Rotational dynamics and protein-protein interactions in the Ca-ATPase mechanism.

We have varied the degree of protein-protein interactions among Ca-ATPase polypeptide chains in sarcoplasmic reticulum using the cleavable homobifunctional cross-linker dithiobissuccinimidyl propionate and have measured both the rotational mobility and calcium-dependent ATPase activity of the Ca-ATPase in order to assess 1) the nature of the microsecond rotational motion measured by saturation transfer EPR (ST-EPR) of the spin-labeled Ca-ATPase and 2) the functional significance of this rotational motion. The Ca-ATPase was labeled specifically and covalently with a maleimide spin label, with full preservation of enzymatic activity. ST-EPR experiments show that cross-linking increases the enzyme's effective rotational correlation time (tau r), thus decreasing its rotational mobility (tau r-1). As the degree of cross-linking is varied, tau r is proportional to the mean molecular weight of the cross-linked aggregate, as predicted by theory, adding to the evidence that ST-EPR measures the overall rotational mobility of the Ca-ATPase with respect to the membrane normal. Furthermore, enzymatic activity correlates with overall protein rotational mobility, suggesting that this motion is functionally important. The second-order inactivation profile resulting from the use of either cross-linking or chemical modification with fluorescein isothiocyanate as modes of inactivation indicates that protein-protein interactions are critical to the reaction mechanism. However, the pattern of cross-linking observed on polyacrylamide gels demonstrates that cross-linking occurs in a random manner, indicating that no specific and stable oligomeric complexes exist. In order to rationalize both the functional need for protein mobility and the evidence that protein-protein interactions are critical and random, we propose that the enzymatic cycle of the Ca-ATPase involves the making and breaking of functionally important protein-protein interactions.

We have varied the degree of protein-protein interactions among Ca-ATPase polypeptide chains in sarcoplasmic reticulum using the cleavable homobifunctional cross-linker dithiobissuccinimidyl propionate and have measured both the rotational mobility and calcium-dependent ATPase activity of the Ca-ATPase in order to assess 1) the nature of the microsecond rotational motion measured by saturation transfer EPR (ST-EPR) of the spin-labeled Ca-ATPase and 2) the functional significance of this rotational motion. The Ca-ATPase was labeled specifically and covalently with a maleimide spin label, with full preservation of enzymatic activity. ST-EPR experiments show that cross-linking increases the enzyme's effective rotational correlation time ( T~) , thus decreasing its rotational mobility ( T ;~) . As the degree of cross-linking is varied, T~ is proportional to the mean molecular weight of the cross-linked aggregate, as predicted by theory, adding to the evidence that ST-EPR measures the overall rotational mobility of the Ca-ATPase with respect to the membrane normal. Furthermore, enzymatic activity correlates with overall protein rotational mobility, suggesting that this motion is functionally important. The second-order inactivation profile resulting from the use of either cross-linking or chemical modification with fluorescein isothiocyanate as modes of inactivation indicates that protein-protein interactions are critical to the reaction mechanism. However, the pattern of cross-linking observed on polyacrylamide gels demonstrates that cross-linking occurs in a random manner, indicating that no specific and stable oligomeric complexes exist. In order to rationalize both the functional need for protein mobility and the evidence that protein-protein interactions are critical and random, we propose that the enzymatic cycle of the Ca-ATPase involves the making and breaking of functionally important protein-protein interactions.
We are interested in understanding the functional importance of a fluid bilayer for optimal membrane function. In the past, a number of correlations have been observed among the enzymatic functions of membrane proteins, including the Ca-ATPase of sarcoplasmic reticulum (SR),' and dynamic properties ( i e . fluidity) of the membrane (reviewed by Thomas, 1985Shinitzky, 1984;and Kates and Manson, 1984). Previously, we have reported that enzymatic function correlates with microsecond protein rotational motion, as reported by maleimide spin labels covalently bound to the Ca-ATPase, better than with lipid fluidity, as reported by lipid spin labels (Thomas et al., 1982;Thomas, 1985). It is our intention in this and the two subsequent papers (Squier and Thomas, 1988;Squier et al., 1988b) to better define the physical nature of the microsecond protein rotational motion reported by the covalent spin label bound to the Ca-ATPase and to explore the functional significance of this rotational mobility.
The overall rotational mobility of the Ca-ATPase about the membrane normal is predicted to be sensitive to both the oligomeric state of the Ca-ATPase and the fluidity of the hydrocarbon environment (Saffman and Delbriick, 1975;. Therefore, combined measurements of protein rotational mobility and lipid hydrocarbon chain dynamics can provide information about the degree of protein-protein interactions (e.g. the oligomeric state) in SR membranes, as well as the role of lipid fluidity in modulating protein mobility.
In order to interpret the observed probe motions in terms of specific protein motions, it is essential to inhibit protein motions specifically and to observe the effects on probe motion. Covalent protein-protein cross-linking is an effective approach (Thomas and Hidalgo, 1978;) since overall protein rotational mobility is predicted to be inversely proportional to the number of proteins cross-linked together (Saffman and Delbriick, 1975;. Therefore, ST-EPR measurements of the spin-labeled Ca-ATPase should also be inversely proportional to the number of crosslinked proteins provided the spin label reports the overall rotational mobility of the Ca-ATPase with respect to the membrane normal, rather than the segmental flexibility of the Ca-ATPase or local motions of the spin label. In addition, cross-linking is an effective means of altering protein-protein interactions and also of studying the spatial distribution of membrane proteins (Downer, 1985).
