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Logo of jbcThe Journal of Biological Chemistry
 
J Biol Chem. 2010 December 10; 285(50): 39150–39159.
Published online 2010 October 2. doi:  10.1074/jbc.M110.142232
PMCID: PMC2998111

Effects of Actin-Myosin Kinetics on the Calcium Sensitivity of Regulated Thin Filaments*

Abstract

Activation of thin filaments in striated muscle occurs when tropomyosin exposes myosin binding sites on actin either through calcium-troponin (Ca-Tn) binding or by actin-myosin (A-M) strong binding. However, the extent to which these binding events contributes to thin filament activation remains unclear. Here we propose a simple analytical model in which strong A-M binding and Ca-Tn binding independently activates the rate of A-M weak-to-strong binding. The model predicts how the level of activation varies with pCa as well as A-M attachment, N·katt, and detachment, kdet, kinetics. To test the model, we use an in vitro motility assay to measure the myosin-based sliding velocities of thin filaments at different pCa, N·katt, and kdet values. We observe that the combined effects of varying pCa, N·katt, and kdet are accurately fit by the analytical model. The model and supporting data imply that changes in attachment and detachment kinetics predictably affect the calcium sensitivity of striated muscle mechanics, providing a novel A-M kinetic-based interpretation for perturbations (e.g. disease-related mutations) that alter calcium sensitivity.

Keywords: Actin, Cardiac Muscle, Kinetics, Myosin, Skeletal Muscle, Muscle Regulation, Thin Filament, Tropomyosin, Troponin, pCa

Introduction

Activation of striated muscle is a calcium-dependent process, with initial studies describing calcium binding as a switch that can turn regulated thin filaments “on” or “off” (1, 2). The basic regulatory apparatus is an actin-associated complex composed of tropomyosin (Tm)2 and troponin (Tn). Early structural and kinetic studies describe regulation in terms of a three state model for the thin filament (blocked, closed, and open) (3, 4, 5). In the absence of calcium, Tm sterically blocks myosin from binding actin, slowing the rate, katt, for strong actin-myosin (A-M) binding (Fig. 1A) (6, 7, 8). Calcium binding to troponin-C (TnC) induces a new structural state of the regulatory complex in which Tm moves to expose myosin binding sites on actin (9, 10). However, whether calcium binding alone is sufficient to activate katt or whether strong A-M binding (the purported closed-to-open transition) is required remains unclear.

FIGURE 1.
A two state model for myosin binding to a regulated thin filament. A, weak-to-strong binding of one myosin head (yellow oval) to a regulatory subunit of a thin filament (bottom to middle) occurs at a rate 1/τoff, which is cooperatively activated ...

Calcium binding is clearly an important trigger for thin filament activation in vivo (11, 12), however, evidence for activation by strong A-M binding cannot be ignored (13, 14, 15). Both the ATPase and mechanics of regulated A-M systems are activated at low [MgATP] (16, 17), presumably because myosin heads strongly bound to the thin filament displace Tm from neighboring myosin binding sites on actin (18). In addition, myosin heads chemically modified to mimic the rigor state similarly activate regulated A-M systems (19). Finally, addition of sufficient MgADP at high [MgATP] has been shown to activate thin filaments in the absence of calcium (20, 21).

Thin filament activation is a highly cooperative process (i.e. activity-pCa curves have Hill coefficients, n, greater than one) (16, 20, 22), allowing for efficient calcium handling in the activation-relaxation cycles of striated muscle. One proposed mechanism for cooperative activation is strong A-M binding (23,25). However, recent studies challenge this model, indicating that cooperativity (specifically the Hill coefficient, n) is determined at the level of the thin filament through eitherTm-Tm end-to-end interactions (26,28) or Ca2+-Tn binding (29, 30).

A lack of an effect of A-M binding on n does not however preclude the potential influence of A-M binding on thin filament activation and, in particular, calcium sensitivity (e.g. pCa50) (17, 31). Specifically, we show both theoretically and experimentally that if A-M binding constitutively rather than cooperatively activates thin filaments (Fig. 1A), the pCa50varies predictably with changes in A-M attachment and detachment kinetics.

