INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Cyclic interactions of myosin heads with actin coupled to ATP hydrolysis are the molecular basis of muscle contraction, cytokinesis, certain types of vesicle transport, and so forth. Several types of muscles contain myosin heavy and light chains characteristic of each type. They differ in the speed of unloaded shortening and in the magnitude of isometric tension. Even in a specific type of muscle these mechanical outputs vary depending on conditions. Nonmuscle myosins and actins also exhibit distinct rates of movement. How does the actomyosin ATPase kinetics determine the mechanical performance of this molecular motor? One approach to this issue is to isolate myosins from various sources, and then compare the kinetics of actin-activated ATPase reaction of these myosins and their mechanical performance. This approach was pioneered by Bárány (1967) with myosins isolated from various muscles having known maximum speeds of shortening. He found that the ATPase activity was proportional to the speed of shortening of the parent muscles. Qualitatively similar correlations have been observed also by other groups with different mammalian smooth muscles (Malmqvist and Arner, 1991; Helper et al., 1988), frog skeletal muscle fibers with different myosin heavy chain composition (Edman et al., 1988), crab muscle fibers of different types (Galler and Rathmayer, 1992), and rabbit aorta and small arterial muscles containing myosin heavy chains differing at the NH₂-termini (DiSanto et al., 1997). Another approach is to substitute various ATP analogs (NTPs) for ATP, using a given type of myosin. This approach was initiated by Blum (1955). Myosin can use a wide variety of NTPs as the energy source for the motile activity. Hasselbach (1956) reported an excellent correlation between the rate of NTP hydrolysis by actomyosin and the isometric tension of glycerinated muscle fibers. More recently, this study has been refined by several groups. It has been recognized that various NTPs have different affinities for actomyosin, and myosins complexed with these NTPs or their products have different affinities for actin (Pate et al., 1993; White et al., 1993). This was not carefully considered in the previous study by Hasselbach. Moreover, accumulation of the NTP hydrolysis products in fibers without an NTP-regeneration system must have reduced the tension. Therefore, the excellent correlation observed in 1956 has to be reexamined. Recent studies have shown that the isometric tension and unloaded shortening speed of skinned fibers in various NTPs have only moderate correlation with the acto-HMM or acto-S1 NTPase activities (Pate et al., 1993; Regnier et al., 1998). We note, however, that measurements of the mechanical properties and the chemical kinetics have not been made under similar conditions. For technical reasons, it is often so in studies with muscle fibers, where the mechanical measurements are made at higher ionic strength, while the measurements of solution chemical kinetics are made at low ionic strength. Moreover, the solution and fiber enzymatic activities have been measured in limited concentrations of NTPs.

Sheetz and Spudich (1983) developed a motility assay wherein myosin-coated particles move along parallel tracks of Nitella actin bundles. After the success of fluorescence microscopy in visualizing fluorescently labeled single actin filaments (Yanagida et al., 1984), a more versatile and stable assay was developed wherein actin filaments move over surfaces coated with myosin filaments (Kron and Spudich, 1986), or proteolytic fragments of myosin (Toyoshima et al., 1987). These developments allow us to investigate actomyosin motility under wide varieties of solution conditions with myosins and actins from diverse species and cell types. It has now become possible to investigate the fundamental question regarding the mechanochemical coupling of the actomyosin motor mentioned above in greater detail. First, it has been shown that the velocity of actin filaments sliding over myosin-coated surfaces and the velocity of myosin-coated beads along actin cables is analogous (with slight differences, depending on conditions) to the speed of unloaded shortening of muscle fibers (Sheetz et al., 1984; Homsher et al., 1992). Despite this analogy, many previous studies have reported no direct correlation between the steady-state actin-activated MgATPase activity of myosin and the rate of movement in the in vitro motility assays. However, we have to be careful in interpreting these results because identical, or very similar, solution conditions have not always been used in the motility and enzymatic assays.