In this study, the cross-linker dithiobissuccinimidyl propionate (DSP) is used to determine the nature of the protein mobility measured by ST-EPR (ie. overall mobility of the protein uersw internal motions) and its functional significance. We have studied enzyme inactivation using both DSP, which varies the concentration of monomer, and fluorescein The abbreviations used are: SR, sarcoplasmic reticulum; MSL, maleimide spin label; ST-EPR, saturation-transfer E P R DSP, dithiobissuccinimidyl propionate; FITC, fluorescein isothiocyanate; (M,.,), mean molecular weight; MOPS, 3-(N-morpholino)propanesulfonic acid; TES, N-tris[hydroxymethyl]methyl-2-aminoethanesulfonic acid; EGTA, (ethylenebis(oxyethylenenitrilo)]tetraacetic acid; SDS, sodium dodecyl sulfate; AMP-PNP, adenosine 5'-(0,y-iminotriphosphate). 9162 isothiocyanate (FITC), which alters the number of active sites. The effects of inactivation on protein mobility and enzymatic activity have been compared with those predicted theoretically for different enzymatic mechanisms in order to determine whether protein-protein interactions are important to the reaction and whether these interactions are static or dynamic.

EXPERIMENTAL PROCEDURES
Fragmented SR-Vesicles were prepared from rabbit skeletal white (fast twitch) muscle essentially as described previously (Fernandez et al., 1980). All experiments were done with the vesicles whose densities equilibrated between 25 and 50% (w/w) sucrose. All preparation was done at 4 "C. The membrane vesicles were suspended in SB buffer (0.3 M sucrose, 1 mM NaN3, 20 mM MOPS (pH 7.0)) and stored in liquid nitrogen.
Purified Ca-ATPase (Warren et al., 1974)"Upon the addition of 10% (w/w) deoxycholate to SR vesicles (0.3 M sucrose, 50 mM KzPO4, 1.0 M KC1 (pH 8.0) at 25 "C) and subsequent collection on a sucrose gradient, the low molecular weight proteins (Le. calsequestrin and calcium-binding protein) were stripped from the membrane, resulting in a.preparation in which the Ca-ATPase accounted for 95 f 5% of the total protein according to densitometer scans of Coomassie Bluestained polyacrylamide gels. This procedure maintains the native vesicle morphology (Herbette et al., 1977), although the Ca-ATPase is more apt to undergo irreversible aggregation (Barrabin et aL, 1984). Deoxycholate (Sigma) was purified through two recrystallizations from ethanol. Protein Assay-By modification of the biuret method (Gornall et al., 1949), i.e. the reaction of protein with 0.03% CuSO4, 0.125% potassium sodium tartrate (KNaC4H4DOs.4H20), 0.625% NaOH, and 0.042% Sterox detergent (Perkin-Elmer), the absorbance at 310 nm was related to protein concentration using bovine serum albumin as a standard. All reagents listed are percent weight by volume unless otherwise stated.
Enzymatic Assays-Steady-state ATPase activity was measured in a solution containing 0.05 mg of protein/ml, 60 mM KC1,6 mM M&12, 2 p M A23187, 25 mM MOPS (pH 7.0), and either 0.1 mM CaC12 or 2 mM EGTA. The reaction was started by the addition of 5 mM ATP, and the initial rate of release of inorganic phosphate was measured by the method of Lanzetta et al. (1979). Alternatively, ADP production was assayed by monitoring absorbance at 340 nm with an enzyme-linked assay (Warren et al., 1974). ATPase activity assayed .in the presence of EGTA (basal activity) was subtracted from that assayed in the presence of CaC12 (total Ca-ATPase activity) in order to obtain calcium-dependent ATPase activity (typically 3-4 pmol of phosphate/mg/min). Typically, the basal (calcium-independent) activities were less than 5% of the total activity. Gel Electrophoresis-Sodium dodecyl sulfate (SDS)-polyacrylamide gel electrophoresis was performed by the method of Laemmli (1970) using either 7.5% acrylamide gels with 3% stacking gels or 2.2% gels (stabilized with 1% agarose) without a stacking gel. The former was used to resolve the Ca-ATPase from a 98-kDa protein, presumably phosphorylase b (Pickart and Jencks, 1984), which we found to be less than 4% of the protein in this preparation (Fig. 1); the latter was used to resolve high molecular weight species, including cross-linked oligomers of the Ca-ATPase. Before electrophoresis, samples (1-2 mg/ml) were incubated in 1% sodium dodecyl sulfate without heating. Gels were stained for protein with Coomassie Blue R-250. Normally, 25 pg of SR was applied to each lane of the 7.5% polyacrylamide slab gel, and 50 pg of SR was applied to each 2.2% polyacrylamide tube gel. These concentrations were chosen from a range of protein concentrations that were linear with respect to the areas of the Coomassie Blue densitometer traces of the gel bands, i.e.
10-50 pg of SR for 7.5% gels and 25-200 pg for the 2.2% gels. These gels indicate that in native SR membranes, about 80 f 10% of the proteins migrate as a 100-kDa band, presumably the Ca-ATPase; this estimation corresponds to about 7 nmol of Ca-ATPase protein/mg.
