Vertebrate Myosin VIIb Is a High Duty Ratio Motor Adapted for Generating and Maintaining Tension*

Kinetic adaptation of muscle and non-muscle myosins plays a central role in defining the unique cellular functions of these molecular motor enzymes. The unconventional vertebrate class VII myosin, myosin VIIb, is highly expressed in polarized cells and localizes to highly ordered actin filament bundles such as those found in the microvilli of the intestinal brush border and kidney. We have cloned mouse myosin VIIb from a cDNA library, expressed and purified the catalytic motor domain, and characterized its actin-activated ATPase cycle using quantitative equilibrium and kinetic methods. The myosin VIIb steady-state ATPase activity is slow (∼1 s-1), activated by very low actin filament concentrations (KATPase ∼ 0.7 μm), and limited by ADP release from actomyosin. The slow ADP dissociation rate constant generates a long lifetime of the strong binding actomyosin·ADP states. ADP and actin binding is uncoupled, which enables myosin VIIb to remain strongly bound to actin and ADP at very low actin concentrations. In the presence of 2 mm ATP and 2 μm actin, the duty ratio of myosin VIIb is ∼0.8. The enzymatic properties of actomyosin VIIb are suited for generating and maintaining tension and favor a role for myosin VIIb in anchoring membrane surface receptors to the actin cytoskeleton. Given the high conservation of vertebrate class VII myosins, deafness phenotypes arising from disruption of normal myosin VIIa function are likely to reflect a loss of tension in the stereocilia of inner ear hair cells.

Members of the myosin family of molecular motors use the chemical energy from ATP binding, hydrolysis, and product release to generate mechanical force, tension, and motility (work output) along actin filaments (1). The myosin family consists of at least 18 classes that share a highly homologous catalytic motor domain that binds actin filaments, hydrolyzes ATP, and generates force.
Although all myosins examined to date share a similar ATPase cycle mechanism, variations in the overall cycling rate, the degree of coupling between the nucleotide-and actin-binding sites, and the lifetimes and distribution of populated biochemical intermediates introduce unique properties to the motor and contribute to the diversity of myosin family members (2). Slow cycling myosins have adapted for slow contractions and tension generation and maintenance, whereas fast cycling myosins are capable of generating rapid contractions and transport (2). Myosins IIb, V, and VI spend a significant fraction (40 to Ͼ90%) of their cycle time bound strongly to actin at physiological nucleotide concentrations due to a high ADP binding affinity and, in some cases, slow rate-limiting ADP release (3)(4)(5)(6) This behavior is dramatically different from that of several characterized class I and II myosins that spend most (Ͼ95%) of their cycle time detached or weakly bound to actin in non-force-generating states.
The fraction of the total ATPase cycle time spent strongly attached to actin is referred to as the duty ratio. A high duty ratio enables myosins to maintain tension (5,6) and to serve as anchoring proteins (myosin VI) (7,8) or to transport biological cargo over long distances (myosins V and VI) (4, 9 -11).
Several enzymatic adaptations have evolved in high duty ratio myosin motors. Rapid and essentially irreversible entry into the strong actinbinding states (3), slow ADP release and flux from strongly to weakly bound states (3,12), equilibrium constants for ATP hydrolysis that largely favor the hydrolysis products (13), weak coupling between actinand nucleotide-binding sites so that myosin can simultaneously bind ADP and actin strongly (14,15), and slow and weak ATP binding (4) all contribute to the high duty ratios of myosin motors.
Vertebrates have two highly conserved class VII myosins (VIIa and VIIb) that are enriched in polarized cells and are thought to play important roles in linking the actin cytoskeleton to adhesion receptors on the cell surface (16). Myosin VIIb is concentrated in the microvilli of intestinal epithelial and kidney brush border, where it is believed to traffic membranes and membrane-associated proteins (17). Myosin VIIa is found in hair cells of the inner ear and in photoreceptor cells of the retina. It is thought that myosin VIIa provides tension and structural integrity to the stereocilia of hair cells by linking transmembrane proteins to actin filament bundles inside the cell (18 -20). Several human diseases, including Usher syndrome type 1b, the most common deafness-blindness disorder in humans, and two other forms of non-syndromic hearing loss, DFNB2 and DFNA11, are caused by mutations of myosin VIIa (21)(22)(23)(24). Mice (shaker1) (25) and zebrafish (mariner) (26) with mutations in myosin VIIa are deaf and display a frayed stereociliary phenotype, consistent with a structural or anchoring role for myosin VIIa. In Dictyostelium, myosin VII plays an important role in cell and particle adhesion and filopodial formation (27).
Despite the physiological and clinical relevance of class VII myosins, understanding the basis of myosin VII function and the deafness disorders that arise from disruption of myosin VIIa has been limited by a lack of information of myosin VII function at the molecular level. In this study, we provide the complete kinetic mechanism of the mouse myosin VIIb catalytic motor domain. This is the first complete kinetic characterization of a vertebrate class VII myosin. Our results demonstrate that myosin VIIb is a high duty ratio motor with weak thermodynamic coupling between ADP and actin binding, favoring a role for class VII myosins in anchoring cellular structures and membrane proteins to the actin cytoskeleton.

MATERIALS AND METHODS
Reagents-All chemicals and reagents were the highest purity commercially available. ATP (ϩ99% purity as assayed by HPLC 3 ) (data not shown) was purchased from Roche Applied Science, and ADP (A-5285; ϩ99% purity as assayed by HPLC) (data not shown) was purchased from Sigma. Nucleotide concentrations were determined by absorbance at 259 nm using ⑀ 259 ϭ 15,400 M Ϫ1 cm Ϫ1 . The N-methylanthraniloyl (mant) derivatives of 2Ј-deoxy-ADP and 2Ј-deoxy-ATP were synthesized as described (14). mant-nucleotide concentrations were determined using ⑀ 255 ϭ 23,300 M Ϫ1 cm Ϫ1 . One molar eq of MgCl 2 was added to nucleotides immediately before use. Pyrenyliodoacetamide came from Molecular Probes (Eugene, OR). Imidazole (fluorescence grade; ϩ99% as assayed by titration) and phalloidin were purchased from Sigma.
