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Originally published In Press as doi:10.1074/jbc.M303583200 on May 19, 2003

J. Biol. Chem., Vol. 278, Issue 31, 28533-28539, August 1, 2003
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The Unique Properties of Tonic Smooth Muscle Emerge from Intrinsic as Well as Intermolecular Behaviors of Myosin Molecules*

Josh E. Baker, Christine Brosseau, Patty Fagnant and David M. Warshaw {ddagger}

From the Department of Molecular Physiology and Biophysics, University of Vermont, Burlington, Vermont 05405

Received for publication, April 7, 2003 , and in revised form, May 14, 2003.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS
 DISCUSSION
 REFERENCES
 
To better understand the molecular basis for some of the unique mechanical properties of tonic smooth muscle, we use a laser trap to assay the mechanochemistry of single smooth muscle heavy meromyosin molecules lacking a seven-amino acid insert in the nucleotide binding loop (minus insert). We measured a second-order ATP-induced actin dissociation rate, kT, of 2.2 x 106 M–1 s–1, an ADP release rate, k–D, of 19 s–1, a second-order ADP binding rate, kD, of 60 x 105 M–1 s–1, and an ADP affinity, KD, of 3.2 µM, which is more than 100-fold greater than that measured for skeletal muscle myosin. By performing in vitro motility studies under nearly identical conditions, we show that the relatively slow actin velocity generated by minus-insert heavy meromyosin is significantly influenced, but not limited, by k–D. Our results support a model in which two separate intermediate steps in the actin-myosin catalyzed ATP hydrolysis reaction are energetically coupled through mechanical interactions, and we discuss this model in the context of the ability of tonic muscle to maintain high forces at low energetic cost (latch).


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
EXPERIMENTAL PROCEDURES
 RESULTS
 DISCUSSION
 REFERENCES
 
Muscle shortening and force generation result from actin-myosin binding events that are coupled to the actin-myosin catalyzed ATP hydrolysis reaction illustrated in Fig. 1. Upon binding to an actin filament (A) and releasing inorganic phosphate (Pi), myosin undergoes a large and discrete rotation of its lever-like light chain domain, which is capable of generating both motion and force (1–5). With the subsequent release of ADP (at the rate k–D) an additional rotation of the light chain domain of myosin has been observed in smooth muscle myosin (6, 7), but unlike the work generating rotation associated with actin binding/Pi release, the rotation associated with ADP release is thought to be a strain-sensing biochemical step (8–10). Following the release of ADP, ATP binding induces the detachment of myosin from the actin filament (at the rate kT), after which ATP is hydrolyzed.



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  		FIG. 1.
Structural and kinetic representation of the actomyosin ATPase reaction. A myosin head (ovals) has a weak affinity for an actin filament (helix) when ATP or ADP and inorganic phosphate, Pi, are bound to myosin. Upon Pi release, the affinity of myosin for actin increases by several orders of magnitude and upon strong binding to actin undergoes a conformational change (a discrete light chain domain rotation) capable of moving actin. An additional light chain domain rotation is thought to occur with ADP release, and the subsequent binding of ATP to myosin decreases the affinity of myosin for actin. M, myosin; A, actin; T, ATP; D, ADP; Pi, inorganic phosphate

 

Muscles differ significantly in their shortening speeds and force-generating capacities. For instance, smooth muscle produces a greater average force per myosin and slower speeds of shortening than skeletal muscle (11). To a large extent these mechanical differences are caused by kinetic differences among the different myosin isoforms that exist within different muscle types (12, 13). For example, phasic and tonic smooth muscle (found in the intestine and aorta respectively) express two myosin heavy chain isoforms that differ by a seven-amino acid insert in a surface loop spanning their nucleotide binding pocket (14–16). Phasic smooth muscle contains primarily the plus-insert myosin, whereas tonic smooth muscle contains primarily the minus-insert myosin. In addition, two essential light chain isoforms are coordinately expressed with the heavy chain isoforms. The acidic isoform (LC17a) is coexpressed with the plus-insert heavy chain whereas the basic isoform (LC17b) co-expresses with the minus-insert heavy chain (17–19). Based on in vitro motility studies, the presence or absence of the seven-amino acid insert in the heavy chain is the sole determinant of the 2-fold faster actin filament velocities for the plus-insert myosin compared with the minus-insert myosin (14, 20, 21), which in part may contribute to the differences in shortening velocity for phasic and tonic smooth muscles (22, 23). The absence of the seven-amino acid insert, in addition to the presence of the LC17b isoform that is coexpressed with the minus-insert heavy chain (24), may be responsible for the unique ability of the tonic muscle to enter a latch state (25) in which high contractile forces are maintained with minimal expenditure of chemical energy (i.e. minimal ATP turnover).

