Spatial Scale and Structural Heterogeneity in Skeletal Muscle Performance

Spatial Scale and Structural Heterogeneity in Skeletal Muscle Performance Abstract Biological movement is an inherently dynamic process, characterized by large spatiotemporal variations in force and mechanical energy. Molecular level interactions between the contractile proteins actin and myosin do work, generating forces and transmitting them to the environment via the muscle’s and supporting tissues’ complex structures. Most existing theories of muscle contraction are derived from observations of muscle performance under simple, tightly controlled, in vitro or in situ conditions. These theories provide predictive power that falls off as we examine the more complicated action and movement regimes seen in biological movement. Our early and heavy focus on actin and myosin interactions have lead us to overlook other interactions and sources of force regulation. It increasingly appears that the structural heterogeneity, and micro-to-macro spatial scales of the force transmission pathways that exist between actin and myosin and the environment, determine muscle performance in ways that manifest most clearly under the dynamic conditions occurring during biological movement. Considering these interactions, along with the dynamics of force transmission tissues, actuators, and environmental physics have enriched our understanding of biological motion and force generation. This symposium brings together diverse investigators to consolidate our understanding of the role of spatial scale and structural heterogeneity role in muscle performance, with the hope of updating frameworks for understanding muscle contraction and predicting muscle performance in biological movement. Early theories of muscle contraction and their limitations An elegant set of experiments suggested that muscle force and work result from the cyclical interactions between overlapping contractile proteins actin and myosin, giving us the sliding filament (Huxley 1953; Huxley and Hanson 1954; Huxley and Niedergerke 1954) and cross-bridge theories (Huxley 1957,, 1969) of muscle contraction. In response to activation, myosin heads bind to actin, forming cross-bridges. While bound, these heads undergo a conformational change that generates force, slides the protein filaments past one another, and hydrolyzes ATP (Engelhardt and Ljubimowa 1939). The sliding filament theory that arose from the work of Gordon et al. (1966) predicts the variation in isometric fiber observed with sarcomere length. Cross-bridge kinetics predict force variation with velocity during isotonic shortening (Hill 1938). The success of these theories in predicting muscle force–length and force–velocity performance under tightly controlled conditions (Hill 1938; Gordon et al. 1966), and the prevalence of actin and myosin in early microscopy and protein isolation studies (Rall 2007), led to their dominance in our understanding of muscle physiology and function. However, these theories do not predict muscle performance well under the more complex, dynamic conditions that dominate biological movement, suggesting that they provide an incomplete framework for understanding muscle contraction. Biological movement requires muscles to undergo repeated stretch-shorten cycles in which muscle velocity, activation patterns, and external loading vary discontinuously (Josephson 1985; Marsh et al. 1992; Tu and Dickinson 1994; Askew and Marsh 1997; Roberts et al. 1997; Biewener et al. 1998; Full et al. 1998; Marsh 1999; Dickinson et al. 2000; Komi 2000; Ahn and Full 2002; Daley and Biewener 2003; Gillis et al. 2005; Hodson-Tole and Wakeling 2007; Morris and Askew 2010; Bohm et al. 2018). However, cross-bridge and sliding filament theories do not predict muscle force production well in active stretch and shortening, during cyclical contractions, or at low activation levels. Muscle shortening velocity at a given isotonic force decreases below that predicted by the force–velocity relationship with decreasing activation level (Brown et al. 1999; Holt et al. 2014), and increases above it as a consequence of muscle gearing (Brainerd and Azizi 2005; Azizi et al. 2008; Eng et al. 2018) and the rapid return of energy stored in elastic tissues by muscle (Azizi and Roberts 2010). Muscle produces high forces, for minimal energetic expenditure, not predicted by cross-bridge and sliding filament theories during active stretch (Abbott and Aubert 1952; Nishikawa 2016). Muscle isometric force at a given length is strongly history-dependent, increasing following stretch and decreasing following shortening (Abbott and Aubert 1952; Edman et al. 1982; Rassier and Herzog 2004; Herzog et al. 2006; Minozzo and Lira 2013), and varies non-linearly with changing muscle activation length (Rack and Westbury 1969; Holt and Azizi 2014). Hence, it is unsurprising that cross-bridge and sliding filament theories are unable to explain or predict muscle performance during biological movement (Askew and Marsh 1998; Marsh 1999; Perreault et al. 2003; Dick et al. 2017). Muscle spatial scale and heterogeneity regulate force production under dynamic conditions Here we suggest that the spatial scale over which muscle operates, and its structural heterogeneity, are responsible for the differences between the actin–myosin based predictions of the cross-bridge and sliding filament theories, and muscle performance during biological movement. Skeletal muscle uses molecular level motors to generate organismal level movements. Each myosin head moves only ∼8 nm during each cross-bridge cycle (Higuchi and Goldman 1995), yet limb movements on the order of centimeters are observed. For this to be achieved, a complex, highly structured, multi-scale force transmission system must exist between cross-bridges and the environment. Myosin cross-bridges and their actin binding sites are small parts of larger contractile proteins. These proteins are arranged into thick and thin filaments and packaged into highly organized structures; sarcomeres. Sarcomeres are precisely aligned in series in and parallel in myofibrils and then muscle cells, or fibers. These fibers are organized, with varying geometric arrangements, into fiber bundles and ultimately entire muscles before, in vertebrates, connecting to the skeleton via connective tissues (for an excellent review of muscle structure and function see Rall 2007). At each of these levels there is significant structural and functional heterogeneity, and systematic variation in this heterogeneity across muscles, species, and pathologies. Here we present papers investigating multiple aspects of this heterogeneity including deformation of the thin filament (Holt and Williams 2018), variation in titin stiffness (Nishikawa et al. 2018; Powers et al. 2018), changes in sarcomere geometry (Taylor-Burt et al. 2018), the role of connective tissues in muscle shape change (Eng et al. 2018), and lateral force transmission (Tijs et al. 2018) in order to improve our understanding of the deviation in muscle performance from cross-bridge and sliding filament theories observed during dynamic muscle contractions, and enrich our understanding and prediction