Kinetic mechanism and regulation of myosin VI.

Myosin VI is the only pointed end-directed myosin identified and is likely regulated by heavy chain phosphorylation (HCP) at the actin-binding site in vivo. We undertook a detailed kinetic analysis of the actomyosin VI ATPase cycle to determine whether there are unique adaptations to support reverse directionality and to determine the molecular basis of regulation by HCP. ADP release is the rate-limiting step in the cycle. ATP binds slowly and with low affinity. At physiological nucleotide concentrations, myosin VI is strongly bound to actin and populates the nucleotide-free (rigor) and ADP-bound states. Therefore, myosin VI is a high duty ratio motor adapted for maintaining tension and has potential to be processive. A mutant mimicking HCP increases the rate of P(i) release, which lowers the K(ATPase) but does not affect ADP release. These measurements are the first to directly measure the steps regulated by HCP for any myosin. Measurements with double-headed myosin VI demonstrate that the heads are not independent, and the native dimer hydrolyzes multiple ATPs per diffusional encounter with an actin filament. We propose an alternating site model for the stepping and processivity of two-headed high duty ratio myosins.

Myosin VI is the only pointed end-directed myosin identified and is likely regulated by heavy chain phosphorylation (HCP) at the actin-binding site in vivo. We undertook a detailed kinetic analysis of the actomyosin VI ATPase cycle to determine whether there are unique adaptations to support reverse directionality and to determine the molecular basis of regulation by HCP. ADP release is the rate-limiting step in the cycle. ATP binds slowly and with low affinity. At physiological nucleotide concentrations, myosin VI is strongly bound to actin and populates the nucleotide-free (rigor) and ADP-bound states. Therefore, myosin VI is a high duty ratio motor adapted for maintaining tension and has potential to be processive. A mutant mimicking HCP increases the rate of P i release, which lowers the K ATPase but does not affect ADP release. These measurements are the first to directly measure the steps regulated by HCP for any myosin. Measurements with double-headed myosin VI demonstrate that the heads are not independent, and the native dimer hydrolyzes multiple ATPs per diffusional encounter with an actin filament. We propose an alternating site model for the stepping and processivity of two-headed high duty ratio myosins.
Myosin VI is unique among members of the myosin superfamily of molecular motors in that it moves toward the pointed ends of actin filaments as opposed to the barbed ends (1). Although the cellular roles of myosin VI are not defined, it has been implicated in membrane trafficking and organelle transport (2)(3)(4) as well as maintaining the structural integrity of inner ear hair cells (5).
Native myosin VI has two "heads," or catalytic domains, that are thought to be regulated by p21-activated kinase phosphorylation in vivo (3). Although the phosphorylation site was not identified directly, it was mapped between amino acids 308 and 631 and believed to be Thr 406 of the actin-binding interface, because flanking sequences have p21-activated kinase recognition sites, and phosphorylation of Thr 406 would be consistent with the TEDS rule (6). All myosins have an acidic residue (Asp or Glu) at this position and are constitutively active or, in the case of Acanthamoeba myosin I, have a serine or threonine that when phosphorylated increases the ATPase rate more than 20-fold (7). Myosin I heavy chain kinases are p21-activated kinase homologues (8,9). Mutagenesis of Acanthamoeba myosin I demonstrates that the phosphorylated and unphosphorylated states are mimicked by replacement of the phosphorylatable threonine with a glutamate or alanine, respectively (10).
The molecular mechanism by which myosin VI achieves its reverse directionality is not known, but it might be linked to unique aspects of the converter domain, the structural element between the motor and light chain binding domains (1). In this study, we define the kinetic mechanism of the actomyosin VI ATPase cycle to ascertain if pointed end-directed motility requires unique biochemical adaptations. In addition, to determine whether myosin VI is regulated by heavy chain phosphorylation and to define the molecular basis of the regulation, we characterized the kinetics of myosin VI with a glutamate or alanine substitution at Thr 406 . As demonstrated for other unconventional myosins (11)(12)(13)(14), kinetic characterization helps define the biological functions and degree of processivity of myosin VI.

