Evidence for two distinct affinities in the binding of divalent metal ions to myosin.

Binding of MS’, and Ca2+, and Mn”+ to myosin was determined by direct measurement of bound and free metals after equilibrium dialysis as well as by an indirect method involving changes in reactivity of a specific thiol group (so-called thiol-1) toward IV-ethylmaleimide caused by the metal ion binding to the protein. The results indicate that with all three metal ions alone, or in mixtures, two bound with relatively high affinity per myosin molecule (equilibrium constants > lo5 M-l). None was found to bind to isolated myosin heads devoid of light chain-2. Both the direct and indirect approach yielded two intrinsic equilibrium constants for all three metal ions at pH 7.6 and various conditions. At low ionic strength and 22-25°C the equilibrium constants were on average for Ca’+, K1 = 2.8 X 10’ M-’ and & = 3.2 X lo6 M-l; for M&+, K1 = 1.6 x 10’ M-’ and I& = 6.1 X lo5 MI’; and for Mn’+, K1 = 3.0 X lo6 M-’ and Kz = 5.1 X lo5 M-l. Two distinct equilibrium constants of similar values were also found for binding of Mg” to myosin in the presence of 2 to 5 mM ADP. Computation analyses of equilibrium data from metal ion mixtures are compatible with the assumption that Mg” and Ca2+ compete independently of one another with their two intrinsic affinity constants for the two binding sites of myosin. Based on this simple model about 50% of the metal binding sites of myosin would be occupied by Ca2+ at around 10m5 M free calcium and 10e3 M free magnesium ion concentrations. At present it cannot be decided whether the two distinct affinities in myosin for metal ion binding originate from pre-existing asymmetry in the two heads of a myosin molecule or whether negative cooperativity is operative between the two binding sites.


Binding
of MS', and Ca2+, and Mn"+ to myosin was determined by direct measurement of bound and free metals after equilibrium dialysis as well as by an indirect method involving changes in reactivity of a specific thiol group (so-called thiol-1) toward IV-ethylmaleimide caused by the metal ion binding to the protein.
The results indicate that with all three metal ions alone, or in mixtures, two bound with relatively high affinity per myosin molecule (equilibrium constants > lo5 M-l). None was found to bind to isolated myosin heads devoid of light chain-2.
Both the direct and indirect approach yielded two intrinsic equilibrium constants for all three metal ions at pH 7.6 and various conditions. At low ionic strength and 22-25°C the equilibrium constants were on average for Ca'+, K1 = 2.8 X 10' M-' and & = 3.2 X lo6 M-l; for M&+, K1 = 1.6 x 10' M-' and I& = 6.1 X lo5 MI'; and for Mn'+, K1 = 3.0 X lo6 M-' and Kz = 5.1 X lo5 M-l. Two distinct equilibrium constants of similar values were also found for binding of Mg" to myosin in the presence of 2 to 5 mM ADP. Computation analyses of equilibrium data from metal ion mixtures are compatible with the assumption that Mg" and Ca2+ compete independently of one another with their two intrinsic affinity constants for the two binding sites of myosin.
Based on this simple model about 50% of the metal binding sites of myosin would be occupied by Ca2+ at around 10m5 M free calcium and 10e3 M free magnesium ion concentrations. At present it cannot be decided whether the two distinct affinities in myosin for metal ion binding originate from pre-existing asymmetry in the two heads of a myosin molecule or whether negative cooperativity is operative between the two binding sites.