Here we develop a model that takes into account established effects of both strong A-M binding (10, 19, 33) and Ca2+-Tn binding on thin filament activation. Based on our previous single molecule measurements (Fig. 1B), we define the extent of thin filament activation, P1, as the fraction of time that a regulatory unit of the thin filament is active. Assuming that strong A-M binding constitutively activates the thin filament, and that Ca2+-Tn binding cooperatively activates the thin filament (Fig. 1A), an analytical expression for P1 is easily derived as a function of [Ca2+] as well as A-M attachment, N·katt, and detachment, kdet, kinetics where N is the number of myosin heads available to bind a given regulatory unit of the thin filament. The model predicts that any perturbation to actin-myosin kinetics that enhances P1 (e.g. increased katt, decreased kdet, or increased N) will increase calcium sensitivity, and any perturbation that decreases P1 (e.g. decreased katt, increased kdet, or decreased N) will decrease calcium sensitivity.

To test this model, we use an in vitro motility assay to determine how changing the model parameters N, katt, kdet, and pCa influences the activation level of the velocity, V, at which thin filaments slide over a bed of skeletal muscle myosin. We show that the combined effects of N, katt, kdet, and pCa on V are accurately described by our minimal model.

The model and data imply that strong A-M binding influences the pCa50 for thin filament activation even in the absence of an effect on n. The model prediction that changes in A-M kinetics alter the pCa50 offers new insights into the molecular basis for factors that change calcium sensitivity such as disease-related mutations to actin, myosin, and regulatory proteins; changes in pH, [MgADP], and myosin phosphorylation associated with muscle fatigue; and changes induced by small molecule effectors of A-M kinetics.

EXPERIMENTAL PROCEDURES

Proteins

Skeletal muscle myosin was prepared from rabbit psoas as previously described and stored in glycerol at −20 °C (34, 35). Actin was purified from rabbit psoas and stored on ice at 4 °C (36). For in vitro motility assays, actin was incubated with tetramethylrhodamine isothiocyanate (TRITC) phalloidin overnight. Troponin and tropomyosin (Tm-Tn) were purified from skeletal muscle as previously described (37, 38).

Buffers

Myosin buffer contained 300 mm KCl, 25 mm imidazole, 1 mm EGTA, 4 mm MgCl2, 10 mm DTT. Actin buffer contained 50 mm KCl, 50 mm imidazole, 2 mm EGTA, 8 mm MgCl2, 10 mm DTT. For all motility experiments, motility buffer (50 mm KCl, 50 mm imidazole, 2 mm EGTA, 8 mm MgCl2, 10 mm DTT, 0.5% methylcellulose, 100 nm Tm-Tn) was used with the MgATP, MgADP, and CaCl2concentrations specified in “Results.” To reconstitute actin into a thin filament 20 nm actin was incubated on ice with 200 nm TmTn in actin buffer for ~20 min. All solutions except myosin buffer contained oxygen scavenger (~6 mg/ml glucose, 0.03 mg/ml glucose oxidase, 0.05 mg/ml catalase). For experiments in which [MgADP] was varied, the ionic strength was maintained by mixing 10 mm MgADP motility buffer with a motility buffer containing the ionic strength equivalent of KCl and no MgADP (39, 40). For experiments in which calcium was varied, calcium was buffered with EGTA, and even at pCa 3 calcium did not significantly (<4%) change the total MgATP concentration, as determined through a ligand binding algorithm (39). For blebbistatin experiments, 1.6 μm blebbistatin (Sigma-Aldrich) was added to the motility buffer, minimizing light exposure during blebbistatin handling and experiments (41).

Activity Assays

The velocity of fluorescently labeled thin filaments sliding over a bed of myosin molecules was measured using an in vitro motility assay at 25 °C for all experiments unless otherwise noted. Flow cells were prepared by attaching a nitrocellulose-coated coverslip to a microscope slide with shim spacers. Unless otherwise noted, flow cells for the motility assay were prepared as follows: 80 μl of 100 μg/ml myosin incubated for 1 min, 80 μl of 0.5 mg/ml BSA incubated for 1 min, 80 μl of 20 nm sonicated F-actin and 1 mm MgATP incubated for 1 min, 2 × 80 μl of actin buffer (no incubation), 2 × 80 μl of 20 nm TRITC-actin incubated for 2 min, and an 80-μl wash with motility buffer. Motility assays were performed using a Nikon TE2000 epifluorescence microscope with fluorescence images digitally acquired with a Roper Cascade 512B camera (Princeton Instruments, Trenton, NJ). For each flow cell, we recorded five 20 s image sequences from five different fields, each containing ~20 - 35 actin filaments. Data obtained from these five fields constituted one (n = 1) experiment. For each image sequence, we analyzed actin movement using Simple PCI tracking software (Compix, Sewickley, PA) to obtain actin-sliding velocities V. Objects were defined by applying an exclusionary area threshold to minimize background noise. Filters were applied to exclude intersecting filaments. The velocities of the moving thin filaments were plotted as a histogram and fitted to two Gaussians corresponding to moving and non-moving populations. The average velocity, V, for the field was taken as the center of the Gaussian fit to the moving populations. The moving population included filaments that move both smoothly and irregularly (42, 43). To determine the calcium dependence of the fraction of moving filaments, the percent moving filaments was defined as the fraction of individual filaments moving at an average V > 0.7 μm/s. The percent of smoothly moving filaments was defined as the fraction of filaments whose standard deviation for velocity is less than half the average velocity for that filament. Experiments were repeated at least three times (n = 3) for each condition.

