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Myosin learns to walk

Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, NY 10021-6399, USA

(e-mail: mehtaa{at}rockvax.rockefeller.edu)

	SUMMARY

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
Recent experiments, drawing upon single-molecule, solution kinetic and structural techniques, have clarified our mechanistic understanding of class V myosins. The findings of the past two years can be summarized as follows: (1) Myosin V is a highly efficient processive motor, surpassing even conventional kinesin in the distance that individual molecules can traverse. (2) The kinetic scheme underlying ATP turnover resembles those of myosins I and II but with rate constants tuned to favor strong binding to actin. ADP release precedes dissociation from actin and is rate-limiting in the cycle. (3) Myosin V walks in strides averaging 36 nm, the long pitch pseudo-repeat of the actin helix, each step coupled to a single ATP hydrolysis. Such a unitary displacement, the largest molecular step size measured to date, is required for a processive myosin motor to follow a linear trajectory along a helical actin track.

Key words: Myosin V, Single-molecule mechanics, Solution kinetics, Load-dependent kinetics, Structure, Molecular models

	Introduction

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
Managing DNA processing and subcellular transport over micrometers requires motor enzymes that will not leave their tracks before completing tasks. To this end, processive enzymes, such as DNA polymerases and helicases undergo many productive catalytic cycles per diffusional encounter with their binding partners (Lohman et al., 1998). Microtubule motors behave likewise (Howard et al., 1989; Block et al., 1990; Vale et al., 1996): a single conventional kinesin molecule can move along isolated microtubules for hundreds of 8-nm steps (Svoboda et al., 1993), each coupled tightly to an ATP hydrolysis (Schnitzer and Block, 1997; Hua et al., 1997; Kojima et al., 1997; Coy et al., 1999a; Iwatani et al., 1999), before dissociating.

Perhaps as a result of history and circumstance, processivity was long assumed to exclude the myosin superfamily of actin-based motors. A few clues, however, had long fueled speculation regarding class V myosins (Titus, 1997; Howard, 1997). Myosin V purified from chick brain consists of two heavy chains, each with an N-terminal motor domain, a neck region, a tail containing a proximal coiled coil, and a C-terminal globular domain (Cheney et al., 1993) presumed to bind cargo and/or specify subcellular localization (Wu et al., 1998; Reck-Peterson et al., 1999). Each 23-nm neck region consists of six IQ repeats, each bound to calmodulin (CaM) or a related light chain (Espindola et al., 2000). The motor domain of myosin V shares 41% sequence identity with that of the non-processive muscle myosin II (Espreafico et al., 1992). Moreover, myosin V is especially abundant in neurons and constitutes 0.2% of total protein in brain, which makes it as prevalent as conventional kinesin (Cheney et al., 1993).

In contrast to muscle myosin II, myosin V does not self-assemble into oligomers and is believed to operate in small numbers (Titus, 1997; Mermall et al, 1998; Provance and Mercer, 1999; Reck Peterson et al., 2000a; Miller and Sheetz, 2000), behavior for which a processive motor is well suited. However, investigators remained skeptical for two reasons. First, how could the kinetic scheme deciphered for closely related myosins be adapted to sustain the prolonged and perhaps coordinated actin binding that processive movement would demand? Second, since myosin moves along a helical actin track, wouldn’t a hypothetical processive myosin with vesicle cargo spiral about this track and become entangled in a dense cytoskeletal mesh?

	Demonstration of processive movement

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
The gliding filament assay (Kron and Spudich, 1986) allows observation of fluorescent polymer tracks moving upon a field of surface-fixed motors. Low densities of muscle myosin II sustained sporadic and slow actin movements (Uyeda et al., 1990; Uyeda et al., 1991), and significantly lower densities of baculovirus-expressed mouse myosin V fragments also supported motility (Wang et al., 2000), but both only in the presence of methylcellulose to restrict actin filament diffusion.

Tissue-purified chick brain myosin V, however, supported actin motility in the absence of methylcellulose (Mehta et al., 1999a) and at motor densities as low as 0.05 molecules/µm² (A. M., unpublished). At saturating ATP concentrations, the actin filament velocity was 300 nm/s at motor densities from 1000 molecules/µm² to 2.7 molecules/µm² (Mehta et al., 1999a) or even 0.05 molecules/µm² (A. M., unpublished). This is consistent with a very high duty ratio (Uyeda et al., 1990; De La Cruz et al., 1999; Moore et al., 2000), the fraction of cycle time spent strongly bound to the track. Under limiting ATP conditions, actin filaments moved faster over motor densities of 2.7 myosin molecules/µm² than they did over 54 molecules/µm². Exogenous ADP inhibited this gliding speed (below), but several millimolar P_i did not.

At low densities, actin filaments threaded through and swiveled about isolated surface contact points (Fig. 1A; Mehta et al., 1999a; Wang et al., 2000), which is reminiscent of microtubules gliding over single kinesin molecules (Howard et al., 1989; Hunt and Howard, 1993). These nodal points may have contained single molecules, several molecules clustered by chance, or aggregates/oligomers that form in solution or on the surface. Gel filtration (Cheney, 1998), equilibrium sedimentation measurements (O. C. Rodriguez and R. E. Cheney, personal communication), images of surface-bound proteins via electron, fluorescence and atomic force microscopy (Cheney et al., 1993; Mehta et al., 1999a; Sakamoto et al., 2000), observations of motility produced by samples depleted of protein by ultracentrifugation (Rock et al., 2000), and kinetic arguments (Howard et al., 1989) excluded both solution oligomerization and surface-induced aggregation.

View larger version (62K): [in this window] [in a new window]   Fig. 1. (A) An actin filament moves over a surface coated with 3.6 myosin V molecules/µm2 in 2 mM ATP. The pointed (green dots) and barbed (yellow dots) ends of the filament are marked when the ends are in the image plane. Panels 1-10 (left to right) show the time course of a filament before (panel 1) and after (panels 2-9) it has bound the surface. The apparent point of surface contact (crosshair) appears pronounced in the average fluorescent intensity throughout the time course of movement (panel 10). Panels 11-20 show the time course of a shorter filament moving over 5.4 molecules/µm2. This filament encounters a second contact point before releasing its first. Nodal swiveling behavior reminiscent of seminal observations with kinesin (Howard et al., 1989; Hunt and Howard, 1993) provided the first hint of myosin V processivity (Wang et al., 2000; Mehta et al., 1999a). Bar, 5 µm. (B) The rate at which actin filaments land and move, as a function of myosin V surface density. A filament was considered ‘landed’ if it moved >0.5 µm and for >2 seconds. (C) The fraction of filaments that moved more than their length (as in panels a11-a20) before dissociating, as a function of surface density. The fit reflects the single molecule model prediction of P(n>1|n>0), where P(N) represents the density-dependent probability that N molecules populate an arbitrary area. Figure reproduced, with permission, from Mehta et al., 1999a (http.//www.nature.com).

