(Received for publication, September 15, 1995; and in revised form, January 17, 1996)
From the
We have examined the energetics of the interactions of two
kinesin constructs with nucleotide and microtubules to develop a
structural model of kinesin-dependent motility. Dimerization of the
constructs was found to reduce the maximum rate of the
microtubule-activated kinesin ATPase 5-fold. Beryllium fluoride and
aluminum fluoride also reduce this rate, and they increase the affinity
of kinesin for microtubules. By contrast, inorganic phosphate reduces the affinity of a dimeric kinesin construct for
microtubules. These findings are consistent with a model in which the
kinesin head can assume one of two conformations, ``strong''
or ``weak'' binding, determined by the nature of the
nucleotide that occupies the active site. Data for dimeric kinesin are
consistent with a model in which kinesinATP binds to the
microtubule in a strong state with positive cooperativity; hydrolysis
of ATP to ADP+P
leads to dissociation of one of the
attached heads and converts the second, attached head to a weak state;
and dissociation of phosphate allows the second head to reattach. These
results also argue that a large free energy change is associated with
formation of kinesin
ADP
P
and that this step is
the major pathway for dissociation of kinesin from the microtubule.
Molecular motors power a wide variety of physiologically important motile processes. These include movements of intracellular organelles, of chromosomes during mitosis and meiosis, and of cytoskeletal components during the process of ameboid motion (Vallee and Shpetner, 1990; Endow and Titus, 1992). These enzymes can be broadly classified into two categories: the myosins, which generate movement along actin-containing microfilaments; and a group of microtubule-based motors that include cytoplasmic dynein and the kinesin family of mechanoenzymes (Endow and Titus, 1992). The myosins remain the best studied group of molecular motors, and much effort has gone into identifying which of the steps in the actomyosin ATPase cycle are responsible for force generation.
Studying the nature of these
myosin-nucleotide intermediate states has been facilitated by the use
of transition metals, which bind to myosinADP stoichiometrically
and with high affinity (Goodno, 1979; Phan and Reisler, 1992; Maruta et al., 1993). Complexes of these metals with myosin
ADP
appear to mimic either the myosin
ATP or
myosin
ADP
P
structures (Fisher et al.,
1994). Thus, aluminum fluoride appears to induce a prehydrolytic
myosin-nucleotide transition state, whereas beryllium induces a
myosin
ATP structure (Fisher et al., 1994). The stability
of these complexes has allowed their study with spectroscopic, NMR, and
crystallographic methods and has provided insight into the structure of
the short lived myosin
ATP and myosin
ADP
P
intermediates. The validity of their use in studying
myosin-nucleotide intermediates has also been supported by the effects
of inorganic phosphate. Phosphate can bind to the active site of
myosin
ADP to generate a myosin
ADP
P
state,
and it has effects that are physiologically similar to those of
vanadate and aluminum fluoride in reducing the affinity of
myosin
ADP for actin (Dantzig and Goldman, 1985).
Compared with
the myosins, the kinesin family of microtubule motors appears to have
to comply with a different set of physiologic constraints. Kinesin
powers movement of organelles along microtubules and, unlike myosin,
appears to operate in isolation (Walker and Sheetz, 1993). Motility
studies in vitro are consistent with this assignment of
function, as single kinesin molecules are able to translocate along
microtubules for several micrometers at maximal velocity without
detaching (Howard et al., 1989). These differences in
physiology suggest that the nature of the force-generating
transition(s) in the kinesin-microtubule ATPase cycle may likewise be
different. Support for this comes from an in vitro motility
study (Romberg and Vale, 1993) which demonstrated that ATPS, (
)vanadate, and aluminum fluoride prolonged the lifetime of
attachment of kinesin to the microtubule; and increasing concentrations
of ADP shortened this lifetime. These findings were interpreted to mean
that the kinesin
ADP
P
state (presumably mimicked
by aluminum fluoride, vanadate, and ATP
S) was strongly bound,
whereas the kinesin
ADP state was weakly bound. However, more
recent kinetic studies (Gilbert et al., 1995) of the kinesin
ATPase cycle could be explained by either of two models. In one,
dissociation of the kinesin-microtubule complex occurs in the
kinesin
ADP
P
state, suggesting that this state
may be weakly bound, whereas in the other, dissociation occurs
in a transition involving a kinesin
ADP intermediate state:
where K is kinesin, M is microtubule, T is ATP, and D is ADP.
