Adv. Exp. Med. Biol., 565:205-219 (2005)

HOW TWO-FOOT MOLECULAR MOTORS
MAY WALK
Kazuhiko Kinosita, Jr.1, M. Yusuf Ali2, Kengo Adachi1, Katsuyuki
Shiroguchi1, and Hiroyasu Itoh3,4

1. INTRODUCTION
Myosins and kinesins each constitute a large family of linear molecular motors thattrack along a filamentous rail, myosins along an actin filament and kinesins along a
microtubule. These motors are powered by free energy derived from ATP hydrolysis,
and the mechanisms of chemo-mechanical conversion in these motors have been underintensive study (Kinosita et al., 1998; Vale and Milligan, 2000; Mehta, 2001; Vale, 2003;
Schliwa and Woehlke, 2003; Endow and Barker, 2003). Most of myosins and kinesins
have two globular domains that bind to the filamentous rail and that hydrolyze ATP in arail-dependent manner. The two domains are usually called “heads” or “motor
domains” and are connected via a neck-like structure to a common stalk. Some of thetwo-headed motors are processive, in that a single molecule moves along a rail for many
ATPase cycles without detaching from the rail. These processive motors appear to“walk,” using the two heads alternately in a hand-over-hand fashion, as has recently been
demonstrated for myosin V (Yildiz et al., 2003) and conventional kinesin (Asbury et al.,
2003; Yildiz et al., 2004). Unlike walking of a human being, molecular motors cannot
rely on inertia, which is negligible for biological molecules that work in water or
membranes. A human has a right and a left foot, but the two heads of a molecularmotor are identical (Fig. 1a). How, then, do they walk? In this article, we focus on
the mechanism(s) that warrant forward, not backward, stepping. Because we discuss
walking mechanisms in this article, we call the heads “feet” and necks “legs.”

1

Okazaki Institute for Integrative Bioscience, National Institutes of Natural Sciences, Higashiyama 5-1,
Myodaiji, Okazaki 444-8787, Japan. 2Department of Physics, Faculty of Physical Sciences, Shahjalal
University of Science and Technology, Sylhet-3114, Bangladesh. 3Tsukuba Research Laboratory, Hamamatsu
Photonics KK, and 4CREST “Creation and Application of Soft Nano-Machine, the Hyperfunctional Molecular
Machine” Team 13*, Tokodai, Tsukuba 300-2635, Japan.
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Figure 1. Walking with two identical feet. The legs are made of elastic vinyl pipes, which can accommodate
both torsional and flexural strains. (a) Two feet of a molecular motor are identical, because they are coded by
the same gene. (b) The two legs are joined in twofold symmetry. Thus the two feet would be oriented in
opposite directions, one toe facing east if the other faces west, unless the legs are flexible. (c) When two feetland simultaneously during walking, both toes must be oriented forward, because the landing sites on the rail
are all identical. Elastic legs would thus be severely distorted. In the configuration shown in this image (b),most of the strain is in torsion of the legs (note the directions of the small bars on the legs) whereas bending isrelatively small. (d) By turning one of the feet by 360°, much of the torsional strain is relieved, resulting insevere bending. The total strain is the same as in c. (e) When the motor moves forward by one step andattains the same posture as in d, a cargo (pink and blue long bars) attached to the body rotates by 180°. A
180° rotation also accompanies every step if the motor steps with the posture in c. (f) Flexible joints in thelegs (arrows) allow the two feet to adopt the same orientation. (g) With flexible joints, landing with two feet
does not introduce strain. (h) But, because of the basic twofold symmetry, the body still tends to rotate 180°
every time the motor steps. (i) With flexible joints, though, the 180° rotations can be prohibited by an
external force without introducing too much strain in the legs. Note that the two legs are now crossed near thejunction (arrows); a small torque suffices to bring about this configuration.

