(Received for publication, September 26, 1996, and in revised form, February 26, 1997)
From the Departments of Internal Medicine and Biochemistry, The University of Iowa, Iowa City, Iowa 52242
The myosin subfragment 1 (S1) MgATPase rate was measured using thin filaments with known extents of Ca2+ binding controlled by varying the ratio of native cardiac troponin versus an inhibitory troponin with a mutation in the sole regulatory Ca2+ binding site of troponin C. Fractional MgATPase activation was less than the fraction of troponins that bound Ca2+, implying a cooperative effect of bound Ca2+ on cross-bridge cycling. Addition of phalloidin did not alter cooperative effects between bound Ca2+ molecules in the presence or absence of myosin S1. When the myosin S1 concentration was raised sufficiently to introduce cooperative myosin-myosin effects, lower Ca2+ concentrations were needed to activate the MgATPase rate. MgATPase activation remained less than Ca2+ binding, implying a true, not just an apparent, increase in Ca2+ affinity. MgATPase activation by Ca2+ was more cooperative than could be explained by cooperativeness of overall Ca2+ binding, the discrepancy between Ca2+ binding and MgATPase activation, or interactions between myosins. The results suggest the thin filament-myosin S1 MgATPase cycle requires calcium binding to adjacent troponin molecules and that this binding is cooperatively promoted by a single cycling cross-bridge. This mechanism is a potential explanation for Ca2+-mediated regulation of cross-bridge kinetics in muscle fibers.
Just as isometric tension is cooperatively activated by Ca2+, so is the cardiac thin filament-myosin S11 MgATPase rate, even under conditions where there is no cooperativity in myosin S1 binding (1, 2). A possible explanation for this behavior is that ATPase activation is proportional to Ca2+ binding to the many TnCs on each thin filament and that this calcium binding is cooperative (3). We tested the idea that Ca2+ binding and MgATPase activation are proportional and found to the contrary that they are not. Instead, fractional MgATPase activation was considerably less than fractional Ca2+ binding and more closely paralleled the number of pairs of adjacent troponins with Ca2+ bound to both.
To accomplish the above experiment, we employ a constitutively inhibitory form of cardiac troponin containing an inactivating mutation of the sole regulatory site of TnC, site II (4). This troponin, designated CBMII-Tn, results in a low thin filament-myosin S1 MgATPase rate that is not increased by the addition of Ca2+, analogous to previous results in which a similar TnC mutant was exchanged into myofibrils or muscle fibers (5-7). CBMII-Tn binds to actin-tropomyosin with an affinity identical to that of normal troponin in the absence of Ca2+. This binding, which is very tight for both normal troponin and for CBMII-Tn (4, 8, 9), permits the present report in which thin filaments are assembled with defined mixtures of normal troponin and CBMII-Tn. In the presence of saturating Ca2+ concentrations, such thin filaments exhibit a fractional saturation of the TnC regulatory sites that is experimentally controllable by varying the relative concentrations of the two forms of troponin. This permits assessment of Ca2+-regulated myosin S1 MgATPase activity in a novel manner as a function of bound Ca2+ rather than as a function of the free Ca2+.
In addition to varying the ratio of the two troponins, the myosin S1 and free Ca2+ concentrations are also systematically varied in the present study. The results imply a previously unrecognized aspect of the cooperativity of muscle activation, that rapid cycling of an isolated cross-bridge depends on Ca2+ binding to adjacent troponin molecules, and also suggest that cross-bridge cycling increases Ca2+ affinity at least locally, regardless of the density of myosin on the thin filament. The relationship between the data and various models of thin filament structure and regulation are discussed.
Cardiac troponin and tropomyosin were
purified from bovine heart using an ether powder technique (10). Rabbit
fast skeletal muscle F-actin was obtained by the method of Spudich and
Watt (11). Because bovine cardiac myosin S1 tends to precipitate at the
concentrations used in many of the experiments, most of the data were
obtained using rabbit fast skeletal muscle chymotryptic myosin S1
purified by ion exchange chromatography (12). Some of the experiments
(see Fig. 1) were repeated using bovine cardiac myosin S1 purified as
described previously (10). CBMII-Tn was prepared by reconstitution (13)
of the ternary troponin complex from bovine cardiac TnI and TnT (13)
and recombinant murine TnC mutant CBMII (4).
