Lipid Fluidity Directly Modulates the Overall Protein Rotational Mobility of the Ca-ATPase in Sarcoplasmic Reticulum*

We have developed a quantitative and relatively model-independent measure of lipid fluidity using EPR and have applied this method to compare the temperature dependence of lipid hydrocarbon chain fluidity, overall protein rotational mobility, and the calcium-dependent enzymatic activity of the Ca-ATPase in sarcoplasmic reticulum. We define membrane lipid fluid- ity to be T/q, where q is the viscosity of a long chain hydrocarbon reference solvent in which a fatty acid spin label gives the same EPR spectrum (quantitated by the order parameter S) as observed for the same probe in the membrane. This measure is independent of the reference solvent used as long as the spectral line shapes in the membrane and the solvent match precisely, indicating that the same type of anisotropic probe motion occurs in the two systems. We argue that this empirical measurement of fluidity, defined in anal-ogy to the macroscopic fluidity (!l‘/q) of a bulk solvent, should be more directly related to protein rotational mobility (and thus to protein function) than are more conventional measures of fluidity, such as the rate or amplitude of rotational motion of the lipid hydrocarbon chains themselves. This new definition thus offers a fluidity measure that is more directly relevant to the protein’s behavior. The direct relationship between this measure of membrane fluidity and protein rotational mobility is supported by measurements in sar- coplasmic reticulum. The overall rotational motion of the spin-labeled Ca-ATPase protein was measured by saturation-transfer EPR. The Arrhenius activation energy for protein rotational mobility (11-12 kcal/mol/ degree)


Lipid Fluidity Directly Modulates the Overall Protein Rotational
Mobility of the Ca-ATPase in Sarcoplasmic Reticulum* (Received for publication, August 28, 1987) Thomas C. Squier$, Diana J. Bigelow$,and David D. Thomas8 From the Department of Biochemistry, University of Minnesota Medical School, Minneapolis, Minnesota 55455 We have developed a quantitative and relatively model-independent measure of lipid fluidity using EPR and have applied this method to compare the temperature dependence of lipid hydrocarbon chain fluidity, overall protein rotational mobility, and the calciumdependent enzymatic activity of the Ca-ATPase in sarcoplasmic reticulum. We define membrane lipid fluidity to be T/q, where q is the viscosity of a long chain hydrocarbon reference solvent in which a fatty acid spin label gives the same EPR spectrum (quantitated by the order parameter S) as observed for the same probe in the membrane. This measure is independent of the reference solvent used as long as the spectral line shapes in the membrane and the solvent match precisely, indicating that the same type of anisotropic probe motion occurs in the two systems. We argue that this empirical measurement of fluidity, defined in analogy to the macroscopic fluidity (!l'/q) of a bulk solvent, should be more directly related to protein rotational mobility (and thus to protein function) than are more conventional measures of fluidity, such as the rate or amplitude of rotational motion of the lipid hydrocarbon chains themselves. This new definition thus offers a fluidity measure that is more directly relevant to the protein's behavior. The direct relationship between this measure of membrane fluidity and protein rotational mobility is supported by measurements in sarcoplasmic reticulum. The overall rotational motion of the spin-labeled Ca-ATPase protein was measured by saturation-transfer EPR. The Arrhenius activation energy for protein rotational mobility (11-12 kcal/mol/ degree) agrees well with the activation energy for lipid fluidity, if defined as in this study, but not if more conventional definitions of lipid fluidity are used. This agreement, which extends over the entire temperature range from 0 to 4OoC, suggests that protein mobility depends directly on lipid fluidity in this system, as predicted from hydrodynamic theory. The same activation energy is observed for the calcium-dependent ATPase activity under physiological conditions, suggesting that protein rotational mobility (dependent on lipid fluidity) is involved in the rate-limiting step of active calcium transport.
Since the general acceptance that biological membranes are fluid structures, there has been an active discussion of the possible role that changes in membrane fluidity could play in triggering or modulating membrane functions (reviewed by Kates and Manson, 1984;Shinitzky, 1984;Deuticke and Haest, 1987). Lipids in most biological membranes under physiological conditions are primarily in the liquid-crystalline phase (McElhaney, 1984); in fact, membrane-bound enzymes reconstituted into pure lipids have consistently demonstrated little or no activity below the phase transition (reviewed by Sandermann, 1978;Shinitzky, 1984;Hidalgo, 1985Hidalgo, , 1987. Although head group composition (reviewed by Hidalgo, 1985) and fatty acyl chain length (and thus bilayer thickness) (Lewis and Engelman, 1983) have been shown to be critical to the functioning of membrane-bound enzymes (Bennett et al., 1980;Caffrey and Feigenson, 1981;Johannsson et al., 1981aJohannsson et al., , 1981bNavarro et al., 1984;East et al., 1984), it is commonly proposed that an important general mechanism for the regulation of membrane function is the modulation of both specific interactions at the lipid-protein interface (Fong and Mc-Namee, 1987;Bigelow and Thomas, 1987) and membrane fluidity, presumably through changes in fatty acid unsaturation and cholesterol content (reviewed by Benga and Holmes, 1984;Shinitzky, 1984;Yeagle, 1985). Many membrane activities have been correlated with membrane fluidity Sinensky et al., 1979;Blanquet, 1983;Bigelow and Thomas, 1987); however, examples in which a precise role for membrane fluidity has been identified are limited (reviewed by Marsh and Watts, 1982;Shinitzky, 1984;Marsh, 1985). We intend to provide more quantitative and useful measurements of membrane fluidity and to determine the relationship between fluidity and function. SR' is an ideal system in which to study the role of membrane fluidity because the Ca-ATPase has little or no selectivity for different phospholipids (Roelofsen, 1981;Caffrey and Feigenson, 1981;.