To extend these observations, we used optical trapping to observe single molecule interactions at high spatial resolution, employing a dual-bead geometry, in which laser traps capture two beads attached at either end of a single actin filament (Finer et al., 1994; Mehta et al., 1998). The filament is then stretched to tension and moved near surface-bound platforms decorated sparsely with myosin molecules. Under conditions (0.9 molecules/µm²) where >90% of attempts to solicit molecular binding events failed, most successful attempts resulted in staircase-like displacement records. Isolated binding agents pulled the filament through 3-5-step increments before stalling against 3.0 ± 0.3 pN and dissociating (Mehta et al., 1999a). Might these agents have been multiple molecules? Statistical arguments demonstrate otherwise: on the basis of the low-surface-protein densities (estimated at 0.08 molecules accessible per average attempt) and assuming Poisson statistics govern the distribution of surface motor attachments, the ratio of single to multiple molecule encounters should have exceeded 25. On the basis of the low fraction of observed binding events per solicitation (5-10%), this ratio should have exceeded 20. Whereas the first of these two ratios requires an estimate for the surface contact area sampled in a given attempt, the second relies on no such estimates. Similar observations have been reported for tissue-purified murine myosin V (Veigel et al., 2001).

Later studies used a different experimental geometry (Rief et al., 2000): the motor was attached to polystyrene beads, which were then trapped and moved near surface-mounted tracks (Block et al., 1990; Kuo and Sheetz, 1993; Svoboda et al., 1993). These experiments used a force clamp technique (Visscher and Block, 1998; Visscher et al., 1999), in which a feedback circuit positions the trap to maintain system tension at a programmed level. This scheme prevents motor stalling and dissociation due to prohibitive optical load. At very low motor:bead stoichiometries, we observed beads step throughout the clamp linearity range (Fig. 2A), the position range over which the circuit maintains a constant force, and move for >1 µm when the trap is turned off. The incidence of stepping behavior over a broad range of motor:bead stoichiometries followed single molecule Poisson statistics (Block et al., 1990) and could not accommodate models requiring more than one molecule to support motility (Fig. 2B). Such assays demonstrated that the molecule remains strongly processive even against 1 pN loads, conditions generally expected to promote more rapid dissociation (Block et al., 1990; Liebler and Huse, 1993). In this experimental geometry, the motor stalled against 2.5 pN; however, this measurement is less reliable since optical loads are applied both along the axis of movement and perpendicular to it.

View larger version (35K): [in this window] [in a new window]   Fig. 2. (A) Illustration of force-clamp records. An optically trapped bead, decorated with myosin V molecules, is moved into close proximity with a surface-mounted actin filament. The bead is subjected to a force-clamp, in which a feedback circuit maintains a constant trap-bead separation and hence constant system tension (left). In some cases, the bead proceeded to step along the actin filament in 36-nm increments (right) as the trap followed. (B) The fraction of beads observed to step as shown in A, as a function of surface density. The solid line reflects a fit of a single molecule model; the dotted line reflects a model posing two molecules as a minimal agent of such stepping behavior. Reduced 2 values for the one- (0.04) and two-molecule (0.98) models rendered relative confidence in the former 25 times that in the latter. Figure reproduced, with permission, from Rief et al., 2000.

View larger version (39K): [in this window] [in a new window]   Fig. 3. Single myosin V molecules, imaged by total internal reflection microscopy, move along isolated actin filaments. Myosin V molecules are shown in green; actin is shown in red. Fluorophores appear to accumulate at the barbed filament end. This suggests that, when a single moving myosin V encounters a problem ahead (an absent or occupied binding site), the trailing head remains anchored upon the filament while the leading head remains unbound. Leading head binding may thus induce trailing head dissociation, which is similar to proposed mechanisms for kinesin (Hancock and Howard, 1999). However, uninteresting phenomena, for instance motors moving off the actin filament end and then adhering nonspecifically to the surface substrate, could also underlie observed accumulation. Figure reproduced, with permission, from Sakamoto et al., 2000.

	Kinetic requirements for a processive myosin

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
Decades of solution kinetic experiments have established a basic scheme for ATP turnover by myosin II (Spudich, 1994); the rate-limiting transition involves isomerization from an ADP-P_i state that has a low affinity for actin (weak binding) to an ADP-P_i state that has a high affinity for actin (strong binding; Eqn 1).

(Equation 1)

After docking with actin in a strong-binding state, myosin releases P_i and performs mechanical work upon actin. Myosin-ADP remains strongly bound to actin. The transition from strong to weak binding follows the subsequent ADP release and ATP binding. In myosin II, these steps are fast compared with the overall cycle time, itself limited by the transition from weak to strong binding. Whereas the weak-to-strong transition governs the overall cycle time, the strong-to-weak transition governs the rate at which myosin can move actin (Spudich, 1994). Low-duty-ratio motors can move at higher speeds, whereas high-duty-ratio motors can operate in smaller numbers (Howard, 1997). A low-duty-ratio motor can achieve processivity by some means of tethering to or encircling its track (Sakakibara et al., 1999; Okada and Hirokawa, 1999), a tactic probably employed by some DNA enzymes. Without this, processivity demands that the two heads of an intact dimer each have a duty ratio >0.5 to ensure that the molecule remains anchored to the track.

Solution kinetic experiments have demonstrated that monomeric myosin V fragments follow the general scheme of myosin II but that there are key kinetic modifications. In particular, the weak-to-strong transition is not rate limiting and occurs more than ten times faster than the cycling rate (De La Cruz et al., 1999). Moreover, ADP release, regulating the strong-to-weak transition, is the rate-limiting step in the overall cycle (De La Cruz et al., 1999; De La Cruz et al., 2000a; De La Cruz et al., 2000b; Rief et al., 2000). Such measurements indicate that in myosin V the necessary kinetic adaptations to support a high duty ratio have evolved.

Three research groups have characterized baculovirus-expressed monomeric myosin V fragments truncated at the C-terminus after one IQ repeat (De La Cruz et al., 1999; De La Cruz et al., 2000a; De La Cruz et al., 2000b), two IQ repeats (Trybus et al., 1999), or all six IQ repeats (Wang et al., 2000) in the neck. In the remainder of this section, I use ‘myosin’ to refer to these monomeric myosin V fragments. Measured actin-activated ATP-turnover rates, estimated from time courses of inorganic P_i production, ranged from 3.3 s^-1 (Trybus et al., 1999; Wang et al., 2000) to 12-15 s^-1 (De La Cruz et al., 1999) under similar solution conditions. These discrepant numbers subsequently spawned widely disparate conclusions regarding the potential for processive movement, a point to which I will return.

