influenced by topographic features such as lateral and vertical dimensions, namely, ridge and groove widths and groove depth ([Formula: see text], respectively). However, experimental studies that independently quantify the effect of the individual dimensions as well as their coupling on cellular function are still limited. In this work, we perform extensive parametric studies in the dimensional space-well beyond the previously studied range in the literature-to explore topographical effects on morphology and migration of Hs27 fibroblasts via static and dynamic analyses of live cell images. Our static analysis reveals that the [Formula: see text] is most significant, followed by the [Formula: see text]. The fibroblasts appear to be more elongated and aligned in the groove direction as the [Formula: see text] increases, but their trend changes after 725 nm. Interestingly, the cell shape and alignment show a very strong correlation regardless of [Formula: see text]. Our dynamic analysis confirms that directional cell migration is also strongly influenced by the [Formula: see text], while the effect of the [Formula: see text] and [Formula: see text] is statistically insignificant. Directional cell migration, as observed in the static cell behavior, shows the statistically significant transition when the [Formula: see text] is 725 nm, showing the intimate links between cell morphology and migration. We propose possible scenarios to offer mechanistic explanations of the observed cell behavior.

Mechanical transmission enables EMT cancer cells to drive epithelial cancer cell migration to guide tumor spheroid disaggregation

Cell phenotype heterogeneity within tumor tissue, especially which due to the emergence of epithelial-mesenchymal transition (EMT) in cancer cells, is associated with cancer invasion and metastasis. However, our understanding of the cellular mechanism(s) underlying the cooperation between EMT cell and epithelial cancer cell migration remains incomplete. Herein, heterotypic tumor spheroids containing both epithelial and EMT cancer cells were generated in vitro. We observed that EMT cells dominated the peripheral region of the self-organized heterotypic tumor spheroid. Furthermore, our results demonstrated that EMT cells could serve as leader cells to improve the collective migration efficiency of epithelial cancer cells and promote dispersion and invasion of the tumor spheroids, which was regulated by the force transition between EMT cells and epithelial cancer cells. Mechanistically, our data further suggest that force transmission is mediated by heterophilic N-cadherin/E-cadherin adhesion complexes between EMT and epithelial cancer cells. Impairment of N-cadherin/E-cadherin adhesion complex formation abrogated the ability of EMT cells to guide epithelial cancer cell migration and blocked the dispersion of tumor spheroids. Together, our data provide new insight into the mechanical interaction between epithelial and EMT cancer cells through heterophilic cadherin adhesion, which enables cooperative tumor cell migration, highlighting the role of EMT cells in tumor invasion.

A mathematical analysis of focal adhesion lifetimes and their effect on cell motility

By analyzing the distributions of focal adhesion (FA) lifetimes from different cell types, we found that a gamma distribution best matched the experimental distributions. In all but one case, it was a unimodal, non-symmetric gamma distribution. We used a mathematical model of cell motion to help understand the mechanics and data behind the FA lifetime distributions. The model uses a detach-rate function to determine how long an FA will persist before it detaches. The detach-rate function that produced distributions with a best-fit gamma curve that closely matched that of the data was both force and time dependent. Using the data gathered from the matching simulations, we calculated both the cell speed and mean FA lifetime and compared them. Where available, we also compared this relationship to that of the experimental data and found that the simulation reasonably matches it in most cases. In both the simulations and experimental data, the cell speed and mean FA lifetime are related, with longer mean lifetimes being indicative of slower speeds. We suspect that one of the main predictors of cell speed for migrating cells is the distribution of the FA lifetimes.

Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte-like fan-shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan-shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.

Soft Polymer-Based Technique for Cellular Force Sensing

Soft polymers have emerged as a vital type of material adopted in biomedical engineering to perform various biomechanical characterisations such as sensing cellular forces. Distinct advantages of these materials used in cellular force sensing include maintaining normal functions of cells, resembling in vivo mechanical characteristics, and adapting to the customised functionality demanded in individual applications. A wide range of techniques has been developed with various designs and fabrication processes for the desired soft polymeric structures, as well as measurement methodologies in sensing cellular forces. This review highlights the merits and demerits of these soft polymer-based techniques for measuring cellular contraction force with emphasis on their quantitativeness and cell-friendliness. Moreover, how the viscoelastic properties of soft polymers influence the force measurement is addressed. More importantly, the future trends and advancements of soft polymer-based techniques, such as new designs and fabrication processes for cellular force sensing, are also addressed in this review.

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

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

Effects of spatial confinement on migratory properties of Dictyostelium discoideum cells

Migratory environments of various eukaryotic cells, such as amoeba, leukocytes and cancer cells, typically involve spatial confinement. Numerous studies have recently emerged, aimed to develop experimental platforms that better recapitulate the characteristics of the cellular microenvironment. Using microfluidic technologies, we show that increasing confinement of Dictyostelium discoideum cells into narrower micro-channels resulted in a significant change in the mode of migration and associated arrangement of the actomyosin cytoskeleton. We observed that cells tended to migrate at constant speed, the magnitude of which was dependent on the size of the channels, as was the locomotory strategy adopted by each cell. Two different migration modes were observed, pseudopod-based and bleb-based migration, with bleb based migration being more frequent with increasing confinement and leading to slower migration. Beside the migration mode, we found that the major determinants of cell speed are its protrusion rate, the amount of F-actin at its leading edge and the number of actin foci. Our results highlighted the impact of the microenvironments on cell behavior. Furthermore, we developed a novel quantitative movement analysis platform for mono-dimensional cell migration that allows for standardization and simplification of the experimental conditions and aids investigation of the complex and dynamic processes occurring at the single-cell level.

