Sam Walcott

A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells

Tissue cells sense and respond to the stiffness of the surface on which they adhere. Precisely how cells sense surface stiffness remains an open question, though various biochemical pathways are critical for a proper stiffness response. Here, based on a simple mechanochemical model of biological friction, we propose a model for cell mechanosensation as opposed to previous more biochemically based models. Our model of adhesion complexes predicts that these cell-surface interactions provide a viscous drag that increases with the elastic modulus of the surface. The force-velocity relation of myosin II implies that myosin generates greater force when the adhesion complexes slide slowly. Then, using a simple cytoskeleton model, we show that an external force applied to the cytoskeleton causes actin filaments to aggregate and orient parallel to the direction of force application. The greater the external force, the faster this aggregation occurs. As the steady-state probability of forming these bundles reflects a balance between the time scale of bundle formation and destruction (because of actin turnover), more bundles are formed when the cytoskeleton time-scale is small (i.e., on stiff surfaces), in agreement with experiment. As these large bundles of actin, called stress fibers, appear preferentially on stiff surfaces, our mechanical model provides a mechanism for stress fiber formation and stiffness sensing in cells adhered to a compliant surface.

Actin cap associated focal adhesions and their distinct role in cellular mechanosensing

The ability for cells to sense and adapt to different physical microenvironments plays a critical role in development, immune responses, and cancer metastasis. Here we identify a small subset of focal adhesions that terminate fibers in the actin cap, a highly ordered filamentous actin structure that is anchored to the top of the nucleus by the LINC complexes; these differ from conventional focal adhesions in morphology, subcellular organization, movements, turnover dynamics, and response to biochemical stimuli. Actin cap associated focal adhesions (ACAFAs) dominate cell mechanosensing over a wide range of matrix stiffness, an ACAFA-specific function regulated by actomyosin contractility in the actin cap, while conventional focal adhesions are restrictively involved in mechanosensing for extremely soft substrates. These results establish the perinuclear actin cap and associated ACAFAs as major mediators of cellular mechanosensing and a critical element of the physical pathway that transduce mechanical cues all the way to the nucleus.

Cytoskeletal Cross-linking and Bundling in Motor-Independent Contraction

Eukaryotic and prokaryotic cells use cytoskeletal proteins to regulate and modify cell shape. During cytokinesis or eukaryotic cell crawling, contractile forces are generated inside the cell to constrict the division site or to haul the rear of the cell forward, respectively. In many cases, these forces have been attributed to the activity of molecular motors, such as myosin II, which, by pulling on actin filaments, can produce contraction of the actin cytoskeleton. However, prokaryotic division is driven by the tubulin-like protein FtsZ and does not seem to require additional molecular motors to constrict the division site. Likewise, Dictyostelium discoideum and Saccharomyces cerevisiae can perform cytokinesis under motor-free conditions. In addition, many crawling cells can translocate when myosin is inhibited or absent. In this review, we point out another force-generation mechanism that can play a significant role in driving these processes in eukaryotes and prokaryotes. This mechanism is mediated by cross-linking and bundling proteins that form effective interactions between cytoskeletal filaments. Some recent studies in this area are reviewed and the physical underpinnings of this force-generation mechanism are explained.

Adhesion dynamics and durotaxis in migrating cells

When tissue cells are plated on a flexible substrate, durotaxis, the directed migration of cells toward mechanically stiff regions, has been observed. Environmental mechanical signals are not only important in cell migration but also seem to influence all aspects of cell differentiation and development, including the metastatic process in cancer cells. Based on a theoretical model suggesting that this mechanosensation has a mechanical basis, we introduce a simple model of a cell by considering the contraction of F-actin bundles containing myosin motors (stress fibers) mediated by the movement of adhesions. We show that, when presented with a linear stiffness gradient, this simple model exhibits durotaxis. Interestingly, since stress fibers do not form on soft surfaces and since adhesion sliding occurs very slowly on hard surfaces, the model predicts that the expected cell velocity reaches a maximum at an intermediate stiffness. This prediction can be experimentally tested. We therefore argue that stiffness-dependent cellular adaptations (mechanosensation) and durotaxis are intimately related and may share a mechanical basis. We therefore identify the essential physical ingredients, which combined with additional biochemical mechanisms can explain durotaxis and mechanosensation in cells.

Mechanical Coupling between Myosin Molecules Causes Differences between Ensemble and Single-Molecule Measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosins force-dependent properties, provide detailed insight into the kinetics of myosins mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.

Nucleation and Decay Initiation Are the Stiffness-Sensitive Phases of Focal Adhesion Maturation

A cell plated on a two-dimensional substrate forms adhesions with that surface. These adhesions, which consist of aggregates of various proteins, are thought to be important in mechanosensation, the process by which the cell senses and responds to the mechanical properties of the substrate (e.g., stiffness). On the basis of experimental measurements, we model these proteins as idealized molecules that can bind to the substrate in a strain-dependent manner and can undergo a force-dependent state transition. The model forms molecular aggregates that are similar to adhesions. Substrate stiffness affects whether a simulated adhesion is initially formed and how long it grows, but not how that adhesion grows or shrinks. Our own experimental tests support these predictions, suggesting that the mechanosensitivity of adhesions is an emergent property of a simple molecular-mechanical system.