EXPERIMENTAL PROCEDURES
Reagents-All reagents were of the highest purity commercially available. ATP was purified by anion exchange chromatography (purity Ͼ99%) or prepared fresh from dry powder (Roche Molecular Biochemicals, 99.7% pure by HPLC, 1 data not shown). N-Methylanthraniloyl derivatives of 2Ј-deoxy-ADP (mantADP) and 2Ј-deoxy-ATP (mantATP) were prepared as described (15). ATP and ADP concentrations were determined by absorbance at 259 nm using an ⑀ 259 of 15,400 M Ϫ1 cm Ϫ1 ; mantADP and mantATP concentrations were measured at 255 nm using an ⑀ 255 of 23,300 M Ϫ1 cm Ϫ1 . A molar equivalent of MgCl 2 was added to nucleotides immediately before use.
Myosin VI Mutagenesis-To create single-headed myosin VI (subfragment 1-like) constructs, porcine myosin VI wild-type cDNA (1) was mutagenized by polymerase chain reaction to substitute Thr 406 with an Ala (T406A) or a Glu (T406E) and truncated at Gly 840 . A Flag tag was inserted at the C terminus to facilitate purification. The recombinant heavy chain protein contains the motor domain and the single calmodulin/light chain binding site (IQ motif).
The two-headed construct (HMM-like) was truncated at Arg 992 to include 20 native heptad repeats of predicted coiled coil and was followed by a leucine zipper (GCN4) to ensure dimerization (16) and then a Flag tag.
Protein Purification and Preparation-Myosin VI constructs with bound calmodulin (CaM), the physiological light chain (17), were purified (1, 12) from baculovirus-infected Sf9 cells (Fig. 1). Excess CaM (0.6 -1.8 M) was included throughout the purification until the final NH 4 (SO 4 ) 2 precipitation. The CaM-to-heavy chain stoichiometry after purification was 1.0 -1.1 as determined from scanning densitometry of wet Coomassie-stained gels. Calmodulin was the only light chain bound as indicated by the Ca 2ϩ -dependent change in gel mobility and comigration with purified calmodulin (data not shown). Purity was more than 98% with most preparations. Actin was the only detectable con-taminant (ϳ2-5%) in some preparations. Preparations with actin contamination were used exclusively for measurements that required unlabeled actin (i.e. steady-state ATPases and mantADP binding to actomyosin VI). We do not know the affinity of CaM binding to myosin VI or if it varies for different states in the ATPase cycle, and thus all experimental measurements were made in the presence of excess (20 -40 M) recombinant human brain CaM.
Steady-state ATPase Activity of Myosin VI-Steady-state ATPase activities were measured at 25.0 (Ϯ 0.1)°C in KMg50 buffer supplemented with the NADH-coupled assay components (13). The myosin VI concentration was 30 -100 nM. Monitoring changes in absorption ( ϭ 340 nm) or fluorescence yielded essentially identical results. The final [MgATP] was 2 mM. By HPLC, the steady-state [ADP] under our experimental conditions is Յ7 M, which inhibits steady-state ATP turnover Ͻ5% (simulations not shown; Refs. [12][13][14]. Determination of the ADP-P i Burst-The amplitude of the ADP-P i burst of myosin VI in the absence of actin was determined at 25 (Ϯ 1)°C in KMg50 buffer using activated charcoal extraction to measure 32 P i generated from the hydrolysis of [␥-32 P]ATP as described (12,13) except samples were mixed manually. The mixing time before quenching was ϳ1-2 s. The final concentrations were 3 M myosin VI and 200 M MgATP.
Transient P i release was measured using the fluorescently labeled mutant (19) of the P i -binding protein (P i BiP) with the instrument in sequential mixing mode (12,14,20). There was ϳ5-fold enhancement in the fluorescence of P i BiP with P i binding ( ex ϭ 430 nm, 455-nm emission filter). We measured a second-order rate constant of ϳ40 M Ϫ1 s Ϫ1 for P i binding to P i BiP in KMg50 (data not shown). Myosin VI (6 M before mixing) was mixed with ATP (400 M before mixing), aged for 300 ms to allow ATP binding and hydrolysis to occur, then rapidly mixed with a range of actin filament concentrations. A 300-ms age time is sufficient to allow formation of myosin-ADP-P i even if hydrolysis is rate-limiting at 9 s Ϫ1 . P i BiP was included in the myosin and actin solutions. To prevent ATP from rebinding to myosin VI after ADP release (i.e. limiting myosin VI to a single turnover), 1 mM MgADP was included with actin prior to mixing. Background P i was removed from all solutions, syringes, and the instrument by incubating with 7-meth-ylguanosine (0.2-0.5 mM) and purine nucleoside phosphorylase (0.2 units ml Ϫ1 ).