Determining which of the above models is the most accurate depiction
of the kinesin ATPase cycle requires direct measurements of the binding
affinities of the various kinesin-nucleotide intermediate states and
the equilibrium constants for the various kinesin-nucleotide
transitions. Efforts in this regard have been made by several
laboratories, which have examined the steady and pre-steady-state
kinetics of these transitions by utilizing bacterially expressed
recombinant fragments of kinesin which contain the amino-terminal motor
domain and variable amounts of the carboxyl-terminal tail (Huang and
Hackney, 1994; Huang et al., 1994; Hackney, 1994a, 1994b;
Gilbert and Johnson, 1993, 1994; Gilbert et al., 1995; Ma and
Taylor, 1995a, 1995b). These studies have confirmed previous
observations using intact kinesin and have extended them by
demonstrating that: 1) ATP binding, hydrolysis, and phosphate release
are rapid relative to subsequent steps in the hydrolysis cycle; 2)
kinesinADP is the predominant species in the system, and release
of ADP is the rate-limiting step; 3) microtubules accelerate ADP
release several thousandfold; and 4) for dimeric kinesin constructs
that contain ADP in the active site, microtubules accelerate release of
only one of the two bound ADP molecules. However, these studies have
not measured binding affinities of stable kinesin
ATP and
kinesin
ADP
P
intermediates and are thus not able
to assign microtubule affinities reliably to several of the
kinesin-nucleotide states depicted above.
In this study, we have
generated two bacterially expressed constructs of human kinesin and
examined the effects of ADP, aluminum fluoride, beryllium fluoride, and
inorganic phosphate on their binding affinities and steady-state ATPase
parameters. These studies indicate that ternary complexes of
kinesinADP with salts of aluminum and beryllium mimic the
kinesin
ATP state, which is strong binding; that inorganic
phosphate reduces the affinity of dimeric kinesin
ADP for
microtubules; and that the dissociation of the
kinesin
ADP
P
complex from microtubules
represents the major dissociation step in the kinesin-microtubule
ATPase mechanism.
Data for K332 ATPase rate versus microtubule concentration were fit to the Michaelis-Menten
equation to determine k and K
. For K413, rate versus microtubule
concentration data had to be corrected for the percentage of K413 which
was monomeric, by fitting the ATPase rate,
, to
where is the fraction of K413 which is monomeric, 1
-
is the fraction which is dimeric, and M is the
concentration of tubulin dimer. The value of
was determined by
equilibrium sedimentation studies of K413 which will be reported
elsewhere. (
)The values of K
and k
for monomeric K413 were determined by
measuring microtubule-activated ATPase activity at a K413 concentration
of 50 nM, where the construct is >95% monomeric.
The effect of EDTA treatment on
nucleotide binding stoichiometry was measured independently for K413 by
the following experiment. Twenty µM K413 in ATPase buffer
was incubated with a 30-fold molar excess of mant ADP for 4 h at 4
°C. The sample was dialyzed against 1,000 volumes of ATPase buffer,
and the remaining mant ADP was removed followed by gel filtration on
Sephadex G-25 (PD-10), which had been equilibrated in ATPase buffer.
The concentration of K413 was measured by its absorbance at 280 nm,
calculated from its amino acid composition ( = 33,650 M
cm
; Gilbert and Johnson(1993)), and the
concentration of mant ADP was measured by its absorbance at 356 nm
(
= 5,800 M
cm
; Hiratsuka(1983)).
Binding data for K332 could be fit to a binding isotherm of the form
where is the fractional binding, defined as the ratio of
sedimented K332 to total K332,
is the maximum
degree of binding, K
is the association constant,
and [M] is microtubule concentration. For K413
ADP
± beryllium fluoride, fitting required a correction for the
fraction of K413 which is dimeric versus monomeric. This was
accomplished by utilizing data from equilibrium sedimentation
studies.
Data were fit to , which assumes: 1)
that the fraction of K413 that is monomeric (
) binds to the
microtubule with affinity K
, determined by
measuring microtubule binding affinity at low K413 concentration, where
the construct is monomeric; 2) that the fraction of K413 which is
dimeric is 1 -
; 3) that each head of a free dimeric K413
molecule can bind to the microtubule affinity constant K
; and 4) that binding of the second head to the
microtubule occurs with affinity constant K
.
