Investigation into the mechanism of thin filament regulation by transient kinetics and equilibrium binding: Is there a conflict?

The striated muscle thin filament is a repeating assembly of the proteins actin, tropomyosin, and troponins I, C, and T. An extensive network of connections exist between the various components. When ligands (either Ca[II] or rigor myosin-S1) associate with the thin filament, there is a perturbation in the network that ultimately leads to contraction. When they dissociate, the muscle relaxes.

Understanding of the details of the regulatory mechanism has changed over the years. Steric interference of myosin binding by tropomyosin-troponin (Haselgrove, 1972; Huxley, 1972; Parry and Squire, 1973) offered an attractive molecular explanation for how regulation occurred but was subsequently found to be a minor part of the mechanism (Chalovich and Eisenberg, 1982). The models of Hill envisaged two structural thin filament states (Hill et al., 1980, 1983). The most widely cited model envisages three such states (blocked, closed, and open; McKillop and Geeves, 1993; Lehman, 2017). These models were derived from equilibrium binding and other experiments in which myosin (M) is not hydrolyzing ATP. Our approach has been to first identify the regulated step in an active actomyosin cycle with a view to then comparing the thin filament ligand sensitivity of different myosin conformers.

Stopped-flow kinetics are ideally suited to investigating the issue of regulation of actomyosin ATP hydrolysis and muscle contraction. In multi-mixing mode, myosin subfragments and ATP are first mixed for 1–2 s to produce the steady-state intermediates (i.e., M-ATP and M–ADP–inorganic phosphate [Pi]) followed by mixing with thin filaments at various stages of activation by ligand (Fig. 1). Such experiments are typically performed at high concentrations of actin and well below physiological ionic strength, due to the highly salt-sensitive interaction of myosin and actin. The availability of reporter probes has enabled specific steps in the cycle (i.e., Pi and ADP dissociation) to be measured. In this work, fluorescent nucleotides and a Pi binding protein have been used. Such reagents are designed only to respond to changes in chemical states. With either type of probe, Pi dissociation (AM-ADP-Pi → AM-ADP + Pi) is demonstrated to be the dominant regulatory mechanism (Heeley et al., 2002, 2006; Houmeida et al., 2010). The combined binding of Ca(II) and rigor myosin-S1 to the thin filament produces a substantial (80–140-fold) activation in the rate of the Pi dissociation step. In contrast, the dissociation of nucleoside diphosphate from post–power stoke myosin is only accelerated 10–12-fold. Thus, regulation is dependent on the thin filament state and also the conformation of the myosin head (pre– vs. post–power stroke).

A number of techniques have been used to investigate the kinetic properties of the myosin (or actomyosin)–product complex, including proton release (Finlayson and Taylor, 1969), changes in intrinsic fluorescence (Bagshaw and Trentham, 1973), and oxygen exchange (Pi/water; Bagshaw and Trentham, 1973). The first “definitive” measurement involved rapid size-exclusion chromatography (Taylor et al., 1970; Lymn and Taylor, 1971). Performed at low temperature to reduce the rate of reaction, the rate of chemical hydrolysis on myosin alone was demonstrated to be some 100-fold faster than the maximum steady-state MgATPase (hydrolysis) rate, indicating that product dissociation (from myosin) is rate-limiting and stimulated by actin. These and other observations led to the formulation of the Lymn–Taylor model (Lymn and Taylor, 1971). Quoting from their 1971 paper, “The essential features are that actomyosin dissociation precedes hydrolysis and activation is produced by recombination of actin with the myosin products complex with displacement of product.” The model provided a biochemical explanation for contraction and is still relevant today.

The Steric Blocking hypothesis proposed that tropomyosin physically hinders the complexation of actin and myosin at low [Ca(II)] but not high (Haselgrove, 1972; Huxley, 1972; Parry and Squire, 1973). However, measurement of the affinity of myosin-S1-ATP and S1-ADP-Pi for thin filaments by time-resolved light scattering (Chalovich et al., 1981) and sedimentation (Chalovich and Eisenberg, 1982) showed the effect of Ca(II) on binding was disproportionately small (approximately twofold) when compared with the effect on the ATPase rate. From these results, it became apparent that regulation could not operate on the basis of a simple steric blocking mechanism. Quoting from Chalovich and Eisenberg (1982), “These data do not support a simple steric blocking model of muscle relaxation. Rather they suggest that, in the absence of Ca(II), troponin-tropomyosin inhibits a kinetic step, perhaps Pi release, in the cycle of ATP hydrolysis.”

