A model of myosin V processivity

Cytoplasmic transport is mediated by a group of molecular motors that typically work in isolation, under conditions where they must move their cargos long distances without dissociating from their tracks. This processive behavior requires specific adaptations of motor enzymology to meet these unique physiologic demands. One of these involves the ability of the two heads of a processive motor to communicate their structural states to each other. In this study, we examine a processive motor from the myosin superfamily myosin V. We have measured the kinetics of nucleotide release, of phosphate release, and of the weak-to-strong transition, as this motor interacts with actin, and we have used these studies to develop a model of how myosin V functions as a transport motor. Surprisingly, both heads release phosphate rapidly upon the initial encounter with an actin filament, suggesting that there is little or no intramolecular strain associated with this step. However, ADP release can be affected by both forward and rearward strain, and under steady-state conditions it is essentially prevented in the lead head until the rear head detaches. Many of these features are remarkably like those underlying the processive movement of kinesin on microtubules, supporting our hypothesis that different molecular motors satisfy the requirement for processive movement in similar ways, regardless of their particular family of origin.

kinetics of specific transitions in the mechanochemical cycle. Addressing these issues is the focus of this study. Our results show that both forward and rearward strain can affect the kinetics of crucial structural transitions in the myosin V ATPase cycle. However, under steady-state conditions, it is the effect of rearward strain in retarding ADP release from the forward head that provides the critical coordination for processivity. Our results also show that phosphate release is rapid for both heads and occurs before the heads bind strongly to actin. Taken together these data provide the first evidence that phosphate is released immediately upon myosin V binding to actin and that it occurs prior to formation of a strong binding state and development of intramolecular strain. Our results demonstrate that only the release of ADP is strain-sensitive, ensuring that both heads will be strongly bound to actin once the lead head finds an actin-binding site. Thus the degree of processivity of myosin V is ultimately limited by the rate at which a newly detached head can find an actin binding site. This arrangement ensures that both heads will be strongly bound to actin once the lead head finds an actin-binding site.

EXPERIMENTAL PROCEDURES
Reagents-The N-methylanthraniloyl derivative of 2Јdeoxy-ADP was synthesized as described previously (24). N-1-Pyrenyl iodoacetamide was obtained from Molecular Probes (Portland, OR). Protease inhibitors and chemicals used for buffers were obtained from Sigma. Pre-poured Sephadex G-25 columns (PD10) were obtained from Amersham Biosciences.
Proteins-Actin was prepared from rabbit acetone powder, and labeling at cysteine 374 with N-1-pyrenyl iodoacetamide was carried out as described before (14). Phosphate-binding protein was purified from Escherichia coli and labeled with MDCC 1 as described (25).
Recombinant Myosin V Expression and Purification-Chicken myosin V cDNA was expressed in two forms. The constructs were based on the previously described two-headed (HMM-like) myosin construct, myosin V-6IQ HMM (7). The construct was used to create either a twoheaded (HMM-like) or single-headed (S1-like) construct. This myosin V-6IQ HMM heavy chain was truncated at Glu-1099, to which was added a leucine zipper (GCN4) to ensure dimerization, then followed by a FLAG tag (for purification). For the single-headed (S1-like) construct, the coiled-coil was removed and the heavy chain was truncated at amino acid Lys-910 to create myosin V-6IQ S1. As for the HMM, a FLAG tag was added after Lys-910 to facilitate purification. Recombinant baculoviruses were generated and used for co-expression in SF9 cells with calmodulin and essential light chains (7). Using the methodology detailed previously (26), purified myosin V HMM or S1 protein was obtained. Fig. 1 illustrates an SDS-PAGE of a purified myosin V HMM 6IQ preparation and demonstrates that a typical yield has high purity and minimal evidence of proteolysis. Concentrations of recombinant myosin V preparations were determined with the Bio-Rad protein assay. The reference samples were recombinant myosin V HMM and S1 whose concentrations were determined by absorbance, using calculated extinction coefficients of 540,240 M Ϫ1 cm Ϫ1 for HMM and 129,610 M Ϫ1 cm Ϫ1 for S1. Complexes of myosin V constructs with 2ЈdmD were formed by pre-incubating S1 and HMM with a 20-fold molar excess of 2ЈdmD, followed by gel filtration on pre-poured Sephadex G-25 columns (PD10, Amersham Biosciences) according to the manufacturer's instructions. Fractional labeling of the complexes with 2ЈdmD was determined by using the extinction coefficient of the fluorescent nucleotide (5700 M Ϫ1 cm Ϫ1 at 356 nm (24)) and the measured protein concentration. Ratios of 2ЈdmD to active site concentration were typically 0.90 -0.95.
Kinetic Methodologies-Kinetic measurements were made using an Applied Photophysics SX.18MV stopped-flow spectrophotometer with an instrument dead time of 1.2 ms (27). The excitation and emission wavelengths for monitoring pyrene-labeled actin and MDCC-labeled phosphate-binding protein fluorescence have been described (10). For studies of 2ЈdmD and 2ЈdmD⅐P i release, mant fluorescence was moni-tored by both direct excitation ( ex ϭ 356 nm) and by energy transfer from vicinal tryptophan residues ( ex ϭ 295 nm), and both methods gave similar results.

RESULTS
Our experimental approach was to compare the kinetics of key steps of the myosin V HMM mechanochemical cycle during the first one to two turnovers to those for an S1 construct, because this would allow us to test the role of internal strain in shaping the kinetics of native myosin V. We also examined the kinetics of several of these steps under steady-state conditions to evaluate the physiologic relevance of our findings.