, the fractional binding of K413, is defined as the ratio of
unsedimented K413 to total K413. Under these conditions, the degree of
binding,
, is determined by the fractional binding of the
monomeric and dimeric species.
Expressing these quantities in terms of the various affinity constants reveals the following (Tanford, 1961).
The validity of using values of in which
were derived from equilibrium sedimentation studies was tested by
setting
as an independent variable in fitting to for the data in Fig. 3A. The value of
derived by this method for K413
ADP at a concentration of
250 nM (
= 0.62, r
=
0.96) was very close to that derived from equilibrium studies (
= 0.60; Footnote 2). Free energies of binding for dimeric K413
were calculated using the microscopic binding constant, K,
whose relationship to the individual macroscopic binding constants, K
,in is as follows (Tanford, 1961)
Figure 3:
Fractional binding versus tubulin
dimer concentration for kinesin constructs. Panel A, K413 at
250 nM (closed squares), 50 nM (open
triangles), and 250 nM K413 + 1 mM BeSO + 5 mM NaF (closed
circles). Data for K413 at 50 nM fit a rectangular
hyperbola, which defines a value of K
of
7.8 µM and stoichiometry of 0.9. Conditions: 20 mM HEPES, 50 mM potassium acetate, 5 mM MgCl
, 1 mM DTT, 1 mM NaN
, 1 mM MgADP, pH 7.20, 25 °C. Data for
K413
ADP ± beryllium fluoride at 250 nM were fit
to (see ``Experimental Procedures''), which
corrects for the reversible dimerization of this construct. Values of
were determined from sedimentation equilibrium studies (Footnote
2). This reveals 1/K
= 0.5 µM and 1/K
= 7.1 µM for
dimeric K413
ADP (stoichiometry 0.8) and 1/K
= 0.6 µM and 1/K
= 0.4 µM for dimeric K413
ADP +
beryllium fluoride (stoichiometry 0.8). Panel B, 100-200
nM K332 (closed squares), K332 + 1 mM BeSO
+ 5 mM NaF (closed
circles), K332 + 1 mM AlNO
+ 5
mM NaF (open triangles), K332 + 1 mM AMPPNP (closed diamonds), and K332 + 10 mM sodium phosphate (open squares). Conditions as in panel A. Data for each sample could be adequately fit to a
rectangular hyperbola, defining values of dissociation constants as
follows: K332
ADP, 20.8 µM (stoichiometry 0.9);
K332
ADP
BeF, 5.6 µM (stoichiometry 0.8);
K332
ADP
AlF, 1.4 µM (stoichiometry 0.8);
K332
AMPPNP, 1.1 µM (stoichiometry 0.8);
K332
ADP
P
, 18.2 µM (stoichiometry
0.8).
where n, the number of microtubule binding sites on
K413, is equal to 2. Thus, a prediction of the model described by is that the individual values of K are
highly correlated with each other. In the presence of cooperativity, K
may be larger (positive cooperativity) or
smaller (negative cooperativity) than expected from that predicted by
the value of K
. In the presence of cooperativity,
the free energy of binding of the second site to a microtubule would be
(Tanford, 1961)
where G
is the
intrinsic free energy of binding in the absence of cooperativity, and
G
(
) is the interaction free energy. The
free energy of binding to the second site on K413 was derived by using
the value of the microscopic constant, K (derived from K
) to determine
G
and by
using the difference between the predicted value of K
(determined from K
by assuming no
interactions) and that determined from .
which assumes that only one head of the K413 dimer can attach to
the microtubule when phosphate occupies the active site. In this
scheme, K is kinesin
ADP, MK
is
kinesin
ADP bound to microtubules, P
is inorganic
phosphate, and K
are association constants
for each step. The apparent dissociation constant, K
, at a given phosphate
concentration, [P
], is defined by
Titration of
the active site of K413 was accomplished by measuring the equilibrium
constant for binding of the fluorescent nucleotide derivatives mant ADP
and mant AMPPNP, using an equilibrium dialysis technique. Scatchard
plot analysis of the data (Fig. 1) demonstrates that K413 binds
mant ADP with one class of binding site, characterized by a
dissociation constant of 0.67 µM and stoichiometry of 0.80
mol of mant ADP/mol of head. By contrast, the dissociation constant of
mant AMPPNP, at 7.1 µM, is approximately 10-fold greater,
and the stoichiometry is 1.3 mol/mol of head. The effect of EDTA
treatment on K413 was investigated by examining the stoichiometry of
mant ADP binding under conditions where it was present in large molar
excess over K413 active sites, in the absence of EDTA. This revealed a
range of stoichiometries of 0.87-0.95 over five separate
measurements (data not shown). Thus, EDTA treatment does appear to
reduce the binding stoichiometry by approximately 8-19%. This
percentage reduction in the binding stoichiometry after EDTA treatment
is very similar to that measured previously, using
[H]ATP binding (Ma and Taylor, 1995b).