2. HINTS ON WALKING MECHANISMS
2.1. Walking with Two Identical Feet
The two legs of a myosin or kinesin molecule emerge from a coiled coil of α-helices(the stalk, or “body”), each helix extending into a leg (see Figs. 2c and d). Because thecoiled coil is twofold symmetric, as confirmed for kinesin (Kozielski et al., 1997) andmyosin (Li et al., 2003), the two identical legs are also arranged, basically, in the same
twofold symmetry: if there were no flexibility, the two feet would be oriented in opposite
directions, making it extremely difficult to walk on landing spots that are unidirectionallyoriented on a rail (Figs. 1b-e). In fact, each leg of kinesin is a single polypeptide chain
and is considered flexible over the entire length, unless it is “docked” onto the foot (Fig.
2d); in a crystal structure of kinesin dimer where both legs were docked (Kozielski et al.,1997), the two feet were not arranged in twofold symmetry, indicating that the short
undocked portion is already flexible. Myosin’s legs are reinforced with light chains(Figs. 2a and b), and thus are probably semi-rigid. Flexibility likely resides at theleg-body junction. Indeed, analyses of rotational Brownian motion of myosin II(conventional myosin) indicated the presence of a flexible joint near the leg-bodyjunction (Kinosita et al., 1984; Ishiwata et al., 1987), and electron micrographs of myosin.

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Figure 2. Postulated lever action in two-foot motors. The motors in this figure move toward right. (a, b)
Scallop myosin. This myosin is non-processive and thus does not “walk.” Nevertheless, we show possible
walking postures in order to indicate lever action (arrow) in myosin: the orange leg (the long α-helix) rotates
between a and b. Flexible joints likely exist around the location indicated by the yellow ball, beyond which
the two α-helices form a coiled coil (the “stalk”; not shown in the figure). Thus, the red leg presumably
undergoes rotational diffusion around the yellow ball. The lever action of the orange leg biases the Brownian
motion of the red foot forward. Each figure is composed of two structures of scallop myosin subfragment 1(S1), arranged arbitrarily. The orange foot/leg in a represents the structure of S1 binding MgADP·VO4, andthat in b is S1 without a nucleotide (Houdusse et al., 2000). The red foot/leg is S1 binding MgADP, whichmimics a structure after detachment from actin (Houdusse et al., 1999). Cyan/blue, essential light chains;
green/dark green, regulatory light chains. The gray disks with a diameter of 5.5 nm represent binding sites onan actin filament. (c, d) Conventional kinesin. The blue and green legs (“neck linkers”) between the balls
are presumably flexible, and thus the red foot undergoes Brownian motion. The flexible green leg in c“docks” onto the orange foot, in an ATP-dependent process, through Brownian motion (wavy arrow). After
docking (d), the Brownian motion of the red foot occurs around the green ball, and thus is biased toward theforward binding site. The docking is equivalent with the lever action in myosin. The gray disks with adiameter of 4 nm represent binding sites on a microtubule. The figures are constructed from a structure of adimeric kinesin (Kozielski et al., 1997) by assigning arbitrary structures to the neck linkers (except the green
one in d) and orienting the central coiled coil (stalk) arbitrarily.

V revealed the angle between the two legs to be quite variable (Walker et al., 2000).
In a crystal of the coiled coil portion of myosin II, the end next to the legs was
disordered (Li et al., 2003).
The flexibility in the undocked legs of kinesin and that at the body-leg junction of
myosin allows the two feet to adopt the same orientation, which is a required posturewhen the two feet simultaneously land during walking. Because the two feet and legs
are identical, the landed posture with least strain must be the same whether one or theother foot leads, although the flexibility may allow many other postures without
imposing much strain. If the motor reaches the unique, most stable posture after every
step, then symmetry dictates that the body must turn around its axis by 180° as theleading and trailing feet swap (Howard, 1996; also see Figs. 1g and h). Hua et al.
(2002) sought for, but did not observe, the 180° reorientations that would accompany
every step in kinesin. They thus suggested inchworm walking in which one foot always