Cross-linking-The Ca-ATPase was reversibly cross-linked with the cleavable homobifunctional reagent DSP (Fig. 2) as described by Kurobe et al. (1983). The cross-linking reaction results in leaky vesicles (Chiesi, 1984). At pH 7.0, this reagent mainly cross-links lysines; the majority of the lysines modified result in intermolecular cross-linking (Kurobe et al., 1983). The normal medium was 0.3 M sucrose, 1.01 mM CaC12, 1.00 mM EGTA, 5 mM AMP-PNP, 20 mM MOPS (pH 7.0); equivalent results were obtained when the calcium and nucleotide concentrations were varied, although the rate of crosslinking was affected. The cross-linking reaction was started by the addition of a small portion of freshly dissolved 0.1 M DSP (Pierce Chemical Co.) in dimethylformamide to SR (4 mg/ml) at a final DSP concentration of 0-5 mM, followed by a 5-min incubation at 22 "c.
The reaction was terminated by the addition of 91 mM glycine. The vesicles were subsequently washed twice in SB buffer.
We have quantitated the extent of cross-linking in two ways based on the densitometer scans of gels. The mean molecular weight relative to the monomer is where ni is the mole fraction of an oligomer composed of n Ca-ATPase molecules, and N is the number of cross-linked species. The mole fraction ( F ) of Ca-ATPase chains that remain monomeric is Cross-linking was reversed by the addition of 5 mM P-mercaptoethanol and incubation for 10 min at 4 "C. In some cases, additional reactivation was observed upon detergent solubilization of SR with 5 mM ClzEg (dodecyl nanoethylene glycol monoether) (solubilizes the Ca-ATPase)  in the assay medium, presumably relieving some nonspecific aggregation. Before cleavage of the disulfide linkage in the cross-linker, solubilization had no effect on the ionophore-stimulated Ca-ATPase activity. The monofunctional reagent 3-(p-hydroxyphenyl)propionic acid N-hydroxysuccinimide ester was used to study the nonspecific effects of chemical cross-linking that might result from the reaction of the lysine moiety.
FITC was solubilized in dimethylformamide and added to the sample in less than 0.5% total volume. Excess unreacted FITC was removed by filtration on a Sephadex G-25 column using 10 mM TES (pH 7.5), 0.1 M KC1 as an elution buffer. The concentration of bound fluorescein was measured spectrophotometrically for membranes solubilized in 5 mM CI2E9; there was no detectable change in the molar absorption coefficient of FITC covalently attached to the protein at 496 nm in comparison with a standard curve of FITC free in solution. The calculated molar absorption coefficient was 8.0 k 0.4 X 10' M" cm" at 496 nm, in agreement with previous observations (Pick and Karlish, 1980). The FITC labeling procedure had no effect on the enzyme's rotational dynamics, as measured by EPR and ST-EPR (see below).
EPR Spectroscopy-EPR spectra were obtained with a Varian E-109 spectrometer as describedpreviously (Squier and Thomas, 1986a), and spectra were digitized and analyzed with a microcomputer (Northstar Co.) interfaced to the spectrometer (Lipscomb and Salo, 1983). Submicrosecond rotational motion of spin labels was detected by conventional EPR (first harmonic absorption in phase, designated Vl) using 100-kHz field modulation (with a peak-to-peak amplitude of 2 G ) and a microwave field amplitude of 0.032 G. Submillisecond rotational motion was detected by saturation-transfer EPR (second harmonic absorption out of phase, designated V'Z) using 50-kHz field modulation (with a modulation amplitude of 5 G) and a microwave field intensity of 0.25 G. All studies were done in the absence of oxygen, which was removed from reference and experimental samples using gas-permeable sample cells purged with NZ (Popp and Hyde, 1981). Temperature was controlled to within 0.5 "C with a Varian V4540 variable temperature controller. Spin concentration was determined by double integration of the digitized conventional (VI) EPR spectra, recorded at low (nonsaturating) microwave power. The relative number of spins per sample was determined by comparison of the number obtained from double integration of the Vl spectrum with the number obtained for a 0.1 mM MSL standard, whose VI spectrum was digitized and doubleintegrated in the same manner. Conventional and ST-EPR (VZ') spectra were all normalized to the same number of spins by dividing each spectrum by a number proportional to the double integral of the Vl spectrum.
During data acquisition, temperature was monitored with a Bailey digital thermometer (Model BAT-12) using a thermocouple probe (IT-21) positioned outside the sample cell in the center of the cavity.
Spectral Amlysis-The effective rotational correlation times (T,) for the experimental ST-EPR spectra were determined by comparing experimental spectra with reference spectra (Fig. 3) using spectral parameter plots published by Squier and Thomas (1986a). The reference spectra were obtained from isotropically tumbling spin-labeled hemoglobin in solutions of known viscosity (7) and temperature (2'). These spectra are commonly interpreted using either the line shape (ratio of line heights e.g. L"/L) or total spectral intensity. As motion increases ( 7 , decreases), there is a reduction in the total spectral intensity. Whereas this reduction in intensity occurs throughout the spectrum, certain regions (e.g. L") are much more sensitive to motion than other regions (e.g. L). In this study, spectra were analyzed with spectral intensity parameters (i.e. SV',; see Fig. 3 0 in Squier and Thomas, 1986a), which select against the weakly immobilized probes that can distort line shape parameters Thomas, 1986a, 1986b). Similar results were obtained using line shape parameters at temperatures less than 10 "C, where the weakly immobilized probes have a negligible effect on the ST-EPR spectrum.