Figure 1: Binding of mant AMPPNP (closed circles) and mant ADP (closed boxes) to nucleotide-free K413. K413 was made nucleotide-free as described (Sadhu and Taylor, 1992) and mixed with a range of concentration of mant nucleotide. Free nucleotide was measured by an equilibrium dialysis method. Scatchard analysis of the data reveals that binding of mant ADP to K413 is characterized by a dissociation constant of 0.67 µM and a stoichiometry of 0.80; for mant AMPPNP, the corresponding values are 7.1 µM and 1.30.
As in the case
of the Drosophila constructs, the K413 and K332 MgATPase
activities are markedly activated by microtubules. At 50 nM K413, the construct is essentially entirely monomeric, and data in Fig. 2A fit conventional Michaelis-Menten kinetics,
defining values of K and k
of 3.5 µM and 35.1 s
,
respectively. Increasing the K413 concentration to 300 nM generated data that needed to be fit to . This defined
values of K
and k
for
dimeric K413 of 0.54 µM and 8.25 s
. Fig. 2B demonstrates the corresponding data for K332,
which defines values of K
and k
of 26.0 µM and 43.6
s
.
Figure 2:
ATPase rate versus tubulin dimer
concentration for kinesin constructs. Panel A, K413 at 300
nM (open squares), 50 nM (open
triangles), and 300 nM in the presence of 1 mM BeSO + 5 mM NaF (open circles).
Data for K413 at 50 nM fit Michaelis-Menten kinetics with k
= 35.1 s
and K
= 3.5 µM. Data for K413
± beryllium fluoride at 300 nM were fit to (see ``Experimental Procedures''), which corrects
for reversible dimerization of this construct. Values of
were
determined from sedimentation equilibrium studies (Footnote 2). This
reveals k
= 8.25 s
and K
= 0.54 µM for dimeric
K413 and k
= 0.83 s
and K
= 0.38 µM for
dimeric K413 + beryllium fluoride. Panel B, corresponding
data for K332 in the absence (closed diamonds) or presence of
1 mM AlNO
+ 5 mM NaF (open
squares), 1 mM BeSO
+ 5 mM NaF (open circles), and 0.5 mM sodium vanadate (open
triangles). Fitting to Michaelis-Menten kinetics reveals the
following: k
= 43.6 s
and K
= 26.0 µM for
K332; k
= 7.2 s
and K
= 4.0 µM for K332
+ beryllium fluoride; k
= 0.08
s
and K
= 3.7
µM for K332 + aluminum fluoride; and k
= 2.9 s
and K
= 5.8 µM for K332
+ sodium vanadate. Panel C, double-reciprocal plot of
data from panel B for K332 in the absence (open
squares) and presence (open circles) of 1 mM BeSO
+ 5 mM NaF. This reveals parallel
curves, as expected for uncompetitive inhibition, and defines a value
of K
of 41
µM.
The kinetics of the microtubule-activated
ATPase activity showed a marked ionic strength dependence. Raising the
ionic strength from 50 mM potassium acetate to 150 mM KCl raised the value of K for K413 to 80
µM and decreased the value of k
to
4 s
(data not shown). Corresponding data for K332
were 97 µM and 10 s
(data not shown).
