Force transients and minimum cross-bridge models in muscular contraction

Oscillatory work and the step that generates force in single myofibrils from rabbit psoas

The elementary molecular step that generates force by cross-bridges (CBs) in active muscles has been under intense investigation in the field of muscle biophysics. It is known that an increase in the phosphate (Pi) concentration diminishes isometric force in active fibers, indicating a tight coupling between the force generation step and the Pi release step. The question asked here is whether the force generation occurs before Pi release or after release. We investigated the effect of Pi on oscillatory work production in single myofibrils and found that Pi-attached state(s) to CBs is essential for its production. Oscillatory work is the mechanism that allows an insect to fly by beating its wings, and it also has been observed in skeletal and cardiac muscle fibers, implying that it is an essential feature of all striated muscle types. With our studies, oscillatory work disappears in the absence of Pi in experiments using myofibrils. This suggests that force is generated during a transition between steps of oscillatory work production, and that the states involved in force production must have Pi attached. With sinusoidal analysis, we obtained the kinetic constants around the Pi release steps, established a CB scheme, and evaluated force generated (and supported) by each CB state. Our results demonstrate that force is generated before Pi is released, and the same force is maintained after Pi is released. Stretch activation and/or delayed tension can also be explained with this CB scheme and forms the basis of force generation and oscillatory work production.

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.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

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.

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.

Comparison of elementary steps of the cross-bridge cycle in rat papillary muscle fibers expressing α- and β-myosin heavy chain with sinusoidal analysis

In mammalian ventricles, two myosin heavy chain (MHC) isoforms have been identified. Small animals express α-MHC, whereas large animals express β-MHC, which contribute to a large difference in the heart rate. Sprague-Dawley rats possessing ~99% α-MHC were treated with propylthiouracil to result in 100% β-MHC. Papillary muscles were skinned, dissected into small fibers, and used for experiments. To understand the functional difference between α-MHC and β-MHC, skinned-fibers were activated under the intracellular ionic conditions: 5 mM MgATP, 1 mM Mg²⁺, 8 mM Pi, 200 mM ionic strength, pH 7.00 at 25 °C. Small amplitude sinusoidal length oscillations were applied in the frequency range 0.13-100 Hz (corresponding time domain: 1.6-1200 ms), and effects of Ca²⁺, Pi, and ATP were studied. The results show that Ca²⁺ sensitivity was slightly less (10-15%) in β-MHC than α-MHC containing fibers. Sinusoidal analysis at pCa 4.66 (full Ca²⁺ activation) demonstrated that, the apparent rate constants were 2-4× faster in α-MHC containing fibers. The ATP study demonstrated that, in β-MHC containing fibers, K ₁ (ATP association constant) was greater (1.7×), k ₂ and k _-2 (cross-bridge detachment and its reversal rate constants) were smaller (×0.6). The Pi study demonstrated that, in β-MHC containing fibers, k ₄ (rate constant of the force-generation step) and k _-4 were smaller (0.75× and 0.25×, respectively), resulting in greater K ₄ (3×). There were no differences in active tension, rigor stiffness, or K ₂ (equilibrium constant of the cross-bridge detachment step). Our study further demonstrated that there were no differences in parameters between fibers obtained from left and right ventricles, but with an exception in K ₅ (Pi association constant).

Cardiac Myosin Binding Protein-C Phosphorylation Modulates Myofilament Length-Dependent Activation