Actin Binding in the Presence of ADP-Previous studies have noted that dimeric myosin V constructs can aggregate actin filaments under conditions that favor strong binding (28,29). This effect is presumed to be due to the presence of extended lever arms, which would allow cross-linking of actin filaments and could interfere with spectroscopic measurements. We have addressed this issue by comparing the kinetics of the light scattering increase produced by mixing myosin V S1⅐ADP with actin to those using HMM⅐ADP. Fig. 2A illustrates a typical light scattering transient, produced by mixing 0.8 M S1 or HMM (active site concentration) with 6 M actin in the presence of 1 mM ADP. For S1 (red), the transient consisted of a rapid phase (inset, red transient), sometimes accompanied by a low amplitude (Ͻ5% total) slow phase. By contrast, mixing with HMM (green) produced two well separated phases. The faster phase (inset, green transient) constituted ϳ60% of the total signal amplitude. The slower phase fit a single exponential process (solid curve), showed little actin concentration dependence, and measured 0.03-0.05 s Ϫ1 . We propose that the fast phase for both the HMM and S1 transients represents strong binding of at least one head to actin, whereas the slow phase seen with HMM is due to cross-linking. The HMMinduced cross-linking could be due to one of two possibilities. First, steric constraints on the lever arm could prevent the second head of HMM from binding strongly to the same actin filament. Because of its limited rotational freedom in the ADP state, the second head would only be able to slowly attach to neighboring actin filaments, producing a cross-linked aggregate. This possibility would predict that mixing HMM with pyrene-labeled actin in the presence of ADP should produce a fluorescence decrease that is the mirror image of the light scattering transient, e.g. two phases of similar amplitude, with the slower phase characterized by a rate constant of 0.03-0.05 s Ϫ1 . The second possibility is that binding of both heads of HMM to the same actin filament is kinetically favored but leads to a system that is internally strained. In this case, strain could be relieved by release of the forward head (with rate constant of 0.03-0.05 s Ϫ1 ), followed by attachment to a neighboring actin filament. In this scenario, mixing of HMM with pyrene-labeled actin should produce a fast fluorescence decrease that is not followed by a slow phase. Furthermore, this possibility would predict that the amplitude of the fast fluorescence decrease should be the same as that for an equimolar S1 concentration. Fig. 2B illustrates the results of mixing 0.8 M (active site concentration) S1⅐ADP (green) or HMM⅐ADP (red) with 6 M pyrene-labeled actin (50% labeled). Strong binding to actin quenches the pyrenyl fluorescence, and for both S1 and HMM, this process (inset) is considerably more rapid than cross-linking ( Fig. 2A). A detailed analysis of the kinetics of this rapid quenching demonstrates biphasic decays for both HMM and S1 (inset), with apparent second order rate constants of 16 -19 M Ϫ1 s Ϫ1 and 1-4 M Ϫ1 s Ϫ1 (data not shown). More important, the total amplitudes of this pyrene fluorescence transient were nearly identical for equimolar active site concentrations of S1 and HMM preparations (Fig. 2B, inset). Finally, it should be noted that over the time scale where cross-linking occurs (Ͼ2 s after mixing with HMM), no further decrease in pyrene fluorescence was seen in the HMM transients. In fact, a small amplitude rising phase was noted, which fit a single exponential process at 0.05-0.07 s Ϫ1 (Fig. 2B, solid curve). As indicated by the discussion above, we interpret these results to mean that, after mixing, both heads of HMM bind relatively rapidly to the same actin filament. We predict that this would generate intramolecular strain, which would be relieved by a slow dissociation of the leading head from one actin filament and its subsequent rebinding to a neighboring filament. Labeling actin with pyrene reduces its affinity for myosin (14). Hence, the combination of rearward strain on the leading head, which would favor its dissociation from actin, with the increased affinity of an ADP-containing head for unlabeled actin, would together lead to rebinding to unlabeled actin subunits on neighboring filaments. This should lead to an overall reduction in pyrene actin subunits with a strongly bound HMM head, because in this experiment, only 50% of the actin subunits were labeled, and this would be manifested by a low amplitude rise in fluorescence at ϳ0.05 s Ϫ1 . This prediction is confirmed in Fig. 2B.
Actin-activated ADP Release-Because ADP release is ratelimiting in the cycle (9), we investigated the effect of strain on the kinetics of ADP release. This was monitored by mixing a complex of S1⅐2ЈdmD or HMM⅐2ЈdmD in the stopped flow with actin plus excess nucleotide. Fig. 3A illustrates the fluorescence transients produced by mixing a complex of 2 M (active site concentration) S1⅐2ЈdmD (red) or HMM⅐2ЈdmD (green) with 20 M actin plus 2 mM ADP. For S1, the transient could be fit to a single exponential decay, reflecting dissociation of the bound 2ЈdmD, and the rate constant of this process varied hyperbolically with actin concentration (Fig. 3A, inset, red circles), defining a maximum rate constant of 15.8 Ϯ 1.6 s Ϫ1 . This result is very similar to previously reported studies that used mant-ADP, which is a mixture of the 2Ј and 3Ј isomers (9). By contrast, the corresponding fluorescence transient for HMM was clearly biphasic, and the two phases had similar amplitudes (Fig. 3B). Only the faster phase showed a dependence of rate constant on actin concentration (Fig. 3A, inset, green boxes), with an extrapolated maximum of 29.5 Ϯ 3.4 s Ϫ1 : nearly twice as large as the corresponding value for S1. The slower phase (inset, green triangles) averaged Ϸ0.3-0.4 s Ϫ1 and showed little variation with actin concentration. These results are consistent with the model illustrated in Fig. 3C, where the fluorescence of the bound 2ЈdmD is symbolized by the magenta rays emanating from the actin-bound heads. We propose that forward strain on the rear head accelerates ADP release by a factor of approximately two, whereas rearward strain on the forward head markedly slows ADP release, to Ϸ0.3 s Ϫ1 . Release of this strain would occur with a slow dissociation of the forward head (at 0.03-0.05 s Ϫ1 ). This would then be rapidly followed by rebinding to a neighboring actin filament, which would likely occur with an altered geometry, one that would be unlikely to generate strain.
