(Received for publication, May 21, 1996, and in revised form, October 17, 1996)
From the Department of Molecular Genetics and Cell Biology, The University of Chicago, Chicago, Illinois 60637
Kinetic and equilibrium properties are compared
for a monomeric kinesin construct (K332) and a dimeric construct
(K379). MtK379 has a low affinity (5 × 104
M1) and a high affinity (5 × 106 M
1) binding site for mant ADP
while MtK332 has a single low affinity site (5 × 104
M
1). Rate constants of dissociation of mant
ADP are <1 s
1 for the high affinity site and 75-100
s
1 for the low affinity site for MtK379. For MtK332, the
effective rate constant is 200-300 s
1. It is proposed
that the two heads of the dimer are different through the interaction
with the microtubule, a strongly bound head with low affinity for
2
-(3
)-O-(N-methylanthraniloyl) adenosine 5
-diphosphate (mant ADP), similar to the single strongly
bound head of the monomer and a weakly bound or detached head with high affinity for mant ADP. Rate of binding of mant ADP gave an
"S"-shaped dependence on concentration for MtK379 and a hyperbolic
dependence for MtK332. Binding of K379·mant ADP dimer to microtubules
releases only one mant ADP at a rate of 50 s
1. The second
strongly bound mant ADP is released by binding of nucleotides to the
other head. Rates are 100 s
1 for ATP, 30 s
1
for AMPPNP or ATP
S, and 2 s
1 for ADP. The rate of
binding of mant ATP to MtK379 showed an "S"-shaped concentration
dependence and limiting rate at zero concentration is <1
s
1 while MtK332 gave a hyperbolic dependence and limiting
rate of 100 s
1. The limiting rate is determined by the
rate of dissociation of mant ADP in the hydrolysis cycle. The evidence
is consistent with an interacting site model in which binding of ATP to
one head is required for release of ADP from the other head in the hydrolysis cycle. This model, in which the cycles are maintained partly
out of phase, is an extension of the alternating site model of Hackney
(Hackney, D. D. (1994) Proc. Nat. Acad. Sci. U. S. A. 91, 6865-6869). It provides a basis for a processive mechanism.
Kinesin is a processive motor which can travel a distance of
micrometers before dissociating from the microtubule (1, 2). An average
step of 8 nm for each ATPase cycle requires 60 cycles before
dissociation and a rate constant of dissociation of less than 0.3 s1 in order to move 1 µm at a velocity of 0.5 µm
s
1. The motor must also satisfy the conflicting
requirement that a single head detaches and reattaches with rate
constant greater than the cycle rate of 50 s
1 to couple
movement steps to the ATPase cycle. To meet these requirements, it is
likely that there is an interaction between heads, mediated by the
constraints of binding to neighboring microtubule sites, which
introduces a phase relation between the ATPase cycles of the two heads.
An interaction between heads was not found in a comparison of monomeric
and dimeric kinesin constructs in the absence of microtubules (3,
4).
Hackney (5) showed that an interaction occurs for the dissociation of ADP since binding of a kinesin-ADP dimer to microtubules leads to the rapid dissociation of ADP from only one head of the dimer. On this basis, an alternating cycle mechanism was proposed for microtubule kinesin ATPase.
Previous kinetic studies of the microtubule kinesin dimer ATPase (6, 7, 8) have been analyzed by treating the heads as essentially identical and independent except for the dissociation of the dimer which requires the detachment of both heads. Although the kinetic scheme has been used to describe possible motility mechanisms, the interaction between the heads is an essential property of the system, and it is necessary to develop a mechanism which takes head interactions into account.
In this work, the kinetic schemes of monomeric kinesin K3321 (3) and dimeric kinesin K379 (7) are compared to determine which steps in the cycle are affected by interaction between heads. The main difference is that the two heads of the dimer are not equivalent in their interactions with microtubule sites and substrates. Two equilibrium constants for ADP binding and two rate constants for ADP dissociation are observed which are equated with nucleotide binding to kinesin heads that are strongly versus weakly bound to microtubule sites. A mechanism is proposed in which the transition from strong to weak binding (or detachment) of one head is coupled to the transition from weak to strong binding of the other head. The scheme is similar to the alternating site model of Hackney (5), but a semiquantitative mechanism is developed based on measurements of the rate constants of the steps in the reaction. A preliminary report of the mant ADP displacement experiments has appeared (9).