Nonlinear least-squares fitting of the data was done with software provided with the instrument or with KaleidaGraph (Synergy Software, Reading, PA). Uncertainties reported are standard errors in the fits unless stated otherwise.
Kinetic modeling and simulations were performed (12)(13)(14) using the following minimum reaction scheme of the actomyosin ATPase, where A is actin and M is myosin VI. The predominant dissociativehydrolysis pathway is highlighted in bold. Rate constants are referred to as k ϩn to indicate transition of the nth reaction step from left to right or from top (attached states) to bottom (dissociated states) as depicted in the scheme; k Ϫn is assigned to the corresponding reverse reactions.

RESULTS
Unless specified, all experimental measurements were made with subfragment 1-like myosin VI consisting of the motor domain and associated light chain. "Myosin VI-HMM" is used when referring to the two-headed construct.
Steady-state ATPase of Myosin VI-The steady-state MgATPase activities of myosin VI-T406E and T406A are activated from Ͻ0.1 s Ϫ1 (v o ) to ϳ8 -9 s Ϫ1 (V max ) by actin filaments (Fig. 2, Table I). The K ATPase of myosin VI-T406E is ϳ3 M. Myosin VI-T406A has a much higher K ATPase of ϳ18 M. Therefore, actin filaments activate the ATPase of myosin VI-T406E and T406A Ն 100-fold but with dramatically different K ATPase values (Fig. 2, Table I).
Myosin VI-T406E-HMM (two catalytic subunits or heads) has a V max of 3.3 s Ϫ1 head Ϫ1 and K ATPase of ϳ0.6 M (Fig. 2, Table I). A reduction in V max and K ATPase suggests the heads of the myosin VI dimer do not act independently (see "Discussion").
The actin concentration dependence of wild-type (Thr 406 ) myosin VI ATPase activity does not fit a hyperbola well (data not shown) but seems to be the sum of two hyperbolas with K ATPase values of ϳ3 and ϳ18 M. This suggests a mixture of phosphorylated and dephosphorylated myosin VI is purified from baculovirus as demonstrated for myosin I (10).
In the absence of an ATP-regenerating system, the maxi-   mum steady-state ATPase rates of wild-type and mutant myosin VI are slow (V max Յ 1 s Ϫ1 , data not shown, see also Ref. 1) because of product inhibition by ADP (13).
Myosin VI Binding to Actin Filaments by Pyrene Fluorescence-As demonstrated for other myosins, strongly bound myosin VI (AM and AM.ADP in Scheme 1) quenches ϳ75% of the pyrene-actin fluorescence. Time courses of the reduction in fluorescence intensity after mixing myosin VI-T406E (Ϯ ADP) or myosin VI-T406A (Ϯ ADP) with pyrene-actin filaments all follow single exponentials ( Fig. 3A) with no distinguishable lag phase (12,21). The myosin and actin concentrations were adjusted such that actin was ϳ10 times the myosin concentration and pseudo first-order requirements were fulfilled. The observed rates (k obs ) depend linearly on the actin filament concentration over the range examined (Fig. 3B). The data were modeled as simple bimolecular reactions according to Schemes 2 and 3, where the * indicates high fluorescence (i.e. unquenched) of pyrene actin. The apparent second-order rate constants (k Ϫ6 and k Ϫ10 ) for myosin VI binding to actin filaments were obtained from the slopes of the lines and are summarized in Table II.
Myosin VI dissociation from pyrene actin was measured by competition after mixing an equilibrated mixture of pyreneactomyosin VI (Ϯ ADP) with an 80-fold excess of unlabeled actin filaments (Fig. 3C). The rate-limiting step, and therefore the step measured, is dissociation of myosin VI bound to pyrene actin. In the presence and absence of ADP, time courses of fluorescence enhancements follow single exponentials and yield the apparent dissociation rates (k ϩ6 and k ϩ10 ) for actomyosin VI dissociation (Table II). The apparent actomyosin VI affinities (K 6 and K 10 ) were determined from the ratio of the rate constants (Table II).
Phosphorylation at Thr 406 has minimal effects (Ͻ2-fold and The solid lines through the data points are the best fits to a rectangular hyperbola (y ϭ start ϩ (amplitude*x)/(K 0.5 ϩ x)). A quadratic form of the equation that takes into account the actin and myosin concentrations yielded identical results. The steady-state parameters determined from the fits were start ϭ v o , amplitude ϭ V max Ϫ v o , K 0.5 ϭ K ATPase , and x ϭ [actin] and are presented in Table I. There was variability in v o between preparations, presumably caused by contaminating actin, so v o was determined from the best fit of the data weighing all data points equally. within the range of uncertainty) on the rates and affinities of actin-filament binding in the strongly bound (AM and AM.ADP) states (Table II).