It is now accepted that the light chain-2 subunits of myosin (the so-called 5,5'-dithiobis (2- skeletal myosin may also have some regulatory function in addition to that derived from the regulatory components, troponin and tropomyosin on the actin filament (6). Myosinlinked regulation has been described in vertebrate smooth muscle (7), and in some cases evidence for a dual system of regulation involving both myosin and actin filaments has been found (8). Several studies suggest that in vertebrate striated muscles, Ca2+ regulatory systems are also simultaneously operating on both filaments (2,9,10). Here, the binding sites for calcium ions on the myosin filament are very likely located in the light chain-2, since studies on the binding of isolated myosin heads, containing this light chain, to actin indicate that actomyosin interaction is looser in the presence of calcium ions than in their absence (11). On the other hand, Ca4+ regulation of the actin-activated ATPase of myosin deficient in light chain-2 was found to be impaired (12,13). But since the cause of this latter effect has been attributed to changes in the affinity of the troponin complex, and not myosin, for the calcium ions, the picture still remains unclear. A further complication is that in the muscle cell the free magnesium ion concentration may be in the range 0.1 to several millimolar whereas the calcium ion concentration rises from values below 10m7 at rest to lo-" to 10m4 M on activation. Thus, the influence of the constant high magnesium ion concentration on the binding sites for Ca2+ on the myosin filament needs investigation. If Mg'+ should also show significant binding it is then important to determine the distribution of myosin types possessing possible combinations of both ions at the physiologically relevant conditions. Direct binding studies using 45Ca2+ done in the presence of variable magnesium ion concentrations indicate that about 2 mol of Ca'+ bind/m01 of intact myosin with apparent equilibrium constants in the range of lo" to 10" M-' (2,14,15). Bremel and Weber (14), using a metal ion buffer system, first noticed that at least one Ca"' binds with a much higher apparent constant of the order of 10" Mm', when magnesium ions are in the micromolar concentration range. However, there are also reports of lower values around lo" to 10" M-' found in the absence of magnesium ions (16,17). On the other hand, the binding of Mg" to myosin has been studied by only indirect means.
Mg'+, in competition with Mn2+, was found to have a relatively low affinity to intact myosin of around l@' M-' (16). But, in contrast, values between 10" and 10' Mm' were observed from the quenching of the intrinsic fluorescence of heavy meromyosin (18). Earlier investigations on the inhibitory effects of magnesium ions on Ca"-and K'-dependent myosin ATPases led to claims of a variety of affinities for these ions to myosin (17,19,20).
In an attempt to clarify the confusion surrounding the binding of Mg'+, we carried logical concentrations, since, in view of the possibility of a regulatory role for calcium ions mentioned above, some interplay between these ions may be expected. Apart from a recent short report (21), no systematic study of direct determination of ions bound to myosin, especially in the presence of both Mg'+ and Cal+, has appeared.
We report here on the binding of the divalent cations Mg"+, Ca"', and Mn2+ to isolated myosin using both the direct method of atomic absorption spectroscopy and the indirect method of thiol group reactivity. The latter technique follows the change in reactivity of the essential thiol-1 group of myosin, whose modification inactivates the K'-dependent ATPase but activates the Ca"-dependent ATPase (22) when tested at high ionic strength (23). Besides the essential thiol-1 and thiol-2 groups, myosin contains so-called nonessential thiol-3 groups which have all been shown to reside in the heavy chain ar.d whose reactivities are allosterically affected by ligand binding (24). This indirect approach has also been used to monitor the binding of Ca"' to troponin-C (25), and responses of spin labels attached to thiol groups have been used to fQllow the binding of these ions to troponin-C (13, 14) and to the isolated myosin light chain-2 (3,26).
In the work presented here both the direct and indirect approaches yielded 2 binding site/myosin molecule of high but distinctly different affinities for all three ions. The results suggest that, even if the binding may take place directly on light chain-2, the microenvironment of a portion of the heavy chains is affected. All three ions displayed exchangeability by direct competition for the 2 high affinity sites/myosin. Analytical computation revealed further, that the ions retained their respective intrinsic affinities unaffected when present in mixtures. In particular, it could be shown that about 50% of the binding sites may be occupied by Ca" under conditions resembling those in activated muscle.  least square procedure as well as iteration calculations also based on the minimum least square sum were then applied to the equilibrium dialysis data for evaluation of binding constants. All computations were run on a computer model PDP 11/20 (Digital Equipment Corp.).