of muscle performance (Nishikawa et al. 2018; Ross et al. 2018). Myofilaments and contractile proteins Force is generated, work done, and ATP hydrolyzed by the cross-bridge interaction between the contractile proteins actin and myosin. These proteins are contained within the thick and thin myofilaments. The actin-rich thin filament has a diameter of approximately 80 Å (Hanson and Lowy 1963), and varies in length from 1.94 to 2.64 µm in vertebrates (Walker and Schrodt 1974; Edman and Reggiani 1987), to 18.6 µm in some invertebrates (Taylor 2000). It is composed of globular actin monomers (G-actin), each containing a potential myosin binding site, arranged into an F-actin polymer with a double helical structure (Holmes et al. 1990; Holmes 2009). Myosin is a large molecular weight protein consisting of a rod-like tail region, a flexible neck, and a globular head containing an actin binding site and ATPase capabilities. Myosin molecules are arranged into thick filaments with a diameter of 100–120 Å (Huxley 1963) and lengths ranging from 1.55 to 1.66 µm in vertebrates (Edman and Reggiani 1987; Lieber et al. 1994) to 10 µm in some invertebrates (Taylor 2000). At rest, the myosin binding sites on actin molecules are blocked by the other major component of the thin filament; the regulatory filamentous protein, tropomyosin which, lies in the groove of the actin helix (Hanson and Lowy 1963). Calcium activation results in the movement of tropomyosin, so exposing myosin-binding sites and enabling actin–myosin cross-bridge binding (Bailey 1946; Ebashi and Endo 1968). The cross-bridge and sliding filament theories assume thick and thin filaments to be rigid (Huxley and Niedergerke 1954; Huxley and Hanson 1954; Huxley and Niedergerke 1958). However, they appear to exhibit some compliance (Huxley and Niedergerke 1954; Huxley and Niedergerke 1958; Periasamy et al. 1990; Huxley et al. 1994; Kolb et al. 2016); thin filament compliance is thought to be responsible for ∼55% of sarcomere compliance (Higuchi et al. 1995). Potentially heterogeneous deformation of these filaments during contraction is now thought to have functional consequences. Thin filament deformation has been suggested to realign binding sites and promote cross-bridge binding through cooperative mechanisms (Daniel et al. 1998). Heterogeneity in deformation due to the binding of cross-bridge to some regions of the thin filament but not others has been suggested to underpin shortening induced force depression and contribute to the decreases in optimum length seen with reduced activation by direct, or tropomyosin-mediated, inhibition of binding of cross-bridges in new regions of overlap (Maréchal and Plaghki 1979; Herzog 1998; Rassier and Herzog 2004; Holt and Azizi 2014; Corr and Herzog 2016; Holt and Williams 2018). Hence, compliance of the thin filament, and potential heterogeneity in deformation along its lengths, may be able to explain some of the phenomena observed during dynamic muscle contractions not predicted by cross-bridge and sliding filament theories. Sarcomeres and the sarcomeric cytoskeleton The precise organization of myofilaments is required for the co-ordination of the force and motion produced by individual molecular motors, and is achieved by the sarcomeric cytoskeleton (Blake and Martin-Rendon 2002; Rall 2007; Gautel and Djinović-Carugo 2016). The cytoskeletal proteins α-actinin and myomesin anchor the thin filaments at the Z-disk, and myosin molecules at the M-line (Maruyama and Ebashi 1965; Granger and Lazarides 1978; Grove et al. 1984; Sanger et al. 2010; Gautel 2011). Titin and nebulin run along the length of the sarcomere keeping the thick filament centered, providing structural integrity at long lengths (Maruyama 1976; Wang et al. 1979), and regulating thin filament and sarcomere length (Wang and Wright 1988; Chu et al. 2016). This sarcomeric cytoskeleton clearly has important architectural and signaling roles in muscle (Gautel 2011). However, it is becoming increasingly obvious that the properties and arrangement of the components of this cytoskeleton, and the resultant structural and functional heterogeneity across sarcomeres, have implications for muscle performance (Labeit et al. 2011; Monroy et al. 2012; Chu et al. 2016; Gautel and Djinović-Carugo 2016). The most notable example of cytoskeletal components contributing to structural and functional heterogeneity is the molecular spring titin (Maruyama 1976; Wang et al. 1979). The stiffness of this spring varies along its length (Gautel and Goulding 1996; Bennett et al. 1997; Linke et al. 1998); with muscle activation (Labeit et al. 2003; Monroy et al. 2012, 2017; Nishikawa et al. 2012; Powers et al. 2014), and potentially force production (Monroy et al. 2012; Nishikawa et al. 2012); and between muscle types (Wang et al. 1991). The properties of this spring have been suggested to contribute to muscle mechanical and energetic performance, underpin history dependence, and explain muscle performance during active stretching and stretch-shorten cycles (Nishikawa et al. 2012, 2018; Minozzo and Lira 2013; Schappacher-Tilp et al. 2015; Nishikawa 2016; Powers et al., 2018). While there is a general pattern of thick and thin filament arrangement, geometric tuning of this arrangement has functional consequences. Vertebrate sarcomeres tend to produce maximum force around 2.2 µm (Gordon et al. 1966), corresponding to maximum overlap between myofilaments (Herzog et al. 2010) and therefore consistent with cross-bridge and sliding filament theories. Variation in myofilament length in invertebrates (Taylor 2000) results in changes in optimum sarcomere length and muscle performance consistent with cross-bridge and sliding filament theories (Josephson 1975; Taylor 2000; Kier and Curtin 2002). However, greater deviations from the basic sarcomere plan result in variations in performance not readily predicted from cross-bridge and sliding filament theories. In an example explored in this issue, the obliquely striated muscles found in the body walls of many soft-bodied invertebrates exhibit unexplained variation in the shape of the force–length relationship (Thompson et al. 2014; Taylor-Burt et al. 2018). Myofibrils and muscle fibers Precise sarcomere alignment into myofibrils and fibers is maintained, even during contraction (Schwiening 2012), by an extensive network of intermediate filaments (Lazarides and Hubbard 1976; Blake and Martin-Rendon 2002). These cells are surrounded by a cell membrane, the sarcolemma, and the inner layer of the extracellular matrix, the endomysium (Purslow and Trotter 1994; Huijing 2002). Myofibrils are anchored to the sarcolemma and endomysium by the dystrophin complex (Koenig et al. 1987; Blake et al. 2002). Heterogeneity along the lengths of myofilaments and fibers, and interactions between components of fibers have been suggested to result in muscle performance not predicted by cross-bridge and sliding filament theories. Inhomogeneities in sarcomere lengths along the length of myofibril and fibers have been observed during muscle contraction (Edman and Reggiani 1984; Morgan 1990; Telley and Denoth 2007). The consequences of these inhomogeneities are unclear; however, they