The preparation of K332, K379, microtubules, and the substrates
2(3
)-mant ATP and 2
-mant, 3
-deoxy-ATP have been described (3).
Apyrase (Sigma, Grade VII) was used to hydrolyze free ADP or mant ADP. Equilibrium measurements of fluorescence were made in
a Perkin-Elmer MPF-44A fluorimeter. Kinetic measurements of
fluorescence were made in the apparatus described previously (4), and
the time course was fitted to one or more exponential terms using the
OLIS Kinfit program. Simulations were done using KINSIM. Microtubule
concentration is expressed as tubulin dimer concentration. K379
concentration is expressed as site concentration (42-kDa molecular
mass). The composition of the standard buffer is 25 mM
PIPES, pH 6.9, 2 mM MgCl2, 1 mM
EGTA, supplemented with NaCl as indicated. Nucleotide stock solutions
contained 1:1 MgCl2 to nucleotide.
The extent of dissociation of mant ADP on mixing
the monomer or dimer complex with microtubules was measured by the
fractional decrease in fluorescence enhancement. Free mant ADP was
separated from the protein-mant ADP complex by the centrifuge column
method (4) before the addition of microtubules. The fluorescence
enhancement decreased with microtubule concentration (Fig.
1). The dissociation was complete at 20 µM
microtubule concentration for K332. The addition of excess ATP gave no
further change in fluorescence. For K379, the decrease in fluorescence
reached a plateau at 20 µM microtubules corresponding to
approximately one-half of the total change in fluorescence. The
addition of ATP to the microtubule-kinesin dimer complex released the
remainder of the mant ADP.
In the experiments, the K379 site concentration is 2 µM; consequently, the free mant ADP concentration is 1 µM after dissociation of one mant ADP per dimer. This concentration appears to be sufficient to nearly saturate a high affinity ADP binding site. For concentrations of K379 of less than 1 µM, more than half of the mant ADP was released.
The rate of dissociation of this strongly bound mant ADP was determined
by addition of apyrase (20 units/ml). The fluorescence decreased with a
rate constant of 0.12 s1 (data not shown). The same
concentration of apyrase added to a myosin subfragment 1-mant ADP
complex at the same bound mant ADP concentration gave a rate constant
of 0.5 s
1 for mant ADP dissociation. Therefore, the
apyrase concentration is sufficient to track mant ADP release from the
MtK379 complex. The rate constant of dissociation of 0.12 s
1, and an apparent second order rate constant for mant
ADP binding of 1.5 µM
1 s
1
gives a binding constant of approximately 107
M
1 which accounts for the retention of the
mant ADP by a high affinity site.
The results imply that the binding of mant ADP to the MtK379 dimer
should fit two equilibrium constants. This inference was tested by
fluorescence titration (Fig. 2). The data for the MtK332 monomer fitted a hyberbola with binding constant of 6 × 104 M1. The enhancement of
fluorescence for the MtK379 dimer was much larger than for MtK332 at
low mant ADP concentrations. More than half of the maximum enhancement
was attained at 2 µM free mant ADP compared to less than
10% of the maximum value for MtK332. The smooth curve was obtained by
fitting the data to a model for binding to two independent sites. The
calculated equilibrium constants are 5 × 106
M
1 and 7 × 104
M
1.
The titration curves provide direct evidence for two classes of binding sites in the MtK379 complex, but the values of the binding constants are approximate. At low concentrations, the calculation of the free mant ADP concentration is subject to error while at a high ratio of mant ADP to sites the signal is small. The binding constant of mant ADP to the MtK332 complex may also be overestimated because the complex is partially dissociated by ADP (dissociation constant, 15 µM in 10 mM NaCl), and mant ADP is very strongly bound to K332. The apparent binding constant obtained from the titration at 30 µM tubulin concentration was 30% smaller than at 20 µM tubulin. The values obtained from the titration curves are in reasonable agreement with values calculated from the rate constants of association and dissociation of mant ADP.