The above proposal was investigated (Rosenfeld and Taylor, 1987a) using a double-mixing stopped-flow spectrofluorimeter in conjunction with the fluorescent nucleotide etheno-ATP, a base-modified analogue (Secrist et al., 1972). The custom-made instrument was pressure-driven with a dead-time of 1–2 ms. An intermix adjustable delay allowed for the selection of a steady-state mixture of myosin bound with either substrate (M-NTP) or products (M-NDP-Pi). The mixture was combined, in the second mix, with thin filaments (either at pCa 4 or 8) containing ATP to eliminate any unwanted rigor activation, and “decay” of the pre–power stroke complex was then monitored for a single turnover of the cycle. The observed rates of the fluorescence changes when plotted against concentration conformed to hyperbolae that extrapolated to maxima of 20–25 (pCa 4) and 1 (pCa 8) per second, at least a 20-fold induction. At the same time, the bound hydrolysis rate was comparatively insensitive to Ca(II) (less than twofold as determined by quench flow). This study provided the first real insight into the mechanism of Ca(II) regulation.

A significant advance in the field was the development of an inorganic phosphate reporter protein (Brune et al., 1994). Bacterial Pi binding protein (PBP) is synthesized in response to Pi starvation whereupon it accumulates in the periplasmic space. It is small, monomeric, contains a single, high-affinity site (K_d, 100 nM), and binds Pi rapidly (rate constant, k, 1.4 × 10⁸ M⁻¹ s⁻¹). Furthermore, the 3-D structure had been solved (Luecke and Quiocho, 1990). Covalent linkage of a coumarin derivative to cysteine-197 (introduced adjacent to the binding cleft) created a reagent having Pi-sensitive emission (Brune et al., 1994). Armed with the fluorescently labeled PBP, it became feasible to track Pi transients directly. Examples are presented in Fig. 2, A and B.

Essentially the same single-turnover, double-mixing approach of Rosenfeld and Taylor (1987a) was taken by White and coworkers in which they were able to use the natural substrate ATP. Using fluorescent PBP, a 1,000-fold acceleration of the rate of dissociation of Pi from pre–power stroke myosin-S1-ADP-Pi by actin relative to myosin alone was demonstrated (White et al., 1997). In these experiments, actin binds to myosin-ATP and myosin-ADP-Pi within the dead-time of the second mix, and the fluorescence trace consists of two components. The faster of the two phases stems from dissociation of Pi from AM-ADP-Pi, whereas the slower emanates from the AM-ATP population in which the rate is limited by the rate of hydrolysis of the ATP bound to AM (see Scheme 1). At 20°C, the maximum rates of the two phases, extrapolated from their concentration dependences, are 75 and 3 s⁻¹ (White et al., 1997; Table 1). This study also provided clear evidence for an ordered release of products, Pi followed by ADP.

In a follow-up to White et al. (1997), regulatory proteins (whole troponin and tropomyosin) were prepared from rabbit skeletal muscle consisting mostly of fast contracting fibers. Because there is variation between different preparations of isolated troponin, reconstituted thin filaments were first assessed by steady-state ATPase assay. Those batches of troponin that produced thin filaments that gave at least 15-fold Ca(II) sensitivity (mole ratio of S1: actin = 1:70 to 1:120; low ionic strength) of the rate were selected for use. The rate of Pi release (i.e., AM-ADP-Pi → AM-ADP + Pi) was demonstrated to be acutely sensitive to the association of Ca(II) and rigor myosin with the thin filament (Heeley et al., 2002) but not in a way predicted by the Three-State or classical Steric Blocking models. When the thin filaments are turned off (i.e., apo, no bound ligands; i.e. , EGTA, and zero rigor), the fluorescence increase is slow and monophasic (Fig. 2 A) and the maximum rate, k obs, at saturation is 0.64 s⁻¹ (Table 1). In all other instances, biphasic kinetics (e.g., Fig. 2 B) are observed with the faster component being attributed to the dissociation of Pi from regulated actomyosin-S1-ADP-Pi. At pCa 4 (zero rigor), k obs is 16 s⁻¹, a 25-fold increase (Table 1). Thus, the effect of Ca(II) is in close agreement with what had been reported earlier under similar conditions: k obs, 1 s⁻¹ (apo) and 20–25 s⁻¹ (pCa 4; Fig. 3 in Rosenfeld and Taylor, 1987a). The effect of rigor myosin binding was studied at a stoichiometry of one rigor-S1A1 to seven actin subunits. The ratio was selected in light of the dependence of Pi dissociation on the amount of rigor S1A1 bound to the thin filament. Maximal activation was attained at 1 rigor S1 per 14 actin subunits (Fig. 5 of Heeley et al., 2002), suggestive of a regulatory unit that is longer than one molecule of tropomyosin or one that comprises both sides of the thin filament. On the basis of this observation, a ratio of 1:7 was assumed to be sufficient to attain saturation. Under these conditions, the maximum rates of Pi dissociation were 30 s⁻¹ (EGTA plus rigor myosin-S1) and 77 s⁻¹ (Ca[II] plus rigor myosin-S1), the latter being the same within experimental error as the rate obtained with unregulated actin (Table 1). Similar results were obtained when rigor S1 was premixed with thin filaments (in a ‘‘T’’ mixer) 5–10 min before being used for a double-mixing experiment in which there was no rigor S1 arising from the first mix (Heeley et al., 2002). While a redistribution of bound heads cannot be ruled out, the lack of an observed effect of premixing on Pi dissociation kinetics indicates that a redistribution either did not occur or was of little consequence. Therefore, from the PBP-based observations, which are a direct measure of the active site departure of Pi, it became evident that both ligands are required for full activation (a fold increase of 100), whereas rigor-bound heads alone are insufficient. At the same time, Ca(II) and rigor myosin had only a small effect, approximately twofold, on the affinity of thin filaments for myosin-ADP-Pi (Table 1).

Similar findings were reported in a parallel study (Heeley et al., 2006) conducted with the deoxyribose modified analogue mant-ATP or 2′ deoxymethanthranolyl (md)–ATP (Hiratsuka, 1983). The strategy, which hinged on a sequential departure of products from the active site of myosin, allowed for the inclusion of mM MgATP in the reconstituted thin filaments (skeletal) to prevent unwanted rigor activation, something that had been a concern in the fluorescent PBP experiments. Using md-ATP, the fold-activations of the product release kinetics for the various ligand combinations are in line with what is observed with PBP (Table 1).

These observations (Heeley et al., 2006) added support to the view that Pi release (AM-ADP-Pi → AM-ADP + Pi) is the primary regulated step of the mechanism.

The isomorphisms that exist between the two sets of regulatory proteins, those in heart and fast skeletal muscle, chiefly reside in the troponin complex, notably the T subunit (reviewed in Wei and Jin, 2016). Cardiac myosin-S1 (which has slower kinetics and weaker affinity for actin than skeletal-S1A1; Siemankowski et al., 1985) and native thin filaments were isolated from porcine ventricle. Transient kinetic analysis of the cardiac system was performed using md-ATP. As stated earlier, the fluorescence nucleotide allowed mM MgATP to be used to ensure that no rigor myosin was bound to the thin filaments. Selected time-course recordings are presented in Fig. 2, C and D. Compared with the skeletal muscle counterpart, there are similarities and differences. The rate constants for cardiac thin filament-induced acceleration of dissociation of md-ADP from regulated-AM-md-ADP-Pi are as follows: 0.49 s⁻¹ (no bound ligands), 24 s⁻¹ (rigor myosin-S1 only), 27 s⁻¹ (Ca[II] only), and 36 s⁻¹ (Ca[II] plus rigor myosin-S1; see Fig. 3 A and Table 1). The fold difference between fully activated and inhibited cardiac thin filaments is ∼80 (Houmeida et al., 2010). Thus, it is apparent that each type of thin filament requires both Ca(II) and rigor S1 binding for full activation, but the cardiac system is more responsive to an individual ligand. For example, Ca(II) alone yields 70% of the maximum observed rate when the thin filament is fully activated. The heightened ligand sensitivity may be related to the fact that the cardiac thin filaments were not reconstituted. That is, they were not assembled in vitro from individual components. More interestingly, it may be a consequence of the comparatively longer length of the predominant cardiac troponin-T isoform (Pearlstone et al., 1986).

The pronounced activation by Ca(II) is also observed at higher ionic strengths, 22 and 100 mM potassium acetate (Kac). For these experiments, skeletal myosin-S1A1 was preferred to cardiac-S1 owing to it having a higher activity. In 22 mM acetate (20°C, pH 7), the concentration dependences of Pi release are well fit by hyperbolic functions: 1.1 s⁻¹ (no bound ligands), 58.4 s⁻¹ (Ca[II] alone), and 73 s⁻¹ (Ca[II] plus rigor myosin-S1; Fig. 3 B). At the higher concentration of salt (100 mM Kac), the rate of product dissociation is linearly dependent upon the thin filament concentration. The second order rate constants are as follows: 2 × 10³ M⁻¹ s⁻¹ (no bound ligand), 1.3 × 10⁵ M⁻¹ s⁻¹ (Ca[II] alone), and 1.8 × 10⁵ M⁻¹ s⁻¹ (Ca[II] plus rigor myosin-S1; Figs. S6 and S7 and Table ST1 in Risi et al., 2017). Thus, the percent activation observed with a mixture of isotypes is similar to that obtained at low ionic strength with protein components derived solely from heart (Fig. 3 A). Specifically, the activation by Ca(II) alone in 22 and 100 mM acetate is 70% of the maximum. The agreement is illustrated by the bar graph in Fig. 5.