Having this caution in mind, let us briefly review several types of previous studies where rates of movement measured in the in vitro motility assays have been compared with the corresponding actin-activated substrate turnover rates in solution. 1) Dependence on myosin species: beads coated with myosin from skeletal muscle and Dictyostelium move on actin cables from Nitella at distinct velocities, and these velocities are proportional to the respective actin-activated ATPase activities (Sheetz et al., 1984). Phosphorylated platelet myosin and phosphorylated turkey gizzard myosin have similar actin-activated ATPase activities, yet show very dissimilar rates of movement in the Nitella-based assay (Umemoto et al., 1989). Skeletal muscle myosin light chain isoforms have the same maximum actin-activated ATPase activity, yet again they translocate actin filaments at distinct velocities (Lowey et al., 1993). Chimera myosins, constructed from Dictyostelium myosin by substituting the 50K/20K junction region with those from other species of myosins, exhibit actin-activated ATPase activities characteristic of the activity of the myosins from which the junction region was donated. The velocities of actin sliding propelled by these chimeras, on the contrary, have no correlation with those driven by the donor myosins (Uyeda et al., 1994). Similarly, no correlation has been found with myosins from other sources (Vale et al., 1984; Higashi-Fujime, 1991). However, we have to be cautious about interpreting these observations, because in most cases actin-activated ATPase activity has been measured at one concentration of actin (Note that Bárány also used one concentration of actin in his 1967 study), and also because the Nitella-based assay tends to show slower motility than the sliding actin filament assay, depending on the myosin type used (Wolenski et al., 1993). Chimeric heavy meromyosins, which are produced by substituting the 50K/20K loop of smooth muscle heavy meromyosin with that from skeletal or -cardiac myosin, lose regulation by regulatory light chain phosphorylation. The chimeras and the wild type, however, show moderate correlation of the motile activity observed in the sliding actin filament assay with the maximum acto-HMM ATPase activity and with the K_m for actin (Rovner et al., 1995). Tryptic cleavage of the 25K/50K loop of skeletal myosin inhibits its motor function without any significant changes in the enzymatic properties of actomyosin, while cleavage of the 50K/20K loop increases the K_m for actin without significant effect on the motor function (Bobkov et al., 1996). The rate constant for dissociation of ADP from various muscle myosins complexed with actin has been compared with the maximum shortening speed of the parent fibers (Siemankowski et al., 1985). These quantities show a strong correlation, although it is still open to question whether the state formed by adding ADP to actomyosin is on the ATP hydrolysis pathway (Sleep and Hutton, 1980). Contrary to this observation, a chimeric myosin containing the Dictyostelium myosin heavy chain with the 25K/50K loop from skeletal myosin propels actin filaments at a velocity slightly slower than the wild type, while the rate of mant-ADP release from the actin-chimera myosin S1 is more than two times larger than that from the actin-wild-type myosin S1 (Murphy and Spudich, 1998) (the affinities of mant-ADP and ADP binding to actin-S1 are similar). 2) Dependence on ATP analogs: the velocity of actin filament translocation has been examined by Shimizu et al. (1991) using 15 ATP analogs. The relative velocities do not correlate well with the actin-activated substrate turnover rates. The actin-activated substrate turnover rate varies in a relatively small range compared to the variation in the velocity of actin translocation. A similar study has been made using naturally occurring nucleotides by another group (Higashi-Fujime and Hozumi, 1996). Again, no correlation is found. In these studies, however, one concentration of actin and one concentration of substrate have been used in the measurements of the enzymatic activities. However, in similar studies a moderate correlation is found between the motile activity and the maximum substrate turnover rate (Pate et al., 1993; Regnier et al., 1998). In these studies the actin concentration is varied, but one concentration of substrate is used in the measurements of the substrate turnover rate. 3) Dependence on actin species: the maximum MgATPase activity of skeletal muscle myosin activated with yeast actin is significantly lower than with skeletal muscle actin, whereas the apparent K_m for yeast actin of myosin heads is slightly larger than for skeletal actin (Cook et al., 1993). Nevertheless, the sliding velocities of both actins are quite similar, while force production of skeletal muscle heavy meromyosin with yeast actin is lower than with skeletal muscle actin (Cook et al., 1993; Kim et al., 1996; Miller et al., 1996). Subtilisin cleavage of skeletal muscle actin at Met-47 and Gly-48 markedly increases the K_m for actin of myosin heads without changing the maximum ATP turnover rate. The sliding velocity of the cleaved actin filaments is slower than that of intact actin filaments (Schwyter et al., 1990). In contrast to the effect of subtilisin cleavage of actin on the actin-activated ATPase of myosin, replacement by mutagenesis of aspartic acid residues of Dictyostelium actin with histidine residues reduces the maximum ATP turnover rate with moderate reduction in the K_m for actin. This replacement also reduces the sliding velocity of actin filaments (Sutoh et al., 1991). Actins modified at Cys-374 by different fluorophores have parallel effects on the velocity of actin sliding over HMM, the maximum actin-activated S1 ATPase activity, and the affinity of actin for S1 in ATP (Crosbie et al., 1994). 4) Dependence on other factors: binding of tropomyosin to actin has a parallel enhancement effect on the actomyosin ATPase activity and the rate of movement (Umemoto et al., 1989; Umemoto and Sellers, 1990; Okagaki et al., 1991; Wang et al., 1993). This effect is ascribed to an increase in the maximum ATPase activity (Umemoto et al., 1989); the optimum pH is around pH 7.0 for the actomyosin ATPase activity (Stone and Prevost, 1973). For the motile activity, the optimum pH has been reported to be around pH 7.0 (Sheetz et al., 1984; Warshaw et al., 1990; Sugiura et al., 1992), or pH 8.5 (Homsher et al., 1992). In the former three studies the rate of movement at pH 8.5 is very much less than at pH 7.0. The cause of this discrepancy is unknown. We have to note, however, that parallel measurements of the pH effects on the ATPase and the motile activities have never been carried out under the identical or very similar solution conditions. Within a range of ionic strength where smooth movement of either actin filaments or myosin-coated beads is observed, the rate of movement increases with increasing ionic strength (Homsher et al., 1992; Umemoto and Sellers, 1990; Warshaw et al., 1990; Harada et al., 1987; Takiguchi et al., 1990; Saito et al., 1994; Vale and Oosawa, 1990). The speed of isotonic and unloaded shortening of skinned muscle fibers also increases with increasing ionic strength when the ionic strength is lower than 100 mM (Gulati and Podolsky, 1981; Arheden et al., 1988). Although an increase in ionic strength is known to reduce the affinity (particularly in the presence of ATP), of myosin heads for actin, a systematic comparison of the effect of ionic strength on the motile activity with that on the actomyosin ATPase activity has never been made.

As seen in recent many reports, the relationship between the rate of movement and the actomyosin ATPase kinetics does not seem as simple as first suggested by Bárány in 1967. Our present situation regarding this central issue of the actomyosin motor seems confused. In part, this confusion may be because the identical or very similar solution conditions have not been used for measurements of the motile and enzymatic activities. Discrepancy is often seen in the previous studies wherein the ATPase assay is performed in a solution whose ionic strength is a few times lower than the motility assay solution. If the affinities for myosin of the two actin species have a different dependence on ionic strength, the order of the affinities can be reversed by changing ionic strength. Thus, we would misconstrue the relationship between the motile activity and the actin affinity for myosin. In the present study, care was taken in this respect. To examine the links between the motor function and the enzymatic reaction of actin-heavy meromyosin the system was perturbed by altering the substrate with various NTPs and divalent cations, and by altering ionic strength. It was also taken into account that various NTPs have different affinities for actomyosin, and that myosins complexed with these NTPs or their products have different affinities for actin. The experiments made with these precautions revealed an excellent correlation between the mechanical properties and the kinetics of substrate hydrolysis. Moreover, to account for these correlations we constructed a model based on an idea that the balance of a positive force and a velocity-dependent negative force determines the maximum velocity of movement. This idea was originally proposed by Huxley (1957). Equations derived from this model linked the chemical kinetics to the actin translocation velocity and the force generated without external load or under a small external load. The equations coincided with the experimentally revealed correlations in the present study, and also with observations from other studies.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Preparation of proteins

Myosin and actin were prepared from rabbit skeletal muscle according to the methods of Tonomura et al. (1966) and Spudich and Watt (1971), respectively. HMM was obtained by chymotryptic digestion of freshly prepared (not glycerinated) myosin according to Weeds and Pope (1977). After centrifugal removal of the nondigested myosin and light meromyosin in a solution of low ionic strength, HMM was quickly frozen in liquid nitrogen and stored in liquid nitrogen. The molar concentration of HMM was estimated on the basis of E₂₈₀^1% = 7.0 and a molecular weight of 3.5 × 10⁵, with correction for the turbidity (1.93 times the 330 nm absorbance was subtracted from the 280 nm absorbance). The molar concentration of F-actin was estimated on the basis of E₂₉₀^1% = 6.5 and a molecular weight of 4.2 × 10⁴ (1.68 times the 330 nm absorbance was subtracted from the 290 nm absorbance to correct for turbidity artifacts).