It has been proposed that the correlation of some membrane functions with lipid fluidity is the result of a general requirement for mobility of membrane-bound proteins (reviewed by Shinitzky, 1984). Support for this proposal has come from the previous findings in our laboratory that the overall rotational mobility of the Ca-ATPase of SR, as well as lipid hydrocarbon chain dynamics, measured by EPR correlates well with enzymatic function under conditions that perturb both functional properties and molecular motions (reviewed by Thomas, 1985Hidalgo, 1985Hidalgo, , 1987. In addition, it has been suggested that the rate-limiting step of calcium transport by this enzyme may be dependent on the fluidity of the bilayer (Moore et al., 1978;Almeida et al., 1982), as well as on the protein rotational mobility (Bigelow et al., 1986;Bigelow and The abbreviations used are: SR, sarcoplasmic reticulum; ST-EPR, saturation-transfer E P R SASL, stearic acid spin label(s); MESL, methyl ester spin label(s); MOPS, 3-(N-morpholino)propanesulfonic acid; EGTA, [ethylenebis(oxyethylenenitrilo)]tetraacetic acid. Thomas, 1987), although this point is controversial (East et al., 1984;Froud et al., 1986aFroud et al., , 1986b. In this study, in order to help resolve this controversy regarding the role of a fluid bilayer in enzymatic function, we have quanti~tively related lipid fluidity to protein rotational mobility. The most important step in this effort was to define lipid fluidity in a way that satisfies two requirements: ( a ) the definition must lend itself to quantitative and unambiguous measurement, and ( b ) there must be a straightforward theoretical prediction for the relationship between lipid fluidity and protein rotational mobility. Most previous studies have focused on the first requirement at the expense of the second. That is, lipid fluidity has usually been characterized by the measurement of lipid probe rotational motions, usually using either fluorescent probes or spin labels. Although these motions can be measured directly and unambiguously, they occur with a much smaller amplitude and on a much faster time scale than overall protein rotational motions, and no reliable theory has been developed to describe their relationship to protein motions. In contrast, a quanti~tive theory has been developed relating the overall brownian rotational diffusion of membrane proteins to the viscosity ( q ) of the surrounding lipids (Saffman and Delbriick, 1975). The key result of this theory is that the protein mobility (rate of rotational diffusion) is directly proportional to T/q, as long as the size and shape of the protein remain constant. This theory suggests that membrane viscosity is obtained more appropriately by measuring the rotational diffusion of membrane proteins, rather than lipid hydrocarbon chain dynamics (Cherry and Godfrey, 1981;Jiihnig, 1986).
Thus, it is appropriate to define fluidity to be T/q, associating fluidity with the lipid viscosity, which describes the potential energy barrier to protein rotational motion. The remaining problem is to define lipid viscosity and to relate it empirically to spectroscopic probe measurements of lipid motions. Since 9 discussed in the theory (Saffman and Delbriick, 1975) describes the motion of a large object (protein) through small solvent molecules (lipids), it is appropriate to define q from the same kind of measurement that is used to measure the macroscopic viscosity of bulk liquids. Thus, a spectroscopic measurement with a lipid probe in a locally ordered long chain solvent, which is structurally similar to a phospholipid bilayer, can be used to calibrate the viscosity of membrane lipids provided that the macroscopic viscosity of the solvent is known at various temperatures. That is, if the spectroscopic measurement gives the same result in the membrane as in the solvent, the two can be said to have the same viscosity (fluidity).
This type of calibration has been employed previously with fluorescent probes, but the measurements of viscosity obtained were dependent upon the probe and the reference solvent chosen (Shinitzky et aL, 1971;Hare and Lussan, 1977). A possible source of these problems is that most of the fluorescent probes and solvents had molecular structures unlike those of phospholipid hydrocarbon chains, making it unlikely that the same kind of anisotropic motions would occur as in the lipid bilayer. The type of measurement usually used in those studies was steady-state fluorescence polarization, which lacks the resolution needed to characterize in detail the type of anisotropic motion occurring.