must reflect variation in the passive or active mechanical properties of sarcomeres (Telley and Denoth 2007). These inhomogeneities have been proposed to be, and largely rejected as, responsible for many of the phenomena observed in muscle not explained by cross-bridge and sliding filament theories (Julian and Morgan 1979; Rassier and Herzog 2004; Minozzo and Lira 2013; Herzog et al. 2015). Despite the rejection of a role in phenomenon such as history dependence (Herzog et al. 2015), these variations in sarcomere length must affect the peak active force a muscle can produce, and the shape of the force–length relationship (Gordon et al. 1966; Willems and Huijing 1994). The relative proportions and organization of the components of a muscle fiber, most notably the myofibrils, mitochondria, and sarcoplasmic reticulum will partially determine a fiber’s mechanical and energetic performance (Schaeffer et al. 1996; Syme and Josephson 2002; Morse et al. 2005; Kragstrup et al. 2011; Schiaffino and Reggiani 2011). The interaction between incompressible fluid contained within the fiber and the restrictive endomysium surrounding it results in changes in intracellular pressure that have the potential to affect muscle performance during contraction (Sejersted et al. 1984; Davis et al. 2003; Gindre et al. 2013; Sleboda and Roberts 2017; Eng et al. 2018). Extrapolation of cross-bridge and sliding filament theories suggests that unloaded active sarcomeres could shorten until the thin filaments contacted opposing Z-disks. However, as sarcomeres shorten, they must also bulge. Connective tissue constraints, and the resulting pressure development, are thought to limit shortening so limiting performance to below that predicted by cross-bridge and sliding filament theories (Gindre et al. 2013; Azizi et al. 2017). Muscles and muscle groups Muscle fibers are grouped into fascicles and then into muscles and muscle groups. Architectural arrangements of fibers and fascicles vary widely; parallel, pennate, and circular configurations are observed in the anuran sartorius (Kargo and Rome 2002), mammalian gastrocnemius (Holt et al. 2016), and cephalopod mantle (Taylor-Burt et al. 2018). Fascicles and the entire muscle are surrounded by perimysium and epimysium. Along with the endomysium, these connective tissues make up the extracellular matrix (Huijing 2002; Purslow 2010). In parallel and pennate muscles, the extracellular matrix merges with proximal and distal aponeuroses (Scott and Loeb 1995; Azizi and Roberts 2009) and tendons (Alexander et al. 1982; Jozsa et al. 1991), before connecting to the skeleton at the origin and insertions. Groups of muscles exist within compartments surrounded by fascia (Huijing 2009; Wilke et al. 2018). Heterogeneity along fascicles and muscles, interactions between contractile and connective tissue, and the force transmission between muscles are likely to result in deviations in performance from cross-bridge and sliding filament theories. As at smaller scales, there is considerable variation in length changes observed along fascicles and muscle during contraction. This occurs to a greater extent in muscles than isolated fibers. One region of a muscle can be shortening while another is lengthening (Ahn et al. 2003,, 2018), and different regions can experience large, systematic, differences in strain (Thompson et al. 2008,, 2014; Taylor-Burt et al. 2018). As in single fibers, the reasons for these variation in sarcomere length are unclear. However, they are indicative of mechanical heterogeneity, and have implications for muscle performance (Ahn et al. 2018). Segments that are shortening, isometric, or lengthening will operate under different force–length and force–velocity conditions making it hard to predict the resultant muscle performance. The interaction of contractile and connective tissues alters muscle performance. Connective tissues can control muscle shape change, and decouple muscle performance from actin–myosin interactions. The connective tissue limits to bulging and shortening predicted at the fiber level are likely to be amplified in intact muscles due to the increase in connective tissue layers (Huijing 2002; Azizi et al. 2017). In addition, asymmetries in connective tissues in the intact muscle are likely to control not only the amount of bulging and shortening, but also the way in which muscle changes shape as it shortens (Holt et al. 2016; Eng et al. 2018). This control of shape change is thought to be responsible for variable gearing; a phenomenon in which the fibers of pennate muscles rotate and increase pennation angle, so increasing shortening velocity above that predicted by the force–velocity relationship, in proportion to muscle force (Brainerd and Azizi 2005; Azizi et al. 2008). Tendons in series with muscle fibers can temporarily store and return energy; amplifying muscle power (Azizi and Roberts 2010), reducing the metabolic cost of level running (Roberts et al. 1997; Holt et al. 2014) or hopping (Biewener et al. 1998), and preventing muscle damage (Roberts and Azizi 2011; Roberts and Konow 2013). Connective tissues within and around muscles not only have the potential to control shape change, but also to act as force transmission pathways. Force generated by actin–myosin interactions can reach the skeleton not only longitudinally along fibers and through the myotendinous junction, but also by being transmitted laterally between fibers within the same muscle via the dystrophin complex (Koenig et al. 1987; Blake et al. 2002) and extracellular matrix (Huijing 2002), and between muscle in the same compartment via epimuscular connections (Street 1983; Maas and Sandercock 2010). The transmission of forces along these lateral pathways is thought to depend on the relative length and positions of muscle, and the properties of connecting materials (Maas et al. 2001,, 2004; Maas and Sandercock 2010; Bernabei et al. 2017). Hence muscular forces at the origin or insertion of a muscle depend not only on the actin–myosin interactions within that muscle, but the actin–myosin interactions of adjacent muscles, and the relationship between muscles (Maas et al. 2001,, 2004; Maas and Sandercock 2010; Bernabei et al. 2017; Tijs et al. 2018). New modeling approaches bridge scales Hill-type muscle models dominate our efforts to predict muscle forces during movement (Zajac 1989; van Leeuwen 1992; Epstein and Herzog 1998; Biewener et al. 2014; Dick et al. 2017; Lai et al. 2018). These models use isometric force–length and isotonic or isovelocity force–velocity relationships scaled linearly to muscle activation level (Zajac 1989), and justify model parameters with extrapolations from cross-bridge theory (Huxley 1953; Huxley and Hanson 1954; Huxley and Niedergerke 1954; Huxley 1957,, 1969). Techniques in organismal musculoskeletal modeling have relied heavily on Hill-type muscle models to provide force predictions for individual muscles (Delp and Loan 2000). Hence, much of our understanding of human and animal movement, and the effects of clinical conditions and interventions, are based on their predictions (MacIntosh et al. 2000; Hutchinson and Garcia 2002; Holzbaur et al. 2005; Hamner