Kinetic Measurements of mant ADP DissociationIt was shown
previously that reaction of the K379·mant ADP dimer with microtubules
plus ATP released both mant ADP molecules at a maximum rate of 30 to 35 s1 obtained by extrapolation of the rate constant
versus microtubule concentration (7). The same experimental
method gave a maximum rate of mant ADP dissociation of 110 s
1 for the K332 monomer (3).
Reaction of K379·mant ADP with microtubules in the absence of ATP
gave approximately half of the maximum fluorescence obtained with ATP
present. The rate constant is 34 s1 at a microtubule site
concentration of 15 µM (Fig.
3A, curve 1). This step is
followed by a small further release at a rate less than 0.5 s
1. The K379 site concentration is 0.5 µM,
and the slow step corresponds to a small extent of dissociation from
the high affinity site. The maximum rate for the first step obtained by
extrapolation of the assumed hyperbolic dependence of the rate constant
on microtubule concentration is 50 s
1 (data not
shown).
The K379·mant ADP complex mixed with microtubules plus a low
concentration of ATP gave a biphasic signal. For curve 2,
the concentration of ATP is 2.5 µM after mixing. The
signal was fitted by rate constants of 30 s1 and 5 s
1 and approximately equal amplitudes for the two steps.
The rate constant of the second step increased linearly with ATP
concentration over a low range of ATP concentrations. The variation in
rate corresponds to an apparent second order rate constant of 2 µM
1 s
1 which is in the range
expected for ATP binding to a MtK379 site.
At high concentrations of ATP, the data fitted a single exponential for
the release of all of the mant ADP. For curve 3, the ATP
concentration is 25 µM and the rate constant is 18 s1 at this microtubule concentration. The value is half
as large as the rate of dissociation of the first mant ADP in the
absence of ATP at the same microtubule concentration.
The results show that after dissociation of one mant ADP from the dimer
the second remains strongly bound and is released by a transition
induced by binding of ATP to the other head in agreement with the
findings of Hackney (5). Both mant ADP molecules are released if the
K379·mant ADP dimer is mixed with microtubules plus AMPPNP. The
maximum rate of mant ADP dissociation obtained by extrapolation
versus microtubule concentration is 18 s1
(data not shown). Therefore a hydrolysis step is not necessary for mant
ADP release from the strongly bound site although the extrapolated
maximum rate was twice as large for ATP compared to AMPPNP.
The observed rate of dissociation of the second mant ADP induced by nucleotide binding is affected by the rate of dissociation of the first mant ADP. Since it was shown that a MtK379 complex can be formed with one mant ADP bound at a high affinity site, this complex was used to measure the actual rate of mant ADP release by the binding of a nucleotide at the other site. The fluorescence signal for reaction of the complex with 1 mM ATP is shown in Fig. 3B (in 50 mM NaCl). The lag before release of mant ADP is 3 to 4 ms. Data collection is triggered 1.5 to 2 ms before flow stops in order to establish a base line. The actual lag before mant ADP release is 2 ms.
The fluorescence signal in Fig. 3B is fitted by a rate
constant of 95 s1. There is a small deviation from the
fit to one exponential term which indicates a small contribution from a
slow step. The amplitude of the slow phase increased with ionic
strength which increases the degree of dissociation of the MtK379
complex. Any K379 which dissociates with mant ADP still bound must
release the nucleotide by rebinding to the microtubule. In 25 mM NaCl, the dissociation of MtK379 by ATP is very small
and no slow phase was detected at this ionic strength.
The rates of dissociation of the strongly bound mant ADP by various
nucleotides are plotted in Fig. 4. ATP released the mant ADP at a rate of 100 s1 with a half-maximum rate at 40 µM which corresponds to the Km value
of MtK379 ATPase. The maximum rate was even larger for 2
-deoxy-ATP. The rate is 90 s
1 for GTP, but the half-maximum occurs at
a much higher concentration as expected from the very high
Km of MtK GTPase (10). AMPPNP and ATP
S, which are
nonhydrolyzed or slowly hydrolyzed nucleotides, gave maximum rates of
30-35 s
1. AMPPNP does not dissociate the MtK379 complex,
but the binding of mant AMPPNP does induce a first order transition
with rate constant of 40 s
1 (data not shown). Even ADP
produces a slow rate of dissociation of 2-3 s
1 which is
still 20 times larger than the spontaneous rate of 0.1 s
1.