Therefore, in this study, we have chosen a combination of spectroscopic probes and reference solvents more likely to approximate lipid motions in the biological membrane, i.e. spin-labeled fatty acid analogs in reference solvents composed of long chain triglycerides. Our spectroscopic measurements, EPR spectra, are quite sensitive to the details of anisotropic rotational motion, providing a very rigorous test of whether the motions are the same in the reference solvents as in the membrane. We have developed an empirical measure of lipid fluidity (TI?), where T and q are the temperature and viscosity of the reference solvent in which the spin label spectrum matches that observed in the membrane. We have evaluated the relevance of this measurement to membrane function and protein dynamics in SR by comparing the temperature dependence of lipid fluidity with that of the calcium-dependent ATPase activity and overall protein rotational mobility of the Ca-ATPase, as measured by saturation-transfer EPR (ST-EPR). This study was undertaken as a result of our previous finding that Arrhenius plots of lipid probe mobility and protein mobility are both linear, but have different apparent activation energies (Bigelow et ul., 1986). In this study, we ask whether the agreement in activation energy is better if a more appropriate measure of lipid fluidity (rather than probe mobility) is employed.

EXPERIMENTAL PROCEDURES
Membrane Preparations-Vesicles of fragmented SR were prepared from rabbit skeletal white (fast twitch) muscle, essentially as described previously (Fernandez et al., 1980), producing a preparation in which 80 f 5% of the protein is the Ca-ATPase (Le. 7.2 nmol of Ca-ATPase/mg) and that contains about 80 phosphoIipids/Ca-ATPase molecule (i.e. 580 nmol of phospholipid/mg of SR) (Bigelow et al., 1986). All preparation was done at 4 "C. The membrane vesicles were suspended in 0.3 M sucrose, 20 mM MOPS (pH 7.0) and stored in liquid nitrogen. Total SR lipids were extracted by a modification (Hidalgo et aL, 1976) of the method of Folch et al. (1957) using nitrogen-saturated solvents to prevent oxidation. This lipid extract, as characterized by fatty acid composition, head group composition, and cholesterol content, is the same as that of the native SR vesicles (Bigelow et al., 1986). The extracted lipid was stored in chloroform/ methanol (2:l) at -20°C. Liposomes were prepared by drying an aliquot of extracted lipid under nitrogen and vortexing in 0.3 M sucrose, 20 mM MOPS (pH 7.0). Enzymatic Assays-Calcium-dependent ATPase activity was normally measured in a solution containing 0.05 mg of SR protein/ml, 60 mM KC1,6 mM MgCL, 2 gM A23187,25 mM MOPS (pH 7.01, and either 0.1 mM CaCL or 2 mM EGTA. The pH of the solution varied between 6.9 and 7.1 from 0 to 40 "C. 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). ATPase activity measured in the presence of EGTA (basal activity) was subtracted from that assayed in the presence of CaC& (total ATPase activity) in order to obtain the calcium-dependent ATPase activity. The calcium-independent ATPase activity was less than 5% of the total ATPase activity. Under these experimental conditions (ie. saturating calcium and ATP), substrate binding is never ratelimiting (Inesi, 1985), allowing us to probe the rate-limiting step of the transport process. Alternatively, ADP production was assayed by monitoring absorbance at 340 nm with the enzyme-linked assay of Warren et al. (1974). Activity assayed in the presence of EGTA (basal activity) was subtracted from that assayed in the presence of CaC& (total Ca-ATPase activity) in order to obtain calcium-dependent ATPase activity. Protein concentrations were determined by a modification of the biuret method using bovine serum albumin as a standard (Gornall et al., 1949).
Calcium transport was measured spectrophotometrically using the differential absorbance of arsenazo 111, a calcium-sensitive dye, as an indicator of extravesicular calcium concentration (Salama and mM KCl, 10 mM M&b, 10 mM MOPS (pH 7.0), 0.1 mM CaC12, and Scarpa, 1983). Reaction conditions were 0.7 mg of SR proteinlml, 80 0.1 mM arsenazo 111. 330 g~ ATP was added to start the reaction. Spectra were recorded sequentially each second with a 1.0-s integration time on a Hewlett-Packard 8451A diode array spectrophotometer. Time-dependent absorbance changes of arsenazo I11 at 675 and 685 nm were calculated from stored spectra. Alternatively, a qualitative index of calcium coupling to ATP hydrolysis was obtained by assaying the calcium-dependent ATPase activity in the presence and absence of 2 PM ionophore A23187 (see above). Reference Soluents-Triglycerides are appropriate model systems for lipid bilayers since they form a homogeneous phase whose bulk Lipid Fluidity and Protein Rotational Mobility i n S R viscosity may be directly measured, and their structure is similar to that of membrane phospholipids. Biological triglycerides (oils) meet these criteria; castor oil (Sigma) and olive oil (Eastman) are relatively homogeneous triglycerides containing approximately 90% ricinoleic and oleic acid, respectively (Sober, 1968;Windholz, 1983), and therefore possess a similar degree of lipid chain unsaturation to that found in SR (Bigelow et al., 1986). Viscosities of these solvents were obtained from standard tables (Mellan, 1970;Weast, 1979). Spin Labeling-Hydrocarbon chain mobility was measured with fatty acid spin labels, N-oxyl-4',4'-dimethyloxazolidine derivatives of stearic acid, designated 5 -, E -, and 16-SASL, and methyl esters of these derivatives, designated 5 -, 12-, and 16-MESL (Aldrich). The number designation indicates the relative position of the nitroxide on the stearic acid. Spin labels were diluted from a stock solution in dimethylformamide into ethanol before adding to liposomes of extracted SR lipids at a ratio of less than one spin labe1/200 phospholipids, with the final ethanol concentration less than 1%. The lipid concentration was made sufficiently high (greater than 50 mM) so that the EPR spectrum contained a negligible contribution from unbound (i.e. aqueous) spin labels. In the case of reference solvents, the spin label was added from an ethanol solution to make a final concentration of 0.1 mM spin label and the final ethanol concentration less than 1%.