ADP weakens the affinity of myosin VI for actin filaments ϳ80-fold independent of phosphorylation at Thr 406 ; the rate of binding to actin is reduced ϳ4 -6-fold, and the rate of dissociation from actin is ϳ10 -20 times more rapid (Table II).
ATP-induced Population of the Weakly Bound States-The fluorescence of pyrene actin was used to monitor formation of the weak binding states of myosin VI after mixing with ATP ( Fig. 4). Concentrations lower than the K ATPase (Table I) were used to ensure ATP-induced dissociation of myosin VI from actin as confirmed by light scattering (data not shown). The addition of MgATP to 0.5 M strongly bound (i.e. quenched) pyrene-actomyosin VI increases the fluorescence to that of pyrene actin alone. The time courses follow single exponentials (Fig. 4, A and B) with rates that depend linearly on the MgATP concentration (Fig. 4C). As for all other characterized myosins, the mechanism of ATP-induced fluorescence enhancement was modeled as a two-step binding reaction.
where AM(ATP) is the quenched collision complex in rapid equilibrium (K 1 Ј) with free nucleotide that isomerizes (k ϩ2 Ј) to the high fluorescence A*M.ATP. At saturating ATP (Ͼ5 mM), 100% of the fluorescence is recovered, demonstrating that k ϩ2 Ј Ͼ Ͼ k Ϫ2 Ј and ATP binding can be considered to be essentially irreversible.
The association rate constants for MgATP binding to actomyosin VI (K 1 Јk ϩ2 Ј) obtained from the initial slopes of the lines are 18.2 (Ϯ 0.2) mM Ϫ1 s Ϫ1 for T406E and 15.2 (Ϯ 0.4) mM Ϫ1 s Ϫ1 for T406A (Table II). The maximum rate of ATP-induced dissociation (k ϩ2 Ј ϩ k Ϫ2 Ј) for both myosin VI mutants is Ͼ250 s Ϫ1 . The equilibrium constant for rapid ATP binding is very weak (1/K 1 Ј Ͼ Ͼ 14 mM) for both myosin VI mutants, suggesting that either ATP dissociates rapidly from the collision complex (rapid k Ϫ1 Ј) or the nucleotide binding site is not readily accessible (slow k ϩ1 Ј, see "Discussion"). From the amplitudes of the transients we estimate apparent K m values of ϳ300 M for both myosin VI mutants.
Although we did not correct for the changes in the ionic strength of the buffer resulting from the addition of mM MgATP, inclusion of an additional 50 mM KCl (corresponding to ϳ12 mM MgATP assuming a net charge of Ϫ2 at pH 7.0) slowed the rate of T406A dissociation at 8 mM MgATP from 113 s Ϫ1 to 91 s Ϫ1 (data not shown). Therefore, we are confident that the SCHEME 4  The smooth line is the best fit to a single exponential with a rate (k obs ) of 161 s Ϫ1 . C, ATP concentration dependence of the k obs for myosin VI-T406E (q) or myosin VI-T406A (E). The apparent second-order association rate constants for ATP binding to actomyosin VI (K 1 Јk ϩ2 Ј) determined from the slopes of the lines are presented in Table II. dependence of the observed rate on [ATP] is linear over the range examined and that changes in ionic strength resulting from the addition of MgATP are not preventing the detection of a biphasic dependence (i.e. saturation) of the observed rates.
At rates Ͼ50 s Ϫ1 , a slow component with a rate of 7-9 s Ϫ1 could be resolved in the transients (data not shown). The amplitude (2-5%) of this phase was variable and could be accounted for by the fraction of ADP in the solution and the experimentally determined rates of ATP binding, ADP binding (presented below), and ADP release (presented below), suggesting that the slow component results from residual ADP in the ATP (22).