Effect ofDivalent
Cations on the Reactivity of the Essential Thiol-1 Group of Myosin-It has been shown that out of the four essential thiol groups in myosin, a thiol-1 always reacts first with MalNet at 25°C irrespective of ionic strength or the presence of metal ions and nucleotides (23). In the absence of nucleotides, however, a thiol-3 group, whose blockage does not affect the enzymic properties, reacts with MalNet as fast as, or even faster, than the essential thiol-1 group (33). time of stopping the reaction. This indicates that the presence of Mgzc increases the reactivity of the essential thiol-1 group at the expense of the nonessential thiol-3 group which reacts along with it. When the alkylation was performed at low myosin concentration but at three or four different MalNet concentrations for a fixed time of 5 min, the slopes of the inactivation plots were found to be linear. In this way it was possible to study quantitatively the effect of intermediate magnesium ion concentrations on the alkylation reaction as illustrated in Fig. 2. A metal ion buffer system was used in order to avoid errors due to trace contaminations of the ions. The average slopes in the extreme cases of EDTA alone (curue a) and with MgClz in excess over EDTA (curve h) were 1. 44 + 0.72 (26 experiments) and 8.14 f 1.32 (20 experiments), respectively. This effect was found not to be due simply to changes in ionic strength. The increase in ionic strength due to the addition of excess MgClt (5 mM) over EDTA (2 IIIM) was usually compensated for by lowering the KC1 concentration by 10 mu. In any case, the effect of magnesium ions on the inactivation rates, observed after incubation of myosin with MalNet in their presence, was not measurably altered by varying the total ionic strength from 0.05 up to 0.15. Even at still higher KC1 concentrations (0.5 to 1.0 M), under which condition myosin is dissolved, increasing the magnesium ion concentration produced gradual increases in inactivation rates, although the essential thiol groups show a slightly slower reaction rate toward MalNet.
The inactivation of the Kf-dependent ATPase is the result of blockage of essential thiol groups located in the heavy chains of myosin (24). On the other hand, the metal ion binding sites are located in the light chains-2 and thus the ion binding seems to alter the interaction between the light and heavy chains. A similar conclusion has been drawn from studies of Mg2' binding to heavy meromyosin (38), in which the quenching of intrinsic fluorescence in heavy meromyosin and the isolated light chain-2 were compared. The increase in the value of the inactivation rate with increasing added MgClz described above, approaches a maximum value observed when the MgClz concentration is about equimolar with that of EDTA, further addition up to 15 mM producing no further effect. Thus, an intermediate value of the inactivation slope, found at an intermediate metal ion concentration between none and excess added ions, was taken as a direct measure of the saturation fraction of cation-protein complex. In this way the relative slopes of a series of K+-dependent ATPase inactivation lines, as the experiment in Fig. 2 illustrates, may be plotted as a function of the calculated free Mg2+ concentration (Fig. 3A). The change in intrinsic fluorescence induced by the binding of these ions to heavy meromyosin has been graphically analyzed elsewhere in A similar way (18). The sharp bend in the curve of the resulting plot implies two classes of binding sites (39), one operating with high affinity over the low range of free metal ion concentration (<l pM) and the other with lower affinity over the higher ligand range (1 to 100 PM).
An opposite behavior with respect to thiol group reactivity is observed when the same experiments are carried out in the presence of nucleotides. Since the binding of ADP to myosin in the presence of EDTA renders the thiol-1 the most reactive of all groups (33), a fast inactivation slope of 8.15 f 1.20 (9  experiments), is found for the K+-dependent ATPase in the absence of Mg2+ at low ionic strength end 25°C. Addition of MgZf leads here to a decrease in the inactitlation slope, reflecting a decline in the reactivity of the thiol-1 group. In the presence of 5 mM MgClz and 2.5 mM ADP the average inactivation slope was found to be 4.12 f 0.47 (11 experiments). Plotting as before intermediate values as percentage change from an experiment consisting of a series of inactivation slopes measured between the extremes of no added Mg"+ and Mg2+ ions in excess of EDTA, produced a saturation curve analogous in form to that found in the absence of ADP (Fig., 3B).