EPR Spectroscopy-EPR spectra were obtained with a Varian E-109 spectrometer as described previously (Squier and Thomas, 1986a;. Submicrosecond rotational motion of spin labels was detected by conventional EPR (first harmonic absorption in phase, designated VI) 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 VZ') using 5O-kHz field modulation (with a modulation amplitude of 5 G ) and a microwave field intensity of 0.25 G. All EPR samples were suspended in 0.3 M sucrose, 20 mM MOPS (pH 7.0). SR samples contained a protein concentration greater than 40 mg/ml. All ST-EPR studies were done in the absence of oxygen. Oxygen was removed from reference and experimental samples using gas-permeable sample cells purged with NO (Popp and Hyde, 1981). Temperature was controlled to within 0.5 "C with a Varian V4540 variable temperature controller. 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 Analysis-Conventional EPR spectra of fatty acid spin labels were evaluated by measuring the effective order parameter S , which depends only on the angular amplitude of the motion of the probe, assuming very fast anisotropic motion (7, < 1 ns; where T~ is the effective rotational correlation time), such that an increase in rate has no effect on the positions of the spectral extrema (see below).
Values of S greater than 0.3 can be measured using the standard formula relating S to both inner and outer extrema (Gaffney and Lin, 1976;Gaffney, 1976), i.e.
where C = 1.4 -0.053 (TII' -T&'). 2Tll' and 2Tll' are the measured inner and outer extrema resolved in the EPR spectrum in gauss (see Fig. 1). For values of S less than 0.3, the outer extrema cannot be resolved (see 12-SASL; Fig. 3), resulting in systematic errors in the calculation of S (Marsh, 1981;Bigelow et al., 1986). However, even at these low values of S, the inner extrema are well resolved. Therefore, in spectra where TI,' values are not resolved, we have used T,, to measure S (valid for S > 0.1) using the relationship (Gaffney, 1976)

of Equation 2:
where TO is the isotropic hyperfine splitting constant in the absence of anisotropic effects. T, is the principal value of the hyperfine 18°C) and olive oil (---; 1O"C, T/v = 2.38 K centipoise"). The spectra of 5-SASL in either olive oil or SR lipid is indicative of the same type of anisotropic motion (see "Experimental Procedures"). The distance between the outer extrema (indicated by arrows) is 2T,', whereas the distance between the inner extrema (indicated by dots) is 2T,'. These spectral positions are used to calculate the order parameter ( S = 0.56; see "Experimental Procedures"). Accurate measurement of the positions of broad extrema, such as in the above spectra, was obtained from extrema recorded with 10-100 times increased instrumental gain. The base line is 100 G wide.
constant for an axially symmetric system (e.g. a lipid bilayer) (Poole, 1983). Values of To and T, correspond to values of T,' at S = 0 (isotropic) and S = 1.0 (ordered), respectively. TO was determined for each spin label and solvent in two ways, which gave results in good agreement. 1) The separation between the low field and high field zero-crossing points (i.e. 2 TO) was measured from a spectrum where S approaches zero, Le. increasing the sample temperature does not further narrow the spectrum. 2) T,' was plotted as a function of S and extrapolated to S = 0 using Equation 1. Similarly, T, was determined by extrapolating this plot to S = 1. Values of To for 5-SASL in castor oil, olive oil, and vesicles made from extracted SR lipid are 13.4, 14.4, and 13.2 G, respectively. Values of T, for 5-SASL in castor oil, olive oil, and vesicles made from extracted SR lipid are 5.5, 4.7, and 6.6 G , respectively. Since Equation 2 can be used over the entire range of spectra obtained in this study, Equation 2 was used to determine the order parameters shown below. For order parameters S > 0.3, where both Equations 1 and 2 are valid, the two methods of measuring S gave good agreement.
The effective rotational correlation times for maleimide spinlabeled SR were determined from ST-EPR spectra using a plot of the Vz' integral uersw correlation time based on reference spectra of known correlation time obtained from isotropically tumbling spinlabeled hemoglobin in aqueous glycerol solutions (Squier and Thomas, 1986a).
Arrhenius Analysis-Apparent activation energies Ea were determined from the slopes (-Ea/R) of Arrhenius plots by using linear regression least-squares analysis as described previously (Bigelow et al., 1986). The report of a change in slope of an Arrhenius plot required that the correlation coefficient above and below the break point was significantly larger than the correlation coefficient for a single line (Bigelow et al., 1986).