The relatively slow actin velocity generated by minus-insert myosin is related in part to the relatively slow ADP release rate of minus-insert myosin (21). Moreover, muscle mechanics and solution biochemical studies suggest that the economic force maintenance of tonic smooth muscle is related to the relatively high ADP affinity of minus-insert myosin, which slows the isometric ATPase rate and prolongs the strongly bound state of myosin at physiological ADP concentrations (8, 9, 26, 27). However, an explicit link between the bulk properties of tonic smooth muscle and the mechanics and kinetics of individual minus-insert smooth muscle myosin molecules remains unclear.

Because of the complexities introduced by compliant structures in muscle, the relationship between muscle mechanics and actin-myosin kinetics is model-dependent (4). For a more direct determination of the molecular basis for the unique mechanical properties of tonic smooth muscle, we use a laser trap to assay the mechanochemistry of single minus-insert heavy meromyosin (HMM)1 molecules. By varying ATP and ADP concentrations, we determine values for the ADP release rate, k–D, the second-order ADP binding rate, kD, and the second-order ATP-induced actin-myosin dissociation rate, kT, one molecule at a time. We then compare the kinetics of minus-insert HMM to those determined previously (4) for skeletal muscle myosin in an effort to explain the differences in the mechanical performance of these two muscle types. Finally, a comparison of our single molecule kinetics measurements with the apparent kinetics of ensemble-based actin filament movement (measured in an in vitro motility assay under nearly identical conditions) suggests that at low ATP concentrations, actin-myosin detachment kinetics alone limit actin velocities but that at high ATP concentrations detachment and attachment kinetics are intimately linked, and both influence actin velocities. These data support a model in which ADP release rate of myosin in muscle is influenced both by intermolecular interactions and by intrinsic myosin properties and may help to explain the ability of tonic smooth muscle to maintain active force with little energy expenditure (i.e. latch).


   EXPERIMENTAL PROCEDURES
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
RESULTS
 DISCUSSION
 REFERENCES
 
Proteins—Minus-insert smooth muscle HMM was expressed in the Baculovirus expression system and thiophosphorylated, as reported previously (20), and stored in glycerol at –20 °C (28). To eliminate kinetically compromised HMM molecules ("dead heads"), HMM was purified immediately before use by centrifugation with equimolar actin and 1 mM ATP in myosin buffer (see "Buffers"). N-Ethylmaleimide-modified skeletal myosin was prepared as described previously (28) and was used to bind actin filaments to polystyrene beads (1.0-µM-diameter polystyrene; Polysciences Inc., Warrington, PA (29)) for use in the laser trap assay. Actin was isolated from chicken pectoralis (30) and incubated overnight with TRITC-labeled phalloidin as described previously (28).

Buffers—Myosin buffer contained 0.3 M KCl, 25 mM imidazole, 1 mM EGTA, 4 mM MgCl2, and 10 mM dithiothreitol, adjusted to pH 7.4. Actin buffer (AB) contained 25 mM KCl, 25 mM imidazole, 1 mM EGTA, 4 mM MgCl2, 10 mM dithiothreitol, and oxygen scavengers (0.1 mg ml–1 glucose oxidase, 0.018 mg ml–1 catalase, 2.3 mg ml–1 glucose), adjusted to pH 7.4. Ligands (1 µM to 1 mM ATP and 0 to 5 mM MgADP) were added to AB, and to maintain a constant ionic strength and a 3 mM free Mg+2 concentration, the KCl and MgCl2 concentrations were adjusted using an algorithm based on Ref. 31.

Laser Trap—A laser trap assay was used as described previously (29, 32, 33). Solutions were added to the flow cell with the following series of incubations: (i) 20 µlof100 µg/ml monoclonal antibody S2.2 for 2 min (34), (ii) 20 µl of 0.5 mg ml–1 bovine serum albumin in myosin buffer for 2 min, (iii) 20 µlof1 µgml–1 HMM for 2 min, (iii) 3 x 20 µl AB, and (iv) 3 x 20 µl of AB with desired ligands, TRITC-actin, and N-ethylmaleimide-coated beads. Experiments were performed at 25 °C.