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leads. We also failed to observe the 180° reorientations in myosin V (Ali et al., 2002)
and myosin VI (Ali et al., 2004). Recent studies, however, have established that myosin
V and kinesin walks in a hand-over-hand fashion in which the two feet alternate in thelead. A single fluorophore attached to one of the two feet of myosin V (Yildiz et al.,2003) or kinesin (Yildiz et al., 2004) advanced, for every two ATP hydrolysis cycles,
over a distance twice the motor’s step size which is the distance traveled by the body ofthe motor in one ATP cycle; inchworm walking would advance the fluorophore by adistance equaling the step size. Also, in some mutant kinesins, dwells between steps
were alternately long and short, indicating an asymmetric hand-over-hand walking withtwo different conformations for two-foot landing (Asbury et al., 2003). Why, then,have the 180° reorientations not been detected so far? Previous observations were madeby attaching a large probe, a microtubule or micron-sized bead, to the motor. The
attached probe may well have broken the symmetry of the motor, as in the mutations, andimpeded the reorientation. With the assumed flexibility, the torque needed to break thesymmetry is small (Fig. 1i). Genuine motion of these motors, without a cargo, might
still involve 180° reorientations, although the flexible joints likely obscure the rotation.
2.2. Lever Action and Biased Diffusion
Until recently, researchers working on myosin and kinesin had somewhat different
views. Because myosin’s legs are likely stiff, prevailing theory states that a landed leg
acts as a lever (Huxley, 1969; Holmes and Geeves, 2000): when a landed ankle is bent
forward, the leg leans forward, carrying the body forward (Figs. 2a and b). The tilting
is best evidenced for myosin V (Walker et al., 2000; Moore et al., 2001; Veigel et al.,
2001; Burgess et al., 2002; Forkey et al., 2003). The lifted leg thus easily finds aforward landing site. Kinesin’s legs, in contrast, are flexible and unlikely to serve as a
stiff lever. Instead, a lower part of a landed leg docks onto the landed foot such that theupper leg emerges from a forward part of the foot (Figs. 2c and d). This biases the
Brownian motion of the lifted foot forward, and the foot lands on a forward site. The
relatively small bias could be efficient, because kinesin’s legs are short and must be fully
extended to reach a forward or backward site: of the two sites that are available, only theforward site can be reached after the docking of the landed foot. The docking in kinesin
may be regarded as the equivalent of the lever action in myosin, and then the two
schemes are apparently quite similar. Myosin researchers, however, tend to stress thelever action whereas kinesin researchers diffusional search. The distinction seems to becoupled to the question of which process produces force: lever action itself in myosin,
and landing of the diffusing foot in kinesin. Is this really so?
3. SPIRAL MOTION OF MYOSIN AROUND AN ACTIN FILAMENT
3.1. Observation of Spiral Motion
Myosin V is now one of the best characterized molecular motors. It moves toward
the barbed, or plus (fast-growing) end of an actin filament using two long (∼23 nm) legs
each reinforced with six light chains (Cheney et al., 1993; see Fig. 3). The movement isprocessive (Mehta et al., 1999; Rief et al., 2000; Sakamoto et al., 2000). The step size.

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Figure 3. Myosin V and myosin VI. Myosin V has two legs each reinforced with six light chains (orange)
and walks on an actin filament (green) toward the barbed, or plus, end (left in the figure). Myosin VI, on theother hand, moves toward the pointed, or minus, end. Previously, myosin VI was thought to bind one lightchain per leg, and thus myosin VI was considered short-legged as shown in this figure. The red portion in thefeet of myosin VI indicates an extra insert not seen in other myosins. Every 13th monomer of the actin
filament is shown in blue. Walking along one side of an actin filament implies an average step size of ∼36
nm. Adapted from Ali et al. (2004).

