The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

Abstract

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.     

Mobility of Molecular Motors Regulates Contractile Behaviors of Actin Networks

Cells generate mechanical forces primarily from interactions between F-actin, cross-linking proteins, myosin motors, and other actin-binding proteins in the cytoskeleton. To understand how molecular interactions between the cytoskeletal elements generate forces, a number of in vitro experiments have been performed but are limited in their ability to accurately reproduce the diversity of motor mobility. In myosin motility assays, myosin heads are fixed on a surface and glide F-actin. By contrast, in reconstituted gels, the motion of both myosin and F-actin is unrestricted. Because only these two extreme conditions have been used, the importance of mobility of motors for network behaviors has remained unclear. In this study, to illuminate the impacts of motor mobility on the contractile behaviors of the actin cytoskeleton, we employed an agent-based computational model based on Brownian dynamics. We find that if motors can bind to only one F-actin like myosin I, networks are most contractile at intermediate mobility. In this case, less motor mobility helps motors stably pull F-actins to generate tensile forces, whereas higher motor mobility allows F-actins to aggregate into larger clustering structures. The optimal intermediate motor mobility depends on the stall force and affinity of motors that are regulated by mechanochemical rates. In addition, we find that the role of motor mobility can vary drastically if motors can bind to a pair of F-actins. A network can exhibit large contraction with high motor mobility because motors bound to antiparallel pairs of F-actins can exert similar forces regardless of their mobility. Results from this study imply that the mobility of molecular motors may critically regulate contractile behaviors of actin networks in cells.     

Contribution of cellular contractility to spatial and temporal variations in cellular stiffness

Scanning probe microscopy and immunofluorescence observations indicated that cellular stiffness was attributed to a contractile network structure consisting of stress fibers. We measured temporal variations in cellular stiffness when cellular contractility was regulated by dosing with lysophosphatidic acid or Y-27632. This experiment revealed a clear relation between cellular stiffness and contractility: Increases in contractility caused cells to stiffen. On the other hand, decreases in contractility reduced cellular stiffness. In both cases, not only the stiffness of the stress fibers but also that of the whole of the cell varied. Immunofluorescence observations of myosin II and vinculin indicated that the stiffness variations induced by the regulation of cellular contractility were mainly due to rearrangements of the contractile actin network on the dorsal surface. Taken together, our findings provide evidence that the actin cytoskeletal network and its contractility features provide and modulate the mechanical stability of adherent cells.     

Hysteresis in the Cell Response to Time-Dependent Substrate Stiffness

Mechanical cues like the rigidity of the substrate are main determinants for the decision-making of adherent cells. Here we use a mechano-chemical model to predict the cellular response to varying substrate stiffnesses. The model equations combine the mechanics of contractile actin filament bundles with a model for the Rho-signaling pathway triggered by forces at cell-matrix contacts. A bifurcation analysis of cellular contractility as a function of substrate stiffness reveals a bistable response, thus defining a lower threshold of stiffness, below which cells are not able to build up contractile forces, and an upper threshold of stiffness, above which cells are always in a strongly contracted state. Using the full dynamical model, we predict that rate-dependent hysteresis will occur in the cellular traction forces when cells are exposed to substrates of time-dependent stiffness.     

Alpha-smooth muscle actin expression upregulates fibroblast contractile activity

To evaluate whether alpha-smooth muscle actin (alpha-SMA) plays a role in fibroblast contractility, we first compared the contractile activity of rat subcutaneous fibroblasts (SCFs), expressing low levels of alpha-SMA, with that of lung fibroblasts (LFs), expressing high levels of alpha-SMA, with the use of silicone substrates of different stiffness degrees. On medium stiffness substrates the percentage of cells producing wrinkles was similar to that of alpha-SMA-positive cells in each fibroblast population. On high stiffness substrates, wrinkle production was limited to a subpopulation of LFs very positive for alpha-SMA. In a second approach, we measured the isotonic contraction of SCF- and LF-populated attached collagen lattices. SCFs exhibited 41% diameter reduction compared with 63% by LFs. TGFbeta1 increased alpha-SMA expression and lattice contraction by SCFs to the levels of LFs; TGFbeta-antagonizing agents reduced alpha-SMA expression and lattice contraction by LFs to the level of SCFs. Finally, 3T3 fibroblasts transiently or permanently transfected with alpha-SMA cDNA exhibited a significantly higher lattice contraction compared with wild-type 3T3 fibroblasts or to fibroblasts transfected with alpha-cardiac and beta- or gamma-cytoplasmic actin. This took place in the absence of any change in smooth muscle or nonmuscle myosin heavy-chain expression. Our results indicate that an increased alpha-SMA expression is sufficient to enhance fibroblast contractile activity.     