Therefore, the binding of a nucleotide ligand to one head induces a
transition of the other head to a state in which mant ADP can
dissociate with a rate constant of more than 100 s1. The
slower rates for ligands other than ATP indicate that a transition
induced by these ligands is rate-limiting. Although the hydrolysis step
is not necessary, the rate of mant ADP dissociation appears to approach
the maximum value characteristic of the actual dissociation step only
for hydrolyzed ligands. Even for ATP the observed rate could
underestimate the actual rate constant of the ADP dissociation step. A
different experiment to obtain an independent estimate of the rate
constant of mant ADP dissociation is described below.
The binding
of mant ADP to MtK332 is relatively weak, and it was shown that the
observed rate constant of binding, extrapolated to zero concentration,
yielded a large apparent rate constant of mant ADP dissociation of up
to 300 s1 (3). The binding of mant ADP to nucleotide-free
MtK379 exhibited quite different kinetic behavior (Fig.
5). At low concentrations, the fluorescence signal
fitted one exponential term, but the observed rate constant was small.
At higher concentrations, the rate constant increased, but the plot
shows upward curvature. The initial slope of the plot gives an apparent
second order rate constant of 1.5 µM
1
s
1, and the line extrapolates to zero within experimental
error (±1 s
1). Therefore, the rate constant of mant ADP
dissociation is very small as expected for binding to a high affinity
site.
The experiments were repeated using the MtK379·ADP complex with the
high affinity site occupied by ADP. In this case, a small amplitude
signal with a large rate constant was obtained at low mant ADP
concentrations. Because part of this small signal is lost in the dead
time, the process was slowed by measuring the rate of binding at
10 °C (Fig. 5). The rate constant is 85 s1 at 5 µM mant ADP which is the lowest concentration that gave a
measurable signal. The data extrapolate to a value of 50 s
1. The binding of mant ADP to MtK332 at 10 °C is
included in the figure for comparison. The extrapolated value is about
200 s
1.
Therefore, MtK379 has a high affinity site for mant ADP (small rate
constant of mant ADP dissociation). The extrapolated value of the rate
constant of <1 s1 corresponds to spontaneous
dissociation from this high affinity site (0.1 s
1 based
on treatment with apyrase). If this site is already occupied, the mant
ADP binds to a low affinity site on the other head (large rate constant
of mant ADP dissociation). The large rate constant corresponds to
dissociation from a strongly bound head since it is similar to the rate
constant of dissociation from the strongly bound head of the MtK332
monomer complex. The rate constant of approximately 75 s
1
at 20 °C is also similar to the rate of release of mant ADP by the
binding of ATP. The correlation suggests that ATP induces a transition
of the ADP-containing head from a weakly bound state with high affinity
for ADP to a strongly bound state with low affinity for ADP.
The "S"-shaped plot of the rate constant versus mant ADP
concentration could provide further evidence for head interactions. However, mant ADP is a mixture of 2 and 3
isomers, and the S-shaped dependence might be explained by differences in the fluorescence signals of the isomers (3, 4). Experiments were done using the
3
-deoxy,2
-mant ADP isomer which does not give a biphasic fluorescence
signal (3). An S-shaped dependence was still obtained for the rate of
binding to MtK379 and a hyperbolic dependence for K379 alone (data not
shown).
Therefore, the S-shaped dependence requires different apparent
rate constants for binding to the two heads. Some upward curvature of
the plot is generated by a model in which the sites have binding constants of 5 × 106 M1 and
5 × 104 M
1 but do not
interact. The displacement of mant ADP from the strongly bound site by
ADP binding to the other head (Fig. 4) indicates that there is
interaction between heads, and this effect can increase the upward
curvature of the rate constant plot.
It has been
shown that the dependence of the rate constant of mant ATP binding to
MtK332 extrapolated to 100 s1 at zero concentration (3)
while for MtK379 the intercept was zero within experimental error and
the concentration dependence was S-shaped(7). The experiments were
repeated with 3
-deoxy,2
-mant ATP to eliminate possible complications
from the use of mixed isomers. The fluorescence signal fitted a single
exponential term, and the concentration dependence of the rate
constants is plotted in Fig. 6. The rate plot has a
large intercept for MtK332 and an essentially zero intercept and S-
shaped dependence for MtK379. Qualitatively, the results show the
presence of two kinds of sites for MtK379 and a single site for MtK332.