Cloning of Myosin VIIb cDNA-A Mus musculus kidney Marathon-Ready cDNA library (Clontech) was used as a template to clone the cDNA encoding the myosin VIIb gene product by PCR with Platinum Taq high fidelity DNA polymerase (Invitrogen). The following primers were used to clone myosin VIIb-1IQ (subfragment 1-like) by PCR: primer 1 (MyoVIIb-5Ј), 5Ј-ATGTCCGTGTTCCGGCTGGG; and primer 2 (MyoVIIb-1IQ-3Ј), 5Ј-CCTGTACTTGTGTCCCCGGAG. DNA sequencing confirmed the identity of the PCR product as the mouse myosin VIIb gene product (GenBank TM accession number NM_032394). The purified fragment encoding residues 1-773 of myosin VIIb was cloned into the pFastBac Dual vector (Invitrogen) carrying calmodulin cDNA in the p10 promoter, and the myosin VIIb-1IQ cDNA, with a FLAG sequence at its C terminus, was cloned into the polyhedrin promoter region.
Protein Expression and Purification-Single-headed mouse myosin VIIb with bound calmodulin (referred to as myosin VIIb) was purified from Sf9 cells by FLAG affinity chromatography (7). Purity was Ն95% for all preparations (Fig. 1). Myosin VIIb and bound calmodulin cosedimented (150,000 ϫ g for 40 min) with actin filaments. All experiments were performed in the presence of 0.4 M calmodulin. Omitting excess calmodulin in measurements did not affect the kinetics of myosin VIIb-1IQ.
Steady-state ATPase Activity-The actin-activated steady-state ATPase activity of myosin VIIb was measured at 25 Ϯ 0.1°C in KMg50 buffer supplemented with 2 mM MgATP using the NADH coupled assay (12). The myosin VIIb concentration was 50 -150 nM. Essentially identical results were obtained by monitoring changes in absorption ( ϭ 340 nm) or fluorescence through a 400-nm colored glass emission filter. Time courses of single turnover ATPase activity in the absence of actin were measured using ATP and mant-ATP.
Stopped-flow Measurements-All experiments were performed in KMg50 buffer with an Applied Photophysics SX.18MV-R stopped-flow apparatus thermostatted at 25 Ϯ 0.1°C. The concentrations stated are final concentrations after mixing. Pyrene ( ex ϭ 366 nm) and mantnucleotide ( ex ϭ 280, 297, or 366 nm) fluorescence was monitored at 90°through a 400-nm long-pass colored glass filter. Long time courses were corrected for minor contributions from photobleaching (7). Intrinsic tryptophan fluorescence ( ex ϭ 280 or 297 nm) was measured through a Schott 320WG filter. Light scattering was measured at 90°w ith excitation at 313 nm. Most time courses shown are of individual, unaveraged, 1000-point transients collected with the instrument in oversampling mode, where the intrinsic time constant for data acquisition is ϳ30 s. Typically, multiple (four to eight) time courses were averaged before analysis. Time courses displayed fast and slow phases were collected on a logarithmic or split time scale.
Using Pro-K software provided with the instrument or with Kaleida-Graph (Synergy Software, Reading, PA), time courses of fluorescence change were fitted to a sum of exponentials (Equation 1), where F(t) is the fluorescence at time t, F ∞ is the final fluorescence intensity, A i is the amplitude, k i is the observed rate constant characterizing the ith relaxation process, and n is the total number of observed relaxations. The value of n was either one (single exponential) or two (double exponential). The dead time of the instrument determined from the reduction of 2,6dichlorophenolindophenol with ascorbic acid in absorbance mode was Ͻ2 ms. Fitting was limited to data beyond 3 ms to account for the instrument dead time and to exclude data acquired during the continuous flow phase of mixing as recommended by the manufacturer.
Uncertainties are reported as standard errors in the fits unless stated otherwise and were propagated using the general formula (Equation 2), where the experimental measurements x 1 , x 2 . . . x n have uncertainties dx 1 , dx 2 . . . dx n and a is a function of x 1 , x 2 . . . x n . 3 The abbreviations used are: HPLC, high pressure liquid chromatography; mant, N-methylanthraniloyl; P i BiP, phosphate-binding protein.  . Concentrated myosin and actomyosin samples were treated with apyrase (0.2 unit/ml, potato grade VII) and equilibrated on ice for 5 min before Ͼ100-fold dilution to the experimental concentrations. The final apyrase concentration after mixing was Յ0.001 unit/ml.
Apyrase has been used to deplete ATP and ADP from actin monomers (30), which bind ADP with a Ͼ Ͼ100-fold affinity (K d ϭ 0.1-1 nM) (31) compared with myosin VIIb and actomyosin VIIb. In addition, the observation that time courses of ATP binding follow single exponentials (data presented below) indicates that all myosin and actomyosin samples were free of bound nucleotides. If some fraction of the myosin had ADP bound, time courses would follow double exponentials, with a fast phase for ATP binding and a slow phase limited by ADP release.
Actin Binding Kinetics-Time courses of myosin VIIb and myosin VIIb⅐ADP binding to pyrene-labeled actin filaments were measured under pseudo first-order conditions with [actin] ϳ10 times greater than [myosin]. To ensure rigor (no nucleotide) conditions, concentrated myosin and actomyosin samples were treated with apyrase. Apyrase was omitted when ADP was present.
