Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration.

Cell migration toward areas of higher extracellular matrix (ECM) rigidity via a process called "durotaxis" is thought to contribute to development, immune response, and cancer metastasis. To understand how cells sample ECM rigidity to guide durotaxis, we characterized cell-generated forces on the nanoscale within single mature integrin-based focal adhesions (FAs). We found that individual FAs act autonomously, exhibiting either stable or dynamically fluctuating ("tugging") traction. We show that a FAK/phosphopaxillin/vinculin pathway is essential for high FA traction and to enable tugging FA traction over a broad range of ECM rigidities. We show that tugging FA traction is dispensable for FA maturation, chemotaxis, and haptotaxis but is critical to direct cell migration toward rigid ECM. We conclude that individual FAs dynamically sample rigidity by applying fluctuating pulling forces to the ECM to act as sensors to guide durotaxis, and that FAK/phosphopaxillin/vinculin signaling defines the rigidity range over which this dynamic sensing process operates.

Shear force enhances adhesion of Pseudomonas aeruginosa by counteracting pilus-driven surface departure.

Fluid flow is thought to prevent bacterial adhesion, but some bacteria use adhesins with catch bond properties to enhance adhesion under high shear forces. However, many studies on bacterial adhesion either neglect the influence of shear force or use shear forces that are not typically found in natural systems. In this study, we use microfluidics and single-cell imaging to examine how the human pathogen Pseudomonas aeruginosa interacts with surfaces when exposed to shear forces typically found in the human body (0.1 pN to 10 pN). Through cell tracking, we demonstrate that the angle between the cell and the surface predicts if a cell will depart the surface. We discover that at lower shear forces, type IV pilus retraction tilts cells away from the surface, promoting surface departure. Conversely, we show that higher shear forces counterintuitively enhance adhesion by counteracting type IV pilus retraction-dependent cell tilting. Thus, our results reveal that P. aeruginosa exhibits behavior reminiscent of a catch bond, without having a specific adhesin that is enhanced by force. Instead, P. aeruginosa couples type IV pilus dynamics and cell geometry to tune adhesion to its mechanical environment, which likely provides a benefit in dynamic host environments.

Multiplexing molecular tension sensors reveals piconewton force gradient across talin-1.

Förster resonance energy transfer (FRET)-based tension sensor modules (TSMs) are available for investigating how distinct proteins bear mechanical forces in cells. Yet, forces in the single piconewton (pN) regime remain difficult to resolve, and tools for multiplexed tension sensing are lacking. Here, we report the generation and calibration of a genetically encoded, FRET-based biosensor called FL-TSM, which is characterized by a near-digital force response and increased sensitivity at 3-5 pN. In addition, we present a method allowing the simultaneous evaluation of coexpressed tension sensor constructs using two-color fluorescence lifetime microscopy. Finally, we introduce a procedure to calculate the fraction of mechanically engaged molecules within cells. Application of these techniques to new talin biosensors reveals an intramolecular tension gradient across talin-1 that is established upon integrin-mediated cell adhesion. The tension gradient is actomyosin- and vinculin-dependent and sensitive to the rigidity of the extracellular environment.

Force generation by groups of migrating bacteria.

From colony formation in bacteria to wound healing and embryonic development in multicellular organisms, groups of living cells must often move collectively. Although considerable study has probed the biophysical mechanisms of how eukaryotic cells generate forces during migration, little such study has been devoted to bacteria, in particular with regard to the question of how bacteria generate and coordinate forces during collective motion. This question is addressed here using traction force microscopy. We study two distinct motility mechanisms of Myxococcus xanthus, namely, twitching and gliding. For twitching, powered by type-IV pilus retraction, we find that individual cells exert local traction in small hotspots with forces on the order of 50 pN. Twitching bacterial groups also produce traction hotspots, but with forces around 100 pN that fluctuate rapidly on timescales of <1.5 min. Gliding, the second motility mechanism, is driven by lateral transport of substrate adhesions. When cells are isolated, gliding produces low average traction on the order of 1 Pa. However, traction is amplified approximately fivefold in groups. Advancing protrusions of gliding cells push, on average, in the direction of motion. Together, these results show that the forces generated during twitching and gliding have complementary characters, and both forces have higher values when cells are in groups.

Substrate-rigidity dependent migration of an idealized twitching bacterium.

