Interactions between Connected Half-Sarcomeres Produce Emergent Mechanical Behavior in a Mathematical Model of Muscle

Most reductionist theories of muscle attribute a fiber's mechanical properties to the scaled behavior of a single half-sarcomere. Mathematical models of this type can explain many of the known mechanical properties of muscle but have to incorporate a passive mechanical component that becomes ∼300% stiffer in activating conditions to reproduce the force response elicited by stretching a fast mammalian muscle fiber. The available experimental data suggests that titin filaments, which are the mostly likely source of the passive component, become at most ∼30% stiffer in saturating Ca2+ solutions. The work described in this manuscript used computer modeling to test an alternative systems theory that attributes the stretch response of a mammalian fiber to the composite behavior of a collection of half-sarcomeres. The principal finding was that the stretch response of a chemically permeabilized rabbit psoas fiber could be reproduced with a framework consisting of 300 half-sarcomeres arranged in 6 parallel myofibrils without requiring titin filaments to stiffen in activating solutions. Ablation of inter-myofibrillar links in the computer simulations lowered isometric force values and lowered energy absorption during a stretch. This computed behavior mimics effects previously observed in experiments using muscles from desmin-deficient mice in which the connections between Z-disks in adjacent myofibrils are presumably compromised. The current simulations suggest that muscle fibers exhibit emergent properties that reflect interactions between half-sarcomeres and are not properties of a single half-sarcomere in isolation. It is therefore likely that full quantitative understanding of a fiber's mechanical properties requires detailed analysis of a complete fiber system and cannot be achieved by focusing solely on the properties of a single half-sarcomere

Revisiting Frank–Starling: regulatory light chain phosphorylation alters the rate of force redevelopment (ktr) in a length-dependent fashion

Force and power in cardiac muscle have a known dependence on phosphorylation of the myosin-associated regulatory light chain (RLC). We explore the effect of RLC phosphorylation on the ability of cardiac preparations to redevelop force (ktr ) in maximally activating [Ca2+ ]. Activation was achieved by rapidly increasing the temperature (temperature-jump of 0.5-20ºC) of permeabilized trabeculae over a physiological range of sarcomere lengths (1.85-1.94 μm). The trabeculae were subjected to shortening ramps over a range of velocities and the extent of RLC phosphorylation was varied. The latter was achieved using an RLC-exchange technique, which avoids changes in the phosphorylation level of other proteins. The results show that increasing RLC phosphorylation by 50% accelerates ktr by ∼50%, irrespective of the sarcomere length, whereas decreasing phosphorylation by 30% slows ktr by ∼50%, relative to the ktr obtained for in vivo phosphorylation. Clearly, phosphorylation affects the magnitude of ktr following step shortening or ramp shortening. Using a two-state model, we explore the effect of RLC phosphorylation on the kinetics of force development, which proposes that phosphorylation affects the kinetics of both attachment and detachment of cross-bridges. In summary, RLC phosphorylation affects the rate and extent of force redevelopment. These findings were obtained in maximally activated muscle at saturating [Ca2+ ] and are not explained by changes in the Ca2+ -sensitivity of acto-myosin interactions. The length-dependence of the rate of force redevelopment, together with the modulation by the state of RLC phosphorylation, suggests that these effects play a role in the Frank-Starling law of the heart.Published versio

An analysis of the temperature dependence of force, during steady shortening at different velocities, in (mammalian) fast muscle fibres

We examined, over a wide range of temperatures (10–35°C), the isometric tension and tension during ramp shortening at different velocities (0.2–4 L0/s) in tetanized intact fibre bundles from a rat fast (flexor hallucis brevis) muscle; fibre length (L0) was 2.2 mm and sarcomere length ~2.5 μm. During a ramp shortening, the tension change showed an initial inflection of small amplitude (P1), followed by a larger exponential decline towards an approximate steady level; the tension continued to decline slowly afterwards and the approximate steady tension at a given velocity was estimated as the tension (P2) at the point of intersection between two linear slopes, as previously described (Roots et al. 2007). At a given temperature, the tension P2 declined to a lower level and at a faster rate (from an exponential curve fit) as the shortening velocity was increased; the temperature sensitivity of the rate of tension decline during ramp shortening at different velocities was low (Q10 0.9–1.5). The isometric tension and the P2 tension at a given shortening velocity increased with warming so that the relation between tension and (reciprocal) temperature was sigmoidal in both. In isometric muscle, the temperature T0.5 for half-maximal tension was ~10°C, activation enthalpy change (∆H) was ~100 kJ mol−1 and entropy change (∆S) ~350 J mol−1 K−1. In shortening, these were increased with increase of velocity so that at a shortening velocity (~4 L0/s) producing maximal power at 35°C, T0.5 was ~28°C, ∆H was ~200 kJ mol−1 and ∆S ~ 700 J mol−1 K−1; the same trends were seen in the tension data from isotonic release experiments on intact muscle and in ramp shortening experiments on maximally Ca-activated skinned fibres. In general, our findings show that the sigmoidal relation between force and temperature can be extended from isometric to shortening muscle; the implications of the findings are discussed in relation to the crossbridge cycle. The data indicate that the endothermic, entropy driven process that underlies crossbridge force generation in isometric muscle (Zhao and Kawai 1994; Davis, 1998) is even more pronounced in shortening muscle, i.e. when doing external work

