How processive is the myosin-V motor?

DAVID A. SMITH*Randall Centre, King’s College London, Guy’s Campus, London SE1 1UL, UK

Received 6 April 2002; accepted in revised form 6 August 2002

Introduction

Recent single-molecule studies of the dimeric myosin-Vmotor highlight the processive nature of this motor onF-actin, which appears to be intermediate betweenmyosin II and the kinesin motor (on microtubules). Byobserving a single fluorescent molecule of myosin V, themean length of a processive run has recently beenestimated at 2.4 lm, or 66 steps (Sakamoto et al., 2000),where each 36 nm step spans one half-repeat of the actinhelix (Mehta et al., 1999; Rief et al., 2000; Walker et al.,2000). A processive run of this length is not observedwith fixed optical traps, which impose an increasingbackward load; up to eight steps have been observed byVeigel et al. (2002). However, trap studies do giveinformation about the attachment kinetics of the dimer,which determines the duty ratio of the motor and hencethe processivity. It is convenient to define the duty ratior as the fraction of time that each head spends attachedto its filament, which is the usual definition for a single-headed motor (Howard, 2001). It is assumed that onehead is always attached in a processive run, which isterminated when both heads are detached. The meannumber of steps in a processive run is a suitable index ofprocessivity.This paper addresses the connection between the duty

ratio and the processivity of a two-headed motor such asmyosin V. It appears that the duty ratio of myosin-Vduring a processive run should be of the order of0.96–0.97, much closer to unity than previously believed(De la Cruz et al., 1999; Veigel et al., 2002). If true, thisvalue has consequences for the mechanism of proces-sivity and the interpretation of recent trap experiments.I assume that the motor makes one forward step everytime one head detaches and rebinds in the presence of asecond bound head, as indicated by the behaviour ofhighly processive motors at low loads. For convenience,suppose also that a head detaches at the same rate fromdoubly bound and singly bound states; this assumptioncan be removed at the expense of an unknown addi-tional rate constant.During a processive run, let the detached head bind at

rate f and subsequently detach at rate g, so that r ¼ f/(f + g). Detached, singly bound and doubly boundstates of the dimer then occur in the ratios (1�r)2:2r

(1�r):r2, leading Viegel et al. (2002) to suggest that theprobability of survival of singly and doubly bound statesafter n steps is (2r� r2)n. However, in a processive runthere is at least one head attached to the filament at alltimes. To calculate processivity, we require instead theprobability Pn of the first detachment from a singlybound motor state after n steps, starting from a statewith both heads attached. The correct result is

Pn ¼ rnð1� rÞ ð1Þ

which can be understood as follows. As long as f, g > 0,one head must eventually detach from the doubly boundstate. However, at each occurrence of the singly boundstate, the motor has a choice between detaching thebound head or binding the other head. The branchingprobabilities for these outcomes must be in the ratio f:g,so that the probability for binding the second head is theduty ratio f/(f + g). After n such choices, the singlybound state survives with probability rn, and 1�r is theprobability of the final detachment which terminates therun. The sum of Pn over all n is unity; every processiverun must eventually terminate.Following Veigel et al., an index n0.5 of processivity

may be defined as the value of n for which Pn ¼ 0:5P0.However, using Equation (1) rather than Veigel’sformula gives

n0:5 ¼ln 2

j ln rj ð2Þ

which predicts a much lower processivity for the sameduty ratio. The table below shows that a duty ratior ¼ 0:7 gives very little processivity, whereas runs withn0:5 ¼ 66 require r ¼ 0:99:

r 0.7 0.8 0.9 0.95 0.96 0.97 0.98 0.99

n0.5 1.94 3.11 6.58 13.5 17.0 22.8 34.3 69.0

Equation (1) has been derived with minimal assump-tions about the operation of two-headed motors, andshould apply to any processive motor for which theseassumptions are approximately realised. To strengthenthe argument, the Appendix A gives a formal analysis oftwo very different models for processive dimeric motors,both of which lead to Equation (1).*E-mail: david.a.smith@kcl.ac.uk

Journal of Muscle Research and Cell Motility 25: 215–217, 2004. 215� 2004 Kluwer Academic Publishers. Printed in the Netherlands.