MgATP Binding to Myosin VI in the Absence of Actin by mantATP Fluorescence-The fluorescent nucleotide 2Ј-deoxy-mantATP ( ex ϭ 365 nm) was used to monitor MgATP binding to myosin VI in the absence of actin (Fig. 5). Time courses of fluorescence enhancement after mixing mantATP with myosin VI do not follow single exponentials but can be fitted to double exponential functions (Fig. 5A). The rate of the fast phase depends on the mantATP concentration for both mutants (Fig.  5B). The second-order association rate constants for ATP binding obtained from the slopes of the lines are 0.27 M Ϫ1 s Ϫ1 for T406E and 0.14 M Ϫ1 s Ϫ1 for T406A. The intercepts give dissociation rate constants of ϳ4 s Ϫ1 for both mutants (Table II).
We could not accurately resolve the slow phase because of interference from photobleaching over long time scales but the rates were ϳ0.2-0.4 s Ϫ1 and, given the uncertainties in the values, difficult to conclude if they depend on the nucleotide concentration. The source of the slow component is unknown, but it may represent a fraction of myosin that binds ATP (but not ADP, see below and Fig. 6A) slowly or an isomerization of myosin and/or nucleotide after binding. We did not investigate this component because it is not likely to be a relevant pathway in the actin-activated ATPase cycle; the rate is much slower than the steady-state turnover rate (Fig. 2B).
In the presence of actin the rates of mantATP binding were too slow (see Fig. 4C, MgATP binding to pyrene actomyosin) to measure accurately or to distinguish the fast and slow phases of the reaction.
There are no detectable changes in tryptophan fluorescence of either myosin VI mutant with ATP (or ADP) binding or ATP hydrolysis (data not shown). Similarly, there are no detectable changes in mantATP (or mantADP) fluorescence ( ex ϭ 295 nm) resulting from energy transfer via tryptophans to the bound mant nucleotides (data not shown). Tryptophans corresponding to chicken skeletal muscle myosin Trp 510 and Trp 595 are absent from myosin VI (Val 504 and Phe 594 , respectively), suggesting that either or both of these residues contribute to the fluorescence changes observed with other myosins. The Trp 510 equivalent (Trp 512 ) monitors the structural change preceding ATP hydrolysis in smooth muscle myosin II (23).  Table II.  Table II. C, time course of mantADP dissociation from actomyosin VI-T406E. An equilibrated mixture of 2Ј-deoxy-mantADP (40 M) and actomyosin VI (1 M) was mixed with 2 mM unlabeled ADP. The smooth line through the data is the best fit to an exponential with a rate of 5.6 s Ϫ1 . VI-T406A (Table II). It is important to clarify that this represents a lower limit for K 3 , because ATP binding appears to be reversible (Fig. 5B, see "Discussion"), and the measured burst amplitude may be low as a result of rapid ATP dissociation. We could not get a reliable signal at higher [ATP].

ADP-P i Burst and the Equilibrium Constant for ATP Hydrolysis (K 3 )-We
The slow rate of ATP binding to actomyosin VI (K 1 Јk ϩ2 Ј, Fig.  4, Table II) precludes measurement of the ADP-P i burst in the presence of actin.
ADP Binding and Dissociation by mantADP Fluorescence-The fluorescence enhancement of 2Ј-deoxy-mantADP upon binding to myosin was used to measure the affinity and rates of ADP binding to myosin VI (Fig. 6, Table II). Time courses of fluorescence enhancements after mixing mantADP with myosin VI and actomyosin VI all follow single exponentials (Fig. 6A) with rates that depend linearly on the concentration of nucleotide (Fig. 6B). Therefore, mantADP binding was modeled as a simple bimolecular reaction according to Schemes 5 and 6, where the * indicates high mantADP fluorescence, yielding the apparent second-order rate constants for mantADP binding (k Ϫ5 and k Ϫ5 Ј) from the slopes of the lines (Table II). The intercepts deviate from the origin and reflect the dissociation rates (k ϩ5 Ј and k ϩ5 ) as confirmed by direct measurement (Fig. 6C).
The rate of mantADP release from actomyosin VI-T406E and -T406A is ϳ6 s Ϫ1 (Fig. 6C, Tables I and 2), which approximates the steady-state ATPase rate of both mutants, suggesting that ADP release is rate-limiting in the presence of actin. Myosin VI-T406E-HMM dissociates mantADP at approximately the same rate (7.0 Ϯ 0.4 s Ϫ1 , Table II). For other characterized myosins (e.g. see Ref. 12), mantADP release from actomyosin is 1.5-2-fold slower than unlabeled ADP.
