The cytoplasm of cells is crowded with cargoes that are being moved processively along tracks of
microtubules or actin by various molecular motors of the kinesin, myosin and dynein family. Efficient
translocation of vesicles and membranous organelles such as mitochondria and endoplastic reticulum
over micrometer distances is an activity crucial to cell life. The best-characterized unconventional
myosin motor stepping processively on actin filaments is myosin V, which is involved in several types
of intracellular transport. Kinesin constitutes a very large family of motor proteins that transports cargo
processively on microtubules at speeds as high as ~1 μm/s, and there are as many as ~50 different
kinesins in humans [61]. The best-characterized so-called conventional kinesin is abundant in nerve
cells. It is double-headed and has an N-terminal motor domain, a coiled coil stalk, and a C-terminal
cargo-binding domain, and transports cargo processively towards the microtubule plus end, i.e., toward the cell membrane. A central issue in the field of molecular motors has been to understand how the
chemical and mechanical steps are coupled and how processive motion occurs using the energy of
ATP hydrolysis in such conventional kinesin and myosin V motors. Various models have been
developed and different mechanisms proposed to explain processive motion by these
molecular motors.
Due to space limitations, it is not possible to study the scores of each and every variant of kinesin,
ncd and myosin V models for processive motility and compare and contrast them. However, the
various alternative mechanisms can be classified, their overall features understood, and the unified
theory applied to the mechanism or model of choice. It is well known that kinesin, ncd and myosin V
heads are structurally equivalent. Hand-over-hand models of processive movement postulate
equivalence of the two heads, i.e. not that the heads are structurally equivalent, which is well-known
and understood as stated above, but that the heads are functionally equivalent, i.e., the same
biochemical (especially ATPase) events occur in both heads except that these events alternate and lag
in time. A subset of these models, called symmetric hand-over-hand models [62, 63] also include the
key proposal of step equivalence, i.e. that all steps are generated in the same way. Thus in symmetric
hand-over-hand models, the rotation is 180o in a clockwise or counterclockwise sense each time, and
the stepping head passes the head attached to the track from the same side (left or right) each time.
Thus, symmetric hand-over-hand models postulate head equivalence and step equivalence [62, 63].
However, experimental data from the Gelles group contradicted the above because the postulated 180o
swiveling or rotation was not observed with each step [64]. To explain these observations, head
equivalence was abandoned and an inchworm model was proposed [64] in which the heads were
functionally inequivalent in that only one head was an active ATPase, and one head always led the
other, but the mechanism retained step equivalence. Thus the inchworm model is head inequivalent but
has step equivalence. Based on single molecule experiments, Block and colleagues postulated an
asymmetric hand-over-hand model of kinesin movement [65] in which the two heads are functionally
equivalent and both hydrolyze ATP alternately, but the steps are non-equivalent in that the stepping
head passes the attached head on alternate sides and the stalk makes compensatory movements to
suppress the 180o rotations. Hence the asymmetric hand-over-hand model has head equivalence but
does not have step equivalence. However, the head equivalence postulated by the asymmetric handover-
hand model is challenged by the observation that heterodimers with ATPase mutation in only one
kinesin head move processively [66]; in other words, processive motion is possible without alternating
catalysis. Further, there exist difficulties for the asymmetric hand-over-hand model in explaining the
exact cause of limping by homodimeric kinesin [65] in which no structural asymmetry is apparent.