Beryllium and aluminum fluoride, like
vanadate, reduce the affinity of myosinADP for actin, since
myosin
ADP
beryllium fluoride and
myosin
ADP
aluminum fluoride mimic the weakly bound
prehydrolytic myosin states (Fisher et al., 1994). The value
of the actin-activated k
is reduced in these
complexes because of the tight binding of the metals to the active site
(Maruta et al., 1993). Thus, if kinesin follows the same
behavior, it would be expected that beryllium fluoride and aluminum
fluoride should decrease the value of k
and
increase the value of K
for the
microtubule-activated kinesin ATPase. As Fig. 2B demonstrates, both transition metals reduce not only k
but also K
for K332,
implying that the kinesin
ADP
BeF and
kinesin
ADP
AlF states are more strongly bound than
kinesin
ADP. Experiments performed in the presence of 0.5 mM sodium vanadate also demonstrate that this transition metal
reduces both k
and K
(Fig. 2B and Table 1). Corresponding data
for K413 in the presence of beryllium fluoride are shown in Fig. 2A. A double-reciprocal plot of the
microtubule-activated K332 ATPase rate versus microtubule
concentration is shown in Fig. 2C for samples in the
absence and presence of 1 mM BeSO
+ 5 mM NaF. This demonstrates essentially parallel curves, as expected
for uncompetitive inhibition, and defines a value of K
for beryllium fluoride of 41 µM. Corresponding
values of K
for aluminum fluoride and vanadate are
1.7 and 35 µM, respectively. Thus, at aluminum and
beryllium concentrations of 1 mM, essentially all of the
active sites of K413
ADP and K332
ADP have transition metal
bound.
The decrease in the value of K implies that the transition metals increase the affinity of
kinesin
ADP for microtubules. This was confirmed by using
tritium-labeled K413 and K332 in an Airfuge binding assay. Data are
summarized in Fig. 3A for K413 at 250 nM and Fig. 3B for K332 and in Table 1. Dissociation
constants for K332
ADP are 5.6 µM in the presence of
beryllium fluoride and 1.4 µM in the presence of aluminum
fluoride, and both values are close to the corresponding values of K
(Table 1). Binding data for K332 in
the presence of 1 mM AMPPNP are nearly superimposable on those
for aluminum fluoride (Fig. 3B and Table 1).
Fitting of binding data for K413
ADP
beryllium fluoride to reveals values of 1/K
and
1/K
of 0.6 and 0.4 µM, respectively (Table 1).
Figure 4:
Effect
of phosphate concentration on K413ADP microtubule affinity. Data
were fit to (see ``Experimental Procedures'') to
determine the dissociation constants of K413
ADP
P
for microtubules (1/K
) and of phosphate for
K413
ADP (1/K
), and this reveals
1/K
= 17.0 µM and
1/K
= 0.8
mM.
This study utilized two constructs derived from a human
homologue of the Drosophila kinesin heavy chain. K413,
containing residues 1-413, is homologous to Drosophila 1-401, a construct that sedimentation equilibrium studies
have revealed is largely dimeric (Correia et al., 1995).
Similar conclusions have been reached with Drosophila 1-392 (Huang et al., 1994). The sedimentation
velocity behavior of K413 is consistent with its capacity to dimerize,
although sedimentation equilibrium studies indicate a dimerization
dissociation constant that is approximately 10-fold larger. This larger dimerization constant may reflect intrinsic
differences between the human and Drosophila sequences or may
be due to the steric and/or ionic effects of the hexahistidine sequence
at the extreme carboxyl terminus of the human construct, which is used
in affinity purification. By contrast, K332 is homologous to the
monomeric Drosophila construct containing residues 1-340
(Huang and Hackney, 1994; Correia et al., 1995), and this is
consistent with its sedimentation velocity behavior as well as its
elution behavior on Sephacryl S-300 and Superose 12 FPLC.
Both K332 and K413 possess an intrinsic MgATPase activity that is
very low. For both, microtubules enhance this ATPase activity several
thousandfold.
A striking feature of the results from
microtubule-activated ATPase studies is that the value of k for monomeric K413 is nearly 5-fold larger
than that for dimeric K413 and is only 19% less than that for the
monomeric construct K332. This finding resolves an apparent discrepancy
between the values of k
reported for Drosophila constructs that have been presumed to be dimeric.
The value of k
for dimeric K413 is close to that
reported for experiments with Drosophila K401 at a kinesin
concentration of 500 nM (10.9 s
; Gilbert
and Johnson(1993)). Equilibrium sedimentation studies have shown that
at this concentration, approximately 90% of the construct is dimeric
(Correia et al., 1995). More recent studies from same
laboratory reported a value of k
of 20
s
(Gilbert et al., 1995). However, in this
study, the K401 concentration was lower, at 200 nM. At this
concentration, approximately 18-20% of the K401 would be
monomeric (Correia et al., 1995). predicts that
an overall rate of 20 s
could be observed if k
for dimeric K401 is 10.9 s
,
and k
for monomeric K401 is approximately 55
s
, which is consistent with our own results. Other
experiments on a Drosophila construct that is 9 residues
shorter measured a value of k
of 47
s
, which is very similar to that for K332 and only
1.3-fold larger than the value of k
for
monomeric K413 (Hackney, 1994a). In this study, the concentration of
the kinesin construct used in the ATPase assay was 8.4 nM. It
is reasonable to assume that the association constant for dimerization
of this construct should be similar to or perhaps less than that for Drosophila K401, and given this, the published data would
indicate that this construct would be >75% monomeric (Correia et
al., 1995). Thus, our data clearly indicate that dimerization of
kinesin markedly inhibits the degree of microtubule activation.