We tested this proposal by mixing HMM⅐2ЈdmD or S1⅐2ЈdmD in the stopped flow with actin plus 2 mM ATP. Because S1 For S1, the transient consisted of a rapid phase (inset, red transient), sometimes accompanied by a low amplitude (Ͻ5% total) slow phase. By contrast, mixing with HMM (green) produced two well separated phases, and the faster phase (inset, green transient) constituted ϳ60% of the total signal amplitude. The amplitude of the faster phase was similar for HMM compared with S1, and in both cases fit a double exponential function (inset). The actin concentration dependence defines apparent second order rate constants of ϳ19 M Ϫ1 s Ϫ1 and 4 M Ϫ1 s Ϫ1 (data not shown). The slower phase fit a single exponential process (solid curve), showed little actin concentration dependence, and measured 0.03-0.05 s Ϫ1 . Conditions: 50 mM KCl, 25 mM HEPES, 2 mM MgCl 2 , 1 mM EGTA, 1 mM dithiothreitol, pH 7.50, 20°C. The HMM transient was offset by 0.3 V to make its morphology more readily distinguishable from that for S1. B, pyrene fluorescence transient produced by mixing 0.8 M S1 (green transient) or HMM (red transient) with 6 M pyrene-labeled actin (50% labeled) in the presence of 1 mM ADP. For both HMM and S1, the decrease in pyrene fluorescence occurred within 1 s after mixing (inset) and could be described by a double exponential function (solid lines through the red and green transients). The actin concentration dependence defines apparent second order rate constants of ϳ16 M Ϫ1 s Ϫ1 and 0.8 M Ϫ1 s Ϫ1 (data not shown). Furthermore, as shown in the inset, the amplitude of the pyrene quenching was nearly identical for HMM and S1 over a range of actin concentrations. For HMM, a low amplitude increase in pyrene fluorescence followed the initial quenching, and it fit a single exponential process at 0.05-0.07 s Ϫ1 (solid curve). Conditions were as in A.
cannot generate internal strain, we would predict that the results with S1 in this experiment should be similar to those for the experiment discussed above. Fig. 4A confirms this. The fluorescence transient for S1 (red) is well fit by a single exponential decay, and the rate constant of the transient shows nearly an identical hyperbolic dependence on actin concentration (inset, red triangles, maximum rate constant 15.2 Ϯ 1.0 s Ϫ1 ). Because we are proposing that forward strain accelerates ADP release from the trailing head, we would also expect that the fluorescence transient for HMM should be biphasic and that the maximum rate for the faster phase should be similar to that in Fig. 3A. The transient for HMM in this experiment (Fig.  4A, green) fits a double exponential decay, and the rate constant of the faster phase shows a hyperbolic dependence on actin concentration, which is very similar to that measured in FIG. 3. Kinetics of actin activated 2dmD release from myosin V constructs in the presence of 2 mM ADP. A, fluorescence transient produced by mixing a complex of 2 M (active site concentration) S1⅐2ЈdmD (red jagged curve) or HMM⅐2ЈdmD (green jagged curve) with 20 M actin plus 2 mM ADP. Nucleotide complexes were formed by preincubating S1 and HMM with a 20-fold molar excess of 2ЈdmD, followed by gel filtration on Sephadex G-25 to remove excess nucleotide. The transient for S1 fit to a single exponential decay, whereas the transient for HMM required a double exponential fit. Inset: plot of rate versus actin concentration for S1 (red) and HMM (green). The rate constant of the single phase for S1 fit a rectangular hyperbola, defining a maximum of 15.  Fig. 2. B, the ratio of the fast phase amplitude of the HMM transient divided by the slow (Ampl fast / Ampl slow ) remained close to 1.0 over a range of actin concentrations. C, schematic of the experimental results for HMM. Immediately after mixing, the two heads of HMM (green and magenta), attach to the actin filament (blue) at 36-nm intervals. The fluorescence emission of 2ЈdmD is enhanced when it is bound to the active site of HMM (symbolized by the magenta rays emanating from the motor domains). Release of 2ЈdmD from the rear head is accelerated 2-fold by the resulting forward strain (symbolized by the forward pointing green arrow on the lever arm) and produces a 50% reduction in fluorescence. By contrast, rearward strain on the forward head (symbolized by the rearward pointing magenta arrow on the lever arm) markedly slows 2ЈdmD release from the forward head, characterized by a rate constant of 0.3-0.4 s Ϫ1 . Strain is then relieved by an even slower dissociation of the ADP-bound head from one actin filament (at 0.03-0.05 s Ϫ1 ), followed by rapid rebinding to a neighboring filament. Given the altered geometry of binding, this would not be associated with the development of strain and is symbolized by the serpentine lever arm in the figure. C, schematic of the experimental results for HMM. ADP dissociates from the rear head of a doubly attached, internally strained HMM at the accelerated rate constant of 28 -30 s Ϫ1 . This is rapidly followed by ATP binding and dissociation of the rear head, which relieves the internal strain (symbolized by the serpentine lever arms). With strain relieved, ADP can now dissociate from the leading head with a rate constant of 12-16 s Ϫ1 . Given that these two steps are essentially irreversible, the observed rate constant for ADP release from the leading head is predicted to be Ϸ [(28 ϫ 12)/(28 ϩ 12)] s Ϫ1 ϭ 8.4 s Ϫ1 .
the presence of ADP (inset, green boxes, maximum rate constant 28.9 Ϯ 5.3 s Ϫ1 ). By contrast, the rate constant of the second phase for the HMM transient in this experiment was considerably faster, with a maximum of 8.8 Ϯ 1.8 s Ϫ1 (inset, green triangles). As in the case of Fig. 3, the relative amplitudes of the two phases for HMM were similar (Fig. 4B). These results are consistent with the scheme depicted in Fig. 4C. Although excess ADP would keep HMM strongly bound and under strain, and while strain would inhibit 2ЈdmD release from the leading head, excess ATP would bind to the trailing head once it had released its 2ЈdmD. This would dissociate the trailing head, relieve the internal strain (symbolized by a serpentine regulatory domain) and allow 2ЈdmD to dissociate from the leading head. A maximum rate constant of 8.8 Ϯ 1.8 s Ϫ1 (Fig. 4A, inset, green triangles) would be consistent with the model depicted in Fig. 4C if release of 2ЈdmD from the trailing head were immediately followed by ATP binding and dissociation from actin, allowing 2ЈdmD to release from the leading head at a rate defined by our studies with S1 (12-15 s Ϫ1 ; Ref. 9 and Fig. 4A).
