Dynamics of cellular focal adhesions on deformable substrates: consequences for cell force microscopy

Cell focal adhesions are micrometer-sized aggregates of proteins that anchor the cell to the extracellular matrix. Within the cell, these adhesions are connected to the contractile, actin cytoskeleton; this allows the adhesions to transmit forces to the surrounding matrix and makes the adhesion assembly sensitive to the rigidity of their environment. In this article, we predict the dynamics of focal adhesions as a function of the rigidity of the substrate. We generalize previous theories and include the fact that the dynamics of proteins that adsorb to adhesions are also driven by their coupling to cell contractility and the deformation of the matrix. We predict that adhesions reach a finite size that is proportional to the elastic compliance of the substrate, on a timescale that also scales with the compliance: focal adhesions quickly reach a relatively small, steady-state size on soft materials. However, their apparent sliding is not sensitive to the rigidity of the substrate. We also suggest some experimental probes of these ideas and discuss the nature of information that can be extracted from cell force microscopy on deformable substrates.     

Contractile equilibration of single cells to step changes in extracellular stiffness

Extracellular stiffness has been shown to alter long timescale cell behaviors such as growth and differentiation, but the cellular response to changes in stiffness on short timescales is poorly understood. By studying the contractile response of cells to dynamic stiffness conditions using an atomic force microscope, we observe a seconds-timescale response to a step change in extracellular stiffness. Specifically, we observe acceleration in contraction velocity (μm/min) and force rate (nN/min) upon a step decrease in stiffness and deceleration upon a step increase in stiffness. Interestingly, this seconds-timescale response to a change in extracellular stiffness is not altered by inhibiting focal adhesion signaling or stretch-activated ion channels and is independent of cell height and contraction force. Rather, the response timescale is altered only by disrupting cytoskeletal mechanics and is well described by a simple mechanical model of a constant velocity actuator pulling against an internal cellular viscoelastic network. Consistent with the predictions of this model, we find that an osmotically expanding hydrogel responds to step changes in extracellular stiffness in a similar manner to cells. We therefore propose that an initial event in stiffness sensing is establishment of a mechanical equilibrium that balances contraction of the viscoelastic cytoskeleton with deformation of the extracellular matrix.     

Measuring single cardiac myocyte contractile force via moving a magnetic bead

One of the biggest problems of heart failure is the heart's inability to effectively pump blood to meet the body's demands, which may be caused by disease-induced alterations in contraction properties (such as contractile force and Young's modulus). Thus, it is very important to measure contractile properties at single cardiac myocyte level that can lay the foundation for quantitatively understanding the mechanism of heart failure and understanding molecular alterations in diseased heart cells. In this article, we report a novel single cardiac myocyte contractile force measurement technique based on moving a magnetic bead. The measuring system is mainly composed of 1), a high-power inverted microscope with video output and edge detection; and 2), a moving magnetic bead based magnetic force loading module. The main measurement procedures are as follows: 1), record maximal displacement of single cardiac myocyte during contraction; 2), attach a magnetic bead on one end of the myocyte that will move with myocyte during the contraction; 3), repeat step 1 and record contraction processes under different magnitudes of magnetic force loading by adjusting the magnetic field applied on the magnetic bead; and 4), derive the myocyte contractile force base on the maximal displacement of cell contraction and magnetic loading force. The major advantages of this unique approach are: 1), measuring the force without direct connections to the cell specimen (i.e., "remote sensing", a noninvasive/minimally invasive approach); 2), high sensitivity and large dynamic range (force measurement range: from pico Newton to micro Newton); 3), a convenient and cost-effective approach; and 4), more importantly, it can be used to study the contractile properties of heart cells under different levels of external loading forces by adjusting the magnitude of applied magnetic field, which is very important for studying disease induced alterations in contraction properties. Experimental results demonstrated the feasibility of proposed approach.     

Geometrical correspondence identified and a new interaction unit suggested in striated muscle

It has long been believed that the periodic structure of the myosin helix is a consequence only of compressing the actin-myosin interaction sites. Here, we identify a length correspondence between the smallest helical unit on the thick filament and the helical pitch of the actin filaments in two different contractile muscles. This suggests a rotation/swing of the filaments that creates a new interaction unit in addition to the single interaction between an actin filament and a myosin head. Numerical characteristics of the single interaction are estimated from discussion about an in vivo interaction utilizing the new unit. The estimated twisted angle of the actin filaments is consistent with that calculated from its torsion rigidity and the evaluated step sizes per cross-bridge can be performed by a single bend of a myosin head. By comparing our evaluated step sizes with experimental results, we conclude that the most plausible mechanism at the force-recovery stage involves swings or rotations of both filaments in the same direction (clockwise).     