Assembly of Thin Filaments with Defined Fractional Saturation of TnC Regulatory Site II
F-actin, tropomyosin, and various mixtures
of troponin and CBMII-Tn were combined in the indicated ratios under
the ionic conditions used in the ATPase experiments. Since troponin
binds to the thin filament with an affinity of 3-5 × 108 M1 (8, 9) and the
µM amounts of the troponins included in the present
experiments were stoichiometric or slightly sub-stoichiometric relative
to the actin concentration, it was anticipated that essentially all of
both added forms of troponin would be bound to the thin filament. This
was tested by a sedimentation experiment. 15.5 µM
F-actin, 2 µM tropomyosin, 1 µM cardiac
troponin (nonradioactive), and 1 µM reconstituted
CBMII-Tn labeled with iodo[14C]acetic acid on TnT Cys-39
were combined in the presence of 100 µM
CaCl2, 5 mM Tris-HCl (pH 7.5), 3.5 mM MgCl2, 8 mM KCl, 1 mM dithiothreitol. The sample was sedimented in a TL100
centrifuge at 25 °C for 20 min at 35,000 rpm. Quantitative
SDS-polyacrylamide gel electrophoresis analysis by gel scanning and
standard curve comparison (14) and liquid scintillation counting of
samples indicated sedimentation of 94% of both troponins combined
(assessed by SDS-polyacrylamide gel electrophoresis) and 92% of the
labeled troponin (assessed by radioactivity). The fraction of actin
pelleting was similar, 93%. All three values agreed within
experimental error.
The ATPase rate was measured by the release
of radioactive phosphate from [-32P]ATP (15)
(NENTM Life Science Products, 2-7 × 107
cpm/µmol) with five or more time points obtained at variable intervals of 20, 60, or 120 s, depending upon the ATPase rate. Conditions and protein concentrations were varied as described in each
figure. The free Ca2+ concentration was varied using 0.5 mM
1,2-bis-(2-amino-5-bromo-phenoxy)ethane-N,N,N
,N
-tetraacetic acid as a Ca2+ chelator and variable concentrations of
CaCl2 (3).
This fraction is
equivalent to the fraction of adjacent troponin·troponin pairs in
contrast to the other possible adjacent pairs: CBMII-Tn·CBMII-Tn,
troponin·CBMII-Tn, and CBMII-Tn·troponin. The number of such
boundaries depends upon two factors: (i) the relative amounts of the
two troponins and (ii) the tendency of the two forms of troponin to
bind in a random or nonrandom pattern. The fractional Ca2+
saturation is = troponin/(troponin + CBMII-Tn). If binding were
random, then the fraction of adjacent pairs with Ca2+ bound
on both elements of the pair would simply equal
2.
However, prior work shows that when the two forms of troponin are
present in excess, they compete in a way that implies positive cooperativity and a small tendency for the two forms of troponin to
segregate from each other (4). This same tendency must be assumed to
exist in the present experiments, which differ in that the troponins
are added in a stoichiometric amount relative to the sites on the actin
filament.
For a closed linear filament including n troponins, with
p = n designated as the number of
troponins with bound Ca2+, the fraction of
tropomyosin·tropomyosin boundaries with Ca2+ bound on
both sides of the boundary can be shown to be as follows.
![]() |
(Eq. 1) |
Simulations (not shown) with Equation 1 show it to be indistinguishable
from f22 = 2 = (p/n)2 when Y = 1 as
expected because binding is random when Y has this value.
Also, Equation 1 gives negligibly different results for n = 30 and n = 200 unless Y
is much larger than is true for the present experiments. Finally,
Equation 1 is numerically indistinguishable from the implicit
relationship between f22 and
that arises
from independent derivations of the functions
f22(Ca2+) and
(Ca2+)
(16).
Fig. 1 shows the effect of altering the fractional Ca2+ saturation of the thin filament by varying the relative concentrations of troponin and CBMII-Tn. The normalized results of six experiments are shown, and it is clear that the relationship between Ca2+ binding and MgATPase rate activation is not a linear one (straight line). Rather, activation lags behind Ca2+ binding. When 50% of the troponins bind Ca2+ and 50% do not, the fractional MgATPase rate activation is only 30-35% that of the maximal stimulation observed for full Ca2+ saturation. The solid line, which does not fit the data, is the result expected if MgATPase activation were proportional to Ca2+ binding regardless of whether Ca2+ binding is cooperative.