Comparison of Anisotropic Motion in Biological Membranes
with Triglyceride Reference Solvents-The motion of SASL in vesicles made from SR lipids is analogous to that observed in biological triglycerides, as can be seen by the virtually identical EPR spectra obtained in the olive oil in comparison t o those obtained in SR (Fig. 1). These spectra show clear evidence for anisotropic (restricted amplitude) rotational motion since the line shapes are qualitatively different from those corresponding to isotropic rotational motion . For both spectra, the inner and outer extrema are at the same field position, indicating that they have the same order parameter ( S ; see "Experimental Procedures"). Similarly excellent line shape matches can be obtained for other spin labels and temperatures in SR using either olive oil or Lipid Fluidity and Protein Rotational Mobility in S R 9181 castor oil and varying the temperature. Therefore, we define lipid fluidity to be T/o, where T is the absolute temperature and 7 is the viscosity of a long chain reference solvent in which the fatty acid spin label gives the same conventional EPR spectrum (as characterized by S) as observed in the membrane. Calibration Plot for Measuring Lipid Fluidity-The data in Fig. 2 were obtained from EPR spectra of lipid analogs (stearic acid spin labels and their corresponding methyl ester derivatives, i.e. 5and 12-SASL and 5-and 12-MESL) in castor oil and olive oil (reference solvents). Fig. 2 illustrates the relationship between measurements of lipid hydrocarbon chain dynamics, expressed as spin label order parameters (S; see "Experimental Procedures"), and fluidity, expressed as T/V. T/v is plotted instead of 1/11 because the diffusion of a macromolecule in either a bulk solvent or a membrane is predicted to be proportional to T/q (Saffman and Delbriick, 1975;. The order parameters for a given T/q are about the same for 5-and 12-SASL in triglycerides (oils; see Fig. 2) as opposed to these spin labels in biological membranes, where there is a large difference in the order parameter for these two labels at the same temperature (Figs. 3 and 4). This highlights the major structural difference between phospholipid bilayers and triglycerides. Phospholipids are extremely amphiphilic molecules that generally form lyotropic smectic mesophases in aqueous solution and consequently display a "fluidity gradient" normal to the bilayer due to the lipid polar head group's strong interaction with the aqueous phase (Tanford, 1980). On the other hand, triglycerides are devoid of water and form thermotropic smectic mesophases resulting from the interdigitation of the triglyceride molecules to form symmetrical layers (Chapman, 1962). In this case, the similar distances of the nitroxide position in 5-and 12-SASL from an end of the stearic acid result in the measurement of a similar order parameter. Likewise, this calibration plot is independent of the charge on the spin label (Fig. 2). Therefore, it is appropriate to use this empirical calibration plot to express measurements of S, obtained from spin labels in SR lipids, in terms of T/g, thus determining the fluidity for the membrane lipids. mobility was probed as a function of temperature at various bilayer depths using stearic acid analogs spin-labeled at several positions along the hydrocarbon chain depths in vesicles of extracted SR lipids (Fig. 3). These vesicles have a lipid composition identical to that in intact SR (Bigelow et al., 1986) and have the advantage of being a homogeneous motional population, allowing us to quantitatively analyze the motional properties. The presence of the Ca-ATPase in intact SR results in a heterogeneous motional population of lipid probes (Thomas et al., 1982), making it difficult to accurately measure the order parameter for either population of probes (Marsh and Watts, 1982;Meirovitch et al., 1984). The exchange between these lipid populations is probably fast (i.e. lo7 s-l) (East et al., 1985) in comparison to the overall rotational motion of the Ca-ATPase (i.e. T , -~ E lo' s-') , indicating that the protein's overall rotational motion is modulated by the entire lipid population (with the possible exception of cholesterol, which may be excluded from the lipid adjacent to the protein) (Silvius et al., 1984). Therefore, to a good approximation, we can estimate the average viscosity experienced by the Ca-ATPase by using vesicles made from extracted SR lipid.

Temperature Dependence of SR Lipid Fluidity-Lipid chain
Spectra obtained from 5or 12-SASL in extracted SR lipids correspond to a homogeneous population of spin labels whose line shapes are characteristic of significant orientational order; however, only spectra from 5-SASL resolve the outer extrema over the entire temperature range studied (i.e. 0-40 "C), allowing S to be calculated from either Equation 1 or 2 (see "Experimental Procedures"). In the case of 12-SASL, the outer extrema are only resolved from 0 to 27 "C, requiring S to be calculated from the inner splitting (i.e. Equation 2) for temperatures above 27°C. In the case of 16-SASL) the spectral anisotropy is almost completely averaged ( S 5 0.1 for most or all of the spectra in Fig. 3, right), indicating little anisotropy (little orientational order), thus preventing the quantitative measurement of S (see "Experimental Procedures"). In the presence of such low order, the precise model describing the rotational motion of stearic acid spin labels is unclear (Bigelow et al., 1986). Therefore, 5and 12-SASL were used for further studies.
As the nitroxide is placed down the fatty acyl chain toward the center of the bilayer, the spectra display a rotational mobility gradient typical of lipid bilayers, from a relatively restricted polar head region (i.e. 5-SASL) to a more mobile terminal methyl region (i.e. 16-SASL). Spectra from 12-SASL exhibit decreased order (increased fluidity) relative to those

Lipid Fluidity and Protein Rotational Mobility in SR
from 5-SASL; however, for both probes, there is a linear decrease in order parameter (increase in fluidity) with increasing temperature (Fig. 4).