Transient Phosphate Release-Transient P i release was measured using a fluorescently labeled mutant (32) of the P i BiP with the instrument in sequential mixing mode (33). Myosin VIIb was mixed with ATP under multiple turnover conditions (final concentrations of 2 M myosin and 30 M MgATP), aged for 200 ms to 10 s to allow ATP binding and hydrolysis to occur, and then rapidly mixed with a range of actin filament concentrations. P i BiP (10 M) was included in the myosin, nucleotide, and actin solutions. Background P i was removed from all solutions, syringes, and the instrument by incubation with 7-methylguanosine (0.2 mM) and purine-nucleoside phosphorylase (0.1 unit/ml).
There was an ϳ5-fold enhancement of the fluorescence of P i BiP with P i binding ( ex ϭ 430 nm, 455-nm long-pass emission filter). The rate and equilibrium constants of P i binding to 7-diethylamino-3-((((2-maleimidyl)ethyl)amino)carbonyl)coumarin-labeled P i BiP under our experimental conditions (KMg50 buffer and 25°C) are as follows: k ϩ ϭ 117 Ϯ 8 M Ϫ1 s Ϫ1 , k Ϫ ϭ 24 s Ϫ1 , and K d ϭ 0.20 M (data not shown).
Equilibrium Constant for ATP Hydrolysis-We measured the equilibrium constant for ATP hydrolysis in the absence of actin using [␥-32 P]ATP (4,33). Measurements were done under multiple (250 M ATP and 4 M myosin VIIb) and single (3 M ATP and 4 M myosin) turnover conditions. The reaction was terminated after ϳ3-5 s with quench solution (2 N HCl and 0.35 M NaH 2 PO 4 ), and [␥-32 P i ] was extracted with activated charcoal and measured by scintillation counting.
Kinetic Modeling-Simulations of reaction time courses were performed with Tenua (provided by Dr. D. Wachsstock; available at www-.geocities.com/tenua4java/), which is based on the kinetic simulation program KINSIM developed by Frieden and co-workers (34).

RESULTS
Actin-activated Steady-state ATPase Activity-Actin enhanced the steady-state ATPase activity of myosin VIIb (Fig. 2) by ϳ60-fold from ϳ0.02 s Ϫ1 ( o ) to 1.17 Ϯ 0.03 s Ϫ1 (k cat ). Single turnover measurements with ATP and mant-ATP yielded a turnover rate in the absence of actin of 0.03 s Ϫ1 and confirmed that Ն90% of the myosin VIIb in our preparations was active. Actin activation of the steady-state ATPase rate fol-lows Michaelis-Menten kinetics. The K m for actin (K ATPase ) calculated from the fit to a hyperbola is 0.66 Ϯ 0.08 M. Parameters varied Ͻ20% between different preparations.
ATP Binding to Myosin VIIb-ATP binding to myosin VIIb was measured by the enhancement of intrinsic tryptophan fluorescence and by energy transfer from bound mant-nucleotide to myosin VIIb tryptophan(s). Time courses of fluorescence change after mixing myosin VIIb with ATP follow single exponentials (Fig. 3), with observed rate constants (k obs ) that depend hyperbolically on [ATP]. ATP binding to myosin VIIb was therefore modeled as a two-step reaction mechanism  (Scheme 1), with formation of a collision complex (M(ATP)) in rapid equilibrium (K 1T ) with free myosin and ATP, followed by isomerization to a high fluorescence complex (M*ATP).
Scheme 1 predicts that the observed rate constant for ATP binding follows a rectangular hyperbola according to Equation 3.
The best fit of the data to Equation 3 yields an equilibrium constant (1/K 1T ) for initial ATP binding of 77 Ϯ 16 M and an isomerization rate constant (k ϩ2T ) of 318 Ϯ 23 s Ϫ1 . The intercept is indistinguishable from the origin, so ATP binding is essentially irreversible (k ϩ2T Ͼ Ͼ k Ϫ2T ϳ 0). The second-order association rate constant for ATP binding The observed rate constants of 2Ј-deoxy-mant-ATP binding (Fig. 3B, inset) are linear over the range examined (5-20 M) and yield K 1mT k ϩ2mT ϭ 1.8 Ϯ 0.1 M Ϫ1 s Ϫ1 (Fig. 3B). The intercept is indistinguishable from the origin, confirming that, like ATP binding, mant-ATP binding is essentially irreversible. Because we were interested primarily in defining the intercept value, low mant-ATP concentrations were examined. Myosin VIIb has a tryptophan at position 484, analogous to Dictyostelium myosin II tryptophan 501, which increases fluorescence at the conformational change preceding ATP hydrolysis (35). It is therefore likely that the observed rate constant for maximum fluorescence change reports the conformational change in myosin VIIb that precedes and limits ATP hydrolysis.
Equilibrium Binding to Actin Filaments-By equilibrium titration, myosin VIIb binds actin strongly and quenches the pyrene fluorescence by ϳ50% in the absence of nucleotides or with bound ADP. Time courses of myosin VIIb and myosin VIIb⅐ADP binding to pyrene-labeled actin filaments follow single exponentials (Fig. 4A, inset), with observed rate constants (k obs ) that depend hyperbolically on the actin filament concentration over the range of actin concentrations examined (Fig. 4A). We therefore modeled myosin VIIb (M) and myosin VIIb⅐ADP (MD) binding to actin filaments as twostep mechanisms (Scheme 3), where A*(M) and A*(MD) are the high fluorescence collision complexes that isomerize to strong binding states (AM and AMD) that quench pyrene fluorescence and dissociate very slowly (k ϩ2A Ͼ Ͼ k Ϫ2A and k ϩ2AD Ͼ Ͼ k Ϫ2AD ) from the filament. SCHEME 2

Parameter
Value Signal ATP binding and hydrolysis Bound ADP has little effect on the kinetics of myosin VIIb binding to actin. In the absence of nucleotide, the equilibrium constant for initial binding (1/K 1A ) obtained from the best fit to Equation 3 is 3. (Fig. 4A). The low values of 1/K 1A and 1/K 1AD suggest they are not rapid equilibria, but each may reflect the product of a collision complex and an attached state with unquenched pyrene fluorescence (36).