The protein rotational mobility is defined in this study as 7m/rr, where Tm and 7, are the effective correlation times of the control (uncross-linked) and cross-linked samples, respectively, recorded at the same temperature. Although cross-linking produces a heterogeneous distribution of cross-linked sizes (shown below), contributions from the different species (presumably corresponding to different 7, values) are not resolved in the ST-EPR spectra . The spectra reflect a spectroscopic average of contributions from various stable cross-linked aggregates of the Ca-ATPase. Nevertheless, since the spectral intensity is a linear sum of the components and since the intensity of hemoglobin reference spectra (Fig. 3) is proportional to log(7,) in the presently observed range (Squier and Thomas, 1986a), the effective correlation times (T?) obtained from the intensities of Ca-ATPase spectra provide a useful indicator of the average rotational mobility as a function of cross-linking. intensity and diagnostic line height ratios (e.g. L"/L) decrease. Each spectrum has been normalized to represent the same number of spins. For more details, see Squier and Thomas (1986a). The base line is 110 G wide.

Electrophoretic Studies of Cross-linking-The
Ca-ATPase was cross-linked with the homobifunctional cross-linker DSP (Fig. 2) so as to alter the degree of interaction among Ca-ATPase polypeptide chains. In order to identify the nature of the motion of the spin-labeled Ca-ATPase that we measure, we considered only low levels of cross-linking, which enabled us to resolve the majority of the cross-linked products on SDS-polyacrylamide gels (Fig. 4).
The Coomassie Blue-stained SDS-polyacrylamide gels (Fig.  4, left) from the control (uncross-linked; left lam) and a crosslinked preparation (right l a n e ) demonstrate the ability of the 2.2% polyacrylamide gel system to resolve protein species in the range of 100-1000 kDa (Louis and Holroyd, 1978). The associated densitometer scans are shown in Fig. 4 (right). In the control sample, there are only two significant bands. The upper band is the Ca-ATPase, migrating with an apparent molecular mass of about 100 kDa. The lower band is calsequestrin, migrating with an apparent molecular mass of about 60 kDa (Louis et al., Louis and Holroyd, 1978). Although different proteins in SR may show varying sensitivity to Coomassie Blue stain, we have avoided potential artifacts in the quantitation of oligomeric complexes by comparing the relative concentrations of only Ca-ATPase-derived complexes. Cross-linking results in a distribution of higher molecular weight species (oligomers), consistent with a process involving random cross-linking of the individual monomeric units (see below). No individual oligomeric species predominate at any degree of cross-linking, and the densitometer scan of the gel shows a distribution of Ca-ATPase oligomeric forms, i.e. monomer through pentamer, whose intensity decreases as a function of higher molecular weight (degree of cross-linking).
More extensive cross-linking of the Ca-ATPase forms more extensive oligomers, such that a maior fraction of the material will not enter the 2.2% polyacrylamide gel, i.e. it  apparent molecular mass greater than lo6 kDa. Calsequestrin is also cross-linked, but only to itself (Louis et al., Louis and Holroyd, 1978). A small amount of this cross-linked material is observed below the cross-linked dimer of the Ca-ATPase, but is readily resolved from the Ca-ATPase. Comparison of densitometer scans from the cross-linked and control samples (Fig. 4) indicates that under these mild crosslinking conditions, little calsequestrin undergoes cross-linking. Therefore, the amount of cross-linked calsequestrin that may co-migrate with the Ca-ATPase is negligible and does not affect the estimation of the relative concentration of different cross-linked Ca-ATPase polypeptide chains (see below).
Effect of Cross-linking on Protein Rotational Mobility-Coincident with cross-linking, there is an increase in ST-EPR spectral intensity (Fig. 5), indicating that the rotational mobility of the Ca-ATPase decreases upon cross-linking, consistent with an increase in the aggregate size. Fig. 6 shows that protein rotational mobility (  complex (see "Experimental Procedures"). ST-EPR was used to measure the rotational mobility (Tm/Tr) of the spin-labeled Ca-ATPase, relative to the control (no cross-linking). Data shown represent the mean obtained from seven data sets whose spectra were obtained at 4, 20, and 37 "C. Error bars represent the standard error of the mean about each data set. The least-squares fit to the data has a slope of 0.87, an intercept of 0.11, and a correlation coefficient of 0.96. complexes; this correlation is predicted by hydrodynamic theory (Saffman and Delbriick, 1975) and indicates that we are primarily measuring the overall rotational motion of the Ca-ATPase with respect to the membrane normal. The proportionality between protein mobility and (MW)-' is independent of the temperature at which spectra are recorded, over a range from 4 to 37 "C (data not shown). Under the present cross-linking conditions (at pH 7.0), there is a minimal amount of intramolecular cross-linking (Kurobe et al., 1983). When we performed the cross-linking under conditions that promote intramolecular cross-linking (i.e. pH 8.0), we observed a poor correlation between protein mobility and (Mw)", and this relationship was quite temperature-dependent (data not shown). The non-zero y axis intercept in Fig. 6 indicates the presence of a small amount of residual protein mobility, probably corresponding to intramolecular motion, that is not completely inhibited by intermolecular crosslinking. This is consistent with the observation that the formation of two-dimensional arrays of the Ca-ATPase does not completely abolish protein mobility as measured by ST-EPR (Lewis and Thomas, 1986).