of myosin V has been estimated to be about 36 nm (Mehta et al., 1999; Rief et al., 2000;
Rock et al., 2001; Tanaka et al., 2002), which coincides with the helical repeat of an actin
filament of 36 nm (Holmes et al., 1990; see Fig. 3). Electron micrographs of myosin V(Walker et al., 2000) have shown that bound feet are separated by ∼36 nm on an actin
filament, corroborating the step size measurements. In most of these previous studies,
however, myosin V could approach an actin filament from only one side, and thus
myosin V may have been forced to step on the actin sites that are 36-nm apart (Fig. 3).
To address this possibility, we designed an experiment in Fig. 4a, where myosin V
could freely rotate around an actin filament that was suspended between two large (4.5µm) beads. We attached a duplex of 1-µm beads to myosin V to facilitate visualizationof rotation. The microscope focus was set such that the bead closer to the observer
appeared white and the bead farther from the observer black. As seen in Fig. 4b, thebead duplex moved in a left-handed spiral around the right-handed double helix of actin.
The rotational pitch was 2.2±0.3 µm per turn, compared to the pitch of the actin double
helix of 72 nm. The slight left-handed spiral can be explained if the step size of myosin
V is slightly less than the actin helical repeat (half pitch) of 36 nm: in Fig. 4a, steppingon blue subunits that are 36-nm apart produces straight motion without spiraling,whereas slightly smaller strides, e.g. on the purple subunits, would lead to a left-handedspiral.
The average step size of myosin V is calculated from the spiral pitch in thefollowing way. If the step size is (36 – x) nm, then myosin V will rotate toward left by
180° × (x/36) per step. To accumulate one turn, myosin V has to make 360° / [180° ×(x/36)] = (72/x) steps, or to proceed over a distance of (72/x) × (36 – x) nm. This latterdistance is equal to the spiral pitch of 2200 nm. Thus, (72/x) × (36 – x) = 2200.
Solving for x yields x = 1.1 nm, and thus the step size is 34.9 nm. (This calculation isslightly different from the one in Ali et al. (2002), but the answer is essentially the same.)With this average step size, the predominant landing site from the position in Fig. 4a ison the blue subunit, or the 13th subunit counting both strands. Occasionally myosin V
lands on the 11th subunit (purple), and less frequently on the 15th or 9th.

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Figure 4. Spiral motion of myosin V around an actin filament. (a) Experimental setup. An actin filament,
fluorescently labeled, was suspended between beads of diameter 4.5 µm placed on a glass surface. To myosin
V, a duplex of 1-µm beads was attached. (b) Sequential images, at 1-s intervals, of spiral motion of myosin V
at 400 µM ATP. Upper frames in a row show transmitted images of the bead duplex, where a bead closer tothe observer appears white and a bead farther away black (see control images at bottom). Lower frames show
fluorescence images of the actin filament (between arrow heads). The dashed line in the upper frames show
the position of the actin filament deduced from the lower frames. The dot in the upper frames indicates thecenter of the bead which we judged to be attached to actin. Bar, 5 µm. Adapted from Ali et al. (2002).

The step size we obtained under no load (viscous load is negligibly small for theslow translational motion) is not so different from the previous estimates. Previous
steps of ∼36 nm were not imposed by experimental geometry. Myosin V naturally
walks almost straight, on one side of an actin filament. The implication is that the leveraction in myosin V occurs, on the average, almost precisely forward, or in a plane
including the actin filament, to let the lifted foot aim from above, not obliquely from side,at the landing sites on the filament. The slight tendency to spiral to the left is explained
if forward bias by the lever action is not sufficient to comfortably place the lifted foot on
the 13th subunit. Or, the ankles of myosin V may have an intrinsic tendency to bendslightly to the left. When many molecules of myosin II carry an actin filament forward,.

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the filament rotates as a right-handed screw (Nishizaka et al., 1993) with a pitch of ∼1µm (Sase et al., 1997). Although myosin II is not processive and thus does not walk,the right-handed spiral can be explained if myosin II “kicks” actin by bending a landed
ankle slightly obliquely to the right. The structure of the foot (motor domain) of
myosin V is similar to that of myosin II (Coureux et al., 2003; Holmes et al., 2003), but asmall difference in the direction of ankle action is not inconceivable.
3.2. Myosin VI May Move Like Kinesin
Myosin VI moves, unlike most other myosins, toward the pointed, or minus, end ofan actin filament (Wells et al., 1999; Homma et al., 2001). It is a processive motor(Rock et al., 2001; Nishikawa et al., 2002), and thus is considered to “walk” using its twofeet. Myosin VI has only one typical light-chain binding site per leg (Wells et al., 1999)
and was initially considered short-legged (Fig. 3). Nevertheless, its step size was long,∼30 nm (Rock et al., 2001) or ∼36 nm (Nishikawa et al., 2002), apparently incompatible
with the expected physical size of the legs. Again, these measurements were made in aconfiguration that allowed myosin VI to approach from one side of an actin filament,
raising the possibility that this constraint somehow forced the short-legged myosin VI to
stride on the 36-nm spaced landing sites on one side of the filament. We thought that, if
we allowed myosin VI to rotate freely around an actin filament, it would spiral more
extensively toward left than myosin V. It might even spiral to the right with a pitch of
72 nm, if its natural step size is smaller than 18 nm such that the motor tracks along one
strand of the actin double helix. So we tested this idea, again using the actin-bridge
assay (Fig. 4a).
A result is shown in Fig. 5a, where the bead duplex spiraled as a right-handed screw
with a pitch of ∼1.4 µm. Many more right-handed spirals were observed, the pitch
averaging 2.4 µm. The shallow right-handed spiral indicates an average step size
slightly greater than 36 nm (e.g., walking on purple subunits in Fig. 5b); the average step
size calculated as above is 37.1 nm. There were, however, many more bead duplexes(>80%) that failed to show clear rotation (>0.5 revolution) during a processive run of afew µm. If these represent straight motion, the step size would be 36 nm (on blue actin
subunits in Fig. 5b). Or, these may also be a part of long-pitch right-handed spiral. In
any event, the average step size of myosin VI somewhat exceeds 36 nm, being thelongest among known molecular motors. Other long steppers include myosin V, andmyosin XI with the average step size of 35 nm (Tominaga et al., 2003).
The long strides of myosin VI are obviously incompatible with walking with shortlegs. In an electron micrograph (Nishikawa et al., 2002), legs of myosin VI weresomehow extended, possibly by unzipping of the stalk coiled coil. Another possibility
that the insert unique to myosin VI (red part in Fig. 3) may adopt an extended
conformation (Rock et al., 2001) has been denied by a recent study (Bahloul et al., 2004)
which shows that the insert is actually a second calmodulin (light chain) binding domain.
More recent work (B. R. Rami and J. A. Spudich, Stanford University, and H. L.
Sweeney and C. Franzini-Armstrong, Pennsylvania University, personal communication)shows that the coiled coil is indeed unzipped over a considerable length and the unzipped
portion is flexible (Fig. 5b). The long and flexible legs can account for theunconstrained step size of 36-37 nm. Thus, myosin VI seems to walk almost likekinesin, relying on biased diffusion. A lower part of the legs of myosin VI is

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Figure 5. Spiral motion of myosin VI around an actin filament. (a) Sequential images, at 0.4-s intervals, ofspiral motion of myosin VI at 400 µM ATP. See Fig. 4 for details. This bead duplex (1 and 0.45-µm)
carried a short actin filament, which also rotated as seen in the fluorescence images in the lower frames. Of
the bead duplexes examined, only ∼15% showed right-handed spiral, as seen in these images. Others moved
straight without spiraling. (b) A recent study (Bahloul et al., 2004) shows that the extra insert in the legsequence (red part in Fig. 3) actually binds a calmodulin light chain. Also, the coiled coil beyond thelight-chain binding region was found to be unzipped. Myosin VI can thus span >36 nm, as required by theright-handed spiraling. Adapted from Ali et al. (2004).