The analysis of the kinetics is more complex for the mant ATPase
reaction than for mant ADP binding, and the evidence is treated under
"Discussion."
The comparison of the kinetic properties of MtK332 monomer and
MtK379 dimer complexes showed significant differences which are
explained by an interacting head mechanism. The MtK332 monomer binds
mant ADP weakly (5 × 104
M1), and the effective rate of mant ADP
dissociation is 100 s
1 to 200 s
1 (3).
MtK379 has a high affinity mant ADP site (5 × 106
M
1) and a low affinity site similar in value
to the monomer complex. The rate constant of dissociation of mant ADP
is 0.1 s
1 for the high affinity site and 50 s
1 to 100 s
1 for the low affinity site.
A possible explanation of these results is that the K379 dimer is bound to the microtubule by only one head. Mant ADP would bind weakly to this head with values similar to the single strongly bound head of the monomer. The detached head would be equivalent to free kinesin and bind mant ADP with high affinity.
Various lines of evidence suggest that this explanation is too simple and that the second head is weakly bound. The rate of dissociation of mant ADP from the high affinity site is 4-5 times larger than the rate for free K332 or K379. The rate of dissociation of the MtK379 complex by ATP or ADP is 5 times slower than for the monomer even if the high affinity site is occupied by ADP.
The dissociation constants of K379 and its nucleotide complexes from microtubules as well as the Km for microtubule activation of the ATPase are at least 5 times smaller than for K332. If the binding constant of a single head is the same for both, then Kdimer = 2Kmono(1 + K2) where K2 is the effective equilibrium constant for binding of the second head. Because Kdimer is larger than 2Kmono, the second head is weakly bound but the value calculated for K2 is only 2 to 4; consequently, the second head is detached part of the time. If the microtubule lattice is saturated, binding by one head (one kinesin dimer per tubulin dimer) can still be more favorable than binding by both heads (one dimer per two tubulin dimers). Unless both heads were attached, at least transiently, it would be very difficult to explain the rapid dissociation of ADP from one head by the binding of ATP to the other head.
A better comparison would be between monomeric and dimeric forms of the same construct. This was not possible for K379 because of the small dimer dissociation constant but human K413 was reported to have a much larger dissociation constant and the dimer form is more strongly bound to microtubules than the monomer (11).
The reaction of mant ADP with the MtK332 monomer was described by a two-step mechanism (3)
![]() |
![]() |
The kinetic evidence is consistent with the mechanism
![]() |
![]() |
![]() |
It was shown previously that the rate of mant ADP dissociation is
30-35 s1 obtained from the reaction of the K379·mant
ADP dimer with microtubules plus ATP (7). In the absence of ATP, the
rate for the release of the first mant ADP was 50 s
1
while the second was dissociated by the action of ATP at approximately 100 s
1. The average rate for two steps in sequence is 33 s
1 which agrees with the previous result.
Further evidence for interaction between heads is given by the S-shaped concentration dependence of the rate of binding of mant ADP to the MtK379 dimer.
Head Interactions in the ATPase CycleThe discussion of the
evidence for interaction between heads is based on experiments on the
binding and dissociation of ADP. The kinetics of binding of mant ATP
provides evidence that head interactions also occur in the ATPase
cycle. The limiting rate constant for the binding of mant ATP,
extrapolated to zero concentration, is approximately 100 s1 for the MtK332 monomer and less than 1 s
1 for the MtK379 dimer (Fig. 6). An analysis of the
kinetic scheme is necessary to interpret this result. For the monomer
the minimum scheme is
![]() |
![]() |
The value of 100 s1 for the MtK332 monomer is consistent
with the value expected from the rate constants and the maximum steady state rate. If the heads of the MtK379 dimer were independent, the
intercept would be 30-40 s
1. Because the intercept is
essentially the effective rate of dissociation of ADP, the value of <1
s
1 means that at a low concentration mant ATP binds
primarily to the weakly bound or detached head and it is hydrolyzed to
mant ADP which remains bound to the high affinity site. Dissociation of
the mant ADP requires the binding and possibly the hydrolysis of ATP on
the other head. At low mant ATP concentrations, the rate of this
process is linear in ATP concentration (ka of 1-2
µM
1 s
1) and the limiting rate
extrapolates to nearly zero.