Random Cross-linking Pattern-Cross-linking can provide information regarding the spatial distribution of Ca-ATPase polypeptide chains with respect to each other in the native membrane (Downer, 1985). Fig. 7 compares the observed distribution of oligomeric species (n-mers), obtained from gel scans, with that predicted for completely random cross-linking, as a function of p, the mean number of cross-links. There is good agreement between predicted and experimental values at low levels of cross-linking (i.e. p 0.5), but not at high levels. Higher molecular weight species are preferentially cross-linked, as seen by the reduced concentration of n-mers (where n is greater than 2) compared to that expected for a completely random process, as can be seen by the absence of species between 500 and 1000 kDa (see Fig. 4). This observation is presumably due to the increased surface area of the large aggregates and the random probability that cross-linking will occur per unit of surface area. This random cross-linking is also observed for the cross-linkers cupric ion complexed with o-phenanthroline and glutaraldehyde (data not shown), although the latter is much less specific, resulting in both intra-and intermolecular cross-linking (Napier et al., 1987).
No difference in the cross-linking pattern was observed under conditions that promote phosphoenzyme formation (ie. pH 7.0, 1.0 mM EGTA, 5 mM MgC12, and 5 mM KH2P04), suggesting no change in the degree of protein-protein interaction. This evidence for random cross-linking suggests that extensive nonspecific protein-proteili interactions occur and that there are no unique stable oligomeric complexes of the Ca-ATPase.
Dependence of Calcium-dependent ATPase Activity on Protein Rotational Mobility-In order to study the relationship between enzyme activity and protein rotational mobility (determined as described in the legend to Fig. 6), we measured the inactivation profile as a function of the amount of crosslinking (Fig. 8). Since the cross-linking process results in leaky vesicles (Chiesi, 1984), we have measured the effect of cross-linking on the calcium-dependent ATPase activity, rather than calcium transport. However, in cases where it has been possible to measure calcium transport, we have always found an agreement between either of these two measurements of enzymatic function and protein mobility (Bigelow et al., 1986;Bigelow and Thomas, 1987). A correlation between steady-state calcium-dependent ATPase activity and protein rotational mobility is observed, adding to the evidence for a functional requirement for protein mobility (Hidalgo et a!., 1978;Thomas, 1985;Bigelow et al., 1986). This correlation is the same at 4, 25, and 37 "C and can be fit to a straight line with a non-zero intercept (see legend to Fig. 8). As discussed above, the non-zero intercept may be the result of residual internal protein mobility. Alternatively, the calcium-dependent ATPase activity may be fit to a second-order relationship with respect to protein mobility (see legend to Fig. 8).
Dependence of Calcium-dependent ATPase Activity on Fraction of Uncross-linked Protein-Although the random crosslinking pattern suggests that no unique, stable oligomeric species exist, it is possible that a transient interaction among Ca-ATPase polypeptide chains (involving a change in affinity or orientation) might be critical to enzymatic function. Therefore, we investigated the relationship between the calcium-  (n -1) .x,, where xn is the mole fraction of oligomers of size n. The solid lines show the predicted functional dependence of these various species assuming random cross-linking (Downer, 1985). The size distribution was obtained from the distribution of Coomassie Blue staining intensity on 2.2% polyacrylamide gels (see Fig. 4).

Protein Mobility
FIG. 8. Dependence of Ca-ATPase activity on protein rotational mobility. The calcium-dependent ATPase activity, relative to that of the control, is plotted against the protein mobility, r-)/rr (Fig. 6). The activity was generally measured at 25 'C, but similar patterns of inhibition were observed at both 4 and 37 "C. The activity of the control sample at 25 'C is 2.2 pmol mg" min".
Each data set represents the mean for three to nine samples, and error bars represent the standard error of the mean. The best fit to a linear function (activity = a X mobility + b ) gives a = 1.13 f 0.10, b = 0.18 f 0.06, and a correlation coefficient of 0.97. The best fit to a second-order relationship (activity =i a X mobility + b ) gives a = 0.97 -C 0.07, b = 0.08 * 0.04 and a correlation coefficient of 0.98. dependent ATPase activity and the fraction (F) of Ca-ATPase polypeptide chains that remain monomeric on gels (Fig. 9). There is a significant concentration of monomer remaining (i.e. F 2 0.3) when enzymatic activity is 90% inhibited. The inactivation profile is consistent with a secondorder dependence of enzymatic activity on F, suggesting that oligomers (probably dimers) are involved in the reaction mechanism (see "Discussion"). Cross-linked samples containing only monomers and dimers likewise show a significant enzymatic inhibition (Fig. 1OB); the remaining activity has the same dependence on F as seen at higher levels of crosslinking, suggesting that all cross-linked dimers are inactive.
In these experiments, we have concentrated our attention on lower levels of cross-linking in order to minimize nonspecific effects and to resolve the distribution of cross-linked species on gels. However, when all the Ca-ATPase is cross-linked (i.e. no material migrates as a monomer on the gel), the calciumdependent ATPase activity is completely inhibited.
