Estimation of Forces on Actin Filaments in Living Muscle from X-ray Diffraction Patterns and Mechanical Data.

Many biological processes are triggered or driven by mechanical forces in the cytoskeletal network, but these transducing forces have rarely been assessed. Striated muscle, with its well-organized structure provides an opportunity to assess intracellular forces using small-angle X-ray fiber diffraction. We present a new methodology using Monte Carlo simulations of muscle contraction in an explicit 3D sarcomere lattice to predict the fiber deformations and length changes along thin filaments during contraction. Comparison of predicted diffraction patterns to experimental meridional X-ray reflection profiles allows assessment of the stepwise changes in intermonomer spacings and forces in the myofilaments within living muscle cells. These changes along the filament length reflect the effect of forces from randomly attached crossbridges. This approach enables correlation of the molecular events, such as the current number of attached crossbridges and the distributions of crossbridge forces to macroscopic measurements of force and length changes during muscle contraction. In addition, assessments of fluctuations in local forces in the myofilaments may reveal how variations in the filament forces acting on signaling proteins in the sarcomere M-bands and Z-discs modulate gene expression, protein synthesis and degradation, and as well to mechanisms of adaptation of muscle in response to changes in mechanical loading.

The influence of physical and physiological cues on atomic force microscopy-based cell stiffness assessment.

Atomic force microscopy provides a novel technique for differentiating the mechanical properties of various cell types. Cell elasticity is abundantly used to represent the structural strength of cells in different conditions. In this study, we are interested in whether physical or physiological cues affect cell elasticity in Atomic force microscopy (AFM)-based assessments. The physical cues include the geometry of the AFM tips, the indenting force and the operating temperature of the AFM. All of these cues show a significant influence on the cell elasticity assessment. Sharp AFM tips create a two-fold increase in the value of the effective Young's modulus (E(eff)) relative to that of the blunt tips. Higher indenting force at the same loading rate generates higher estimated cell elasticity. Increasing the operation temperature of the AFM leads to decreases in the cell stiffness because the structure of actin filaments becomes disorganized. The physiological cues include the presence of fetal bovine serum or extracellular matrix-coated surfaces, the culture passage number, and the culture density. Both fetal bovine serum and the extracellular matrix are critical for cells to maintain the integrity of actin filaments and consequently exhibit higher elasticity. Unlike primary cells, mouse kidney progenitor cells can be passaged and maintain their morphology and elasticity for a very long period without a senescence phenotype. Finally, cell elasticity increases with increasing culture density only in MDCK epithelial cells. In summary, for researchers who use AFM to assess cell elasticity, our results provide basic and significant information about the suitable selection of physical and physiological cues.

The myosin duty ratio tunes the calcium sensitivity and cooperative activation of the thin filament.

In striated muscle, calcium binding to the thin filament (TF) regulatory complex activates actin-myosin ATPase activity, and actin-myosin kinetics in turn regulates TF activation. However, a quantitative description of the effects of actin-myosin kinetics on the calcium sensitivity (pCa50) and cooperativity (nH) of TF activation is lacking. With the assumption that TF structural transitions and TF-myosin binding transitions are inextricably coupled, we advanced the principles established by Kad et al. [Kad, N., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 16990-16995] and Sich et al. [Sich, N. M., et al. (2011) J. Biol. Chem. 285, 39150-39159] to develop a simple model of TF regulation, which predicts that pCa50 varies linearly with duty ratio and that nH is maximal near physiological duty ratios. Using in vitro motility to determine the calcium sensitivity of TF sliding velocities, we measured pCa50 and nH at different myosin densities and in the presence of ATPase inhibitors. The observed effects of myosin density and actin-myosin duty ratio on pCa50 and nH are consistent with our model predictions. In striated muscle, pCa50 must match cytosolic calcium concentrations and a maximal nH optimizes calcium responsiveness. Our results indicate that pCa50 and nH can be predictably tuned through TF-myosin ATPase kinetics and that drugs and disease states that alter ATPase kinetics can, through their effects on calcium sensitivity, alter the efficiency of muscle contraction.

Rotational model for actin filament alignment by myosin.

Dynamics of the actomyosin cytoskeleton regulate cellular processes such as secretion, cell division, cell motility, and shape change. Actomyosin dynamics are themselves regulated by proteins that control actin filament polymerization and depolymerization, and myosin motor contractility. Previous theoretical work has focused on translational movement of actin filaments but has not considered the role of filament rotation. Since filament rotational movements are likely sources of forces that direct cell shape change and movement we explicitly model the dynamics of actin filament rotation as myosin II motors traverse filament pairs, drawing them into alignment. Using Monte Carlo simulations we find an optimal motor velocity for alignment of actin filaments. In addition, when we introduce polymerization and depolymerization of actin filaments, we find that alignment is reduced and the filament arrays exist in a stable, asynchronous state. Further analysis with continuum models allows us to investigate factors contributing to the stability of filament arrays and their ability to generate force. Interestingly, we find that two different morphologies of F-actin arrays generate the same amount of force. We also identify a phase transition to alignment which occurs when either polymerization rates are reduced or motor velocities are optimized. We have extended our analysis to include a maximum allowed stretch of the myosin motors, and a non-uniform length for filaments leading to little change in the qualitative results. Through the integration of simulations and continuum analysis, we are able to approach the problem of understanding rotational alignment of actin filaments by myosin II motors.

A model of NMDA receptor control of F-actin treadmilling in synaptic spines and their growth.

Synaptic spines grow as a consequence of the formation of F-actin filaments at the spine head. The dynamics of F-actin in the spine head upon excitation of N-methy-D-aspartate (NMDA) receptors has recently been investigated experimentally, but there is no quantitative account of how these dynamic changes occur upon activation of these receptors; this we now supply. Dynamics of F-actin at the apex of lamellipodia have been investigated in detail, giving rise to the treadmilling theory of F-actin dynamics, involving catalysis by profilin, for which quantitative models are now available. Here, we adapt such a model to describe the dynamics of F-actin in the synaptic-spine head and show that it gives quantitative descriptions of this treadmilling phenomena which are well fitted by Monte Carlo simulations. Next, the means by which excitation of NMDA receptors enhances the activity of profilin through activity of the Rho small GTPase RhoA and the specific kinase ROCK is discussed. This is then used to model the NMDA receptor excitatory enhancement of profilin and so the treadmilling process of F-actin dynamics in spine growth. Such modelling provides a quantitative description of the synaptic-spine dynamics of the filamentous to globular actin ratio that is observed experimentally.

Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a markov model of the cardiac thin filament.

We developed a Markov model of cardiac thin filament activation that accounts for interactions among nearest-neighbor regulatory units (RUs) in a spatially explicit manner. Interactions were assumed to arise from structural coupling of adjacent tropomyosins (Tms), such that Tm shifting within each RU was influenced by the Tm status of its neighbors. Simulations using the model demonstrate that this coupling is sufficient to produce observed cooperativity in both steady-state and dynamic force-Ca(2+) relationships. The model was further validated by comparison with reported responses under various conditions including inhibition of myosin binding and the addition of strong-binding, non-force-producing myosin fragments. The model also reproduced the effects of 2.5 mM added P(i) on Ca(2+)-activated force and the rate of force redevelopment measured in skinned rat myocardial preparations. Model analysis suggests that Tm-Tm coupling potentiates the activating effects of strongly-bound cross-bridges and contributes to force-Ca(2+) dynamics of intact cardiac muscle. The model further predicts that activation at low Ca(2+) concentrations is cooperatively inhibited by nearest neighbors, requiring Ca(2+) binding to >25% of RUs to produce appreciable levels of force. Without excluding other putative cooperative mechanisms, these findings suggest that structural coupling of adjacent Tm molecules contributes to several properties of cardiac myofilament activation.

The energetic cost of activation in mouse fast-twitch muscle is the same whether measured using reduced filament overlap or N-benzyl-p-toluenesulphonamide.

AIM: Force generation and transmembrane ion pumping account for the majority of energy expended by contracting skeletal muscles. Energy turnover for ion pumping, activation energy turnover (E(A)), can be determined by measuring the energy turnover when force generation has been inhibited. Most measurements show that activation accounts for 25-40% of isometric energy turnover. It was recently reported that when force generation in mouse fast-twitch muscle was inhibited using N-benzyl-p-toluenesulphonamide (BTS), activation accounted for as much as 80% of total energy turnover during submaximal contractions. The purpose of this study was to compare E(A) measured by inhibiting force generation by: (1) the conventional method of reducing contractile filament overlap; and (2) pharmacological inhibition using BTS. METHODS: Experiments were performed in vitro using bundles of fibres from mouse fast-twitch extensor digitorum longus (EDL) muscle. Energy turnover was quantified by measuring the heat produced during 1-s maximal and submaximal tetanic contractions at 20 and 30 degrees C. RESULTS: E(A) measured using reduced filament overlap was 0.36 +/- 0.04 (n = 8) at 20 degrees C and 0.31 +/- 0.05 (n = 6) at 30 degrees C. The corresponding values measured using BTS in maximal contractions were 0.46 +/- 0.06 and 0.38 +/- 0.06 (n = 6 in both cases). There were no significant differences among these values. E(A) was also no different when measured using BTS in submaximal contractions. CONCLUSION: Activation energy turnover is the same whether measured using BTS or reduced filament overlap and accounts for slightly more than one-third of isometric energy turnover in mouse EDL muscle.

Evaluating spatial constraints in cellular assembly processes using a monte carlo approach.

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.

Force generation in single conventional actomyosin complexes under high dynamic load.

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel 'isometric' optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.

Ca(2+) activation and tension cost in myofilaments from mouse hearts ectopically expressing enteric gamma-actin.

To determine the significance of actin isoforms in chemomechanical coupling, we compared tension and ATPase rate in heart myofilaments from nontransgenic (NTG) and transgenic (TG) mice in which enteric gamma-actin replaced >95% of the cardiac alpha-actin. Enteric gamma-actin was expressed against three backgrounds: mice expressing cardiac alpha-actin, heterozygous null cardiac alpha-actin mice, and homozygous null cardiac alpha-actin mice. There were no differences in maximum Ca(2+) activated tension or maximum rate of tension redevelopment after a quick release and rapid restretch protocol between TG and NTG skinned fiber bundles. However, compared with NTG controls, Ca(2+) sensitivity of tension was significantly decreased and economy of tension development was significantly increased in myofilaments from all TG hearts. Shifts in myosin isoform population could not fully account for this increase in the economy of force production of TG myofilaments. Our results indicate that an exchange of cardiac alpha-actin with an actin isoform differing in only five amino acids has a significant impact on both Ca(2+) regulation of cardiac myofilaments and the cross-bridge cycling rate.

Assessment of stress fiber orientation during healing of radial keratotomy wounds using confocal microscopy.

Radial keratotomy (RK) is a refractive surgical procedure in which partial thickness incisions are made in the cornea in order to alter its shape. Previous studies suggest that RK wounds undergo changes in wound gape in response to the ingrowth of myofibroblasts which mediate subsequent wound contraction and may modulate changes in corneal curvature seen after RK. A recent quantitative analysis of f-actin organization in full-thickness incisional wounds in the rabbit demonstrated that microfilament bundles (stress fibers) present in myofibroblasts align parallel to the long axis of the wound during wound contraction. To investigate whether the same pattern of alignment occurs after RK, a similar analysis of f-actin organization was undertaken using the cat RK model. Radial keratotomy wounds were studied from 10 to 28 days after surgery using en block staining with fluorescein isothiocyanate (FITC) phalloidin, and three-dimensional (3-D) datasets (z-series of en face optical sections) were collected using laser confocal microscopy at various regions within the wound. In addition, conventional en face sections were double-labeled using combinations of phalloidin and antibodies to fibronectin and alpha 5 beta 1 integrin. Myofibroblast ingrowth started in the bottom of the wound and progressed anteriorly. At 10 to 14 days, f-actin was predominantly distributed in long, thick bundles (stress fibers) within the wound. These fibers appeared to be randomly oriented anteriorly, but became progressively more aligned with the long axis of the wound posteriorly. At 21 days, the stress fibers were predominantly oriented parallel to the long axis of the wound at all levels. F-actin, fibronectin and integrin were coaligned at both the 14 and 21 day time points. Since the majority of wound closure occurs between 14 and 28 days after surgery, we conclude that parallel alignment of the actin filament-fibronectin-integrin assembly in the cat RK model is associated with wound contraction.