The intercept yields the actomyosin dissociation rate constants (k Ϫ2A and k Ϫ2AD ) but is subject to a large uncertainty, so dissociation was measured directly by competition with unlabeled actin filaments (Fig.  4B). Myosin VIIb dissociates from actin filaments with k Ϫ2A ϭ 0.054 Ϯ 0.0002 s Ϫ1 . Myosin VIIb⅐ADP dissociates with a comparable rate constant (k Ϫ2AD ) of 0.043 Ϯ 0.0001 s Ϫ1 . The actin affinities of myosin VIIb are comparable in the presence (K AD ϭ 2.6 Ϯ 1.0 nM) and absence (K A ϭ 4.5 Ϯ 1.0 nM) of ADP.
ATP Binding to Actomyosin VIIb-ATP binding to actomyosin VIIb induces population of the weak binding states and dissociates the complex at the low actomyosin concentrations used, permitting ATP binding to be monitored by changes in light scattering and pyrene-labeled actin fluorescence enhancement. Time courses of pyrene fluorescence enhancement (Fig. 5A) and light scattering reduction (Fig. 5B, inset) after mixing actomyosin VIIb with ATP follow single exponentials, with observed rate constants (k obs ) that depend hyperbolically on the ATP concentration (Fig. 5B), consistent with a two-step mechanism for ATP binding to actomyosin VIIb, followed by rapid dissociation (Scheme 4), where AM(ATP) is the collision complex in rapid equilibrium ( with actomyosin (AM) and free nucleotide that isomerizes (k ϩ2T Ј) to an unquenched weak binding state (A*M⅐ATP) that dissociates rapidly The rate and equilibrium constants for ATP binding to actomyosin VIIb were obtained by fitting the hyperbolic [ATP] dependence of the observed rate constants to Equation 3. The equilibrium constant for actomyosin VIIb⅐ATP collision complex formation (1/K 1T Ј) is 657 Ϯ 61   (TABLE  ONE and Scheme 2).
Actin-activated P i Release-Time courses of P i release after mixing myosin VII⅐ADP⅐P i with actin filaments show a rapid exponential phase, followed by a slow linear phase (Fig. 6A). The burst corresponds to the first turnover of P i release after actin binding, and the linear phase reflects steady-state ATP turnover. The observed rate constant of the burst depends linearly on the actin concentration over the range examined (0 -20 M) (Fig. 6B). The rate constant for myosin VIIb ADP⅐P i binding to actin (k ϩAP i ) is 5.9 Ϯ 0.2 M Ϫ1 s Ϫ1 . The maximum rate of actin-activated P i release (k ϪP i Ј) is Ͼ100 s Ϫ1 , so P i release does not limit the ATPase cycle in the presence of actin. The burst amplitude was unaffected by the age time (0.2-10 s) of the first mixture (myosin mixed with ATP; see "Materials and Methods"), indicating that ATP binding, hydrolysis, and equilibrium formation of myosin VIIb⅐ADP⅐P i (limited by k ϩH ϩ k ϪH at the ATP concentration used) is Ն20 s Ϫ1 . There is no burst phase in the absence of actin because P i release is rate-limiting (k ϪP i ϭ 0.02 s Ϫ1 ). In the presence of P i BiP, P i release is irreversible, so the reverse P i binding reactions (k ϩP i and k ϩP i Ј) were not considered in the analysis.
mant-ADP Binding to Myosin and Actomyosin VIIb-2Ј-Deoxymant-ADP binding to myosin VIIb and actomyosin VIIb was monitored by the fluorescence enhancement of the mant moiety ( ex ϭ 366 nm) or by fluorescence resonance energy transfer from myosin VIIb to bound mant-ADP ( ex ϭ 280) with essentially identical results. Time courses of mant-ADP binding to myosin VIIb (Fig. 7A) and actomyosin VIIb (Fig.  7B) follow double exponentials, with fast phase observed rate constants (k mD,fast ) that depend linearly on the mant-ADP concentration over the range examined (Fig. 7C) and slow phase observed rate constants that depend hyperbolically on the mant-ADP concentration (Fig. 7D). The biphasic time courses and mant-ADP concentration dependence of the fast and slow phases indicate that mant-ADP (mD) binding to myosin VIIb (M) and actomyosin VIIb (AM) follows sequential two-step mechanisms (Scheme 5), with population of two high fluorescence (indicated by * and Ј) mant-ADP states that are in a reversible equilibrium.
It is likely that a diffusion-limited collision complex in rapid equilibrium, which by definition has spectroscopic properties similar to those of free myosin VIIb or actomyosin VIIb, precedes formation of the first high fluorescence state (see below for evidence supporting an ADP collision complex). We did not consider a parallel pathway with binding to a mixed myosin population because the relative amplitudes of the two phases measured in association (Fig. 7, A and B) and dissociation ( The observed rate constants (k mD,fast ) depend linearly on the mant-ADP concentration (Fig. 7C), yielding comparable apparent second-order association rate constants (k ϩ1mD ) for myosin VIIb (3.1 Ϯ 0.1 M Ϫ1 s Ϫ1 ) and actomyosin VIIb (3.4 Ϯ 0.2 M Ϫ1 s Ϫ1 ) (TABLE TWO) from the slopes. The intercepts define the dissociation rate constant of the first high fluorescence state (k Ϫ1mD ) and, although subject to uncertainty, are slightly larger for actomyosin VIIb (7.0 Ϯ 2.2 s Ϫ1 ) than for myosin VIIb (4.5 Ϯ 1.6 s Ϫ1 ).