Since in these experiments the bound amount of Mg"+ could not be obtained from the difference between total and free concentration of metal ion, it was not possible to use a Scatchard plot or related plots (40) for analyzing the data. Transformation of the experimental points from Fig. 3 by plotting the ratio of the fraction of protein-ion complex to that of free protein against free ion concentration yields two linear portions of the overall curve (Fig. 4, A and B). The slopes of these lines are equal to the equilibrium constants in the high and low affinity range. In the particular experiments shown in Fig.  4 their values are 8.32 X 10" and 1.10 x lo5 M-' for Mg"' binding alone as well as 1.67 x lo7 and 2.10 x 10" Mm' for Mg"+ binding in the presence of ADP.
The binding of Mg2+ was also examined in the same way at 0.6 M KC1 when myosin is dissolved. Here again two affinities for the metal ion binding were apparent. Average values for the equilibrium constants from several experiments for binding of magnesium and calcium ions under different conditions are summarized in Table I  Equilibrium constants Equilibrium constants for the binding of Mg*+ and Ca*+ ions to myosin determined by both thiol group reactivity and equilibrium dialysis techniques at pH 7.6 as described under "Methods." The evaluation of Kl and KS from the thiol group method is described in the text. K, and Kz as well as the number of binding sites (nl and n2) of equilibrium dialysis data were derived from linear regressions of Scatchard plots. Averages of 2 to 10 experiments each. Method  affinity const.ant between different experiments under one set of conditions, although some larger scatter was observed for the low affinity constant. But even in the experiments of Mg2+ binding in the presence of ADP or at high ionic strength the two constants remained always separated from one another by a factor of at least 10. At low ionic strength the low affinity constant was around 100 and 200 times lower than the high affinity one for magnesium and calcium ion binding, respectively. As this method does not, however, yield information on the number of binding sites in the two affinity ranges it needs to be complemented by direct determinations of the amount of bound metal ions.
Equilibrium Binding Studies-The amount of bound as well as free ions (Mg" or Ca2+) were measured after equilibrium dialysis by atomic absorption spectroscopy. Treating the results according to Scatchard (41) revealed rather sharp bending of the plots in a hyperbolic fashion in all cases. Such a Scatchard plot for Mg2+ binding in the presence of ADP is shown in Fig. 5. Both sections of data could be well fitted by a straight line. These lines had virtually the same slopes as the tangents to the computed curve fit (42) at the axes as well as intercepts on the abscissa. As expected, this correspondence was valid only in those cases where the affinities of the two classes of sites differed sufficiently, as in this example. A complication may arise in this particular case from the fact that the Mg . ADP complex also binds to myosin. At the point where, for example, 1.42 mol of Mg2+ were bound per mol of myosin, the concentration of the Mg . ADP complex was computed to be 24 PM, i.e. about 1% of the total 2 mM ADP present. Since the binding constant for ADP to myosin is only around 1 order of magnitude lower than that for Mg-ADP (43), binding of magnesium ions via the Mg . ADP complex to the active sites can be neglected. Under these conditions, and certainly at lower Mg 2+ ion concentrations, the active sites would be occupied almost exclusively with ADP only. Hence, there is no measurable contribution to the total amount of Mg2+ found bound to myosin from these ions in the Mg-ADP complex. That this is so is supported by the similar stoichiometry and affinity constants for magnesium ion binding found in the absence of ADP. These parameters for magnesium and calcium ion binding under different conditions are summarized in Table I.
The values for the higher and lower affinity constants from equilibrium dialysis and the indirect alkylation technique show a good correspondence.
Just one cation binds with each affinity per myosin. In the equilibrium technique the constant of the higher affinity and the number for the two binding sites varied by no more than &20% in different experiments. Again a larger variation occurred in the constant of lower affinity.