A single bead was caught in each of the two laser traps, and each bead was attached to the end of a single actin filament. The actin filament was pre-tensioned to ~4 pN and positioned over a silica pedestal coated sparsely with HMM. By projecting the bright-field image of one of the beads onto a quadrant photodiode detector, separate signals were acquired for bead movement in directions parallel and perpendicular to the long axis of the actin filament. Both signals were recorded for at least ~120 s (a data trace) before moving the actin to another pedestal. Data traces were rejected if displacements were detected in the perpendicular direction, and the remaining data traces were filtered at 2 kHz and then digitized at 4 kHz.

In Vitro Motility—The solutions used in our in vitro motility experiments were nearly identical to those used in the laser trap experiments, except in our motility experiments the HMM concentration was 100 µg/ml, and the final AB contained methylcellulose (33). Movement of fluorescent actin filaments over an HMM-coated surface was recorded as described previously (28), and actin filament velocities, V, were determined from video recordings of filament movement using an ExpertVision motion analysis system (Motion Analysis, Santa Rosa, CA) as described previously (35). Experiments were performed at 25 °C.

Laser Trap Data Analysis—Upon strong binding to an actin filament in a laser trap, HMM displaces the actin filament and causes a reduction in the Brownian motion of the bead-actin-bead system (see Fig. 2a) by adding its stiffness to the bead-actin-bead system (29, 36). Both phenomena are used to determine the duration, ton, of actin-myosin strong binding events.



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  		FIG. 2.
Effects of [ATP] on ton. a, three characteristic data traces acquired at 1, 0.01, and 0.001 mM ATP show an increase in event durations, ton, with decreasing [ATP]. b, characteristic plots of MV densities, {rho}on(tw), versus window widths, tw (top two), and ton distributions, non(t), versus ton (bottom) obtained from individual data records acquired at 1, 0.01, and 0.001 mM ATP. To obtain values for kT and k–D, these and similar plots were fitted to the following equations. In those equations, p = 0.25(k–D + kD[ADP] + kT[ATP])2 – k–DkT[ATP], q = –1/2(k–D + kD[ADP] + kT[ATP]), and A is the product of {Delta}t and the number of events in the data set, N (4). The symbols indicate the center of a bin of width {Delta}t.

 

Depending on the number of events observed in a given data trace, one of two methods was used for extracting kinetic rate constants from ton data. For experimental conditions that resulted in data traces containing relatively few actin-myosin binding events (i.e. <40 events in a 2-min trace), ton for each event was measured directly, and for a set of data records the number of events, non, having ton values between t and t + {Delta}t, was plotted in a histogram. This distribution, non(t), was then used to estimate kinetic rate constants (4).

For experimental conditions that resulted in data records containing a relatively large number of events, we used a mean-variance (MV) analysis (29, 37). Briefly, this approach involves moving a time window of width tw, through a displacement trace and then plotting the mean and variance of each window in a two-dimensional MV histogram. Because only events with durations >=tw appear in the event region of an MV histogram, the event density, {rho}on, varies with window width, tw, reflecting the stochastic nature of event durations (i.e. the detachment kinetics). Thus kinetic rate constants can be determined from an analysis (4) of {rho}on(tw) without tallying individual events.

Based on the scheme in Fig. 1, actin-myosin detachment is a two-step biochemical process, and, in the absence of Pi, three rates contribute to a ton distribution: the effective ADP release rate, k–D, the ADP binding rate, kD, and the second-order ATP-induced dissociation rate, kT. Values for the kinetic rate constants, k–D, kD, and kT, were determined using an analysis of non(t) and {rho}on(tw) distributions acquired at various ligand concentrations, as described previously (4).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS
DISCUSSION
 REFERENCES
 
Single Molecule Determination of k–D and kT—To determine values for the ADP release rate, k–D, and for the second-order ATP-induced actin dissociation rate, kT, of minus-insert smooth muscle HMM (Fig. 1), we characterized the effect of different ATP concentrations on the duration of actin-myosin binding events observed in the laser trap assay. Fig. 2 shows sample data traces obtained at three different ATP concentrations and, consistent with the kinetic scheme in Fig. 1, shows that attachment times, ton, tend to increase with decreasing ATP concentrations. The distribution of ton values obtained at each ATP concentration was accurately described by kinetic equations based on the scheme in Fig. 1 (4). Assuming that the detachment rate for minus-insert myosin saturates at 1 mM ATP (i.e. [1 mM] x kT » k–D), we fitted ton distributions acquired at 1 mM ATP (Fig. 2, top) to a single exponential (4), shown in Equation 1.