Reversibility of Cross-linking-In order to ensure that the DSP-induced inhibition of ATPase activity is a result of the intermolecular cross-linking, rather than the modification of a specific chemical moiety necessary for the ATPase reaction (e.g. an essential lysine), we investigated the reversibility of the cross-linking reaction and the effect of a monofunctional reagent (3-( p-hydroxypheny1)propionic acid N-hydroxysuccinimide ester) on the ATPase activity. At low levels of crosslinking (where the calcium-dependent ATPase activity is 50% of the control activity), both the cross-linking (Fig. 1OB) and the enzymatic inhibition are fully reversible provided nucleotide is present during the cross-linking reaction (Kurobe et al., 1983). Although we do not observe complete reversibility when samples are cross-linked in the absence of nucleotide or at high levels of cross-linking (Fig. 10, C and D), a major fraction of the activity is restored. Most significantly, the relationship between enzymatic activity and F is the same for the partial data set in which inactivation is fully reversible as Reversibility was assayed as the reappearance of both the 100-kDa species and the calcium-dependent ATPase activity subsequent to addition of 5 mM @-mercaptoethanol.
it is for the entire data set, indicating that no systematic error is occurring due to an irreversible conformational change resulting from the cross-linking reaction. Furthermore, the relationship between enzymatic activity and F for the partially reactivated membranes is in agreement with the data presented in Fig. 9. This result, in combination with the evidence that little or no intramolecular cross-linking is occurring (discussed above), indicates that the inactivation is largely caused by intermolecular cross-linking. However, we cannot rule out the possibility that some denaturation may be responsible for the irreversible inhibition observed at the higher levels of cross-linking. For this reason, we will base our conclusions primarily on those studies involving lesser degrees of cross-linking, where enzymatic inhibition is completely reversible, i.e. F > 0.45 (see Fig. 9).
In order to assess the effects of chemical modification itself on enzymatic inhibition, we have used the monofunctional reagent 3-(p-hydroxyphenyl)propionic acid N-hydroxysuccinimide ester, which possesses only one highly reactive functional group, which, like the reactive functional group in DSP, is a succinimide ester. In the presence of AMP-PNP, the addition of a 10 mM concentration of this monofunctional reagent results in a much smaller inhibition of the calciumdependent ATPase activity than for the bifunctional reagent. The observed inhibition is about 10% of that observed for the bifunctional reagent and is consistently accompanied by a small amount of irreversible protein association as evidenced by the appearance of higher molecular weight species on a 2.2% polyacrylamide gel. Thus, the relationship between the ATPase activity and F is the same as seen in Fig. 9, indicating that the inactivation is caused by aggregation, whatever the mechanism, and that the modification of the reactive functional group. does not by itself inactivate the enzyme.
Inactivation by FITC-In order to unequivocally rule out any systematic error in the quantitation of the relationship between enzymatic activity and F (Fig. 9), as would occur if some of the cross-linked aggregate had residual ATPase activity, we have used an independent means to inhibit enzyme activity, i.e. chemical modification with FITC. The specific and covalent attachment of FITC to the Ca-ATPase prevents ATP binding to the active site (Pick and Karlish, 1980;Andersen et al., 1982) and does not affect the rotational mobility of the Ca-ATPase as measured by ST-EPR, indicating that FITC modification of the Ca-ATPase does not result in any gross conformational change of the enzyme or its state of association. The two methods of inhibition (cross-linking and active site blockage) yield essentially the same dependence between calcium-dependent ATPase activity and F (Fig.  9). Ionophore stimulation of the calcium-dependent ATPase activity is analogous to that observed in unmodified SR, indicating that the ATPase activity of the unmodified species is coupled to calcium transport.
FITC Binding to Ca-ATPase-There has been some question regarding both the maximal stoichiometry of FITC binding to the Ca-ATPase and the absolute specificity of this reaction (Andersen et al., 1982;Swoboda and Hasselbach, 1985). We have used the purified Ca-ATPase in order to avoid systematic errors resulting from either the reaction of FITC with proteins other than the Ca-ATPase or the estimation of the concentration of the Ca-ATPase as determined from densitometer scans of stained gels, which must assume that Coomassie Blue is equally sensitive to all proteins. Using a purified preparation, we find that FITC incorporation saturates at 7.2 f 0.5 nmol of FITC/mg of SR protein, in good agreement with our estimation of the concentration of the Ca-ATPase (i.e. 8.2 k 0.4 nmol of Ca-ATPase/mg of SR), suggesting that FITC binding saturates at a level of 1 mol of FITC/mol of Ca-ATPase.
The site specificity of the FITC reaction, unlike that of the DSP reaction, is not affected by the presence of nucleotide, which acts kinetically to slow the reaction of FITC with lysine 515, but does not change the relationship between ATPase activity and the amount of FITC bound . Furthermore, maximal cross-linking with DSP (under conditions that protect lysine 515) does not modify the amount of FITC that can bind, indicating that (i) the cross-linking reaction does not expose any additional residues reactive with FITC, which might occur if enzyme denaturation were to occur; and (ii) FITC does not react with any residues that are reactive with DSP. Therefore, we conclude that under our experimental conditions, the single FITC-binding site is both specific and saturable.
The stoichiometry of inactivation by FITC is virtually identical to that in the cross-linking study (Fig. 9), suggesting that the inhibition of enzyme activity through intermolecular cross-linking is equivalent to the inhibition through the specific inactivation of the ATP-binding site. This suggests that the inactivation profile is an accurate representation of the relationship between function and the concentration of unmodified Ca-ATPase monomeric polypeptide chains.

DISCUSSION
Summary of Results-We have used ST-EPR to analyze the microsecond rotational mobility of the Ca-ATPase in SR, as affected by interprotein cross-linking. The results provide quantitative support for the proposal that ST-EPR measures primarily the overall rotational mobility of the Ca-ATPase with respect to the membrane normal and help us interpret the functional relevance of a large body of data involving measurements of protein rotational mobility in SR. A correlation of these protein mobility measurements with the func-tional effects of cross-linking and FITC derivatization provides insight into the role of protein dynamics in the Ca-ATPase reaction mechanism.
ST-EPR Spectra Are Sensitive to Overall Rotational Mobility of MSL-labeled Ca-ATPase-Evidence for this includes: 1) the linear relationship between protein mobility and (M,,.)-' (Fig. 6) and 2) the temperature-independent change in protein mobility relative to the control. This linear relationship (Fig.  6) is precisely the one predicted by hydrodynamic theory (Saffman and Delbriick, 1975;Peters and Cherry, 1982;Hughes et al., 1982) for the overall rotational motion of a membrane protein about the membrane normal, indicating that ST-EPR most probably measures the overall rotational mobility of the spin-labeled Ca-ATPase, in agreement with previous proposals (Hidalgo et al., 1978;Thomas and Hidalgo, 1978;Squier and Thomas, 1986b) and other recent results (Squier et al., 1988b;Squier and Thomas, 1988). Nevertheless, the non-zero y axis intercept in Fig. 6 suggests that the spectra are also affected by some residual internal protein mobility, and this is consistent with the observation that the decavanadate-induced formation of two-dimensional Ca-ATPase arrays does not completely immobilize the same probe (Lewis and Thomas, 1986).
Functional Role of Protein Mobility-Protein mobility correlates with enzymatic activity, suggesting that overall protein rotational mobility is functionally important. In this study, protein mobility was altered by changing the degree of protein-protein interaction (aggregate size). The observed correlation between the calcium-dependent ATPase activity and protein mobility (Fig. 8) is essentially the same as that achieved with partial delipidation, which also increases protein aggregation (Squier and Thomas, 1988). In other studies, protein mobility has been altered through changing the lipid fluidity (Hidalgo et al., 1978;Bigelow et al., 1986;Bigelow and Thomas, 1987). The observed relationships among Arrhenius plots of lipid fluidity, protein rotational mobility, and calciumdependent ATPase activity, with identical activation energies for all three processes, suggest a direct relationship (Bigelow et al., 1986;Squier et al., 1988b). However, when protein mobility is modified selectively, i.e. with negligible effects on lipid fluidity (Hidalgo et al., 1978;Thomas et al., 1982;Squier and Thomas, 1988;this study), the correlation between protein rotational mobility and enzymatic activity is maintained, suggesting that the apparent functional requirement of fluid lipids is due to a primary need for protein mobility.
Analysis of Cross-linking-The random cross-linking pattern (Fig. 7) cannot rule out the presence of functionally significant complexes, but it indicates that many nonspecific (apparently random) protein-protein interactions occur between Ca-ATPase polypeptide chains. Since long-term protein associations tend to be preferentially cross-linked (reviewed by Peters and Richards, 1977), these results suggest that stable Ca-ATPase oligomers of a particular size do not exist in the absence of cross-linking. The lack of an effect of enzyme phosphorylation on cross-linking also indicates, in agreement with previous results by other methods (Hymel et al., 1984;Thomas, 1986, 1988), that most of these interactions are not affected by phosphoenzyme formation.
Theoretical Curves Describing Mechanistic Models-In our analysis of the enzyme inactivation by cross-linking, we have worked at a protein concentration where the relationship between densitometer peak areas and the relative protein concentrations is linear. We have quantified only those gel bands that arise from the Ca-ATPase, thereby avoiding errors that could arise due to differential staining of different proteins. Furthermore, under mild cross-linking conditions such that only monomers and dimers are observed, we see the same second-order relationship between ATPase activity and the concentration of monomer (Fig. lOB), suggesting that all cross-linked aggregates are completely inhibited. Finally, in order to rule out any systematic errors in the quantitation of the relationship between enzymatic activity and the concentration of unmodified Ca-ATPase, we also used FITC to specifically inhibit ATP binding, thereby altering the concentration of functionally competent species by a completely independent method.
The possible role of protein-protein interactions is examined (Fig. 9) by comparing the experimental inactivation profile with the predicted curves for three different models.
(a) A first-order inactivation process (enzyme activity is proportional to F ) corresponds to a model in which the Ca-ATPase is a functional monomer throughout the enzymatic cycle. ( b ) A second-order inactivation process (enzyme activity proportional to F') corresponds to a model in which the Ca-ATPase is a functional dimer at any step or throughout the enzymatic cycle. ( c ) A modification of model b is presented in which enzyme activity is proportional to (2F -1)'; this corresponds to a model involving the formation of an irreversible interaction (dead-end complex) between each modified protein and an unmodified protein. Of these models, the data ( Fig. 9) are clearly most consistent with model b, involving dimers, regardless of whether inactivation occurs by DSP (which decreases F by forming stable and presumably inactive oligomers) or by FITC (which decreases F by blocking the ATP-binding site), in agreement with previous work using radiation inactivation (Hymel et al., 1984).
The second-order relationship observed between the enzymatic activity and F suggests either that 1) interactions of Ca-ATPase polypeptide chains are involved in enzyme action or 2) conformational changes that normally occur within a monomer are prevented by intermolecular cross-linking. The FITC-modified enzyme is fully capable of transporting calcium by hydrolysis of acetyl phosphate or other small nucleotide analogs that are not sterically blocked by FITC binding (Pick and Bassilian, 1981). This argues against case 2 above, thus suggesting that protein-protein interactions per se are important to enzymatic function. The random cross-linking pattern (Fig. 7) indicates that these interactions are not longlived and thus that dynamic protein-protein interactions are important. Therefore, these results support previous studies (discussed above) suggesting that the overall rotational diffusion of the Ca-ATPase is a functionally important motion that is rate-limiting under physiological conditions (Hidalgo et al., 1978;Bigelow et al., 1986;Squier and Thomas, 1988), and we propose that protein rotational mobility is involved in making and breaking specific protein-protein interactions that are important in the reaction mechanism.