Cardiac myosin binding protein-C (cMyBP-C) phosphorylation is an important regulator of contractile function, however, its contributions to length-dependent changes in cross-bridge (XB) kinetics is unknown. Therefore, we performed mechanical experiments to quantify contractile function in detergent-skinned ventricular preparations isolated from wild-type (WT) hearts, and hearts expressing non-phosphorylatable cMyBP-C [Ser to Ala substitutions at residues Ser273, Ser282, and Ser302 (i.e., 3SA)], at sarcomere length (SL) 1.9 μm or 2.1μm, prior and following protein kinase A (PKA) treatment. Steady-state force generation measurements revealed a blunting in the length-dependent increase in myofilament Ca(2+)-sensitivity of force generation (pCa50) following an increase in SL in 3SA skinned myocardium compared to WT skinned myocardium. Dynamic XB behavior was assessed at submaximal Ca(2+)-activations by imposing an acute rapid stretch of 2% of initial muscle length, and measuring both the magnitudes and rates of resultant phases of force decay due to strain-induced XB detachment and delayed force rise due to recruitment of additional XBs with increased SL (i.e., stretch activation). The magnitude (P2) and rate of XB detachment (k rel) following stretch was significantly reduced in 3SA skinned myocardium compared to WT skinned myocardium at short and long SL, and prior to and following PKA treatment. Furthermore, the length-dependent acceleration of k rel due to decreased SL that was observed in WT skinned myocardium was abolished in 3SA skinned myocardium. PKA treatment accelerated the rate of XB recruitment (k df) following stretch at both SL's in WT but not in 3SA skinned myocardium. The amplitude of the enhancement in force generation above initial pre-stretch steady-state levels (P3) was not different between WT and 3SA skinned myocardium at any condition measured. However, the magnitude of the entire delayed force phase which can dip below initial pre-stretch steady-state levels (Pdf) was significantly lower in 3SA skinned myocardium under all conditions, in part due to a reduced magnitude of XB detachment (P2) in 3SA skinned myocardium compared to WT skinned myocardium. These findings demonstrate that cMyBP-C phospho-ablation regulates SL- and PKA-mediated effects on XB kinetics in the myocardium, which would be expected to contribute to the regulation of the Frank-Starling mechanism.

Cardiac myosin binding protein C phosphorylation affects cross-bridge cycle's elementary steps in a site-specific manner

Based on our recent finding that cardiac myosin binding protein C (cMyBP-C) phosphorylation affects muscle contractility in a site-specific manner, we further studied the force per cross-bridge and the kinetic constants of the elementary steps in the six-state cross-bridge model in cMyBP-C mutated transgenic mice for better understanding of the influence of cMyBP-C phosphorylation on contractile functions. Papillary muscle fibres were dissected from cMyBP-C mutated mice of ADA (Ala273-Asp282-Ala302), DAD (Asp273-Ala282-Asp302), SAS (Ser273-Ala282-Ser302), and t/t (cMyBP-C null) genotypes, and the results were compared to transgenic mice expressing wide-type (WT) cMyBP-C. Sinusoidal analyses were performed with serial concentrations of ATP, phosphate (Pi), and ADP. Both t/t and DAD mutants significantly reduced active tension, force per cross-bridge, apparent rate constant (2πc), and the rate constant of cross-bridge detachment. In contrast to the weakened ATP binding and enhanced Pi and ADP release steps in t/t mice, DAD mice showed a decreased ADP release without affecting the ATP binding and the Pi release. ADA showed decreased ADP release, and slightly increased ATP binding and cross-bridge detachment steps, whereas SAS diminished the ATP binding step and accelerated the ADP release step. t/t has the broadest effects with changes in most elementary steps of the cross-bridge cycle, DAD mimics t/t to a large extent, and ADA and SAS predominantly affect the nucleotide binding steps. We conclude that the reduced tension production in DAD and t/t is the result of reduced force per cross-bridge, instead of the less number of strongly attached cross-bridges. We further conclude that cMyBP-C is an allosteric activator of myosin to increase cross-bridge force, and its phosphorylation status modulates the force, which is regulated by variety of protein kinases.