The slow phase arises from isomerization of the initial high fluorescence state (M⅐mD* or AM⅐mD*) to the second high fluorescence state (M⅐mDЈ or AM⅐mDЈ). The observed rate constants of the slow phase (k mD,slow ) depend hyperbolically on the mant-ADP concentration (Fig.  7D) and are related to the elementary rate constants (14) by Equation 5, which is the sum of the isomerization rate constants (k mD,isom ϭ k ϩ2mD ϩ k Ϫ2mD ), accounting for the population of the initial high fluorescence state that can undergo isomerization. The maximum observed rate constant (achieved when k ϩ1mD [mD] Ͼ Ͼ k Ϫ1mD and k ϩ1mD [mD]/k Ϫ1mD Ͼ Ͼ 1) is equal to k mD,isom and is more rapid for actomyosin VIIb (4.0 Ϯ 0.4 s Ϫ1 ) than for myosin VIIb (2.1 Ϯ 0.1 s Ϫ1 ).
The intercepts in Fig. 7D reflect the net dissociation rate constant (k off ) of M⅐mDЈ and AM⅐mDЈ. The values of k off were measured directly by competitive displacement of an equilibrated mixture of myosin VIIb or actomyosin VIIb and mant-ADP with excess ADP (Fig. 7E). Time courses of mant-ADP release are biphasic, with the slow phase comprising a majority (ϳ73% with myosin VIIb and ϳ80% with actomyosin VIIb) of the total amplitude. We attribute the fast phase to the fraction of M⅐mD* (or AM⅐mD*) populated at equilibrium that dissociates bound mant-ADP quickly and the slow phase to the fraction of M⅐mDЈ. The larger amplitudes of the slow phases indicate that the isomerization equilibria (K 2mD and K 2mD Ј) favor (k ϩ2mD Ͼ k Ϫ2mD and k ϩ2mD Ј Ͼ k Ϫ2mD Ј) formation of the second high fluorescence states (M⅐mDЈ and AM⅐mDЈ). The rates and amplitudes were the same when mant-ADP was competed with excess ATP and when actin was fully (equimolar actin and myosin VIIb) or partially (5 M actin and 100 nM myosin VIIb) decorated with myosin.
The fast dissociation rate constants (k off,fast ) reflect the sum of the rate constants leading to loss of M⅐mD* and AM⅐mD* (k off,fast ϭ k Ϫ1mD ϩ k ϩ2mD ) and are slightly more rapid for myosin (k off,fast ϭ 8.4 Ϯ 0.2 s Ϫ1 ) than for actomyosin (k off,fast ϭ 6.9 Ϯ 0.1 s Ϫ1 ). The relative amplitude of the fast phase (A off,fast ) (14) is equal to Equation 6.
The slow observed dissociation rate constants (k off,slow ) are defined by the elementary rate constants in Scheme 5 when dissociation is irreversible (k ϩ1mD [mD] ϭ 0; achieved by competition with excess ADP) and is more rapid than isomerization preceding dissociation (k Ϫ1mD Ͼ Ͼ k Ϫ2mD ) (14) according to Equation 7, which reflects the isomerization preceding mant-ADP release (k Ϫ2mD ) times the probability that mant-ADP will continue to dissociate. The values of k off,slow are also more rapid in the absence (k off,slow ϭ 0.54 Ϯ 0.005 s Ϫ1 ) than in the presence (k off,slow ϭ 0.36 Ϯ 0.002 s Ϫ1 ) of actin. A knowledge of k ϩ1mD , k mD,isom , k off,slow , and k off,fast and the relative amplitudes of the dissociation time course phases allow us to calculate the rate and equilibrium constants for mant-ADP binding (TABLE  TWO). Kinetic simulations using the derived constants are consistent with the observed concentration dependence of the observed binding constants and amplitudes (data not shown).
The overall myosin VIIb⅐mant-ADP binding affinity (dissociation equilibrium constant K mD,overall ), accounting for the equilibrium population of both high fluorescence ADP states, is shown in Equation 8.
The overall affinity for mant-ADP (14) can be calculated from Equation 9, where the coefficient K 2mD /(1 ϩ K 2mD ) accounts for contributions of the isomerization equilibrium to the overall affinity. Similarly, the overall actomyosin VIIb⅐mant-ADP affinity (K mD,overall Ј) can be calculated using the appropriate forms of Equations 8 and 9. The overall mant-ADP binding affinities are K mD,overall ϭ 0.20 Ϯ 0.05 M for myosin VIIb and K mD,overall Ј ϭ 0.37 Ϯ 0.10 M for actomyosin VIIb (TABLE TWO). In summary, mant-ADP binding kinetics are consistent with population of two stable, strong ADP binding, and high fluorescence myosin⅐mant-ADP and actomyosin⅐mant-ADP states, and actin binding has little effect on the rate and equilibrium constants that govern mant-ADP binding and release from myosin VIIb, suggesting a weak coupling between ADP and actin binding.
To determine whether the slow actomyosin⅐mant-ADP isomerization is a relevant on-pathway reaction (14), we measured actin-activated mant-ADP release from myosin⅐mant-ADP⅐P i . Time courses after mixing myosin⅐mant-ADP⅐P i with actin ( ex ϭ 280 nm) are biphasic (Fig.  7F). The fast phase depends on the actin concentration (data not shown), indicating that it reports an actin binding event. The slow phase limits dissociation of bound mant-ADP and occurs at ϳ0.2-0.3 s Ϫ1 over the actin concentration range examined (2-18 M), comparable with k off,slow , consistent with slow mant-ADP dissociation being part of the actin-activated ATPase cycle pathway. The amplitudes of the transients were independent of the age time (0.2-5 s) of the first mixture (myosin with mant-ATP), indicating that equilibrium population (limited by k ϩH ϩ k ϪH ) of myosin⅐ADP⅐P i is Ն20 s Ϫ1 .