An increase in enzymatic activity with increasing degrees of truncation has been reported not only for kinesin, but also for other microtubule motors, such as ncd (Stewart et al., 1993; Huang and Hackney, 1994; Huang et al., 1994; Chandra et al., 1993). One possible explanation for this inhibition is that the conformational changes that occur during the power stroke of the kinesin ATPase cycle may be linked to a rate-limiting rotation of one head relative to the other, which would be mediated through the dimerization segment contained within the carboxyl-terminal 81 residues of K413 (Fig. 5). Loss of dimerization, either by dilution of K413 or by truncation of the dimerization segment, would lower the energy barrier for this conformational change and accelerate this rate-limiting step.
Figure 5:
Structural model of the
kinesin:microtubule mechanochemical cycle. Panel A, model of
the K332microtubule interactions. The tubulin dimer is depicted
as the arrow-shaped structure, and its binding site for
kinesin is depicted as the vertically shaded box. The kinesin
monomer is depicted as the comma-shaped structure. In the
presence of ADP ± P
(MKD/MKD
P
), kinesin assumes a
weak binding conformation, symbolized by the rounded shape of
the microtubule-associated end of the molecule. When ATP occupies the
active site (MKT), kinesin assumes a strong binding
conformation, symbolized by the squared-off shape of the
microtubule-associated end of the molecule. Panel B, model of
the K413
microtubule interactions. In this figure, the two kinesin
heads are shaded differently to distinguish them. In addition,
the dimerization segment, containing portions of the
-helical tail
segments of each monomer, is shaded separately. In the absence
of nucleotide, or when ATP occupies the active site (MKT, MK), binding to the microtubule demonstrates positive
cooperativity, presumably because of a stabilizing of the orientation
of the second kinesin head (cross-hatched) by attachment of
the first head (dotted) to the microtubule binding site (vertically shaded box). Hydrolysis of ATP to ADP+P
(MKD
P
) leads to a
weakening of the affinity of the cross-hatched head of the
kinesin dimer. This is postulated to lead to a change in flexibility of
the dimerization segment, which allows a rotation of the second (dotted) head and prevents this head from attaching to the
microtubule. Dissociation of phosphate (MKD) allows the
unattached (dotted) head to reattach weakly to the next
available downstream binding site. This is presumed to stabilize the
interaction of the other (cross-hatched) head, whose
microtubule affinity is thereby enhanced. Dissociation of ADP from the
active sites enhances the affinity of the attached heads to that seen
in the presence of ATP and regenerates a fully attached
state.
Active site titrations with mant ADP and mant AMPPNP give the expected result of one class of binding site with an approximately 1:1 stoichiometry. The affinity of mant ADP for K413, determined in this study by equilibrium methods, is approximately 2 orders of magnitude lower than that measured with the complete heavy chain-light chain complex (Hackney, 1988; Sadhu and Taylor, 1992). The large difference in affinities between intact kinesin and the truncated constructs may reflect the trapping of nucleotide in the active site of intact kinesin when it assumes the folded conformation (see above; Hackney(1992)). In contrast to myosin, which binds AMPPNP with higher affinity than ADP (Trybus and Taylor, 1982), kinesin binds with the reverse order of affinities: the dissociation constant of mant AMPPNP binding to K413 is approximately 10 times larger than that for ADP (Fig. 1). This argues that kinesin interacts with nucleotide in a manner distinct from that for myosin.
The results of microtubule binding studies with the
monomeric construct K332 will be discussed first, as their
interpretation is more straightforward. Binding studies in the presence
of 1 mM MgADP yielded dissociation constants that are close to
the corresponding values of K. The
relationship between the midpoint of the ATPase titration and the
dissociation constant was explicitly developed in a previous study of
the actosubfragment 1 ATPase mechanism (Rosenfeld and Taylor, 1984),
and the four-state model derived in that study can be applied to the
case of kinesin as well. This model, as applied to kinesin, assumes
that the kinesin
ATP and kinesin
ADP
P
states are in rapid equilibrium with microtubules, an assumption
that is supported by recent studies (Gilbert et al., 1995).