Phosphorylation of cMyBP-C affects contractile mechanisms in a site-specific manner

Cardiac myosin binding protein-C (cMyBP-C) is a cardiac-specific, thick-filament regulatory protein that is differentially phosphorylated at Ser(273), Ser(282), and Ser(302) by various kinases and modulates contraction. In this study, phosphorylation-site-specific effects of cMyBP-C on myocardial contractility and cross-bridge kinetics were studied by sinusoidal analysis in papillary and trabecular muscle fibers isolated from t/t (cMyBP-C-null) mice and in their counterparts in which cMyBP-C contains the ADA (Ala(273)-Asp(282)-Ala(302)), DAD (Asp(273)-Ala(282)-Asp(302)), and SAS (Ser(273)-Ala(282)-Ser(302)) mutations; the results were compared to those from mice expressing the wild-type (WT) transgene on the t/t background. Under standard activating conditions, DAD fibers showed significant decreases in tension (~50%), stiffness, the fast apparent rate constant 2πc, and its magnitude C, as well as its magnitude H, but an increase in the medium rate constant 2πb, with respect to WT. The t/t fibers showed a smaller drop in stiffness and a significant decrease in 2πc that can be explained by isoform shift of myosin heavy chain. In the pCa-tension study using the 8 mM phosphate (Pi) solution, there was hardly any difference in Ca(2+) sensitivity (pCa50) and cooperativity (nH) between the mutant and WT samples. However, in the solutions without Pi, DAD showed increased nH and slightly decreased pCa50. We infer from these observations that the nonphosphorylatable residue 282 combined with phosphomimetic residues Asp(273) and/or Asp(302) (in DAD) is detrimental to cardiomyocytes by lowering isometric tension and altering cross-bridge kinetics with decreased 2πc and increased 2πb. In contrast, a single change of residue 282 to nonphosphorylatable Ala (SAS), or to phosphomimetic Asps together with the changes of residues 273 and 302 to nonphosphorylatable Ala (ADA) causes minute changes in fiber mechanics.

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

A slackening to zero tension by large length release (~20%) and a restretch of active muscle fibres cause a fall and a redevelopment in tension. According to the model of Brenner (Proc Natl Acad Sci USA 85(9):3265-3269, 1988), the rate constant of tension redevelopment (k TR) is the sum of attachment and detachment rate constants, hence is limited by the fast reaction. Here we propose a model in which, after restretch, cross-bridges cycle many times by stretching series elastic elements, hence k(TR) is limited by a slow reaction. To set up this model, we made an assumption that the stepping rate (v) decreases linearly with tension (F), which is consistent with the Fenn effect. The distance traveled by a cross-bridge stretches series elastic elements with stiffness σ. With these assumptions, we set up a first order differential equation, which results in an exponential time course with the rate constant k(TR) = ση(0)ν(0)(1 - λ)/F(1), where λ = ν(1)/ν(0), η = step size, the subscript 0 indicates unloaded condition, and the subscript 1 indicate isometric condition. We demonstrate that the ATP hydrolysis rate (=[myosin head]/ν(0)) is proportionate to k(TR) as the ambient temperature is changed, and that the published data fit to this relationship well if λ = 0.28. We conclude that k(TR) is limited by the cross-bridge turnover rate; hence it represents the rate constant of the slowest reaction of the cross-bridge cycle, i.e. the ADP isomerization step before ADP is released.

Diversity and similarity of motor function and cross-bridge kinetics in papillary muscles of transgenic mice carrying myosin regulatory light chain mutations D166V and R58Q

Mechanical properties of skinned papillary muscle fibers from transgenic mice expressing familial hypertrophic cardiomyopathy associated mutations D166V and R58Q in myosin regulatory light chain were investigated. Elementary steps and the apparent rate constants of the cross-bridge cycle were characterized from the tension transients induced by sinusoidal length changes during maximal Ca(2+) activation, together with ATP, ADP, and Pi studies. The tension-pCa relation was also tested in two sets of solutions with differing Pi and ionic strength. Our results showed that in both mutants the fast apparent rate constant 2πc and the rate constants of the cross-bridge detachment step (k2) were smaller than those of wild type (WT), demonstrating the slower cross-bridge kinetics. D166V showed significantly smaller ATP (K1) and ADP (K0) association constants than WT, displaying weaker ATP binding and easier ADP release, whereas those of R58Q were not significantly different from WT. In tension-pCa study, both D166V and R58Q mutations exhibited increased Ca(2+) sensitivity and less cooperativity. We conclude that, while the two FHC mutations have similar clinical manifestations and prognosis, some of the mechanical parameters of cross-bridges (K0, K1) are differently modified, whereas some others (Ca(2+)-sensitivity, cooperativity, k2) are similarly modified by these two FHC associated mutations.