Actin-activated HMM NTPase assays

In the measurements below the concentration of HMM was adjusted, depending on the actin concentrations, NTPs and divalent cations, so that hydrolyzed NTP at the last time point amounts to <15% of the initial amount of NTP. In the first set of experiments we used various NTPs to alter the enzymatic kinetics of acto-HMM. NTPs we used are ATP, CTP, TTP, UTP, ITP, and GTP. Actin was polymerized in a solution containing 100 mM KCl, 1 mM MgCl₂, 0.2 mM CaCl₂, 5 mM Tris-HCl (pH 8.0), and 0.2 mM ATP. To remove ATP from the actin sample, the polymerized actin was centrifuged at 150,000 × g for 1 h. The resulting pellet was dispersed in Buffer A (25 mM KCl, 25 mM imidazole-HCl (pH 7.6), 2 mM MgCl₂, 0.2 mM CaCl₂) and dialyzed against the same buffer. HMM was mixed with various concentrations of F-actin in Buffer A. The NTPase reaction was initiated by the addition of NTP. The concentration of NTP was varied. In the second set of experiments we used various divalent cations as the complexing agents with ATP. Divalent cations we used are Mg²⁺, Mn²⁺, Ni²⁺, and Sr²⁺, all in the chloride form. Except for the case of Mg²⁺, actin pellet was dispersed in Buffer B (25 mM KCl, 25 mM imidazole-HCl (pH 7.6), 0.2 mM CaCl₂) and dialyzed against Buffer B. The ATPase reaction was initiated by adding 2 mM ATP and 2 mM divalent cation together to a solution containing HMM and various concentrations of F-actin in Buffer B. In the third set of experiments actin-activated HMM MgATPase activity was measured in solutions of various ionic strengths. The solvents (Buffer C) contained various concentrations of KCl, 25 mM imidazole-HCl (pH 7.6), 2 mM MgCl₂, and 0.2 mM CaCl₂. The concentration of MgATP was 2 mM. When the acto-HMM MgATPase activities were measured at [ATP] < 0.2 mM, an ATP-regeneration system consisting of phosphoenol pyruvate, pyruvate kinase, NADH, and lactate dehydrogenase was used. The reaction was monitored by measuring the time course of the change in absorption of NADH at 340 nm. In all the other cases, amounts of phosphate liberated at 25°C were quantified by the method of Fiske and Subbarow (1925). The activities of HMM alone at each condition of substrate or ionic strength were subtracted from each determined activity of acto-HMM under the identical condition. The NTPase activities were determined by analyzing the amounts of phosphate liberated at six time points by the least-squares criterion. The absence of the perturbation effect of Mn²⁺, Ni²⁺, and Sr²⁺ upon the phosphate assay was confirmed.

Determination of kinetic parameters

At a given concentration of NTP the acto-HMM NTPase activity, V_NTP, was measured as above at seven different actin concentrations. The maximum activity (V_m^A) at infinite concentration of actin and the actin concentration, K_0.5^A, that gave the half maximum activity were determined, a simple hyperbolic dependence of V_NTP on actin concentration being assumed. The values of V_m^A and K_0.5^A were obtained at six different concentrations of NTP. The maximum activity (V_max; see Table 1 for parameters) at infinite concentrations of actin and NTP, and the actin concentration, K_m^A (K_0.5^A at infinite concentration of NTP), were determined, simple hyperbolic dependence of V_m^A and K_0.5^A on MgNTP concentration being assumed. The MgNTP concentration, K_m^N, at which V_m^A is half of V_max, was determined from the relationship of V_m^A versus [MgNTP].

In vitro motility assay

Sliding filament in vitro motility assays were carried out as described in (Toyoshima et al., 1987) with some modifications. The temperature was maintained at 25°C for all assays. To pre-remove ATP-insensitive HMM, 5 µM HMM was mixed with 10 µM F-actin in a solution containing 0.1 M KCl, 3 mM MgCl₂, 0.2 mM CaCl₂, and 5 mM Tris-HCl (pH 8.0) at 25°C. The mixture was incubated for 20 min and then cooled to 0°C. After adding 2 mM ATP and 1 mM potassium pyrophosphate, the mixture was immediately centrifuged at 150,000 × g for 1 h. HMM in the supernatant was diluted to 0.3 µM with Buffer A, and then applied to a flow cell (~50 µl in volume) made of two coverslips (24 × 36 mm² and 22 × 22 mm²), where the larger coverslip had been coated with nitrocellulose. The cell was incubated for 2 min. Unattached HMM was washed out by applying 50 µl of Buffer A from one side of the cell and by sucking, with a piece of filter paper, from the other side of the cell. This wash was repeated five times. BSA (1 mg/ml, 100 µl) dissolved in Buffer A was then applied to the cell, incubated for 2 min, and unattached BSA was washed either with Buffer A (when NTPs were the alterant), Buffer B (when divalent cations were the alterant), or Buffer C (when [KCl] was the alterant). Tetramethylrhodamine-phalloidine-labeled F-actin (2 nM, 100 µl) in the same buffer solution was applied to the cell and incubated for 30 s. The motion of actin filaments was initiated by applying 100 µl of a test solution that additionally contained oxygen-scavenging reagents (1% 2-mercaptoethanol, 4.5 mg/ml glucose, 0.216 mg/ml glucose-oxidase, 0.36 mg/ml catalase). When Ni²⁺ was used as a complexing agent with ATP, 2-mercaptoethanol was omitted from the oxygen-scavenging reagents. The test solution conditions were the same as those used for the actin-activated HMM NTPase assays. Both open sides of the flow cell were sealed with white Vaseline. The sliding motion of individual actin filaments was observed under an epiluminescence fluorescence microscope (Olympus IX70, Tokyo, Japan; equipped with an oil-immersion objective, 100×, NA 1.35), the images being taken with a SIT video camera (C2400-08, Hamamatsu Photonics, Shizuoka, Japan) and being recorded with a Hi8 video cassette recorder (EVO-9650, Sony, Tokyo, Japan). The recorded images were digitized with an image processor (Excel, Nippon Avionics, Osaka, Japan) and the two-dimensional coordinates of the rear end of each actin filament were chased frame by frame. Length of a track connecting these coordinates during a given period of time was calculated and averaged over >50 actin filaments. The sliding velocity was obtained by dividing the average value of the lengths of tracks by the given period of time.