A key question is whether post–power stroke myosin (having an “open” switch II conformation) is equivalent in terms of its regulation to that of myosin containing ADP-Pi in the active site (pre–power stroke, “closed” switch II conformation). This was investigated via the same procedure that has been described except that a fluorescent analogue of ADP (instead of ATP) was employed in the first mix. With etheno-ADP and all skeletal muscle proteins, the rate is increased 15-fold by Ca(II) binding (Rosenfeld and Taylor, 1987b). With deoxyribose mant-ADP (md-ADP), which has faster dissociation kinetics than native ADP (Siemankowski and White, 1984), and all cardiac proteins, the change is smaller, some sixfold (Fig. 4; Houmeida et al., 2010). Further, when used individually or together, Ca(II) and rigor myosin-S1 all brought about a similar increase in the release rate of the nucleoside diphosphate (from regulated AM-md-ADP). The maximum rates at 20°C are 64 s⁻¹ (no bound ligands), 357 s⁻¹ (Ca[II] alone), 332 s⁻¹ (rigor myosin-S1 alone), and 359 s⁻¹ (Ca[II] plus rigor myosin-S1). It is apparent, therefore, that regulation is significantly diminished in scale compared to when myosin-S1 has both products, ADP and Pi, in the active site (Fig. 3 A).

Phosphate dissociation (from regulated actomyosin-S1-ADP-Pi) is generally accepted to be the stage in the contraction of striated muscle that produces force (reviewed in Houdusse and Sweeney, 2016). The authors have investigated the regulation of this step in transient kinetic experiments designed to mimic a working actomyosin cycle. This approach differs from that of other work, such as steady-state kinetics and myosin binding to the thin filament, in that it monitors the rate of decay of the pre–power stroke complex (regulated actomyosin-S1-ADP-Pi). Comparison of four defined conditions, (1) no bound ligands, (2) maximal activation by Ca(II), (3) maximal activation by rigor myosin, and (4) maximal activation by Ca(II) and rigor myosin together, reveals a strong dependence of the rate of Pi release on the liganded state of the thin filament. In other words, this part of the AM cycle is a regulatory focal point. Our observations, which have been overlooked, are at odds with the Three-State model (McKillop and Geeves, 1993) that was formulated to account for the association of strong binding myosin intermediates with the thin filament. Points of disagreement are as follows.

First, the maximum acceleration of Pi release of 80–140-fold (depending on the source of the thin filaments) requires the association of both Ca(II) and rigor myosin-S1 with the thin filament. That is, either ligand by itself is insufficient to fully activate the thin filament. The Three-State model predicts maximal activation by rigor binding alone.

Second, thin filaments containing only bound Ca(II) accelerate Pi release by 25–50-fold relative to inactivated thin filaments (EGTA, zero rigor; Table 1). The model predicts a smaller effect of Ca(II). The extent of cardiac thin filament activation by Ca(II) alone (70% of maximum) is observed over a range of ionic strengths (Fig. 3 B and Fig. 5). From this it is evident that Ca(II) is the main thin filament activator in heart and that any rigor-bound heads that arise during the course of a contraction will have only a relatively small additional effect. Thus, there is quantitative disagreement between the transient kinetic results and the degree to which the three states of skeletal and cardiac thin filaments are populated at different concentrations of Ca(II) (Maytum et al., 2003).

What is the reason for the lack of agreement? A realistic kinetic model of regulation of the actomyosin ATP hydrolysis cycle that occurs in muscle must account for the regulation of ATP hydrolysis and the power stroke. Experimental scenarios where ATP hydrolysis is not taking place are unlikely to provide satisfactory models for regulation and appear to be monitoring other interesting aspects of the system. We contend that a major source of disagreement is the nonequivalence of pre– or post–power stroke myosin with respect to activation of the thin filament. Thus, the level of regulation depends not only on the thin filament state but the conformation of myosin as well.

Finally, the pattern of regulation that we have characterized has been fit to an allosteric model comprising two states, inactive and active, that differ in their ability to activate Pi release (Scheme 2). In the case of apo thin filaments, the equilibrium strongly favors the inactive state. The association of Ca(II) and rigor heads to the thin filament shifts the equilibrium toward the active conformer to varying degrees depending on protein isotype. But in both instances (skeletal and cardiac), maximal activation requires that both ligands are associated with the thin filament.

This work was supported by Canadian Institutes of Health Research and Natural Sciences and Engineering Research Council of Canada grants to D.H. Heeley; National Institutes of Health grants HL41776 and EB00209 to H.D. White; and National Institutes of Health grants NIH GM1992 and NHLBI HL 20592 and Muscular Dystrophy Association of America grants to E.W. Taylor.

The authors declare no competing financial interests.

Author contributions: The authors contributed equally to the experimentation. The article was written by D.H. Heeley after extensive discussions with H.D. White and E.W. Taylor.

Henk L. Granzier served as editor.