ADP Binding to Actomyosin VIIb Measured by Kinetic Competition with ATP-To measure the binding properties of ADP and to evaluate if mant modification interferes with binding, we measured ADP binding to pyrene-labeled actomyosin by kinetic competition with ATP (7). Time courses of pyrene fluorescence enhancement after mixing pyrenelabeled actomyosin VIIb with a solution of ADP and ATP are biphasic and can be well fitted to double exponentials (Fig. 8, A and B), with fast ( Fig. 8C) and slow (Fig. 8D) phases that depend hyperbolically on [ADP]. The hyperbolic [ADP] dependence of the fast phase observed rate constant (Fig. 8C) indicates that ADP binding to actomyosin VIIb is (at least) a two-step process. Therefore, competitive ATP and ADP binding to actomyosin VIIb (AM) can be described by the parallel reaction mechanism shown in Scheme 6, where A* denotes a high (unquenched) pyrene fluorescence and the parentheses indicate collision complexes in rapid equilibrium with dissociated species.
The observed rate constant of the fast phase reflects depletion of free actomyosin and depends on the sum of the observed rate constants for ATP and ADP binding, which can be expressed in terms of the rate and equilibrium constants for nucleotide binding under conditions in which binding is essentially irreversible (k Ϫ2T Ј and k Ϫ2D Ј ϳ 0, fulfilled in this case because nucleotide dissociation is much slower than association) (7) according to Equation 10, where K 1D Ј is the association equilibrium constant for actomyosin VIIb⅐ADP collision complex formation. Fitting the [ADP] dependence of k fast to Equation 10 with K 1T Ј and k ϩ2T Ј constrained to values obtained independently from ATP binding experiments (Fig. 5) yields k ϩ2D Ј ϭ 326 Ϯ 7.7 s Ϫ1 and 1/K 1D Ј ϭ 62.8 Ϯ 8.1 M (Fig. 8C). The rate constant for ADP binding to actomyosin VIIb (K 1D Јk ϩ2D Ј) is 5.
The slow phase of the reaction arises from actomyosin VIIb⅐ADP formed during kinetic partitioning in the fast phase that dissociates bound ADP and then binds ATP (7). The observed rate constant of the slow phase (k slow ) is equal to the rate constant of ADP dissociation (k Ϫ2D Ј) times the probability that ATP will bind instead of ADP according to Equation 11, where k ATP and k ADP represent the observed rate constants for ATP (Equation 12) and ADP (Equation 13) binding, respectively.
In the presence of ADP, ADP rebinds; k ADP increases; and k slow decreases in an [ADP]-dependent manner (Fig. 8D). When k ATP Ͼ Ͼ k ADP , such as when [ADP] approaches zero, k ADP is insignificant; ADP release is essentially irreversible; and k slow simplifies to k Ϫ2D Ј. The rate constant of ADP release from actomyosin VIIb (k Ϫ2D Ј) obtained by extrapolating the best fit of k slow versus [ADP] to the limit of [ADP] ϭ 0 (i.e. the intercept) is 1.52 Ϯ 0.02 s Ϫ1 (Fig. 8D). The overall K d for ADP binding to actomyosin VIIb (1/K 1D ЈK 2D Ј) is 0.30 Ϯ 0.037 M (TABLE  ONE and Scheme 2). The pyrene fluorescence change is proportional to the concentration of weakly bound A*M⅐ATP and M*ATP. The relative amplitudes of the fast and slow phases (Fig. 9A) reflect partitioning into strongly bound actomyosin⅐ADP and weakly bound myosin⅐ATP states. The amplitude of the fast phase reflects the probability that ATP will bind rather than ADP and is related to the observed rate constants for ADP and ATP binding according to Equation 14, where ⌬F max is the amplitude of fluorescence change with ATP alone and ⌬F obs is the observed amplitude in the presence of ADP. Because the association rate constants for ADP (K 1D Јk ϩ2D Ј) and ATP (K 1T Јk ϩ2T Ј) are comparable, actomyosin VIIb partitions equally into weak and strong binding states at [ADP]/[ATP] ϳ 0.8 (Fig. 9A).
The final fluorescence represents the equilibrium partitioning of weak and strong binding states as dictated by the nucleotide binding affinities and concentrations. There is an [ADP]-dependent reduction of the total fluorescence changes (Fig. 9B)    and is dependent on the nucleotide binding affinities and concentrations according to Equation 15, where K ATP(app) reflects the apparent ATP affinity that dictates the steady-state [ATP] dependence of the shift from strongly to weakly bound states. The best fit of the total fluorescence change (Fig. 9B) to Equation 15 with the overall ADP binding affinity constrained to the value determined from the ratio of the rate constants (0.30 M) yields a K ATP(app) of 0.21 Ϯ 0.02 M. Essentially identical results were obtained by monitoring the light scattering of actin filaments (data not shown), indicating that the weak binding states are detached from actin at the protein concentrations used.
