A re-interpretation of the rate of tension redevelopment (k(TR)) in active muscle

Biomechanical evaluation of flash-frozen and cryo-sectioned papillary muscle samples by using sinusoidal analysis: cross-bridge kinetics and the effect of partial Ca2+ activation

We examined the integrity of flash-frozen and cryo-sectioned cardiac muscle preparations (introduced by Feng and Jin, 2020) by assessing tension transients in response to sinusoidal length changes at varying frequencies (1-100 Hz) at 25 °C. Using 70-μm-thick sections, we isolated fiber preparations to study cross-bridge (CB) kinetics: preparations were activated by saturating Ca2+ as well as varying concentrations of ATP and phosphate (Pi). Our results showed that, compared to ordinary skinned fibers, in-series stiffness decreased to 1/2, which resulted in a decrease of isometric tension to 62%, but CB kinetics and Ca2+ sensitivity were little affected. The pCa study demonstrated that the rate constant of the force generation step (2πb) is proportionate to [Ca2+] at < 5 μM, suggesting that the activation mechanism can be described by a simple second order reaction. We also found that tension, stiffness, and magnitude parameters are related to [Ca2+] by the Hill equation, with a cooperativity coefficient of 4-5, which is consistent with the fact that Ca2+ activation mechanisms involve cooperative multimolecular interactions. Our results support the long-held hypothesis that Process C (Phase 2) represents the CB detachment step, and Process B (Phase 3) represents the force generation step. Moreover, we discovered that constant H may represent the work-performing step in cardiac preparations. Our experiments demonstrate excellent CB kinetics with two well-defined exponentials that can be more distinguished than those found using ordinary skinned fibers. Flash-frozen and cryo-sectioned preparations are especially suitable for multi-institutional collaborations nationally and internationally because of their ease of transportation.

Mechanical Evaluation of Frozen and Cryo-Sectioned Papillary Muscle Samples by Using Sinusoidal Analysis: Cross-bridge Kinetics and the Effect of Partial Ca2+ activation

The use of frozen and cryo-sectioned cardiac muscle preparations, introduced recently by (Feng & Jin, 2020), offers promising advantages of easy transport and exchange of muscle samples among collaborating laboratories. In this report, we examined integrity of such preparation by studying tension transients in response to sinusoidal length changes and following concomitant amplitude and phase shift in tension time courses at varying frequencies. We used sections with 70 μm thickness, isolated fiber preparations, and studied cross-bridge (CB) kinetics: we activated the preparations with saturating Ca2+, and varying concentrations of ATP and phosphate (Pi). Our experiments have demonstrated that this preparation has the normal active tension and elementary steps of the CB cycle. Furthermore, we investigated the effect of Ca2+ on the rate constants and found that the rate constant r 4 of the force generation step is proportionate to [Ca2+] when it is <5 μM. This observation suggests that the activation mechanism can be described by a simple second order reaction. As expected, we found that magnitude parameters including tension and stiffness are related to [Ca2+] by the Hill equation with cooperativity of 4-5, consistent to the fact that Ca2+ activation mechanisms involve cooperative multimolecular interactions. Our results are consistent with a long-held hypothesis that process C (phase 2 of step analysis) represents the CB detachment step, and process B (phase 3) represents the force generation step. In this report, we further found that constant H may also represent work performance step. Our experiments have demonstrated excellent CB kinetics with reduced noise and well-defined two exponentials, which are better than skinned fibers, and easier to handle and study than single myofibrils.

Mechanisms of Frank-Starling law of the heart and stretch activation in striated muscles may have a common molecular origin