et al. 2010; Arnold et al. 2013; Steele et al. 2013; Hutchinson et al. 2015). This use of Hill-type models is problematic as cross-bridge and sliding filament theories do not predict or explain muscle performance well under the dynamic condition relevant to biological movement (Perreault et al. 2003; Lee et al. 2013; Nishikawa et al. 2018), likely due to the effects of spatial scale across which force must be transmitted, and the heterogeneous nature of these force transmission pathways. Potentially more problematic is the fact that not only are these models likely subject to large errors, but that errors are likely to vary systematically across a range of locomotor conditions. If muscle performance scales non-linearly with activation level (Rack and Westbury 1969; Brown et al. 1999; Holt and Azizi 2014; Holt et al. 2014), but models are based entirely on maximally activated muscle performance (Zajac 1989), model errors are likely to increase at lower levels of muscle activation level (Perreault et al. 2003). If tissue-level models fail to include the material properties of connective tissues they will neglect any effect of muscle shape change, and their predictions will be systematically worse for older muscles with increased connective tissue stiffness (Gao et al. 2008; Holt et al. 2016; Azizi et al. 2017). The failure of cross-bridge and sliding filament theories to predict any history dependence means that these effects will be absent from such model results (Herzog 1998), despite their presumed prevalence during the stretch-shorten cycles ubiquitous to biological movement (Askew and Marsh 1998). As our improving understanding of muscle biophysics and increasing exploration of performance under dynamic conditions have revealed the limitations of Hill-type models, a variety of approaches have been taken to develop muscle models incorporating additional phenomenological and structural aspects of muscle. Modifications to Hill-type models have been made to include recruitment of different fiber types, history dependence, material properties, inertia, and muscle geometry (Brown and Loeb 2000; Brown et al. 1996; Ettema 2002; Dick et al. 2017; Lai et al. 2018; Ross et al. 2018). These corrected Hill-type models have been extensively used as embedded models in whole-body and limb simulations (Delp et al. 1990; Millard et al. 2013). A more radical adaptation of the Hill-type model has included a winding-spring system to explore the role of titin in active muscle (Nishikawa et al. 2012; LeMoyne et al. 2014; Tahir et al. 2018). Finite element models have been used to examine the effects of cardiac and skeletal muscle material properties and geometries on performance (Yucesoy and Huijing 2012; Rahemi et al. 2014; Krishnamurthy et al. 2016). Excitation-contraction coupling models have delved into electrical excitability and transmission of depolarization (Tveito et al. 2011; Wilhelms et al. 2013). Spatially explicit models have dealt with consequences of multi-scale force transmission and heterogeneities in force production from the single motor to the myofibrillar levels (Daniel et al. 1998; Chase et al. 2004; Tanner et al. 2007; Campbell 2009; Williams et al. 2010, 2013). New spatially explicit models add titin and gain the ability to look at the effects of clinically relevant mutations, something previously done primarily at the single myofilament level (Sewanan et al. 2016; Powers et al. 2018). The common theme among these models is an increase in the processes included, and steps taken, in an attempt to replicate or explain elements of muscle performance during biological movement, not predicted by Hill-type models. These models have added varying degrees of explanatory power. Adding recruitment of different muscle fibers to Hill-type muscle models seemed to provide only modest improvements in predictions (Lee et al. 2013), however, there seem to be potential for greater improvements with the inclusion of other parameters (Ross et al. 2018). The phenomenological inclusion of history dependence to models has demonstrated the potential for this phenomenon to improve the control and stability of movement (Ettema 2002). Exploration of the active role of titin has suggested that the winding filament hypothesis may underpin history dependence, and has highlighted the importance of titin isoform in muscle performance (LeMoyne et al. 2014; Tahir et al. 2018). Finite element models have demonstrated the potential for regional variation in activation and lateral force transmission through connective tissues to alter muscle performance (Yucesoy and Huijing 2012; Rahemi et al. 2014). Spatially explicit models have shown the importance of disorder to the recruitment of cross-bridges, the spread of activation along tropomyosin to cooperativity, and the dependence of the length–tension relationship on thick–thin filament spacing changes (Daniel et al. 1998; Tanner et al. 2007; Williams et al. 2013). The addition of each mechanism creates a richer, but less parsimonious, picture of muscle contraction. Conclusions The emerging picture of muscle performance described in this paper is that of a heterogeneous, multi-scale, system whose current state can only be specified in a high-dimensional landscape. Dimensions of this landscape include the current configuration or localization of each of the scales in the system, from kinetic states of single motors to body position within the environment; the energetics at each scale, from ATP concentrations in a single cross-bridge’s locality to the storage and return of energy in deformable locomotion substrates; and the histories of all dimensions. Classic experiments in the field tended to exhaustively explore a highly-constrained region in this landscape, but a new wave of work is starting to integrate across scales and time periods during dynamic contractions, and is uncovering significant structural and functional heterogeneity in the process. Stitching together the early observations from these experiments into a richer picture of the high-dimensional space muscle occupies is a major task for the next several decades of muscle research, but one that we can lay the groundwork for today by specifying the bounds of our early local exploration and showing they connect to the larger landscape. For now, we hope that the following papers help identify the aspects of structural and functional heterogeneity across spatial scales that provide the greatest additions to our framework for understanding muscle contraction. Acknowledgments We would like to thank all the participants in the symposium for contributing their work and insight. Funding Funding for this symposium was provided by the Society for Integrative and Comparative Biology (DVM and DCM), Company of Biologists, and Aurora Scientific. 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Spatial Scale and Structural Heterogeneity in Skeletal Muscle Performance

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Oxford University Press
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© The Author(s) 2018. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved. For permissions please email: journals.permissions@oup.com.