To observe myosin binding to actin, investigators used pyrene-labelled actin, whose fluorescence weakens when myosin binds tightly. In the absence of nucleotide, myosin fragments bound to actin with nanomolar to picomolar affinity (Trybus et al., 1999; De La Cruz et al., 1999) and rates approaching the diffusion limit (De La Cruz et al., 1999). ATP bound actomyosin at 2-9x10⁵ M^-1 s^-1 (Trybus et al., 1999; De La Cruz et al., 1999; De La Cruz et al., 2000a; Wang et al., 2000) and dissociated the actomyosin complex at 850-870 s^-1 (Trybus et al., 1999; De La Cruz et al., 1999; De La Cruz et al., 2000a). Hence, in the presence of physiological ATP (mM) concentrations, actomyosin dissociates rapidly compared with steady-state cycling.

To measure the rate of ATP hydrolysis, De La Cruz et al. tracked ADP-P_i formation on fast time scales using quench flow (De La Cruz et al., 1999; De La Cruz et al., 2000a). They observed a 120 s^-1 burst rate that was limited by ATP binding, followed by a slow rise whose rate depended on the actin concentration. The 120 s^-1 burst reflects events preceding the initial hydrolysis event and thus provides an underestimate of the hydrolysis rate. Indirect hydrolysis rate estimates exploited a property shared by many myosins: ATP hydrolysis enhances the intrinsic fluorescence of tryptophan residues in the motor domain. The maximum rate provides an estimate of the ATP hydrolysis rate (Johnson and Taylor, 1978): the sum of the forward and reverse hydrolysis rate constants for myosin V was so measured at 200-800 s^-1 (Trybus et al., 1999; De La Cruz et al., 1999; De La Cruz et al., 2000b). In the absence of actin, P_i release from the myosin-ADP-P_i state is very slow and rate limiting.

In the presence of actin, the transition from a weak- to a strong-binding myosin-ADP-P_i state limits the rate of cycling by myosins I and II. Myosins limited by this transition will have a low duty ratio, and it is difficult to reconcile such a property with dimer processivity. To observe this transition, De La Cruz et al. mixed myosin with ATP, aged the mixture for 14 ms to allow for ATP binding and hydrolysis, and then added actin and a ‘P_i detector’ (De La Cruz et al., 1999). They observed a fast phosphate burst that depended linearly on actin concentration; the highest measurement, not yet actin-saturated, was >200 s^-1. Because this reflects the transition from weak to strong binding, followed by strong binding to actin and P_i release, it provides an underestimate of the transition rate of weak to strong binding. Since this estimate exceeded all measured steady-state turnover rates by more than an order of magnitude, it excluded the possibility that the weak-to-strong transition or Pi release is rate limiting for actomyosin V cycling.

Myosin-ADP was estimated by pyrene fluorescence observations to bind actin with 6-8 nM affinity (Trybus et al., 1999; De La Cruz et al., 1999). Investigators measured ADP release from actomyosin in three ways. First, a fluorescently modified nucleotide mant-ADP, whose fluorescence increases with myosin binding, allows direct tracking of ADP binding and release. After allowing equilibrium binding of mant-ADP to actomyosin and then flushing with unlabelled ATP, investigators observed a fluorescence increase with rates of 12-16 s^-1 (De La Cruz et al., 1999; De La Cruz et al., 2000b) and 17-19 s^-1 (Trybus et al., 1999). Second, pyrene actin can be pre-incubated with myosin-ADP and then flushed with excess ATP. Under these conditions, myosin must release ADP before binding ATP and releasing actin. An observed rate of fluorescence increase slower than the 2-9x10⁵ M^-1 s^-1 for ATP binding would thus reflect the preceding event, ADP release. A second slow rate was indeed observed and had rates of 13.5-14.5 s^-1 (Trybus et al., 1999), and 11.5 s^-1 (Wang et al., 2000). Since this experiment involves a series of three transitions, De La Cruz et al. (De La Cruz et al., 1999) modeled like data using independently measured rates of ADP release and ATP binding, yielding fits consistent with rates of mant-ADP dissociation (above). Third, Trybus et al. pre-incubated actomyosin with ADP, flushed it with excess ATP and monitored subsequent actomyosin dissociation by light scattering (Trybus et al., 1999). This yielded a slow phase of 17-22 s^-1, which presumably reflects ADP release.

The above rate estimates broadly agree: ADP release at 10-20 s^-1, rapid dissociation from actin in the presence of ATP, and rapid hydrolysis of ATP. However, the discrepant steady-state cycling rate estimates lead to entirely different conclusions: Trybus et al. and Wang et al. compared their 3.3 s^-1 cycling rate measurement with a 10-20 s^-1 ADP-release measurement and concluded that ADP release does not limit the cycle time; rather, they concluded that their myosin V fragments fall short of the 0.5 duty ratio (Trybus et al., 1999; Wang et al., 2000). By contrast, De La Cruz et al. estimated both the cycling rate and ADP release at 12-17 s^-1 and concluded that ADP release limits the cycling rate (De La Cruz et al., 1999). They argued that such a high monomer duty ratio could enable the intact dimer to move processively.

The key to this discrepancy may lie in a phenomenon all three labs noted and a theme of growing relevance to myosin enzymologists: high affinity for ADP (De La Cruz et al., 2000b). ADP bound to actoymyosin at 9-15x10⁶ M^-1 s^-1 (De La Cruz et al., 1999; Wang et al., 2000; De La Cruz et al., 2000a; De La Cruz et al., 2000b), 5-20 times the 0.7-1.6x10⁶ M^-1 s^-1 ATP-binding rate, and with ten times the affinity of ATP (De La Cruz et al., 1999; Wang et al., 2000). Hence, if ADP accumulates over the several minutes routinely taken in steady-state cycling measurements, it will compete with ATP for binding to actomyosin and thus slow the observed production of P_i. In fact, significant non-linearities appear in the measured P_i production rates (De La Cruz et al., 1999), and attempted fits to linear rates can yield artifactually low turnover-rate estimates from extended time courses. De La Cruz et al. used two methods to circumvent this problem. First, they measured a 12-15 s^-1 ATP-turnover rate from heavy data sampling in the brief initial period of turnover, before ADP could accumulate, using steady-state Pi generation and quench flow under saturating actin conditions (De La Cruz et al., 1999). Second, they used an ATP-regeneration system to prevent ADP accumulation (De La Cruz et al., 2000a; De La Cruz et al., 2000b). This provided an independent 12-17 s^-1 measurement. De La Cruz et al. further demonstrated, using rate constants measured by the three labs, that an attempted cycling rate measurement performed over 20-300 s would yield an observed 2-4 s^-1 rate (De La Cruz et al., 2000b). Hence, several lines of evidence support the notion that 3.3 s^-1 measurements had underestimated a 12-14 s^-1 rate. Moreover, an entirely different experiment, independent of any cycling rate estimate, demonstrated that ADP release limits the rate of chemomechanical cycling by an intact dimer moving on actin.