The dashed lines in Fig. 1 are theoretical curves for the fraction of troponin·troponin boundaries with Ca2+ bound on both sides, which depends in part upon the degree of cooperativity in the binding of the two forms of troponin to the thin filament. The equilibrium constant Y governs the tendency of troponin and CBMII-Tn to separately cluster on the thin filament rather than bind randomly (3, 4). Y also dictates the cooperativity of Ca2+ binding to a thin filament containing only normal troponin, with Y > 1 indicating positive cooperativity. The experimentally determined value of Y is approximately 1.5 (4), and the long dashes in Fig. 1 correspond to this value. A slightly better fit is found with Y = 4, as indicated by the theoretical curve represented with shorter dashes. This might suggest that the true value for Y is greater than the previously measured value of about 1.5. A more likely explanation is that the degree of MgATPase rate activation does not precisely correspond to the fraction of troponin·troponin pairs that have Ca2+ on both sides. In either case, the deviation from linearity in Fig. 1 indicates that Ca2+ binding to more than one troponin is required for full actin activation of ATP hydrolysis at any given thin filament site.
An important aspect of the cooperative process illustrated in Fig. 1 is that it is not due to interactions between myosin S1 molecules. The myosin S1 concentration was only 1% that of the actin concentration, making myosin·myosin cooperativity unlikely. To confirm this experimentally, the MgATPase rate was shown to be linear with the myosin S1 concentration over a 16-fold range (0.25-4% that of the actin concentration). Linearity with myosin S1 concentration was shown both at pCa 5 and at pCa 5.89 (10-15% activation) for thin filaments with troponin and no CBMII-Tn and at pCa 5 for thin filaments with 50% troponin and 50% CBMII-Tn (data not shown).
The curvature in Fig. 1 is not attributable to hyperbolic dependence of the MgATPase rate on the regulated actin concentration in the presence of saturating Ca2+ concentrations (10, 17). Any such tendency would work in the reverse direction, producing a convex relationship or else tending to straighten a concave curve such as shown. This is not a major factor in Fig. 1 in any case because the MgATPase rates for the Ca2+-saturated thin filaments are about one-fourth to one-third the Vmax observed with saturating thin filament concentrations (data not shown). The actin concentration for the data sets in the figure are below the actin Kapp, which diminishes the importance of this consideration.
Phalloidin Does Not Alter Cooperative Interactions between Troponin MoleculesThe polymerization ability of the
troponin·tropomyosin complex (18-20) and atomic models of
actin·actin contacts in F-actin (4, 21) suggest that longitudinal
contacts along the thin filament are the most likely source of
cooperativity. However, this does not exclude the possibility that
cooperativity occurs across rather than along the actin filament. To
test this, we added phalloidin, which binds near the thin filament axis
with an orientation that is invariant with thin filament conformation (22) and both decreases thin filament flexibility and alters strand-strand interactions (23-25). Any cooperativity that was dependent upon such interactions might be changed by the addition of
phalloidin. The Fig. 2 inset shows that the
cooperative effect of bound Ca2+ on MgATPase rate
activation was similar to results found in the absence of phalloidin.
The results are indistinguishable from Fig. 1.
The main portion of Fig. 2 provides a measurement of Ca2+-dependent cooperative interactions between troponin molecules on the thin filament in the absence of myosin, again in the presence of phalloidin. This experiment differs from the ATPase data in that the sum of the troponin and CBMII-Tn concentrations is in constant excess relative to the sites on the thin filament. The two forms of troponin compete for binding sites on actin-tropomyosin, and the pattern of this competition implies that these binding sites (for troponin) interact in a manner sensitive to Ca2+. This experiment measures the value of the cooperativity parameter and equilibrium constant Y, which is found to be 1.7 ± 0.4 in the presence of phalloidin. This result implies weak Ca2+-sensitive interactions of a strength indistinguishable from that found previously in the absence of phalloidin (4). Curve-fitting of the data also results in a value for KR, the fold-increase in the affinity of troponin for actin·tropomyosin that results from Ca2+ dissociation from site II. KR is 2.4 ± 0.2 in the presence of phalloidin, which is indistinguishable from KR in the absence of phalloidin, 2.2 ± 0.1 (4).