Traction Forces Control Cell-Edge Dynamics and Mediate Distance Sensitivity during Cell Polarization

Traction forces are generated by cellular actin-myosin system and transmitted to the environment through adhesions. They are believed to drive cell motion, shape changes, and extracellular matrix remodeling [1-3]. However, most of the traction force analysis has been performed on stationary cells, investigating forces at the level of individual focal adhesions or linking them to static cell parameters, such as area and edge curvature [4-10]. It is not well understood how traction forces are related to shape changes and motion, e.g., forces were reported to either increase or drop prior to cell retraction [11-15]. Here, we analyze the dynamics of traction forces during the protrusion-retraction cycle of polarizing fish epidermal keratocytes and find that forces fluctuate together with the cycle, increasing during protrusion and reaching maximum at the beginning of retraction. We relate force dynamics to the recently discovered phenomenological rule [16] that governs cell-edge behavior during keratocyte polarization: both traction forces and probability of switch from protrusion to retraction increase with the distance from the cell center. Diminishing forces with cell contractility inhibitor leads to decreased edge fluctuations and abnormal polarization, although externally applied force can induce protrusion-retraction switch. These results suggest that forces mediate distance sensitivity of the edge dynamics and organize cell-edge behavior, leading to spontaneous polarization. Actin flow rate did not exhibit the same distance dependence as traction stress, arguing against its role in organizing edge dynamics. Finally, using a simple model of actin-myosin network, we show that force-distance relationship might be an emergent feature of such networks.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Fabrication and Implementation of a Reference-Free Traction Force Microscopy Platform

Quantifying cell-induced material deformation provides useful information concerning how cells sense and respond to the physical properties of their microenvironment. While many approaches exist for measuring cell-induced material strain, here we provide a methodology for monitoring strain with sub-micron resolution in a reference-free manner. Using a two-photon activated photolithographic patterning process, we demonstrate how to generate mechanically and bio-actively tunable synthetic substrates containing embedded arrays of fluorescent fiducial markers to easily measure three-dimensional (3D) material deformation profiles in response to surface tractions. Using these substrates, cell tension profiles can be mapped using a single 3D image stack of a cell of interest. Our goal with this methodology is to make traction force microscopy a more accessible and easier to implement tool for researchers studying cellular mechanotransduction processes, especially newcomers to the field.

Reference-Free Traction Force Microscopy Platform Fabricated via Two-Photon Laser Scanning Lithography Enables Facile Measurement of Cell-Generated Forces

Cells sense and respond to the physical nature of their microenvironment by mechanically probing their surroundings via cytoskeletal contractions. The material response to these stresses can be measured via traction force microscopy (TFM). Traditional TFM platforms present several limitations including variable spatial resolution, difficulty in attaining the full three-dimensional (3D) deformation/stress profile, and the requirement to remove or relax the cells being measured to determine the zero-stress state. To overcome these limitations, we developed a two-photon, photochemical coupling approach to fabricate a new TFM platform that provides high-resolution control over the 3D placement of fluorescent fiducial markers for facile measurement of cell-generated shear and normal components of traction forces. The highly controlled placement of the 3D marker array provides a built-in, zero stress state eliminating the need to perturb the cells being measured while also providing increased throughput. Using this platform, we discovered that the magnitude of cell-generated shear and normal force components are linked both spatially and temporally. The facile nature and increased throughput of measuring cell-generated forces afforded by this new platform will be useful to the mechanotransduction community and others.

Role of KCa3.1 Channels in Modulating Ca2+ Oscillations during Glioblastoma Cell Migration and Invasion

Cell migration and invasion in glioblastoma (GBM), the most lethal form of primary brain tumors, are critically dependent on Ca²⁺ signaling. Increases of [Ca²⁺]_i in GBM cells often result from Ca²⁺ release from the endoplasmic reticulum (ER), promoted by a variety of agents present in the tumor microenvironment and able to activate the phospholipase C/inositol 1,4,5-trisphosphate PLC/IP₃ pathway. The Ca²⁺ signaling is further strengthened by the Ca²⁺ influx from the extracellular space through Ca²⁺ release-activated Ca²⁺ (CRAC) currents sustained by Orai/STIM channels, meant to replenish the partially depleted ER. Notably, the elevated cytosolic [Ca²⁺]_i activates the intermediate conductance Ca²⁺-activated K (KCa3.1) channels highly expressed in the plasma membrane of GBM cells, and the resulting K⁺ efflux hyperpolarizes the cell membrane. This translates to an enhancement of Ca²⁺ entry through Orai/STIM channels as a result of the increased electromotive (driving) force on Ca²⁺ influx, ending with the establishment of a recurrent cycle reinforcing the Ca²⁺ signal. Ca²⁺ signaling in migrating GBM cells often emerges in the form of intracellular Ca²⁺ oscillations, instrumental to promote key processes in the migratory cycle. This has suggested that KCa3.1 channels may promote GBM cell migration by inducing or modulating the shape of Ca²⁺ oscillations. In accordance, we recently built a theoretical model of Ca²⁺ oscillations incorporating the KCa3.1 channel-dependent dynamics of the membrane potential, and found that the KCa3.1 channel activity could significantly affect the IP₃ driven Ca²⁺ oscillations. Here we review our new theoretical model of Ca²⁺ oscillations in GBM, upgraded in the light of better knowledge of the KCa3.1 channel kinetics and Ca²⁺ sensitivity, the dynamics of the Orai/STIM channel modulation, the migration and invasion mechanisms of GBM cells, and their regulation by Ca²⁺ signals.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Nanoparticle-Cell Interaction: A Cell Mechanics Perspective