Analytical Model for Regulation of Unloaded Thin Filament Sliding

Based on single molecule mechanical measurements, we previously proposed a simple two-state model (Fig. 1A) for thin filament activation (17). According to this model, the first myosin head to bind a blocked regulatory unit of the thin filament (Fig. 1A, bottom to middle) does so at a rate 1/τoff and constitutively activates that regulatory unit, such that subsequent binding of additional myosin heads (Fig. 1A, middle to top) occurs at a maximally activated rate of katt. Here we expand this model to include the effects of calcium by simply assuming that calcium cooperatively activates 1/τoff from a basal rate of b·katt at no added calcium (where 1/b describes the effectiveness of regulatory proteins at inhibiting actin-myosin binding in the absence of calcium) to a maximally activated rate of approximately katt at saturating calcium. For a minimal model, we assume that both katt and the A-M detachment rate, kdet, are independent of both calcium and the number of myosin heads strongly bound to a regulatory unit. However any dependences of katt and kdet on calcium and the number of strongly bound myosin heads could easily be incorporated into this model when these relationships are better characterized experimentally. Refining the model to include a variable katt (or the addition of any other variables) will only improve the accuracy with which this model describes experimental data. The regulatory subunit of the thin filament is defined as the length of the thin filament that is activated upon the binding of one myosin head to actin. The number of myosin heads available to bind to a given subunit is given by N. Regulation of actin sliding velocities, V, is described most simply as the fractional activation, P1, of a maximally activated velocity, Vo, or Equation 1.

equation image

Here we assume the classical approximation for Vo in Equation 2,

equation image

where d is the myosin stepsize (assumed here to be 10 nm) (44) and τon is the average time a given myosin head spends bound to the thin filament. For a simple two-step detachment scheme (MgADP release followed by MgATP-induced dissociation) τon is Equation 3,

equation image

where kD is the MgADP release rate, Km is the MgATP concentration at which τon is twice its minimum value, and KI is the affinity of MgADP for actin-bound myosin (45). According to a two-step actin-myosin detachment scheme,

equation image

where kT is the second-order MgATP-induced dissociation rate. A more detailed derivation of Equation 3 has been previously published (45).

Single molecule studies of regulated thin filaments have provided insight into the molecular mechanism for thin filament activation and the biochemical basis for P1 (Fig. 1B) (17). Specifically, thin filaments partially activated by N myosin heads available to bind a regulatory subunit exhibit relatively long periods, τoff, of inactivity during which no myosin heads are bound to the thin filament punctuated by periods, τ1, when after an initial A-M binding event the thin filament is activated and moves with a cascade of A-M binding events (Fig. 1B). Accordingly, the level of activation, P1, is the fraction of time the thin filament is activated and is given by Equation 5.

equation image

The time, τ1, that at least one myosin head is bound to a regulatory unit is calculated as the inverse of the probability (1 − r)N, that no heads are bound to the activated thin filament multiplied by the relaxation rate, katt + kdet, (the rate at which equipartition is achieved), or Equation 6.

equation image

Here the duty ratio, r, is the fraction of time a given myosin head spends strongly bound to an activated thin filament in Equation 7,

equation image

where the detachment rate for a given myosin head is simply Equation 8.

