HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
Biophys J, March 2002, p. 1679-1681, Vol. 82, No. 3
![]() |
LETTER |
---|
The regulation of muscle contraction is a complex process that involves
changes in both the organization of the troponin subunits and the
orientation of tropomyosin on actin. The changes in tropomyosin may
alter the manner in which myosin binds to actin, but, in our view,
the more important change is an allosteric alteration of the ability
of actin to participate in the catalysis of ATP hydrolysis. Because
the ATPase activity of the system is closely coupled to muscle
contraction, we have used the prediction of ATPase activity as our
guide to successful modeling. At the same time we recognize that it
is important to be consistent with the known structural changes of
the components and other data, including the manner in which myosin
binds to actin. The roots of the Hill model (the model that we
support), similar to that of the M and G model (McKillop and Geeves,
1993) came from an explanation of
the binding of myosin to actin. The Hill model began as a description
of the equilibrium binding, whereas the M and G model was fashioned
around the kinetics of binding.
The following observations are our primary benchmarks: 1) inhibition of
ATPase activity by tropomyosin-troponin occurs without displacement
of the S1-ATP and S1-ADP-Pi complexes from actin. (2) Inhibition is
characterized by a large change in the kcat for ATP
hydrolysis over a wide range of conditions. (3) Under conditions of
high occupancy of actin sites with nucleotide-free S1, the ATPase
activity is enhanced beyond that in the absence of regulatory
proteins. These observations have been reviewed earlier (Chalovich,
1992). The model of Hill et al.
(1980)
is consistent with
all of these observations (Hill et al., 1981
).
The M and G model does describe the binding of myosin to actin, but it is not
known if that model can predict the features of regulation of ATPase
activity that were outlined above. At a minimum it seems that an
allosteric change in actin activity must be incorporated into the M
and G model so that the effect of Ca2+ on the
kcat for ATP hydrolysis can be simulated. The evidence
for actin allostery is growing (Miki and Hozumi, 1991; Egelman, 2001
). Other models incorporating
allosterism, such as that proposed by Tobacman and Butters (2000)
, are likely to be successful
in simulating the regulation of ATPase activity.
Geeves and Lehrer imply that the Hill model is inconsistent with the known
structural states of the regulated actin filament. We assert that
there is no inconsistency (Fig. 1). The
ability of actin to accelerate the ATPase activity of myosin and the
ability of muscle to contract are dependent on whether each troponin
is bound to 0, 1, or 2 calcium ions. Binding of rigor
type S1 to regulated actin produces an even greater ATPase activity
than seen with calcium alone, and greater than that seen with
pure actin. This latter point is important in that it can not be
explained by simply blocking/unblocking the binding of myosin to
actin by the regulatory proteins. Several examples of this
potentiation of ATPase activity exist (Eisenberg and Weihing, 1970; Murray et al.,
1982
; Williams et al., 1988
; Fredricksen and
Chalovich, 2001
). The structural states that
have been studied thus far correspond to the low Ca2+-low
S1 occupancy state, the high Ca2+-low S1 occupancy state, and the low
Ca2+-high S1 occupancy state. These three states correspond to
states 1(0), 1(2), and 2(0) in the
Hill model where the subscripts denote the number of
Ca2+-ions bound to troponin. It is not known how the structure
of troponin and tropomyosin is changed when only
1 Ca2+ is bound to troponin.
|
Geeves and Lehrer believe that the positions of tropomyosin are more readily
explained in terms of a multiple-step binding of myosin to actin. We
do not think that there are scientific grounds for making this
distinction. It should be noted that incorporation of multiple-step
binding into the M and G model requires some assumptions. Data
supporting multiple-step binding of rigor S1 and S1-ADP to actin are
strong (Trybus and Taylor, 1980; Geeves and Halsall,
1987
). However, the idea that the
equilibrium constant for the first process, K1, is
the same for all nucleotide states is an approximation (Taylor,
1991
). Also, the M and G model
incorporates a blocked state to which no myosin can bind. Yet, there
are many data showing binding of S1-ATP-like states to actin in the
absence of Ca2+. Furthermore, in the current structural
view of the regulated actin filament, none of the positions of
tropomyosin overlap the putative site of electrostatic (low affinity)
binding of the S1-ATP and S1-ADP-Pi states (Vibert et al., 1997
). The Hill model does
not assume that all myosin nucleotide complexes bind along the
same two-step binding pathway and so is consistent with these
and other data that show a difference between S1-ATP-like and
S1-ADP-like states (Brenner et al., 1999
).
It is worth reiterating that we do not take exception to two-step binding of
myosin to actin. The question is: what is the relationship of this
two-step binding to regulation of muscle contraction? It is not
necessary to incorporate two-step binding to explain the regulation
of ATPase activity (Hill et al., 1981). The Hill model was
criticized because it was thought that the Hill model could not
explain the kinetics of binding of myosin to actin unless
multiple-step binding was included. We showed recently that the Hill
model could simulate the binding kinetics with either actin or S1 in
excess (Chen et al., 2001
). We did additional
simulations since the publication of that paper. It is also possible
to simulate the data in Figure 4 in the presence of
Ca2+ with k1 = 2 µM
1s
1 and
k1' = 10 s
1 (see Table 3 of the
original paper). That is, the value of K1 in the
Hill model need not change with Ca2+. Incidentally, while
responding to this letter we noticed a typographical error in Figure
1; L should
be written as
0/
0.
Geeves and Lehrer stated correctly that we have not modeled all of their data. It is possible that in future studies we may find cases where it is necessary to include multiple-step binding. This can be included into our model just as any additional intermediate nucleotide state in the cycle of ATP hydrolysis can be included should we wish to simulate a particular event. The inclusion of an additional binding step is not the only difference between our models. The differences are summarized in the legend to Figure 1.
The point was made that tropomyosin should be treated as a continuous cable,
but the Hill model assumed that a single tropomyosin covering seven
actin monomers acts as a unit. In the M and G model, the size of the
cooperative unit changes with conditions. Tobacman and Butters
(2000) have incorporated a very large
degree of flexibility into their model by allowing each actin monomer
to be treated independently. In the Hill model, the cooperativity is
altered by the strength of the interaction between adjacent
tropomyosin molecules (the parameter Y). It is also possible
to make the size of the cooperative unit variable in the Hill model
while still preserving the more fundamental differences with the M
and G model. It is mathematically nontrivial to rigorously
incorporate this flexibility into either the Hill model or the M and
G model. Because this level of detail was not necessary to simulate
the regulation of ATPase activity, it was not incorporated into our
model. We must not lose sight of the fact that this is a
model.
![]() |
FOOTNOTES |
---|
.
Submitted October 25, 2001, and accepted for publication November 13, 2001.
![]() |
REFERENCES |
---|
J. M. Chalovich*
B. Yan
B. Brenner
Y.-D. Chen
*Department of Biochemistry, The Brody School of Medicine at East Carolina University, Greenville, North Carolina
Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health Bethesda, Maryland
Department of Molecular and Cell Physiology, Medical School Hannover, Hannover, Germany
Biophys J, March 2002, p. 1679-1681, Vol. 82, No. 3
© 2002 by the Biophysical
Society 0006-3495/02/03/1679/03 $2.00
|
HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |