Fine structure and contraction of isolated muscle actomyosin

Summary A modified thread model of isolated cross-striated muscle actomyosin was produced, which a priori consisted of both actin and myosin filaments forming a random network. This modified model contracts to the same extent as the normal model which lacks myosin filaments prior to contraction.The striking difference in the contraction behavior of the two models indicates 1) that in the normal model myosin filament formation occurs during contraction and 2) that the pre-existence of myosin filaments in the modified model increases the speed of contraction. Hence, the sliding mechanism involving myosin filaments is able to operate at a higher speed than the sliding mechanism which utilizes oligomeric myosin.     

Actin depolymerization drives actomyosin ring contraction during budding yeast cytokinesis

Actin filaments and myosin II are evolutionarily conserved force-generating components of the contractile ring during cytokinesis. Here we show that in budding yeast, actin filament depolymerization plays a major role in actomyosin ring constriction. Cofilin mutation or chemically stabilizing actin filaments attenuate actomyosin ring constriction. Deletion of myosin II motor domain or the myosin regulatory light chain reduced the contraction rate and also the rate of actin depolymerization in the ring. We constructed a quantitative microscopic model of actomyosin ring constriction via filament sliding driven by both actin depolymerization and myosin II motor activity. Model simulations based on experimental measurements support the notion that actin depolymerization is the predominant mechanism for ring constriction. The model predicts invariability of total contraction time regardless of the initial ring size, as originally reported for C. elegans embryonic cells. This prediction was validated in yeast cells of different sizes due to different ploidies.     

A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells

How adherent and contractile systems coordinate to promote cell shape changes is unclear. Here, we define a counterbalanced adhesion/contraction model for cell shape control. Live-cell microscopy data showed a crucial role for a contractile meshwork at the top of the cell, which is composed of actin arcs and myosin IIA filaments. The contractile actin meshwork is organized like muscle sarcomeres, with repeating myosin II filaments separated by the actin bundling protein α-actinin, and is mechanically coupled to noncontractile dorsal actin fibers that run from top to bottom in the cell. When the meshwork contracts, it pulls the dorsal fibers away from the substrate. This pulling force is counterbalanced by the dorsal fibers’ attachment to focal adhesions, causing the fibers to bend downward and flattening the cell. This model is likely to be relevant for understanding how cells configure themselves to complex surfaces, protrude into tight spaces, and generate three-dimensional forces on the growth substrate under both healthy and diseased conditions.     

An electrodynamic (moving field) theory of muscular contraction

It is proposed that muscular contraction is the result of electrostatic attraction between oppositely charged areas on actin and myosin filaments. On the latter charged areas are assumed to be moving, always a step ahead of stationary charged areas on actin filaments, the moving charges pulling the stationary charges, hence the actin filaments, with them. It may be noted that electric motors in human technology work on a similar moving field principle. On myosin filaments minute charged areas are assumed to spiral along the surface of the filament on 2 or 3-start helical paths, probably the latter, thus engaging with adjacent actin filaments in a screw-like fashion. The spiralling charges follow each other like peristaltic waves, engaging with an increasing number of static fields on actin filaments as interdigitation proceeds. The source of the electrostatic charges are assumed to be minute voltaic cells, one associated with every myosin head. It is suggested that they could be calcium-magnesium cells, calcium adsorbed by troponin complexes on actin filaments constituting one electrode, and magnesium complexed with ATP on myosin filaments the other. The potential difference that has to exist between actin and myosin filaments, if muscles are to be capable of developing a maximum force of 20 N per cm2, is calculated at about 50 mV.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

A mathematical model for sarcomere mechanics in cross-striated muscles taking into account the stretch and twist of actin filaments

A model of sarcomere mechanics, which takes into account the elongation of the actin and myosin filaments and twisting of the actin filaments during muscle contraction is suggested. The model accounts for the experimentally observed phenomena of the stretch and twist of actin filaments due to strong binding of myosin heads and pulling force. Some model parameters were estimated from published experimental data. The results of modelling suggest that the twist of actin filaments may play an essential role in mechanical responses of contracting muscle fibres to stepwise changes in their length.     

Mechanism of brush border contractility studied by the quick-freeze, deep-etch method

We have analyzed terminal web contraction in sheets of glycerinated chicken small intestine epithelium and in isolated intestinal brush borders using a quick-freeze, deep-etch, rotary shadow replication technique. In the presence of Mg-ATP at 37 degrees C, the terminal web region of each cell in the glycerinated sheet and of each isolated brush border became severely constricted at the level of its zonula adherens (ZA). Consequently, the individual brush borders rounded up, splaying out their microvilli in fanlike patterns. The most prominent ultrastructural changes that occurred during terminal web contraction were a dramatic decrease in the diameter of the circumferential ring composed of a bundle of 8-9-nm filaments adjacent to the zonula adherens and a decrease in the number of cross-linkers between the microvillus rootlets. Microvilli were not retracted into the terminal web. We have used myosin S1 decoration to demonstrate that most of the circumferential bundle filaments are actin and that the actin filaments are arranged in the bundle with mixed polarity. Some filaments within the bundle did not decorate with myosin S1 and had tiny projections that appeared to be attached to adjacent actin filaments. Because of their morphology and immunofluorescent localization of myosin within this region of the terminal web, we propose that these undecorated filaments are myosin. From these results, we conclude that brush border contraction is caused primarily by an active sliding of actin and myosin filaments within the circumferential bundle of filaments associated with the ZA.     

Dynamic Network Morphology and Tension Buildup in a 3D Model of Cytokinetic Ring Assembly

During fission yeast cytokinesis, actin filaments nucleated by cortical formin Cdc12 are captured by myosin motors bound to a band of cortical nodes and bundled by cross-linking proteins. The myosin motors exert forces on the actin filaments, resulting in a net pulling of the nodes into a contractile ring, while cross-linking interactions help align actin filaments and nodes into a single bundle. We used these mechanisms in a three-dimensional computational model of contractile ring assembly, with semiflexible actin filaments growing from formins at cortical nodes, capturing of filaments by neighboring nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin filament density at the cell cortex, morphologies of condensing node-filament networks, and regimes of cortical tension by varying the node pulling force and strength of cross-linking among actin filaments. Results show that cross-linking interactions can lead to confinement of actin filaments at the simulated cortical boundary. We show that the ring-formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars, and meshworks can appear in the process of ring assembly. These results are consistent with prior experiments with mutations in actin-filament turnover regulators, myosin motor activity, and changes in the concentration of cross-linkers that alter the morphology of the condensing network. Transient star shapes appear in some simulations, and these morphologies offer an explanation for star structures observed in prior experimental images. Finally, we quantify tension along actin filaments and forces on nodes during ring assembly and show that the mechanisms describing ring assembly can also drive ring constriction once the ring is formed.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

Hugh E. Huxley: The Compleat Biophysicist

The sliding filament model of muscle contraction, put forward by Hugh Huxley and Jean Hanson in 1954, is 60 years old in 2014. Formulation of the model and subsequent proof was driven by the pioneering work of Hugh Huxley (1924–2013). We celebrate Huxley’s integrative approach to the study of muscle contraction; how he persevered throughout his career, to the end of his life at 89 years, to understand at the molecular level how muscle contracts and develops force. Here we show how his life and work, with its focus on a single scientific problem, had impact far beyond the field of muscle contraction to the benefit of multiple fields of cellular and structural biology. Huxley introduced the use of x-ray diffraction to study the contraction in living striated muscle, taking advantage of the paracrystalline lattice that would ultimately allow understanding contraction in terms of single molecules. Progress required design of instrumentation with ever-increasing spatial and temporal resolution, providing the impetus for the development of synchrotron facilities used for most protein crystallography and muscle studies today. From the time of his early work, Huxley combined electron microscopy and biochemistry to understand and interpret the changes in x-ray patterns. He developed improved electron-microscopy techniques, thin sections and negative staining, that enabled answering major questions relating to the structure and organization of thick and thin filaments in muscle and the interaction of myosin with actin and its regulation. Huxley established that the ATPase domain of myosin forms the crossbridges of thick filaments that bind actin, and introduced the idea that myosin makes discrete steps on actin. These concepts form the underpinning of cellular motility, in particular the study of how myosin, kinesin, and dynein motors move on their actin and tubulin tracks, making Huxley a founder of the field of cellular motility.     