The order parameters plotted in Fig. 4 can be expressed in terms of fluidity using the calibration plot of S versus T/q in Fig. 2, and the resulting values of T/q can be plotted in the form of an Arrhenius plot (Fig. 5) since the rate of overall protein rotational motion (measured by ST-EPR) (Squier et al., 1988) is predicted to be proportional to T / q (Saffman and Delbriick, 1975). The slopes, i.e. apparent activation energies, are 11.5 * 0.3 and 11.0 f 0.4 kcal/mol/degree for 5-and 12-SASL, respectively. Thus, although the absolute values of SR lipid fluidity depend on the depth of the probe, due to the fluidity gradient, their activation energies are the same. Values of the membrane viscosity measured in this study range from 0.27 poise at 39 "C at the 12-position along the hydrocarbon chain to 8.8 poise at 0 "C at the 5-position along the hydrocarbon chain, in general agreement with independent measurements of membrane viscosity (Almeida et al., 1982;Jahnig, 1986). the microsecond rotational mobility characteristic of many membrane proteins; and in the case of the Ca-ATPase, it is primarily sensitive to the overall rotational motion of the Ca-ATPase with respect to the membrane normal Squier et al., 1988). An Arrhenius plot demonstrates a linear temperature dependence of protein rotational mobility ( T~-' ) , with an apparent activation energy of 11.2 f 0.4 kcal/mol/ egree (Fig. 6). This activation energy is the same as that observed for T/q in SR lipids ( Fig. 5 and Table I). Thus, as predicted from theory (Saffman and Delbriick, 1975), the rate of protein rotational motion is proportional to T/q (Fig. 7), indicating that our definition of fluidity (T/q) is appropriate. . Correlation times were obtained through the comparison of reference spectra corresponding to isotropic motion. The Arrhenius activation energy was computed (see "Experimental Procedures") to be 10.7 f 0.5 kcal/mol/degree for this data set, with a correlation coefficient of 0.988. When an attempt was made to fit this plot to two lines, the mean correlation coefficient was 0.973, indicating that the single line fit was superior, confirming previous results (Bigelow et al., 1986). Similar results were obtained with six other data sets with an activation energy for protein rotational motion of 11.2 f 0.5 kcal/mol/degree (mean f S.E.). In contrast, a definition of fluidity as either the rate or amplitude of lipid chain motions measured by EPR spectral parameters does not yield an activation energy comparable to that of protein motion (Bigelow et al., 1986). Apparent activation energies for lipid chain motions in SR lipids were measured to be 3.0 and 3.6 kcal/mol/degree for 5-and 12-SASL, respectively.

Temperature Dependence of Ca-ATPase Rotational Mobility in SR-
Temperature Dependence of Enzymatic Activity-The functional significance of the modulation of enzyme rotational mobility by lipid fluidity is suggested by the measurement of the activation energies for Ca-ATPase activity in SR (Table  I and Fig. 8). Although we have focused our attention on the calcium-dependent ATPase activity, this activity is coupled to calcium transport. The Arrhenius plot of the calciumdependent ATPase activity in SR (in the presence of KCl, i.e. normal assay conditions; Fig. 8) exhibits a change in slope TABLE I E. for dynamic processes in SR Effective activation energies (E.) were calculated from Arrhenius plots of lipid fluidity (Fig. 5), protein mobility (Fig. 6), and enzymatic activity (+KCI; Fig. 8).
(break) at 20 f 1 "C, with apparent activation energies of 11.8 f 0.4 and 23 f 1 kcal/mol/degree, above and below 20 "C, respectively. In either the absence of KC1 or the presence of diethyl ether, the rate-limiting step of ATP hydrolysis is temperature-independent, and the apparent activation energies are 22 +-1 kcal/mol/degree. The observation of Arrhenius activation energies that are modified between two discrete values as a function of temperature, salt, or ether concentration supports the concept that Arrhenius plots of Ca-ATPase activity accurately measure the rate-limiting step of the enzymatic reaction and that the change in slope is the result of a temperature-dependent change in the rate-limiting step.
These perturbations affect the reaction mechanism in different ways: the absence of KC1 slows the overall reaction rate, whereas the addition of ether accelerates the reaction rate. Using both conventional and saturation-transfer EPR to probe the effect of these perturbants on the membrane dynamics, we find that KC1 has no effect on either the protein or lipid dynamics. On the other hand, diethyl ether fluidizes the membrane (Bigelow and Thomas, 1987), resulting in greater protein rotational mobility. These results suggest that protein mobility contributes an important, albeit not exclusive, effect on the rate-limiting step and that, under assay conditions that preferentially reduce the phosphatase activity of the Ca-ATPase (ie. minus KCl) or that accelerate protein mobility (plus ether), protein mobility is not rate-limiting.