(Eq. 1)
Using Equation 1 we obtained an average value for k–D of 19 s–1. Because a laser trap assay measures the kinetics of actin-myosin dissociation starting from the state occupied at the onset of actin-myosin binding, k–D in Fig. 1 is an effective ADP release rate that describes all isomerizations of the ADP-bound state (A.M.D.), some of which might be missed in kinetic studies that measure actin-myosin dissociation following the rapid introduction of ATP in the presence of ADP.

We also obtained ton distributions at 1 or 10 µM ATP (Fig. 2b), from which we obtained a value for kT of 2.2 x 106 M–1 s–1 (see legend of Fig. 2). Based on the above estimates for k–D and kT, we calculate a value for Km(on) = k–D/kT of 8.6 ± 5 µM.

Single Molecule Determination of kD—We determined a value for the second-order ADP binding constant, kD, by using a laser trap to acquire actin-myosin binding events at different ADP concentrations. Consistent with Fig. 1, Fig. 3 shows that ton increases dramatically with increasing [ADP]. From ton distributions acquired at 1 mM ATP and 0, 1, 3, or 5 mM ADP, we obtained an average value for kD of 60 x 105 M–1 s–1 (see Fig. 3).



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  		FIG. 3.
Effects of [ADP] on ton. a, three characteristic data traces obtained at 1 mM ATP and 0, 1, and 5 mM ADP. b, characteristic plots of MV densities, {rho}on(tw), versus window width, tw, or ton distributions, non(t), versus ton obtained from data records acquired at 1 mM ATP and 0, 1, and 5 mM ADP. These plots are fit (line) to the Equations 4 and 5, setting kT = 1.6 x 106 M–1 s–1 and k–D = 19 s–1 as determined above. Plots are normalized to the MV density at 20 ms.

 

In Fig. 4, we plotted the average ton, or the attachment lifetime ({tau}on), obtained at different ADP concentrations both for minus-insert smooth muscle HMM and for skeletal muscle myosin obtained previously using similar methods (4). Based on the above estimates for k–D and kD, we calculate a value for the effective ADP binding constant, KD, of 3.2 µM, which is roughly two orders of magnitude lower than the KD estimated for skeletal muscle myosin (4).



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  		FIG. 4.
Effects of [ADP] on {tau}on. Mean ton ({tau}on) values were calculated for each ton distribution as shown in the equation below (4), setting kT = 2.2 x 106 M–1 s–1, k–D = 19 s–1, and kD equal to the value obtained from each ton distribution obtained at 1 mM ATP. These values are plotted (squares) versus [ADP]. For comparison, {tau}on values obtained previously (4) from skeletal muscle myosin at 100 µM ATP are included in this plot (circles).

 

Actin Movement Generated by One and Many Myosin Molecules—In the laser trap assay, actin movement generated by a single myosin molecule is closely associated with myosin strong binding and Pi release (4). Fig. 5 shows that the displacement generated by minus-insert HMM can move an actin filament at a velocity of roughly 6–9 µm s–1. This velocity, presumably limited by the viscous drag on the beads in the laser trap (32), is similar for all muscle myosins we have tested, including skeletal muscle myosin (also shown in Fig. 5). The speed of actin filament movement generated by a single myosin molecule is independent of ligand content (data not shown) and is significantly greater than the speed of actin filament movement generated by an ensemble of minus-insert myosin molecules in the in vitro motility assay (see Table I). The slower velocity observed in ensemble experiments is presumably because of actin-attached myosin molecules that impede the working step of a given myosin (4). If working steps are fully attenuated by a myosin ensemble, actin velocities, V, will be limited by actin-myosin detachment kinetics (38, 39), and the relationship between V and [ATP] would be expected to obey Michaelis-Menten kinetics, shown in Equation 2, where Km(vel) = k–D/kT is the ATP concentration at which the actin filament velocity is half of its maximum value, Vmax (4).