To confirm the ADP dissociation rate constant measured by kinetic competition and to evaluate if the two actomyosin⅐mant-ADP states and biphasic release kinetics are specific for mant-ADP, we measured ADP release from pre-equilibrated complexes of pyrene-labeled actomyosin⅐ADP. Actomyosin VIIb was pre-equilibrated with 1 M (ϳ1/K 1D ЈK 2D Ј) or 30 M (Ͼ Ͼ1/K 1D ЈK 2D Ј) ADP and rapidly mixed with 100 M (after mixing) or excess (2 mM after mixing) ATP. When [ADP] ϭ 1 M, time courses are biphasic (Fig. 10), with a fast phase corresponding to ATP binding to free actomyosin (k obs ϭ 106 Ϯ 7 s Ϫ1 at 100 M ATP, consistent with ATP binding experiments in Fig. 5) and a slow phase that is limited by ADP release at 0.7 Ϯ 0.1 s Ϫ1 . The amplitude of the slow phase is ϳ60%, consistent with an actomyosin VIIb⅐ADP binding affinity (1/K 1D ЈK 2D Ј) of ϳ0.7 M, comparable with that estimated from the ratio of the rate constants determined by kinetic competition (0.3 M). When [ADP] ϭ 30 M, the fast phase is absent, and time courses follow a single exponential, with an observed rate constant of 0.8 Ϯ 0.1 s Ϫ1 , reflecting ADP release from pyrene-labeled actomyosin⅐ADP. Identical results were obtained by monitoring the light scattering intensities (data not shown), eliminating the possibility of interference from pyrene modification of actin. The ADP release of ϳ0.8 s Ϫ1 measured with pyrene-labeled actin is comparable with the steady-state ATPase rate of ϳ1 s Ϫ1 . We attribute the slower rate of mant-ADP release to mant modification, as reported for some other myosins (14).
These results indicate that the equilibrium population of two high ADP affinity actomyosin states and a slow isomerization linking the two are not observed with pyrene-labeled actin and that the behavior may be specific for mant-ADP. If two strong ADP-binding states are populated with pyrene-labeled actomyosin⅐ADP, the isomerization equilibrium largely favors the second state, so no rapidly dissociating species (AM⅐mD* in Scheme 5) is populated at equilibrium, and the isomerization rate constant is rapid.
Direct Measurement of the Myosin VIIb Duty Ratio-The fraction of myosin VIIb (0.7 M) strongly bound to 2 M pyrene-labeled actin filaments in the presence of 2 mM ATP measured from the fluorescence of pyrene-labeled actin is ϳ0.8 (Fig. 11B).

DISCUSSION
Overall Behavior of Myosin VIIb-The myosin VIIb steady-state ATPase activity is slow (1.17 Ϯ 0.03 s Ϫ1 ) and is activated by very low actin concentrations (K ATPase ϭ 0.66 Ϯ 0.08 M). ADP release from actomyosin limits the overall cycling rate. ATP binding, dissociation from actin, ATP hydrolysis detached from actin, and actin-activated P i release are Ͼ Ͼ10 times more rapid than ADP release, and the equilibria favor progression through the cycle. As a result, myosin VIIb is a high duty ratio motor that remains strongly bound to actin and ADP for most of its ATPase cycle time. The slow ADP release delays completion of the  cross-bridge cycle and allows myosin VIIb to maintain tension at low energy costs.
The K ATPase of a myosin with rapid ATP binding and hydrolysis and slow rate-limiting ADP release is related to the rate and equilibrium constants of the ATPase cycle (13) according to Equation 16, where K H(app) is the apparent equilibrium constant for ATP hydrolysis in the presence of actin ("app" is used to distinguish from K H , the true equilibrium constant for ATP hydrolysis of detached myosin), k ϩAP i is the association rate constant for myosin⅐ADP⅐P i binding to actin filaments (taken as 5.9 M Ϫ1 s Ϫ1 ; note that, if actin-activated P i release occurs via a two-step mechanism, this term would take a form of a hyperbola, accounting for the collision complex affinity and maximum rate constant of P i release (4, 9 -11)), and k Ϫ2D Ј is ADP release (taken to be 1.5 s Ϫ1 ). The K ATPase predicted from the experimentally determined rate and equilibrium constants is 0.55 M, comparable with the experimentally observed K ATPase of 0.66 M (Fig. 2  Duty ratio ϭ The actin concentration predicted to yield 50% strongly bound heads (K dr ) in the presence of 2 mM ATP is 0.55 M (Fig. 11A and TABLE THREE). At 2 M actin, the predicted duty ratio is ϳ0.8, comparable with the duty ratio measured directly from the fluorescence of pyrenelabeled actin (Fig. 11B). Because actomyosin VIIb⅐ADP is the predominantly populated intermediate during steady-state cycling, the K dr is the same as the K ATPase (compare Figs. 2 and 11A). Note that the K dr will be reduced in the presence of ADP because the observed ADP release rate constant is slower (Fig. 8D). Although it is difficult to know with certainty the actin filament concentrations encountered by myosin VIIb in a cell, particularly with no knowledge of the degree of competition with additional actin filament-binding proteins, binding site accessibility, and excluded volume effects, it is reasonable to conclude that myosin VIIb has a duty ratio near unity under physiological conditions. Communication between Nucleotide-and Actin-binding Sites-ADP (D) and actin (A) binding to myosin (M) is linked by the closed reaction scheme shown in Scheme 7.
Detailed balance requires that, in the absence of external energy input or consumption, the product of the four equilibrium constants equal unity; and therefore, K 1AD K 2AD /K 1A K 2A must equal K D,overall /K D,overall Ј. The ratios define the degree of thermodynamic coupling between ADP and actin binding (i.e. to what extent the binding of one affects the other).