Velocity transients and viscoelastic resistance to active shortening in cat papillary muscle.

When isotonic force steps were applied to activated papillary muscles, the velocity was almost never constant. Early rapid shortening associated with the step persisted for 2-7 ms after the step ends. The early rapid shortening is attributed to lightly damped series elastic recoil and velocity transients of the contractile elements. In most steps, the subsequent velocity declines progressively with shortening, and most of the decline in velocity can be accounted for by compression of a viscoelastic element in parallel with the contractile elements. To demonstrate this, the time course of isotonic velocity was compared with a model in which the force-velocity characteristics of the contractile element were assumed to be constant, and the decline in velocity was due to increasing compression of the viscoelastic element. This model predicted the observed results except that the predicted velocities rose progressively above the measured values for steps to light loads applied late in the twitch, and fell below the velocity trace for heavy loads applied early in the twitch. These deviations would occur if rapid shortening caused deactivation late in the twitch, and if activation were rising early in the twitch. A conditioning step applied to the muscle during the rise of force depressed both isometric force and maximum velocity measured at the peak of force; isometric force was more depressed with later conditioning steps than with earlier steps, while maximum velocity was depressed by about the same extent with both early and late steps. This difference between the effects on isometric force and maximum velocity are explained by a combination of deactivation and viscoelastic load.     

Mechanical output of the cat soleus during treadmill locomotion: in vivo vs in situ characteristics

To study the mechanical output of skeletal muscle, four adult cats were trained to run on a treadmill and then implanted under sterile conditions and anesthesia with a force transducer on the soleus tendon and EMG electrodes in the muscle belly. After a two-week recovery period, five consecutive step cycles were filmed at treadmill speeds of 0.8, 1.3 and 2.2 m s-1. Locomotion data in vivo included individual muscle force, length and velocity changes and EMG during each step cycle. Data for an average step cycle at each speed were compared to the force-velocity properties obtained on the same muscle under maximal nerve stimulation and isotonic loading conditions in situ. Results indicate that the force and power generated at a given velocity of shortening during late stance in vivo were greater at the higher speeds of locomotion than the force and power generated at the same shortening velocity in situ. Strain energy stored in the muscle-tendon unit during the yield phase in early stance is felt to be a major contributor to the muscle's enhanced mechanical output during muscle shortening in late stance.     

A model for cell motility on soft bio-adhesive substrates

Mechanical stiffness of bio-adhesive substrates has been recognized as a major regulator of cell motility. We present a simple physical model to study the crawling locomotion of a contractile cell on a soft elastic substrate. The mechanism of rigidity sensing is accounted for using Schwarz's two-spring model Schwarz et al. (2006). The predicted dependency between the speed of motility and substrate stiffness is qualitatively consistent with experimental observations. The model demonstrates that the rigidity dependent motility of cells is rooted in the regulation of actomyosin contractile forces by substrate deformation at each anchorage point. On stiffer substrates, the traction forces required for cell translocation acquire larger magnitude but show weaker asymmetry which leads to slower cell motility. On very soft substrates, the model predicts a biphasic relationship between the substrate rigidity and the speed of locomotion, over a narrow stiffness range, which has been observed experimentally for some cell types.     

The biophysics and biochemistry of smooth muscle contraction.

In this review the biophysics and biochemistry of smooth muscle contraction are dealt with. We describe a new model for the study of bronchial smooth muscle, which facilitates study of cellular contractile mechanisms. A new concept emerging is that study of steady-state mechanical parameters such as maximal isometric force (Po) velocity is inadequate because two types of crossbridges (normally cycling (NBR) and latch) seem to be sequentially active during smooth muscle contraction. Thus quick-release techniques are required to characterize the force-velocity properties of the two types of bridges. Pathophysiological processes that affect the muscle's shortening ability seem to affect the early NBRs only. With respect to maximal shortening capacity of the smooth muscle, the role of loading is very important. The differences between isotonic, elastic, and viscous loading are considerable. Ultimately, the time course and magnitude of loading should exactly resemble that operative in vivo. Once again, it is the characteristic of loading in the early phase of contraction that is crucial, as most of the shortening in smooth muscle occurs early in the contraction. While the maximum force developed by smooth muscle per unit cross-sectional area is the same as for striated muscle, the velocity is 50 times less. The properties of the series and parallel elastic elements of smooth muscle are described. The latter, when in compression mode, acts as an internal resistance to shortening and probably limits it. Isotonic relaxation has therefore not been studied in smooth muscle. We have developed a shortening parameter that is independent of the load on the muscle and of the initial length of the muscle's contractile element. We report the novel observation that isotonically relaxing smooth muscle reactivates itself, resulting in terminal slowing of the relaxation process. With respect to the biochemistry of smooth muscle contraction, contractile (actin isoforms, myosin heavy and light chains and their isoforms), regulatory (calmodulin-4 Ca2+, myosin light chain kinase, myosin light chain and its phosphorylation, tropomyosin, caldesmon, and calponin), and cytoskeletal (chiefly desmin and vimentin) proteins are discussed. While the kinase activates the contractile system, caldesmon and calponin modulate the activity downward. The cytoskeletal proteins desmin, vimentin, and alpha-actinin could constitute the muscle cell's internal resistor.     

Rigidity sensing at the leading edge through alphavbeta3 integrins and RPTPalpha

Cells require optimal substrate stiffness for normal function and differentiation. The mechanisms for sensing matrix rigidity and durotaxis, however, are not clear. Here we showed that control, Shp2-/-, integrin beta1-/-, and talin1-/- cell lines all spread to a threefold greater area on fibronectin (FN)-coated rigid polyacrylamide surfaces than soft. In contrast, RPTPalpha-/- cells spread to the same area irrespective of rigidity on FN surfaces but spread 3x greater on rigid collagen IV-coated surfaces than soft. RPTPalpha and alphavbeta3 integrins were shown previously to be colocalized at leading edges and antibodies to alphavbeta3 blocked FN rigidity sensing. When FN beads were held with a rigid laser trap at the leading edge, stronger bonds to the cytoskeleton formed than when held with a soft trap; whereas back from the leading edge and in RPTPalpha-/- cells, weaker bonds were formed with both rigid and soft laser traps. From the rigidity of the trap, we calculate that a force of 10 pN generated in 1 s is sufficient to activate the rigidity response. We suggest that RPTPalpha and alphavbeta3 at the leading edge are critical elements for sensing FN matrix rigidity possibly through SFK activation at the edge and downstream signaling.     

Polyacrylamide Gels for Invadopodia and Traction Force Assays on Cancer Cells

Rigid tumor tissues have been strongly implicated in regulating cancer cell migration and invasion. Invasive migration through cross-linked tissues is facilitated by actin-rich protrusions called invadopodia that proteolytically degrade the extracellular matrix (ECM). Invadopodia activity has been shown to be dependent on ECM rigidity and cancer cell contractile forces suggesting that rigidity signals can regulate these subcellular structures through actomyosin contractility. Invasive and contractile properties of cancer cells can be correlated in vitro using invadopodia and traction force assays based on polyacrylamide gels (PAAs) of different rigidities. Invasive and contractile properties of cancer cells can be correlated in vitro using invadopodia and traction force assays based on polyacrylamide gels (PAAs) of different rigidities. While some variations between the two assays exist, the protocol presented here provides a method for creating PAAs that can be used in both assays and are easily adaptable to the user’s specific biological and technical needs.     

Characterization of penile erectile states using external computer-based monitoring

The states of penile erection have not been quantified to establish their relationship to intracorporal fluid pressure and to soft tissue constraint. Computer-based circumferential rigidity sensing during erectile cycles now permits circumferential size and rigidity characterization. Measurements during dynamic infusion cavernometry and cavernosography relate intracorporal pressure and axial rigidity to circumference and circumferential rigidity characterization. Tumescence/rigidity coupling and tissue elastic contributions are identified from the combined data.     

Isokinetic plantar flexion: experimental results and model calculations

In isokinetic experiments on human subjects, conducted to determine moments that can be exerted about a joint at different angular velocities, joint rotation starts as soon as the moment increases above the resting level. This contraction history differs from the one in experiments on isolated muscle, where the force is allowed to increase to an isometric level before shortening is initiated. The purpose of the present study was to determine the influence of contraction history on plantar flexing moments found during maximal voluntary plantar flexion on an isokinetic dynamometer. In ten subjects, plantar flexing moments were measured as a function of ankle angle at different angular velocities. They were also calculated using a model of the muscle-tendon complex of the human triceps surae. The model incorporates elastic tendinous tissue in series with muscle fibers. The input of the model consists of time histories of active state (the force generating capacity of contractile elements) and shortening velocity of the muscle-tendon complex. Different time courses of active state were offered at fixed length of the muscle-tendon complex. The time course yielding a close match between the calculated rise of plantar flexing moment and the rise measured during fixed angle contractions was used to calculate moment-angle curves for isokinetic plantar flexion. The active state value reached when a peak occurred in calculated moment-angle curves was found to be lower if the angular velocity was made higher. Comparing measured and calculated results, it was concluded that moment-angular velocity diagrams determined in studies of isokinetic plantar flexion in human subjects reflect not only the influence of shortening velocity of contractile elements on the force which can be produced by plantar flexors.     

Comparative trends in shortening velocity and force production in skeletal muscles

Skeletal muscles are diverse in their properties, with specific contractile characteristics being matched to particular functions. In this study, published values of contractile properties for >130 diverse skeletal muscles were analyzed to detect common elements that account for variability in shortening velocity and force production. Body mass was found to be a significant predictor of shortening velocity in terrestrial and flying animals, with smaller animals possessing faster muscles. Although previous studies of terrestrial mammals revealed similar trends, the current study indicates that this pattern is more universal than previously appreciated. In contrast, shortening velocity in muscles used for swimming and nonlocomotory functions is not significantly affected by body size. Although force production is more uniform than shortening velocity, a significant correlation with shortening velocity was detected in muscles used for locomotion, with faster muscles tending to produce more force. Overall, the contractile properties of skeletal muscles are conserved among phylogenic groups, but have been significantly influenced by other factors such as body size and mode of locomotion.     

Bone modeling response to voluntary exercise in the hindlimb of mice

The functional adaptation of juvenile mammalian limb bone to mechanical loading is necessary to maintain bone strength. Diaphyseal size and shape are modified during growth through the process of bone modeling. Although bone modeling is a well-documented response to increased mechanical stress on growing diaphyseal bone, the effect of proximodistal location on bone modeling remains unclear. Distal limb elements in cursorial mammals are longer and thinner, most likely to conserve energy during locomotion because they require less energy to move. Therefore, distal elements are hypothesized to experience greater mechanical loading during locomotion and may be expected to exhibit a greater modeling response to exercise. In this study, histomorphometric comparisons are made between femora and tibiae of mice treated with voluntary exercise and a control group (N = 20). We find that femora of exercised mice exhibit both greater bone growth rates and growth areas than do controls (P < 0.05). The femora of exercised mice also have significantly greater cortical area, bending rigidity, and torsional rigidity (P < 0.05), although bending and torsional rigidity are comparable when standardized by bone length. Histomorphometric and cross-section geometric properties of the tibial midshaft of exercised and control mice did not differ significantly, although tibial length was significantly greater in exercised mice (P < 0.05). Femora of exercised mice were able to adapt to increased mechanical loading through increases in compressive, bending, and torsional rigidity. No such adaptations were found in the tibia. It is unclear if this is a biomechanical adaptation to greater stress in proximal elements or if distal elements are ontogenetically constrained in a tradeoff of bone strength of distal elements for bioenergetic efficiency during locomotion.     

Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions from Discrete Fiber Network Simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element–based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.     

Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions from Discrete Fiber Network Simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element–based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.     

Human soleus single muscle fiber function with exercise or nutrition countermeasures during 60 days of bed rest

The soleus muscle has been consistently shown to atrophy more than other leg muscles during unloading and is difficult to protect using various exercise countermeasure paradigms. However, the efficacy of aerobic exercise, a known stimulus for oxidative adaptations, has not been tested in combination with resistance exercise (RE), a known hypertrophic stimulus. We hypothesized that a concurrent exercise program (AE + RE) would preserve soleus fiber myosin heavy chain (MHC) I size and function during 60 days of bed rest. A secondary objective was to test the hypothesis that a leucine-enriched high protein diet would partially protect soleus single fiber characteristics. Soleus muscle biopsies were obtained before and after bed rest from a control (BR; n = 7), nutrition (BRN; n = 8), and exercise (BRE; n = 6) group. Single muscle fiber diameter (Dia), peak force (Po), contractile velocity, and power were studied. BR decreased (P < 0.05) MHC I Dia (-14%), Po (-38%), and power (-39%) with no change in contractile velocity. Changes in MHC I size (-13%) and contractile function (approximately 30%) from BRN were similar to BR. BRE decreased (P < 0.05) MHC I Dia (-13%) and Po (-23%), while contractile velocity increased (P < 0.05) 26% and maintained power. These soleus muscle data show 1) the AE + RE exercise program maintained MHC I power but not size and strength, and 2) the nutrition countermeasure did not benefit single fiber size and contractile function. The divergent response in size and functional MHC I soleus properties with the concurrent exercise program was a unique finding further highlighting the challenges of protecting the unloaded soleus.     

Role of the membrane concanavalin A binding site in platelet-fibrin interactions

Concanavalin A was employed to study the role of platelet membrane glycoproteins in platelet-fibrin interactions during clot formation. A rheological technique was used to study the interactions, measuring the clot rigidity and platelet contractile force simultaneously during the formation of network structure. Concanavalin A lowered the clot rigidity and contractile force of a platelet-rich plasma clot by a small extent. Plasma glycoproteins probably compete with platelet membranes for concanavalin A binding in platelet-rich plasma. Both native concanavalin A (tetrameric) and succinyl concanavalin A (dimeric) lowered the clot rigidity and contractile force of a washed platelet-fibrin clot dramatically, almost down to those values found for fibrin clots. Inhibition studies with alpha-methyl-D-mannoside indicated that the concanavalin A effects were specific for the concanavalin A binding capacity to platelets. The effects of native concanavalin A on platelet-fibrin clots were only partially reversible, while the succinyl concanavalin A effects were completely reversible. The observed concanavalin A effects are probably mainly due to concanavalin A binding to platelet membrane glycoproteins. The concanavalin A binding site appears to play an important role in the fibrin binding to platelets.     

Age differences in knee extension power, contractile velocity, and fatigability.

The purposes of this study were to examine age and gender differences in knee extensor strength, power, and fatigue using open- and closed-chain testing procedures. We tested the hypothesis that specific strength (strength/unit muscle mass) would not differ by age, whereas age differences in specific power and fatigue would remain consequent to blunted maximal contractile velocity. Skeletal muscle performance was examined in 28 young (26.9 +/- 0.7 yr) and 24 older (63.6 +/- 0.8 yr) men and women. Assessments included one-repetition maximum strength for knee extension, leg press, and squat; concentric knee extensor peak power, velocity, and fatigability; and sit-to-stand power, fatigability, and relative neural activation (electromyograph activity during sit-to-stand movement normalized to electromyograph activity during isometric maximum voluntary contraction). Thigh lean mass (TLM; kg) was assessed by dual-energy X-ray absorptiometry. Specific strength (N/kg TLM) and specific power (W/kg TLM) were estimated by dividing absolute values by TLM. Age differences in specific strength were observed for knee extension only (young, 41.2 +/- 1.0 N/kg TLM; older, 32.4 +/- 1.0 N/kg TLM; P < 0.05). Adjustment for TLM did not negate age differences in knee extension specific power (25-41% lower in older; P < 0.05) across loads tested. Older adults experienced fatigue across 10 repetitions of knee extension as peak velocity fell by 24% (P < 0.05). Deficits in concentric power persist after adjustment for TLM as maximum contractile velocity falls markedly with aging. Older adults are less capable of sustaining maximum concentric velocity during repetitive contractions. These findings suggest that velocity impairments are a possible contributor to mobility loss and falls risk among older adults. Interventions for improving contractile velocity should be pursued.     

Body size effects on locomotion and load carriage in the highly polymorphic leaf-cutting ants Atta colombica and Atta cephalotes

Leaf-cutting ants reduce their walking speed under the weightof the leaf fragments they carry, an effect likely to havesome consequence for the foraging performance of a colony.I manipulated loads carried by workers from two Atta speciesto determine how load mass and body size affect walking speed.A comparison of speeds before and after load manipulation indicatesthat change in load mass has a linear effect on velocity. Several different regression models of speed as a function of loadsand body size have similar fit to the data, so a single bestmodel cannot easily be identified. However, there is statisticalevidence that the slope of the linear effect is more pronouncedfor smaller ants, an outcome most consistent with a regression model based on loading ratio, a metric that scales load massrelative to body mass. I then examined the effect of loadingratio on the leaf transport rate (the product of load massand carriage velocity). It has been claimed that this rateis maximized over a range of loading ratios that is the samefor all ants regardless of their size. However, I found thata latent body mass effect persists in the relation of transportrate to loading ratio, even though loading ratio is alreadyscaled relative to body mass. The maxima seem to be reachedonly at artificially elevated loading ratios, so that transportrates with natural fragments tend to be sub-maximal. This conclusionis in agreement with analytical predictions of rate-maximizingload masses derived from the regression models. Thus, loadingratio does not adequately scale load mass relative to bodysize when used in this context (effect on leaf transport rate),and should be used cautiously. Ants are likely to accommodateloads through modulation of both stride length and step frequency,but precisely how this takes place requires future study.