Based on molecular systems biology approaches, Nath has proposed a rotation-twist energy storage
mechanism for processive molecular motors such as kinesin, ncd and myosin V [11], which was
subsequently developed in further detail [10]. In this mechanism, one head of the motor binds weakly
to the α-tubulin subunit on the microtubule or to actin while the other head binds strongly to the β-
tubulin subunit on the microtubule or to actin. To take the example of kinesin, only the head bound to
the β-tubulin subunit on the microtubule is an active ATPase because the interactions of the α-tubulin
with the bound kinesin head are not strong enough to release the MgADP bound in that head; hence no
ATP hydrolysis occurs in the head bound to the α-tubulin subunit on the microtubule. Further, the two
steps occur due to different causes; the first one occurs due to ATP binding and its subsequent
hydrolysis (called “the chemical stroke” [10, 11]), while the cause of the second step is the torsional
strain in the V-shaped molecule up to hinge-1 due to the ATP hydrolysis Coulombic energy released
upon Pi release, though the step itself takes place after the trigger of ADP release from the head and
the release of the torsional strain (called “the physical stroke” [10, 11]). In the physical and chemical
strokes, the rear head passes the bound front head from different sides and the strokes have different
trajectories; moreover, since the strokes originate from different causes, they differ in their kinetics,
and thus the rotation-twist energy storage mechanism for processive molecular motors has head
inequivalence and step inequivalence. The mechanism has no difficulty in explaining the observations
in Ref. 66 because in the mechanism, only one head hydrolyzes an ATP molecule to move the doubleheaded
molecule processively by ~8 nm, and further, the progressive shortening of the coiled coil in
the truncated constructs [65] hamper the storage of elastic strain in the molecule which adversely
affects the performance of the physical stroke and therefore increases the propensity of the molecule to
limp. The mechanism is simpler and more elegant and is ideally expected to operate in vivo. The
mechanism can readily be adapted to the case in vitro when both heads bind to β-tubulin subunits on
the microtubule, the only difference being that ATP binding will now be required to unbind the second
head also (i.e. the head that had bound earlier to the α-tubulin subunit on the microtubule), as
discussed later, in which case the mechanism can be said to have head equivalence but no step
equivalence. It should be noted that there is considerable experimental evidence for specific interaction
of kinesin and ncd motor heads with both α- and β-tubulin [67-70]. Moreover, the weaker affinity of
the specific binding site on α-tubulin may prevent its identification, or it is likely that both the heads
may preferably bind to the higher-affinity specific sites on β-tubulin in vitro, and another positive
point of the new mechanism is that it assigns a role to the second weaker but specific binding site
identified by biochemical labeling and electron microscopy techniques [67-70] in motor function. The
function of these weaker, specific motor-binding sites on the microtubule that have been revealed by
experiment had hitherto been unknown. Finally, it should also be noted that the inchworm model was
also defective because it did not solve the difficult problem of how the motor moved both heads by
hydrolyzing a single ATP molecule. This is not a defect in the new mechanism.
Recent fluorescence labeling and single molecule studies from Selvin’s group have clearly
invalidated the inchworm model of processive motion and shown that kinesin moves in a hand-overhand
fashion [71]. Other models have also been proposed in which the two heads are 4 nm apart [72,
73], and Hackney’s classical experimental data also mean that there are two motor head binding sites
with different affinities on the microtubule [74, 75]. These models are unable to explain the 16 nm
steps seen in single molecule studies, which imply that the two heads of kinesin are 8 nm apart [71].
The limping seen in homodimeric kinesin has proved very difficult to explain, and Selvin and
colleagues have recently stated that kinesin could indeed walk symmetrically and that the observed
limping was due to the experimental conditions [76]. Unfortunately, their explanation contradicts the
experimental data of the Gelles group [64]. Impressive evidence that kinesin moves by an asymmetric
hand-over-hand model has also been produced recently [65, 77], and, in particular, Block and
colleagues favor a gated front head model [77].
However, in addition to the question of limping by homodimeric kinesin constructs which has not
been satisfactorily answered to date by the asymmetric hand-over-hand model of motility, there is
another even more fundamental and central question that has not been asked till now, but needs to be asked now and sorely requires an unequivocal answer. This question is the following: Does kinesin
move forward processively in steps of 16 nm head-to-head (i.e. 8-nm steps for movement of the center
of mass of the double-headed molecule) against a load of ~7 pN, the maximum force against which
kinesin molecules have been consistently recorded to step forward in various expertly-performed stateof-
the-art single molecule experiments [72, 78-80], and not ~half the load of ~7 pN, i.e. ~3.5-4 pN,
where it is certainly known to move forward processively with 8-nm (center of mass) steps [65]?