	Single-molecule stepping kinetics and their mechanistic implications

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
Repeatable solution kinetic measurements of rate constants reflect statistics describing stochastic processes, such as the release of one molecule from a binding partner. A rate constant reflects the probability of an event occurring per unit time. When individual molecules are observed directly, a stochastic process will yield variable measurements. However, large numbers of such measurements give rise to robust distributions, from which one can infer the number and rates of biochemical transitions that limit the rate of the observed event (Schnitzer and Block, 1995). In the case of an individual stepping molecule, the distribution of dwell times () separating discrete steps contains information about the biochemical transitions limiting the rate of mechanical advances (Svoboda et al., 1994; Schnitzer and Block, 1995; Schnitzer and Block, 1997; Hua et al., 1997; Kojima et al., 1997; Visscher et al., 1999).

Such transitions can depend on load in interesting ways (see below), but, for now, note that a molecule moving against elastic load, such as a stationary optical trap or glass fiber, will experience steadily increasing resistance as it further strains the probe. Since each step occurs against a different load, one cannot combine all observed dwell times to generate a meaningful distribution. To circumvent this problem, Rief et al. used a feedback circuit that moved the optical trap so as to clamp the load at a programmed level (Visscher and Block, 1998; Visscher et al., 1999; Rief et al., 2000). Observations in the presence (Rief et al., 2000) or absence (Mehta et al., 1999a) of such feedback indicate that the mean stepping rate (^-1) under all ATP conditions remains independent of load below 1 pN. Rief et al. thus observed dwell periods under a clamped 1 pN load and under various solution conditions (Rief et al., 2000). We reached three conclusions. (1) The stepping process at 2 mM ATP and negligible ADP concentration can be described by a single, rate-limiting 12.5 s^-1 transition. (2) The stepping process at 2 mM ATP and 200 µM ADP, where the speed of movement is slowed by 50%, can be described by a single apparent rate-limiting 6.4 s^-1 transition, which means that ADP release limits the stepping rate. If ADP release were not responsible for the apparent 12.5 s^-1 transition measured in the absence of exogenous ADP, then one would have instead observed two apparent transitions in series, each of rate 12.5 s^-1, when sufficient ADP was added to slow the speed by 50%. Moreover, the data show that when ADP rebinding slows the cycling rate, the release of post-hydrolysis ADP and the release of rebound ADP must occur at the same rate. (3) The stepping process under varied ATP concentrations gives rise to a single apparent ATP-dependent transition per mechanical step, which has a rate constant of 0.9x10⁶ M^-1 s^-1, which compares favorably with the above described 0.7-1.6x10⁶ M^-1 s^-1 ATP-binding rate measured in solution. These measurements show that mechanical steps against 1 pN of resistance remain tightly coupled to ATP hydrolysis events, regardless of ATP concentration. The data exclude scenarios in which one ATP binding event precedes more than one mechanical step or two or more ATP binding events precede each mechanical step. All of the aforementioned observations, of course, pertain to 1 pN loads, which do not affect the stepping rate. Distinct behavior occurs when the molecule steps against higher loads, a point to which I now turn.

Linear molecular motors often exhibit strain-sensitive biochemistry. Perhaps the best-known example is the Fenn effect in muscle (Fenn, 1924), the slowing of both heat and work output when a contracting muscle faces successively greater resistance beyond a certain point. This reflects a decrease in the rate of ATP turnover, which is effected by a load-dependent decrease in the rate of crossbridge detachment, when cyclical crossbridge attachments serve mainly to bear tension (see Hibberd and Trentham, 1986). Single-molecule experiments have unearthed several other examples of load-dependent chemistry (Mehta et al., 1999b, Ishii and Yanagida, 2000). (1) Early observations of non-processive binding events by muscle myosin II demonstrated that 4-7 pN loads accelerate actomyosin dissociation at limiting ATP concentrations but decelerate it at saturating ATP concentrations (Finer et al., 1994). While the latter observation is consistent with the Fenn effect in muscle, the former indicates that ATP binding or myosin-ATP dissociation from actin is accelerated by strain. (2) Early observations of kinesin revealed a linear force-velocity curve under all ATP conditions (Svoboda and Block, 1994; Meyhofer and Howard, 1995; Kojima et al., 1997; Coppin et al., 1997; see also Hunt et al., 1994). This implied that K_M^T, the ATP concentration required for turnover at half the maximal rate, does not vary with load (Svoboda and Block, 1994; Meyhofer and Howard, 1995). Controversial interpretations of these data (Howard, 1995) were clarified only after more sophisticated and precise measurements showed the K_M^T indeed increases with load (Visscher et al., 1999), through at least one load-dependent transition rate related to binding ATP or committing it to hydrolysis (Visscher et al., 1999; Schnitzer et al., 2000). (3) Observations of RNA polymerase demonstrated that the transcription rate remains independent of load below 20 pN (Wang et al., 1998; Davenport et al., 2000) and drops sharply as the load rises above this (Wang et al., 1998). From these data, Wang et al. concluded that load-dependent transitions in the absence of load occur 5x10⁴ times faster than load-independent transitions (Wang et al., 1998). Moreover, load affected the cycling rate through a characteristic distance of around 5-bp repeats, which reflects either molecular strain or enzyme slippage along the DNA template in the transcriptionally upstream direction. (4) Recent observations of DNA polymerases reveal quite different behavior: addition of each base in the complementary strand is rate limited by a load-dependent transition, perhaps one from weak to strong binding between the template strand and its growing partner (Wuite et al., 2000; Maier et al., 2000). The associated characteristic distance spans multiple bases on the ssDNA template, indicating that more than one base participates in this transition. Investigators are presently characterizing load-dependent statistical kinetics of the lambda exonuclease (Perkins et al., 2001) and the bacteriophage 29 DNA-packaging motor (Tans et al., 2001).