In vitro motility assays with noncycling cross-bridges

Chemically damaged and therefore noncycling HMM was prepared by extensive treatment of HMM with NEM. HMM (30 µM) dialyzed against 30 mM KCl, 25 mM Tris-HCl (pH 8.0), and 0.1 mM PMSF was mixed with 9 mM NEM and incubated for 1 h at 25°C. The sample was cooled in an ice-water bath, mixed with 180 mM dithiothreitol, and dialyzed against a large volume of 25 mM KCl, 2 mM MgCl₂, 0.2 mM CaCl₂, 25 mM TES-KOH (pH 7.0), 1 mM 2-mercaptoethanol, and 0.1 mM PMSF. The modified sample was frozen in liquid nitrogen and stored in liquid nitrogen. Intact HMM pretreated for removing ATP-insensitive HMM heads was mixed with NEM-treated HMM at given ratios in either Buffer A, Buffer B, or Buffer C. The total concentration of intact and noncycling HMM was adjusted to 0.3 µM. The succeeding procedures were the same as those mentioned in the preceding subsection. Immediately after initiating the movement of actin filaments, the fluorescent images of actin filaments were recorded at five different surface areas. The recording time per one area was adjusted depending on the velocity of sliding actin filaments. When the velocity was relatively high, it was minimized to be 20 s. When the velocity was very low, it was ~2 min. After recording, ~40 actin filaments on one observation area were arbitrarily picked up for analysis of the average sliding velocity as a function of the molar ratio () of NEM-HMM to intact HMM. The data were obtained from the five observation areas and then averaged.

Determination of the relative magnitude of sliding force

When actin filaments are sliding freely on HMM, the time-averaged active force generated by a cross-bridge must be balanced with the time-averaged resistive force generated by a cross-bridge that is attached to actin, but not generating active force. Let's call the active force in this situation "sliding force." We estimated the relative magnitude of sliding force as follows. We measure the average sliding velocity, V_s, as a function of . V_s would decrease with increasing . The intercept of the initial tangent of the V_s versus  relationship to the abscissa gives a value of  = _s. The _s value is taken as the relative magnitude of sliding force. The theoretical basis of this method is given in the Discussion.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Sliding Velocity as a Function of NTP Concentration

Sliding velocity, V_s, of actin filaments was measured in an in vitro motility assay using various NTPs. Various nucleotides have different affinities for HMM and acto-HMM (Pate et al., 1993; White et al., 1993). Rigor complexes of acto-HMM, even when in small fractions, may produce resistive drag force against actin filaments sliding, resulting in a reduction of the velocity. To estimate the full ability of each NTP to support acto-HMM motility without rigor complexes and to estimate the apparent Michaelis-Menten constant for each NTP (K_s^N: NTP concentration at which V_s is half of its maximum value), V_s was measured at various NTP concentrations. Fig. 1, a and b give plots of V_s versus [NTP]. At first glance, V_s seemed to show Michaelian saturation as a function of [NTP], i.e., V_s = V_s^max/(1 + K_s^N/[NTP]). Similar experiments have previously been made with ATP (Sheetz et al., 1984; Homsher et al., 1992; Umemoto and Sellers, 1990; Warshaw et al., 1990; Harada et al., 1987) and with the other nucleotides (Cooke and Bialek, 1979; Pate et al., 1993; Regnier et al., 1998). Some of these studies, where data of V_s versus [MgNTP] have been analyzed quantitatively, have assumed Michaelian saturation behavior. Careful inspection of these and our own data showed that they did not exactly obey the Michaelian relationship. At [NTP] lower than K_s^N, V_s tends to deviate downward from the Michaelian fitting curve. However, at [NTP] moderately higher than K_s^N, V_s tends to deviate upward (see, e.g., Fig. 5 in Homsher et al., 1992; Fig. 3 in Tawada and Sekimoto, 1991). A theoretical consideration regarding this issue under a certain condition led to a mixture of a modified Michaelian equation, i.e., V_s = V_s^max/(1 + (K_s^N)²/[NTP]²) and the original Michaelian equation (see Discussion). So, we assumed a modified saturation behavior, V_s = V_s^max/(1 + (K_s^N)ⁿ/[NTP]ⁿ), where the parameter, n, is one of the parameters to be determined from a least-squares fitting of the data to this modified Michaelian equation. As listed in Table 2, the value of n varied from 1.4 to 2.2 depending on the data, the average value being 1.66. The results are summarized in Table 2, together with the results obtained from the Michaelian data fitting. The standard deviations and ² tests were always smaller when the modified Michaelian saturation with n as a variable was assumed than when the original Michaelian saturation was assumed (Table 2). Although we hereafter describe only values for V_s^max and K_s^N obtained with the modified Michaelian data fitting, there were no major differences in the corresponding values obtained with the two types of data fitting (except for the case with ITP).

View larger version (20K): [in this window] [in a new window]   FIGURE 1   Substrate concentration dependence of velocity of actin filament translocation over HMM for (a) ATP (), CTP (), TTP (); and (b) UTP (), GTP (), and ITP (). Lines are fits to the modified Michaelian equation with n as a variable to be determined, i.e., Vs = Vsmax/(1 + (KsN)n/[NTP]n).

The value of V_s^max for CTP was similar to that obtained with ATP. This similarity was observed previously in in vitro motility assays (Regnier et al., 1998), although in muscle fibers CTP produces shortening velocity 30-50% less than those obtained with ATP (Pate et al., 1993; Wahr and Metzger, 1998). The K_s^N for ATP agreed with published values (Cooke and Bialek, 1979; Ferenczi et al., 1984; Homsher et al., 1992; Regnier et al., 1998). The values of K_s^N for CTP, TTP, and UTP were quite similar to each other (~0.8 mM, 14 times greater than for ATP), while the values of V_s^max for these NTPs varied over a relatively wide range. This indicates that the apparent affinity of NTP for acto-HMM does not correlate with V_s^max. The values of K_s^N for GTP and ITP were >29 times larger than for ATP, and these nucleotides were poor substrates for producing the sliding motion of actin filaments, as was previously observed with muscle fibers (Pate et al., 1993; Regnier et al., 1998) and in the in vitro motility assays (Regnier et al., 1998; Higashi-Fujime and Hozumi, 1996).

Kinetic parameters of acto-HMM NTPase

At a given concentration of NTP the acto-HMM NTPase activity, V_NTP, was measured at various actin concentrations. The NTPs used here were the same as used above. With all the NTPs used V_NTP displayed simple hyperbolic saturation behavior as a function of [actin] (data not shown). When the relationship of V_NTP versus [actin] was analyzed with the modified Michaelian equation, with n as a variable to be determined, we obtained n = 1.0 on the average. The values of V_m^A (V_NTP at infinite actin concentration) and K_0.5^A ([actin] at which V_NTP is half of V_m^A) for all six nucleotides were obtained by analyzing the hyperbolic saturation curves by the least-squares criterion to fit the equation V_NTP = V_m^A/(1 + K_0.5^A/[actin]). Although these parameters, V_m^A and K_0.5^A, must be less sensitive to the presence of a small amount of rigor complexes than V_s, they (except for those with ATP) may not be saturated in the presence of a millimolar concentration of NTP. We, therefore examined these parameters as a function of NTP concentration. V_m^A and K_0.5^A with CTP were nearly saturated at 1 mM CTP. However, these parameters with TTP, UTP, GTP, and ITP were not saturated at 1 mM [substrates]. V_m^A displayed Michaelian saturation behavior as a function of [MgNTP]. K_0.5 versus [MgNTP] also showed Michaelian saturation behavior. From these saturation curves V_max (V_NTP at infinite [NTP] and infinite [actin]) and K_m^A (K_0.5^A at infinite [NTP]) were estimated. These values are listed in Table 2. Both V_max and K_m^A decreased in the same order, ATP > CTP > TTP > UTP > ITP > GTP, with K_m^A varying more widely than V_max. The NTP concentrations, K_m^N, at which V_m^A is half of V_max, are also listed in Table 2. K_m^N with ATP was 9 µM, 6.6 times less than the value of K_s^N. K_m^N with CTP could not be accurately determined because this value seemed so small and the hydrolysis rate is so high that V_m^A could not be measured at low concentrations of [MgCTP] (effective CTP-regeneration systems are not available). This parameter, however, seemed to be ~0.1 mM, 6.9 times less than the value of K_s^N. TTP, UTP, and GTP gave values of K_m^N that were in the submillimolar range, 3-4 times less than the respective values of K_s^N. The value of K_m^N for ITP was 1 mM, 2.1 times less than the value of K_s^N. Thus the ratio, K_s^N/K_m^N, is markedly dependent on NTP. The values obtained for the NTPase activity of HMM alone, V_HMM, at 6 mM [NTP] are also listed in Table 2. V_HMM increased in the order CTP < ATP < TTP < UTP < GTP < ITP, approximately the inverse order to those with V_max and K_m^A.

Comparison of motile activity and NTPase kinetics with various NTPs

Here, we examine the relationships between the sliding velocity and the kinetic parameters obtained above. Two kinds of plots, (a) V_s^max versus V_max and (b) V_s^max versus K_m^A, are given with open circles and with circles with a cross in Figs. 2 and 3, respectively. Although the curve of V_s^max versus V_max relationship was concave downward, it suggests a strong correlation between the rate of hydrolysis and the sliding velocity. Previous studies with muscle fibers have reported only moderate correlations between the maximum rate of actin-activated hydrolysis of NTPs by acto-S1 or acto-HMM and the unloaded shortening velocity of muscle fibers (White et al., 1993; Pate et al., 1993; Regnier et al., 1998). In these studies, however, the solution conditions were different in the mechanical and enzymatic measurements, and the concentrations of NTP used for measurements of the hydrolysis rates were fixed at 1 mM, irrespective of the NTP used. Moderate or very poor correlations were also reported in studies with the in vitro actin filament sliding assays (Higashi-Fujime and Hozumi, 1996; Regnier et al., 1998). In the study reporting very poor correlation (Higashi-Fujime and Hozumi, 1996), the hydrolysis rate was measured at a fixed concentration of actin (3.6 µM). A correlation as good as is observed here between the sliding velocity and apparent K_m for actin (K_m^A) (Fig. 3) has never been reported before. Similar examinations have been done previously using various NTPs in muscle fibers and in in vitro motility assays (White et al., 1993; Pate et al., 1993; Regnier et al., 1998). However, results similar to ours were not observed. This may be in part because the previous studies used different solution conditions for measuring the sliding velocity and the enzymatic kinetics.

View larger version (16K): [in this window] [in a new window]   FIGURE 2   The relationship between the maximum sliding velocity (Vsmax) and the maximum acto-HMM NTPase activity (Vmax, Pi/s/head). The substrate was altered with MgATP (), MgCTP, MgTTP, MgUTP, MgGTP, MgITP (), or with MnATP, NiATP, SrATP (). The ionic strength was altered with KCl (, ). In this case MgATP was used as substrate. The maximum acto-HMM NTPase activities are those at infinite [NTP] and infinite [actin].

View larger version (23K): [in this window] [in a new window]   FIGURE 3   The relationship between the maximum sliding velocity (Vsmax) and the Km for actin (i.e., KmA). The substrate was altered with MgATP (), MgCTP, MgTTP, MgUTP, MgGTP, MgITP (), or with MnATP, NiATP, SrATP (). The ionic strength was altered with KCl (, ). In this case MgATP was used as substrate. The values of KmA are those at infinite [NTP]. The inset is the relationship between Vsmax vs. obtained when ionic strength was varied.