Answering this question is crucial because in the optical trap experiments, for constant energy input
from ATP, it is readily possible to satisfy the energy balance by reducing the force by a factor of ~2
and thereby obtain an increase in the step size by a factor of ~2. In a way, this question has already
been answered by single molecule experiments on kinesin at an intermediate force range of 4.5-5.3
pN, where already, kinesin starts to step backwards [77]. Hence the all-important question arises: Why
does kinesin step backwards at intermediate loads of 4-5 pN, well below the experimentally measured
stall force of ~7 pN? In fact, it should have stepped forward processively even at a ~7 pN rearward
load, in accordance with the single molecule experiments of several groups, including Block’s own
group [72, 78-80]. Unless the step size (8 nm based on center of mass movement) in these in vitro
experiments is larger than the actual step size in vivo, and therefore the energy of ATP is insufficient
to supply the energy for processive forward stepping against the intermediate rearward load of even 4-
5 pN (let alone ~7 pN), and therefore the rearward load wins and pulls the kinesin molecule
backwards, it is not possible to explain the observation of backward stepping at these intermediate
loads, according to our analysis. In the absence of a demonstration of processive forward stepping with
16 nm head-to-head steps at the maximum load against which kinesin molecules are known to move
forward processively [72, 78-80], the proposal of hand-over-hand models that the molecule always
advances by 16 nm head-to-head steps (8 nm movement of the center of mass) is significantly
weakened. I predict that this question will prove to be the Achilles heel for the asymmetric hand-overhand
model. Ideally, what is needed is a molecular mechanism for forward processive motility that
works up to the maximum force (~7 pN for kinesin) and not a mechanism that works only up to ~half
the maximum force, and when the load is increased slightly beyond this value, the motor begins to
move in the backward direction. The rotation-twist (RT) energy storage mechanism for processive
molecular motors offers the further advantage that it explains forward processive motion under vertical
loading that we expect in vivo due to the presence of the cargo at the C-terminal end of kinesin. It
should also be pointed out that the asymmetric hand-over-hand model is not the only model that
includes alternation between two different configurations during processive stepping; the RT
mechanism also shares this attribute [10, 11]. Hence we believe that the rotation-twist (RT) energy
storage mechanism for processive molecular motors should also be included among candidate
mechanisms in the field of motility along with symmetric and asymmetric hand-over-hand and
inchworm models.
The RT mechanism is readily able to explain the experimental facts [62-80] and also possesses
several new and attractive features. Thus the data on processive movement of kinesin against the
maximal load of ~7 pN [72, 78-80] is explained by the RT mechanism by postulating that in these
experiments the two kinesin heads must have bound to α- and β-tubulin on the microtubule. In the
experiments in which the two heads are bound to adjacent β-tubulin subunits on the microtubule,
forward processive motion can readily occur at a load value up to approximately half the maximum load, with the larger step size of 16 nm (head-to-head), as observed [65]. Thus, forward processive
motion is possible in both cases, but not against the high ~7 pN load in the case when both kinesin
motor heads bind to β-tubulin subunits on the microtubule. Thus, from the point of view of the RT
mechanism, kinesin can move with 4 nm center of mass (= 8 nm head-to-head) steps or with 8 nm
center of mass (= 16 nm head-to-head) steps. The two cases depend on whether one head binds to β-
tubulin and the other to the adjacent α-tubulin subunit of the microtubule track (former case) or
whether both heads bind to adjacent β-tubulin subunits of the microtubule track (latter case). Since a
motor head is bound weakly to α-tubulin (compared to the binding of the counterpart motor head
bound to β-tubulin), it does not require MgATP binding to help its release from the microtubule, as the
stored strain energy in the molecule after the chemical stroke and release of Pi is sufficient by itself to
release such a (rear) head bound to α-tubulin [10, 11]. This is also consistent with the longstanding
observation of the presence of two motor head binding sites with different affinities on the microtubule
[74, 75]. On the other hand, if both motor heads bind to β-tubulin, then the stored strain energy is not
sufficient to release the rear head bound to β-tubulin and requires help from another energy source,
which we propose to be MgATP binding to the rear head in the RT mechanism. Applying the unified
theory to the RT mechanism, we can state with full confidence that the first (rear) head is moved (past
the bound front head) from one side by a clockwise rotation viewed from the C-terminal cargo end of
conventional kinesin due to the ~9 kJ/mol MgATP binding energy (i.e. the surplus energy released
over that required to unbind the head from the microtubule) plus the ~9 kJ/mol energy released upon
the process of hydrolysis of the MgATP (that had just bound in that head) that occurs when the head is
free from the microtubule track (and before Pi release, which requires binding of the head to the next
binding site on the track). This is the “chemical step” [10, 11]. In the “physical step” [10, 11], the
Coulombic repulsion energy between MgADP and Pi released upon Pi release into the medium (~18
kJ/mol according to the unified theory) causes an elastic (primarily torsional) strain that helps move
the second head (the present rear head) past the bound front head from the other side (compared to that
in the earlier “chemical step”) by a counterclockwise rotation viewed from the C-terminal cargo end
either without requiring MgATP binding in the second (rear) head in the case when the head is bound
to α-tubulin, or also requiring MgATP binding in the rear head to help release the head in the case
when it is bound to β-tubulin. The limping of homodimeric kinesin [65] is readily explained by the RT
mechanism because as the kinesin stalk is progressively shortened, the energy storage process in the
molecule is progressively hampered and the torsional rigidity required to generate torque by the
physical stroke about hinge-1 [10, 11] is progressively compromised.