Effects of Ca2+ Concentration and Myosin S1 Concentration on the Thin Filament-Myosin S1 MgATPase RateThe
experiment in Fig. 1 employed a mixture of normal troponin and
CBMII-Tn. An extrapolation of these results suggests that for a thin
filament with normal troponin only, the MgATPase rate will not increase
in proportion to Ca2+ binding as the free Ca2+
concentration is increased. Fig. 3A shows the
normalized MgATPase rate as a function of the free Ca2+
concentration in the presence of either low myosin S1 concentrations as
were also present in Fig. 1 (Fig. 3, ) or in the presence of much
higher myosin S1 concentrations (Fig. 3,×). The rightmost two
curves show the difference between Ca2+ binding
(short dashes) and adjacent Ca2+ pair binding
(solid curve, fit to MgATPase data (
)) according to Fig.
1 under conditions where myosin·myosin cooperativity is precluded by
low myosin S1 concentrations. The Kapp from the
ATPase curve underestimates the true binding constant, but this
discrepancy is small, 3.7 versus 2.4 × 105
M
1 for Kbinding
versus Kapp. The relationship between
these curves is determined by Fig. 1; if the short dash
curve in Fig. 3A is set as the independent variable and
the solid curve as the dependent variable, then a graph
describing the data in Fig. 1 is the result. However, the lines
actually were obtained by a best fit of Equation 1 to the experimental
data (
). Assuming the MgATPase rate is proportional to the fraction
of adjacent troponin pairs with Ca2+ on both sides, then
the best fit regulatory site Ca2+ affinity is 3.7 ± 0.6 × 105 M
1 and the
cooperativity parameter Y = 3.4 ± 0.9. The mean
value for Y from 10 such experiments was 5 ± 1, corresponding to a Hill coefficient of 2.2 (3) and similar to the level
of cooperativity reported previously (1, 3, 13, 26, 27).
The analysis in Fig. 3A indicates that there is little difference in the cooperative shapes for Ca2+ binding and for Ca2+ pair binding (the solid and short dash curves are equally steep). Similarly, if Y is set at a noncooperative value of 1, both curves are less steep but they remain parallel, and the relationship between them is still consistent with Fig. 1 (not shown). This indicates that Fig. 1 is consistent with the data in Fig. 3A, but only if overall Ca2+ binding to the thin filament regulatory sites is cooperative. Since this process is known to have little cooperativity for reconstituted thin filaments (3, 4, 28, 29), some other explanation will be needed to rationalize the larger cooperativity observed for MgATPase activation versus the free Ca2+ concentration (Fig. 3A and Ref. 1).
Another source of cooperativity in MgATPase assays is effects of myosin
S1 on the thin filament. Careful studies of Weber and co-workers (30)
using skeletal muscle regulatory proteins have shown increased MgATPase
rates, increased Ca2+ affinity, and apparent
Ca2+ affinity (32, 33). These effects are observed when the
myosin concentration is high relative to actin or when conditions favor strong actin-myosin bond formation (34). Fig. 3B shows the
potentiating effect of high myosin S1 concentrations on the thin
filament-myosin S1 MgATPase rate using cardiac regulatory proteins.
For an actin concentration of 5 µM, the MgATPase rate
deviated from linearity when the myosin S1 concentration was >3
µM. This deviation correlated with a shift in the
Ca2+ Kapp in MgATPase versus
pCa experiments. There was no shift for 3 µM myosin
S1 (not shown), a small shift for 5 µM myosin S1 (not shown), and a 2.5-fold shift in Kapp in the
presence of 10 µM myosin S1 (Fig. 3A, ×). The
apparent Ca2+ affinity from these and other titrations was
2.4 ± 0.2 × 105 M1 in
the presence of 0.3 µM myosin S1 and 6.0 ± 0.9 × 105 M
1 in the presence of 10 µM myosin S1.
Comparison among the three curves in Fig. 3A
shows that MgATPase rate activation of 10 µM myosin S1
(×) occurs at even lower Ca2+ concentrations than the
calculated Ca2+ saturation of the regulatory sites
(short dashes) when the myosin concentration is low. If the
high myosin S1 (×) versus low myosin S1 () MgATPase rate
shift had occurred without any change in true Ca2+ binding,
MgATPase activation would precede fractional Ca2+ binding.
This would be the opposite of the relationship in Fig. 1, a convex
rather than a concave curve. This possibility is evaluated and excluded
by Fig. 3C, which shows fractional MgATPase activation as a
function of bound Ca2+. Even in the presence of high myosin
S1 concentrations that "potentiate" the thin filament,
Ca2+ binding precedes fractional activation. Therefore, the
shift seen in Fig. 3A (× versus
) involves a
myosin-induced increase in Ca2+ affinity. However, there
may also be some change in the precise relationship between fractional
Ca2+ binding and fractional MgATPase rate activation; Fig.