The suggestion that specific protein-protein interactions occur during the enzymatic cycle is in apparent contradiction to the observation of a random cross-linking pattern that is not altered by phosphoenzyme formation. However, the high density of Ca-ATPase polypeptide chains promotes many nonspecific interactions, such that a distribution of associated complexes occurs (Martonosi and Beeler, 1983;Abney and Owicki, 1985); and therefore, the random cross-linking pattern alone cannot rule out the presence of transient, functional oligomeric complexes of the Ca-ATPase.
Relationship to Other Work on Ca-ATPase Protein-Protein Interactions-Evidence has been presented from a variety of sources that oligomeric structures of the Ca-ATPase in SR are involved in ion translocation (reviewed by Martonosi and Beeler, 1983;. For example, the Hill coeffi-cient for calcium binding is greater than 2 at alkaline pH (Watanabe et al., 1981), indicating the presence of more than two calcium sites in the functional complex. In addition, the Mg2+ dependence of phosphoenzyme hydrolysis is sensitive to the degree of protein-protein association (Yamamoto et al., 1984), and there is a phosphorylation-dependent change in the distance between fluorescent probes on adjacent Ca-ATPase polypeptide chains (Bigelow et al., 1988;Squier et al., 1988a). The second-order inactivation of ATPase activity demonstrated in this study strengthens these previous interpretations that suggested protein-protein interactions are an important part of the reaction cycle. The similarities between the free energy change involved in the formation of phosphoenzyme from inorganic phosphate (de Meis et al., 1982;Pickart and Jencks, 1984) and the free energy change associated with a monomer-to-dimer transition in detergent-solubilized SR (Silva and Verjovski-Almeida, 1985) suggest that these may be related processes. The ligand-dependent formation of ordered arrays whose unit cell contains either dimeric or monomeric species (depending on the ligand) of the Ca-ATPase suggests that there may be a ligand-induced change that alters the nature of the interaction among Ca-ATPase polypeptide chains (Taylor et ul., 1984(Taylor et ul., , 1986Dux et al., 1985). However, protein rotational mobility is not affected by phosphorylation Thomas, 1986,1988), arguing against a simple monomer-to-dimer transition induced by the cycle. Instead, we propose that more subtle changes in proteinprotein interaction are important to the continuation of the reaction cycle (Bigelow et al., 1988;Squier et al., 1988a) and that these changes require protein rotational mobility. Although the size of an associated complex (e.g. dimer) might not change during the cycle, the required orientation of interacting proteins might change, and this would require rotational mobility. This proposal is consistent with the report that cross-linking the Ca-ATPase polypeptide chains subsequent to calcium binding allows the translocation of only two calciums/enzyme upon subsequent addition of ATP (Kurobe et al., 1983).
Relationship to Work on Detergent-solubilized Ca-ATPase-There are numerous reports of detergent-solubilized monomeric preparations of the Ca-ATPase that demonstrate full ATPase activity Tanford, 1977,1978;Moller et al., 1980;Highsmith and Murphy, 1982;Andersen et al., 1983;Ludi and Hasselbach, 1985;Silva and Verjovski-Almeida, 1985;reviewed by Hidalgo, 1985reviewed by Hidalgo, , 1987. Nevertheless, it is difficult to apply results in detergent to the reaction that occurs in the enzyme's native membrane environment. For example, the soluble preparations are less stable than the native preparation (McIntosh and Ross, 1985), suggesting that either protein-protein or lipid-protein interactions are necessary to maintain the stable conformation of the enzyme throughout the reaction cycle. Detergents and other bilayerdisrupting agents often activate the Ca-ATPase activity in reconstituted preparations (Moore et al., 1981), indicating that the membrane offers constraints that are not present in detergent solution. For example, diethyl ether has no effect in detergent solution but activates the Ca-ATPase in native membranes %fold, apparently by releasing the physical constraints imposed upon the Ca-ATPase by adjacent lipids or proteins (Bigelow and Thomas, 1987). The crowded membrane may provide physical barriers to conformational changes within the enzyme that are necessary for enzymatic function, and protein-protein interactions in the membrane may affect conformational changes within the "subunits," in analogy to the allosteric control occurring in hemoglobin (reviewed by Ackers and Smith, 1987).
Conclusions-The effects of cross-linking on protein rotational mobility (Fig. 6) show that ST-EPR is sensitive to the overall mobility of the Ca-ATPase with respect to the membrane normal, although some intramolecular motion is probably also present. The apparently random cross-linking pattern (Fig. 7), the correlation of Ca-ATPase activity with protein rotational mobility (Fig. 8), and the agreement between the two inactivation profiles and their second-order dependence on F (Fig. 9), combined with other results indicating that protein mobility may be rate-limiting under physiological conditions (Bigelow et al., 1986;Bigelow and Thomas, 1987;Squier et al., 1988b), suggest that dynamic protein-protein interactions are important to the enzymatic cycle and that rotational diffusion of the Ca-ATPase is important in making and breaking these interactions. More detailed information about the Ca-ATPase structure during the reaction cycle will be required to characterize these interactions further and to determine their relationship to conformational transitions within the enzyme.