presumably semi-rigid, and its lever action would serve the purpose of biasing the
diffusion of a lifted foot forward.
4. TOE UP-DOWN MECHANISM
4.1. Moving Forward against a Backward Force
Myosin and kinesin both appear to walk forward by biasing the diffusion of thelifted foot by an action of the landed ankle, either lever action or docking. Does thismechanism really warrant that the lifted foot lands on a forward, not backward, site?
Such a mechanism, alone, would not work properly when the body is pulled backward,
particularly when the legs are flexible as in kinesin and myosin VI. If the legs are
flexible over a large part, diffusion will even be biased backward (Fig. 6a). In kinesin,the free energy difference between the docked and undocked states is small (Rice et al.,2003), implying that docking would fail when the body is pulled back by a load. Then,
there will be little bias for diffusion, or backward diffusion may be preferred (Fig. 2c).

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Figure 6. How to move forward against a backward force (arrows). (a) If legs are flexible over aconsiderable length, diffusion would move the lifted foot toward a backward site. (b) Under a high backward
force, the presumably semi-rigid leg of myosin V may also be bent backward, such that the diffusion is biased
backward.

Myosin V might appear to be free from these problems, but its legs cannot be perfectly
rigid. Veigel et al. (2002) have estimated its leg stiffness to be 0.2 pN/nm, implyingthat the body would be pulled back by 10 nm under 2 pN of backward force (Fig. 6b).
Also, the ankle of the landed foot may yield under the external force, because sustaining
2 pN at the end of the 23-nm leg requires a torque of 46 pN·nm, comparable to the torqueof the powerful rotary motor F1-ATPase (Yasuda et al., 1998; Kinosita et al., 2004). In
spite of these problems, all these motors are known to move forward under a few pN of
backward load. An additional mechanism, other than biasing the translational diffusionof the lifted foot by moving the effective pivot forward, must be involved.
4.2. Toe Up-Down Mechanism
The mechanism we propose (Ali et al., 2004) is the ankle action in the lifted foot:proper up-down motion of the lifted toe will orient the sole correctly such that landing on
a forward site is favored over a backward site even if the body is pulled backward. The
toe up-down mechanism warrants forward motion even if legs are completely flexible.
To illustrate the mechanism, let us again use the toy model introduced in Fig. 1.
First we deal with the case of semi-rigid legs as in myosin V (Fig. 7). We assume thepresence of a flexible joint near the leg-body junction (Fig. 1f), and thus there will belittle torsional strain in the two legs. Bending strain, however, cannot be relieved by theflexible joint. In Fig. 7, a posture with a bent leg is attained only at the expense of ahigh energetic cost, or is rarely attained (unless coupled to a reaction accompanying alarge drop in free energy).
Figure 7a1 shows a posture of the motor after the trailing foot (green) is lifted fromthe rail. The ankle of the leading foot (red) is already bent forward (lever action), suchthat the pivot for rotary diffusion of the lifted leg is forward of the landed foot (red) andis ready to bring the green foot forward. However, if the lifted toe is up, as in Fig. 7a1,
the sole will be misoriented after a forward swing (Fig. 7a2), making forward landing
difficult. Forced landing would bend the leg severely (Fig. 7a3). Natural landing sites
for the toe-up foot will be next to the landed foot (Fig. 7a4), front or back, and thus the
motor will hardly walk forward.