3C appears to show less deviation from linearity than does
Fig. 1. In this regard, it should be noted that strongly bound
cross-bridges can activate the thin filament under appropriate
conditions, even in the absence of any Ca2+ binding
(31).
When
only 25% of the troponins on the thin filament are capable of binding
Ca2+, i.e. 75% of the troponin is of the form
CBMII-Tn, a gradual increase in the Ca2+ concentration
produces a small level of activation that is shown in Fig.
4. The figure is a normalized composite of four
experiments, and in all of them the noise precluded any assessment of
Y. The data is noisy because a 25:75 ratio of
troponin:CBMII-Tn produces only a low MgATPase rate (Fig. 1); the
average Ca2+-saturated rate is twice the EGTA rate for
these data sets. The solid curve is a noncooperative binding
isotherm. Comparison of the data points to this theoretical
curve suggests that cooperativity may actually be present (the data
deviates from the curve), but this may be an artifact of the
normalization of each data set.
The Kapp could be measured with enough
precision, 4.3 ± 1.2 × 105
M1, to permit comparison to the value found
for thin filaments with fully normal troponin, 2.4 ± 0.2 × 105 M
1 (n = 10, with representative data shown in Fig. 3A,
). This was
unexpected, since the CBMII-Tn might have cooperatively interacted with
adjacent troponin molecules to decrease Ca2+ affinity. It
is unclear why a modest increase in apparent affinity occurred instead,
but the effect is small in any case.
The thin filament has at least three conformations: an inhibited state in the presence of EGTA, a Ca2+-induced state, and an active state observed in the presence of strongly binding myosin cross-bridges (35-37). These structures have been compared with three-dimensional reconstructions of myosin S1-decorated thin filaments (38, 39), leading to the conclusion that tropomyosin interferes with the binding site for myosin S1 in the inhibited state and (to a lesser extent) in the Ca2+ state but not in the active state. Solution studies of cross-bridge thin filament binding support this conclusion (40) even though the initial stage of myosin S1·ATP binding to the thin filament is Ca2+-insensitive (10, 41). The structural data strongly suggest that completion of the MgATPase cycle requires a local conformational change in the thin filament from the Ca2+-induced state to a myosin-induced state. Otherwise, tropomyosin would prevent tight actin·myosin binding that is part of the cycle. To explain the deviation from linearity in Fig. 1, we now suggest that this single cross-bridge-induced conformational change requires Ca2+ binding to more than one troponin positioned on adjacent tropomyosin molecules along the thin filament. This interpretation parallels implications drawn from the very cooperative equilibrium binding of myosin S1 to the thin filament (42-44). Such binding is so cooperative that theoretical models (45, 46) explaining it invoked a myosin-promoted conformational change for the tropomyosin·troponin-7 actin unit that strongly depended upon the same myosin-induced conformational change in adjacent units. The kinetics of tight thin filament-myosin S1 binding suggest a similar conclusion (47). Longitudinal cooperativity of this type is also implied by studies of muscle fibers subjected to partial extraction of TnC (48-51). In fact, the nonlinear relationship in Fig. 1 is very similar to tension versus TnC data in skeletal muscle fibers (50). We suggest that this type of cooperative interaction between adjacent regulatory units also occurs during the MgATPase cycle, even for single, isolated myosin heads along the thin filament.
Strongly binding cross-bridges increase the affinity of Ca2+ for the thin filament (28, 31, 52-55). This process has been invoked to explain the leftward shift in MgATPase versus pCa curves that occurs with high myosin S1 concentrations or low ATP concentrations (32, 33) using skeletal muscle proteins. The most direct explanation for the shift would be a true change in Ca2+ affinity at the regulatory site(s) of TnC. The present data show that this shift also occurs when cardiac troponin·tropomyosin is used and, more importantly, confirms the previous interpretation. By studying the relationship between MgATPase rate and bound Ca2+ using CBMII-Tn, Fig. 3 demonstrates that this shift is caused primarily by a myosin-induced increase in affinity and not primarily by a change in the relationship between Ca2+ binding and activation.