Vertebrate cardiac muscle generates progressively larger systolic force when the end diastolic chamber volume is increased, a property called the "Frank-Starling Law", or "length dependent activation (LDA)". In this mechanism a larger force develops when the sarcomere length (SL) increased, and the overlap between thick and thin filament decreases, indicating increased production of force per unit length of the overlap. To account for this phenomenon at the molecular level, we examined several hypotheses: as the muscle length is increased, (1) lattice spacing decreases, (2) Ca2+ sensitivity increases, (3) titin mediated rearrangement of myosin heads to facilitate actomyosin interaction, (4) increased SL activates cross-bridges (CBs) in the super relaxed state, (5) increased series stiffness at longer SL promotes larger elementary force/CB to account for LDA, and (6) stretch activation (SA) observed in insect muscles and LDA in vertebrate muscles may have similar mechanisms. SA is also known as delayed tension or oscillatory work, and universally observed among insect flight muscles, as well as in vertebrate skeletal and cardiac muscles. The sarcomere stiffness observed in relaxed muscles may significantly contributes to the mechanisms of LDA. In vertebrate striated muscles, the sarcomere stiffness is mainly caused by titin, a single filamentary protein spanning from Z-line to M-line and tightly associated with the myosin thick filament. In insect flight muscles, kettin connects Z-line and the thick filament to stabilize the sarcomere structure. In vertebrate cardiac muscles, titin plays a similar role, and may account for LDA and may constitute a molecular mechanism of Frank-Starling response.

Phosphate has dual roles in cross-bridge kinetics in rabbit psoas single myofibrils

In this study, we aimed to study the role of inorganic phosphate (P_i) in the production of oscillatory work and cross-bridge (CB) kinetics of striated muscle. We applied small-amplitude sinusoidal length oscillations to rabbit psoas single myofibrils and muscle fibers, and the resulting force responses were analyzed during maximal Ca²⁺ activation (pCa 4.65) at 15°C. Three exponential processes, A, B, and C, were identified from the tension transients, which were studied as functions of P_i concentration ([P_i]). In myofibrils, we found that process C, corresponding to phase 2 of step analysis during isometric contraction, is almost a perfect single exponential function compared with skinned fibers, which exhibit distributed rate constants, as described previously. The [P_i] dependence of the apparent rate constants 2πb and 2πc, and that of isometric tension, was studied to characterize the force generation and P_i release steps in the CB cycle, as well as the inhibitory effect of P_i. In contrast to skinned fibers, P_i does not accumulate in the core of myofibrils, allowing sinusoidal analysis to be performed nearly at [P_i] = 0. Process B disappeared as [P_i] approached 0 mM in myofibrils, indicating the significance of the role of P_i rebinding to CBs in the production of oscillatory work (process B). Our results also suggest that P_i competitively inhibits ATP binding to CBs, with an inhibitory dissociation constant of ∼2.6 mM. Finally, we found that the sinusoidal waveform of tension is mostly distorted by second harmonics and that this distortion is closely correlated with production of oscillatory work, indicating that the mechanism of generating force is intrinsically nonlinear. A nonlinear force generation mechanism suggests that the length-dependent intrinsic rate constant is asymmetric upon stretch and release and that there may be a ratchet mechanism involved in the CB cycle.

Ex vivo Methods for Measuring Cardiac Muscle Mechanical Properties

Cardiovascular disease continues to be the leading cause of morbidity and mortality in the United States and thousands of manuscripts each year are aimed at elucidating mechanisms underlying cardiac disease. The methods for quantifying cardiac performance are quite varied, with each technique assessing unique features of cardiac muscle mechanical properties. Accordingly, in this review, we discuss current ex vivo methods for quantifying cardiac muscle performance, highlighting what can be learned from each method, and how each technique can be used in conjunction to complement others for a more comprehensive understanding of cardiac function. Importantly, cardiac function can be assessed at several different levels, from the whole organ down to individual protein-protein interactions. Here, we take a reductionist view of methods that are commonly used to measure the distinct aspects of cardiac mechanical function, beginning with whole heart preparations and finishing with the in vitro motility assay. While each of the techniques are individually well-documented in the literature, there is a significant need for a comparison of the techniques, delineating the mechanical parameters that can are best measured with each technique, as well as the strengths and weaknesses inherent to each method. Additionally, we will consider complementary techniques and how these methods can be used in combination to improve our understanding of cardiac mechanical function. By presenting each of these methods, with their strengths and limitations, in a single manuscript, this review will assist cardiovascular biologists in understanding the existing literature on cardiac mechanical function, as well as designing future experiments.