The above studies of kinesin and DNA-based motors involve motors that have small step lengths (perhaps 0.3 nm for various DNA motors) and/or fast stepping rates (100 s^-1 for kinesin) that allow thermal noise to mask the underlying molecular trajectory. Attempts to extract mechanistic information from velocity measurements give rise to difficult and often controversial interpretations (see Howard, 1995), because load can affect such measurements in different ways. For instance, load could affect the chemomechanical coupling efficiency, the incidence of backward slippage, the rate of catalysis, and/or the unitary step distance. Although investigators have advanced conclusions regarding load-dependent catalysis by all the above DNA-based motors, competing models - for instance, that an increased rate of slippage slows the enzymes against high load without affecting the catalysis rate - remain formally possible. Myosin V, in contrast to these motors, has a step size large enough and a stepping rate slow enough to allow direct observation of dwell periods between steps under all relevant load and ATP conditions. My co-workers and I observed myosin V stepping against an elastic load (Mehta et al., 1999a). We measured the load corresponding to every observed dwell period separating two successive steps and preceding a forward step in the dual-bead trapping geometry, and we made two observations. First, the stepping rate at limiting (1 µM) ATP concentrations does not vary with load (Fig. 4, open circles). Second, the stepping rate at saturating (2 mM) ATP concentrations is independent of load below 1.5 pN and drops exponentially with loads above 2 pN (Fig. 4, closed squares).

View larger version (18K): [in this window] [in a new window]   Fig. 4. Load-dependent dwell times separating adjacent step transitions and preceding forward-directed steps. Open boxes represent 1 µM ATP, and closed circles 2 mM ATP. The line traversing the closed circles reflects a fit of Eqn 3 to the data. Figure reproduced, with permission, from Nature (Mehta et al., 1999a).

(Equation 2)

where F represents the load, the coupling ratio between chemical and mechanical cycling, K_M^T the ATP concentration required for cycling at half the maximal rate, and k_cat the cycling rate under saturating ATP concentration.

, k_cat and K_M^T are posed as functions of the external load, F, k_cat and K_M^T are functions of the various cycle rate constants. might depend on the ATP concentration, since potential kinetic partitioning into an unproductive catalytic cycle can depend on the transition rates of the productive one. K_M^T under a 1 pN force clamp (Rief et al., 2000) and in an unloaded gliding filament assay (M. Rief, unpublished) have both been measured at 12 µM (Rief et al., 2000). has been measured at 1 against 1 pN under all ATP concentrations (Rief et al., 2000). Below, I assume Michaelis-Menten dependence of the stepping rate against all loads.

Tight coupling between chemical and mechanical cycling means that =1, whereas loose coupling implies higher or lower values. Note that by ‘coupling’ I mean the link between a chemical cycle and a mechanical step in either the forward or backward direction. Hence, <1 implies cycling without movement. Investigators in the kinesin field have followed a different convention, one that considers the only meaningful coupling to be with mechanical steps in the forward direction (Svoboda and Block, 1994; Meyhofer and Howard, 1995; Coppin et al., 1997; Schnitzer and Block, 1997; Hua et al., 1997; Visscher et al., 1999). Owing to the distance and timescales of molecular stepping relative to thermal noise, kinesin does not allow direct identification of step intervals under low load and saturating ATP concentration. This makes a retreat and subsequent advance to restore the initial position indistinguishable from a period of mechanical quiescence. Hence, a significant presence of backward steps linked to chemical cycles would necessarily imply ‘loose coupling’, more than one chemical cycle per forward step. Since myosin V allows direct observation of step transitions under all load and ATP conditions, it demands a more nuanced vocabulary, one that distinguishes mechanical inactivity from successive backward and forward steps. Hence, discussion of myosin V focuses on dwell times separating two mechanical steps and preceding a forward-directed step. By contrast, most discussion of kinesin focuses on the velocity at which individual motors move (Svoboda and Block, 1994; Meyhofer and Howard, 1995; Coppin et al., 1997; Visscher et al., 1999). These differences in the observed variable and in the semantic convention must be kept in mind when one compares published observations in the two fields.

Since dwell periods at 1 µM ATP ([ATP]<<K_M^T) appear to be independent of load (Mehta et al., 1999a), (F, 1 µM) k_cat(F)/K_M^T(F) is independent of the load F. Furthermore, if one neglects contrived scenarios in which load accelerates k_cat(F)/K_M^T(F) and depresses (F, 1 µM) by the same fractional amount, (F, 1 µM) remains constant (1) under all loads that the molecule can move against. Hence, the effective ATP-binding rate k_cat(F)/K_M^T(F), encompassing binding of ATP and committing it to hydrolysis, does not vary with load. Note that kinesin, in which the binding of ATP is coupled to a significant conformational change (Rice et al., 1999), exhibits a load-dependent k_cat(F)/K_M^T(F) (Visscher et al., 1999), which can be explained by a rapid and reversible load-dependent isomerization after reversible binding of ATP and necessarily before commitment to its hydrolysis (Schnitzer et al., 2000). Such models can be excluded for myosin V.

Load-dependent myosin V dwell periods at 2 mM ATP ([ATP]>>K_M^T) demonstrate that (F, 2 mM) k_cat(F) remains independent of load below 1.5 pN and falls sharply as the load rises over 2 pN. One or both of the following scenarios might therefore be the case. (1) The coupling efficiency at 2 mM ATP falls sharply at >2 pN loads, even as the efficiency at 1 µM ATP remains independent of load. This suggests that branching to an unproductive cycle occurs more frequently from the state preceding ADP release than it does from the state preceding binding of ATP or its commitment to hydrolysis. (2) k_cat(F) falls sharply at >2 pN loads. As per the above arguments, this requires K_M^T(F) also to fall sharply at loads >2 pN. In the simplest model of one strain-sensitive biochemical transition per cycle, this transition can effect identical load dependence of both k_cat(F) and K_M^T(F). Such load-dependent chemistry offers a more efficient way than loss of coupling to fulfill the suspected organelle-tethering function of myosin V (Wu et al., 1998; Rogers and Gelfand, 1998; Mermall et al., 1998), for the same reason the Fenn effect enables a more efficient muscle response to arresting load. If attachments serve merely to bear tension without working against it, then it serves the molecule well to delay its dissociation from actin and thus better conserve ATP.

Additionally, if k_cat(F) alone accounts for the observed load-dependent dwell times, one can model the dwell times =k_cat(F)^-1 using Boltzmann’s law (Eqn 3):

(3)

where ₁ represents load-independent transitions, ₂ the load-dependent transition, F the load, d the characteristic distance over which load affects the catalysis rate, and kT the thermal energy (Wang et al., 1998).

Fitting this model to the data (Mehta et al., 1999a) shows that as the load F approaches zero, the load-dependent transition occurs a hundred times faster than the load-independent transitions. The load-dependent transition becomes rate-limiting at >2 pN. Load would affect the relevant transition rate over a characteristic distance - reflecting slippage, strain or arrested movement - of 10-15 nm, on the order of but less than the measured step size.