Perhaps the greatest significance of the above conclusion is that it
suggests a mechanism for the problematic cooperativity of MgATPase
activation in the presence of low myosin S1 concentrations. This
cooperativity is difficult to explain because Ca2+ binding
per se is much less cooperative (4, 56) and because the
newly described cooperative effects of bound
Ca2+ (Fig. 1) fail to provide an explanation. This is
demonstrated in Fig. 3A, which shows the relationship
between cooperative activation by Ca2+ of the MgATPase rate
under low myosin S1 conditions (, solid line) and implied
fractional Ca2+ binding under the same conditions
(short dashes). The theoretical curves in Fig. 3A
are based upon the nearest neighbor analysis described under
"Experimental Procedures," but the general shape of the curves is
dictated by the data, not the equations. The steepness of the
solid curve is chosen to match the empirical, model-independent MgATPase observations (
), and the short
dash curve matches the corresponding extent of Ca2+
binding implied by Fig. 1. The fact that these curves are parallel shows that cooperative Ca2+ binding is implied by the
MgATPase data. If instead, one begins with the assumption that
Ca2+ binding is not cooperative, then a similar analysis
(curves not shown) demonstrates that MgATPase activation would have
little cooperativity, which is contrary to experimental results. These comparisons indicate that either overall Ca2+ binding is
more cooperative than has been found in most reports (reviewed in Ref.
56; see also Ref. 4) or, more likely, that the MgATPase rate
cooperativity involves a local (i.e. near the cross-bridge
binding site on the thin filament) myosin-induced increase in
Ca2+ binding. More specifically, we suggest that at
intermediate Ca2+ concentrations there is myosin-induced
binding of additional Ca2+ to the thin filament site(s)
adjacent to the cycling cross-bridge and that this phenomenon occurs
for isolated cross-bridges that are not acting in concert.
In a schematic representation of this model (Fig. 5),
three categories of actin monomers within the thin filament are
distinguished: actin sites with one nearby Ca2+-troponin,
sites with several successive Ca2+-troponins, and sites
with a strongly bound myosin S1 nearby. (To retain their separate
characteristics, the sites may need greater separation from each other
than shown in the figure.) All the troponins have the potential to bind
Ca2+ in the figure (no CBMII is present), but the free
Ca2+ concentration is subsaturating. The nonlinear results
in Fig. 3B and the myosin S1-induced shift in
Kapp in Fig. 3A are examples of the
third potentiated class of sites producing faster myosin cycling than
at other sites, as described previously by Weber and co-workers (30,
32). To explain the cooperative effect of the Ca2+
concentration on the MgATPase rate in the absence of potentiated sites, it is now proposed that Ca2+ binding is locally
cooperative at the first class of sites, where single myosins cycle,
and that this cross-bridge-induced binding of additional
Ca2+ is important for completion of the cycle.
A long-standing issue in muscle regulation is whether and to what extent the Ca2+ concentration alters cross-bridge kinetics (58) as opposed to controlling the recruitment of a variable number of cross-bridges, all with the same kinetics (59). More recent analyses of cross-bridge function have established that several processes have a graded response to the Ca2+ concentration (49, 60-67). The present data pertain to this problem. For example, force development occurs in several steps, including at least one transition before phosphate release (49, 63, 65, 68). Most studies indicate that the rate of force development is very sensitive to the Ca2+ concentration (49, 60, 61, 65, 66). These observations can be explained if the MgATPase model in Fig. 5 is also applicable in muscle fibers. An early kinetic step producing strong myosin binding can be expected to alter the position of the tropomyosin strand and raise the Ca2+ affinity of adjacent troponin(s) (36, 56). The Ca2+ dependence of force generation kinetics can be explained if the concentration-dependent binding of additional Ca2+ to adjacent troponin(s) alters the rate constants for completion of the power stroke and/or reversal of the early transition. This suggested mechanism for graded activation is an additional aspect of regulation, compatible with an additional control point dependent upon the density of bound cross-bridges (sites 2 and 3 in Fig. 5 have different properties) and with either steric or allosteric effects on recruitment (61, 69-71). Mechanical studies will be needed to explore this proposal. Investigation of the transient and steady state properties of muscle fibers in which native TnC has been partially replaced by CBMII may prove a useful approach.
We thank Earl Homsher for many informative discussions of Ca2+-mediated regulation and for helpful critique of an earlier version of this manuscript. We also thank Jay Chyung for valuable assistance during development of the theoretical model.