Omecamtiv mecarbil lowers the contractile deficit in a mouse model of nebulin-based nemaline myopathy

Nemaline myopathy (NEM) is a congenital neuromuscular disorder primarily caused by nebulin gene (NEB) mutations. NEM is characterized by muscle weakness for which currently no treatments exist. In NEM patients a predominance of type I fibers has been found. Thus, therapeutic options targeting type I fibers could be highly beneficial for NEM patients. Because type I muscle fibers express the same myosin isoform as cardiac muscle (Myh7), the effect of omecamtiv mecarbil (OM), a small molecule activator of Myh7, was studied in a nebulin-based NEM mouse model (Neb cKO). Skinned single fibers were activated by exogenous calcium and force was measured at a wide range of calcium concentrations. Maximal specific force of type I fibers was much less in fibers from Neb cKO animals and calcium sensitivity of permeabilized single fibers was reduced (pCa₅₀ 6.12 ±0.08 (cKO) vs 6.36 ±0.08 (CON)). OM increased the calcium sensitivity of type I single muscle fibers. The greatest effect occurred in type I fibers from Neb cKO muscle where OM restored the calcium sensitivity to that of the control type I fibers. Forces at submaximal activation levels (pCa 6.0–6.5) were significantly increased in Neb cKO fibers (~50%) but remained below that of control fibers. OM also increased isometric force and power during isotonic shortening of intact whole soleus muscle of Neb cKO mice, with the largest effects at physiological stimulation frequencies. We conclude that OM has the potential to improve the quality of life of NEM patients by increasing the force of type I fibers at submaximal activation levels.

Yank: the time derivative of force is an important biomechanical variable in sensorimotor systems

The derivative of force with respect to time does not have a standard term in physics. As a consequence, the quantity has been given a variety of names, the most closely related being 'rate of force development'. The lack of a proper name has made it difficult to understand how different structures and processes within the sensorimotor system respond to and shape the dynamics of force generation, which is critical for survival in many species. We advocate that ∂[Formula: see text]/∂t be termed 'yank', a term that has previously been informally used and never formally defined. Our aim in this Commentary is to establish the significance of yank in how biological motor systems are organized, evolve and adapt. Further, by defining the quantity in mathematical terms, several measurement variables that are commonly reported can be clarified and unified. In this Commentary, we first detail the many types of motor function that are affected by the magnitude of yank generation, especially those related to time-constrained activities. These activities include escape, prey capture and postural responses to perturbations. Next, we describe the multi-scale structures and processes of the musculoskeletal system that influence yank and can be modified to increase yank generation. Lastly, we highlight recent studies showing that yank is represented in the sensory feedback system, and discuss how this information is used to enhance postural stability and facilitate recovery from postural perturbations. Overall, we promote an increased consideration of yank in studying biological motor and sensory systems.

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.

Thick-Filament Extensibility in Intact Skeletal Muscle

Myofilament extensibility is a key structural parameter for interpreting myosin cross-bridge kinetics in striated muscle. Previous studies reported much higher thick-filament extensibility at low tension than the better-known and commonly used values at high tension, but in interpreting mechanical studies of muscle, a single value for thick-filament extensibility has usually been assumed. Here, we established the complete thick-filament force-extension curve from actively contracting, intact vertebrate skeletal muscle. To access a wide range of tetanic forces, the myosin inhibitor blebbistatin was used to induce low tetanic forces in addition to the higher tensions obtained from tetanic contractions of the untreated muscle. We show that the force/extensibility curve of the thick filament is nonlinear, so assuming a single value for thick-filament extensibility at all force levels is not justified. We also show that independent of whether tension is generated passively by sarcomere stretch or actively by cross-bridges, the thick-filament extensibility is nonlinear. Myosin head periodicity, however, only changes when active tension is generated under calcium-activated conditions. The nonlinear thick-filament force-extension curve in skeletal muscle, therefore, reflects a purely passive response to either titin-based force or actomyosin-based force, and it does not include a thick-filament activation mechanism. In contrast, the transition of myosin head periodicity to an active configuration appears to only occur in response to increased active force when calcium is present.

Development of apical hypertrophic cardiomyopathy with age in a transgenic mouse model carrying the cardiac actin E99K mutation