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1540-7063
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1557-7023
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10.1093/icb/icy057
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Abstract

Abstract Biological movement is an inherently dynamic process, characterized by large spatiotemporal variations in force and mechanical energy. Molecular level interactions between the contractile proteins actin and myosin do work, generating forces and transmitting them to the environment via the muscle’s and supporting tissues’ complex structures. Most existing theories of muscle contraction are derived from observations of muscle performance under simple, tightly controlled, in vitro or in situ conditions. These theories provide predictive power that falls off as we examine the more complicated action and movement regimes seen in biological movement. Our early and heavy focus on actin and myosin interactions have lead us to overlook other interactions and sources of force regulation. It increasingly appears that the structural heterogeneity, and micro-to-macro spatial scales of the force transmission pathways that exist between actin and myosin and the environment, determine muscle performance in ways that manifest most clearly under the dynamic conditions occurring during biological movement. Considering these interactions, along with the dynamics of force transmission tissues, actuators, and environmental physics have enriched our understanding of biological motion and force generation. This symposium brings together diverse investigators to consolidate our understanding of the role of spatial scale and structural heterogeneity role in muscle performance, with the hope of updating frameworks for understanding muscle contraction and predicting muscle performance in biological movement. Early theories of muscle contraction and their limitations An elegant set of experiments suggested that muscle force and work result from the cyclical interactions between overlapping contractile proteins actin and myosin, giving us the sliding filament (Huxley 1953; Huxley and Hanson 1954; Huxley and Niedergerke 1954) and cross-bridge theories (Huxley 1957,, 1969) of muscle contraction. In response to activation, myosin heads bind to actin, forming cross-bridges. While bound, these heads undergo a conformational change that generates force, slides the protein filaments past one another, and hydrolyzes ATP (Engelhardt and Ljubimowa 1939). The sliding filament theory that arose from the work of Gordon et al. (1966) predicts the variation in isometric fiber observed with sarcomere length. Cross-bridge kinetics predict force variation with velocity during isotonic shortening (Hill 1938). The success of these theories in predicting muscle force–length and force–velocity performance under tightly controlled conditions (Hill 1938; Gordon et al. 1966), and the prevalence of actin and myosin in early microscopy and protein isolation studies (Rall 2007), led to their dominance in our understanding of muscle physiology and function. However, these theories do not predict muscle performance well under the more complex, dynamic conditions that dominate biological movement, suggesting that they provide an incomplete framework for understanding muscle contraction. Biological movement requires muscles to undergo repeated stretch-shorten cycles in which muscle velocity, activation patterns, and external loading vary discontinuously (Josephson 1985; Marsh et al. 1992; Tu and Dickinson 1994; Askew and Marsh 1997; Roberts et al. 1997; Biewener et al. 1998; Full et al. 1998; Marsh 1999; Dickinson et al. 2000; Komi 2000; Ahn and Full 2002; Daley and Biewener 2003; Gillis et al. 2005; Hodson-Tole and Wakeling 2007; Morris and Askew 2010; Bohm et al. 2018). However, cross-bridge and sliding filament theories do not predict muscle force production well in active stretch and shortening, during cyclical contractions, or at low activation levels. Muscle shortening velocity at a given isotonic force decreases below that predicted by the force–velocity relationship with decreasing activation level (Brown et al. 1999; Holt et al. 2014), and increases above it as a consequence of muscle gearing (Brainerd and Azizi 2005; Azizi et al. 2008; Eng et al. 2018) and the rapid return of energy stored in elastic tissues by muscle (Azizi and Roberts 2010). Muscle produces high forces, for minimal energetic expenditure, not predicted by cross-bridge and sliding filament theories during active stretch (Abbott and Aubert 1952; Nishikawa 2016). Muscle isometric force at a given length is strongly history-dependent, increasing following stretch and decreasing following shortening (Abbott and Aubert 1952; Edman et al. 1982; Rassier and Herzog 2004; Herzog et al. 2006; Minozzo and Lira 2013), and varies non-linearly with changing muscle activation length (Rack and Westbury 1969; Holt and Azizi 2014). Hence, it is unsurprising that cross-bridge and sliding filament theories are unable to explain or predict muscle performance during biological movement (Askew and Marsh 1998; Marsh 1999; Perreault et al. 2003; Dick et al. 2017). Muscle spatial scale and heterogeneity regulate force production under dynamic conditions Here we suggest that the spatial scale over which muscle operates, and its structural heterogeneity, are responsible for the differences between the actin–myosin based predictions of the cross-bridge and sliding filament theories, and muscle performance during biological movement. Skeletal muscle uses molecular level motors to generate organismal level movements. Each myosin head moves only ∼8 nm during each cross-bridge cycle (Higuchi and Goldman 1995), yet limb movements on the order of centimeters are observed. For this to be achieved, a complex, highly structured, multi-scale force transmission system must exist between cross-bridges and the environment. Myosin cross-bridges and their actin binding sites are small parts of larger contractile proteins. These proteins are arranged into thick and thin filaments and packaged into highly organized structures; sarcomeres. Sarcomeres are precisely aligned in series in and parallel in myofibrils and then muscle cells, or fibers. These fibers are organized, with varying geometric arrangements, into fiber bundles and ultimately entire muscles before, in vertebrates, connecting to the skeleton via connective tissues (for an excellent review of muscle structure and function see Rall 2007). At each of these levels there is significant structural and functional heterogeneity, and systematic variation in this heterogeneity across muscles, species, and pathologies. Here we present papers investigating multiple aspects of this heterogeneity including deformation of the thin filament (Holt and Williams 2018), variation in titin stiffness (Nishikawa et al. 2018; Powers et al. 2018), changes in sarcomere geometry (Taylor-Burt et al. 2018), the role of connective tissues in muscle shape change (Eng et al. 2018), and lateral force transmission (Tijs et al. 2018) in order to improve our understanding of the deviation in muscle