The data in Table I are composed from experiments involving a dozen different myosin preparations some of which were prepared in the presence of MgClz and dithiothreitol instead of EDTA. However, no significant differences could be seen between protein preparations.
Beside the fact that the two equilibrium constants differ under all conditions significantly, it emerges from both techniques that for binding of Mg2+ at low ionic strength and 25°C they are closer to one another when ADP was present. At 25" and 4"C, the fist calcium ion binds with higher affinity than Mg2+, whereas the second one binds with a comparable affinity to that of the second magnesium ion.
In the muscle cell the concentration of Ca'+ fluctuates according to the states of activation and rest. Since the concentration of ionized Mg2+ is not known precisely (44) binding of Ca2' was also measured in the presence of different concentrations of Mg2+. The higher the magnesium ion concentration the more the points tended to approach a straight line in the Scatchard plot whose slope indicated a lower apparent affinity constant for the Ca2+ binding when magnesium ions were present. In the case with 1 mM MgC12, which is shown in

Harrington
(2) who measured Ca"' binding to myosin in the presence of 0.3 mM MgC12 by a method based on the partition of radioactive 45Ca2' between an insoluble metal ion chelator and the protein in solution. If the linear regression comprises only the fist 8 points in the Scatchard plot of Fig. 6 the resulting equilibrium constant of 8.46 X lo4 M-' is still more than three orders of magnitude lower than for the binding of the first calcium ion in the absence of MgCl,. Points obtained at higher calcium ion concentrations indicate binding at sites of very low affinity in addition to the two sites of high affinity as also reported by others (2,4,14,16).
The fact that the difference in K1 and Kz found in the absence of magnesium ions disappears in their presence in the millimolar concentration range immediately raises the question of the mode of action of these ions on the Ca" binding. Curve fitting according to a nonlinear least square program was therefore carried out on the binding data when the amount of Ca" bound/myosin was plotted against logarithm of free calcium ion concentration.
The free magnesium ion concentration and the values of their binding constants, namely 1 X lo7 and 5 X 10" Mm' for K, and Kg, respectively (rounded values from Table I for Mg'+ binding alone), were explicitly taken into account. In this calculation it was assumed that both types of ions could compete for the same sites in order to see if direct competition explains the observed apparent affinities for calcium ions. The computed values for K, and K2 were 1.7 x 10' and 5.2 x 10" M-' which stand in good agreement with those values found for Ca2+ in the absence of Mg'+ (Table I). Iterative computations were also performed at each data point individually and the calculated values for K1 and K2 stemming from experiments involving the same magnesium ion concentration were then averaged geometrically.
As Table II shows, this approach also yields values for the affinities of Ca"+ to myosin in the presence of different amounts of MgCL similar to those observed in the absence of Mg'+. These results strongly indicate that the interaction of Mg'+ with myosin does not actively affect the binding of calcium ions but simply displaces them competitively. Under this model one can calculate at any Cast concentration the relative percentage of the different species of myosin molecules bearing two cations, given the binding constants for both metal ions and the total MgCl* concentration; 5 x lo* and 5 x 10" Mm' were used for K1 and K2, respectively, for Ca2+ binding (rounded values taken from averages of Table   I and II for affinity constants of calcium ions) and for K, and K2 of Mg"+ the same as above. Out of the four species, Mg,MMg,, Mg1MCa2, CalMMgz, and CalMCa2, where M stands for myosin and the subscripts 1 and 2 for the binding constants K1 and Kz, Fig. 7    is predominant at the point where the myosin is 50% saturated with Ca'+.
Manganese ions, whose binding to protein is often studied because it can be conveniently followed by ESR spectroscopy, have also been investigated (4,16,45). Therefore, the direct binding studies reported were extended to this cation. The Scatchard plot (Fig. 8) of these data looked somewhat different from those for the other two ions, since it indicates two sites (n = 2.35) with the same apparent affinity (K = 1.73 X lo5 M-I).
This result is in good agreement with literature reports (4, 16), although Bagshaw (4) appears to have calculated the value of K from only three data points which lie in the range between 1 and 2 bound/myosin.