In both humans and mice, the Glu-99-Lys (E99K) mutation in the cardiac actin gene (ACTC) results in little understood apical hypertrophic cardiomyopathy (AHCM). To determine how cross-bridge kinetics change with AHCM development, we applied sinusoidal length perturbations to skinned papillary muscle fibres from 2- and 5-month old E99K transgenic (Tg) and non-transgenic (NTg) mice, and studied tension and its transients. These age groups were chosen because our preliminary studies indicated that AHCM develops with age. Fibres from 5-month old E99K mice showed significant decreases in tension, stiffness, the rate of the medium-speed exponential process and its magnitude compared to non-transgenic control. The nucleotide association constants increased with age, and they were significantly larger in E99K compared to NTg. However, there were no large differences in the rates of the cross-bridge detachment step, the rates of the force generation step, or the phosphate association constant. Our result on force/cross-bridge demonstrates that the decreased active tension of E99K fibres was caused by a decreased amount of force generated per each cross-bridge. The effects were generally less or insignificant at 2 months. A pCa-tension study showed increased Ca²⁺-sensitivity (pCa₅₀) with age in both the E99K and NTg sample groups, and pCa₅₀ was significantly larger (but only for 0.05-0.06 pCa units) in E99K than in NTg groups. A significant decrease in cooperativity (n_H) was observed only in 5-month old E99K mice. We conclude that the AHCM-causing ACTC E99K mutation is associated with progressive alterations in biomechanical parameters, with changes smaller at 2 months but larger at 5 months, correlating with the development of AHCM.

Kinetic coupling of phosphate release, force generation and rate-limiting steps in the cross-bridge cycle

A basic goal in muscle research is to understand how the cyclic ATPase activity of cross-bridges is converted into mechanical force. A direct approach to study the chemo-mechanical coupling between P_i release and the force-generating step is provided by the kinetics of force response induced by a rapid change in [P_i]. Classical studies on fibres using caged-P_i discovered that rapid increases in [P_i] induce fast force decays dependent on final [P_i] whose kinetics were interpreted to probe a fast force-generating step prior to P_i release. However, this hypothesis was called into question by studies on skeletal and cardiac myofibrils subjected to P_i jumps in both directions (increases and decreases in [P_i]) which revealed that rapid decreases in [P_i] trigger force rises with slow kinetics, similar to those of calcium-induced force development and mechanically-induced force redevelopment at the same [P_i]. A possible explanation for this discrepancy came from imaging of individual sarcomeres in cardiac myofibrils, showing that the fast force decay upon increase in [P_i] results from so-called sarcomere 'give'. The slow force rise upon decrease in [P_i] was found to better reflect overall sarcomeres cross-bridge kinetics and its [P_i] dependence, suggesting that the force generation coupled to P_i release cannot be separated from the rate-limiting transition. The reasons for the different conclusions achieved in fibre and myofibril studies are re-examined as the recent findings on cardiac myofibrils have fundamental consequences for the coupling between P_i release, rate-limiting steps and force generation. The implications from P_i-induced force kinetics of myofibrils are discussed in combination with historical and recent models of the cross-bridge cycle.

High ionic strength depresses muscle contractility by decreasing both force per cross-bridge and the number of strongly attached cross-bridges

An increase in ionic strength (IS) lowers Ca(2+) activated tension in muscle fibres, however, its molecular mechanism is not well understood. In this study, we used single rabbit psoas fibres to perform sinusoidal analyses. During Ca(2+) activation, the effects of ligands (ATP, Pi, and ADP) at IS ranging 150-300 mM were studied on three rate constants to characterize elementary steps of the cross-bridge cycle. The IS effects were studied because a change in IS modifies the inter- and intra-molecular interactions, hence they may shed light on the molecular mechanisms of force generation. Both the ATP binding affinity (K1) and the ADP binding affinity (K 0) increased to 2-3x, and the Pi binding affinity (K5) decreased to 1/2, when IS was raised from 150 to 300 mM. The effect on ATP/ADP can be explained by stereospecific and hydrophobic interaction, and the effect on Pi can be explained by the electrostatic interaction with myosin. The increase in IS increased cross-bridge detachment steps (k2 and k-4), indicating that electrostatic repulsion promotes these steps. However, IS did not affect attachment steps (k-2 and k4). Consequently, the equilibrium constant of the detachment step (K2) increased by ~100%, and the force generation step (K4) decreased by ~30%. These effects together diminished the number of force-generating cross-bridges by 11%. Force/cross-bridge (T56) decreased by 26%, which correlates well with a decrease in the Debye length that limits the ionic atmosphere where ionic interactions take place. We conclude that the major effect of IS is a decrease in force/cross-bridge, but a decrease in the number of force generating cross-bridge also takes place. The stiffness during rigor induction did not change with IS, demonstrating that in-series compliance is not much affected by IS.