Kinetics of Phosphate and Product Release-We measured the kinetics of actin-activated phosphate release from myosin V S1 and HMM at equal active site concentrations in a sequential mixing experiment. Nucleotide-free S1 or HMM was mixed with a 10-fold molar excess of ATP, the complex was allowed to age for 1 s to allow population of the myosin V⅐ADP⅐P i state, and it was then mixed with varying concentrations of actin plus 2 mm ADP. Phosphate release was monitored with MDCClabeled phosphate-binding protein (MDCC-PBP), as previously described (10), with a MDCC-PBP⅐myosin concentration ratio of 7:1 after the second mix. Fig. 5 illustrates an example of the resulting fluorescence transients for HMM (red) and S1 (black) at final active site concentrations of 0.5 M and at a final actin concentration of 5 M. For both constructs, the fluorescence fit a single exponential process (solid curves in Fig. 5). The S1⅐HMM amplitude ratio averaged 1.28 Ϯ 0.18 over a range of actin concentrations (Fig. 5, inset). Finally, the rates of phosphate release from both S1 (Fig. 6B, closed red circles) and HMM (Fig. 7B, closed red circles) showed a similar hyperbolic dependence on actin concentration, defining maximum rates of 198 Ϯ 18 s Ϫ1 for S1 and 228 Ϯ 32 s Ϫ1 for HMM. We next examined the kinetics of product release in the following experiment. S1 was mixed with a 10-fold molar excess of 2ЈdmT in a sequential stopped flow, the sample was aged for 1 s to allow formation of an S1⅐2ЈdmD⅐P i intermediate, and the complex was then mixed with actin plus 2 mM ATP. Because phosphate release from S1 is very rapid, we would expect that the resulting fluorescence decay, reflecting mant-ADP release, should be monophasic. Furthermore, it should be identical to the red transient depicted in Fig. 4A and have the same rate constant dependence on actin concentration as seen in the inset of that figure. In fact, we observed a more complex fluorescence decay, which is illustrated in Fig. 6A (red transient). The decay was biphasic and fit a double exponential function (solid line). The rate constant for the faster phase (Fig. 6B, closed blue boxes) varied hyperbolically with actin concentration (solid blue curve), defining a maximum rate constant of 200 Ϯ 75 s Ϫ1 . Fig. 6B also shows that this process and phosphate release (red circles) occur with similar rate constants over a wide range of actin concentrations. The rate constant of the slower phase (open blue boxes) showed little variation with actin concentration, and averaged 10 -14 s Ϫ1 . This is very close to the maximum rate constant for 2ЈdmD release from S1 (Figs. 3A and 4A), and we propose that it reflects the release of 2ЈdmD in this experiment as well. The faster phase could be due to one of two possibilities: a conformational change in the catalytic site that precedes 2ЈdmD release and that occurs with either the weakto-strong transition or phosphate release, or rapid release of 2ЈdmD from a sub-population of S1 molecules that are damaged. To distinguish between these two possibilities, we performed the following experiments. First, S1 was mixed in a sequential mixer with a slight molar excess of unlabeled ATP, aged for 1 s, and then mixed with actin plus 200 M 2Ј-deoxymant-ATP. The mant fluorescence was monitored by energy transfer from vicinal tryptophan residues. If a subpopulation of damaged S1 molecules released nucleotide rapidly, we would expect a biphasic fluorescence increase that would be the mirror image of the red fluorescence transient in Fig. 6A. Conversely, if ADP release were preceded by a rapid conformational change, we would expect to see only a single phase in the fluorescence increase, reflecting ADP release at 12-15 s Ϫ1 , and the rate constant would vary little with actin concentration. The inset in Fig. 6A demonstrates an example of the resulting fluorescence transient. The fluorescence increase fits a single exponential process with little actin concentration dependence. Its mean value of 10.2 Ϯ 1.6 s Ϫ1 (Fig. 6B, solid green circles) is nearly identical to that for ADP release. Note that, at a final concentration of 100 M in this experiment, 2ЈdmT would be expected to bind to a vacant catalytic site of acto-S1 with a rate constant of ϳ100 s Ϫ1 (9). Thus, our finding of a monophasic rise in fluorescence in this experiment is not due to a limitation in 2ЈdmT concentration.
If the initial rapid fluorescence drop represents a conformational change that accompanies phosphate release, then it follows that the fluorescence intensity of myosin V⅐2ЈdmD⅐P i should be higher than that for myosin V⅐2ЈdmD. We can therefore make one further prediction: mixing S1 with a sub-stoichiometric amount of 2ЈdmT should produce an initial rise in fluorescence that is larger than that seen with an equivalent amount of 2ЈdmD. Because phosphate release would be very slow in the absence of actin (0.02 s Ϫ1 (9)), this initial rise should then be followed by a slow decay as the S1⅐2ЈdmD⅐P i is converted to S1⅐2ЈdmD. Fig. 6C compares fluorescence transients produced by mixing 7.5 M S1 with 5 M 2ЈdmT and 5 M 2ЈdmD. Consistent with the prediction, the initial rise produced by mixing with 2ЈdmT (red transient) is followed by a slow decay with a rate constant of 0.011 s Ϫ1 (solid blue curve), to a FIG. 5. Measurement of actin-activated phosphate release from myosin V⅐ADP⅐P i . 2 M nucleotide-free construct was mixed with a 10-fold molar excess of ATP, the complex was allowed to age for 1 s to allow population of the myosin V⅐ADP⅐P i state, and it was then mixed with 10 M actin plus 2 mm ADP. All samples contained 3.5 M MDCC-PBP. Phosphate release was monitored with MDCC-PBP, and the fluorescence increase fit a single exponential process for both S1 (green) and HMM (red), described by rates of 23.1 and 42.0 s Ϫ1 , respectively. Inset: ratio of amplitudes of the single exponential fit were plotted as S1⅐HMM amplitude ratio versus actin concentration. The mean amplitude ratio over this range of actin concentrations was 1.28 Ϯ 0. 18. final voltage nearly identical to that seen by mixing with 2ЈdmD (green transient). Finally, as predicted, mixing 7.5 M S1 with a 5-fold molar excess of 2ЈdmT produces a transient whose amplitude is 2.4-fold larger than that seen with an equivalent concentration of 2ЈdmD (Fig. 6D).