Experimental and Computational Investigation of the Role of Stress Fiber Contractility in the Resistance of Osteoblasts to Compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell’s actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.     

Dynamic role of cross-linking proteins in actin rheology

We develop a computational model to compare the relative importance of unbinding and unfolding of actin cross-linking proteins (ACPs) in the dynamic properties of the actin cytoskeleton. We show that in the strain-stiffening regime with typical physiological and experimental strain rates, unbinding events are predominant with negligible unfolding. ACPs unbound by greater forces experience larger displacements, with a tendency to rebind to different filaments. At constant strain, stress relaxes to physiological levels by unbinding only—not unfolding—of ACPs, which is consistent with experiments. Also, rebinding of ACPs dampens full relaxation of stress. When the network is allowed to return to a stress-free state after shear deformation, plastic deformation is observed only with unbinding. These results suggest that despite the possibility of unfolding, unbinding of ACPs is the major determinant for the rheology of the actin network.     

Acto-myosin based response to stiffness and rigidity sensing

Cells sense the rigidity of their environment and respond to it. Most studies have been focused on the role of adhesion complexes in rigidity sensing. In particular, it has been clearly shown that proteins of the adhesion complexes were stretch-sensitive and could thus trigger mechano-chemical signaling in response to applied forces. In order to understand how this local mechano-sensitivity could be coordinated at the cell scale, we have recently carried out single cell traction force measurements on springs of varying stiffness. We found that contractility at the cell scale (force, speed of contraction, mechanical power) was indeed adapted to external stiffness and reflected ATPase activity of non-muscle myosin II and acto-myosin response to load. Here we suggest a scenario of rigidity sensing where local adhesions sensitivity to force could be coordinated by adaptation of the acto-myosin dependent cortical tension at the global cell scale. Such a scenario could explain how spreading and migration are oriented by the rigidity of the cell environment.Key words: single cell, mechano-sensing, mechano-transduction, contractility, spreading, polarization     

A mathematical model of the coupled mechanisms of cell adhesion,contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell’s cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell’s boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.     

Influence of surface topography on the human epithelial cell response to micropatterned substrates with convex and concave architectures

Background

Understanding the fundamental mechanisms underlying the cellular response to topographical surface features will extend our knowledge regarding the regulation of cell functions. Analyzing the cellular response to different topographical features, over multiple temporal and spatial scales, is central to understanding and guiding several biological functions. We used micropatterned substrates with convex and concave architectures to evaluate the behaviors of human epithelial cells on these substrates.

Results

Pillar and pit substrates caused heterogeneous spatial growth and distribution, with differences in cell density, over 48 h. Regional densities and distribution were significantly increased at pillar sidewalls, and at pit sidewalls and bottoms compared with those on flat unpatterned areas. Time-lapse observations revealed that different mechanisms of cell migration were dependent upon pillar and pit features. Cells on pillar substrate migrated towards the sidewall, whereas cells on pit substrate tended to move towards the sidewalls and bottom. Cytoskeletal staining of F-actin and vinculin showed that this migration can be attributed to difference in spatial reorganization of actin cytoskeleton, and the formation of focal adhesions at various points on the at the convex and concave corners of pillar and pit substrates. Cells cultured on the pillar substrate had stress fibers with extended filopodia and immature focal contacts at the sidewalls and convex corners, similar to those on the flat unpatterned substrate. Cells at the sidewalls and concave corners of pit substrate had more contractile stress fibers and stable focal contacts compared with cells on the pillar substrate. We also found that the substrate structures affect cell-cell contact formation via E-cadherin, and that this was associated with reorganization of the actin cytoskeleton at the sidewall, and at the convex and concave corners of the substrate.

Conclusion

Migration is an important factor affecting spatial growth and distribution. Heterogeneity at various locations was caused by different migratory behaviors at the convex and concave corners of pillar and pit substrates. We propose that this investigation is a valuable method for understanding cell phenotypes and the heterogeneity during spatial growth and distribution of epithelial cells during culture.

     

Computational Analysis of Viscoelastic Properties of Crosslinked Actin Networks

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G′) increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G′ as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a ‘supportive framework,’ as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.     

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles’ cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.     

Actin cytoskeletal dynamics in smooth muscle contraction

Smooth muscles develop isometric force over a very wide range of cell lengths. The molecular mechanisms of this phenomenon are undefined, but are described as reflecting "mechanical plasticity" of smooth muscle cells. Plasticity is defined here as a persistent change in cell structure or function in response to a change in the environment. Important environmental stimuli that trigger muscle plasticity include chemical (e.g., neurotransmitters, autacoids, and cytokines) and external mechanical signals (e.g., applied stress and strain). Both kinds of signals are probably transduced by ionic and protein kinase signaling cascades to alter gene expression patterns and changes in the cytoskeleton and contractile system. Defining the signaling mechanisms and effector proteins mediating phenotypic and mechanical plasticity of smooth muscles is a major goal in muscle cell biology. Some of the signaling cascades likely to be important include calcium-dependent protein kinases, small GTPases (Rho, Rac, cdc42), Rho kinase, protein kinase C (PKC), Src family tyrosine kinases, mitogen-activated protein (MAP) kinases, and p21 activated protein kinases (PAK). There are many potential targets for these signaling cascades including nuclear processes, metabolic pathways, and structural components of the cytoskeleton. There is growing appreciation of the dynamic nature of the actin cytoskeleton in smooth muscles and the necessity for actin remodeling to occur during contraction. The actin cytoskeleton serves many functions that are probably critical for muscle plasticity including generation and transmission of force vectors, determination of cell shape, and assembly of signal transduction machinery. Evidence is presented showing that actin filaments are dynamic and that actin-associated proteins comprising the contractile element and actin attachment sites are necessary for smooth muscle contraction.     

A quantitative analysis of contractility in active cytoskeletal protein networks

Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of purified F-actin, muscle myosin II motors, and α-actinin cross-linkers. We show that contractility occurs above a threshold motor concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of ∼1 μN, or ∼100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the (local) activity of molecular motors and the cross-linker density and binding affinity.     

Rho GTPase signaling modulates cell shape and contractile phenotype in an isoactin-specific manner

Rho family small GTPases (Rho, Rac, and Cdc42) play an important role in cell motility, adhesion, and cell division by signaling reorganization of the actin cytoskeleton. Here, we report an isoactin-specific, Rho GTPase-dependent signaling cascade in cells simultaneously expressing smooth muscle and nonmuscle actin isoforms. We transfected primary cultures of microvascular pericytes, cells related to vascular smooth muscle cells, with various Rho-related and Rho-specific expression plasmids. Overexpression of dominant positive Rho resulted in the formation of nonmuscle actin-containing stress fibers. At the same time, -vascular smooth muscle actin (VSMactin) containing stress fibers were disassembled, resulting in a dramatic reduction in cell size. Rho activation also yielded a disassembly of smooth muscle myosin and nonmuscle myosin from stress fibers. Overexpression of wild-type Rho had similar but less dramatic effects. In contrast, dominant negative Rho and C3 exotransferase or dominant positive Rac and Cdc42 expression failed to alter the actin cytoskeleton in an isoform-specific manner. The loss of smooth muscle contractile protein isoforms in pericyte stress fibers, together with a concomitant decrease in cell size, suggests that Rho activation influences "contractile" phenotype in an isoactin-specific manner. This, in turn, should yield significant alteration in microvascular remodeling during developmental and pathologic angiogenesis. vascular smooth muscle actin; Rho GTPase; pericyte; myosin; cytoskeleton     

Cytoskeletal modulation of electrical and mechanical activity in cardiac myocytes