DISCUSSION
Summary of Results-We have explored the functional significance of lipid fluidity in SR to the Ca-ATPase reaction mechanism by quantitatively comparing the lipid hydrocarbon chain dynamics, as measured by conventional EPR spectra of stearic acid spin labels in SR lipids, with the overall rotational mobility of the protein, as measured by ST-EPR spectra of maleimide spin-labeled Ca-ATPase. In order to make this comparison, it was necessary to construct an empirical calibration plot (Fig. 2) relating the lipid probe dynamics to lipid fluidity (T/v, where 1 is the viscosity). The validity of our calibration plot is supported by the linear relationship between T/TJ and the protein rotational mobility (7r-1) (Fig.   7), as predicted by hydrodynamic theory (Saffman and Delbriick, 1975;Hughes et al., 1982;Peters and Cherry, 1982;Wiegel and Heringa, 1985). Thus, protein mobility is modulated directly by lipid fluidity in SR. The apparent activation energy (from an Arrhenius analysis) of lipid fluidity (Fig. 5) is the same as that for protein mobility (Fig. 6). Under nearphysiological conditions (above 20 "C in the presence of KCl), the Arrhenius activation energy of the calcium-dependent ATPase activity ( Fig. 8 and Table I) is the same as that of both lipid fluidity and protein mobility, suggesting that membrane fluidity (as defined by both lipid and protein mobility) is essential to the rate-limiting step of the Ca-ATPase reaction. Under other assay conditions (achieved by decreasing the temperature below ZOO, removing KCl, or adding diethyl ether), the Ca-ATPase activation energy is about twice that of fluidity (Fig. 8), suggesting that a different step has become rate-limiting.
Choice of Reference Solvent-The appropriate model system for motion in a membrane bilayer is a structure resembling a phospholipid, but whose bulk viscosity can be readily measured. The latter criterion rules out the use of lyotropic crystals (e.g. hydrated phospholipids) as calibration standards since the presence of water prevents the direct measurement of the bulk viscosity. Triglycerides, however, exist as thermotropic liquid crystals, forming a homogeneous phase whose bulk viscosity may be directly measured. Biological triglycerides possess a similar structure to phospholipids (i.e. unsaturation at the 9-position and ordered acyl chains that form a smectic mesophase (Chapman, 1962;Seelig, 1976); synthetic oils (e.g. paraffin) have much less structural similarity to biological phospholipids, possessing neither the characteristic unsaturation nor the triglyceride backbone. The reference solvents chosen are ordered long chain hydrocarbons, in which the type of molecular motion is similar to that in membranes, as confirmed by the observation that the EPR line shapes of fatty acid spin labels in these solvents have the same characteristic features as those observed with the same spin labels in lipid bilayers. EPR order parameters, characterizing probe motions in these solvents, were plotted against log(T/v), where T is temperature and l/v is viscosity. The resulting calibration plots are independent of the solvent used, the position of the nitroxide group along the fatty acid chain, and the charge on the probe, supporting the model independence of using these calibration plots. Castor oil was chosen due to its uniquely wide range of relevant viscosities. Olive oil, being more fluid, was used for comparison purposes in order to demonstrate the solvent independence of the measured spectral parameter.

Correlation between Protein Mobility and Lipid Fluidity-
Previous studies of the Ca-ATPase and other membrane proteins have, in general, compared protein rotational mobility directly with the mobility of lipid probes without translating the latter into fluidity, as defined in this study. Nevertheless, qualitative correlations between protein and lipid probe mobility have often been demonstrated (reviewed by Shinitzky, 1984;Thomas, 1985) most dramatically as a large decrease in protein mobility below the first-order phase transition temperature in a recombinant membrane having only one lipid component Peters and Cherry, 1982). Some aspects of the theory of membrane protein rotational motion (Saffman and Delbriick, 1975) have been verified quantitatively, e.g. the ratio of translational to rotational diffusion coefficients and the relationship of both coefficients to the size of the protein (Peters and Cherry, 1982;Vaz et al., 1982). The primary technical contribution of this study is to show that our definition of lipid fluidity, based on spectroscopic measurements of the effective viscosity 7, leads to a dependence of protein mobility on fluidity that agrees quantitatively with the prediction of hydrodynamic theory (Saffman and Delbriick, 1975). That is, overall protein rotational mobility with respect to the membrane normal should be proportional to T / v , as long as the size and shape of the protein remain constant. Using the empirical calibration relating the motional properties of fatty acid spin labels to lipid fluidity presented in this paper, other modifiers of lipid fluidity (e.g. diethyl ether) have also been shown to modulate protein rotational mobility through lipid fluidity (Bigelow and Thomas, 1987).