The indication of only one affinity for manganese ions was obtained without addition of another divalent cation, although the level of free Mg2+ was around 1 IJM according to measurement and could not be lowered further under the experimental conditions. On the other hand, there was no detectable contamination by Ca2+ and this metal was not found bound to the protein in these experiments.
Since there was no indication of a higher value for the affinity of the fist manganese ion, the same types of calculations as explained above were also performed taking into account the presence of 1 PM Mg'+. However, from the least square fitting program, which gave K1 = 4.1 X 10" and K2 = 5.4 X lo5 M-', and the iteration procedure on each experimental point which gave on average K1 = 7.8 X lo5 and K2 = 1.2 X. lo" M-', there was indication of a significant difference between K, and K2 also for this ion. Thus Mn2' has the lowest affinity to myosin of the three metal ions tested. In order to corroborate the model that myosin contains two high affinity binding sites for which all three metal ions compete, the individual amounts of bound ions were measured in mixtures of Ca2+ and Mg2+ as well as Mn2+ and Mg'+. In no case is the total number of bound ions greater than 2.9/myosin indicating that the different ions do not bind specifically to distinct sites. In fact, as the amount bound for the one type of ion increased that for the second ion decreased reciprocally.
In the fdw cases where the value of total ions bound/myosin was sightly above 2, this most probably was due to binding to nonspecific sites of low affinity as described above. Isolated myosin heads which were devoid of light chain-2 did not exhibit changes in the reactivity of their thiol-1 group with magnesium, calcium, or manganese ions, indicating, as expected of such preparations (4,11,46,47), that they do not bind metal ions. Furthermore, in the direct equilibrium dialysis, no binding was observed. Even in the presence of 10 PM free magnesium ions and 2 mM ADP where the concentration of the complex Mg. ADP would be around 40 PM, no magnesium ions were found bound to the protein. This observation confiims the deductions drawn above in the case of myosin, namely, that insignificant amounts of the metal ion are bound to the active site in the form of the complex Mg. ADP under conditions of such low free magnesium ion concentrations.

DISCUSSION
Divalent metal ion binding to myosin was studied by using two different techniques, equilibrium dialysis and following the changes in thiol group reactivity. The latter method has been used to follow the binding of Ca"' to troponin-C (25) yielding results in agreement with those from other methods. Although it is an indirect method, it shows certain clear features in the work reported here. For example, the thiol group reactivity changes occur over two distinct concentration ranges of the metal ion. The effect also shows clear saturation characteristics and hence seems to result from formation of metal. protein complexes at two classes of binding sites. On the other hand, the results from the direct binding studies reveal that 2 metal ions bind/myosin with high but different affinities. These affinities correspond to distinct concentration ranges of the free metal ion which were found to cover just those concentration ranges where the thiol group reactivity is affected. Hence, although the experimental conditions employed in the two methods differ widely, namely 10 to 50 times higher protein concentrations and 500 to 1000 times longer equilibration times used in the direct compared to indirect method, they yielded the same binding affinities.
Since the direct equilibrium dialysis method shows that just one ion binds with each affinity, it must be concluded that the binding of each ion in succession is responsible for the thiol group reactivity changes over first the low, and then the high, free ion concentration ranges seen in the curves of Fig. 3. The rather distinct bend in the isotherms at around 50% of the saturation level indicates that both ions cause similar changes in thiol group reactivity. This effect in turn reflects similar changes in the microenvironment of the respective cysteine residues located in the myosin heavy chains (48,49). As the metal ions are known to bind to the pair of light chains-2 (1, 2,4), it follows that the interaction between each of these light chains and the heavy chains is altered in a similar way. These conclusions corroborate our original assumption underlying the graphical analysis that the relative change in thiol group reactivity is equal to the saturation fraction of the total of 2 metal ions binding/myosin.