equation image

The average time,τoff, that it takes at least one of N myosin heads to bind a regulatory unit of the thin filament (Fig. 1B) is the inverse of the rate for the initial A-M binding event that triggers the binding cascade shown in Fig. 1B. We assume that this rate is the sum of calcium-dependent (Equation 9),

equation image

and calcium-independent (Equation 10),

equation image

terms, where the calcium dependence of 1/τoff is described by the Hill equation with a cooperative coefficient of n and a calcium-Tn binding affinity of KCa. The cooperative coefficient for Ca-Tn binding has been suggested to result from either multiple calcium binding sites on TnC (46) and/or through adjacent Tm-Tm interactions along the thin filament (22, 26, 27, 47). The calcium-independent term describes the basal attachment rate of b·katt, which presumably results from thermal fluctuations of Tm (48). Thus, we have Equations 11 and 12.

equation image

or

equation image

RESULTS

Activation of regulated thin filaments is influenced both by calcium binding to TnC (49) and by myosin strong binding to actin (Fig. 1A) (16). Here we show how these effects combine to influence the calcium sensitivity of muscle mechanics. Optical trap studies provide a clear picture of the molecular mechanism of thin filament activation by A-M binding (Fig. 1B) (17). Specifically, the level of thin filament activation, P1, is simply the fraction of time a regulated subunit of the thin filament is activated (Fig. 1B) (17), which is easily calculated in terms of A-M attachment, katt, and detachment, kdet, kinetics as well as the number of myosin heads, N, available to bind to a regulatory unit of the thin filament (Equation 5). To incorporate the effects of calcium into this model, we simply assume that katt is cooperatively activated by calcium binding to TnC, reaching a maximally activated rate at saturating calcium (Equation 12).

The Effects of Calcium on Thin Filament Velocities and the Fraction of Smoothly Moving Filaments

As previously reported (31, 42), Fig. 2A shows that calcium activates thin filament sliding velocities, V. Fig. 2B shows that the increase in V upon addition of calcium correlates with an increase in the percent of filaments moving discontinuously and smoothly, consistent with previous observations (42, 43). Fits of these data were obtained using the Hill equation to obtain approximate Vmax and pCa50 values (subsequent fits were obtained through the modeling of Equation 1 to the data using the values presented in Table 1). The thin filament velocities reported are averaged over long distances of thin filament travel, which sample a wide range of myosin densities.

FIGURE 2.
Effects of Ca2+ on thin filament sliding measured in an in vitro motility assay. A, in a motility assay with 100 μg/ml myosin, 1 mm MgATP, performed at 25 °C, actin filament sliding velocities, V, are activated upon addition of calcium. ...
TABLE 1
Model parameter values and calculated pCa50/Vmax values for all model fits

Decreasing kdet (Increasing P1) Activates Regulated Thin Filaments

Equation 5 describes how decreasing the effective rate of A-M detachment, kdet, increases P1 via an increase in τ1 (Equation 6), the time that at least one myosin head is bound to a regulatory unit, and thus activates the thin filament to produce velocity, V. To test this hypothesis we decreased kdet either by decreasing [MgATP] or by increasing [MgADP]. We determined the corresponding effects on V as a measure of P1 (Equation 1) using an in vitro motility assay.

Fig. 3A shows a plot of V as a function of [MgATP] obtained both in the absence of calcium (pCa 10) at 25 °C and 30 °C and for saturating calcium (pCa 3) at 25 °C. Consistent with previous studies (16, 17), in the absence of calcium, when the [MgATP] concentration is decreased the thin filament becomes partially activated by rigor heads. As [MgATP] is further decreased a peak velocity is reached at which point the thin filament velocity is maximally activated and exhibits a velocity consistent with that observed in the presence of saturating calcium (pCa 3). Further decrease in [MgATP] results in a decrease in velocity with no change in the level of activation; this decrease in velocity is due to the [MgATP] dependence of thin filament sliding velocities. These datasets are accurately fitted by Equation 1 using the parameters in Table 1 (Fig. 3A, solid lines). The peaks in the V versus [MgATP] curves occur at the MgATP concentrations at which V approaches maximal activation. Below this [MgATP], velocities obtained at both pCa 3 and 10 decrease together due to the [MgATP] dependence of Vo (Equation 3) (45). According to Equation 5, the right shift in the activation peak with increased temperature results from enhanced activation (i.e. Increased P1) modeled here as an increase in katt.

FIGURE 3.
Effect of [MgATP]and [MgADP] on thin filament sliding velocities measured in an in vitro motility assay. A, in a motility assay with 100 μg/ml myosin at pCa3 and 25 °C, the thin filament is fully activated at all times, and V(●) ...