Our results would predict that the corresponding experiment with HMM should produce a fluorescence decrease consisting of three phases. The first would be associated with the conformational changes that also lead to phosphate release and would be rapid. The second would be due to release of 2ЈdmD from the trailing head at 28 -30 s Ϫ1 (Figs. 3A and 4A), and the third would be due to release of 2ЈdmD from the leading head at 8 -9 s Ϫ1 (Fig. 4A). Furthermore, the amplitudes of the slower two phases should be equal to each other, because each phase represents 2ЈdmD release from an active site. Fig. 7A illustrates the fluorescence transient produced by mixing 4 M HMM⅐2ЈdmD⅐P i with 40 M actin plus 2 mM ATP. The transient (red jagged curve) can be fit to three exponential terms (solid black curve). Furthermore, the two slower phases demonstrated similar amplitudes over a range of actin concentrations (Fig. 7B). Fig. 7C demonstrates that the fastest phase (solid blue boxes) varies hyperbolically with actin concentration, defining a maximum rate constant of 165.7 Ϯ 28.6 s Ϫ1 . Furthermore, over the range of actin concentrations tested, the rate constant for this phase is similar to that for phosphate release (solid red circles). The second phase (open blue boxes) also varies hyperbolically with actin concentration, and this dependence extrapolates to a maximum rate constant of 26.6 Ϯ 4.7 s Ϫ1 . Finally, the third phase (solid blue circles) shows little actin concentration dependence and averages 9.4 Ϯ 1.1 s Ϫ1 . As a further test of these results, we mixed HMM with a slight molar excess of unlabeled ATP and then with actin plus 200 M 2ЈdmT, as was discussed above for S1. The inset in Fig. 7A demonstrates that the fluorescence transient resulting from mixing HMM⅐ADP⅐P i with 100 M actin plus 200 M 2ЈdmT is clearly biphasic and could be fit to two exponential terms with rate constants of 22.5 and 5.9 s Ϫ1 .
The Weak-to-Strong Transition-We utilized the quenching of pyrene-labeled actin (14) to monitor the kinetics of the weakto-strong transition in myosin V by means of the following For 2ЈdmT, an initial rapid rise in fluorescence is followed by a slow decay with rate constant of 0.11 s Ϫ1 (solid blue curve), whereas for 2ЈdmD, only a rapid rising phase is seen. Note that the final voltage for the transient with 2ЈdmT is nearly identical to that for 2ЈdmD. D, fluorescence transients produced by mixing 7.5 M nucleotide-free myosin V S1 in the stopped flow with 37.5 M 2ЈdmT (red transient) or 2ЈdmD (green transient). The amplitude of the transient with 2ЈdmT is 2.4-fold larger than that for 2ЈdmD. experiment. HMM or S1 at equimolar active site concentrations was mixed with a 5-fold molar excess of ATP in a sequential stopped flow as described above. The mixture was allowed to age for 1 s to allow population of the myosin V⅐ADP⅐P i state, and it was then mixed with a 5-fold molar excess of pyrenelabeled actin plus 2 mM ADP. The decrease in fluorescence fit a single exponential decay for both HMM and S1 (data not shown). The rate constant for this process varied hyperbolically with actin concentration (Fig. 8) for both HMM (solid blue boxes) and S1 (open red boxes), defining maximum rates of 46.9 Ϯ 13.3 s Ϫ1 and 22.4 Ϯ 4.0 s Ϫ1 , respectively. The S1⅐HMM amplitude ratio averaged 1.13 Ϯ 0.40 over a range of actin concentrations (Fig. 8, inset).
Product Release and Strong Binding in the Steady State-We have demonstrated that ADP release by the rear head is accelerated 2-fold during the first turnover of a processive run. Furthermore, our results with the kinetics of the weak-tostrong transition argue that, once the trailing head is released, it swings forward and reattaches to the actin filament very rapidly. This would predict that, in the steady state, product should be released at 28 -30 s Ϫ1 . However, a different result would be expected if, under steady-state conditions, strain only affected ADP release from the leading head. In this situation, ADP release from the trailing head would occur at the unstrained rate of 12-15 s Ϫ1 , which would produce an overall rate for product release from the two heads of 8 -10 s Ϫ1 . We evaluated this issue by measuring the rate of mant nucleotide release in the following sequential mixing experiment. A complex of 2 M HMM plus 15 M actin was mixed with 100 M 2ЈdmT. The mixture was incubated for 2 s to achieve a steady-state distribution, and it was subsequently mixed with 4 mM ATP. We would predict the resulting transient to consist of a small amplitude rapid decrease in fluorescence, representing phosphate release by a small fraction of heads, followed by a single phase of further fluorescence decrease, due to product release from the two heads. Fig. 9A (red transient) depicts the results for HMM, confirming a small amplitude (9% of the total) decrease at 47 s Ϫ1 , consistent with the rate of phosphate release at this actin concentration (Fig. 7B), followed by the major phase characterized by a rate constant of 8.8 s Ϫ1 . For S1 (green transient), a similar biphasic transient was observed with rate constants of 54 s Ϫ1 (12% of total signal amplitude) and 12.2 s Ϫ1 . As with HMM, the rate constant for the faster phase for S1 was consistent with that for phosphate release (Fig. 6B).
Our argument that rearward strain on the leading head controls processivity in myosin V predicts that, under steadystate conditions, an appreciable fraction of the forward heads is strongly bound, and presumably, experiencing rearward  8. Kinetics of formation of a strong binding state. HMM or S1 was mixed with a 5-fold molar excess of ATP, the mixture was allowed to age for 1 s, and it was then mixed with a 5-fold molar excess of pyrene-labeled actin plus 2 mM ADP. The resulting decrease in fluorescence fit a single exponential decay for both HMM and S1 (data not shown). The rate constant for this process varied hyperbolically with actin concentration for both HMM (solid blue boxes) and S1. Inset: the S1⅐HMM amplitude ratio for the pyrene actin signal averaged 1.13 Ϯ 0.40 over a range of actin concentrations. strain. We examined this by mixing in the stopped flow myosin V HMM with a 5-fold molar excess of pyrene-labeled actin in the presence of 2 mM ATP (final concentration) and measuring the final level of fluorescence after 2 s (prior to any appreciable cross-linking). Results were compared with a similar experiment in the presence of 2 mM ADP, and the ratio of the signal amplitudes under the two conditions is plotted versus actin concentration in Fig. 9B. This demonstrates a mean amplitude ratio of 0.81 Ϯ 0.04. Given the amplitude data in Fig. 8, this implies that all of the trailing heads and ϳ50% of the leading heads are strongly bound to actin during a processive run. This result effectively eliminates models of myosin V processivity that do not include an intermediate in which both heads are strongly attached (12). DISCUSSION The purpose of these studies was to determine how mechanical strain influences the enzymology of myosin V and how strain-mediated effects lead to processivity. Our approach was to compare the kinetics of the weak-to-strong transition, phosphate release, and ADP release for an S1 construct, which cannot generate internal strain, to those for an HMM construct, which can.
Actin Binding in the Presence of ADP-Although our HMM preparations were able to cross-link actin filaments in the presence of ADP, our results with light scattering and pyrene actin fluorescence quenching clearly show that this cross-linking reaction is slow, becoming apparent only after ϳ5 s after mixing, and it is well resolved kinetically from the initial strong binding of the heads to actin. Furthermore, our results with S1 and HMM (Fig. 2B) are consistent with a model in which both heads of HMM initially bind to the same actin filament to generate an internally strained system. In this model (see below) ADP release from the lead head would be markedly slowed by rearward strain. We do find that the initial rapid strong binding of HMM and S1 to actin in the presence of ADP is biphasic, with apparent second order rate constants similar to those published previously for myosin V S1 and myosin V S1⅐ADP (9). We believe that this biphasic behavior is a result of the lower temperature used in our current studies (20°C), which enhances formation of a rigor conformation even in the presence of ADP. 2 Nevertheless, our results do clearly indicate that, for kinetic processes that are completed in Ͻ2-3 s, cross-linking of actin by HMM should not produce confounding effects.
The Strain-sensitive Step-If intramolecular strain mediates the inter-head communication needed to prevent premature dissociation, it must work by altering the kinetics of one or more steps in the mechanochemical cycle. One of these steps must be rate-limiting, which for myosin V is ADP dissociation (9). Our results support this conclusion, because they show that ADP release is strain-dependent under conditions where both heads initially bind to actin. Under these conditions, we found that, although forward strain accelerates ADP release by a factor of ϳ2.0, rearward strain slows ADP release at least 50-fold (Figs. 3 and 4). Thus, the major effect of strain appears to be on the leading head. This conclusion raises a question about the physiologic relevance of strain-accelerated ADP release from the trailing head. We examined this issue by measuring the release of 2ЈdmD under steady-state conditions (Fig.  9A) and found that, during the course of a processive run, strain only affects ADP release from the leading head. These results imply that gating of two-headed myosin V during steady-state processive movement is achieved by preventing the ADP-releasing isomerization of the lead head, rather than by accelerating the ADP-releasing isomerization of the rear head. This difference in the ADP release rates from the rear head in the steady state versus the initial encounter implies that the geometry of the initial encounter is different from that of subsequent encounters. This is reasonable, because under the conditions of most of the experiments in this study , both heads are in the same state (e.g. ADP-P i or ADP) prior to the initial encounter with actin. By contrast, during processive movement, the two heads would generally be in different enzymatic states to ensure that at least one head is strongly bound to actin at all times.
A somewhat different conclusion was reached in previous The mixture was incubated for 2 s to achieve a steady-state distribution, and it was subsequently mixed with 4 mM ATP. We would predict the resulting transient to consist of a small amplitude rapid decrease in fluorescence, representing phosphate release by a small fraction of heads, followed by a single phase of further fluorescence decrease, due to product release from the two heads. The results for HMM (red transient) demonstrate a small amplitude (9% of the total) fluorescence decrease with rate constant of 47 s Ϫ1 , consistent with the rate of phosphate release at this actin concentration (Fig. 7B), followed by the major phase characterized by a rate constant of 8.8 s Ϫ1 . For S1 (green transient), a similar biphasic transient was observed with rate constants of 54 s Ϫ1 (12% of total signal amplitude) and 12.2 s Ϫ1 . As with HMM, the rate constant for the faster phase for S1 was consistent with that for phosphate release (Fig. 6B) optical trap studies (5), which reported an ϳ1.5-fold acceleration of ADP release from the rear head by the lead head during processive stepping. However, this conclusion was based on comparisons of single encounters of two-headed myosin V molecules with encounters during processive runs. What was observed was that the lifetime of the state preceding ADP release was ϳ107 ms in a single encounter case, versus 67-75 ms during a processive run. It was concluded that ADP release from the rear head was faster during processive movement than during a single-headed encounter. However, our results suggest a different interpretation. A lifetime of 67-to 75-ms duration would correspond to an ADP dissociation rate of 13-15 s Ϫ1 , which is what we observed for an S1 construct that cannot generate internal strain. We suggest instead that the event of 107-ms duration that these authors noted was due to a two-headed single encounter, and not simply interaction by one head, as argued in that study (5). If the HMM single encounter was two-headed, as we have concluded from our data in this study, then its duration at saturating ATP concentrations would be Ϸ33 ms (30 s Ϫ1 ADP off rate from rear head) plus Ϸ77 ms (13 s Ϫ1 ADP off rate from the lead head) ϭ Ϸ110 ms, which is in very good agreement with the duration measured by Veigel et al. (5). Thus, we believe that the data of Veigel et al. is in fact consistent with our conclusion, that a modest acceleration of ADP release from the rearward head only occurs during an initial two-headed encounter and is not present during a processive run.