Actin binding has minimal (Ͻ2-fold reduction) effects on the rates and affinities of mantADP binding (Table II). Dissociation (Fig. 6C) occurs at ϳ6 s Ϫ1 from both myosin-VI mutants in the presence (k ϩ5 Ј) and absence (k ϩ5 ) of actin. The association rate constants of mantADP are reduced only slightly (Ͻ2-fold) by binding to actin.
Myosin VI-T406E binds mantADP with a 3-4-fold higher affinity (K 5 and K 5 Ј) than does T406A because of a more rapid association rate constant both in the presence (k Ϫ5 ) and absence (k Ϫ5 Ј) of actin filaments (Table II). Therefore, actomyosin VI binds MgADP more tightly than MgATP (K m values for ATP ϳ 300 M): ϳ30 -40 times more tightly for T406E and 10 -15 times more tightly for T406A. P i Release-Time courses of P i release after mixing myosin VI-ADP-P i with actin filaments show a rapid exponential burst phase followed by a slow linear phase for both myosin VI mutants (Fig. 7, A and B). The burst corresponds to the first turnover of P i release after actin binding, and the slow linear phase reflects steady-state ATPase activity.
The burst was measured without interference from the linear phase by including ADP (1 mM) with actin (data not shown). ADP competes with ATP and limits myosin to a single ATP turnover. There is no burst phase for either mutant in the absence of actin (curve c in Fig. 7, A and B), thus P i release is rate-limiting (k ϩ4 ϳ 0.04 s Ϫ1 ).
The P i release burst rate depends hyperbolically on the actin filament concentration for both myosin VI mutants (Fig. 7C) and was therefore modeled as a two-step binding reaction according to Scheme 7.
In the presence of P i BiP, P i release is irreversible, so k Ϫ4 Ј is not considered in the analysis.
At all actin concentrations examined, P i release from myosin The V max and K ATPase values obtained from the linear phase of these curves are lower than those obtained with the NADH assays (Fig. 2) because of the low ATP concentration (100 M versus 2 mM) and ADP inhibition without an ATP regenerating system. VI-T406E is more rapid than from myosin VI-T406A (Fig. 7C). The maximum rate of P i release (k ϩ4 Ј) obtained from the best fit of the data to a hyperbola is ϳ90 s Ϫ1 for myosin VI-T406E and ϳ30 s Ϫ1 for myosin VI-T406A (Table II). The affinity of myosin VI-ADP-P i for actin filaments (K 9 ) is ϳ30 -40 M for both mutants, which is similar to skeletal muscle myosin II (20). Therefore, P i release is not rate-limiting for actomyosin VI, and the effect of phosphorylation at Thr 406 is to increase the maximum rate of P i release ϳ3-fold.
Steady-state Distribution and Lifetimes of Biochemical States-Knowing most of the rate and equilibrium constants in the myosin VI ATPase cycle (Table II) allows us to predict the steady-state distribution and lifetimes of the biochemical intermediates (Fig. 8). Myosin VI is a high duty ratio motor that predominantly populates the strong binding (AM.ADP and AM) states at physiological nucleotide concentrations (2.2 mM MgATP, 12 M MgADP, pH 7.0; Ref. 24). Both mutants are high duty ratio motors at Ͼ60 M actin. The duty ratio depends on the [actin] at Ͻ60 M actin (14). Heavy chain phosphorylation slightly increases the fraction of cycle time spent in the strongly bounds states, thus increasing the duty ratio.

DISCUSSION
Overview of the Myosin-VI ATPase-The most notable features of the myosin-VI ATPase are (a) the rate-limiting ADP release in the presence of actin (k ϩ5 Ј), (b) the rapid P i release in the presence of actin (k ϩ4 Ј) that is increased by mimicking the phosphorylation of Thr 406 , (c) the slow rate of ATP binding when bound to actin (K 1 Јk ϩ2 Ј), and (d) the minimal effect of actin on ADP binding, release, and affinity. In combination, these kinetic adaptations ensure that myosin VI has a high duty ratio (i.e. spends a significant proportion of its ATPase cycle strongly bound to actin). As with myosin V (12, 13), rate-limiting ADP release results in the predominant intermediate being strongly bound (AM.ADP, Fig. 8). However, because ATP binding is weak and slow (Table II), a significant fraction of myosin VI will populate the rigor state (AM, Fig. 8) at physiological nucleotide concentrations. Additionally, these kinetic adaptations are what one would expect for a processive two-headed myosin (discussed below) or as proposed for myr1 (25), a motor that is adapted for maintaining tension.