Phosphate enhances myosin-powered actin filament velocity under acidic conditions in a motility assay

Elevated levels of inorganic phosphate (P(i)) are believed to inhibit muscular force by reversing myosins force-generating step. These same levels of P(i) can also affect muscle velocity, but the molecular basis underlying these effects remains unclear. We directly examined the effect of P(i) (30 mM) on skeletal muscle myosins ability to translocate actin (V(actin)) in an in vitro motility assay. Manipulation of the pH enabled us to probe rebinding of P(i) to myosins ADP-bound state, while changing the ATP concentration probed rebinding to the rigor state. Surprisingly, the addition of P(i) significantly increased V(actin) at both pH 6.8 and 6.5, causing a doubling of V(actin) at pH 6.5. To probe the mechanisms underlying this increase in speed, we repeated these experiments while varying the ATP concentration. At pH 7.4, the effects of P(i) were highly ATP dependent, with P(i) slowing V(actin) at low ATP (<500 μM), but with a minor increase at 2 mM ATP. The P(i)-induced slowing of V(actin), evident at low ATP (pH 7.4), was minimized at pH 6.8 and completely reversed at pH 6.5. These data were accurately fit with a simple detachment-limited kinetic model of motility that incorporated a P(i)-induced prolongation of the rigor state, which accounted for the slowing of V(actin) at low ATP, and a P(i)-induced detachment from a strongly bound post-power-stroke state, which accounted for the increase in V(actin) at high ATP. These findings suggest that P(i) differentially affects myosin function: enhancing velocity, if it rebinds to the ADP-bound state, while slowing velocity, if it binds to the rigor state.

Smooth muscle heavy meromyosin phosphorylated on one of its two heads supports force and motion.

Smooth muscle myosin is activated by regulatory light chain (RLC) phosphorylation. In the unphosphorylated state the activity of both heads is suppressed due to an asymmetric, intramolecular interaction between the heads. The properties of myosin with only one of its two RLCs phosphorylated, a state likely to be present both during the activation and the relaxation phase of smooth muscle, is less certain despite much investigation. Here we further characterize the mechanical properties of an expressed heavy meromyosin (HMM) construct with only one of its RLCs phosphorylated (HMM-1P). This construct was previously shown to have more than 50% of the ATPase activity of fully phosphorylated myosin (HMM-2P) and to move actin at the same speed in a motility assay as HMM-2P (Rovner, A. S., Fagnant, P. M., and Trybus, K. M. (2006) Biochemistry 45, 5280–5289). Here we show that the unitary step size and attachment time to actin of HMM-1P is indistinguishable from that of HMM-2P. Force-velocity measurements on small ensembles show that HMM-1P can generate approximately half the force of HMM-2P, which may relate to the observed duty ratio of HMM-1P being approximately half that of HMM-2P. Therefore, single-phosphorylated smooth muscle HMM molecules are active species, and the head associated with the unphosphorylated RLC is mechanically competent, allowing it to make a substantial contribution to both motion and force generation during smooth muscle contraction.

A Mechanical Model of Actin Stress Fiber Formation and Substrate Elasticity Sensing in Adherent Cells

Tissue cells sense and respond to the stiffness of the surface on which they adhere. Precisely how cells sense surface stiffness remains an open question, though various biochemical pathways are critical for a proper stiffness response. Here, based on a simple mechanochemical model of biological friction, we propose a mechanical model for cell mechanosensation as opposed to previous more biochemically-based models. Our model of adhesion complexes predicts that these cell-surface interactions provide a viscous drag that increases with the elastic modulus of the surface. Using the force-velocity relation of myosin II, we show that myosin generates greater force the slower the adhesion complexes slide. Then, using a simple cytoskeleton model, we show that an external force applied to the cytoskeleton causes actin filaments to aggregate and orient parallel to the direction of force application. The greater the external force, the faster this aggregation occurs. As the steady-state probability of forming these bundles reflects a balance between the time scale of bundle formation and destruction (due to actin turnover), more bundles are formed when the cytoskeleton time-scale is small (i.e. on stiff surfaces), in agreement with experiment. As these bundles seem related to stress fibers, large bundles of actin that appear preferentially on stiff surfaces, our mechanical model provides a mechanism for stress fiber formation and stiffness sensing in cells adhered to a compliant surface.

Effects of Cardiac Myosin Binding Protein-C on Actin Motility Are Explained with a Drag-Activation-Competition Model

Although mutations in cardiac myosin binding protein-C (cMyBP-C) cause heart disease, its role in muscle contraction is not well understood. A mechanism remains elusive partly because the protein can have multiple effects, such as dual biphasic activation and inhibition observed in actin motility assays. Here we develop a mathematical model for the interaction of cMyBP-C with the contractile proteins actin and myosin and the regulatory protein tropomyosin. We use this model to show that a drag-activation-competition mechanism accurately describes actin motility measurements, while models lacking either drag or competition do not. These results suggest that complex effects can arise simply from cMyBP-C binding to actin.