Skeletal muscle contraction. The thorough definition of the contractile event requires both load acceleration and load mass to be known

<p>Abstract</p> <p>Background</p> <p>The scope of this work is to show that the correct and complete definition of the system of muscle contraction requires the knowledge of both the mass and the acceleration of the load.</p> <p>Results</p> <p>The aim is achieved by making use of a model of muscle contraction that operates into two phases. The first phase considers the effects of the power stroke in the absence of any hindrance. In the second phase viscous hindrance is introduced to match the experimental speed and yield of the contraction. It is shown that, at constant force of the load, changing load acceleration changes the time course of the pre-steady state of myofibril contraction. The decrease of the acceleration of the load from 9.8 m.s^-2to 1 m.s^-2increases the time length of the pre-steady state of the contraction from a few microseconds to many hundreds of microseconds and decreases the stiffness of the active fibre.</p> <p>Conclusions</p> <p>We urge that in the study of muscle contraction both the mass and the acceleration of the load are specified.</p

Large-scale Models Reveal the Two-component Mechanics of Striated Muscle

This paper provides a comprehensive explanation of striated muscle mechanics and contraction on the basis of filament rotations. Helical proteins, particularly the coiled-coils of tropomyosin, myosin and α-actinin, shorten their H-bonds cooperatively and produce torque and filament rotations when the Coulombic net-charge repulsion of their highly charged side-chains is diminished by interaction with ions. The classical “two-component model” of active muscle differentiated a “contractile component” which stretches the “series elastic component” during force production. The contractile components are the helically shaped thin filaments of muscle that shorten the sarcomeres by clockwise drilling into the myosin cross-bridges with torque decrease (= force-deficit). Muscle stretch means drawing out the thin filament helices off the cross-bridges under passive counterclockwise rotation with torque increase (= stretch activation). Since each thin filament is anchored by four elastic α-actinin Z-filaments (provided with force-regulating sites for Ca2+ binding), the thin filament rotations change the torsional twist of the four Z-filaments as the “series elastic components”. Large scale models simulate the changes of structure and force in the Z-band by the different Z-filament twisting stages A, B, C, D, E, F and G. Stage D corresponds to the isometric state. The basic phenomena of muscle physiology, i. e. latency relaxation, Fenn-effect, the force-velocity relation, the length-tension relation, unexplained energy, shortening heat, the Huxley-Simmons phases, etc. are explained and interpreted with the help of the model experiments

Portable stove use is associated with lower lung cancer mortality risk in lifetime smoky coal users

Domestic fuel combustion from cooking and heating, to which about 3 billion people worldwide are exposed, is associated with increased lung cancer risk. Lung cancer incidence in Xuanwei is the highest in China, and the attributable risk of lung cancer from unvented smoky coal burning is greater than 90%. To evaluate any lung cancer mortality reduction after changing from unvented stoves to portable stoves, we used lifetime smoky coal users in a retrospective cohort of all farmers born during 1917–1951 and residing in Xuanwei in 1976. Of the 42 422 enrolled farmers, 4054 lifetime smoky coal users changed to portable stoves, 4364 did not change, and 1074 died of lung cancer. Lung cancer morality associated with stove change was assessed by product-limit survival curves and multivariate Cox regression models. Both men (P<0.0001) and women (P<0.0001) who changed to portable stoves had a significantly increased probability of survival compared with those who did not change. Portable stoves were associated with decreased risk of lung cancer mortality in male participants (hazard ratio (HR)=0.62, 95% confidence interval (CI)=0.46–0.82) and female participants (HR=0.41, 95% CI=0.29–0.57). Portable stove use is associated with reduced lung cancer mortality risk, highlighting a cost-effective intervention that could substantially benefit health in developing countries

Muscle Contraction and Force: the Importance of an Ancillary Network, Nutrient Supply and Waste Removal

Muscle contraction studies often focus solely on myofibres and the proteins known to be involved in the processes of sarcomere shortening and cross-bridge cycling, but skeletal muscle also comprises a very elaborate ancillary network of capillaries, which not only play a vital role in terms of nutrient delivery and waste product removal, but are also tethered to surrounding fibres by collagen ”wires”. This paper therefore addresses aspects of the ancillary network of skeletal muscle at both a microscopic and functional level in order to better understand its role holistically as a considerable contributor to force transfer within muscular tissue

Stress Generation and Filament Turnover during Actin Ring Constriction

We present a physical analysis of the dynamics and mechanics of contractile actin rings. In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo. We present a general analysis of force balances and material exchange and estimate the relevant parameter values. We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers