Effect of series elasticity on delay in development of tension relative to stiffness during muscle activation

Nebulin increases thin filament stiffness and force per cross-bridge in slow-twitch soleus muscle fibers

Nebulin stabilizes the thin filament and regulates force generation in skeletal muscle, but its precise role is not understood. Using conditional knockout mice, Kawai et al. demonstrate that nebulin functions to increase the force per cross-bridge in skinned slow-twitch soleus muscle fibers.

Nebulin (Neb) is associated with the thin filament in skeletal muscle cells, but its functions are not well understood. For this goal, we study skinned slow-twitch soleus muscle fibers from wild-type (Neb⁺) and conditional Neb knockout (Neb⁻) mice. We characterize cross-bridge (CB) kinetics and the elementary steps of the CB cycle by sinusoidal analysis during full Ca²⁺ activation and observe that Neb increases active tension 1.9-fold, active stiffness 2.7-fold, and rigor stiffness 3.0-fold. The ratio of stiffness during activation and rigor states is 62% in Neb⁺ fibers and 68% in Neb⁻ fibers. These are approximately proportionate to the number of strongly attached CBs during activation. Because the thin filament length is 15% shorter in Neb⁻ fibers than in Neb⁺ fibers, the increase in force per CB in the presence of Neb is ∼1.5 fold. The equilibrium constant of the CB detachment step (K₂), its rate (k₂), and the rate of the reverse force generation step (k₋₄) are larger in Neb⁺ fibers than in Neb⁻ fibers. The rates of the force generation step (k₄) and the reversal detachment step (k₋₂) change in the opposite direction. These effects can be explained by Le Chatelier’s principle: Increased CB strain promotes less force-generating state(s) and/or detached state(s). Further, when CB distributions among the six states are calculated, there is no significant difference in the number of strongly attached CBs between fibers with and without Neb. These results demonstrate that Neb increases force per CB. We also confirm that force is generated by isomerization of actomyosin (AM) from the AM.ADP.Pi state (ADP, adenosine diphophate; Pi, phosphate) to the AM*ADP.Pi state, where the same force is maintained after Pi release to result in the AM*ADP state. We propose that Neb changes the actin (and myosin) conformation for better ionic and hydrophobic/stereospecific AM interaction, and that the effect of Neb is similar to that of tropomyosin.

L71F mutation in rat cardiac troponin T augments crossbridge recruitment and detachment dynamics against α-myosin heavy chain, but not against β-myosin heavy chain

The N-terminal extension of human cardiac troponin T (TnT), which modulates myofilament Ca²⁺ sensitivity, contains several hypertrophic cardiomyopathy (HCM)-causing mutations including S69F. However, the functional consequence of S69F mutation is unknown. The human analog of S69F in rat TnT is L71F (TnT_L71F). Because the functional consequences due to structural changes in the N-terminal extension are influenced by the type of myosin heavy chain (MHC) isoform, we hypothesized that the TnT_L71F-mediated effect would be differently modulated by α- and β-MHC isoforms. TnT_L71F and wild-type rat TnT were reconstituted into de-membranated muscle fibers from normal (α-MHC) and propylthiouracil-treated rat hearts (β-MHC) to measure steady-state and dynamic contractile parameters. The magnitude of the TnT_L71F-mediated attenuation of Ca²⁺-activated maximal tension was greater in α- than in β-MHC fibers. For example, TnT_L71F attenuated maximal tension by 31% in α-MHC fibers but only by 10% in β-MHC fibers. Furthermore, TnT_L71F reduced myofilament Ca²⁺ sensitivity by 0.11 pCa units in α-MHC fibers but only by 0.05 pCa units in β-MHC fibers. TnT_L71F augmented rate constants of crossbridge recruitment and crossbridge detachment dynamics in α-MHC fibers but not in β-MHC fibers. Collectively, our data demonstrate that TnT_L71F induces greater contractile deficits against α-MHC than against β-MHC background.

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or "clamped" in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.

The effects of force inhibition by sodium vanadate on cross-bridge binding, force redevelopment, and Ca2+ activation in cardiac muscle

Strongly bound, force-generating myosin cross-bridges play an important role as allosteric activators of cardiac thin filaments. Sodium vanadate (Vi) is a phosphate analog that inhibits force by preventing cross-bridge transition into force-producing states. This study characterizes the mechanical state of cross-bridges with bound Vi as a tool to examine the contribution of cross-bridges to cardiac contractile activation. The K(i) of force inhibition by Vi was approximately 40 microM. Sinusoidal stiffness was inhibited with Vi, although to a lesser extent than force. We used chord stiffness measurements to monitor Vi-induced changes in cross-bridge attachment/detachment kinetics at saturating [Ca(2+)]. Vi decreased chord stiffness at the fastest rates of stretch, whereas at slow rates chord stiffness actually increased. This suggests a shift in cross-bridge population toward low force states with very slow attachment/detachment kinetics. Low angle x-ray diffraction measurements indicate that with Vi cross-bridge mass shifted away from thin filaments, implying decreased cross-bridge/thin filament interaction. The combined x-ray and mechanical data suggest at least two cross-bridge populations with Vi; one characteristic of normal cycling cross-bridges, and a population of weak-binding cross-bridges with bound Vi and slow attachment/detachment kinetics. The Ca(2+) sensitivity of force (pCa(50)) and force redevelopment kinetics (k(TR)) were measured to study the effects of Vi on contractile activation. When maximal force was inhibited by 40% with Vi pCa(50) decreased, but greater force inhibition at higher [Vi] did not further alter pCa(50). In contrast, the Ca(2+) sensitivity of k(TR) was unaffected by Vi. Interestingly, when force was inhibited by Vi k(TR) increased at submaximal levels of Ca(2+)-activated force. Additionally, k(TR) is faster at saturating Ca(2+) at [Vi] that inhibit force by > approximately 70%. The effects of Vi on k(TR) imply that k(TR) is determined not only by the intrinsic properties of the cross-bridge cycle, but also by cross-bridge contribution to thin filament activation.

Sarcomere dynamics during muscular contraction and their implications to muscle function

This article attempts to identify the key aspects of sarcomere inhomogeneity and the dynamics of sarcomere length changes in muscle contraction experiments and focuses on understanding the mechanics of myofibrils or muscle fibres when viewed as independent units of biological motors (the half-sarcomeres) connected in series. Muscle force generation has been interpreted traditionally on the basis of the kinetics of crossbridge cycling, i.e. binding of myosin heads to actin and consecutive force generating conformational change of the head, under controlled conditions and assuming uniformity of sarcomere or half-sarcomere behaviour. However, several studies have shown that re-distribution of internal strain within myofibrils and muscle fibres may be a key player, particularly, during stretch or relaxation so that force kinetics parameters are strongly affected by sarcomere dynamics. Here, we aim to shed light on how force generation, crossbridge kinetics, and the complex sarcomere movements are to be linked and which mechanical concepts are necessary to develop a comprehensive contraction model of a myofibril.

Cross-bridge versus thin filament contributions to the level and rate of force development in cardiac muscle

In striated muscle thin filament activation is initiated by Ca(2+) binding to troponin C and augmented by strong myosin binding to actin (cross-bridge formation). Several lines of evidence have led us to hypothesize that thin filament properties may limit the level and rate of force development in cardiac muscle at all levels of Ca(2+) activation. As a test of this hypothesis we varied the cross-bridge contribution to thin filament activation by substituting 2 deoxy-ATP (dATP; a strong cross-bridge augmenter) for ATP as the contractile substrate and compared steady-state force and stiffness, and the rate of force redevelopment (k(tr)) in demembranated rat cardiac trabeculae as [Ca(2+)] was varied. We also tested whether thin filament dynamics limits force development kinetics during maximal Ca(2+) activation by comparing the rate of force development (k(Ca)) after a step increase in [Ca(2+)] with photorelease of Ca(2+) from NP-EGTA to maximal k(tr), where Ca(2+) binding to thin filaments should be in (near) equilibrium during force redevelopment. dATP enhanced steady-state force and stiffness at all levels of Ca(2+) activation. At similar submaximal levels of steady-state force there was no increase in k(tr) with dATP, but k(tr) was enhanced at higher Ca(2+) concentrations, resulting in an extension (not elevation) of the k(tr)-force relationship. Interestingly, we found that maximal k(tr) was faster than k(Ca), and that dATP increased both by a similar amount. Our data suggest the dynamics of Ca(2+)-mediated thin filament activation limits the rate that force develops in rat cardiac muscle, even at saturating levels of Ca(2+).

A simple model with myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers

The contribution of thick and thin filaments to skeletal muscle fiber compliance has been shown to be significant. If similar to the compliance of cycling cross-bridges, myofilament compliance could explain the difference in time course of stiffness and force during the rise of tension in a tetanus as well as the difference in Ca(2+) sensitivity of force and stiffness and more rapid phase 2 tension recovery (r) at low Ca(2+) activation. To characterize the contribution of myofilament compliance to sarcomere compliance and isometric force kinetics, the Ca(2+)-activation dependence of sarcomere compliance in single glycerinated rabbit psoas fibers, in the presence of ATP (5.0 mM), was measured using rapid length steps. At steady sarcomere length, the dependence of sarcomere compliance on the level of Ca(2+)-activated force was similar in form to that observed for fibers in rigor where force was varied by changing length. Additionally, the ratio of stiffness/force was elevated at lower force (low [Ca(2+)]) and r was faster, compared with maximum activation. A simple series mechanical model of myofilament and cross-bridge compliance in which only strong cross-bridge binding was activation dependent was used to describe the data. The model fit the data and predicted that the observed activation dependence of r can be explained if myofilament compliance contributes 60-70% of the total fiber compliance, with no requirement that actomyosin kinetics be [Ca(2+)] dependent or that cooperative interactions contribute to strong cross-bridge binding.