The observation that dwell periods do not vary with loads <1.5 pN indicates (F, 2 mM) k_cat(F) remains independent of loads <1.5 pN (Mehta et al., 1999a). Also, (F, 2 mM) 1 under 1 pN of load (Rief et al., 2000). If one dismisses ad hoc notions of exactly offsetting load dependences in (F, 2 mM) and k_cat(F), the data show that k_cat(F) remains independent of load below 1.5 pN. Hence, the rate-limiting transition, presumably ADP release, cannot depend on load. Some investigators have alluded to a load-dependent ADP release (Walker et al., 2000), but the apparent discrepancy could be semantic. Although the observed 12.5 s^-1 transition rate does not vary with load, the rate of a transition from a slow-releasing ADP state to a 12.5 s^-1 ADP-release state could very well depend on load. Such a transition has been proposed on thermodynamic grounds (De La Cruz et al., 1999) and is reminiscent of suggested transitions in other myosins (Jontes et al., 1997; Cremo and Geeves, 1998; Rosenfeld et al., 2000; Geeves et al., 2000).

As observed for kinesin (Svoboda and Block, 1994; Meyhofer and Howard, 1995; Coppin et al., 1997; Kojima et al., 1997), myosin V experiences reverse-directed steps. Unlike kinesin, in which the frequency of backward steps appears to be independent of load (Coppin et al., 1997; Visscher et al., 1999), myosin V experiences more reverse-directed steps under higher loads (Mehta et al., 1999a; Rief et al., 2000). At 1 µM ATP, dwell periods preceding forward steps (mean 1.62±0.15 sec, n=125) (Mehta et al., 1999a) did not differ in mean from those preceding reverse steps (mean 1.44±0.18, n=62) (Mehta et al., 1999a), which demonstrates that transition rates involved in backward steps are slower than those involved in forward steps. Note the relevance of semantic convention here: this is described as ‘tight coupling’ between ATP binding events and mechanical steps, the direction of the steps being a separate issue. The prevailing convention in kinesin study would cast this as ‘loose coupling’ (<1) between ATP binding events and forward steps.

Unlike kinesin, myosin V occasionally steps backwards two or three times in sequence (Mehta et al., 1999a). This implies that a ‘ratcheting’ and load-dependent strong binding transition to preserve the last forward step - like that suggested for kinesin (Coppin et al., 1997) - need not be considered for myosin V; the molecule concludes a backward step in a state competent to step backwards again. Additionally, when loads are rapidly oscillated between vanishing and super-stall levels, the fraction of steps occurring in the reverse direction are 13% (n=456) and 37% (n=107) at 2 mM and 1 µM ATP respectively (computed from table 1 of Mehta et al., 1999a). This suggests that kinetic partitioning into a reverse-step process occurs from states that precede ATP binding or its commitment to hydrolysis.

	The step size

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
Because adjacent monomers in an actin filament are arranged helically and not linearly, a processive motor moving from one monomer to the next would spiral around the track and consequently make vesicle transport problematic. A myosin motor could, however, step across the long-pitch pseudo-repeat of the actin helix, reaching from one actin monomer to the next one sharing the same azimuth, and thus linearize its track. This is no small feat, since the required step distance would span 13 actin subunits and 36 nm, larger than any other molecular step distance observed to date. Some observers had long speculated that the unusually long, 23-nm neck region (Cheney et al., 1993) evolved so the two heads could bind an actin filament while separated by the 36 nm pseudo-repeat distance (Howard, 1997). Moreover, this neck region resembles a molecular lever for myosin II, amplifying a small conformational change within the motor domain (Uyeda et al., 1996; Anson et al., 1996; Suzuki et al., 1998; Dominguez et al., 1998; Corrie et al., 1999; Warshaw et al., 2000; Shih et al., 2000; Ruff et al., 2001; but also see Tanaka et al., 2000; Molloy et al., 2000). Myosin V may require its long neck to leverage motor domain shape changes into 36 nm steps.

Initial observation of chick myosin V stepping employed the dual-beam geometry of Finer et al. (Finer et al., 1994). Myosin V pulled suspended individual actin filaments in discrete steps of 15-40 nm. These distances reflect movement not of the molecule but, rather, of a bead in a stationary optical trap and attached to a single actin filament. Potentially non-linear elastic linkages separating the bead from the filament, or separating the molecule from the microscope coverslip surface, could absorb some of the molecular step distance, masking it from our view.

To circumvent the series elasticity problem, we moved one optical trap through large-amplitude triangle-wave oscillations while isolated myosin V molecules bound and moved the attached actin filament (Mehta et al., 1999a). In the absence of myosin binding, the beads followed the waveform of the optical trap. Upon myosin binding, however, one of the beads exhibited clipping of this waveform in areas of maximum tension. Such clipping indicates that, during the high-tension phase of each trap oscillation cycle, the trap continues to move but the bead no longer follows it; this effect requires - and hence demonstrates - that all connections separating the bead from the surface are rigid relative to the optical trap. Hence, stepwise advances of the clipped level accurately reflect protein movements. Multiple data sets at various ATP concentrations and trap oscillation frequencies produced data distributions centered around 34-38 nm, demonstrating that the molecule indeed has the large step size required to linearize its helical track. Both forward and backward steps were of this size. The distribution widths remained large, with standard deviations of individual data sets ranging from 5 nm to 11 nm. This suggested that the myosin V molecule does not step along the pitch pseudo-repeat precisely but does so only on average; this is probably still sufficient to avoid problematic spiraling behavior. However, these experiments left open the possibility that limited rotation of the trapped filament, over the 0.1-1 sec dwell periods separating step transitions, could generate a random shift in the next available actin monomer bearing the necessary azimuth, hence spreading the step measurement distribution. Since an optically trapped 1 µm bead exhibits a rotational persistence time of 1 second (Einstein, 1956), significant rotation of the trapped beads can occur between successive molecular steps. Veigel et al. measured similar step distributions of murine myosin V, also using the dual beam geometry (Veigel et al., 2001). Rather than oscillating one of the traps, they characterized the series elastic element and corrected the raw data for its effects.

Rief et al. observed chick myosin V stepping in a force-clamped single-bead assay, which allows observation of longer step sequences and meaningful analysis of stepping kinetics (see above; Rief et al., 2000). An additional advantage is that any elastic connections remain similarly strained throughout the range of stepping and thus cannot absorb any displacements produced by the attached motor (Visscher and Block, 1998). Furthermore, the actin filament is mounted upon a surface and cannot rotate. We observed regular steps of mean 40.2 nm, matching earlier measurements within calibration uncertainties, which were unusually high owing to the small size of the beads used. The distribution standard deviation of several data sets combined narrowed to a still uncomfortably large 6.4 nm. Moreover, the motor exhibited occasional 20-nm step advances under 2 pN load conditions. The dwell periods following 20 nm steps, which lasted seconds and always ended with an added 20 nm advance or retreat, exhibited high bead-position variance and thus a less rigid linkage with the surface. The relative rarity of such steps suggests that they involve transitions off the normal cycling pathway, and it remains difficult to interpret them. Nevertheless, the motor might have advanced part of its unitary step distance, adopted a less rigid linkage with the track involving only one bound head, and could then have retreated or advanced the remainder of the unitary step after a pause.