Progress in the field of nanoparticles has enabled the rapid development of multiple products and technologies; however, some nanoparticles can pose both a threat to the environment and human health. To enable their safe implementation, a comprehensive knowledge of nanoparticles and their biological interactions is needed. In vitro and in vivo toxicity tests have been considered the gold standard to evaluate nanoparticle safety, but it is becoming necessary to understand the impact of nanosystems on cell mechanics. Here, the interaction between particles and cells, from the point of view of cell mechanics (i.e., bionanomechanics), is highlighted and put in perspective. Specifically, the ability of intracellular and extracellular nanoparticles to impair cell adhesion, cytoskeletal organization, stiffness, and migration are discussed. Furthermore, the development of cutting-edge, nanotechnology-driven tools based on the use of particles allowing the determination of cell mechanics is emphasized. These include traction force microscopy, colloidal probe atomic force microscopy, optical tweezers, magnetic manipulation, and particle tracking microrheology.

Repellent and Attractant Guidance Cues Initiate Cell Migration by Distinct Rear-Driven and Front-Driven Cytoskeletal Mechanisms

Attractive and repulsive cell guidance is essential for animal life and important in disease. Cell migration toward attractants dominates studies [1, 2, 3, 4, 5, 6, 7, 8], but migration away from repellents is important in biology yet relatively little studied [5, 9, 10]. It is widely held that cells initiate migration by protrusion of their front [11, 12, 13, 14, 15], yet this has not been explicitly tested for cell guidance because cell margin displacement at opposite ends of the cell has not been distinguished for any cue. We argue that protrusion of the front, retraction of the rear, or both together could in principle break cell symmetry and start migration in response to guidance cues [16]. Here, we find in the Dictyostelium model [6] that an attractant—cAMP—breaks symmetry by causing protrusion of the front of the cell, whereas its repellent analog—8CPT—breaks symmetry by causing retraction of the rear. Protrusion of the front of these cells in response to cAMP starts with local actin filament assembly, while the delayed retraction of the rear is independent of both myosin II polarization and of motor-based contractility. On the contrary, myosin II accumulates locally in the rear of the cell in response to 8CPT, anticipating retraction and required for it, while local actin assembly is delayed and couples to delayed protrusion at the front. These data reveal an important new concept in the understanding of cell guidance.

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In attractant, cell front protrusion breaks cell symmetry and starts migration

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In repellent, cell rear retraction breaks cell symmetry and starts migration

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Myosin II motor is not required for front-driven migration toward attractant

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Biased myosin II motor contractility drives rear-driven migration away from repellent

Protein-Substrate Adhesion in Microcontact Printing Regulates Cell Behavior

Microcontact printing (μCP) is widely used to create patterns of biomolecules essential for studies of cell mechanics, migration, and tissue engineering. However, different types of μCPs may create micropatterns with varied protein-substrate adhesion, which may change cell behaviors and pose uncertainty in result interpretation. Here, we characterize two μCP methods for coating extracellular matrix (ECM) proteins (stamp-off and covalent bond) and demonstrate for the first time the important role of protein-substrate adhesion in determining cell behavior. We found that, as compared to cells with weaker traction force (e.g., endothelial cells), cells with strong traction force (e.g., vascular smooth muscle cells) may delaminate the ECM patterns, which reduced cell viability as a result. Importantly, such ECM delamination was observed on patterns by stamp-off but not on the patterns by covalent bonds. Further comparisons of the displacement of the ECM patterns between the normal VSMCs and the force-reduced VSMCs suggested that the cell traction force plays an essential role in this ECM delamination. Together, our results indicated that μCPs with insufficient adhesion may lead to ECM delamination and cause cell death, providing new insight for micropatterning in cell-biomaterial interaction on biointerfaces.

Mechanosensitive Adhesion Explains Stepping Motility in Amoeboid Cells

Cells employing amoeboid motility exhibit repetitive cycles of rapid expansion and contraction and apply coordinated traction forces to their environment. Although aspects of this process are well studied, it is unclear how the cell controls the coordination of cell length changes with adhesion to the surface. Here, we develop a simple model to mechanistically explain the emergence of periodic changes in length and spatiotemporal dynamics of traction forces measured in chemotaxing unicellular amoeba, Dictyostelium discoideum. In contrast to the biochemical mechanisms that have been implicated in the coordination of some cellular processes, we show that many features of amoeboid locomotion emerge from a simple mechanochemical model. The mechanism for interaction with the environment in Dictyostelium is unknown and thus, we explore different cell-environment interaction models to reveal that mechanosensitive adhesions are necessary to reproduce the spatiotemporal adhesion patterns. In this modeling framework, we find that the other motility modes, such as smooth gliding, arise naturally with variations in the physical properties of the surface. Thus, our work highlights the prominent role of biomechanics in determining the emergent features of amoeboid locomotion.

Leading from the Back: The Role of the Uropod in Neutrophil Polarization and Migration

Cell motility is required for diverse biological processes including development, homing of immune cells, wound healing, and cancer cell invasion. Motile neutrophils exhibit a polarized morphology characterized by the formation of leading-edge pseudopods and a highly contractile cell rear known as the uropod. Although it is known that perturbing uropod formation impairs neutrophil migration, the role of the uropod in cell polarization and motility remains incompletely understood. Here we discuss cell intrinsic mechanisms that regulate neutrophil polarization and motility, with a focus on the uropod, and examine how relationships among regulatory mechanisms change when cells change their direction of migration.

