Millisecond-scale biochemical response to change in strain

Advances in understanding the energetics of muscle contraction

Muscle energetics encompasses the relationships between mechanical performance and the biochemical and thermal changes that occur during muscular activity. The biochemical reactions that underpin contraction are described and the way in which these are manifest in experimental recordings, as initial and recovery heat, is illustrated. Energy use during contraction can be partitioned into that related to cross-bridge force generation and that associated with activation by Ca2+. Activation processes account for 25-45% of ATP turnover in an isometric contraction, varying amongst muscles. Muscle energy use during contraction depends on the nature of the contraction. When shortening muscles produce less force than when contracting isometrically but use energy at a greater rate. These characteristics reflect more rapid cross-bridge cycling when shortening. When lengthening, muscles produce more force than in an isometric contraction but use energy at a lower rate. In that case, cross-bridges cycle but via a pathway in which ATP splitting is not completed. Shortening muscles convert part of the free energy available from ATP hydrolysis into work with the remainder appearing as heat. In the most efficient muscle studied, that of a tortoise, cross-bridges convert a maximum of 47% of the available energy into work. In most other muscles, only 20-30% of the free energy from ATP hydrolysis is converted into work.

Measurement of Nucleotide Hydrolysis Using Fluorescent Biosensors for Phosphate

Assays for the detection of inorganic phosphate (P_i) are widely used to measure the activity of nucleotide hydrolyzing enzymes, such as ATPases and GTPases. The fluorescent biosensors for P_i, described here, are based on fluorescently labeled versions of E. coli phosphate-binding protein (PBP), which translates P_i binding into a large change in fluorescence intensity. In comparison with other P_i-detection systems, these biosensors are characterized by a high sensitivity (sub-micromolar P_i concentrations) and high time resolution (tens of milliseconds), and they are therefore particularly well suited for measurements of phosphate ester hydrolysis in real time. In this chapter, it is described how the P_i biosensors can be used to measure kinetics of ATPase and GTPase reactions, both under steady state and pre-steady state conditions. An example protocol is given for determining steady state kinetic parameters, K_m and k_cat, of the ATP-dependent chromatin remodeler Chd1, in a plate reader format. In addition, the measurement of P_i release kinetics under pre-steady state conditions is described, including a detailed experimental procedure for a single turnover measurement of ATP hydrolysis by the ABC-type ATPase SufBC using rapid mixing.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Energy turnover in mammalian skeletal muscle in contractions mimicking locomotion: effects of stimulus pattern on work, impulse and energetic cost and efficiency

Active muscle performs various mechanical functions during locomotion: work output during shortening, work absorption when resisting (but not preventing) lengthening, and impulse (force-time integral) whenever there is active force. The energetic costs of these functions are important components in the energy budget during locomotion. We investigated how the pattern of stimulation and movement affects the mechanics and energetics of muscle fibre bundles isolated from wild rabbits (Oryctolagus cuniculus). The fibres were from muscles consisting of mainly fast-twitch, type 2 fibres. Fibre length was held constant (isometric) or a sinusoidal pattern of movement was imposed at a frequency similar to the stride frequency of running wild rabbits. Duty cycle (stimulation duration×movement frequency) and phase (timing of stimulation relative to movement) were varied. Work and impulse were measured as well as energy produced as heat. The sum of net work (work output-work input) and heat was taken as a measure of energetic cost. Maximum work output was produced with a long duty cycle and stimulation starting slightly before shortening, and was produced quite efficiently. However, efficiency was even higher with other stimulation patterns that produced less work. The highest impulse (considerably higher than isometric impulse) was produced when stimulation started while the muscle fibres were being lengthened. High impulse was produced very economically because of the low cost of producing force during lengthening. Thus, locomotion demanding high work, high impulse or economical work output or impulse requires a distinct pattern of stimulation and movement.