Unlike other characterized myosins, actin does not affect the rate of ADP release from myosin VI (k ϩ5 ϭ k ϩ5 Ј) of either mutant. ADP release is the rate-limiting step of the ATPase cycle in the presence of actin, but P i release (k ϩ4 ) is rate-limiting in the absence of actin. Relocation of the rate-limiting step by actin results from accelerating P i release such that it is faster than ADP release (k ϩ5 Ј).
Kinetic and Structural Implications of Heavy Chain Phosphorylation-The V max of amoeboid myosin-I isoforms is regulated by heavy chain phosphorylation at the equivalent of myosin VI-Thr 406 . This acceleration is most likely caused by the increase in the rate of P i release (k ϩ4 Ј), which is ratelimiting in the presence and absence of actin (11). Although heavy chain phosphorylation affects the same kinetic step of myosin VI, it does not alter the V max of the actomyosin ATPase cycle, because ADP release is rate-limiting for myosin VI-T406A and myosin VI-T406E.
The K ATPase of a myosin with rate-limiting ADP release (k ϩ5 Ј ϭ V max ) can be related to the rate of P i release (k ϩ4 Ј), the affinity of myosin ADP-P i for actin filaments (K 9 in units of M Ϫ1 ), and the equilibrium constant for ATP hydrolysis (K 3 ) according to Equation 1 (14).
Using our experimentally determined parameters (Tables I and  II) we calculate K ATPase values of 5 M for T406E and 18 M for T406A, which are in close agreement with the experimentally determined values (Fig. 2B, Table I). Therefore, myosin-VI regulation by phosphorylation at Thr 406 reduces the K ATPase , a macroscopic constant, by directly increasing the rate of P i release, a microscopic rate constant. Because Equation 1 accounts for the steady-state regulation, it is unlikely that the AM.ATP state is significantly populated by myosin VI during steady-state turnover. Also, note that the ratios of k cat /K ATPase (Table I) and k ϩ4 Ј/K 9 (Table II) are similar, within experimental uncertainties, because both parameters are reporting the rate of myosin-ADP-P i binding to actin as predicted from Equation 1 (14). It has been proposed (11) that a negative charge at the TEDS rule site of the HCM loop facilitates actin binding and P i release, and thus phosphorylation at this site might influence the actin-binding affinities of myosin. However, given that the rates and affinities of the strong (AM and AM.ADP) and weak (AM.ADP.P i ) binding states of myosin VI are essentially unaffected by mimicking phosphorylation at Thr 406 (Table II) and that the rate of P i release is affected by the mutation only in the presence of actin (Table II), phosphorylation of the HCM loop is likely to affect an actin-bound intermediate distinct from the weakly bound AM.ADP.P i state and the strongly bound AM and AM.ADP states (Scheme 1). Therefore, Scheme 1 is an oversimplification of the ATPase reaction mechanism, and at least one additional intermediate is likely to exist. Scheme 8 is the minimal mechanism needed to account for the following: (a) P i release is slow in the absence of actin (Table II), (b) structural (26,27) and mechanical (28) measurements identify at least two (A)M.ADP.P i conformational states, (c) P i release is a two-step process (28), and (d) heavy chain phosphorylation accelerates P i release but only in the presence of actin (Fig. 7, Table II). SCHEME 8 FIG. 8. Steady-state distribution of biochemical states. Simulations were performed using experimentally determined rate constants (Table II)  Following this mechanism, we propose that k ϩ4A Ј, the conformational change preceding P i release, is regulated by heavy chain phosphorylation at Thr 406 . This transition limits P i release and is accelerated by actin. AM.ADP.P i does not release phosphate and AM † .ADP.P i releases P i (k ϩ4B Ј) quickly (Scheme 8). The AM † .ADP.P i state is equated with an open back-door structure that permits P i release (27) and the AM.ADP.P i state with the closed back-door. In the absence of actin, k ϩ4a is rate-limiting and not regulated by heavy chain phosphorylation.
In addition to regulating the transition that precedes P i release in the presence of actin, the T406E mutation alters the ADP affinity in the presence as well as the absence of actin (Table II), demonstrating that intramolecular interactions involving the HCM loop are transmitted to the nucleotide binding pocket independent of actin binding.