performance from cross-bridge and sliding filament theories observed during dynamic muscle contractions, and enrich our understanding and prediction of muscle performance (Nishikawa et al. 2018; Ross et al. 2018). Myofilaments and contractile proteins Force is generated, work done, and ATP hydrolyzed by the cross-bridge interaction between the contractile proteins actin and myosin. These proteins are contained within the thick and thin myofilaments. The actin-rich thin filament has a diameter of approximately 80 Å (Hanson and Lowy 1963), and varies in length from 1.94 to 2.64 µm in vertebrates (Walker and Schrodt 1974; Edman and Reggiani 1987), to 18.6 µm in some invertebrates (Taylor 2000). It is composed of globular actin monomers (G-actin), each containing a potential myosin binding site, arranged into an F-actin polymer with a double helical structure (Holmes et al. 1990; Holmes 2009). Myosin is a large molecular weight protein consisting of a rod-like tail region, a flexible neck, and a globular head containing an actin binding site and ATPase capabilities. Myosin molecules are arranged into thick filaments with a diameter of 100–120 Å (Huxley 1963) and lengths ranging from 1.55 to 1.66 µm in vertebrates (Edman and Reggiani 1987; Lieber et al. 1994) to 10 µm in some invertebrates (Taylor 2000). At rest, the myosin binding sites on actin molecules are blocked by the other major component of the thin filament; the regulatory filamentous protein, tropomyosin which, lies in the groove of the actin helix (Hanson and Lowy 1963). Calcium activation results in the movement of tropomyosin, so exposing myosin-binding sites and enabling actin–myosin cross-bridge binding (Bailey 1946; Ebashi and Endo 1968). The cross-bridge and sliding filament theories assume thick and thin filaments to be rigid (Huxley and Niedergerke 1954; Huxley and Hanson 1954; Huxley and Niedergerke 1958). However, they appear to exhibit some compliance (Huxley and Niedergerke 1954; Huxley and Niedergerke 1958; Periasamy et al. 1990; Huxley et al. 1994; Kolb et al. 2016); thin filament compliance is thought to be responsible for ∼55% of sarcomere compliance (Higuchi et al. 1995). Potentially heterogeneous deformation of these filaments during contraction is now thought to have functional consequences. Thin filament deformation has been suggested to realign binding sites and promote cross-bridge binding through cooperative mechanisms (Daniel et al. 1998). Heterogeneity in deformation due to the binding of cross-bridge to some regions of the thin filament but not others has been suggested to underpin shortening induced force depression and contribute to the decreases in optimum length seen with reduced activation by direct, or tropomyosin-mediated, inhibition of binding of cross-bridges in new regions of overlap (Maréchal and Plaghki 1979; Herzog 1998; Rassier and Herzog 2004; Holt and Azizi 2014; Corr and Herzog 2016; Holt and Williams 2018). Hence, compliance of the thin filament, and potential heterogeneity in deformation along its lengths, may be able to explain some of the phenomena observed during dynamic muscle contractions not predicted by cross-bridge and sliding filament theories. Sarcomeres and the sarcomeric cytoskeleton The precise organization of myofilaments is required for the co-ordination of the force and motion produced by individual molecular motors, and is achieved by the sarcomeric cytoskeleton (Blake and Martin-Rendon 2002; Rall 2007; Gautel and Djinović-Carugo 2016). The cytoskeletal proteins α-actinin and myomesin anchor the thin filaments at the Z-disk, and myosin molecules at the M-line (Maruyama and Ebashi 1965; Granger and Lazarides 1978; Grove et al. 1984; Sanger et al. 2010; Gautel 2011). Titin and nebulin run along the length of the sarcomere keeping the thick filament centered, providing structural integrity at long lengths (Maruyama 1976; Wang et al. 1979), and regulating thin filament and sarcomere length (Wang and Wright 1988; Chu et al. 2016). This sarcomeric cytoskeleton clearly has important architectural and signaling roles in muscle (Gautel 2011). However, it is becoming increasingly obvious that the properties and arrangement of the components of this cytoskeleton, and the resultant structural and functional heterogeneity across sarcomeres, have implications for muscle performance (Labeit et al. 2011; Monroy et al. 2012; Chu et al. 2016; Gautel and Djinović-Carugo 2016). The most notable example of cytoskeletal components contributing to structural and functional heterogeneity is the molecular spring titin (Maruyama 1976; Wang et al. 1979). The stiffness of this spring varies along its length (Gautel and Goulding 1996; Bennett et al. 1997; Linke et al. 1998); with muscle activation (Labeit et al. 2003; Monroy et al. 2012, 2017; Nishikawa et al. 2012; Powers et al. 2014), and potentially force production (Monroy et al. 2012; Nishikawa et al. 2012); and between muscle types (Wang et al. 1991). The properties of this spring have been suggested to contribute to muscle mechanical and energetic performance, underpin history dependence, and explain muscle performance during active stretching and stretch-shorten cycles (Nishikawa et al. 2012, 2018; Minozzo and Lira 2013; Schappacher-Tilp et al. 2015; Nishikawa 2016; Powers et al., 2018). While there is a general pattern of thick and thin filament arrangement, geometric tuning of this arrangement has functional consequences. Vertebrate sarcomeres tend to produce maximum force around 2.2 µm (Gordon et al. 1966), corresponding to maximum overlap between myofilaments (Herzog et al. 2010) and therefore consistent with cross-bridge and sliding filament theories. Variation in myofilament length in invertebrates (Taylor 2000) results in changes in optimum sarcomere length and muscle performance consistent with cross-bridge and sliding filament theories (Josephson 1975; Taylor 2000; Kier and Curtin 2002). However, greater deviations from the basic sarcomere plan result in variations in performance not readily predicted from cross-bridge and sliding filament theories. In an example explored in this issue, the obliquely striated muscles found in the body walls of many soft-bodied invertebrates exhibit unexplained variation in the shape of the force–length relationship (Thompson et al. 2014; Taylor-Burt et al. 2018). Myofibrils and muscle fibers Precise sarcomere alignment into myofibrils and fibers is maintained, even during contraction (Schwiening 2012), by an extensive network of intermediate filaments (Lazarides and Hubbard 1976; Blake and Martin-Rendon 2002). These cells are surrounded by a cell membrane, the sarcolemma, and the inner layer of the extracellular matrix, the endomysium (Purslow and Trotter 1994; Huijing 2002). Myofibrils are anchored to the sarcolemma and endomysium by the dystrophin complex (Koenig et al. 1987; Blake et al. 2002). Heterogeneity along the lengths of myofilaments and fibers, and interactions between components of fibers have been suggested to result in muscle performance not predicted by cross-bridge and sliding filament theories. Inhomogeneities in sarcomere lengths along the length of