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

A simple model of cardiac muscle was designed for multiscale simulation of heart mechanics. Relaxed cardiac muscle was described as a transversally isotropic hyperelastic material. Active tension caused by actin-myosin crossbridges depends on the ensemble averaged strain of myosin heads bound to actin. Calcium activation was modeled by Ca²⁺ binding to troponin-C. To account for the dependence of troponin affinity for Ca²⁺ on myosin heads strongly bound to actin, the kinetics of troponin binding to Ca²⁺ in the overlap zone of the thin and thick filaments and outside it were separated. The changes in the length of these zones during muscle shortening or lengthening were accounted for explicitly. Simplified version of the model contains only 5 ordinary differential equations (ODE). Model parameters were estimated from a limited set of experiments with skeletal and cardiac muscle. Simulations have shown that model reproduces qualitatively a number of experimental observations: steady-state force-velocity and stiffness-velocity relations; mechanical responses to step changes in muscle length or load; steep Ca²⁺-tension relationship and its dependence on sarcomere length tension (the Frank-Starling mechanism); tension, shortening and Ca²⁺-transients in twitch isometric and isotonic contractions, tension development and redevelopment upon fast change in Ca²⁺ concentration or muscle release followed by re-stretch. We believe that the model can be effectively used for modeling contraction and relaxation of the heart.

Phosphorylation of the regulatory light chain of myosin in striated muscle: methodological perspectives

Phosphorylation of the regulatory light chain (RLC) of myosin modulates cellular functions such as muscle contraction, mitosis, and cytokinesis. Phosphorylation defects are implicated in a number of diseases. Here we focus on striated muscle where changes in RLC phosphorylation relate to diseases such as hypertrophic cardiomyopathy and muscular dystrophy, or age-related changes. RLC phosphorylation in smooth muscle and non-muscle cells are covered briefly where relevant. There is much scientific interest in controlling the phosphorylation levels of RLC in vivo and in vitro in order to understand its physiological function in striated muscles. A summary of available and emerging in vivo and in vitro methods is presented. The physiological role of RLC phosphorylation and novel pathways are discussed to highlight the differences between muscle types and to gain insights into disease processes.

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.

Force generation in cardiac muscle cells is driven by changes in calcium concentration. Relatively small changes in the calcium concentration over the course of a heart beat lead to the large changes in force required to fully contract and relax the heart. This is known as ‘cooperative activation’, and involves a complex interaction of several proteins involved in contraction. Current computer models which reproduce force generation often do not represent these processes explicitly, and stochastic approaches that do tend to require large amounts of computational power to solve, which limit the range of investigations in which they can be used. We have created an new computational model that captures the underlying physiological processes in more detail, and is more efficient than stochastic approaches, while still being able to run a large range of simulations. The model is able to explain the biological processes leading to the cooperative activation of muscle. In addition, the model reproduces how this cooperative activation translates to normal muscle function to generate force from changes in calcium across three different species.

The lifetime of the actomyosin complex in vitro under load corresponding to stretch of contracting muscle

During eccentric contraction, muscle is lengthening so that the actin-myosin cross-bridges bear a load that exceeds the force they generate during isometric contraction. Using the optical trap technique, we simulated eccentric contraction at the single molecule level and investigated the effect of load on the skeletal actomyosin lifetime at different ATP concentrations. The range of the loads was up to 17 pN above the isometric level. We found that the frequency distribution of the lifetime of the actin-bound state of the myosin molecule was biphasic: it quickly rose and then decreased slowly. The rate of the slow phase of this distribution increased with both the load and the ATP concentration. The fast phase accelerated sharply with the load, but it was independent of ATP concentration. The presence of the fast phase demonstrates that some transition(s) in the actomyosin complex occur before the myosin head becomes able to bind ATP and detach from actin. Its high sensitivity to the load indicates that the transition is load-dependent.

An enhanced model of cross-bridge operation with internal elasticity

A recent study has shown (as reported by Rosenfeld, Eur Biophys J 41:733-753, 2012) that an apparatus consisting of a cycling pump, a lever, and charged beads is able to generate force in accordance with Hill's force-velocity relation. Here, we show that a spring integrated into this microscopic model of a myosin motor allows reproducing, in general terms, the muscle fiber responses to sudden changes in fiber length. The time course of relaxation is governed by the same hindering force that determines the maximal value of muscle contraction velocity. Any single one of the exceptionally simple parts of the proposed model device corresponds to some element of the real myosin head and interacts with any other part in accordance with the laws of Newton, Coulomb, and Hooke. In essence, the model demonstrates that Coulomb repulsion should be understood as the physical source of muscle force. Accordingly, some fictitious master equation with ad hoc postulated rate constants is not needed to explain the essential mechanical characteristics of a muscle. The current model still contains no mechanism that could account for superfast relaxations within periods of about 0.1 ms.

Mechano-signaling in heart failure

Mechanosensation and mechanotransduction are fundamental aspects of biology, but the link between physical stimuli and biological responses remains not well understood. The perception of mechanical stimuli, their conversion into biochemical signals, and the transmission of these signals are particularly important for dynamic organs such as the heart. Various concepts have been introduced to explain mechanosensation at the molecular level, including effects on signalosomes, tensegrity, or direct activation (or inactivation) of enzymes. Striated muscles, including cardiac myocytes, differ from other cells in that they contain sarcomeres which are essential for the generation of forces and which play additional roles in mechanosensation. The majority of cardiomyopathy causing candidate genes encode structural proteins among which titin probably is the most important one. Due to its elastic elements, titin is a length sensor and also plays a role as a tension sensor (i.e., stress sensation). The recent discovery of titin mutations being a major cause of dilated cardiomyopathy (DCM) also underpins the importance of mechanosensation and mechanotransduction in the pathogenesis of heart failure. Here, we focus on sarcomere-related mechanisms, discuss recent findings, and provide a link to cardiomyopathy and associated heart failure.

Why muscle is an efficient shock absorber

Skeletal muscles power body movement by converting free energy of ATP hydrolysis into mechanical work. During the landing phase of running or jumping some activated skeletal muscles are subjected to stretch. Upon stretch they absorb body energy quickly and effectively thus protecting joints and bones from impact damage. This is achieved because during lengthening, skeletal muscle bears higher force and has higher instantaneous stiffness than during isometric contraction, and yet consumes very little ATP. We wish to understand how the actomyosin molecules change their structure and interaction to implement these physiologically useful mechanical and thermodynamical properties. We monitored changes in the low angle x-ray diffraction pattern of rabbit skeletal muscle fibers during ramp stretch compared to those during isometric contraction at physiological temperature using synchrotron radiation. The intensities of the off-meridional layer lines and fine interference structure of the meridional M3 myosin x-ray reflection were resolved. Mechanical and structural data show that upon stretch the fraction of actin-bound myosin heads is higher than during isometric contraction. On the other hand, the intensities of the actin layer lines are lower than during isometric contraction. Taken together, these results suggest that during stretch, a significant fraction of actin-bound heads is bound non-stereo-specifically, i.e. they are disordered azimuthally although stiff axially. As the strong or stereo-specific myosin binding to actin is necessary for actin activation of the myosin ATPase, this finding explains the low metabolic cost of energy absorption by muscle during the landing phase of locomotion.

The effects of Ca2+ and MgADP on force development during and after muscle length changes

The goal of this study was to compare the effects of Ca²⁺ and MgADP activation on force development in skeletal muscles during and after imposed length changes. Single fibres dissected from the rabbit psoas were (i) activated in pCa²⁺4.5 and pCa²⁺6.0, or (ii) activated in pCa²⁺4.5 before and after administration of 10 mM MgADP. Fibres were activated in sarcomere lengths (SL) of 2.65 µm and 2.95 µm, and subsequently stretched or shortened (5%SL at 1.0 SL.s⁻¹) to reach a final SL of 2.80 µm. The kinetics of force during stretch were not altered by pCa²⁺ or MgADP, but the fast change in the slope of force development (P₁) observed during shortening and the corresponding SL extension required to reach the change (L₁) were higher in pCa²⁺6.0 (P₁ = 0.22±0.02 P_o; L₁ = 5.26±0.24 nm.HS^.1) than in pCa²⁺4.5 (P₁ = 0.15±0.01 P_o; L₁ = 4.48±0.25 nm.HS^.1). L₁ was also increased by MgADP activation during shortening. Force enhancement after stretch was lower in pCa²⁺4.5 (14.9±5.4%) than in pCa²⁺6.0 (38.8±7.5%), while force depression after shortening was similar in both Ca²⁺ concentrations. The stiffness accompanied the force behavior after length changes in all situations. MgADP did not affect the force behavior after length changes, and stiffness did not accompany the changes in force development after stretch. Altogether, these results suggest that the mechanisms of force generation during and after stretch are different from those obtained during and after shortening.