(Eq. 2)
To compare the detachment kinetics (k–D and kT) of individual myosin molecules with the apparent kinetics (Equation 2) of actin velocities, V, generated by a myosin ensemble in the motility assay, we measured V over a wide range of ATP concentrations (from 0.01 to 1.0 mM). In Fig. 6 we plot these values and fit them to Equation 2, obtaining a value for Km(vel) of 23 ± 3 µM. This is significantly greater than the value of Km(on) = 8.6 µM estimated above from our single molecule data. A similar difference was reported previously (4) for skeletal muscle myosin.



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  		FIG. 5.
Time course for a mechanical step generated by both a single minus-insert smooth muscle HMM molecule (a) and a skeletal muscle myosin molecule (b). Each step is plotted on a long (bottom) and short (top) time scale and is fitted by an exponential rise with similar time constants (~1.5 ms; curved line), describing the damped response time of the trapped beads (32). The viscosity-limited actin velocity (Vactin) during the initial portion of the exponential rise is ~7 µm s–1.

 

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  		TABLE I
Actin motility and rate constants obtained from single molecule ton data

 


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  		FIG. 6.
Effects of [ATP] on actin filament velocities. Actin velocities, V, measured in a motility assay are plotted versus [ATP] and fitted to Equation 2 (line), giving a value for Km of 23 µM. Each data point represents the average velocity from three different experiments, with S.E. represented by error bars.

 

The discrepancy between Km(vel) and Km(on) indicates a departure from a detachment limited model of actin velocity. According to a detachment limited model, V ~ d/{tau}on, where d is the average myosin step size (4), and thus d/V estimated from motility data and {tau}on measured in the laser trap should have the same [ATP] dependence; i.e. Km(on) should equal Km(vel). To gain further insight into why Km(on) does not equal Km(vel), in Fig. 7 we plotted d/V and {tau}on values versus 1/[ATP] both for minus-insert HMM and for skeletal muscle myosin (4). Fig. 7 shows that for both minus-insert and skeletal muscle myosin, actin filament velocities at low ATP concentrations are approximately equal to d/{tau}on measured in the laser trap but exceed d/{tau}on at high ATP concentrations, indicating that at high [ATP], actin velocities are not limited by the detachment kinetics measured in the laser trap.



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  		FIG. 7.
Comparison of {tau}on and d/V values versus 1/[ATP]. The mean ton ({tau}on) was calculated for each ton distribution as {tau}on = 1/k–D + 1/kT[ATP], setting kT = 2 x 106 M–1 s–1 and using k–D values obtained from each ton distribution. {tau}on values (squares), along with values for d/V (circles; d = 8 nm), are plotted versus 1/[ATP]. The top solid line is {tau}on = 1/k–D + 1/kT[ATP] with kT = 2.2 x 106 M–1 s–1 and k–D = 19 s–1. The bottom dashed line is the best fit of d/V data acquired at [ATP] < 35 µM to the equation below (4), giving k–D = 19 s–1 and kT = 2.2 x 106 M–1 s–1. Inset, for comparison, values reported previously (4) for {tau}on (squares) and d/V (circles) are plotted for skeletal muscle myosin. The top solid line is {tau}on = 1/k–D + 1/kT[ATP] with kT = 7.6 x 106 M–1 s–1 and k–D = 100 s–1.

 


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS
 DISCUSSION
REFERENCES
 
The unique properties of tonic smooth muscle, such as a slow shortening velocity, a high average force per cross-bridge (40–42), and the ability to maintain force (or latch) with minimal energetic expenditure (25, 43), are important for the function of the tissues within which they operate (e.g. blood vessels). These tissue-level properties have been correlated with the kinetics of the actin-myosin ATPase reaction. For example, the slow speed of shortening of tonic smooth muscle and its capacity to enter the latch state appear to be related to the kinetics of the ADP binding and release steps of the ATPase reaction of minus-insert smooth muscle myosin (44, 45). The single myosin molecule data presented here support this view and further suggest that an equally important contributor to the unique properties of tonic smooth muscle may be the interactions between myosin molecules that exist within an ensemble of myosin motors.