Traction force and its regulation during cytokinesis in Dictyostelium cells

Cytokinesis is the final stage of cell division. Dictyostelium cells have multiple modes of cytokinesis, including cytokinesis A, B and C. Cytokinesis A is a conventional mode, which depends on myosin II in the contractile ring. Myosin II null cells divide depending on substratum-attachment (cytokinesis B) or in a multi-polar fashion independent of the cell cycle (cytokinesis C). We investigated the traction stress exerted by dividing cells in the three different modes using traction force microscopy. In all cases, the traction forces were directed inward from both poles. Interestingly, the traction stress of cytokinesis A was the smallest of the three modes. Latrunculin B, an inhibitor of actin polymerization, completely diminished the traction stress of dividing cells, but blebbistatin, an inhibitor of myosin II ATPase, increased the traction stress. Myosin II is proposed to contribute to the detachment of cell body from the substratum. When the cell-substratum attachment was artificially strengthened by a poly-lysine coating, wild type cells increased their traction stress in contrast to myosin II null and other cytokinesis-deficient mutant cells, which suggests that wild type cells may increase their own power to conduct their cytokinesis. The cytokinesis-deficient mutants frequently divided unequally, whereas wild type cells divided equally. A traction stress imbalance between two daughter halves was correlated with cytokinesis failure. We discuss the regulation of cell shape changes during cell division through mechanosensing.

Simultaneous measurement of the Young's modulus and the Poisson ratio of thin elastic layers

The behavior of cells and tissue is greatly influenced by the mechanical properties of their environment. For studies on the interactions between cells and soft matrices, especially those applying traction force microscopy the characterization of the mechanical properties of thin substrate layers is essential. Various techniques to measure the elastic modulus are available. Methods to accurately measure the Poisson ratio of such substrates are rare and often imply either a combination of multiple techniques or additional equipment which is not needed for the actual biological studies. Here we describe a novel technique to measure both parameters, the Youngs's modulus and the Poisson ratio in a single experiment. The technique requires only a standard inverted epifluorescence microscope. As a model system, we chose cross-linked polyacrylamide and poly-N-isopropylacrylamide hydrogels which are known to obey Hooke's law. We place millimeter-sized steel spheres on the substrates which indent the surface. The data are evaluated using a previously published model which takes finite thickness effects of the substrate layer into account. We demonstrate experimentally for the first time that the application of the model allows the simultaneous determination of both the Young's modulus and the Poisson ratio. Since the method is easy to adapt and comes without the need of special equipment, we envision the technique to become a standard tool for the characterization of substrates for a wide range of investigations of cell and tissue behavior in various mechanical environments as well as other samples, including biological materials.

Three-Dimensional Reflectance Traction Microscopy

Cells in three-dimensional (3D) environments exhibit very different biochemical and biophysical phenotypes compared to the behavior of cells in two-dimensional (2D) environments. As an important biomechanical measurement, 2D traction force microscopy can not be directly extended into 3D cases. In order to quantitatively characterize the contraction field, we have developed 3D reflectance traction microscopy which combines confocal reflection imaging and partial volume correlation postprocessing. We have measured the deformation field of collagen gel under controlled mechanical stress. We have also characterized the deformation field generated by invasive breast cancer cells of different morphologies in 3D collagen matrix. In contrast to employ dispersed tracing particles or fluorescently-tagged matrix proteins, our methods provide a label-free, computationally effective strategy to study the cell mechanics in native 3D extracellular matrix.

For whom the cells pull: Hydrogel and micropost devices for measuring traction forces

While performing several functions, adherent cells deform their surrounding substrate via stable adhesions that connect the intracellular cytoskeleton to the extracellular matrix. The traction forces that deform the substrate are studied in mechanotrasduction because they are affected by the mechanics of the extracellular milieu. We review the development and application of two methods widely used to measure traction forces generated by cells on 2D substrates: (i) traction force microscopy with polyacrylamide hydrogels and (ii) calculation of traction forces with arrays of deformable microposts. Measuring forces with these methods relies on measuring substrate displacements and converting them into forces. We describe approaches to determine force from displacements and elaborate on the necessary experimental conditions for this type of analysis. We emphasize device fabrication, mechanical calibration of substrates and covalent attachment of extracellular matrix proteins to substrates as key features in the design of experiments to measure cell traction forces with polyacrylamide hydrogels or microposts. We also report the challenges and achievements in integrating these methods with platforms for the mechanical stimulation of adherent cells. The approaches described here will enable new studies to understand cell mechanical outputs as a function of mechanical inputs and advance the understanding of mechanotransduction mechanisms.

Shape and Area of Keratocytes Are Related to the Distribution and Magnitude of Their Traction Forces

Fish epidermal keratocytes maintain an overall fan shape during their crawling migration. The shape-determination mechanism has been described theoretically and experimentally on the basis of graded radial extension of the leading edge, but the relationship between shape and traction forces has not been clarified. Migrating keratocytes can be divided into fragments by treatment with the protein kinase inhibitor staurosporine. Fragments containing a nucleus and cytoplasm behave as mini-keratocytes and maintain the same fan shape as the original cells. We measured the shape of the leading edge, together with the areas of the ventral region and traction forces, of keratocytes and mini-keratocytes. The shapes of keratocytes and mini-keratocytes were similar. Mini-keratocytes exerted traction forces at the rear left and right ends, just like keratocytes. The magnitude of the traction forces was proportional to the area of the keratocytes and mini-keratocytes. The myosin II ATPase inhibitor blebbistatin decreased the forces at the rear left and right ends of the keratocytes and expanded their shape laterally. These results suggest that keratocyte shape depends on the distribution of the traction forces, and that the magnitude of the traction forces depends on the area of the cells.