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Figure 7. Toe up-down mechanism for the case of semi-rigid legs. (a) If the lifted toe is up, landing on a
forward site is difficult, and natural landing would be on a nearby site (a4), if one is available. (b) If the toegoes down upon lifting of the foot, landing with the least strain will be on a distant forward site. (c) A
backward force will pull the pivot backward (c1), but, as long as the lifted toe is down, landing on a distantforward site is favored. Under a high force, landing on a nearby site is equally probable (c4). Note that, in
c4, bending of the red leg is caused by the external force. Adapted from Ali et al. (2004).

If, on the other hand, the lifted toe goes down, as in Fig. 7b1, re-landing on the
backward site will be prohibited (Fig. 7b2), whereas landing on a distant forward site
will be smooth and natural (Fig. 7b3). Landing on a nearby site would result in a strain(Fig. 7b4) and thus is much less likely.
A nice feature of the toe up-down mechanism is that it operates properly even in thepresence of a backward force that tends to pull back the pivot beyond the position of thelanded foot (Fig. 7c1). Thanks to the sole orientation, backward landing is stillprohibited (Fig. 7c2), whereas a small thermal agitation will allow landing on a distantforward site (Fig. 7c3). Landing on a nearby site is also allowed under a high backward
force (Fig. 7c4), but this is the condition where the motor begins to stall.

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Figure 8. Toe up-down mechanism for the case of completely flexible legs. The legs in the model are madeof metal chains. (a) The size of the legs are such that landing on a distant forward site is allowed only when
the legs are fully extended and the leading toe is down and trailing toe up. (b, c) With the green toe up,
forward landing is impossible. (d) As long as the green toe is down, there is no hope in backward landing.
(e, f) If a lower part of legs is stiff, oblique landing on a side of the cylindrical rail is also prohibited. The
postures here represent the lowest possible position for the green foot, which fails to reach a blue foot markbelow.

The toe up-down mechanism also works with flexible legs, as long as landing sites
are widely separated such that landing requires almost full extension of the legs. This isbecause, on a fully extended leg, the orientation of the sole is restricted, in the same way
as in a rigid leg. In Fig. 8, the legs of the toy model are made of flexible chains.
Suppose, for the moment, that only those landing sites (foot marks) that are at the top of
the rail cylinder are available. This situation applies to kinesin on a microtubule. The
green foot can land on the forward site if its toe is down (Fig. 8a), but it cannot land if
the toe is up (Figs. 8b and c). When the green toe is down, forward movement iswarranted because landing on the backward site is impossible (Fig. 8d). The
preferential forward landing also operates in the presence of backward force. In Fig. 8d,even if the red ankle yields to a backward force and bends backward (kinesin “undocks”
by backward pull), the green foot cannot reach the backward site as long as its toe
remains down. Forward landing (Fig. 8a) would still be possible, when the body
happens to move forward by Brownian motion (a rare event when the backward force ishigh).
On an actin filament along which myosin VI moves, all foot marks in Fig. 8 arebasically available for landing. Unless the legs are too long, however, landing on a
distant backward site is prohibited when the green toe is down (Fig. 8d). In addition,
the presumably stiff lower portion of the legs of myosin VI opposes oblique landing on aside of the filament (Figs. 8e and f). Thus, toe-down landing will be made primarily on
a distant forward site (Fig. 8a), and occasionally on sites next to the landed foot. The
frequency of landing on a nearby site depends critically on the make of the legs andankles (less easy if shanks are long and ankles are bent acutely), and also on the
backward load. The large variation in the size of individual steps of myosin VI (Rock12