Single Molecule Actomyosin Detachment Kinetics—Using a laser trap as a mechanochemical assay, we determined kinetic rate constants for the two-step actin-myosin detachment process illustrated in Fig. 1. This was achieved by recording and analyzing actin-myosin attachment event durations, ton, over a wide range of ATP and ADP concentrations under nearly unloaded conditions, low ionic strength, a temperature of 25 °C, and a pH of 7.4. These rate constants are summarized in Table I.

The values we obtained for the second-order ATP-induced dissociation rate, kT, of 2.2 x 106 M–1 s–1, the effective ADP release rate, k–D, of 19 s–1, and the second-order ADP binding rate, kD, of 60 x 105 M–1 s–1 are similar to values obtained previously (9, 10, 46, 47) from solution and muscle studies. This implies that the actin-myosin mechanical cycle (measured with a laser trap) is intimately linked to the enzymatic cycle (measured in a test tube). Thus the 9-fold slower V and 4-fold greater average force for the minus-insert smooth muscle myosin compared with that of skeletal muscle myosin should be apparent as differences in the kinetics measured in the laser trap (see Table I). In fact, all of the measured rate constants (k–D, kD, and kT) for minus-insert HMM contribute to making actin-myosin detachment slower for minus-insert than for skeletal muscle myosin, which correlates with the slower V and higher average force of minus-insert myosin.

Differences in the kinetics associated with nucleotide entry (kD and kT) and exit (k–D) from the catalytic site have been attributed to the length of a surface loop that spans the opening to the nucleotide binding pocket (39, 47, 48). However, this relationship may be isoform-dependent and not universally applicable (49). When the plus- and minus-insert smooth muscle myosins were compared in the laser trap in a previous study (21), both k–D and kT were slower by a factor of two for the minus insert. The shorter loop of minus-insert myosin potentially restricts the thermal fluctuations of the nucleotide binding pocket, thus slowing the entry of ATP and the exit of ADP from the catalytic site. Although this is consistent with our observation that k–D and kT are slower in the minus-insert myosin than in skeletal muscle myosin (see Table I), this hypothesis is difficult to reconcile with our observation that the ADP binding rate is 10-fold faster in the minus-insert myosin than in skeletal muscle myosin. It may be that other structural factors within the nucleotide binding pocket or adjoining domains contribute to the faster ADP binding rate.

Determinants of Actin Movement—Actin filament movement generated by the working step of a single minus-insert HMM molecule in a laser trap is extremely fast (roughly 6–9 µms–1). In fact, because it is limited by the viscous drag on the bead in the laser trap assay, this observed velocity is an underestimate of the capacity of myosin for moving an actin filament (see Fig. 5). The high speed of actin movement generated by a single myosin molecule appears to be a common property of all myosins we have tested. In contrast, the actin velocities generated by an ensemble of myosin molecules do vary among different myosin types and are considerably slower (0.3 µm s–1 for minus-insert HMM; see Table I) than the single molecule velocities, presumably because individual mechanical steps are attenuated by other actin-attached myosin molecules in the ensemble, resulting in an actin velocity that is limited by myosin detachment (i.e. V ~ d/{tau}on). This is supported by the minus-insert and skeletal myosin motility data (Fig. 7) where actin velocities are limited by detachment kinetics (i.e. V ~ d/{tau}on) at low ATP concentrations. However, at high ATP concentrations (e.g. 1 mM ATP), V is roughly 2-fold greater than d/{tau}on, indicating that the detachment rate measured in the laser trap does not determine V (i.e. V > d/{tau}on). In fact, across all muscle myosins that we have characterized actin velocities measured in the motility assay are at least a factor of two greater than d/{tau}on measured in the laser trap (13). Two possible explanations are that at high [ATP] (i) myosin heads bound to actin do not fully attenuate the displacement of myosins undergoing their mechanical step, which means that V is not strictly limited by detachment kinetics and that the high inherent velocity of the individual mechanical steps contributes to V of the ensemble, or (ii) V is detachment-limited, but detachment (presumably limited by ADP release) is accelerated because of actin filament movement (see below).

ADP Release: Structural and Energetic Considerations— Structural studies indicate that in addition to the rotation of the light chain binding domain of smooth muscle myosin associated with Pi release (see Fig. 1) a further rotation occurs upon ADP release (6, 7, 50). This additional rotation was thought to be a work-producing transition (7), but subsequent studies challenged this view (10, 51), suggesting instead that the rotation associated with ADP release is a strain-sensing mechanism (8, 9).