Nucleotide Binding to Myosin VI-The rate of MgATP binding to actomyosin VI (Scheme 4, Table II) is ϳ50 -100 times slower than for other characterized myosins with the exception of rat liver myosin I (myosin I␣, myr1 gene product), which has a similar binding rate of ϳ17 mM Ϫ1 s Ϫ1 (22,25). However, the molecular basis for slow ATP binding seems different for the two myosin classes. First, myosin VI has a maximum rate (k ϩ2 ) Ͼ250 s Ϫ1 , but myr1 has a k ϩ2 of ϳ30 s Ϫ1 (in the absence of calcium, Ref. 25) that accounts for the slow rate of ATP binding. Second, the equilibrium constant for rapid ATP binding (K 1 Ј) Ϫ1 is ϳ2 mM for myr1 but Ͼ Ͼ14 mM for myosin VI. Therefore, ATP binds slowly to myr1 because of a slow k ϩ2 but binds slowly to myosin VI because of a monstrously weak (K 1 Ј) Ϫ1 .
The slow rates of nucleotide (ATP and ADP) binding to myosin VI and actomyosin VI suggest that myosin VI exists in equilibrium between a state that binds nucleotide rapidly (open) and one that does not (closed). The sum of the rates defining the equilibrium constant between the open and closed states in the presence of actin must be rapid (Ͼ250 s Ϫ1 ), because it cannot be detected when measuring ATP-induced dissociation from pyrene actin ( Fig. 4; see Ref. 22). If this transition requires significant conformational rearrangement, nucleotide binding is likely to be load-dependent.
ATP binds myosin VI slower than ADP in the presence of actin (Table II). The slower rate may be caused by a conformation of myosin VI, in which there is interference with ␥-phosphate coordination in the pocket. Possibilities include a unique position of the converter (1) that may orient switch-2 in an unfavorable conformation or slow dehydration of the active site.
The interaction of myosin VI (M) with ADP (D) and actin filaments (A) is defined by four equilibrium constants: K 5 , K 5 Ј, K 6 , and K 10 (Scheme 9).
The product of the equilibrium constants defining a cyclic path (in thermodynamic equilibrium with no external input or consumption of free energy) must equal 1. Using our experimentally determined rate and equilibrium constants (Table II), we obtain a product of ϳ50 for both myosin VI mutants (50 for T406E and 56 for T406A) even though the values of the individual equilibrium and rate constants are different. This suggests that the source of the discrepancy in the linkage is similar for the two mutants, independent of phosphorylation, and probably reflects a limitation in the ability to measure all the relevant intermediates in the pathway (12). A discrepancy in the detailed balance of Scheme 1 for myosin V has been partially attributed to isomerization of actomyosin-ADP states (12), which based on cryo-electron microscopy reconstructions of myosin VI is likely to occur (1).
Implications for Processivity of Two-headed Myosin VI-There are two minimum requirements for a processive twoheaded myosin in which the motor domains are not independently processive. First, each motor domain must have a high duty ratio (Ͼ0.5), such that at least one motor domain is always attached to actin. Second, there is likely to be some form of communication between the motor domains, at a minimum to bias the position of lead head attachment and perhaps coordinating the catalytic cycles.
Myosin V motor domain has a high duty ratio (12)(13)(14), and the native double-headed molecule is processive (29,30), but the mechanism of head-head coordination is not yet resolved. Myosin VI also has a high duty ratio (Fig. 8), and the twoheaded molecule has lower V max and K ATPase values than the single-headed molecule (Fig. 2B, Table I). An ϳ2-fold reduction in the V max of the two-headed molecule (Fig. 2B, Table I) is consistent with half-site reactivity and suggests that the heads of the dimer do not act independently but alternate in a sequential manner such that their catalytic cycles are out of phase (31). Both single-and double-headed myosin VI release mantADP at about the same rate (ϳ6 -7 s Ϫ1 , Table II), so we can rule out the possibility that the V max is slower for the two-headed molecule because of a slower ADP release rate. We can also rule out that P i release is slow and rate-limiting because this would increase the K ATPase (Equation 1) not lower it.
A k cat /K ATPase greater than the productive encounter frequency (k ϩ4 Ј/K 9 ) is expected if a molecule hydrolyzes multiple ATPs per encounter with an actin filament (32). The k cat / K ATPase and k ϩ4 Ј/K 9 of single-headed myosin VI are similar within experimental uncertainties (T406E ϳ3 M Ϫ1 s Ϫ1 ; T406A FIG. 9. Alternating site model for the coordination and processive stepping of two-headed high duty ratio myosins (see text below, "Model for Processivity," for description). SCHEME 9