The cardiac myocyte has an intracellular scaffold, the cytoskeleton, which has been implicated in several cardiac pathologies including hypertrophy and failure. In this review we describe the role that the cytoskeleton plays in modulating both the electrical activity (through ion channels and exchangers) and mechanical (or contractile) activity of the adult heart. We focus on the 3 components of the cytoskeleton, actin microfilaments, microtubules, and desmin filaments. The limited visual data available suggest that the subsarcolemmal actin cytoskeleton is sparse in the adult myocyte. Selective disruption of cytoskeletal actin by pharmacological tools has yet to be verified in the adult cell, yet evidence exists for modulation of several ionic currents, including I(CaL), I(Na), I(KATP), I(SAC) by actin microfilaments. Microtubules exist as a dense network throughout the adult cardiac cell, and their structure, architecture, kinetics and pharmacological manipulation are well described. Both polymerised and free tubulin are functionally significant. Microtubule proliferation reduces contraction by impeding sarcomeric motion; modulation of sarcoplasmic reticulum Ca(2+) release may also be involved in this effect. The lack of effect of microtubule disruption on cardiac contractility in adult myocytes, and the concentration-dependent modulation of the rate of contraction by the disruptor nocodazole in neonatal myocytes, support the existence of functionally distinct microtubule populations. We address the controversy regarding the stimulation of the beta-adrenergic signalling pathway by free tubulin. Work with mice lacking desmin has demonstrated the importance of intermediate filaments to normal cardiac function, but the precise role that desmin plays in the electrical and mechanical activity of cardiac muscle has yet to be determined.     

Hypoxia alters biophysical properties of endothelial cells via p38 MAPK- and Rho kinase-dependent pathways

Hypoxia alters the barrier function of the endothelial cells that line the pulmonary vasculature, but underlying biophysical mechanisms remain unclear. Using rat pulmonary microvascular endothelial cells (RPMEC) in culture, we report herein changes in biophysical properties, both in space and in time, that occur in response to hypoxia. We address also the molecular basis of these changes. At the level of the single cell, we measured cell stiffness, the distribution of traction forces exerted by the cell on its substrate, and spontaneous nanoscale motions of microbeads tightly bound to the cytoskeleton (CSK). Hypoxia increased cell stiffness and traction forces by a mechanism that was dependent on the activation of Rho kinase. These changes were followed by p38-mediated decreases in spontaneous bead motions, indicating stabilization of local cellular-extracellular matrix (ECM) tethering interactions. Cells overexpressing phospho-mimicking small heat shock protein (HSP27-PM), a downstream effector of p38, exhibited decreases in spontaneous bead motions that correlated with increases in actin polymerization in these cells. Together, these findings suggest that hypoxia differentially regulates endothelial cell contraction and cellular-ECM adhesion. endothelial barrier; cytoskeleton; actin dynamics; stiffness; tensile stress     

Actin cytoskeletal dynamics in smooth muscle: a new paradigm for the regulation of smooth muscle contraction

A growing body of data supports a view of the actin cytoskeleton of smooth muscle cells as a dynamic structure that plays an integral role in regulating the development of mechanical tension and the material properties of smooth muscle tissues. The increase in the proportion of filamentous actin that occurs in response to the stimulation of smooth muscle cells and the essential role of stimulus-induced actin polymerization and cytoskeletal dynamics in the generation of mechanical tension has been convincingly documented in many smooth muscle tissues and cells using a wide variety of experimental approaches. Most of the evidence suggests that the functional role of actin polymerization during contraction is distinct and separately regulated from the actomyosin cross-bridge cycling process. The molecular basis for the regulation of actin polymerization and its physiological roles may vary in diverse types of smooth muscle cells and tissues. However, current evidence supports a model for smooth muscle contraction in which contractile stimulation initiates the assembly of cytoskeletal/extracellular matrix adhesion complex proteins at the membrane, and proteins within this complex orchestrate the polymerization and organization of a submembranous network of actin filaments. This cytoskeletal network may serve to strengthen the membrane for the transmission of force generated by the contractile apparatus to the extracellular matrix, and to enable the adaptation of smooth muscle cells to mechanical stresses. Better understanding of the physiological function of these dynamic cytoskeletal processes in smooth muscle may provide important insights into the physiological regulation of smooth muscle tissues.     

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.