Clearly the geometry of this initial encounter must be different from that of subsequent encounters, because both heads begin in pre-power stroke states. The data of Veigel et al. (5) suggest that the heads are binding to actin monomers that are ϳ25 nm apart and that this geometry allows the lead head to strain the rear head in a manner that accelerates ADP release. When the processive behavior of a myosin V with a short (4IQ) lever arm was characterized, the short lever arms constrained the lead head to take 24-nm steps during steady-state movement (7). Intriguingly, the steady-state ADP release rate from the rear head was accelerated about 2-fold compared with wild-type myosin V. One way to explain these findings is to argue that ADP release is accelerated from the rearward head by forward strain, but only when this strain has a torsional component, e.g. a component orthogonal to the long actin filament axis. Because myosin V traffics through a densely branching and intersecting actin meshwork within the cell, it may be advantageous to have a mechanism that accelerates ADP release from a rear head if the lead head side-steps onto a different actin filament. Under these conditions, the lead head might not experience any appreciable rearward strain, which would allow a simultaneous release of ADP from both heads, thus terminating a processive run. Acceleration of ADP release from the rear head under these conditions might therefore help prevent this premature run termination.
Phosphate Release and Movement of Switch I-Phosphate cannot be released from myosin in the pre-power stroke state that initially binds weakly to actin, because it is surrounded by the elements of the nucleotide binding pocket, which include the P loop, switch I, and switch II (15)(16)(17). Thus, the structural changes accompanying binding to actin must open an escape route, referred to as a "back door," to enable the release of phosphate (18). Although the mechanism for this process has not been defined, our results with the fluorescent nucleotide 2Ј-deoxy-mant-ATP (Figs. 6 and 7) provide insight into what these structural changes might be. Mixing a complex of S1⅐2ЈdmD⅐P i or HMM⅐2ЈdmD⅐P i with actin produced an initial rapid drop in mant fluorescence, which we have shown is due to a change in the environment of mant nucleotide while it is still bound to the active site. This fluorescence transition provides the first experimental evidence that a conformational change in the nucleotide-binding pocket accompanies phosphate release. This conformational change follows the initial weak binding to actin, hence, the free energy that drives this process must be derived from actin binding, and this in turn argues that phosphate release is accompanied by an increase in actin affinity. It should be noted that this increase in affinity would not constitute "strong" binding, because it precedes the step in the cycle that quenches the pyrene fluorophor on actin (Fig. 8). Insights into the structural basis for this change come from crystallographic studies of Dictyostelium myosin II complexed with 2ЈdmD and of nucleotide-free myosin V (17,19). These studies have shown that the mant fluorophor in complexes of Dictyostelium myosin II:2ЈdmD is within 2-3 Å of asparagine 214 and aspartate 215, two polar residues located in switch I. If opening of the phosphate back door and movement of the upper 50 kDa subdomain were coupled to movement of switch I, and if this movement of switch I brought these two polar residues in closer proximity to the mant fluorophor, then phosphate release would be accompanied by a quenching of the mant emission, a prediction supported by the data in Figs. 6 and 7. The fact that phosphate release from both heads is rapid implies that intramolecular strain does not affect this step. One possibility is that the conformational changes that lead to phosphate release do not cause the lever arm to swing. Although the mant signal discussed above could indicate an involvement of switch I, the structural changes responsible for phosphate release remain unclear and will require further study.
The Weak-to-Strong Transition-We have shown that the quenching of the pyrene fluorophor on actin (Fig. 8) occurs after phosphate release for both monomeric and dimeric myosin V constructs. Furthermore, we argue, based on the data in Figs. 6 and 7, that phosphate release produces an increase in actin affinity that precedes the pyrene-quenching step. Combining this information allows us to propose a pathway for the myosin V mechanochemical cycle as in Reaction 1, REACTION 1 where the asterisks refer to states of enhanced mant fluorescence emission, the actin binding affinity is indicated by subscripts, and where A is actin, M is myosin V, D is ADP, and P i is inorganic phosphate. Conformational changes that occur in the catalytic site and open the phosphate back door quench the mant fluorescence and allow phosphate to be released. We propose that formation of the initially weak actin bond releases sufficient free energy to drive a change in the conformation of the catalytic site. This would be associated with an increase in actin affinity to an "intermediate" level, one that does not quench the pyrene fluorophor. This is indicated in the reaction pathway by the intermediate subscript. This step would then be followed by formation of a strong binding conformation, with its associated quenching of the pyrene fluorophor, followed in turn by release of 2ЈdmD. As in the case of phosphate release, the S1⅐HMM amplitude ratio for the pyrene signal change (Fig. 8, inset) was somewhat larger than 1.0 over a range of actin concentrations. This suggests that, although the majority of HMM molecules can bind both heads strongly to actin following phosphate release, a small subpopulation can only bind strongly via one head. This in turn implies that there is a branch in the myosin V mechanochemical pathway, and this issue will be discussed in the following section.
A Model of Myosin V Processivity-Our results allow us to propose a new model of myosin V processivity, which is summarized in Fig. 10. We enter the cycle with the species indicated by the red arrow, with the ADP-containing head (red) strongly bound to actin and the ADP-P i -containing head (green) unbound or weakly bound. At this point, one of two events can occur, indicated by the branching pathway. ADP could be released from the rear head at the unstrained rate constant of 12-16 s Ϫ1 , and this is indicated by the lightly shaded arrows in the reaction pathway marked by the green number 1. Given millimolar intracellular ATP concentrations (20 -23), this would rapidly lead to dissociation. Alternatively, the second (green) head could release its phosphate at 228 s Ϫ1 (Fig. 7B), which would be followed by formation of a species in which both heads are strongly bound (at 47 s Ϫ1 , Fig. 8). Release of ADP from the rear head followed by ATP binding and forward stepping would complete the cycle, indicated by the pathway marked by the green number 2.