Three-dimensional balance of cortical tension and axial contractility enables fast amoeboid migration

Fast amoeboid migration requires cells to apply mechanical forces on their surroundings via transient adhesions. However, the role these forces play in controlling cell migration speed remains largely unknown. We used three-dimensional force microscopy to measure the three-dimensional forces exerted by chemotaxing Dictyostelium cells, and examined wild-type cells as well as mutants with defects in contractility, internal F-actin crosslinking, and cortical integrity. We showed that cells pull on their substrate adhesions using two distinct, yet interconnected mechanisms: axial actomyosin contractility and cortical tension. We found that the migration speed increases when axial contractility overcomes cortical tension to produce the cell shape changes needed for locomotion. We demonstrated that the three-dimensional pulling forces generated by both mechanisms are internally balanced by an increase in cytoplasmic pressure that allows cells to push on their substrate without adhering to it, and which may be relevant for amoeboid migration in complex three-dimensional environments.

Interplay between motility and cell-substratum adhesion in amoeboid cells

The effective migration of amoeboid cells requires a fine regulation of cell-substratum adhesion. These entwined processes have been shown to be regulated by a host of biophysical and biochemical cues. Here, we reveal the pivotal role played by calcium-based mechanosensation in the active regulation of adhesion resulting in a high migratory adaptability. Using mechanotactically driven Dictyostelium discoideum amoebae, we uncover the existence of optimal mechanosensitive conditions-corresponding to specific levels of extracellular calcium-for persistent directional migration over physicochemically different substrates. When these optimal mechanosensitive conditions are met, noticeable enhancement in cell migration directionality and speed is achieved, yet with significant differences among the different substrates. In the same narrow range of calcium concentrations that yields optimal cellular mechanosensory activity, we uncovered an absolute minimum in cell-substratum adhesion activity, for all considered substrates, with differences in adhesion strength among them amplified. The blocking of the mechanosensitive ion channels with gadolinium-i.e., the inhibition of the primary mechanosensory apparatus-hampers the active reduction in substrate adhesion, thereby leading to the same undifferentiated and drastically reduced directed migratory response. The adaptive behavioral responses of Dictyostelium cells sensitive to substrates with varying physicochemical properties suggest the possibility of novel surface analyses based on the mechanobiological ability of mechanosensitive and guidable cells to probe substrates at the nanometer-to-micrometer level.

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg-Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree.

Novel protein Callipygian defines the back of migrating cells

Asymmetric protein localization is essential for cell polarity and migration. We report a novel protein, Callipygian (CynA), which localizes to the lagging edge before other proteins and becomes more tightly restricted as cells polarize; additionally, it accumulates in the cleavage furrow during cytokinesis. CynA protein that is tightly localized, or "clustered," to the cell rear is immobile, but when polarity is disrupted, it disperses throughout the membrane and responds to uniform chemoattractant stimulation by transiently localizing to the cytosol. These behaviors require a pleckstrin homology-domain membrane tether and a WD40 clustering domain, which can also direct other membrane proteins to the back. Fragments of CynA lacking the pleckstrin homology domain, which are normally found in the cytosol, localize to the lagging edge membrane when coexpressed with full-length protein, showing that CynA clustering is mediated by oligomerization. Cells lacking CynA have aberrant lateral protrusions, altered leading-edge morphology, and decreased directional persistence, whereas those overexpressing the protein display exaggerated features of polarity. Consistently, actin polymerization is inhibited at sites of CynA accumulation, thereby restricting protrusions to the opposite edge. We suggest that the mutual antagonism between CynA and regions of responsiveness creates a positive feedback loop that restricts CynA to the rear and contributes to the establishment of the cell axis.

Describing directional cell migration with a characteristic directionality time

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration.

A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.

Poldip2 controls vascular smooth muscle cell migration by regulating focal adhesion turnover and force polarization

Polymerase-δ-interacting protein 2 (Poldip2) interacts with NADPH oxidase 4 (Nox4) and regulates migration; however, the precise underlying mechanisms are unclear. Here, we investigated the role of Poldip2 in focal adhesion turnover, as well as traction force generation and polarization. Poldip2 overexpression (AdPoldip2) in vascular smooth muscle cells (VSMCs) impairs PDGF-induced migration and induces a characteristic phenotype of long cytoplasmic extensions. AdPoldip2 also prevents the decrease in spreading and increased aspect ratio observed in response to PDGF and slightly impairs cell contraction. Moreover, AdPoldip2 blocks focal adhesion dissolution and sustains H2O2 levels in focal adhesions, whereas Poldip2 knockdown (siPoldip2) significantly decreases the number of focal adhesions. RhoA activity is unchanged when focal adhesion dissolution is stimulated in control cells but increases in AdPoldip2-treated cells. Inhibition of RhoA blocks Poldip2-mediated attenuation of focal adhesion dissolution, and overexpression of RhoA or focal adhesion kinase (FAK) reverses the loss of focal adhesions induced by siPoldip2, indicating that RhoA and FAK mediate the effect of Poldip2 on focal adhesions. Nox4 silencing prevents focal adhesion stabilization by AdPoldip2 and induces a phenotype similar to siPoldip2, suggesting a role for Nox4 in Poldip2-induced focal adhesion stability. As a consequence of impaired focal adhesion turnover, PDGF-treated AdPoldip2 cells are unable to reduce and polarize traction forces, a necessary first step in migration. These results implicate Poldip2 in VSMC migration via regulation of focal adhesion turnover and traction force generation in a Nox4/RhoA/FAK-dependent manner.

Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion

Migrating cells exert traction forces when moving. Amoeboid cell migration is a common type of cell migration that appears in many physiological and pathological processes and is performed by a wide variety of cell types. Understanding the coupling of the biochemistry and mechanics underlying the process of migration has the potential to guide the development of pharmacological treatment or genetic manipulations to treat a wide range of diseases. The measurement of the spatiotemporal evolution of the traction forces that produce the movement is an important aspect for the characterization of the locomotion mechanics. There are several methods to calculate the traction forces exerted by the cells. Currently the most commonly used ones are traction force microscopy methods based on the measurement of the deformation induced by the cells on elastic substrate on which they are moving. Amoeboid cells migrate by implementing a motility cycle based on the sequential repetition of four phases. In this paper we review the role that specific cytoskeletal components play in the regulation of the cell migration mechanics. We investigate the role of specific cytoskeletal components regarding the ability of the cells to perform the motility cycle effectively and the generation of traction forces. The actin nucleation in the leading edge of the cell, carried by the ARP2/3 complex activated through the SCAR/WAVE complex, has shown to be fundamental to the execution of the cyclic movement and to the generation of the traction forces. The protein PIR121, a member of the SCAR/WAVE complex, is essential to the proper regulation of the periodic movement and the protein SCAR, also included in the SCAR/WAVE complex, is necessary for the generation of the traction forces during migration. The protein Myosin II, an important F-actin cross-linker and motor protein, is essential to cytoskeletal contractility and to the generation and proper organization of the traction forces during migration.

Both contractile axial and lateral traction force dynamics drive amoeboid cell motility

Chemotaxing Dictyostelium discoideum cells adapt their morphology and migration speed in response to intrinsic and extrinsic cues. Using Fourier traction force microscopy, we measured the spatiotemporal evolution of shape and traction stresses and constructed traction tension kymographs to analyze cell motility as a function of the dynamics of the cell's mechanically active traction adhesions. We show that wild-type cells migrate in a step-wise fashion, mainly forming stationary traction adhesions along their anterior-posterior axes and exerting strong contractile axial forces. We demonstrate that lateral forces are also important for motility, especially for migration on highly adhesive substrates. Analysis of two mutant strains lacking distinct actin cross-linkers (mhcA(-) and abp120(-) cells) on normal and highly adhesive substrates supports a key role for lateral contractions in amoeboid cell motility, whereas the differences in their traction adhesion dynamics suggest that these two strains use distinct mechanisms to achieve migration. Finally, we provide evidence that the above patterns of migration may be conserved in mammalian amoeboid cells.

Migration of dendritic cells: physical principles, molecular mechanisms, and functional implications

Dendritic cells (DCs) constitute a complex cell population that resides in both peripheral tissues and lymphoid organs. Their major function in tissues is to patrol their environment in search of danger-associated antigens to transport to lymph nodes and present to T lymphocytes. This process constitutes the first step of the adaptive immune response and relies on specific DC properties, including a high endocytic capacity as well as efficient motility in confined three-dimensional environments. Although cell motility has been widely studied, little is known on how the geometric characteristics of the environment influence DC migration and function. In this review, we give an overview of the basic physical principles and molecular mechanisms that control DC migration under confinement and discuss how such mechanisms impact the environment-patrolling capacity of DCs.

Traction force microscopy in rapidly moving cells reveals separate roles for ROCK and MLCK in the mechanics of retraction

Retraction is a major rate-limiting step in cell motility, particularly in slow moving cell types that form large stable adhesions. Myosin II dependent contractile forces are thought to facilitate detachment by physically pulling up the rear edge. However, retraction can occur in the absence of myosin II activity in cell types that form small labile adhesions. To investigate the role of contractile force generation in retraction, we performed traction force microscopy during the movement of fish epithelial keratocytes. By correlating changes in local traction stress at the rear with the area retracted, we identified four distinct modes of retraction. "Recoil" retractions are preceded by a rise in local traction stress, while rear edge is temporarily stuck, followed by a sharp drop in traction stress upon detachment. This retraction type was most common in cells generating high average traction stress. In "pull" type retractions local traction stress and area retracted increase concomitantly. This was the predominant type of retraction in keratocytes and was observed mostly in cells generating low average traction stress. "Continuous" type retractions occur without any detectable change in traction stress, and are seen in cells generating low average traction stress. In contrast, to many other cell types, "release" type retractions occur in keratocytes following a decrease in local traction stress. Our identification of distinct modes of retraction suggests that contractile forces may play different roles in detachment that are related to rear adhesion strength. To determine how the regulation of contractility via MLCK or Rho kinase contributes to the mechanics of detachment, inhibitors were used to block or augment these pathways. Modulation of MLCK activity led to the most rapid change in local traction stress suggesting its importance in regulating attachment strength. Surprisingly, Rho kinase was not required for detachment, but was essential for localizing retraction to the rear. We suggest that in keratocytes MLCK and Rho kinase play distinct, complementary roles in the respective temporal and spatial control of rear detachment that is essential for maintaining rapid motility.