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et al., 2001; Nishikawa et al., 2002) may result from mixing of ∼36-nm strides with shortones (±5.5 nm for the adjacent landing sites).
4.3. How to Walk Forward
In our view, at least four mechanisms are needed to let a two-foot motor walk
forward: (1) the lever action or docking in the landed foot, (2) diffusion of the lifted foot,(3) toe up-down in the lifted foot, and (4) preferential detachment of the rear foot. (1)The lever action has been considered, by many myosin researchers, to play the central
role in throwing the lifted leg forward. Its true significance, however, might be inpreventing the pivot from pulled back too much by a backward force (Fig. 6). (2)Diffusion around the pivot is the only way by which the lifted foot move, whether
forward or backward. It is quite unlikely that ATP-dependent conformational changes
alone, in the landed and/or lifted feet, carry the lifted foot all the way onto a landing site.
Passive diffusion must be involved, which assists forward and backward movements
equally. (3) Toe up-down in the lifted foot, we propose, plays the major role inselecting a forward landing site over backward ones. (4) When both feet land, it must
be the rear foot that is lifted first. This is accomplished by a strain dependence of thenucleotide kinetics in the feet. For kinesin, for example, pulling a landed foot forward
has been shown to increase the affinity of that foot for ADP (Uemura and Ishiwata,2003). This would take place in the rear foot, and the affinity for a microtubule bindingsite is weakened when kinesin’s foot binds ADP.
In somewhat different contexts, a human being also uses the four mechanisms above
when he/she walks. The major differences, apart from the distinction between the rightand left feet, are that a human relies on inertia, particularly in (2) and (4), and that gravity
helps in (2) and (3).
5. ACKNOWLEDGMENTS
We thank M. Fukatsu for the toy model, and S. Ishiwata, S. Uemura, and the membersof Kinosita lab for discussion. This work was supported in part by Grants-in-Aid from
the Ministry of Education, Culture, Sports, Science and Technology of Japan. M. Y.
Ali was, and K. Shiroguchi is, a Research Fellow of the Japan Society for the Promotionof Science.
6. REFERENCES
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DISCUSSION
Pollack: Could you comment on how single-headed kinesins could advance along a
microtubule?
Kinosita: Some part of kinesin would stick non-specifically to the microtubule, as has
been shown for KIF1A, and another part would pull the molecule forward, by a leveraction or by extending itself forward by diffusion followed by binding to a microtubule
site.
Gonzalez: Without strain, on which direction would myosin V move?
Kinosita: If there were no strain-dependent regulation of nucleotide kinetics, either foot,front or rear, could be lifted from actin. The motor would still move forward, but theefficiency would be low, because lifting the front foot would not contribute to forward
motion while ATP is expended.
Pollack: (comment) With single filaments sliding past one another, you do see backward
steps of n × 2.7 nm.
Sugi: One single question is the biased diffusion you mentioned in your talk is the same
as so-called Brownian ratchet mechanism?
Kinosita: The Brownian ratchet, in my opinion, is a broad term that applies to almost.

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15

any mechanisms of molecular machines. Moving the pivot forward, by a lever action,
to help forward landing is a kind of ratchet. Assuring forward landing by bringing thetoe up, without necessarily the pivot motion, is another way of realizing a ratchet.
Kushmerick: You stated the ATP synthesis by F1-ATPase may be nearly 100% efficient.
What is the efficiency of the H+ proton-driven component of FoF1 ATP synthase? Is theoverall FoF1 rotary motor reversible?
Kinosita: For ATP synthesis, I expect the number efficiency (the number of ATP
molecules synthesized per 120-degree rotation) to be close to one, under favorable
nucleotide concentrations and at low rotary speeds. The energetic efficiency (freeenergy for ATP synthesis divided by mechanical work done on the gamma subunit) is
critically dependent on the nucleotide concentrations and applied torque, and would behigh only near reversal (low torque). Peter Gräber’s group, among others, has shownthat FoF1 ATP synthase is reversible, and that synthesis/hydrolysis in F1 is balanced by
the proton flow through Fo. When the proton motive force across Fo is greater than thefree energy needed for ATP synthesis, ATP is synthesized. ATP is hydrolyzed when
the proton motive force is lower. They have shown that synthesis of one ATP molecule
requires translocation of about four protons, but, in addition, some protons may leakthrough the membrane or the Fo motor. Thus, experimental determination of theefficiency of synthesis is very difficult.