myofibril and fibers have been observed during muscle contraction (Edman and Reggiani 1984; Morgan 1990; Telley and Denoth 2007). The consequences of these inhomogeneities are unclear; however, they must reflect variation in the passive or active mechanical properties of sarcomeres (Telley and Denoth 2007). These inhomogeneities have been proposed to be, and largely rejected as, responsible for many of the phenomena observed in muscle not explained by cross-bridge and sliding filament theories (Julian and Morgan 1979; Rassier and Herzog 2004; Minozzo and Lira 2013; Herzog et al. 2015). Despite the rejection of a role in phenomenon such as history dependence (Herzog et al. 2015), these variations in sarcomere length must affect the peak active force a muscle can produce, and the shape of the force–length relationship (Gordon et al. 1966; Willems and Huijing 1994). The relative proportions and organization of the components of a muscle fiber, most notably the myofibrils, mitochondria, and sarcoplasmic reticulum will partially determine a fiber’s mechanical and energetic performance (Schaeffer et al. 1996; Syme and Josephson 2002; Morse et al. 2005; Kragstrup et al. 2011; Schiaffino and Reggiani 2011). The interaction between incompressible fluid contained within the fiber and the restrictive endomysium surrounding it results in changes in intracellular pressure that have the potential to affect muscle performance during contraction (Sejersted et al. 1984; Davis et al. 2003; Gindre et al. 2013; Sleboda and Roberts 2017; Eng et al. 2018). Extrapolation of cross-bridge and sliding filament theories suggests that unloaded active sarcomeres could shorten until the thin filaments contacted opposing Z-disks. However, as sarcomeres shorten, they must also bulge. Connective tissue constraints, and the resulting pressure development, are thought to limit shortening so limiting performance to below that predicted by cross-bridge and sliding filament theories (Gindre et al. 2013; Azizi et al. 2017). Muscles and muscle groups Muscle fibers are grouped into fascicles and then into muscles and muscle groups. Architectural arrangements of fibers and fascicles vary widely; parallel, pennate, and circular configurations are observed in the anuran sartorius (Kargo and Rome 2002), mammalian gastrocnemius (Holt et al. 2016), and cephalopod mantle (Taylor-Burt et al. 2018). Fascicles and the entire muscle are surrounded by perimysium and epimysium. Along with the endomysium, these connective tissues make up the extracellular matrix (Huijing 2002; Purslow 2010). In parallel and pennate muscles, the extracellular matrix merges with proximal and distal aponeuroses (Scott and Loeb 1995; Azizi and Roberts 2009) and tendons (Alexander et al. 1982; Jozsa et al. 1991), before connecting to the skeleton at the origin and insertions. Groups of muscles exist within compartments surrounded by fascia (Huijing 2009; Wilke et al. 2018). Heterogeneity along fascicles and muscles, interactions between contractile and connective tissue, and the force transmission between muscles are likely to result in deviations in performance from cross-bridge and sliding filament theories. As at smaller scales, there is considerable variation in length changes observed along fascicles and muscle during contraction. This occurs to a greater extent in muscles than isolated fibers. One region of a muscle can be shortening while another is lengthening (Ahn et al. 2003,, 2018), and different regions can experience large, systematic, differences in strain (Thompson et al. 2008,, 2014; Taylor-Burt et al. 2018). As in single fibers, the reasons for these variation in sarcomere length are unclear. However, they are indicative of mechanical heterogeneity, and have implications for muscle performance (Ahn et al. 2018). Segments that are shortening, isometric, or lengthening will operate under different force–length and force–velocity conditions making it hard to predict the resultant muscle performance. The interaction of contractile and connective tissues alters muscle performance. Connective tissues can control muscle shape change, and decouple muscle performance from actin–myosin interactions. The connective tissue limits to bulging and shortening predicted at the fiber level are likely to be amplified in intact muscles due to the increase in connective tissue layers (Huijing 2002; Azizi et al. 2017). In addition, asymmetries in connective tissues in the intact muscle are likely to control not only the amount of bulging and shortening, but also the way in which muscle changes shape as it shortens (Holt et al. 2016; Eng et al. 2018). This control of shape change is thought to be responsible for variable gearing; a phenomenon in which the fibers of pennate muscles rotate and increase pennation angle, so increasing shortening velocity above that predicted by the force–velocity relationship, in proportion to muscle force (Brainerd and Azizi 2005; Azizi et al. 2008). Tendons in series with muscle fibers can temporarily store and return energy; amplifying muscle power (Azizi and Roberts 2010), reducing the metabolic cost of level running (Roberts et al. 1997; Holt et al. 2014) or hopping (Biewener et al. 1998), and preventing muscle damage (Roberts and Azizi 2011; Roberts and Konow 2013). Connective tissues within and around muscles not only have the potential to control shape change, but also to act as force transmission pathways. Force generated by actin–myosin interactions can reach the skeleton not only longitudinally along fibers and through the myotendinous junction, but also by being transmitted laterally between fibers within the same muscle via the dystrophin complex (Koenig et al. 1987; Blake et al. 2002) and extracellular matrix (Huijing 2002), and between muscle in the same compartment via epimuscular connections (Street 1983; Maas and Sandercock 2010). The transmission of forces along these lateral pathways is thought to depend on the relative length and positions of muscle, and the properties of connecting materials (Maas et al. 2001,, 2004; Maas and Sandercock 2010; Bernabei et al. 2017). Hence muscular forces at the origin or insertion of a muscle depend not only on the actin–myosin interactions within that muscle, but the actin–myosin interactions of adjacent muscles, and the relationship between muscles (Maas et al. 2001,, 2004; Maas and Sandercock 2010; Bernabei et al. 2017; Tijs et al. 2018). New modeling approaches bridge scales Hill-type muscle models dominate our efforts to predict muscle forces during movement (Zajac 1989; van Leeuwen 1992; Epstein and Herzog 1998; Biewener et al. 2014; Dick et al. 2017; Lai et al. 2018). These models use isometric force–length and isotonic or isovelocity force–velocity relationships scaled linearly to muscle activation level (Zajac 1989), and justify model parameters with extrapolations from cross-bridge theory (Huxley 1953; Huxley and Hanson 1954; Huxley and Niedergerke 1954; Huxley 1957,, 1969). Techniques in organismal musculoskeletal modeling have relied heavily on Hill-type muscle models to provide force predictions for individual muscles (Delp and Loan 2000). Hence, much