Cross talk between matrix elasticity and mechanical force regulates myoblast traction dynamics

Growing evidence suggests that critical cellular processes are profoundly influenced by the cross talk between extracellular nanomechanical forces and the material properties of the cellular microenvironment. Although many studies have examined either the effect of nanomechanical forces or the material properties of the microenvironment on biological processes, few have investigated the influence of both. Here, we performed simultaneous atomic force microscopy and traction force microscopy to demonstrate that muscle precursor cells (myoblasts) rapidly generate a significant increase in traction when stimulated with a local 10 nN force. Cells were cultured and nanomechanically stimulated on hydrogel substrates with controllable local elastic moduli varying from ~16-89 kPa, as confirmed with atomic force microscopy. Importantly, cellular traction dynamics in response to nanomechanical stimulation only occurred on substrates that were similar to the elasticity of working muscle tissue (~64-89 kPa) as opposed to substrates mimicking resting tissue (~16-51 kPa). The traction response was also transient, occurring within 30 s, and dissipating by 60 s, during constant nanomechanical stimulation. The observed biophysical dynamics are very much dependent on rho-kinase and myosin-II activity and likely contribute to the physiology of these cells. Our results demonstrate the fundamental ability of cells to integrate nanoscale information in the cellular microenvironment, such as nanomechanical forces and substrate mechanics, during the process of mechanotransduction.

Contraction-driven cell motility

We propose a mechanism for the initiation of cell motility that is based on myosin-induced contraction and does not require actin polymerization. The translocation of a cell is induced by symmetry breaking of the motor-driven flow, and the ensuing asymmetry gives rise to a steady motion of the center of mass of a cell. The predictions of the model are consistent with observations on keratocytes.

Mechanism of cell rear retraction in migrating cells

For decades, ever growing data on myosin II provides strong evidence that interaction of myosin-II-motor-domain with actin filaments within cells retracts the cell rear during actin-based cell migration. Now it is clear myosin II motor-activity is not the sole force involved. Alternative force-generating mechanisms within cells clearly also exist to power cell rear retraction during actin-based cell migration. Given that nematode sperm cells migrate without actin and without cytoskeletal motor proteins it is perhaps not surprising other types of force power cell rear retraction in actin-based systems. Here, cell rear retraction driven by actin filament depolymerisation, actin filament crosslinking, cell front protrusion and possibly apparent membrane tension and their importance relative to myosin II-motor-based contractility are discussed.

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html.

Measuring traction forces of motile dendritic cells on micropost arrays

Dendritic cells (DCs) migrate from sites of inflammation to secondary lymphoid organs where they initiate the adaptive immune response. Although motility is essential to DC function, the mechanisms by which they migrate are not fully understood. We incorporated micropost array detectors into a microfluidic gradient generator to develop what we consider to be a novel method for probing low magnitude traction forces during directional migration. We found migration of primary murine DCs is driven by short-lived traction stresses at the leading edge or filopodia. The traction forces generated by DCs are smaller in magnitude than found in neutrophils, and of similar magnitude during chemotaxis and chemokinesis, at 18 ± 1.4 and 16 ± 1.3 nN/cell, respectively. The characteristic duration of local DC traction forces was 3 min. The maximum principal stress in the cell occurred in the plane perpendicular to the axis of motion, forward of the centroid. We illustrate that the spatiotemporal pattern of traction stresses can be used to predict the direction of future DC motion. Overall, DCs show a mode of migration distinct from both mesenchymal cells and neutrophils, characterized by rapid turnover of traction forces in leading filopodia.

Actin depolymerization-based force retracts the cell rear in polarizing and migrating cells

In migrating cells, the relative importance of myosin II contractility for cell rear retraction varies [1-12]. However, in myosin II-inhibited polarizing cells, actin organization is compromised [13-18]; thus it remains unclear whether myosin II is simply required for correct actin arrangement or also directly drives rear retraction [9]. Ascaris sperm cells lack actin and associated motors, and depolymerization of major sperm protein is instead thought to pull the cell rear forward [19, 20]. Opposing views exist on whether actin could also have this function [19, 20] and has not been directly experimentally sought. We probe function at high temporal resolution in polarizing fibroblasts that establish migration by forming the cell rear first [9, 15, 21]. We show that in cells with correctly organized actin, that actin filament depolymerization directly drives retraction of the rear margin to polarize cells and spatially accounts for most cell rear retraction during established migration. Myosin II contractility is required early, to form aligned actin bundles that are needed for polarization, and also later to maintain bundle length that ensures directed protrusion at the cell front. Our data imply a new mechanism: actin depolymerization-based force retracts the cell rear to polarize cells with no direct contribution from myosin II contractility.

Traction forces of neutrophils migrating on compliant substrates

Proper functioning of the innate immune response depends on migration of circulating neutrophils into tissues at sites of infection and inflammation. Migration of highly motile, amoeboid cells such as neutrophils has significant physiological relevance, yet the traction forces that drive neutrophil motion in response to chemical cues are not well characterized. To better understand the relationship between chemotactic signals and the organization of forces in motile neutrophils, force measurements were made on hydrogel surfaces under well-defined chemotactic gradients created with a microfluidic device. Two parameters, the mean chemoattractant concentration (C(M)) and the gradient magnitude (Δc/Δx) were varied. Cells experiencing a large gradient with C(M) near the chemotactic receptor K(D) displayed strong punctate centers of uropodial contractile force and strong directional motion on stiff (12 kPa) surfaces. Under conditions of ideal chemotaxis--cells in strong gradients with mean chemoattractant near the receptor K(D) and on stiffer substrates--there is a correlation between the magnitude of force generation and directional motion as measured by the chemotactic index. However, on soft materials or under weaker chemotactic conditions, directional motion is uncorrelated with the magnitude of traction force. Inhibition of either β(2) integrins or Rho-associated kinase, a kinase downstream from RhoA, greatly reduced rearward traction forces and directional motion, although some vestigial lamellipodium-driven motility remained. In summary, neutrophils display a diverse repertoire of methods for organizing their internal machinery to generate directional motion.