Direct real-time detection of the actin-activated power stroke within the myosin catalytic domain

We have used transient kinetics, nanosecond time-resolved fluorescence resonance energy transfer (FRET), and kinetics simulations to resolve a structural transition in the Dictyostelium myosin II relay helix during the actin-activated power stroke. The relay helix plays a critical role in force generation in myosin, coupling biochemical changes in the ATPase site with the force-transducing rotation of the myosin light-chain domain. Previous research in the absence of actin showed that ATP binding to myosin induces a dynamic equilibrium between a bent prepower stroke state of the relay helix and a straight postpower stroke state, which dominates in the absence of ATP or when ADP is bound. We now ask whether actin binding reverses this transition and if so, how this reversal is coordinated with actin-activated phosphate release. We labeled a Cys-lite Dictyostelium myosin II motor domain with donor and acceptor probes at two engineered Cys residues designed to detect relay helix bending. We then performed transient time-resolved FRET following stopped-flow mixing of actin with labeled myosin, preincubated with ATP. We determined the kinetics of actin-activated phosphate release, using fluorescent phosphate-binding protein. The results show that actin binding to the myosin.ADP.P complex straightens the relay helix before phosphate dissociation. This actin-activated relay helix straightening is reversible, but phosphate irreversibly dissociates from the postpower stroke state, preventing reversal of the power stroke. Thus, relay helix straightening gates phosphate dissociation, whereas phosphate dissociation provides the thermodynamic driving force underlying force production.

On mechanosensation, acto/myosin interaction, and hypertrophy

Current concepts of mechanosensation are general and applicable to almost every cell type. However, striated muscle cells are distinguished by their ability to generate strong forces via actin/myosin interaction, and this process is fine-tuned for optimum contractility. This aspect, unique for actively contracting cells, may be defined as "sensing of the magnitude and dynamics of contractility," as opposed to the well-known concepts of the "perception of extracellular mechanical stimuli." The acto/myosin interaction, by producing changes in ATP, ADP, Pi, and force on a millisecond timescale, may be regarded as a novel and previously unappreciated mechanosensory mechanism. In addition, sarcomeric mechanosensory structures, such as the Z-disc, are directly linked to autophagy, survival, and cell death-related pathways. One emerging example is telethonin and its ability to interfere with p53 metabolism and hence apoptosis (mechanoptosis). In this article, we introduce contractility per se as an important mechanosensory mechanism, and we differentiate extracellular from intracellular mechanosensory effects.

Stretch of contracting cardiac muscle abruptly decreases the rate of phosphate release at high and low calcium

The contractile performance of the heart is linked to the energy that is available to it. Yet, the heart needs to respond quickly to changing demands. During diastole, the heart fills with blood and the heart chambers expand. Upon activation, contraction of cardiac muscle expels blood into the circulation. Early in systole, parts of the left ventricle are being stretched by incoming blood, before contraction causes shrinking of the ventricle. We explore here the effect of stretch of contracting permeabilized cardiac trabeculae of the rat on the rate of inorganic phosphate (P(i)) release resulting from ATP hydrolysis, using a fluorescent sensor for P(i) with millisecond time resolution. Stretch immediately reduces the rate of P(i) release, an effect observed both at full calcium activation (32 μmol/liter of Ca(2+)), and at a physiological activation level of 1 μmol/liter of Ca(2+). The results suggest that stretch redistributes the actomyosin cross-bridges toward their P(i)-containing state. The redistribution means that a greater fraction of cross-bridges will be poised to rapidly produce a force-generating transition and movement, compared with cross-bridges that have not been subjected to stretch. At the same time stretch modifies the P(i) balance in the cytoplasm, which may act as a cytoplasmic signal for energy turnover.