Hugh E. Huxley: The Compleat Biophysicist

The sliding filament model of muscle contraction, put forward by Hugh Huxley and Jean Hanson in 1954, is 60 years old in 2014. Formulation of the model and subsequent proof was driven by the pioneering work of Hugh Huxley (1924–2013). We celebrate Huxley’s integrative approach to the study of muscle contraction; how he persevered throughout his career, to the end of his life at 89 years, to understand at the molecular level how muscle contracts and develops force. Here we show how his life and work, with its focus on a single scientific problem, had impact far beyond the field of muscle contraction to the benefit of multiple fields of cellular and structural biology. Huxley introduced the use of x-ray diffraction to study the contraction in living striated muscle, taking advantage of the paracrystalline lattice that would ultimately allow understanding contraction in terms of single molecules. Progress required design of instrumentation with ever-increasing spatial and temporal resolution, providing the impetus for the development of synchrotron facilities used for most protein crystallography and muscle studies today. From the time of his early work, Huxley combined electron microscopy and biochemistry to understand and interpret the changes in x-ray patterns. He developed improved electron-microscopy techniques, thin sections and negative staining, that enabled answering major questions relating to the structure and organization of thick and thin filaments in muscle and the interaction of myosin with actin and its regulation. Huxley established that the ATPase domain of myosin forms the crossbridges of thick filaments that bind actin, and introduced the idea that myosin makes discrete steps on actin. These concepts form the underpinning of cellular motility, in particular the study of how myosin, kinesin, and dynein motors move on their actin and tubulin tracks, making Huxley a founder of the field of cellular motility.     

Comparative maps of motion and assembly of filamentous actin and myosin II in migrating cells

To understand the mechanism of cell migration, one needs to know how the parts of the motile machinery of the cell are assembled and how they move with respect to each other. Actin and myosin II are thought to be the major structural and force-generating components of this machinery (Mitchison and Cramer, 1996; Parent, 2004). The movement of myosin II along actin filaments is thought to generate contractile force contributing to cell translocation, but the relative motion of the two proteins has not been investigated. We use fluorescence speckle and conventional fluorescence microscopy, image analysis, and computer tracking techniques to generate comparative velocity and assembly maps of actin and myosin II over the entire cell in a simple model system of persistently migrating fish epidermal keratocytes. The results demonstrate contrasting polarized assembly patterns of the two components, indicate force generation at the lamellipodium-cell body transition zone, and suggest a mechanism of anisotropic network contraction via sliding of myosin II assemblies along divergent actin filaments.     

Recent X-ray Diffraction and Electron Microscope Studies of Striated Muscle

The sliding filament model for muscular contraction supposes that an appropriately directed force is developed between the actin and myosin filaments by some process in which the cross-bridges are involved. The cross-bridges between the filaments are believed to represent the parts of the myosin molecules which possess the active sites for ATPase activity and actin-binding ability, and project out sidewise from the backbone of the thick filaments. The arrangement of the cross-bridges is now being studied by improved low-angle X-ray diffraction techniques, which show that in a resting muscle, they are arranged approximately but not exactly in a helical pattern, and that there are other structural features of the thick filaments which give rise to additional long periodicities shown up by the X-ray diagram. The actin filaments also contain helically arranged subunits, and both the subunit repeat and the helical repeat are different from those in the myosin filaments. Diffraction diagrams can be obtained from muscles in rigor (when permanent attachment of the cross-bridges to the actin subunits takes place) and now, taking advantage of the great increase in the speed of recording, from actively contracting muscles. These show that changes in the arrangement of the cross-bridges are produced under both these conditions and are no doubt associated in contraction with the development of force. Thus configurational changes of the myosin component in muscle have been demonstrated: these take place without any significant over-all change in the length of the filaments.     

Apoptotic regulation of epithelial cellular extrusion

Cellular extrusion is a mechanism that removes dying cells from epithelial tissues to prevent compromising their barrier function. Extrusion occurs in all observed epithelia in vivo and can be modeled in vitro by inducing apoptosis in cultured epithelial monolayers. We established that actin and myosin form a ring that contracts in the surrounding cells that drives cellular extrusion. It is not clear, however, if all apoptotic pathways lead to extrusion and how apoptosis and extrusion are molecularly linked. Here, we find that both intrinsic and extrinsic apoptotic pathways activate cellular extrusion. The contraction force that drives cellular extrusion requires caspase activity. Further, necrosis does not trigger the cellular extrusion response, but instead necrotic cells are removed from epithelia by a passive, stochastic movement of epithelial cells.     

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.     

Forces measured with micro-fabricated cantilevers during actomyosin interactions produced by filaments containing different myosin isoforms and loop 1 structures

Background

There is evidence that the actin-activated ATP kinetics and the mechanical work produced by muscle myosin molecules are regulated by two surface loops, located near the ATP binding pocket (loop 1), and in a region that interfaces with actin (loop 2). These loops regulate force and velocity of contraction, and have been investigated mostly in single molecules. There is a lack of information of the work produced by myosin molecules ordered in filaments and working cooperatively, which is the actual muscle environment.

Methods

We use micro-fabricated cantilevers to measure forces produced by myosin filaments isolated from mollusk muscles, skeletal muscles, and smooth muscles containing variations in the structure of loop 1 (tonic and phasic myosins). We complemented the experiments with in-vitro assays to measure the velocity of actin motility.

Results

Smooth muscle myosin filaments produced more force than skeletal and mollusk myosin filaments when normalized per filament overlap. Skeletal muscle myosin propelled actin filaments in a higher sliding velocity than smooth muscle myosin. The values for force and velocity were consistent with previous studies using myosin molecules, and suggest a close correlation with the myosin isoform and structure of surface loop 1.

General significance

The technique using micro-fabricated cantilevers to measure force of filaments allows for the investigation of the relation between myosin structure and contractility, allowing experiments to be conducted with an array of different myosin isoforms. Using the technique we observed that the work produced by myosin molecules is regulated by amino-acid sequences aligned in specific loops.     

Super helix formation of actin filaments in an in vitro motile system.

Muscle contraction results from relative sliding of actin and myosin filaments. However, the possibility that actin filaments twist or rotate during sliding has not yet been experimentally investigated. We found that a super helix of an actin filament is formed in an in vitro motile system. This fact suggests that an actin filament twists and rotates due to a torque component of a sliding force generated at cross-bridges.     

Three-dimensional arrangement of F-actin in the contractile ring of fission yeast

The contractile ring, which is required for cytokinesis in animal and yeast cells, consists mainly of actin filaments. Here, we investigate the directionality of the filaments in fission yeast using myosin S1 decoration and electron microscopy. The contractile ring is composed of around 1,000 to 2,000 filaments each around 0.6 mum in length. During the early stages of cytokinesis, the ring consists of two semicircular populations of parallel filaments of opposite directionality. At later stages, before contraction, the ring filaments show mixed directionality. We consider that the ring is initially assembled from a single site in the division plane and that filaments subsequently rearrange before contraction initiates.     

Cooperative [Ca²+]-dependent regulation of the rate of myosin binding to actin: solution data and the tropomyosin chain model

The regulation of muscle contraction by calcium involves interactions among actin filaments, myosin-S1, tropomyosin (Tm), and troponin (Tn). We have extended our previous model in which the TmTn regulatory units are treated as a continuous flexible chain, and applied it to transient kinetic data. We have measured the time course of myosin-S1 binding to actin-Tm-Tn filaments in solution at various calcium levels with [actin]/[myosin] ratios of 10 and 0.1, which exhibit modest slowing as [Ca(2+)] is reduced and a lag phase at low calcium. These observations can be explained if myosin binds to actin in two steps, where the first step is rate-limiting and blocked by TmTnI at low calcium, and the second step is fast, reversible, and controlled by the neighboring configuration of coupled tropomyosin-troponin units. The model can describe the calcium dependence of the observed myosin binding reactions and predicts cooperative calcium binding to TnC with competition between actin and Ca-TnC for the binding of TnI. Implications for theories of thin-filament regulation in muscle are discussed.     

Possible role of helix-coil transitions in the microscopic mechanism of muscle contraction.

Local helix-coil transitions in the coiled coil portion of myosin have long been implicated as a possible origin of tension generation in muscle. From a statistical mechanical theory of conformational transitions in coiled coils, the free energy required to form a randomly coiled bubble in the hinge region of myosin of the type conjectured by Harrington (Harrington, W. F., 1979, Proc. Natl. Acad. Sci. USA, 76:5066-5070) is estimated to be approximately 25 kcal/mol. Unfortunately this is far more than the free energy available from ATP hydrolysis if the crossbridges operate independently. Thus, in solution such bubbles are predicted to be absent, and the theory requires that the rod portion of myosin be a hingeless, continuously deforming rod. While such bubble formation in vivo cannot be entirely ruled out, it appears to be unlikely. We further conjecture that in solution the swivel located between myosin subfragments 1 and 2 (S-2 and S-1) is due to a locally random conformation of the chains caused by the presence of a proline residue at the point that physically separates the coiled coil from the globular portion of myosin. On attachment of S-1 to actin in the strong binding state, the configurational entropy of the random coil in the swivel region is greatly reduced relative to the case where the ends are free. This produces a spontaneous coil-to-helix transition in the swivel region that causes rotation of S-1 and the translation of actin. Thus, the model predicts that the actin filaments are pushed rather than pulled past the thick filaments by the crossbridges. The specific mechanism of force generation is examined in detail, and a simple statistical mechanical realization of the model is proposed. We find that the model gives a substantial number of qualitative and at times quantitative predictions in accord with experiment, and is particularly appealing in that it provides a simple means of free energy transduction--the well known fact that topological constraints shift the equilibrium between helical and random coil states.