In the RT mechanism, MgATP binding to the rear head releases binding energy which unbinds the
rear head from the microtubule track and gives it a clockwise torque (seen from the C-terminal cargo
end), and it is perfectly reasonable that when the head starts to slow down or even pauses, as the sharp
input of energy due to the release of MgATP binding energy in the head that initiated the chemical step
gradually loses its effect, bond cleavage of MgATP occurs in the head and the release of the requisite
quantum of hydrolysis energy (as detailed in the unified theory) continues to drive the head to its next
binding site on the microtubule and helps it complete the chemical step, i.e. MgATP binding and
MgATP hydrolysis acting in sequence cause the chemical stroke. This is a superior proposal to the
central tenet of the gated front head model in which MgATP binding to the front head causes the rear
head to step forward [77]. The RT energy storage mechanism also differs from the gated rear head model in which Pi release from the rear head (but not ATP binding to the rear head or the subsequent
ATP hydrolysis that is postulated to occur in the rear head while it is still bound to the microtubule)
causes the rear head (now containing bound ADP) to step forward past the bound front head. In both
gated front head and gated rear head models within the hand-over-hand mechanisms, internal strain in
the kinesin molecule is only used to reduce the affinity (of the leading head for ATP in the gated front
head model, or of the rear head for the microtubule in the gated rear head model). It is only in the RT
mechanism that elastic (twisting) strain energy is stored in the molecule and used to cause the forward
stepping of the rear head past the bound front head upon release of the stored strain energy, i.e., for
performance of useful external work, which in our opinion is a great leap in our thinking and a
progressive step forward for models of processive motility. In this sense, the RT energy storage
mechanism and the symmetric or asymmetric hand-over-hand models belong to different classes of
models of processive motility.
Finally the new molecular mechanism for processive motility is simpler, contains fewer
biochemical steps, is aesthetically pleasing and elegant, and, especially significant in the context of
processive motors, faster than previous models of processivity. The aspects discussed in this section
are also applicable to unconventional myosins, and in fact, the mechanism has also been readily
adapted to explain the processive motion of unconventional myosins such as myosin V on actin
filaments [10, 11] and in the field of myosin motility, it may play an important progressive role. A key
achievement of the RT energy storage mechanism in unconventional myosin motility is that it offers
an increase of efficiency of intracellular transport by a factor of two over all previous mechanisms, a
very large and significant improvement [11]. This is because, in all previous mechanisms, two ATP
molecules are consumed for a forward movement of the center of mass of the double-headed myosin
by 72 nm, while in the RT energy storage mechanism only a single ATP molecule is used to power the
center of mass of the myosin forward by 72 nm. An identical rotation-twist energy storage molecular
mechanism applies to the motility of the non-claret disjunctional (ncd) motor, with one extra turn in
the ncd neck coiled coil (compared to kinesin) constituting the relaxed state of ncd, thus accounting for
movement of the ncd motor towards the minus end of the microtubule. In conclusion, it can be stated
that this section has clearly indicated a large number of useful applications of the unified theory to
various processive molecular motors involved in intracellular motility, which is crucial to cell life.
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