Step size measurements are consistent with electron microscopic observation of apparently walking myosin V molecules. Walker et al. imaged actin filaments decorated sparsely with baculovirus-expressed murine-sequence myosin V dimer fragments (Walker et al., 2000). Under some conditions, they observed a fraction of dimers with both heads bound to the same double helical actin filament separated by 9-17 actin subunits (Fig. 5). The dominant peak in the distribution reflected head separation by 13 actin subunits, one 36-nm pseudo-repeat, but subsidiary peaks appeared at 11 and 15 subunits, in agreement with the spread in observed step lengths. Hence, structural observations further supported the notion that myosin V steps across the actin pseudo-repeat only on average and not precisely and sometimes misses the 13th subsequent subunit by two or four subunits in either direction. Such variability in the step measurement could either derive from an erratic molecular walk or from conformational disorder within the actin filament (Egelman and DeRosier, 1992).

View larger version (85K): [in this window] [in a new window]   Fig. 5. Electron micrographs of single myosin V molecules attached to single actin filaments. The shown molecules have two motor domains spaced by 13 subunits, which is the most common spacing observed. Several molecules appear to mimic a snowboarder’s riding stance, in which their leading neck arcs forward, as if under tension to move forward. Figure reproduced, with permission, from Nature (Walker et al., 2000).

The leading head in such walking intermediates is presumably trapped in a pre-stroke intermediate, of the sort that is so transiently populated in myosin II as to defy experimental access to date (but see Uyeda et al., 2001). Hence, the micrographs of walking intermediates may provide the first high-resolution images of an actin-bound myosin in its pre-stroke state, a textbook example of Pollard’s (Pollard, 2000) ‘switch and win’ strategy - when a target protein denies experimental access to something, abandon it for a more accommodating relative. Intriguingly, the head-neck angle adopted by the leading head in the observed walking intermediate resembles that adopted by isolated (actin-free) myosin V molecules in solution with ATP (Burgess et al., 2001); these molecules are presumably trapped in an ADP-Pi state. The head-neck orientation adopted by the trailing head resembled that of isolated myosin V molecules in the absence of ATP (Burgess et al., 2001).

Curiously, Walker et al. observed only single head attachments, and many heads dissociated at 1 mM ATP and in 100 mM KCl (Walker et al., 2000). However, this finding may have origins in the method of specimen preparation (P. Knight, personal communication). Moreover, these experiments involve expressed HMM constructs that have not yet been observed to behave processively (Moore et al., 2001). It remains possible that such constructs are weakly processive and thus detach frequently from the track under saturating ATP conditions (Walker et al., 2000). Alternatively, the kinetically dominant intermediate under saturating ATP may have only one head strongly bound to actin.

The product of a 36-nm step (Mehta et al., 1999a; Rief et al., 2000; Walker et al., 2000; Veigel et al., 2001) and a 3-pN stall force (Mehta et al., 1999a) exceeds 100 zJ, the energy released by a single ATP hydrolysis under physiological conditions (Bagshaw, 1982). Observations of tight chemomechanical coupling between ATP hydrolysis and mechanical steps, even against high loads (see above), might lead to predictions of unusually high efficiency in converting chemical energy to mechanical work. Such predictions neglect the incidence of ATP-consuming reverse steps against high loads. If an ensemble of molecules were pre-loaded at 2-3 pN, a large fraction would proceed to step backwards and perform negative work, making the ensemble efficiency, the only meaningful thermodynamic variable, far less than 100%. Nonetheless, the observed frequency of apparent ‘super-energetic’ steps (work output exceeds mean free energy input) should be rather small on statistical mechanical grounds (see Landau and Lifschitz, 1980). Three factors could explain such observations. First, the motors do not move against 3 pN; the most energetic observed forward steps, against somewhat smaller loads, should fall short of producing 100 zJ and hence occur frequently. Second, the above described 36 nm step measurements - in which elastic linkages have been finessed out of the experiment - do not involve loads in excess of 2 pN. The molecule may thus advance by <36 nm when facing higher loads. Third, the free energy released by ATP hydrolysis under experimental flow cell conditions in the presence of an ATP-regenerating system may be slightly higher than 100 zJ.

Although various experiments demonstrate that myosin V walks with a stride length of 36 nm, the potential for smaller substeps within this stride remains unclear. Walker et al. observed the head-neck junctions in walking intermediates in averaged electron micrographs (Walker et al., 2000). On the basis of the difference between the head-neck angle describing the leading head and that describing the lagging head, they estimated that a shape change in the motor domain could account only for a 26 nm advance. Moreover, Veigel et al., using a dual-beam optical-trapping geometry, measured 20-25-nm unitary steps (non-processive) produced by a truncated monomer fragment containing one motor domain and six IQ repeats bound to light chains (Veigel et al., 2001).

On the basis of these data, Walker et al. (Walker et al., 2000) have suggested that a 20-26 nm conformational change must be supplemented by 10-16 nm - an estimate that, intriguingly, accords well with the characteristic distance associated with load-dependent mechanochemistry (above). This supplement may reflect a diffusive search that strains the molecule (Walker et al., 2000; see also Huxley, 1957). However, there are three reasons to question this hypothesis. Firstly, this required diffusion to induce strain would probably span on the order of a millisecond in the absence of external load (see Berg and von Hippel, 1985). Load should slow this search significantly: the 2 pN clamp (Rief et al., 2000) imposes upon the molecule 1.8 to 2.2 pN of tension; the minimum energy barrier confronting the hypothetical diffusion is thus 10-16 nmx1.8 pN=18-29 zJ=4.5-7.2 kT. By Boltzmann statistics (see Landau and Lifschitz, 1980), such loading will slow the search by at least e^4.5-7.2100-1000-fold, meaning the search will take 0.1-1 second on average. Under this 2 pN clamp, however, we observed rapid 36-nm steps with <3-ms rise times and no apparent intermediate dwell (Rief et al., 2000). Altough we observed occasional 20 nm substeps, followed by dwells spanning seconds (above), the relative rarity of these smaller steps suggests that the associated transitions are off the normal kinetic pathway. Secondly, the notion of a biased diffusive search that strains the molecule might predict that the stride length would more often fall short of 36 nm than exceed it, especially in solution studies where isolated molecules need not follow linear trajectories along the helical actin track. By contrast, electron micrographs of walking intermediates (Walker et al., 2000) show the opposite asymmetry: the molecule more often steps to the 15th following subunit than it does to the 11th. Thirdly, the angle change measured in the averaged electron micrographs may underestimate the actual shape change in the motor domain, especially if the leading head in these images has already executed a partial power-stroke then arrested by internal load. Although the measured 20-25 nm monomer step size (Veigel et al., 2001) dovetails nicely with the structure-based estimate (Walker et al., 2000), there is no evidence that this measurement matches the power stroke of an intact dimer in stride.