Given the rate constants we have measured in this study, we can make testable predictions about myosin V processivity. If phosphate and ADP concentrations are submicromolar, their dissociation from myosin V becomes essentially irreversible. Under these conditions, the probability that a motor will dissociate from its actin track will be directly related to the fraction of molecules that proceed along the upper pathway, and this would predict a run length of 1/0.05 ϭ 20 steps at 50 mM KCl and 20°C. This value is approximately half the run length of previous reports (35,36). However, these studies were performed at higher temperatures (23-30°C). We note that, although the rate constant for actin-activated phosphate release from S1⅐ADP⅐P i at 20°C reaches a maximum (Fig. 6B), previous experiments at 25°C showed no such evidence of saturation, and this argues that the kinetics of phosphate release have a strong temperature dependence (9). Therefore, we argue that the longer run lengths reported previously can be entirely consistent with our model when temperature effects are taken into consideration. The two heads of myosin V are depicted as ellipses shaded red and green to distinguish them, the lever arms are the correspondingly shaded linear structures, and the heptad repeats are shaded black. The cycle begins with the species indicated by the red arrow, with the rear, ADP-containing head (red) strongly bound to actin, and with the forward, ADP-P i -containing head (green) weakly bound or unbound. Three potential reaction schemes are possible, indicated by the green numbers in the right margin. ADP could be released from the rear head before the forward head could release its phosphate, leading to ATP induced dissociation of the myosin V dimer (scheme 1). However, scheme 2 is kinetically favored. In this reaction, phosphate is released from the leading head, producing an internally strained complex with ADP in both heads (indicated by the forward and rearward pointing arrows). Strain-accelerated release of ADP from the rear head is followed by ATP binding and dissociation, which relieves the strain (symbolized by the serpentine lever arms). Forward stepping toward the next actin docking site to complete the cycle. Our data also indicate that rearward strain on the forward head blocks ADP release. This feature would be necessary to prevent the doubly-attached, internally strained myosin V intermediate from proceeding down reaction pathway 3 and dissociating prematurely.
Our calculation presumes that weak attachment of the leading head, occurring with rate constant k p , provides sufficient stability to the doubly attached myosin V to effectively prevent motor dissociation. This assumption is supported by the fact that myosin V binds to actin in the weak binding state with an affinity 10-to 20-fold higher than that for nonprocessive myosins (30). Our model also predicts that, although essentially all of the S1⅐ADP⅐P i motors should release their phosphate during the first enzymatic turnover, a smaller percentage of HMM motors would do so. This is confirmed by the ratio of amplitudes illustrated in the inset in Fig. 5.
If the only effect of strain was the acceleration of ADP release from the rear head, myosin V would terminate its processive run after only one or two turnovers. This is illustrated in Fig.  10 by the reaction pathway marked with the green numbers 2 and 3. In this reaction mechanism, an intermediate is generated in which the rear head is in rigor and the forward head contains ADP in its active site. If ADP could dissociate from this forward head, ATP would rapidly bind to both heads of this doubly attached species; the motor would follow the reaction pathway indicated by the green number 3, and it would dissociate from actin. The only way to prevent this from happening (indicated by the red X in the figure) would be to block ADP release from the forward head while the rear head is strongly bound, and presumably, while the system is experiencing internal strain. Our results from this study confirm this prediction (Figs. 2 and 3) and imply that, by dissociating only the trailing head, ATP binding converts the potential energy of mechanical strain to forward motion.
While this manuscript was under review, a single molecule processivity study of myosin V by Baker et al. (31) was published. That study put forward a model of processivity that was very different from the one proposed above. The main difference was that the data of Baker et al. was consistent with lead head attachment being quite slow (ϳ5/s), thus limiting the rate and degree of processive movement. In contrast, our phosphate release rate suggests that lead head attachment is extremely rapid (Ͼ200/s). The possible explanation for this difference can be found in earlier published work, which demonstrates that the equilibrium constant for ATP hydrolysis is increased by Ͼ15-fold at 25°C when an essential light chain occupies the first IQ motif, compared with when CaM occupies this site (32).
Although it was pointed out that this would not be significant at physiologic temperature, because the equilibrium constant for hydrolysis greatly increases with temperature, it poses a problem for room temperature assays. A 40-fold decrease in the equilibrium constant for ATP hydrolysis would lower the rate constant for lead head attachment from ϳ200/s to ϳ5/s. We suggest that this is the source of discrepancy between our work and that of Baker et al. (31).
Another surprising finding of Baker et al. was that increasing ADP concentration decreased the degree of processivity. However, this finding is consistent with our results (Fig. 2B), which argue that myosin V⅐ADP is in a dynamic equilibrium between two states: one that binds actin strongly and ADP weakly (A⅐(M⅐D)* strong ) and that quenches the fluorescence of pyrene-labeled actin, and one that binds actin with intermediate affinity and ADP strongly (A⅐(M⅐D)* intermediate ) and that does not quench pyrene fluorescence. We propose that this equilibrium is strain-dependent; e.g. rearward strain on the forward head favors formation of the A⅐(M⅐D)* intermediate state, while forward strain on the rearward head favors the A⅐(M⅐D)* strong state. Furthermore, our finding that phosphate release is much faster than the rate of pyrene actin quenching implies that the A⅐(M⅐D)* intermediate state can be populated under steady-state conditions. Increasing ADP concentrations would then stabilize the rearward head, enhancing the probability that the forward head could dissociate from actin. If ATP then dissociated the rear head, a processive run would terminate.
Comparison to Kinesin-Although the myosin V and kinesin motor domains share some basic structural elements, such as the P loop, switch 1, and switch 2, they share little sequence homology and are generally thought to have come from different motor superfamilies (33). It is thus not surprising; for example, although pre-and post-hydrolytic states are weak and strong binding, respectively, for myosin V, the opposite is true for kinesin (34). Despite these and other differences, however, these two motors share a striking number of similarities in the mechanisms by which they achieve processivity. In both motors, forward strain on the trailing head can accelerate its release for its track by ϳ2-fold, yet in both motors, this strain-mediated acceleration of nucleotide release is not necessary for the motor to be processive (Ref. 13 and this study). In both motors, rearward strain in the leading head inhibits motor dissociation. For both motors, strain appears to produce these effects by altering the kinetics of nucleotide binding and/or release from the active site. Furthermore, the dominant effect of strain for both is on the leading head, and this effect is the major determinant of how the motor behaves in the steady state. The striking similarities in mechanism between these two unrelated motors suggests that the physiologic demand for processivity shapes a motor's enzymology in a stereotypical way, regardless of its family of origin, and they also support the argument that understanding a motor's enzymology in vitro provides valuable insights into its functional role in vivo.