Consequences

According to table, the processivity of myosin-Vobserved by Sakamoto et al. (1999) requires r ¼ 0.97.They observed the motor to move at l lm/s, indicating alifetime of 36/1000 ¼ 0.036 s per 36 nm step. This speedis determined by the detachment rate, so g » 28 s�1.Thus the rate of reattachment after a singly boundperiod during a processive run is f ¼ 28/(1� 0:97) ¼930 s�1.Similar estimates apply to myosin-V moving actin in

the double-bead optical trap experiment. The 67 msmean dwell time of doubly bound periods observed atthe start of a sequence of steps gives g » 15 s�1. Theobserved run of eight steps is terminated when myosinforce is balanced by the traps, which gives a weak lowerbound for n0.5; nevertheless, the table shows thatn0.5 > 8 requires r > 0.92. Thus f > 15/(1� 0:92) ¼190 s�1. However, the index of unloaded processivity islikely to be much bigger than eight. Equivalently, therebinding rates f of the second head for the free motorand the motor in trap experiments should be similar,since in each case motor and filament are held inproximity by the bound head. Thus f is generallyestimated at 1000 s�1. This quantity is not related to theinitial binding rate of the detached motor, whichrequires both heads to search for the filament byBrownian motion and may be two to four orders ofmagnitude lower.Spudich and Rock (2002) have proposed two versions

of the alternating-head model for myosin V. Bothversions employ a working stroke of 25 nm for eachhead, but differ only by the angles that the lever arm of asingly bound myosin makes with the filament. In theirFigure 1, version a requires the lever-arms to open up by11 nm for the detached head to reach the next forwardsite, whereas version b allows the next site to be accessedwithout straining the arms. In case b, rebinding shouldbe limited by the time taken for this head to locate theforward site by relatively free Brownian motion, withoutwaiting for a large thermally driven strain. The 1 mstime implied by our estimate of f is 10 times the estimateof Veigel et al. (0.1 ms), which assumes version a. Aneven longer waiting time is indicated by the high-noiseperiod of reduced stiffness reported by these authors,although further analysis may be needed to substantiatetheir claim that these periods arise from the singlybound motor. In fact, Spudich and Rock show that thetrap data of Veigel et al. strongly support version b forunrelated reasons (isolated steps and the first step are25 nm rather than 36 nm).Kinetic uncertainties are likely to reappear in the

context of how processive myosin-V needs to be underphysiological conditions to move filaments or transportcargo. In melanocytes, myosin V is not required forlong-range transport, which occurs on microtubules, butrather for circulating vesicles on a secondary mesh ofactin filaments, notably at the tips of dendrites (Wuet al., 1998); for this purpose a processivity index of 28

(giving a run of 1 lm) would be sufficient. The modelsproposed here would require r ¼ 0.97 or more, whichimplies rebinding rates of 1000 s�1 if g ¼ 30 s�1. Thus ifEquation (1) is correct, duty ratios of 0.7–0.9 are quiteinadequate to explain the cellular processivity of myosinV, even though these values are substantially larger thanthose for myosin II.

Appendix A. The processivity of two models of dimeric

motors.

1. An alternating-head model

Consider the kinetic scheme in Figure 1A for analternating-head model where identical heads A, B ex-change between trailing and leading positions on puta-tive binding sites (separated by 36 nm for myosin-V onactin). Only the trailing head is allowed to detach at rateg; the trailing head then becomes the leading head whichcan then bind at rate f. For each head the duty ratio r isf/(f + g). As in the main text, all steps are assumed tobe in the same direction.To calculate the probability Pn that both heads first

detach after n steps, define a state index k which tracks

Fig. 1. Step-separated kinetics of two hypothetical mechanisms for

processive motility of a dimeric motor AB on a polymeric filament.

Motor states are specified by the heads bound to the filament (none, A,

B or AB) and the number of steps made. A: an alternating-head model,

where only the trailing head of a doubly bound state can detach from

the filament and can reattach only after becoming the leading head. B:

either head can detach at any stage. In both cases, each visit to a singly

attached state is associated with a step of fixed size, probably after

formation.