To test whether A-M activation in Fig. 3A is a kdet effect or whether it is unique to rigor activation, we decreased kdet by increasing [MgADP] at 1 mm MgATP (Equation 8). Fig. 3B is a plot of V as a function of [MgADP] obtained at both pCa 10 and 3. These datasets were accurately fitted to Equation 1 using the parameters in Table 1 (Fig. 3B, solid lines). Like the [MgATP]-induced decrease in kdet in Fig. 3A, an [MgADP]-induced decrease in kdet results in a peak V when kdet is sufficiently slow to maximally activate the thin filament. Above this peak MgADP concentration, V slows due to the [MgADP] dependence of V0 (Equation 3). These results suggest that the thin filament is in general activated by strong binding and not just rigor binding.

Decreasing kdet (Increasing P1) Enhances Calcium Sensitivity

Equation 5 predicts that increasing the level of thin filament activation (P1) by decreasing kdet will increase calcium sensitivity (pCa50). To test this prediction, we used in vitro motility to measure the pCa dependence of the sliding velocities, V, of regulated thin filaments at 1.0 and 0.05 mm MgATP (Fig. 4). Consistent with the data in Fig. 3A, partial activation was observed at low [MgATP] even in the absence of calcium. Consistent with our model, calcium sensitivity was enhanced (pCa50 6.27) at 0.05 mm MgATP relative to that at 1 mm MgATP (pCa50 5.41). Both datasets were accurately described by Equation 1 (Fig. 4, solid lines) using the parameters in Table 1.

FIGURE 4.
The effects of [MgATP]and pCa on thin filament sliding velocities measured in an in vitro motility assay. With 100 μg/ml myosin and 1 mm MgATP at 25 °C, V increases sigmoidally with increasing [Ca2+] (●). Decreasing [MgATP] to ...

Decreasing kdet (increasing P1) via addition of MgADP is similarly predicted to increase calcium sensitivity (Equation 5). Such an effect has been reported by Van Buren and co-workers (31) and is consistent with our model predictions (data not shown).

Decreasing N·katt (Decreasing P1) Inactivates Regulated Thin Filaments

In addition to its dependence on kdet, P1 is predicted (Equation 5) to decrease when the rate of strong A-M binding, N·katt, decreases either through decreasing N or by slowing katt due to their influences on both τoff (Equation 6) and τ1 (Equation 6). The former can be achieved by decreasing the myosin surface density in a motility assay, whereas the latter can be achieved through addition of actin-myosin ATPase inhibitors and possibly by decreasing temperature (Fig. 3A).

To test this hypothesis, we measured the [MgATP]-dependence of V at two different myosin surface densities. Fig. 5 shows the [MgATP] dependence of V at pCa 10 and two different myosin surface densities obtained from incubating the coverslip with 100 μg/ml and 25 μg/ml myosin. The data show a leftward shift in the activation peak with decreasing myosin surface density corresponding to a lower level of activation (i.e. a lower P1). These data are accurately described by Equation 1 using the parameters in Table 1 (Fig. 5, solid lines), where the decrease in myosin concentration is described as a decrease in N from 20 to ~6.

FIGURE 5.
The effects of myosin surface density and [MgATP] on thin filament sliding velocities measured in an in vitro motility assay. At pCa 10, 25 °C, and 25 μg/ml (○)V is activated at low [MgATP] as shown in Fig. 3A. Increasing the myosin ...

Increasing N·katt (Increasing P1) Enhances Calcium Sensitivity

As demonstrated above, calcium sensitivity is enhanced when P1 is increased through a decrease in kdet. Similarly, our model predicts that calcium sensitivity can be enhanced by increasing P1 through an increase in N·katt. Van Buren and co-workers showed previously that calcium sensitivity is enhanced by increasing N (Table 1) (31). In fact their pCa-V curves obtained at different myosin densities (replotted in Fig. 6A) are all globally fit to Equation 1 by varying only N (Fig. 6A, solid lines), fixing all other parameters to the values shown in Table 1. Although an absolute value for N is difficult to calculate, Fig. 6B shows clearly that the relationship between the fitted parameter, N, and the myosin concentrations used by Van Buren and co-workers is roughly linear. This linear relationship between N and myosin concentration is consistent with studies by Harris and Warshaw (50) demonstrating that the myosin density on the coverslip varies linearly with the myosin concentration and that the number of myosin heads available to bind an actin filament varies linearly with the myosin density on the coverslip. Therefore, N is expected to vary linearly with myosin concentration (Fig. 6B).

FIGURE 6.
The effect of myosin density on the pCa dependence of Vmax (reproduced from Gorga et al., Ref. 31). A, data are replotted from Gorga et al. (31) originally obtained using in vitro motility assay to measure the effects of myosin surface density on the ...

To further test the hypothesis that inhibiting A-M binding kinetics, N·katt, decreases calcium sensitivity, we studied the effects of blebbistatin, a known inhibitor of myosin attachment kinetics (51, 52, 53), on the pCa dependence of V. Fig. 7 shows that in addition to a decrease in overall velocity, the addition of 1.6 μm blebbistatin decreased the pCa50 from 5.93 to 5.27. These data sets are accurately described by Equation 1 using the parameters in Table 1 (Fig. 7, solid lines), where here we have modeled the effects of blebbistatin as a decrease in katt from 23.2 s−1 to 1.2 s−1.

FIGURE 7.
The effects of blebbistatin on thin filament sliding velocities measured using an in vitro motility assay. In a motility assay with 1 mm MgATP, 100 μg/ml myosin, and no added blebbistatin, V varies sigmoidally with pCa (●) as shown in ...

DISCUSSION

Model for Thin Filament Activation

The model proposed herein is easily described in terms of the mechanochemistry of myosin interactions with regulated thin filaments illustrated in Fig. 2, based on the single molecule studies of Kad et al. (17). Submaximal activation by N myosin heads available for binding to a regulatory subunit of the thin filament shows relatively long periods, τoff, when no myosin heads are bound to the thin filament followed by periods, τ1, during which the binding of a single myosin head initiates thin filament movement through a cascade of A-M binding events. The level of activation, P1, is simply the fraction of time the thin filament is activated, which is easily calculated (Equation 5) in terms of the kinetic model in Fig. 1.

One unique aspect of this model is that thin filament activation by A-M binding is assumed to be constitutive, not cooperative. Specifically, P1 is determined by τ1 and τoff, where τ1 is a function of a constitutively activated (constant) A-M binding rate, N·katt (Equations 6 and 12), and τoff is defined only when no myosin heads are bound to actin (Equations 5 and 6). This is consistent with recent observations showing that strong A-M binding does not affect the Hill coefficient, n, for thin filament activation (14, 15). This observed lack of an effect of A-M binding on n, however, does not exclude the possibility that strong A-M binding affects thin filament regulation and calcium sensitivity (pCa50).

In fact, Equation 5 predicts that changes in katt, kdet, and N have significant and predictable effects on the level of thin filament activation and the pCa50 (Fig. 8). We tested and confirmed the accuracy of these predictions by determining the combined effects of varying katt, kdet, pCa, and N on thin filament sliding velocities, V. The data from these experiments were all accurately fitted to Equation 1 (Table 1). Our fits of Equation 1 to experimental data would improve significantly if we modified our model to include new variables, such as a katt that depends on the number of myosin heads bound to a regulatory unit, and such modifications might be warranted (see below).

FIGURE 8.
Model predictions for changes in the pCa50 curve. Equation 1 predicts that changes in katt and kdet will alter the level of activation, measured through pCa50 and Vo. These plots illustrate how any perturbation (i.e. addition of inhibitors, changing temperature, ...

Two plots were not accurately described by the model parameters constrained by other datasets. These were the [MgATP]- and [MgADP]-dependent velocity curves obtained at saturating calcium (pCa 3). However, because these datasets were obtained under fully activated conditions, their deviation from Equation 1 need not result from inaccuracies in our model of regulation; rather they are consistent with the non-Michaelis-Menten kinetics for the [MgATP] dependence of Vo demonstrated previously (45, 54).

In general, all of our experimental data follow the basic trends described by Equation 1. When the level of activation, P1, is increased, actin sliding velocities become more sensitive to further increases in activation (e.g. addition of calcium, decrease in [MgATP], increase in [MgADP] etc.). The opposite is also true:decreasing P1makes actin sliding velocities less sensitive to factors that activate the thin filament (e.g. decreased kdet, increased N·katt, and increased calcium).