The p90 ribosomal S6 kinase (RSK) is a mediator of smooth muscle contractility

In the canonical model of smooth muscle (SM) contraction, the contractile force is generated by phosphorylation of the myosin regulatory light chain (RLC₂₀) by the myosin light chain kinase (MLCK). Moreover, phosphorylation of the myosin targeting subunit (MYPT1) of the RLC₂₀ phosphatase (MLCP) by the RhoA-dependent ROCK kinase, inhibits the phosphatase activity and consequently inhibits dephosphorylation of RLC₂₀ with concomitant increase in contractile force, at constant intracellular [Ca²⁺]. This pathway is referred to as Ca²⁺-sensitization. There is, however, emerging evidence suggesting that additional Ser/Thr kinases may contribute to the regulatory pathways in SM. Here, we report data implicating the p90 ribosomal S6 kinase (RSK) in SM contractility. During both Ca²⁺- and agonist (U46619) induced SM contraction, RSK inhibition by the highly selective compound BI-D1870 (which has no effect on MLCK or ROCK) resulted in significant suppression of contractile force. Furthermore, phosphorylation levels of RLC₂₀ and MYPT1 were both significantly decreased. Experiments involving the irreversible MLCP inhibitor microcystin-LR, in the absence of Ca²⁺, revealed that the decrease in phosphorylation levels of RLC₂₀ upon RSK inhibition are not due solely to the increase in the phosphatase activity, but reflect direct or indirect phosphorylation of RLC₂₀ by RSK. Finally, we show that agonist (U46619) stimulation of SM leads to activation of extracellular signal-regulated kinases ERK1/2 and PDK1, consistent with a canonical activation cascade for RSK. Thus, we demonstrate a novel and important physiological function of the p90 ribosomal S6 kinase, which to date has been typically associated with the regulation of gene expression.

ATP binding and cross-bridge detachment steps during full Ca²⁺ activation: comparison of myofibril and muscle fibre mechanics by sinusoidal analysis

Single myofibrils 50–60 μm length and 2–3 μm diameter were isolated from rabbit psoas muscle fibres, and cross-bridge kinetics were studied by small perturbations of the length (∼0.2%) over a range of 15 frequencies (1–250 Hz). The experiments were performed at 15◦C in the presence of 0.05–10 mM MgATP, 8mM phosphate (Pi), 200 mM ionic strength with KAc (acetate), pCa 4.35–4.65, and pH 7.0. Two exponential processes, B and C, were resolved in tension transients. Their apparent rate constants (2πb and 2πc) increased as the [MgATP] was raised from 0.05 mM to 1mM, and then reached saturation at [MgATP] ≥ 1. Given that these rate constants were similar (c/b ∼1.7) at [Pi] ≥ 4 mM, they were combined to achieve an accurate estimate of the kinetic constants: their sum and product were analysed as functions of [MgATP]. These analyses yielded K1 =2.91 ± 0.31 mM −1, k2 =288 ± 36 s−1, and k−2 =10 ± 21 s−1 (±95% confidence limit, n =13 preparations), based on the cross-bridge model: AM+ATP ↔ (step 1) AM.ATP ↔ (step 2) A+M.ATP, where K1 is the ATP association constant (step 1), k2 is the rate constant of the cross-bridge detachment (step 2), and k−2 is the rate constant of its reversal step. These kinetic constants are respectively comparable to those observed in single fibres from rabbit psoas (K1 =2.35 ± 0.31 mM −1, k2 =243 ± 22 s−1, and k−2 =6 ± 14 s−1; n =8 preparations) when analysed by the same methods and under the same experimental conditions. These values are respectively not significantly different from those obtained in myofibrils, indicating that the same kinetic constants can be deduced from myofibril and muscle fibre studies, in terms of ATP binding and cross-bridge detachments steps. The fact that K1 in myofibrils is 1.2 times that in fibres (P≈0.05) may be explained by a small concentration gradient of ATP, ADP and/or Pi in single fibres.