We have to be careful in concluding that the two excellent correlations shown with open circles and circles with a cross in Figs. 2 and 3 are significant. The two kinetic parameters, V_max and K_m^A are, in principle, independent of each other. Yet, they varied in a similar way when the substrate was altered with various MgNTPs. It is, therefore, possible that only one of the two types of correlations is significant, and that another is just accidental. To clarify this aspect we have to perturb the acto-HMM system by other methods and examine the two relationships again.

Motility and kinetics with substrates, ATP complexed with various divalent cations

As second perturbants of the acto-HMM system we used substrates, ATP complexed with various divalent cations (Me²⁺). We chose Mg²⁺, Mn²⁺, Ni²⁺, and Sr²⁺ for the Me²⁺. All of these ions, with ATP, supported movement of actin filaments over HMM. First, we measured the dependence of sliding velocity on the substrate concentration. The data for the four substrates were analyzed by least-squares fitting to the modified Michaelian equation with n as a variable to be determined (i.e., V_s = V_s^max/(1 + (K_s^N)ⁿ/[S]ⁿ)) and to the original Michaelian equation. The results are summarized in Table 3. The standard deviations and ² tests were again often smaller with the former analysis than the latter. Because of this we choose the results obtained from the modified Michaelian data fitting. The data for V_s^max yielded the relationship Mg > Mn > Ni > Sr. MnATP was an effective substrate, its V_s^max being 77% of that with MgATP. SrATP was a very poor substrate, its V_s^max being <2% of that with MgATP. These substrates showed relatively high affinities for acto-HMM, and their values of K_s^N were in the submillimolar range. Because K_m^N must be a few times less than K_s^N, several measurements with these substrates were thereafter made at a fixed substrate concentration, 2 mM, which is sufficient to provide almost complete saturation of the nucleotide binding sites. The acto-HMM Me²⁺ ATPase activity exhibited again a simple hyperbolic saturation behavior as a function of actin concentration. The values V_max and K_m^A are listed in Table 3. MnATP gave the highest V_max, 1.7 times greater than that for MgATP, while its K_m^A value was smaller than that for MgATP. NiATP was an effective substrate with V_max, which was 64% of that obtained with MgATP, and its K_m^A value was about half of that for MgATP. SrATP was a very poor substrate. However, HMM complexed with SrATP or its product had the highest affinity for actin. Plots V_s^max versus V_max, shown with closed circles and a circle with a cross in Fig. 2, indicate only a moderate correlation between the sliding velocity and the maximum hydrolysis rate of Me²⁺ ATP by acto-HMM. As mentioned above, the MnATPase activity was 1.7 times greater than the MgATPase activity. Nevertheless, the sliding velocity with MnATP was 77% of that with MgATP. The relationship V_s^max versus K_m^A, shown with closed circles and a circle with a cross in Fig. 3, however, indicated that the sliding velocity was highly correlated with K_m^A, although the fitted line did not intercept the origin. The hydrolysis rates, V_HMM, of these Me²⁺ ATP by HMM alone are also listed in Table 3. The 1/V_HMM increased in the order SrATP < MgATP < NiATP < MnATP. This order was quite different from that of V_s^max, indicating no correlation between the two quantities.

Comparison of motile activity and MgATPase kinetics at various ionic strengths

As a third perturbant of the acto-HMM system, we chose differing ionic strengths. When ionic strength in the in vitro motility assays is higher than ~80 mM, actin filaments or myosin-coated beads tend to dissociate from the respective partners. At lower ionic strengths the rate of movement increases with increasing ionic strength (Harada et al., 1987; Umemoto and Sellers, 1990; Warshaw et al., 1990; Takiguchi et al., 1990; Vale and Oosawa, 1990; Homsher et al., 1992; Saito et al., 1994). With the help of methylcellulose, which reduces the lateral diffusion of actin filaments from the myosin-coated surface (Uyeda et al., 1990), the sliding velocity of actin filaments can increase as ionic strength is elevated even higher than 80 mM (Homsher et al., 1992). Despite general acceptance of this acceleration effect of ionic strength, quantitative analysis of the effect has not been performed, and therefore the underlying mechanism has not been well understood. Here, we reexamined the ionic strength effect on the rate of actin filament translocation. The ionic strength of solution was varied with KCl. MgATP was used as substrate and its concentration was fixed at 2 mM. As shown in Table 4, V_s^max increased smoothly with increasing [KCl], with a slight upward deviation from a linear relationship. The maximum rate (V_max) of MgATP hydrolysis by acto-HMM was nearly constant over [KCl] from 5 mM to 50 mM (Table 4). K_m^A was, however, increased with increasing [KCl], with upward deviation at higher [KCl] from a linear relationship (Table 4). These distinct behaviors of V_max and K_m^A as a function of [KCl] made the relationships V_s^max versus V_max and V_s^max versus K_m^A very different (squares and circles with a cross in Figs. 2 and 3, respectively). V_s^max varied widely, without almost no changes in V_max. In contrast to this, V_s^max increased with increasing K_m^A. The MgATPase activity of HMM alone, V_HMM, increased, in a linear manner, with increasing [KCl] (Table 4). This enhancement effect of [KCl] gave a relationship between V_s^max versus V_HMM that was completely opposite to that observed when the substrate was altered with various MgNTPs (Table 2).

Sliding force

It has been recognized that actin filaments would not slide smoothly over HMM when the HMM sample is partially damaged. Based on this phenomenon, Haeberle developed a method for estimating relative magnitude of active force exerted on actin filaments in the in vitro motility assays (Haeberle, 1994). Chemically damaged and therefore noncycling HMM that is mixed with intact HMM imposes an external load on sliding actin filaments and thereby slows the sliding motion. When the molar ratio () of noncycling HMM to intact HMM is increased with keeping the total HMM amount constant, the movement of actin filaments is eventually stalled. We prepared noncycling HMM by extensively treating HMM with NEM. This NEM-HMM had neither Ca²⁺ NTPase nor actin-activated NTPase activities. Actin filaments attached to the surface that had been coated with this damaged HMM never detached from the surface in the presence of any Mg²⁺-NTPs. NEM-HMM, therefore, seemed unable to associate with NTP.