The positive curvature of the plot of rate constant versus concentration (Fig. 6) provides further evidence for the interaction between heads. Binding of mant ATP to the second head increases the rate of mant ADP release and thereby increases the observed rate constant. The ATPase results make the important point that the MtK379·mant ADP complex generated by hydrolysis behaves in the same way as the complex formed by binding mant ADP to MtK379.
The Interacting Site MechanismHackney (5) proposed an
alternating site mechanism for the ATPase cycle. Although the ratio of
steady state rates for MtK332 and MtK379 is a factor of 2 (50-60
s1 versus 25-30 s
1), this
correlation is probably a coincidence. The cycle on one head is delayed
at the state in which ADP is strongly bound. If the other head had to
bind ATP and complete most of a cycle, the release of ADP would be
delayed by 15-20 ms, but the lag in mant ADP release is less than 2 ms
in the experiments (Fig. 3B); thus, the coupled step must
occur early in the cycle. The scheme is better described as a cycle in
which the two heads are partly out of phase.
A processive run of the motor begins with the binding of the K·ADP dimer to the microtubule followed by the release of ADP from one head. The Mt symbol is omitted in the scheme since we consider transitions between associated states.
![]() |
![]() |
![]() |
![]() |
![]() |
Step 2 in which the heads interchange strongly and weakly bound states probably includes additional transitions which are not specified in the preliminary mechanism. However, the mechanism is highly processive if the transitions of the two heads are coupled such that one head of the dimer is always in a strongly bound state. It is proposed that efficient coupling is necessary for high processivity. Step 2 in the scheme may include an intermediate in which both heads are weakly bound and dissociation of the complex competes with the transition to a strongly bound state.
The pathway of dissociation of the dimer is still unclear. In the
monomer case, it was proposed that dissociation of K·ADP is the main
step and this pathway accounts for the small processivity of the
monomer (3). The rate of dissociation of MtK379 by ATP of 10 s1 is too large to be compatible with high processivity
(7).
The K560 dimer (9) has a much smaller rate of dissociation consistent with the high processivity of this construct (2), and this system is better suited to an investigation of the pathway of dissociation.
Relation of the Kinetic Scheme to Structural Studies and MotilityImage reconstruction of the microtubule-kinesin complex has provided evidence for two structural states. The distal part of the kinesin monomer tilts toward the plus end of the microtubule for the nucleotide-free or AMPPNP complex. while in the presence of ADP the distal part is more nearly perpendicular (12, 13). A similar correlation of the orientation in the presence or absence of ADP has also been observed for the actin-smooth muscle myosin subfragment 1 complex (14).
There are more than two biochemical states and some of them may not be
distinguishable at the resolution of the reconstructions. Also, if
there are two ADP states, the more stable state at equilibrium under
the conditions of sample preparation is likely to be observed. The
cartoon (Fig. 7) represents a possible correlation of
our biochemical scheme with structural proposals, but a number of cartoons can be drawn (5, 13).
The strongly and weakly bound states are assigned to tilted and more nearly perpendicular structural states. The model bears an obvious similarity to actomyosin models (14, 15, 16). Net motion in one direction requires an asymmetry in the interaction of the two heads with the microtubule lattice sites. It is introduced by assumption because it is determined by structure rather than biochemistry. Heads in a strong-weak state in the order shown in the figure are assumed to have a lower strain energy than a weak-strong state. The coupled transition of strong-weak to weak-strong requires dissociation of the trailing head and preferential rebinding to the next available lattice site in the positive direction.
In this type of model, the coupling of a positive step to the ATPase cycle is less than one to one because there is a non-zero probability for the heads to be on the same pair of tubulin dimer sites after completion of a cycle (a zero step). Also, the motor can stall at a finite ATPase cycle rate. The increase in strain energy for a positive step against an external force increases the probability of taking zero or negative steps which appears to be a property of the system (17).
We thank Aldona Rukuiza for expert technical assistance.