Correlation between cross-bridge kinetics obtained from Trp fluorescence of myofibril suspensions and mechanical studies of single muscle fibers in rabbit psoas

Our goal is to correlate kinetic constants obtained from fluorescence studies of myofibril suspension with those from mechanical studies of skinned muscle fibers from rabbit psoas. In myofibril studies, the stopped-flow technique with tryptophan fluorescence was used; in muscle fiber studies, tension transients with small amplitude sinusoidal length perturbations were used. All experiments were performed using the equivalent solution conditions (200 mM ionic strength, pH 7.00) at 10°C. The concentration of MgATP was varied to characterize kinetic constants of the ATP binding step 1 (K (1): dissociation constant), the binding induced cross-bridge detachment step 2 (k (2), k (-2): rate constants), and the ATP cleavage step 3 (k (3), k (-3)). In myofibrils we found that K (1) = 0.52 ± 0.08 mM (±95% confidence limits), k (2) = 242 ± 24 s(-1), and k (-2) ≈ 0; in muscle fibers, K (1) = 0.46 ± 0.06 mM, k (2) = 286 ± 32 s(-1), and k (-2) = 57 ± 21 s(-1). From these results, we conclude that myofibrils and muscle fibers exhibit nearly equal ATP binding step, and nearly equal ATP binding induced cross-bridge detachment step. Consequently, there is a good correlation between process C (phase 2 of step analysis) and the cross-bridge detachment step. The reverse detachment step is finite in fibers, but almost absent in myofibrils. We further studied partially cross-linked myofibrils and found little change in steps 2 and 3, indicating that cross-linking does not affect these steps. However, we found that K (1) is 2.5× of native myofibrils, indicating that MgATP binding is weakened by the presence of the extra load. We further studied the phosphate (Pi) effect in myofibrils, and found that Pi is a competitive inhibitor of MgATP, with the inhibitory dissociation constant of ~9 mM. Similar results were also deduced from fiber studies. To characterize the ATP cleavage step in myofibrils, we measured the slow rate constant in fluorescence, and found that k (3) + k (-3) = 16 ± 1 s(-1).

Measuring myosin cross-bridge attachment time in activated muscle fibers using stochastic vs. sinusoidal length perturbation analysis

The average time myosin cross bridges remain bound to actin (t(on)) can be measured by sinusoidal length perturbations (sinusoidal analysis) of striated muscle fibers using recently developed analytic methods. This approach allows measurements of t(on) in preparations possessing a physiologically relevant myofilament lattice. In this study, we developed an approach to measure t(on) in 5-10% of the time required for sinusoidal analysis by using stochastic length perturbations (white noise analysis). To compare these methods, we measured the influence of MgATP concentration ([MgATP]) on t(on) in demembranated myocardial strips from mice, sampling muscle behavior from 0.125 to 200 Hz with a 20-s burst of white noise vs. a 300-s series of sinusoids. Both methods detected a similar >300% increase in t(on) as [MgATP] decreased from 5 to 0.25 mM, differing by only 3-14% at any [MgATP]. Additional experiments with Drosophila indirect flight muscle fibers demonstrated that faster cross-bridge cycling kinetics permit further reducing of the perturbation time required to measure t(on). This reduced sampling time allowed strain-dependent measurements of t(on) in flight muscle fibers by combining 10-s bursts of white noise during periods of linear shortening and lengthening. Analyses revealed longer t(on) values during shortening and shorter t(on) values during lengthening. This asymmetry may provide a mechanism that contributes to oscillatory energy transfer between the flight muscles and thoracic cuticle to power flight. This study demonstrates that white noise analysis can detect underlying molecular processes associated with dynamic muscle contraction comparable to sinusoidal analysis, but in a fraction of the time.