To address the physiological relevance of the rotation associated with ADP release, we present a simple model in which myosin, when undergoing a rotation, performs both external, wext, and internal work, wint (Fig. 8), where the internal work involves the extension of compliant elements within the contractile system and/or within other myosin heads attached to the same actin filament. The mechanochemical equations that describe the partitioning of the free energy associated with this rotation are based on the formalism developed by Baker and co-workers (4, 52, 53) (see Fig. 8). Specifically, the free energy, –{Delta}µ, available for external work, wext, with the ADP-dependent rotation depends on both the chemical free energy change (i.e. RTln(KD/[ADP])) and the internal work, wint, associated with the rotation as shown in Equation 3.

(Eq. 3)
When wint is negligible myosin light chain domain rotations associated with net ADP release can perform work if –{Delta}µ > 0 (or [ADP] < KD). However, if –{Delta}µ < 0 (or [ADP] > KD), then work cannot be performed; rather energy input is required for net ADP release (and the associated myosin rotations) to occur. Skeletal muscle myosin has a KD of ~370 µM (see Fig. 4 and Table I), which is ~ 40-fold larger than the basal ADP concentrations of ~8–11 µM ADP found in skeletal muscle (54), and thus ADP release is energetically favorable in skeletal muscle.



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  		FIG. 8.
A chemical model for the ADP release step of myosin. a, top, myosin undergoes a discrete rotation of its light chain domain upon ADP release, which can perform both internal, wint, and external, wext work. Bottom, according to the model of Baker and Thomas (53) the energy landscape for this transition is tilted by the internal work, wint, performed with a working step of size, d', that stretches compliant elements. The remaining free energy, –{Delta}µ, is the energy available for external work, wext. The Arrhenius equations for the forward and reverse rates are k–D {propto} exp[–bwint/RT] and k+D {propto} exp[(1 – b)wint/RT], respectively, where b is the fraction of wint performed before the transition state. b, an illustration of how the mechanical interactions can accelerate ADP release even under isometric conditions. In an ensemble experiment, the working step of a given myosin head (left side, top to bottom) can, through local actin movements (straight arrow) made possible by compliant elements (illustrated as springs in the actin filament), affect the force exerted on another myosin head attached to the same actin filament, accelerating the release of ADP and the associated light chain domain rotation (curved arrow leading to rotated dashed structure). M, myosin; A, actin; T, ATP; D, ADP.

 

Interestingly for tonic smooth muscle, myosin kinetics and muscle metabolism combine to make KD/[ADP] ~1200-fold less than that in skeletal muscle. For minus-insert smooth muscle HMM, KD is ~3 µM, which is ~30-fold less than the basal ADP levels in smooth muscle of ~20–100 µM (55), and thus considerable energy input (RTln[3/100] ~ –3.5 RT) is required for ADP release in tonic smooth muscle. Even more energy input is required if the associated rotation occurs against a positive load (i.e. wint is positive in Equation 3). In solution studies or in an unloaded laser trap assay, the energy needed to proceed through the ADP release step must be derived from thermal energy, but in an in vitro motility assay or in shortening muscle, other myosin molecules in the ensemble can provide this needed energy input through their working steps at the expense of their ability to perform external work (Fig. 8b). In essence, the working step of one myosin head can assist the release of ADP from myosin heads already attached to actin (see Fig. 8b). This transfer of energy between heads in a myosin ensemble can accelerate ADP release, which is slowed by positive strain within the myosin head because of its force generation upon attachment to actin, and might help to explain why actin filament velocities at 1 mM ATP in the motility assay are faster than would be predicted by the detachment rate determined in the laser trap (see Fig. 7). According to this view, the velocities measured in the motility assay are still limited by k–D, consistent with the conclusion of previous studies (44), but mechanical interactions in the ensemble experiment make k–D faster than that measured in the laser trap.

Implications for Latch—The model for ADP release illustrated in Fig. 8, together with the high ADP affinity of the minus-insert myosin reported in this paper, may provide new insight into the latch phenomenon in smooth muscle. Smooth muscle myosin is activated by phosphorylation of the myosin regulatory light chain through a calcium-calmodulin-dependent increase in myosin light chain kinase activity, whereas relaxation is mediated by phosphatase-dependent dephosphorylation (for review see Ref. 56). During prolonged contractions, intracellular calcium concentrations fall, leading to deactivation of the tissue, but even as the extent of light chain phosphorylation declines and the ATPase rate decreases, smooth muscle myosin maintains high levels of force in what is referred to as the latch state.