Further evidence for mediation of the interaction between light chain-2 and the heavy chains by cation binding has recently been reported from observations on the intrinsic fluorescence of heavy meromyosin (39). Differences in the digestion of myosin by various proteolytic enzymes between the presence and absence of divalent cations also support the view of altered interchain interactions (4,11,30,47,50).
In the present work, both approaches revealed high affinity binding of all magnesium, calcium, and manganese ions by myosin and yielded similar values for the respective equilibrium constants. Furthermore, these values are in agreement with those from other laboratories.
In particular the claim that calcium ions bind more tightly than Mg'+ (1,17,21,50,51), and are more effective in replacing Mn"+ (16), is in line with our results in which calcium ions display the highest affinity of all three. In the cases of Mg"' and Ca" a clear differentiation between the two high affinity sites is revealed by both methods employed in this work, whereby the first ion is bound more tightly than the second one, K, being on average 100 times larger than K2. The additional presence of ADP in the millimolar concentration range did not change these findings in the case of magnesium ion binding to myosin. The second class of sites with a constant Kg of around 10" M-' for all three ions is not to be confused with the often reported low affinity sites with affinities of the order of 10" M-' (2,4,14,16), since with a single exception of Mg"' binding in high salt at 25"C, Kz is never lower than lo" M-'. Furthermore, the measurements reported here on the number of ions bound in systems containing mixtures of two different cations strongly indicate that there is a total of just 2 sites/myosin occupied by either ion at free concentrations around lo-" M. The difference between the 2 high affinity sites does not appear to influence the competitive binding of Mg'+ and Ca"', since good fits to the data can be calculated using the simple assumption that the ions bind independently of one another. In other words, even in the presence of millimolar concentrations of Mg"' where both sites appear to have the same affinity for calcium ions (Fig. 6), one Ca'+ still binds with its high intrinsic affinity of around 10" Mm'. Thus, it is just this site whose affinity for Ca'+ appears to be so markedly affected by the presence of Mg"+. This may be explained by the fact that the competing magnesium ions also have a higher affinity for it than for the second site.
The shifts induced by magnesium ions in the curves of Ca'+ binding to myosin published by Bremel and Weber (14) are in agreement with our observations. Increasing the magnesium ion concentration from 3 pM to 1 mM raises the calcium ion concentration required for the binding of the first Ca2+ by a factor of about lo", but for the second ion by a factor of only about 10 (see Fig. 3 of Ref. 14). On the other hand, the Scatchard plots of our data on Ca"' binding were always linear over the range of the first ion to bind in the absence as well as in the presence of MgC12. They did not display the upward convex curvature found by others for Ca'+ binding to myosin in the absence or presence of 100 pM MgCl, (14, 15) which was interpreted as the result of positive cooperativity. Calculation of the statistically corrected intrinsic affinity constants by our nonlinear least square program from the binding data of Fabian et al. (see Fig. 2 of Ref. 15) yielded for & a value which was about twice that for Kl. The data of Bremel and Weber (14) for Ca2+ binding in the presence of low MgCh concentrations yield values of KI higher than KZ when treated in the same way. Therefore, caution should be exerted with interpretation especially when convex curvature occurs in the Scatchard plot within the range of the fist ligand which binds since such curvature may be caused by even small deviation of the experimental points from a smooth binding curve (42). To our knowledge only one other report claims positive cooperativity whereby magnesium ion binding to heavy meromyosin, followed by fluorometric titration, yielded an affinity constant Kz, for the second binding step, a factor of 3.6 times larger than Kl (18). In this case the slope of the Hill plot is about 1.6 only, indicating incomplete cooperativity (52). In view of these values it can hardly be taken as finally established that metal ions bind to myosin with positive cooperativity.