Model representation of the nonlinear step response in cardiac muscle

Motivated by the need for an analytical tool that can be used routinely to analyze data collected from isolated, detergent-skinned cardiac muscle fibers, we developed a mathematical model for representing the force response to step changes in muscle length (i.e., quick stretch and release). Our proposed model is reasonably simple, consisting of only five parameters representing: (1) the rate constant by which length change–induced distortion of elastic elements is dissipated; (2) the stiffness of the muscle fiber; (3) the amplitude of length-mediated recruitment of stiffness elements; (4) the rate constant by which this length-mediated recruitment takes place; and (5) the magnitude of the nonlinear interaction term by which distortion of elastic elements affects the number of recruited stiffness elements. Fitting this model to a family of force recordings representing responses to eight amplitudes of step length change (±2.0% baseline muscle length in 0.5% increments) enabled four things: (1) reproduction of all the identifiable features seen in a family of force responses to both positive and negative length changes; (2) close fitting of all records from the whole family of these responses with very little residual error; (3) estimation of all five model parameters with a great degree of certainty; and (4) importantly, ready discrimination between cardiac muscle fibers with different contractile regulatory proteins but showing only subtly different contractile function. We recommend this mathematical model as an analytic tool for routine use in studies of cardiac muscle fiber contractile function. Such model-based analysis gives novel insight to the contractile behavior of cardiac muscle fibers, and it is useful for characterizing the mechanistic effects that alterations of cardiac contractile proteins have on cardiac contractile function.

Length-dependent modulation of cytoskeletal remodeling and mechanical energetics in airway smooth muscle

Actin cytoskeletal remodeling is an important mechanism of airway smooth muscle (ASM) contraction. We tested the hypothesis that mechanical strain modulates the cholinergic receptor-mediated cytoskeletal recruitment of actin-binding and integrin-binding proteins in intact airway smooth muscle, thereby regulating the mechanical energetics of airway smooth muscle. We found that the carbachol-stimulated cytoskeletal recruitment of actin-related protein-3 (Arp3), metavinculin, and talin were up-regulated at short muscle lengths and down-regulated at long muscle lengths, suggesting that the actin cytoskeleton--integrin complex becomes enriched in cross-linked and branched actin filaments in shortened ASM. The mechanical energy output/input ratio during sinusoidal length oscillation was dependent on muscle length, oscillatory amplitude, and cholinergic activation. The enhancing effect of cholinergic stimulation on mechanical energy output/input ratio at short and long muscle lengths may be explained by the length-dependent modulation of cytoskeletal recruitment and crossbridge cycling, respectively. We postulate that ASM functions as a hybrid biomaterial, capable of switching between operating as a cytoskeleton-based mechanical energy store at short muscle lengths to operating as an actomyosin-powered mechanical energy generator at long muscle lengths. This postulate predicts that targeting the signaling molecules involved in cytoskeletal recruitment may provide a novel approach to dilating collapsed airways in obstructive airway disease.

Tropomyosin period 3 is essential for enhancement of isometric tension in thin filament-reconstituted bovine myocardium

Tropomyosin (Tm) consists of 7 quasiequivalent repeats known as "periods," and its specific function may be associated with these periods. To test the hypothesis that either period 2 or 3 promotes force generation by inducing a positive allosteric effect on actin, we reconstituted the thin filament with mutant Tm in which either period 2 (Delta2Tm) or period 3 (Delta3Tm) was deleted. We then studied: isometric tension, stiffness, 6 kinetic constants, and the pCa-tension relationship. N-terminal acetylation of Tm did not cause any differences. The isometric tension in Delta2Tm remained unchanged, and was reduced to approximately 60% in Delta3Tm. Although the kinetic constants underwent small changes, the occupancy of strongly attached cross-bridges was not much different. The Hill factor (cooperativity) did not differ significantly between Delta2Tm (1.79 +/- 0.19) and the control (1.73 +/- 0.21), or Delta3Tm (1.35 +/- 0.22) and the control. In contrast, pCa(50) decreased slightly in Delta2Tm (5.11 +/- 0.07), and increased significantly in Delta3Tm (5.57 +/- 0.09) compared to the control (5.28 +/- 0.04). These results demonstrate that, when ions are present at physiological concentrations in the muscle fiber system, period 3 (but not period 2) is essential for the positive allosteric effect that enhances the interaction between actin and myosin, and increases isometric force of each cross-bridge.