Various mechanisms have been proposed to explain the ability of tonic smooth muscle to sustain active force with little ATP consumption (43). Murphy and co-workers (25) proposed that force maintenance was because of the presence of actin-attached dephosphorylated cross-bridges that have a significantly reduced rate of detachment and thus maintain force for long periods prior to relaxation. An alternate view proposed by Butler and co-workers (57) suggested that the cycling rate of a given myosin head, regardless of its phosphorylation state, depends on the fraction of phosphorylated heads in the ensemble and is thus modulated as the extent of phosphorylation changes during a contraction. Finally, the Somlyos and their co-workers (58) proposed that latch results from the high ADP affinity of minus-insert myosin leading to a longer attached lifetime, which activates the thin filament and allows cooperative binding of both phosphorylated and dephosphorylated myosin to actin. This strong binding would maintain force for sustained periods of time.

Based on our simple model the transfer of energy among actin-attached myosin heads, which we propose accelerates ADP release rate in the motility assay, might also play an important role in latch. Specifically, in an active, isometric muscle as a myosin head attaches to actin and undergoes its working step, the internal work it performs is effectively linked to other attached myosin heads through compliant elements that exist within and external to the myofilaments (59, 60). We propose that the internal work performed by the newly attached head diminishes the internal work required for ADP release from the already attached neighboring heads, thus accelerating their ADP release rate (see model above and Fig. 8). The unique aspect of this model is that the ADP release rate is coupled to the attachment rate via the transfer of mechanical energy through compliant linkages. In smooth muscle, as the level of myosin phosphorylation declines with prolonged stimulation, the rate of cross-bridge attachment (the step regulated by light chain phosphorylation (61)) is slowed significantly. According to our model, upon myosin dephosphorylation the reduction in the cross-bridge attachment rate results in a concomitant reduction in the ADP release rate, prolonging the force-bearing strong binding states. By regulating the attachment rate of the smooth muscle myosin working step through light chain phosphorylation, ADP release itself is then regulated indirectly through energetic coupling of myosin heads within the ensemble. This potential scenario, in combination with cooperative myosin binding because of smooth muscle thin filament activation by myosin strong binding (62), presents an attractive explanation for the latch state in tonic smooth muscle.

The above model for communication among heads in an ensemble is not unlike models proposed for the acceleration of ADP release through communications between the two heads of a non-muscle myosin V molecule, where coordination of the two heads of a myosin V dimer may be critical for processivity, i.e. multiple working steps per diffusional encounter (63). For myosin V, ADP release from one head of a dimer is accelerated via the work performed on it by the working step of the second head (64). The energetic coupling between the working step of one head and the ADP release of another, whether the heads are part of the same molecule (as in myosin V) or within an ensemble (as in smooth muscle), is enhanced in molecular motors with high, force-dependent ADP affinities (e.g. myosin V with a KD of ~ 5 µM and minus-insert myosin with a KD of ~ 3 µM). This energetic coupling favors a scenario in which a force-bearing myosin head detaches from actin only when another myosin head has undergone its working step and is ready to maintain the force. We suggest that this is an important aspect of processivity, as well as latch.


   FOOTNOTES
 
* This work was supported in part by National Institutes of Health Grants HL07647 (to J. E. B.) and AR47906 and HL59408 (to D. M. W.) and by the Totman Fund for Cerebrovascular Research (to D. M. W.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Back

{ddagger} To whom correspondence should be addressed. Tel.: 802-656-4300; Fax: 802-656-0747; E-mail: warshaw{at}physiology.med.uvm.edu.

1 The abbreviations used are: HMM, heavy meromyosin; TRITC, tetramethylrhodamine isothiocyanate; AB, actin buffer; MV, mean-variance. Back


   ACKNOWLEDGMENTS
 
We thank K. Trybus and A. Rovner for providing the minus-insert smooth muscle HMM, A. Federico for assistance with experiments, J. Patlak, J. Moore, and N. Kad for helpful discussions, and G. Kennedy for expertise in instrumentation design.



   REFERENCES
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 INTRODUCTION
 EXPERIMENTAL PROCEDURES
 RESULTS
 DISCUSSION
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