We estimated the relative magnitude of active force that is generated by a cross-bridge when cross-bridges are propelling actin filaments to slide without external load or under a small external load. We call this active force "sliding force." The method for this estimation and the basis of this method are described in Materials and Methods and Discussion, respectively. In the first set of experiments we studied the dependence of the relative magnitude of sliding force on NTPs. The concentration of NTP was first fixed at 2 mM. The sliding velocity decreased linearly with increasing , as demonstrated in the inset of Fig. 4. The intercept to the abscissa (i.e., _s) of the initial tangent of the V_s versus , which is supposed to be proportional to the magnitude of sliding force, was roughly constant over the NTPs used (Fig. 4 and Table 2). Since 2 mM of NTPs (except for ATP) do not saturate the nucleotide binding site of HMM, these measurements were repeated at various concentrations of NTP (from 1 to 6 mM). We could not, however, find NTP-concentration dependence of the _s values, even with GTP and ITP, whose affinities for acto-HMM were low compared with the other NTPs. Also in the second set of experiments, where divalent cations that complex with ATP were varied, the _s values were quite similar to each other (Table 3). In this experiment Sr²⁺ ATP was omitted because of the very small rate of movement. In the third set of experiments, where MgATP was used as substrate and the ionic strength was varied with various [KCl], _s showed a tendency to decline with increasing [KCl] (Table 4). In this experiment the resistive force by NEM-HMM may vary depending on [KCl]. It is likely that the higher [KCl] may result in less resistive force. The tendency for sliding force to decline with increasing [KCl] may, therefore, be more significant than that of _s.

View larger version (43K): [in this window] [in a new window]   FIGURE 4   Relative magnitude of sliding forces in various MgNTPs and its dependency on [MgNTP]. The ionic strength was kept constant by adjusting [KCl]. The inset shows dependence of sliding velocity in MgATP upon the molar ratio () of NEM-HMM to intact HMM. The linear line intercepts the abscissa at  = s.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

A kinetic scheme of the actomyosin ATPase

Before we discuss the experimental results obtained in the present study, we briefly describe the kinetics of the actomyosin ATPase reaction. The kinetic scheme shown here accounts for the results of various kinetic experiments. Myosin heads are distinguished according to their actin-binding kinetics (Stein et al., 1979), i.e., "weak-binding states" and "strong-binding states." ATP binds to a rigor cross-bridge (step 1) to form a weakly bound state (A · M · ATP), followed rapidly by dissociation of actin (A) from myosin (M) (step 2), or by hydrolysis of the -phosphate (step 3). After hydrolysis of the -phosphate (step 3 and step 5), a weakly bound state (A · M · ADP · Pi) forms, which is in a rapid equilibrium with the M · ADP · Pi state (step 4). The weakly bound cross-bridge then isomerizes to a strong-binding state (step 6). The bound phosphate is released (step 7) to form A · M* · ADP, which is followed by isomerization (step 8). Finally, ADP is released (step 9) to form a rigor cross-bridge. Rate limitation of the ATPase cycle in solution has been variously thought to occur at the isomerization step (step 6) (Stein et al., 1979, 1984), at the Pi release step (step 7) (Webb and Trentham, 1981; Hibberd and Trentham, 1986; Barman et al., 1998) (the two states, A · M · ADP · Pi and A · M* · ADP · Pi, are not distinguished), or at the cleavage step (step 3) (Rosenfeld and Taylor, 1984; White et al., 1997) (deduced from observations that a high concentration of actin suppresses the ATPase activity at very low ionic strength). Using a fluorescent Pi-probe and caged-ATP in single muscle fibers, He et al. (1997, 1998) have observed that the onset of tension development is slightly earlier than that of Pi release, indicating that A · M* · ADP · Pi contributes to the force-generating state. Other studies have also presented evidence that both A · M* · ADP · Pi and A · M* · ADP contribute to the force-generating state (Lund et al., 1987; Dantzig et al., 1992; Cooke, 1995). Although a consensus about the rate-limiting step in the ATPase cycle has not been reached, it has been generally accepted that 1) myosin heads reside predominantly in the weak-binding state(s) in which they are in a rapid equilibrium between the actin-attached and detached states, and 2) an intermediate just after the power stroke is A · M · ADP. Although in a part of the subsequent discussion we assume the rate-limiting step to be step 6, we do not intend to validate this assumption. The results given below are not strongly associated with this assumption. The ATPase kinetic scheme cited here probably hold for almost all the other nucleotides, as suggested by Pate et al. (1993); White et al. (1993); and Regnier et al. (1998); although the GTPase probably has a different kinetic mechanism (Eccleston and Trentham, 1979; White et al., 1997).

View larger version (6K): [in this window] [in a new window]   Scheme 1

Resistive drag forces

Actin-attached cross-bridges that are not executing the power stroke produce a resistive force opposing sliding movement, because these cross-bridges are pulled and deformed passively by moving actin filaments. In a high concentration of substrate, such resistive cross-bridges are in the post-power stroke state (from which NDP is released) and in the weak-binding states. To the authors, it seems controversial whether weakly bound cross-bridges produce resistive force to such an extent that it affects or determines the sliding velocity (Warshaw et al., 1990; Homsher et al., 1992; Cuda et al., 1997; Brenner, 1990). First, we examine this issue quantitatively, since this issue seems to have the key to understanding the link between the chemistry and the mechanics in skeletal actomyosin. If for a time T a resistive cross-bridge remains attached to a sliding actin filament (velocity, V_s), it is pulled for a distance of V_sT. When averaged over the cycle time (T_c = 1/V_max) of the NTPase reaction, the resistive force, f_r, becomes