Myosins tailored for generating rapid sliding velocities (e.g. muscle myosins) display large coupling (15) and can bind either actin or ADP at a given time. Myosins that function as tension sensors (e.g. myosins IIb, V, and VI) display weak coupling (15) and can simultaneously bind actin and ADP strongly. The product of the equilibrium constants in Scheme 7 is ϳ0.9 using the overall mant-ADP affinity for actomyosin (K mD,overall ) and ϳ1.1 using the overall ADP affinity for pyrene-labeled actomyosin (K D,overall Ј), indicating an energetically balanced scheme. Actin and ADP binding to myosin VIIb is essentially uncoupled (K D,overall ϭ 1/K D,overall Ј and K 1AD K 2AD ϭ 1/K 1A K 2A ), and myosin VIIb remains strongly bound to actin and ADP even at low micromolar concentrations (Fig. 11). The high affinity for actin filaments (ϳ2 nM with bound ADP) and the slow dissociation rate constant (ϳ0.04 s Ϫ1 ) indicate that the forces required to detach myosin VIIb from actin must be large.
The high actin affinity and the weak thermodynamic coupling between ADP and actin binding are consistent with a role for myosin VIIb in anchoring bound cargo to actin filaments. The tail domain of myosin VIIb is very similar to that of myosin VIIa, which binds adhesion complexes (27) and membrane proteins (16), suggesting that myosin VIIb links membrane components such as cell-surface receptors and/or ion channels of the renal and intestinal brush borders to the actin cytoskeleton.
The overall ADP affinity for actomyosin VIIb is considerably lower than the physiological concentrations (37). Although ATP binding will be favored over ADP under physiological conditions (millimolar ATP and micromolar ADP) (Fig. 9) in the absence of load, the high ADP affinity suggests that myosin VIIb is likely to undergo a rotation of the regulatory domain (i.e. tail swing) with strong ADP binding (15) and that ADP release from actomyosin VIIb is load-dependent. When the opposing load is large, strong ADP and actin binding (actomyosin⅐ADP state) would be favored by inhibiting ADP release. Conversely, an external load that favors rotation to the rigor conformation could facilitate ADP release.
Comparison with Other Tension-generating Myosins-Smooth muscle myosin II (38), non-muscle myosin IIb (6), and myosin VI (4) have also been proposed to be tension-generating and tension-sensing motors (15). There are, however, significant differences in the enzymatic properties of these myosins. Actin-activated P i release (rather than ADP release) limits smooth muscle myosin II and non-muscle myosin IIb cycling, causing a significant fraction of the total myosin to populate the weak binding states at physiological nucleotide concentrations (in the absence of load).
The ATPase cycle of myosin VI (like myosin VIIb) is limited by ADP release. However, the lifetimes of the strongly bound ADP states are  NOVEMBER 25, 2005 • VOLUME 280 • NUMBER 47 much longer for myosin VIIb than for myosin VI due to the much slower rate of ADP release (ϳ1 s for actomyosin VIIb versus ϳ160 ms for actomyosin VI). Consequently, the turnover rate of myosin VIIb is significantly slower than that of myosin VI as well. In addition, the affinity of myosin VIIb⅐ADP for actin filaments (ϳ2 nM) is Ͼ20-fold stronger than the affinity of myosin VI⅐ADP for actin (47 nM) (7), and the dissociation rate constant of the actomyosin⅐ADP complex is also slower for myosin VIIb. Therefore, the forces required to detach myosin VIIb⅐ADP from actin are presumably larger than those required to detach myosin VI⅐ADP from actin. The slow cycling rate, long lifetime of the strongly bound actomyosin⅐ADP states, tight binding and slow dissociation of the actomyosin⅐ADP complex, and weak coupling between ADP and actin binding favor a role for single-headed myosin VIIb in anchoring bound cargo to the actin cytoskeleton even under large external loads. Implications for Class VII Myosin Function-Vertebrates have two highly conserved class VII myosins, VIIa and VIIb. Myosin VIIb differs from myosin VIIa in that it contains a highly positively charged 19amino acid insertion in the actin-binding loop (loop 2). Myosin VIIa (39) has a much weaker K ATPase compared with myosin VIIb, but a comparable maximum turnover rate (k cat ϳ 0.4 s Ϫ1 ). The basic loop 2 insert of myosin VIIb is likely to promote weak myosin⅐ADP⅐P i binding to actin via ionic interactions (40,41) and to accelerate the second-order rate constant for actin-activated P i release, accounting for the lower K ATPase (Equation 16).
While this manuscript was in review, a manuscript characterizing the ATPase cycle kinetics of Drosophila myosin VIIb was published (42). ADP release from actomyosin limits the overall actin-activated ATPase cycles of both Drosophila and mouse myosin VIIb. However, the rate of ADP release (which limits ATP binding and actin detachment) from Drosophila actomyosin VIIb is ϳ10-fold faster compared with mouse actomyosin VIIb, so the lifetime of strongly bound Drosophila actomyosin VIIb⅐ADP will be shorter at physiological nucleotide concentrations.
Another notable difference between the Drosophila and mouse VIIb isoforms is in the K ATPase values. Drosophila myosin VIIb has a K ATPase of 39 M, whereas mouse myosin VIIb has a K ATPase 0.66 M. The larger K ATPase value of Drosophila myosin VIIb arises from a slower rate constant of myosin⅐ADP⅐P i binding to actin (k ϩAP i ) and more rapid ADP release (k Ϫ2D ) (Equation 16). Similarly, the K dr of Drosophila myosin VIIb will be much higher than that of mouse myosin VIIb (Equation 17). The duty ratio of mouse myosin VIIb at 2 M actin is ϳ0.8. However, Drosophila myosin VIIb will achieve a duty ratio of 0.8 only at ϳ50 M actin (Fig. 11A). We hypothesize these differences arise from the basic loop 2 insert found in mouse myosin VIIb that is absent in Drosophila myosin VIIb. Because vertebrate myosin VIIa also lacks the basic loop 2 insert, it is likely to have a slower k ϩAP i and higher K dr compared with vertebrate myosin VIIb.