Motor protein function in skeletal muscle-a multiple scale approach to contractility

We present an approach to skeletal muscle contractility and its regulation over different scales ranging from biomechanical studies in intact muscle fibers down to the motility and interaction of single motor protein molecules. At each scale, shortening velocities as a measure for weak cross-bridge cycling rates are extracted and compared. Experimental approaches include transmitted light microscopy, second harmonic generation imaging of contracting myofibrils, and fluorescence microscopy of single molecule motility. Each method yields image sequences that are analyzed with automated image processing algorithms to extract the contraction velocity. Using this approach, we show how to isolate the contribution of the motor proteins actin and myosin and their modulation by regulatory proteins from the concerted action of electro-mechanical activation on a more complex cellular scale. The advantage of this approach is that averaged contraction velocities can be determined on the different scales ranging from isolated motor proteins to sarcomere levels in myofibrils and myofibril arrays within the cellular architecture. Our results show that maximum shortening velocities during in situ electrical activation of sarcomere contraction in intact single muscle cells can substantially deviate from sliding velocities obtained in oriented in vitro motility assays of isolated motor proteins showing that biophysical contraction kinetics not simply translate linearly between contractility scales. To adequately resolve the very fast initial mechanical activation kinetics of shortening at each scale, it was necessary to implement high-speed imaging techniques. In the case of intact fibers and single molecule motility, we achieved a major increase in temporal resolution up to frame rates of 200-1000 fps using CMOS image sensor technology. The data we obtained at this unprecedented temporal resolution and the parameters extracted can be used to validate results obtained from computational models of motor protein interaction and skeletal muscle contractility in health and muscle disease. Our approach is feasible to explain the possible underlying mechanisms that contribute to different shortening velocities at different scales and complexities.

Molecular basis of the catch state in molluscan smooth muscles: a catchy challenge

The catch state (or 'catch') of molluscan smooth muscles is a passive holding state that occurs after cessation of stimulation. During catch, force and, in particular, resistance to stretch are maintained for long time periods with low (or no) energy consumption at basal intracellular free [Ca2+]. The catch state is initiated by Ca2+-stimulated dephosphorylation of the titin-like protein twitchin and is inhibited by cAMP-dependent phosphorylation of twitchin. In addition, catch is pH sensitive, but the reason for this is unknown. According to a traditional model, catch is due to slower cross-bridge cycles where myosin heads remain longer attached to the actin filaments after force generation, possibly caused by a hindered release of ADP from the myosin heads. However, this model was disproved by recent findings which showed that (i) inhibitors of myosin function, such as vanadate, do not affect catch force; (ii) factors which terminate the catch state do not accelerate myosin head detachment kinetics and (iii) a catch-like high resistance to stretch is still inducible when force development is prevented. Thus, catch probably involves passive linkage structures interconnecting the myofilaments (catch linkages). For example twitchin could (i) tie myosin heads to the thin filaments, (ii) mechanically lock them in a stretch resistant state or (iii) interconnect thick and thin filaments directly. However, it is questionable if these mechanisms are sufficient since twitchin seems to be about 15-times less abundant than myosin. Therefore, in addition, interconnections between thick filaments could exist, which could involve e.g. paramyosin or twitchin. Catch could even involve changes in the compliance of thick filaments. The function of myorod, found specifically in catch muscles in equal abundance with myosin, is not known. The suggestion is made here that catch linkages are present already during active contraction either as ratchet-like elements resisting stretch and not opposing shortening or in some kind of 'standby' mode ready to transform suddenly into the working mode by stretches or after Ca2+ removal following cessation of stimulation.