According to this model, the relation between steady-state velocity and
microtubule concentration is
where k and k
are the weighted forward and reverse rate constants,
respectively, for the nucleotide hydrolysis step, and K
is the association
constant of kinesin
ADP
P
for the microtubule.
For both kinesin and the microtubule-kinesin complex, k
k
(Ma and
Taylor, 1995a, 1995b; Gilbert and Johnson, 1994), which leads to
where K =
1/K
. Since the model
predicts that the intrinsic affinities of kinesin
ADP and
kinesin
ADP
P
are essentially equal, this leads
to the prediction that for K332
ADP, K
K
, which is supported by the data in Table 1.
Experiments with K332ADP + beryllium
fluoride and aluminum fluoride support the contention that kinesin
interacts with nucleotide in a manner distinct from that for myosin.
Both transition metals were found to enhance the affinity of K332 for
microtubules. In the case of aluminum fluoride, the enhancement in
affinity was the same as that seen with AMPPNP. This contrasts markedly
with the case of myosins, where these transition metals, as well as
inorganic phosphate, reduce the affinity of myosin for actin,
as expected with the assignment of the myosin
ATP and
myosin
ADP
P
states as weak binding (Goodno and
Taylor, 1982; Yamakawa and Goldman, 1991; Phan and Reisler, 1992).
Previous studies of kinesin with aluminum fluoride and ATP
S in an in vitro motility assay suggested that kinesin has reversed
the cycle, that kinesin
ADP is weak binding and kinesin
ATP
and kinesin
ADP
P
are strong binding (Romberg and
Vale, 1993). Interpretation of these results and of our own, however,
depends on an unambiguous assignment of the conformation for
kinesin
ADP
aluminum fluoride and
kinesin
ADP
beryllium fluoride. The results of our study
indicate that aluminum and beryllium fluoride mimic prehydrolytic
kinesin-nucleotide states, which is supported by crystallographic data
from myosin (Fisher et al., 1994) and that these states are
strongly binding, the opposite of what is seen in myosin.
Binding
data for K332 can be interpreted by a relatively simple model, in which
monomeric kinesin can attach to the tubulin dimer in one of two
conformations: a strong binding state that releases approximately
-8.0 kcal/mol of binding free energy, and a weak binding state
that releases approximately -6.4 kcal/mol (Fig. 5A). The data in Table 1and Fig. 3B can then be explained by assuming that
K332ADP assumes a weak conformation, whereas K332
AMPPNP and
K332
ADP
aluminum fluoride assume the strong conformation.
Interpretation of the binding studies with K413 is more complicated
because of the reversible dimerization that occurs with this
species and the need to account for one-site versus two-site binding of the dimer. The model defined by gave a superior fit to the data (
= 0.011 for K413
ADP and K413
ADP
BeF) than
that for a simple hyperbolic isotherm (
=
0.10). However, initial attempts to fit the data to led to
large standard errors for 1/K
and
1/K
because of the high degree of correlation
between these parameters. This is consistent with the model described
by , since the values of K
and K
are related to each other (see
``Experimental Procedures''; Tanford(1961)). Improved fitting
required use of the Moore-Penrose inverse and led to values of K
and K
which had acceptable
errors. It is proposed that each head of the K413 dimer can assume a
strong or a weak conformation. Furthermore, it is presumed that
monomeric K413
ADP, like K332
ADP, attaches to the
microtubule via a weak interaction only. We propose that each head of
K413
ATP, mimicked by K413
ADP + beryllium fluoride or
aluminum fluoride, is in a strong conformation. If these two heads
behave in an identical and independent manner, then K
= (K
)/4 (Tanford, 1961). Fitting of
binding data, however, demonstrates that K
= 1.5(K
). This implies that binding
of the second head of the K413
ATP dimer demonstrates positive cooperativity and releases an additional -1.1 kcal/mol of
interaction-free energy. Although the structural basis for this
cooperative interaction was not determined from this study, one
possibility is that the binding of the first head stabilizes the
orientation of the second head so that its binding is more favorable.