(1)

where  is an elastic constant of a resistive cross-bridge and  is the fraction of this resistive state over all states. Now, we roughly estimate the magnitude of f_r in ATP, using values of , , and T. Although  may vary depending on the state concerned, the reported values for different states are similar to each other: 0.65 pN/nm, measured directly using a single-molecule technique in the midst of an ATPase cycle (Mehta et al., 1997); 0.58 pN/nm, measured directly using a single-molecule technique in the rigor state (Nishizaka et al., 1995). So, we assume  = 0.6 pN/nm for all the resistive states. For weakly bound cross-bridges, the time, T, equals 1/k₂ or 1/k₄. Hereafter, we assume k₂ = k₄ (k_w) and k₊₂ = k₊₄ (k_+w). The rate constant of dissociation of myosin heads with ATP from actin is likely to be ~2000 s¹, inferring from the values obtained previously under various solution conditions. So, we assume T = 0.5 ms. Skeletal actomyosin has a low duty ratio, the fraction of time that a cross-bridge spends generating active force. The ratio is suggested to be ~0.1 (Cooke, 1997), and myosin heads reside predominantly in the weak-binding state(s). Taking these features into account, the total fraction of weakly bound cross-bridges is supposed to be ~0.8. These values for , T, , and V_s = 4.3 µm/s result in f_r = 0.51 pN per a weakly bound cross-bridge. As will be shown later, this magnitude is comparable to the time-averaged active force per a cross-bridge, but significantly lower than the force required to unbind a rigor head from actin. The lifetime of the post-power stroke state is determined by the rate constant of ADP dissociation from the actin-bound cross-bridge (here we distinguish the resistive forces produced by A · M · ADP and A · M · ATP. The latter is counted among those produced by weakly bound cross-bridges.) Although the rate constant of ADP dissociation on the ATP hydrolysis pathway has not been determined, we assume that it is similar to the rate constant (k_AD) of ADP dissociation from the state formed by externally adding ADP to actomyosin. For rabbit skeletal actomyosin, k_AD is ~1000 s¹ (700-1000 s¹ at 25°C, Siemankowski et al., 1985; 1400 s¹ at 20°C, Borejdo et al., 1985). So, we assume T = 1 ms. The fraction of the post-power stroke state is supposed to be very small (Barman et al., 1998). Tentatively, we assume  = 0.023, because  must equal T/T_c = 1/42 (T_c = 1/V_max = 42.4 ms). These values lead to a rough estimate, f_r = 0.029 pN, 17.6 times less than that produced by a weakly bound cross-bridge. We have to note here that a cross-bridge in the post-power stroke state produces a resistive force just once during an ATPase cycle, while in the weak-binding states a cross-bridge produces it many times. Here, for simplicity, we neglected the reductive effect of elastic deformation on the lifetime (T) of weakly bound cross-bridges. The rate of ADP dissociation may be affected by the elastic deformation. Here, we do not consider it. When the deformation energy, E_d = 0.5 × (V_sT)², is comparable to or larger than the thermal energy, E₀ ~ 4 × 10²¹ J, T should be reduced significantly, as has been demonstrated in the acto-HMM rigor bond (Nishizaka et al., 1995). The deformation accelerates the rate of dissociation from actin by a factor of e^E_d/E₀ (Bell, 1978). So, the probability of finding a cross-bridge that bound to actin at time zero and keeps associating with actin till time t is proportional to P(t)  exp(₀^t k_we^E_d/E₀ dt). Therefore, the lifetime, T, can be determined by T = ₀ t P(t)dt/₀ P(t)dt. Performing the integrations numerically, we find that the lifetime of a weakly bound cross-bridge is slightly reduced to 0.3 ms (the resistive force, 0.31 pN). A slight increase in the dissociation rate hardly affects the fraction of weakly bound cross-bridges because a high concentration of actin shifts the rapid equilibrium to the actin-attached side. Although the difference in the resistive forces produced in the weak-binding states and in the post-power stroke state became smaller (10.7 times), it is still large. Even when we choose a lower value, 700 s¹, for the ADP dissociation rate ( becomes 0.034), the difference in the resistive forces is still 5 times. After all, we reached an estimate that resistive force is produced predominantly by weakly bound cross-bridges. Hereafter, we neglect resistive forces produced by cross-bridges in the post-power stroke state. We also neglect the deformation effect on the lifetime of weakly bound cross-bridges, because it is not so large. As will be seen later, deformation energy stored in weakly bound cross-bridges is rather independent of nucleotides (a longer lifetime and a slower rate of movement cancel out each other to give a similar deformation energy).

Dependence of sliding velocity on substrate concentration

Sliding velocity (V_s) of actin filaments decreases with decreasing substrate concentration, [S] (Fig. 1, a and b). This is certainly due to the resistive forces produced by the nucleotide-free rigor cross-bridges (i.e., AM). The lifetime, T_rig, of an AM rigor cross-bridge is determined by

(2)

where k₊₁ is the second-order rate constant of nucleotide binding. When averaged over T_rig + T_c, the resistive force per an AM rigor cross-bridge is given by

(3)

where _rig = T_rig/(T_rig + T_c), and V_sT_rig cannot exceed the force (F_u) required to rupture an AM rigor cross-bridge. If it exceeds F_u, the average resistive force should be replaced with 0.5 × _rigF_u. For a while we consider the case where V_sT_rig < F_u holds. Including the resistive force produced by a weakly bound cross-bridge, a balance of the time-averaged forces regarding one cross-bridge is expressed as follows.

(4)

where f_s is sliding force (active force) averaged over T_c, _w is the fraction of weakly bound cross-bridges in T_c, and T_w(1/k_w) is the lifetime of weakly bound cross-bridges. This equation is independent of the concentration of HMM on the coverslip (above certain threshold level). Solving this equation for V_s, we obtain

(5)

By substituting 1/k_w, 1/(k₊₁[S]), and 1/V_max into T_w, T_rig, and T_c, respectively, we obtain

(6)

where V_s^max and K_s^N are respectively defined by

(7)

(8)

Here, V_s^max is the maximum sliding velocity, K_s^N is the substrate concentration at which V_s is half of V_s^max, and K_m^A is the actin concentration at which the enzymatic activity is half of V_max and approximately equals k_w/k_+w. Here, we assumed that f_s is constant, although it must vary depending on V_s. Equation 6 is the same as the modified Michaelian equation, with n = 2. Now, we consider the case where V_sT_rig > F_u holds. In this case, substitution of F_u for V_sT_rig in Eq. 4 leads to

(9)

where V_s^max is the same as that in Eq. 7, but K_s^N is newly given by

(10)

For a range [S] ~ K_s^N, Eq. 9 can roughly be approximated to the original Michaelian equation (n = 1) as

(11)

Equation 6 holds for [S] that satisfies the condition, F_u > V_sT_rig. Putting this condition and T_rig = 1/(k₊₁[S]) into Eq. 6, we obtain the following quadratic inequality:

(12)

Solving this inequality for [S], we find that in the case F_u > F₀(