Contractile properties of rabbit psoas muscle fibres inhibited by beryllium fluoride

The structure of truncated, recombinant Dictyostelium myosin motor domain complexed with Mg.ADP and slowly dissociating analogues of Pi has previously been characterized as two main states (S1-MgADP plus BeFx vs. A1F4- or Vi). The BeFx bound state is thought to mimic the weak actin-binding M.ATP complex, while the states with A1F4- or Vi bound mimic the M.ADP.Pi state. While the effects of A1F4- and Vi on fibre mechanics have been previously described (Chase et al., 1994, 1993), the effects of BeFx have not been characterized in detail. At pCa 4.5 (12 degrees C), we measured (i) steady-state isometric tension, (ii) stiffness (KS; 1 kHz sinusoids), and (iii) unloaded shortening velocity (Vu; slack test) in single skinned muscle fibres from rabbit psoas. Results were compared when tension was inhibited with either BeFx or 2,3-butanedione-monoxime (BDM) or modulated by altering myoplasmic [Ca2+]. With 3 mM total fluoride, 1 mM BeFx inhibited both tension and KS by approximately 50% (compared to 7-10 mM BDM and 50-100 microM A1F4-). Increasing [BeFx] to 10 mM further reduced tension to approximately 15% P0, but had little further effect on KS; with BDM and altered [Ca2+], KS scaled more proportionately with tension. Inhibition of tension and KS by BeFx was more rapidly reversible, compared with slow recovery from tension inhibition with A1F4- or Vi. Vu exhibited a complex dependence on [BeFx], being relatively unaffected by concentrations < or = 1 mM, and becoming inhibited steeply for [BeFx] above this level. With BDM, Vu co-varied more directly with force. Our results suggest that BeFx may induce a different cross-bridge state in fibres than do A1F4- or Vi, but all three analogues of Pi form complexes that mimic crossbridge states that follow ATP hydrolysis.

Modelling and simulation of motility in actomyosin systems

We present a model mechanism for simulating the diffusive motion and fluctuations inherent in myofibrillar sarcomere and its subunits at the molecular level. The model couples Langevin dynamics with Huxley kinetics to reproduce the transient patterns of momentum transfer, force generation and resulting motility due to the interactive activities of actin and myosin crossbridges. When myosin is detached from actin, our model predicts Brownian displacements centered at 0 +/- 8 nm (mean +/- SD, n = 265,308) and it is broadly distributed due to the Brownian noise. Attachment events produced displacements with step sizes of approximately 8 +/- 6 nm (mean +/- SD, n = 34,693), which is in agreement with some recent optical-tweezers transducer experimental results. The proposed model could form the basis for a complete qualitative and quantitative description of the evolving complex interactions of the molecular proteins--actin and myosin--in the overall framework of muscular contraction studies.

Phosphate release and force generation in cardiac myocytes investigated with caged phosphate and caged calcium

The phosphate (P(i)) dissociation step of the cross-bridge cycle was investigated in skinned rat ventricular myocytes to examine its role in force generation and Ca(2+) regulation in cardiac muscle. Pulse photolysis of caged P(i) (alpha-carboxyl-2-nitrobenzyl phosphate) produced up to 3 mM P(i) within the filament lattice, resulting in an approximately exponential decline in steady-state tension. The apparent rate constant, k (rho i), increased linearly with total P(i) concentration (initial plus photoreleased), giving an apparent second-order rate constant for P(i) binding of 3100 M(-1) s(-1), which is intermediate in value between fast and slow skeletal muscles. A decrease in the level of Ca(2+) activation to 20% of maximum tension reduced k (rho i) by twofold and increased the relative amplitude by threefold, consistent with modulation of P(i) release by Ca2+. A three-state model, with separate but coupled transitions for force generation and P(i) dissociation, and a Ca(2+)-sensitive forward rate constant for force generation, was compatible with the data. There was no evidence for a slow phase of tension decline observed previously in fast skeletal fibers at low Ca(2+), suggesting differences in cooperative mechanisms in cardiac and skeletal muscle. In separate experiments, tension development was initiated from a relaxed state by photolysis of caged Ca(2+). The apparent rate constant, k(Ca), was accelerated in the presence of high P(i) consistent with close coupling between force generation and P(i) dissociation, even when force development was initiated from a relaxed state. k(Ca) was also dependent on the level of Ca(2+) activation. However, significant quantitative differences between k (rho i) and k(Ca), including different sensitivities to Ca(2+) and P(i) indicate that caged Ca(2+) tension transients are influenced by additional Ca(2+)-dependent but P i-independent steps that occur before P(i) release. Data from both types of measurements suggest that kinetic transitions associated with P(i) dissociation are modulated by the Ca(2+) regulatory system and partially limit the physiological rate of tension development in cardiac muscle.