Hydrolysis of ATP to ADP+P
is proposed to do two
things: it alters the conformation of both heads (to weak binding) as
well as their relative orientation, making it sterically impossible for
the second head to attach to the microtubule at all. Release of
phosphate, to generate a kinesin
ADP dimer, would allow the second
head to reattach. Results of fitting to indicate that for
K413
ADP, K
= (K
)/14.2, which is nearly four times smaller than
predicted from a noninteracting system. These data can be interpreted
to mean that phosphate release has no effect on the intrinsic
microtubule affinity of kinesin
ADP; rather, that weak attachment
of the second head (dotted in Fig. 5B)
stabilizes the interaction of the first head (cross-hatched in Fig. 5B) with the microtubule and enhances its
affinity. This model thus predicts that in the absence of a second
head, binding of kinesin
ADP should be weak and that phosphate
should have no effect. The data with K332 and monomeric K413 support
this ( Table 1and Fig. 5A). Furthermore, it is
proposed that the strong reattachment of one of the K413
ADP heads
to the microtubule generates force and accelerates release of its bound
nucleotide. This is consistent with the finding that K
K
for
K413
ADP and explains why microtubules accelerate the release of
bound ADP from only one head of dimeric kinesin constructs (Hackney,
1994b).
This model is also consistent with the relative affinities
of ADP versus AMPPNP for K413 (Fig. 1). Differences in
the energetics of microtubule binding between K413ATP (mimicked
by K413
AMPPNP or K413
ADP
beryllium fluoride) and
K413
ADP should be reflected in reciprocal differences in the
energetics of binding of AMPPNP versus ADP if the
conformational changes between K413
ADP and K413
ATP are
driven by nucleotide binding. Calculation from the nucleotide binding
data reveals a difference of 2.8 kcal/mol, which is close to the value
calculated from microtubule affinities, of 2.3 kcal/mol. Finally, the
effect of phosphate on K413
ADP is not due to a destabilizing of
microtubules, as some studies have shown that phosphate enhances microtubule stability, with an apparent dissociation constant of
25 mM (Carlier et al., 1988; Schlistra et
al., 1991), whereas others see no effect of inorganic phosphate
over this concentration range (Caplow et al., 1989).
These
results therefore predict that dissociation of the microtubule-kinesin
complex during the ATPase cycle should occur upon formation of the
weakly bound kinesinADP
P
complex, as suggested
by one of two models proposed on the basis of kinetic studies (Gilbert et al., 1995). This study provided a kinetic explanation for
processivity through the relatively slow rate of dissociation and the
rapid rate of rebinding of the weakly bound kinesin intermediate. Our
results demonstrate that the most weakly bound K413 intermediate
(K413
ADP
P
) has a dissociation constant for
microtubules which is still significantly lower than the local
concentration of tubulin intracellularly (Gilbert et al.,
1995). Thus, our data indicate that at least one head of the kinesin
dimer would likely remain attached to the microtubule at all times in
the ATPase cycle. It also predicts that there is a large free energy
change associated with hydrolysis of ATP in the kinesin-microtubule
complex. This free energy change presumably drives the power stroke and
if so, should be reflected in a significant conformational change in
the kinesin molecule. As a subsequent study will demonstrate, this can
be detected through fluorescent anisotropy decay studies on labeled
kinesin preparations.
The model presented here is also
consistent with several recent structural models of the
kinesin-microtubule and ncd-microtubule complex. Hydrolysis of ATP
would lead to dissociation of one head and pivoting of the attached
head toward the adjacent tubulin subunit. This would enable the
unattached head of the kinesin dimer, presumably containing ADP, to
attach to the next site along the microtubule protofilament. Since the
kinesin head is smaller than the tubulin heterodimer, attachment of the
second head could only occur in one direction because of simple steric
considerations. This model is similar to those proposed previously
(Hirose et al., 1995; Hackney, 1994b), except that it assigns
ATP hydrolysis and the production of kinesinADP
P
as the step that leads to detachment and pivoting of the kinesin
molecule. Directionality in this model could be explained by assuming
that the more weakly attached of the two kinesin
ATP heads is the
one that detaches after hydrolysis and that for kinesin, this is the
head which is closer to the(-) end. Thus, directionality becomes
an intrinsic consequence of the polarity of the microtubule lattice.
Reversal of directionality, as is seen in ncd, could then simply result
from reversing the affinities of the two heads in the ATP-bound state.