Mechanical properties of the extracellular matrix are important determinants of cellular migration in diverse processes, such as immune response, wound healing, and cancer metastasis. Moreover, recent studies indicate that even bacterial surface colonization can depend on the mechanics of the substrate. Here, we focus on physical mechanisms that can give rise to substrate-rigidity dependent migration. We study a "twitcher", a cell driven by extension-retraction cycles, to idealize bacteria and perhaps eukaryotic cells that employ a slip-stick mode of motion. The twitcher is asymmetric and always pulls itself forward at its front. Analytical calculations show that the migration speed of a twitcher depends non-linearly on substrate rigidity. For soft substrates, deformations do not lead to build-up of significant force and the migration speed is therefore determined by stochastic adhesion unbinding. For rigid substrates, forced adhesion rupture determines the migration speed. Depending on the force-sensitivity of front and rear adhesions, forced bond rupture implies an increase or a decrease of the migration speed. A requirement for the occurrence of rigidity-dependent stick-slip migration is a "sticky" substrate, with binding rates being an order of magnitude larger than unbinding rates in absence of force. Computer simulations show that small stall forces of the driving machinery lead to a reduced movement on high rigidities, regardless of force-sensitivities of bonds. The simulations also confirm the occurrence of rigidity-dependent migration speed in a generic model for slip-stick migration of cells on a sticky substrate.

Size-dependent control of colloid transport via solute gradients in dead-end channels.

Transport of colloids in dead-end channels is involved in widespread applications including drug delivery and underground oil and gas recovery. In such geometries, Brownian motion may be considered as the sole mechanism that enables transport of colloidal particles into or out of the channels, but it is, unfortunately, an extremely inefficient transport mechanism for microscale particles. Here, we explore the possibility of diffusiophoresis as a means to control the colloid transport in dead-end channels by introducing a solute gradient. We demonstrate that the transport of colloidal particles into the dead-end channels can be either enhanced or completely prevented via diffusiophoresis. In addition, we show that size-dependent diffusiophoretic transport of particles can be achieved by considering a finite Debye layer thickness effect, which is commonly ignored. A combination of diffusiophoresis and Brownian motion leads to a strong size-dependent focusing effect such that the larger particles tend to concentrate more and reside deeper in the channel. Our findings have implications for all manners of controlled release processes, especially for site-specific delivery systems where localized targeting of particles with minimal dispersion to the nontarget area is essential.

Calcium oscillations in wounded fibroblast monolayers are spatially regulated through substrate mechanics.

The maintenance of tissue integrity is essential for the life of multicellular organisms. Healing of a skin wound is a paradigm for how various cell types localize and repair tissue perturbations in an orchestrated fashion. To investigate biophysical mechanisms associated with wound localization, we focus on a model system consisting of a fibroblast monolayer on an elastic substrate. We find that the creation of an edge in the monolayer causes cytosolic calcium oscillations throughout the monolayer. The oscillation frequency increases with cell density, which shows that wound-induced calcium oscillations occur collectively. Inhibition of myosin II reduces the number of oscillating cells, demonstrating a coupling between actomyosin activity and calcium response. The spatial distribution of oscillating cells depends on the stiffness of the substrate. For soft substrates with a Young's modulus E ~ 360 Pa, oscillations occur on average within 0.2 mm distance from the wound edge. Increasing substrate stiffness leads to an average localization of oscillations away from the edge (up to ~0.6 mm). In addition, we use traction force microscopy to determine stresses between cells and substrate. We find that an increase of substrate rigidity leads to a higher traction magnitude. For E < ~2 kPa, the traction magnitude is strongly concentrated at the monolayer edge, while for E > ~8 kPa, traction magnitude is on average almost uniform beneath the monolayer. Thus, the spatial occurrence of calcium oscillations correlates with the cell-substrate traction. Overall, the experiments with fibroblasts demonstrate a collective, chemomechanical localization mechanism at the edge of a wound with a potential physiological role.

Role of the Membrane for Mechanosensing by Tethered Channels.

Biologically important membrane channels are gated by force at attached tethers. Here, we generically characterize the nontrivial interplay of force, membrane tension, and channel deformations that can affect gating. A central finding is that minute conical channel deformation under force leads to significant energy release during opening. We also calculate channel-channel interactions and show that they can amplify the force sensitivity of tethered channels.

Cell-ECM traction force modulates endogenous tension at cell-cell contacts.

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

Clutch model for focal adhesions predicts reduced self-stabilization under oblique pulling.

Cell-matrix adhesions connect the cytoskeleton to the extracellular environment and are essential for maintaining the integrity of tissue and whole organisms. Remarkably, cell adhesions can adapt their size and composition to an applied force such that their size and strength increases proportionally to the load. Mathematical models for the clutch-like force transmission at adhesions are frequently based on the assumption that mechanical load is applied tangentially to the adhesion plane. Recently, we suggested a molecular mechanism that can explain adhesion growth under load for planar cell adhesions. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which for thermodynamic reasons, leads to the association of further molecules with the cluster, which we refer to as self-stabilization. Here, we generalize this model to forces that pull at an oblique angle to the plane supporting the cell, and examine if this idealized model also predicts self-stabilization. We also allow for a variable distance between the parallel planes representing cytoskeletal F-actin and transmembrane integrins. Simulation results demonstrate that the binding mechanism and the geometry of the cluster have a strong influence on the response of adhesion clusters to force. For oblique angles smaller than about 40∘, we observe a growth of the adhesion site under force. However this self-stabilization is reduced as the angle between the force and substrate plane increases, with vanishing self-stabilization for normal pulling. Overall, these results highlight the fundamental difference between the assumption of pulling and shearing forces in commonly used models of cell adhesion.

Shear force enhances adhesion of Pseudomonas aeruginosa by counteracting pilus-driven surface departure.

Fluid flow is thought to prevent bacterial adhesion, but some bacteria use adhesins with catch bond properties to enhance adhesion under high shear forces. However, many studies on bacterial adhesion either neglect the influence of shear force or use shear forces that are not typically found in natural systems. In this study, we use microfluidics and single-cell imaging to examine how the human pathogen Pseudomonas aeruginosa interacts with surfaces when exposed to shear forces typically found in the human body (0.1 pN to 10 pN). Through cell tracking, we demonstrate that the angle between the cell and the surface predicts if a cell will depart the surface. We discover that at lower shear forces, type IV pilus retraction tilts cells away from the surface, promoting surface departure. Conversely, we show that higher shear forces counterintuitively enhance adhesion by counteracting type IV pilus retraction-dependent cell tilting. Thus, our results reveal that P. aeruginosa exhibits behavior reminiscent of a catch bond, without having a specific adhesin that is enhanced by force. Instead, P. aeruginosa couples type IV pilus dynamics and cell geometry to tune adhesion to its mechanical environment, which likely provides a benefit in dynamic host environments.

Type-IV pili tune an adhesion-migration trade-off during surface colonization of Pseudomonas aeruginosa.

Bacterial pathogenicity relies on both firm surface adhesion and cell dissemination. How twitching bacteria resolve the fundamental contradiction between adhesion and migration is unknown. To address this question, we employ live-cell imaging of type-IV pili (T4P) and therewith construct a comprehensive mathematical model of Pseudomonas aeruginosa migration. The data show that only 10% to 50% of T4P bind to substrates and contribute to migration through random extension and retraction. Individual T4P do not display a measurable sensory response to surfaces, but their number increases on cellular surface contact. Attachment to surfaces is mediated, besides T4P, by passive adhesive forces acting on the cell body. Passive adhesions slow down cell migration and result in local random motion on short time scales, which is followed by directionally persistent, superdiffusive motion on longer time scales. Moreover, passive adhesions strongly enhance surface attachment under shear flow. Δ pilA mutants, which produce no T4P, robustly stick to surfaces under shear flow. In contrast, rapidly migrating Δ pilH cells, which produce an excessive number of T4P, are easily detached by shear. Wild-type cells sacrifice migration speed for robust surface attachment by maintaining a low number of active pili. The different cell strains pertain to disjunct regimes in a generic adhesion-migration trait space. Depending on the nature of the adhesion structures, adhesion and migration are either compatible or a trade-off is required for efficient bacterial surface colonization under different conditions.

Nonlinear, electrocatalytic swimming in the presence of salt.

A small, bimetallic particle in a hydrogen peroxide solution can propel itself by means of an electrocatalytic reaction. The swimming is driven by a flux of ions around the particle. We model this process for the presence of a monovalent salt, where reaction-driven proton currents induce salt ion currents. A theory for thin diffuse layers is employed, which yields nonlinear, coupled transport equations. The boundary conditions include a compact Stern layer of adsorbed ions. Electrochemical processes on the particle surface are modeled with a first order reaction of the Butler-Volmer type. The equations are solved numerically for the swimming speed. An analytical approximation is derived under the assumption that the decomposition of hydrogen peroxide occurs mainly without inducing an electric current. We find that the swimming speed increases linearly with hydrogen peroxide concentration for small concentrations. The influence of ion diffusion on the reaction rate can lead to a concave shape of the function of speed vs. hydrogen peroxide concentration. The compact layer of ions on the particle diminishes the reaction rate and consequently reduces the speed. Our results are consistent with published experimental data.

Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer.

Active diffusiophoresis-swimming through interaction with a self-generated, neutral, solute gradient-is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. First, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity on the swimmer and the concentration field. This effect, which we term "reaction induced concentration distortion," strongly influences the particle speed. Building on these insights, we employ irreversible, linear thermodynamics to formulate an energy balance. This approach highlights the importance of solute convection for a consistent treatment of the energetics. The efficiency of swimming is calculated numerically and approximated analytically. Finally, we define an efficiency of transport for swimmers which are moving in random directions. It is shown that this efficiency scales as the inverse of the macroscopic distance over which transport is to occur.

Generic self-stabilization mechanism for biomolecular adhesions under load.

Mechanical loading generally weakens adhesive structures and eventually leads to their rupture. However, biological systems can adapt to loads by strengthening adhesions, which is essential for maintaining the integrity of tissue and whole organisms. Inspired by cellular focal adhesions, we suggest here a generic, molecular mechanism that allows adhesion systems to harness applied loads for self-stabilization through adhesion growth. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which, for thermodynamic reasons, leads to association of further molecules with the cluster. Self-stabilization robustly increases adhesion lifetimes in broad parameter ranges. Unlike for catch-bonds, bond rupture rates can increase monotonically with force. The self-stabilization principle can be realized in many ways in complex adhesion-state networks; we show how it naturally occurs in cellular adhesions involving the adaptor proteins talin and vinculin.

Sparse inference and active learning of stochastic differential equations from data.

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and neural-network-based inference for empirical modelling, a physical interpretation of the results often remains challenging. Here, we focus on direct inference of governing differential equations from data, which can be formulated as a linear inverse problem. A Bayesian framework with a Laplacian prior distribution is employed for finding sparse solutions efficiently. The superior accuracy and robustness of the method is demonstrated for various cases, including ordinary, partial, and stochastic differential equations. Furthermore, we develop an active learning procedure for the automated discovery of stochastic differential equations. In this procedure, learning of the unknown dynamical equations is coupled to the application of perturbations to the measured system in a feedback loop. We show that active learning can significantly improve the inference of global models for systems with multiple energetic minima.

Quantitative Analysis of Myofibroblast Contraction by Traction Force Microscopy.

Myofibroblasts play important roles in physiological processes such as wound healing and tissue repair. While high contractile forces generated by the actomyosin network enable myofibroblasts to physically contract the wound and bring together injured tissue, prolonged and elevated levels of contraction also drive the progression of fibrosis and cancer. However, quantitative mapping of these forces has been difficult due to their extremely low magnitude ranging from 100 pN/µm2 to 2 nN/µm2. Here, we provide a protocol to measure cellular forces exerted on two-dimensional compliant elastic hydrogels. We describe the fabrication of polyacrylamide hydrogels labeled with fluorescent fiducial markers, functionalization of substrates with ECM proteins, setting up the experiment, and imaging procedures. We demonstrate the application of this technique for quantitative analysis of traction forces exerted by myofibroblasts.

EPB41L5 controls podocyte extracellular matrix assembly by adhesome-dependent force transmission.

The integrity of the kidney filtration barrier essentially relies on the balanced interplay of podocytes and the glomerular basement membrane (GBM). Here, we show by analysis of in vitro and in vivo models that a loss of the podocyte-specific FERM-domain protein EPB41L5 results in impaired extracellular matrix (ECM) assembly. By using quantitative proteomics analysis of the secretome and matrisome, we demonstrate a shift in ECM composition characterized by diminished deposition of core GBM components, such as LAMA5. Integrin adhesome proteomics reveals that EPB41L5 recruits PDLIM5 and ACTN4 to integrin adhesion complexes (IACs). Consecutively, EPB41L5 knockout podocytes show insufficient maturation of integrin adhesion sites, which translates into impaired force transmission and ECM assembly. These observations build the framework for a model in which EPB41L5 functions as a cell-type-specific regulator of the podocyte adhesome and controls a localized adaptive module in order to prevent podocyte detachment and thereby ensures GBM integrity.

Efficiency of surface-driven motion: nanoswimmers beat microswimmers.

Surface interactions provide a class of mechanisms which can be employed for propulsion of micrometer and nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.