Correlation of Calcium-dependent ATPase Activity with Membrane Fluidity-A number of previous studies have obtained evidence qualitatively correlating lipid probe mobility (related to lipid fluidity) with calcium-dependent ATPase activity in SR. A substantial decrease of lipid probe mobility, relative to that observed under physiological conditions, has consistently produced a decrease in calcium-dependent ATPase activity whether the decrease in lipid fluidity was achieved by substitution of a more solid lipid (Hidalgo et al., 1976Hesketh et al., 1976) or by a decrease in temperature (Hidalgo et al., 1976;Hesketh et al., 1976;Bigelow et al., 1986). An apparent exception to this principle was obtained with cholesterol, which decreases lipid fluidity in SR vesicles without affecting enzymatic activity (Warren et al., 1975;Johannsson et al., 1981b). However, since at normal lipid-toprotein ratios cholesterol analogs do not exchange into (i.e. are preferentially excluded from) the layer of lipids directly surrounding the protein (Warren et al., 1975;Simmonds et al., 1982Silvius et al., 1984), the effective viscosity experienced by the Ca-ATPase is unaffected by the presence of cholesterol. However, when the lipid content is reduced so that cholesterol must directly interact with the Ca-ATPase, Le. at lipid-to-protein ratios less than or equal to 30, cholesterol has significant and complex effects . Similarly, an increase in boundary lipid fluidity, caused by the addition of diethyl ether, has been shown to activate both calcium-dependent ATPase and associated transport activity, although there is an optimal fluidity above which the enzymatic activity decreases (Bigelow and Thomas, 1987). Thus, changes in lipid fluidity consistently modulate Ca-ATPase activity as long as they include the boundary lipid. Although East et al. (1984) emphasized the importance of membrane thickness rather than fluidity within a given membrane thickness, they also observed a correlation between hydrocarbon chain mobility and enzymatic activity, supporting our conclusion that there is a direct relationship between hydrocarbon chain mobility and enzymatic activity.
Inhibitors of Calcium-dependent ATPase Activity That Do Not Affect Fluidity-However, a number of physical perturbations have been shown to substantially inhibit the Ca-ATPase activity without greatly affecting lipid fluidity, even in the boundary layer, e.g. changes in bilayer thickness (Moore et al., 1981;Caffrey and Feigensen, 1981;Johannsson et al., 1981aJohannsson et al., , 1981bEast et al., 1984)) protein-protein cross-linking (Thomas et al., 1982;Squier et al., 1988), addition of nonaqueous solvents (Squier and Thomas, 1988), addition of decavanadate (Lewis and Thomas, 1986), and the addition of millimolar calcium . Thus, there are clearly other physical constraints affecting the enzymatic activity of the Ca-ATPase besides lipid fluidity. Nevertheless, in the cases above where protein rotational mobility has also been monitored, decreases in protein mobility (usually due to protein aggregation) consistently accompanied the inhibition of the Ca-ATPase Lewis and Thomas, 1986;Squier and Thomas, 1988;Squier et al., 1988). Thus, the apparent functional requirement for membrane fluidity in SR can most simply be interpreted as a requirement for enzyme mobility, as proposed previously Hidalgo et al., 1978;Moore et al., 1978;Almeida et al., 1982Almeida et al., , 1984Bigelow et al., 1986;Bigelow and Thomas, 1987).

Possible Role for Protein Mobility in Ca-ATPase Mecha-
nism-It is beyond the scope of this study to define the role of specific protein motions in the Ca-ATPase mechanism because high resolution structural data for the enzyme do not yet exist and because further measurements of protein dynamics must be made and correlated with specific steps in the reaction cycle. There are many aspects of protein mobility that may prove to be important to the enzymatic mechanism of the Ca-ATPase, from small-scale conformational fluctuations (not detected directly by the probe in this study) to overall protein rotations (which our probe directly detects). Rotational mobility could facilitate specific protein-protein interactions necessary for ion translocation, as previously suggested (Singer, 1974;Dutton et al., 1976), and we have obtained evidence supporting this proposal in SR (Squier et al., 1988). Orientational constraints could limit the rate of productive associations between Ca-ATPase polypeptide chains, resulting in a rate constant for the process of protein association that is slower than the diffusion-limited process by several orders of magnitude (Berg and von Hippel, 1985), thus reconciling the time scale of protein rotation (about lo-' s at 37 "C) with the time scale of enzyme turnover (about 10" s at 37 "C). Rates of rotational and lateral diffusion are related; both are predicted to be inversely proportional to the viscosity of the surrounding medium (Saffman and Delbriick, 1975;Hughes et al., 1982;Peters and Cherry, 1982). Therefore, the results from this study do not distinguish between the functional significance of rotational uersus lateral diffusion.
Conclusions-This and the two previous papers (Squier et al., 1988;Squier and Thomas, 1988), as well as earlier studies Thomas and Hidalgo, 1978;Thomas et al., 1982;Squier and Thomas, 1986b;Bigelow et al., 1986;Bigelow and Thomas, 1987), have probed the physical and functional significance of rotational dynamics in SR. When either the mean molecular weight of the spin-labeled Ca-ATPase oligomer or the fluidity of the hydrocarbon chain environment is altered, we find that the relationship between membrane fluidity and protein rotational mobility agrees with that predicted theoretically (Saffman and Delbriick, 1975). Whenever protein mobility has been perturbed, it has been found that there is a direct correlation with enzymatic activity. Under physiological conditions, protein rotational mobility has the same Arrhenius activation energy as enzymatic activity; and conditions that increase protein mobility (e.g. diethyl ether) change the rate-limiting step at physiological temperatures, suggesting that protein mobility is involved in the rate-limiting step (phosphoenzyme decomposition). In fact, conditions that selectively inhibit phosphoenzyme decomposition also decrease protein mobility, emphasizing the importance of protein mobility to the enzymatic reaction mechanism (Squier and Thomas, 1988). The methods developed in this study should be directly applicable to other membrane systems and should provide a useful tool in clarifying the quantitative role of membrane fluidity in the mechanisms of integral membrane enzymes.