of our understanding of human and animal movement, and the effects of clinical conditions and interventions, are based on their predictions (MacIntosh et al. 2000; Hutchinson and Garcia 2002; Holzbaur et al. 2005; Hamner et al. 2010; Arnold et al. 2013; Steele et al. 2013; Hutchinson et al. 2015). This use of Hill-type models is problematic as cross-bridge and sliding filament theories do not predict or explain muscle performance well under the dynamic condition relevant to biological movement (Perreault et al. 2003; Lee et al. 2013; Nishikawa et al. 2018), likely due to the effects of spatial scale across which force must be transmitted, and the heterogeneous nature of these force transmission pathways. Potentially more problematic is the fact that not only are these models likely subject to large errors, but that errors are likely to vary systematically across a range of locomotor conditions. If muscle performance scales non-linearly with activation level (Rack and Westbury 1969; Brown et al. 1999; Holt and Azizi 2014; Holt et al. 2014), but models are based entirely on maximally activated muscle performance (Zajac 1989), model errors are likely to increase at lower levels of muscle activation level (Perreault et al. 2003). If tissue-level models fail to include the material properties of connective tissues they will neglect any effect of muscle shape change, and their predictions will be systematically worse for older muscles with increased connective tissue stiffness (Gao et al. 2008; Holt et al. 2016; Azizi et al. 2017). The failure of cross-bridge and sliding filament theories to predict any history dependence means that these effects will be absent from such model results (Herzog 1998), despite their presumed prevalence during the stretch-shorten cycles ubiquitous to biological movement (Askew and Marsh 1998). As our improving understanding of muscle biophysics and increasing exploration of performance under dynamic conditions have revealed the limitations of Hill-type models, a variety of approaches have been taken to develop muscle models incorporating additional phenomenological and structural aspects of muscle. Modifications to Hill-type models have been made to include recruitment of different fiber types, history dependence, material properties, inertia, and muscle geometry (Brown and Loeb 2000; Brown et al. 1996; Ettema 2002; Dick et al. 2017; Lai et al. 2018; Ross et al. 2018). These corrected Hill-type models have been extensively used as embedded models in whole-body and limb simulations (Delp et al. 1990; Millard et al. 2013). A more radical adaptation of the Hill-type model has included a winding-spring system to explore the role of titin in active muscle (Nishikawa et al. 2012; LeMoyne et al. 2014; Tahir et al. 2018). Finite element models have been used to examine the effects of cardiac and skeletal muscle material properties and geometries on performance (Yucesoy and Huijing 2012; Rahemi et al. 2014; Krishnamurthy et al. 2016). Excitation-contraction coupling models have delved into electrical excitability and transmission of depolarization (Tveito et al. 2011; Wilhelms et al. 2013). Spatially explicit models have dealt with consequences of multi-scale force transmission and heterogeneities in force production from the single motor to the myofibrillar levels (Daniel et al. 1998; Chase et al. 2004; Tanner et al. 2007; Campbell 2009; Williams et al. 2010, 2013). New spatially explicit models add titin and gain the ability to look at the effects of clinically relevant mutations, something previously done primarily at the single myofilament level (Sewanan et al. 2016; Powers et al. 2018). The common theme among these models is an increase in the processes included, and steps taken, in an attempt to replicate or explain elements of muscle performance during biological movement, not predicted by Hill-type models. These models have added varying degrees of explanatory power. Adding recruitment of different muscle fibers to Hill-type muscle models seemed to provide only modest improvements in predictions (Lee et al. 2013), however, there seem to be potential for greater improvements with the inclusion of other parameters (Ross et al. 2018). The phenomenological inclusion of history dependence to models has demonstrated the potential for this phenomenon to improve the control and stability of movement (Ettema 2002). Exploration of the active role of titin has suggested that the winding filament hypothesis may underpin history dependence, and has highlighted the importance of titin isoform in muscle performance (LeMoyne et al. 2014; Tahir et al. 2018). Finite element models have demonstrated the potential for regional variation in activation and lateral force transmission through connective tissues to alter muscle performance (Yucesoy and Huijing 2012; Rahemi et al. 2014). Spatially explicit models have shown the importance of disorder to the recruitment of cross-bridges, the spread of activation along tropomyosin to cooperativity, and the dependence of the length–tension relationship on thick–thin filament spacing changes (Daniel et al. 1998; Tanner et al. 2007; Williams et al. 2013). The addition of each mechanism creates a richer, but less parsimonious, picture of muscle contraction. Conclusions The emerging picture of muscle performance described in this paper is that of a heterogeneous, multi-scale, system whose current state can only be specified in a high-dimensional landscape. Dimensions of this landscape include the current configuration or localization of each of the scales in the system, from kinetic states of single motors to body position within the environment; the energetics at each scale, from ATP concentrations in a single cross-bridge’s locality to the storage and return of energy in deformable locomotion substrates; and the histories of all dimensions. Classic experiments in the field tended to exhaustively explore a highly-constrained region in this landscape, but a new wave of work is starting to integrate across scales and time periods during dynamic contractions, and is uncovering significant structural and functional heterogeneity in the process. Stitching together the early observations from these experiments into a richer picture of the high-dimensional space muscle occupies is a major task for the next several decades of muscle research, but one that we can lay the groundwork for today by specifying the bounds of our early local exploration and showing they connect to the larger landscape. For now, we hope that the following papers help identify the aspects of structural and functional heterogeneity across spatial scales that provide the greatest additions to our framework for understanding muscle contraction. Acknowledgments We would like to thank all the participants in the symposium for contributing their work and insight. Funding Funding for this symposium was provided by the Society for Integrative and Comparative Biology (DVM and DCM), Company of Biologists, and Aurora Scientific. 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Published: Aug 1, 2018

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