Effects of gel thickness on microscopic indentation measurements of gel modulus

In vitro, animal cells are mostly cultured on a gel substrate. It was recently shown that substrate stiffness affects cellular behaviors in a significant way, including adhesion, differentiation, and migration. Therefore, an accurate method is needed to characterize the modulus of the substrate. In situ microscopic measurements of the gel substrate modulus are based on Hertz contact mechanics, where Young's modulus is derived from the indentation force and displacement measurements. In Hertz theory, the substrate is modeled as a linear elastic half-space with an infinite depth, whereas in practice, the thickness of the substrate, h, can be comparable to the contact radius and other relevant dimensions such as the radius of the indenter or steel ball, R. As a result, measurements based on Hertz theory overestimate the Young's modulus. In this work, we discuss the limitations of Hertz theory and then modify it, taking into consideration the nonlinearity of the material and large deformation using a finite-element method. We present our results in a simple correction factor, ψ, the ratio of the corrected Young's modulus and the Hertz modulus in the parameter regime of δ/h ≤ min (0.6, R/h) and 0.3 ≤R/h ≤ 12.7. The ψ factor depends on two dimensionless parameters, R/h and δ/h (where δ is the indentation depth), both of which are easily accessible to experiments. This correction factor agrees with experimental observations obtained with the use of polyacrylamide gel and a microsphere indentation method in the parameter range of 0.1 ≤δ/h ≤ 0.4 and 0.3 ≤R/h ≤ 6.2. The effect of adhesion on the use of Hertz theory for small indentation depth is also discussed.

The SCAR/WAVE complex is necessary for proper regulation of traction stresses during amoeboid motility

A combination of traction force and F-actin measurements shows that cells lacking either of the SCAR/WAVE complex proteins SCAR and PIR121 exhibit an altered cell motility cycle and spatiotemporal distribution of tractions stresses, which correlate in magnitude with F-actin levels.

Cell migration requires a tightly regulated, spatiotemporal coordination of underlying biochemical pathways. Crucial to cell migration is SCAR/WAVE–mediated dendritic F-actin polymerization at the cell's leading edge. Our goal is to understand the role the SCAR/WAVE complex plays in the mechanics of amoeboid migration. To this aim, we measured and compared the traction stresses exerted by Dictyostelium cells lacking the SCAR/WAVE complex proteins PIR121 (pirA⁻) and SCAR (scrA⁻) with those of wild-type cells while they were migrating on flat, elastic substrates. We found that, compared to wild type, both mutant strains exert traction stresses of different strengths that correlate with their F-actin levels. In agreement with previous studies, we found that wild-type cells migrate by repeating a motility cycle in which the cell length and strain energy exerted by the cells on their substrate vary periodically. Our analysis also revealed that scrA⁻ cells display an altered motility cycle with a longer period and a lower migration velocity, whereas pirA⁻ cells migrate in a random manner without implementing a periodic cycle. We present detailed characterization of the traction-stress phenotypes of the various cell lines, providing new insights into the role of F-actin polymerization in regulating cell–substratum interactions and stresses required for motility.

Mechanisms of Cell Propulsion by Active Stresses

The mechanisms by which cytoskeletal flows and cell-substrate interactions interact to generate cell motion are explored using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell-substrate friction. It is found that 1) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, 2) gradients in cell-substrate friction can induce motion even when the active stresses are symmetrically distributed, 3) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell, and 4) the cell velocity depends biphasically on the cell-substrate adhesion strength if active stress is enhanced by adhesion. Specific experimental tests of the calculated dependences are proposed.

An Oscillatory Contractile Pole-Force Component Dominates the Traction Forces Exerted by Migrating Amoeboid Cells

We used principal component analysis to dissect the mechanics of chemotaxis of amoeboid cells into a reduced set of dominant components of cellular traction forces and shape changes. The dominant traction force component in wild-type cells accounted for ~40% of the mechanical work performed by these cells, and consisted of the cell attaching at front and back contracting the substrate towards its centroid (pole-force). The time evolution of this pole-force component was responsible for the periodic variations of cell length and strain energy that the cells underwent during migration. We identified four additional canonical components, reproducible from cell to cell, overall accounting for an additional ~20% of mechanical work, and associated with events such as lateral protrusion of pseudopodia. We analyzed mutant strains with contractility defects to quantify the role that non-muscle Myosin II (MyoII) plays in amoeboid motility. In MyoII essential light chain null cells the polar-force component remained dominant. On the other hand, MyoII heavy chain null cells exhibited a different dominant traction force component, with a marked increase in lateral contractile forces, suggesting that cortical contractility and/or enhanced lateral adhesions are important for motility in this cell line. By compressing the mechanics of chemotaxing cells into a reduced set of temporally-resolved degrees of freedom, the present study may contribute to refined models of cell migration that incorporate cell-substrate interactions.