Model Limitations

In this report, we have developed a minimal model because our data does not further constrain the model. In doing so, we have purposely avoided unresolved controversies in the field. Taking this approach has allowed us to provide a solid foundation for modeling thin filament activation; nevertheless, the model will be modified and added to as the full details and mechanisms of thin filament regulation emerge. For example, many studies indicate that thin filaments are cooperatively activated by actin-myosin binding (3, 16, 20, 23). This phenomenon could be accounted for in our model by introducing a variable katt that is influenced by the number of myosin heads bound to actin. Moreover, katt may also be influenced by calcium, in which case a calcium-dependent katt can be introduced. When the calcium and actin-myosin binding dependence of katt are better quantified, an appropriate variable katt can be easily incorporated into this model.

Further, in this report, we describe calcium binding to TnC using the phenomenological Hill equation. In doing so, we do not address the detailed molecular mechanisms underlying Ca-TnC binding. It is well established that Ca-TnC binding is a cooperative process, but whether this cooperativity arises from multiple binding sites on troponin-C (46), adjacent interactions between Tn molecules facilitated by Tm (22, 26, 27, 47), or long distance interactions between regulatory proteins that span greater lengths of the thin filament (55) remains unresolved. Until these details are fully understood we have chosen to describe the Hill coefficient, n, for cooperative activation of thin filaments in terms of cooperative binding of calcium to troponin. That said, the Hill coefficient, n, for cooperative activation is probably influenced by many molecular mechanisms, including actin-myosin binding. Again, it is our intent that as the explicit details describing these phenomena emerge and are better understood, key components of the model will be added or altered to more accurately represent thin filament regulation.

Implications of our Model

The data presented herein support the use of Equation 1 as a tool for interpreting the mechanism for observed changes in pCa50. For example, the observation that increasing temperature right-shifts the peak of the [MgATP]-V curve in Fig. 3A indicates that temperature increases the level of thin filament activation, P1. According to Equation 5, this results from either an increased katt or a decreased kdet. Because a decrease in kdet is inconsistent with an increase in temperature, our data suggest that increasing temperature activates the thin filament primarily by enhancing katt. Moreover, the data in Fig. 3A predict that increasing temperature will increase the calcium sensitivity of striated muscle, consistent with the data of Sweitzer and Moss showing that temperature enhances calcium sensitivity in both myocardium and skeletal muscle (56). Again our model suggests that this increased calcium sensitivity results from the temperature dependence of katt not kdet.

Our model predictions that changes in katt and kdet affect the pCa50 (Fig. 8) have implications for physiological states exhibited by striated muscle. For example, it has been proposed that certain myosin modifications associated with skeletal muscle fatigue (e.g. myosin phosphorylation) increase the MgADP affinity for myosin (57). According to our model, in the presence of MgADP these perturbations would increase the calcium sensitivity of skeletal muscle under conditions of fatigue.

One of the most interesting applications of the model is in regards to human disease. Mutations to myosin, actin, and regulatory proteins have been implicated in different muscle diseases such as hypertrophic and dilated cardiomyopathies. Some of these mutations result in a significant change in the calcium sensitivity of thin filament activation (32, 58). Equation 1 provides an explicit link between actin-myosin kinetics and changes in calcium sensitivity as an underlying mechanism, and may help to better establish the connection between actin-myosin kinetics, calcium sensitivity, and human disease phenotypes.

In summary, we have developed a novel model for striated muscle activation in which calcium cooperatively activates the thin filament, and strong A-M binding constitutively activates the thin filament (Fig. 1). The model makes clear predictions (Equation 1, Fig. 8) for how actin-myosin attachment and detachment kinetics influence calcium sensitivity. The model lends novel insight into the kinetic mechanisms underlying changes in pCa50 observed in a variety of physiologically relevant modifications. Moreover, the model provides testable predictions for how observed changesin actin-myosin kinetics alter pCa50. Future studies will test the strength of this model as a predictive and interpretive tool for better understanding the basic mechanisms of striated muscle regulation in both normal and disease states.

Acknowledgments

We thank Dr. Peter Van Buren, Kelly Begin, and Dr. Feng Hong for help with Tm and Tn purification protocols, Dr. Kevin Facemyer for helpful comments, and Del Jackson for help with technical and computer support.

*This work was supported, in whole or in part, by Grants 5P20RR018751-06, 1R21AR055749-01, 1R01HL090938-01 from the National Institutes of Health.

2The abbreviations used are:

Tm
tropomyosin
A-M
actin-myosin
Tn
troponin complex
TnC
troponin-C
pCa
−log[Ca2+]
TRITC
tetramethylrhodamine isothiocyanate.

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