216

both the number of heads bound and the number ofsteps: odd and even values of k label singly and doublybound states respectively, and k increases by two everytime the motor steps forwards. Each k-state can bevisited once and once only. Let Pk(t) be the probabilityof state k at time t, starting from k ¼ 0 at zero time(P0(0) ¼ 1). For odd values of k, let Qk(t) be theprobability at time t of the first doubly detached state,so that Pn ¼ Q2n+1(¥). Reattachment from this statewill not occur if the motor/filament diffuses away.Then

_P0ðtÞ ¼ �gP0;

_P1ðtÞ ¼ gP0 � ðf þ gÞP1; _Q1ðtÞ ¼ gP1;_P2ðtÞ ¼ fP1 � gP2;

_P3ðtÞ ¼ gP2 � ðf þ gÞP3; _Q3ðtÞ ¼ gP3;_P4ðtÞ ¼ fP3 � gP4;

. . .

ðA:1Þ

Thus QkðtÞ ¼ gR t0 Pkðt0Þdt0 for odd values of k. If

Qk(t) is defined in the same way for even values of k,these functions satisfy the same differential equationsas the Pk and give the correct termination probabilitiesfor k odd. This sequence starts with Q0(t) ¼1� exp(�gt). The steady-state solution of these equa-tions gives limiting forms for Qk(t) at long times,namely rn for k ¼ 2n and rn (1�r) for k ¼ 2n + 1. Thelatter is the required termination probability Pn inEquation (1).

2. An inchworm model

As an extreme counterexample, suppose that bothleading and trailing heads may detach with rate g andbind with rate f, so that the kinetics of the two heads aretruly independent (Figure 1B). Again, r ¼ f/(f + g). Inthis case, a different mechanism is required for directedmotility, for example, by a singly bound head slidingfrom one site to the next between stationary periods ofdouble attachment. This model is reminiscent of recentobservations of repeated stepping with a truncated one-

headed motor (Tanaka et al., 2002). The correspondingkinetic equations are

_P0ðtÞ ¼ �2gP0;

_P1ðtÞ ¼ 2gP0 � ðf þ gÞP1; _QðtÞ ¼ gP1;_P2ðtÞ ¼ fP1 � 2gP2;

_P3ðtÞ ¼ 2gP2 � ðf þ gÞP3; _Q3ðtÞ ¼ gP3;_P4ðtÞ ¼ fP3 � 2gP4;

. . .

ðA:2Þ

This model gives the same result for Qk(¥) when k isodd, though not for k even. Thus Equation (1) alsoapplies here, and the connection between duty ratio andindex of processivity is as before (Equation 2).

References

De La Cruz EM, Wells AL, Rosenfeld SS, Ostap EM and Sweeney HL

(1999) The kinetic mechanism of myosin V. Proc Nat Acad Sci

USA 96: 13726–13731.

Howard J (2001) Mechanics of Motor Proteins and the Cytoskeleton.

Sinauer Associates Inc, Sunderland, Massachusetts.

Mehta AD, Rock RS, Rief M, Spudich JA, Mooseker M and Cheney

RE (1999) Myosin V is a processive actin-based motor.Nature 400:

590–593.

Rief M, Rock RS, Mehta AD, Mooseker MS, Cheney RE and Spudich

JA (2000) Myosin V stepping kinetics: a molecular model for

processivity. Proc Nat Acad Sci USA 97: 9482–9486.

Sakamoto TL, Amitani ER, Yokota X and Ando T (2000) Direct

observation of processive movement by individual myosin V

molecules. Biochem Biophys Res Comm 272: 586–590.

Spudich JA and Rock RS (2002) A crossbridge too far. Nature Cell

Biol 4: E8–E10.

Tanaka H, Homma AH, Katayama E, Ikebe R, Saito J, Yanagida T

and Ikebe M (2002) The motor domain determines the large step of

myosin-V. Nature 415: 192–195.

Veigel C, Wang F, Bartoo ML, Sellers JR and Molloy JE (2002) The

gated gate of the processive molecular motor, myosin V. Nature

Cell Biol 4: 59–65.

Walker ML, Burgess SA, Wang F, Hammer JA, Trinick J and Knight

PJ (2000) Two-headed binding of a processive myosin to F-actin.

Nature 405: 804–807.

Wu X, Bowers B, Rao K, Wei Q and Hammer JA (1998) Visualization

of melanosome dynamics within wild-type and dilute melanocytes

suggests a paradigm for myosin V function in vivo. J Cell Biol 14:

1899–1918.

217