	Molecular models for processive myosin V motion

Top SUMMARY Introduction Demonstration of processive... Kinetic requirements for a... Single-molecule stepping... The step size Molecular models for processive... Conclusions and future... REFERENCES

 
It might seem premature to posit models for myosin V processivity, given our lack of solution kinetic data from the intact dimer. Nonetheless, several such models have been proposed. On the basis of the above data, I believe any model should accommodate the following observations.

(1) Myosin V is a highly efficient processive motor (Mehta et al., 1999a; Sakamoto et al., 2000; Rief et al., 2000) that moves in steps averaging 36 nm (Mehta et al., 1999a; Rief et al., 2000; Veigel et al., 2001).

(2) The molecule couples ATP binding events tightly to mechanical steps. This remains true under all observed loads at limiting ATP concentrations and at least for loads below 1.5 pN at saturating ATP concentrations (Rief et al., 2000).

(3) A 12-18 s^-1 ADP release is rate-limiting during steady-state cycling of expressed monomers (De La Cruz et al., 1999; De La Cruz et al., 2000b) and tissue-purified dimers (Rief et al., 2000).

(4) This rate-limiting transition is independent of load (Mehta et al., 1999a; Rief et al., 2000).

(5) When ADP rebinding slows the cycling rate, the release of post-hydrolysis ADP and the release of rebound ADP occur at similar rates (De La Cruz et al., 1999; Rief et al., 2000).

(6) ATP binding promotes rapid dissociation of monomer fragments from actin (Trybus et al., 1999; De La Cruz et al., 1999; Wang et al., 2000; De La Cruz et al., 2000a).

(7) The dissociated myosin head hydrolyzes ATP quickly (Trybus et al., 1999; De La Cruz et al., 1999; De La Cruz et al., 2000a)

(8) Myosin-ADP-P_i monomers bind actin and then release P_i quickly (De La Cruz et al., 1999; De La Cruz et al., 2000a).

(9) Myosin and myosin-ADP bind actin with high affinity (Trybus et al., 1999; De La Cruz et al., 1999).

(10) The rate of ATP binding and its commitment to hydrolysis (k_cat/K_M^T) is independent of load (Mehta et al., 1999a).

(11) A load-dependent transition might become rate-limiting at saturating ATP concentrations, but only at loads exceeding 2 pN. Under vanishing load, this transition occurs >100 times faster than the rate-limiting step (Mehta et al., 1999a; >1200 s^-1). These conclusions assume that tight chemomechanical coupling is preserved at high load.

(12) A kinetically prevalent intermediate state, at least at limiting ATP concentrations, has both heads bound to actin, 36 nm apart on average (Walker et al., 2000).

(13) Intramolecular strain affects the two bound heads asymmetrically (Walker et al., 2000).

(14) Reverse-directed stepping occurs under high load and more often at limiting ATP concentrations than at saturating ATP concentrations (Mehta et al., 1999a).

(15) The kinetics of reverse stepping do not differ from the kinetics of ATP binding and forward stepping at limiting ATP concentrations (1 µM ATP, 1 s^-1 rate of stepping and of ATP binding, see above).

Our preferred model (Rief et al., 2000; see also Vale and Milligan, 2000) presents the most straightforward scheme to account for available kinetic data (Fig. 6). Initially, both heads are strongly bound to actin; the leading (pre-stroke) head is ADP bound, and the rear (post-stroke) head is nucleotide-free (12). ATP binds the trailing head, promoting its rapid dissociation (6). Intramolecular strain is then discharged in a power stroke that moves the detached head forward to become the new leading head, a process that may or may not involve a succession of smaller substeps. The new leader rapidly hydrolyzes ATP (7) and binds actin (8). The events between dissociation and rebinding - in effect commitment to hydrolysis of ATP - cannot be rate limited by a slow rebinding immediately following a fast and reversible conformational change (Schnitzer et al., 2000) or by a slow conformational change. If it were, the commitment to ATP hydrolysis would be rate limited by a necessarily load-dependent movement, and the scheme would violate (10). Once the new leader rebinds actin, it rapidly releases P_i (8) and strains the trailing head towards forward movement (13). The trailing head remains bound to its actin site and to ADP. The following transition, a rate-limiting (3,5) and load-independent (4) ADP release from the trailing head, completes the cycle. Hence, the kinetically dominant intermediate at saturating ATP concentrations has both heads bound strongly to actin, a prediction that has not yet been verified.

View larger version (13K): [in this window] [in a new window]   Fig. 6. Molecular model proposed by Rief et al. (Rief et al., 2000). Grey motor domains correspond to weak (low affinity) binding to actin, and black motor domains correspond to strong (high affinity) binding to actin.

In this model, processivity hinges on a race: once the trailing head dissociates, the leading (bound) head undergoes an isomerization from a slow ADP-release state to a 12 s^-1 ADP release state, releases ADP, binds ATP and then dissociates from actin. This sequence of events must be outpaced by the free head moving forward and rebinding actin, or the molecule will jettison its track; the degree of processivity will depend on the relative rates of bound head dissociation and free head rebinding. This model predicts greater processivity under limiting ATP. Such a kinetic competition differs from the hand-over-hand model presently reigning over kinesin, in which binding of the leading head induces release of the rear one (Hackney, 1994; Gilbert et al., 1995; Ma and Taylor, 1997; Gilbert et al., 1998; Hancock and Howard, 1999; Crevel et al., 1999). Whereas hand-over-hand movement has been intimated for myosin V (De La Cruz et al., 1999), it is difficult to reconcile with observations that stepping dimers and solution monomers cycle at the same, 12 s^-1 rate. By contrast, during ATP turnover, monomeric kinesin releases microtubules more slowly than dimers cycle (Hancock and Howard, 1999), which suggests that each head of the intact dimer accelerates microtubule release by its partner.

An alternative model of myosin V processivity (E. M. De La Cruz, personal communication) proposes that the kinetically dominant steady-state intermediate in the presence of s