On the other hand, the results presented in this report argue strongly against positive cooperativity being operative during metal binding. Firstly, Scatchard plots represent a very sensitive method of treating binding data, deviations from linearity being readily observed. However, for the binding of both Mg2+ and Ca'+, straight lines were always obtained with correlation coefficients above 0.9 over the range where the first metal ion binds. Secondly, the experiments covered a wide range of conditions including different temperatures, the presence and absence of ADP, with or without chelators, and the inclusion of a high background concentration of Mg2+ in the case of calcium ion binding. Furthermore, both the direct and indirect methods consistently yielded a value for the affinity of the second cation some 2 orders of magnitude lower than the first. The computations bring even more evidence against positive cooperativity as the data for the binding of one metal alone could always be best fitted by a model consistent with negatively cooperative interactions within a duplex molecule (53). In this case however, it cannot be decided whether we are dealing with a symmetric duplex where the two binding sites are originally identical in the absence of metal ions or with an heterogeneous duplex displaying no interaction, because, the overall binding equations for these two models are identical possessing only two independent parameters, namely, the two formation constants (54). A third possibility is a difference in binding properties between two types of myosin isozymes. The existence of homodimeric isozymes with respect to light chains-l and light chains-3 has been demonstrated (55) even within single fibers (56,57).
The role of Ca" binding to myosin as the trigger involved in the activation of muscle contraction has been questioned on kinetic grounds (21). The kinetic measurements indicate that the dissociation of Mg2' is too slow to allow for a switching on mechanism. Nevertheless, calcium ion concentrations of the order of lo-" M may be achieved in muscle during sustained activity, and, as the calculations presented here show, around 50% of the metal binding sites of myosin would be occupied by Ca2+ even in the presence of 1 mM free magnesium ion concentration. Since these calculations are applied to the system at equilibrium, they represent simply a time average of all the binding steps involved. If now the high and low affinity sites are to be attributed to two types of isozymes, one would have to conclude that one type becomes preferentially occupied by calcium ions, while the other retains magnesium ions, during muscle activity. But it is difficult to imagine how changes in only about half of all myosin molecules could be responsible for physical and structural changes observed in myosin fdaments (2,9). It is obviously a more attractive proposal that each myosin contains a bound calcium ion so that one head per myosin is somehow involved in the regulation of muscle activity, if not directly in the switching mechanism then operating as a modulator in the interaction between myosin and actin. The calculated distribution of the Ca2+ over the various possible cation-myosin combinations under this assumption indeed shows that the state containing just one Ca"' in the higher affinity and a Mg2+ in the lower affinity site would predominate.
Measurements made by indirect methods on isolated light chains-2 have established that they bind calcium ions with an affinity around lo5 to lo6 M-' and magnesium ions around lo3 M-' (1, 2). The affinity for Ca2+ is lowered by an order of magnitude when the chain becomes phosphorylated, although Mg2+ binding remains unaffected (26). A larger difference of around four orders of magnitude for Ca2+ binding has been reported for myosin to which light chain-2 in either the dephosphorylated or phosphorylated form has been reattached (3), whereby the higher affinity was nevertheless lowered considerably by the presence of 1 mM Mg2+ (58). These observations would naturally suggest that the existence of two distinct binding affinities in myosin is due to the two states of phosphorylation of the light chain-2. The fact that just around half of these light chains is in each state in our myos'in preparations would then explain the finding of two distinct affinities reported here. Consequently, questions of the cause of the metal ion binding behavior would also now apply to phosphorylation.
Does the duplex myosin molecule possess heterogenous and independently functioning heads, or do the heads interact cooperatively, or do two separate myosin species exist, explaining the intermediate degree of phosphorylation? Other independent evidence points indeed to a type of intramolecular interaction. For example, the light chains-2 are identical with one another in the isolated state (59, 60), yet it appears from recombination experiments that only one is removed from each myosin molecule by treatment with 5,5'dithiobis(2-nitrobenzoic acid) (59), indicating that they adopt an asymmetric relationship to one another. Then, out of the possibilities considered, that which envisages two populations of myosin species with different binding and phosphorylation properties seems the most unlikely. Thus myosin, with its distinguishable subunit properties arising from either intrinsic asymmetry or concerted subunit interactions, would belong to the large class of multimeric proteins in which subunit interactions are thought to play a major role in controlling their enzymic properties (61).