A novel spin-label for study of membrane protein rotational diffusion using saturation transfer electron spin resonance. Application to selectively labelled class I and class II-SH groups of the shark rectal gland Na+/K+-ATPase

Na+/K+-ATPase in membranous preparations from the rectal gland of Squalus acanthias has been spin-labelled either on Class I -SH groups, which maintain overall ATPase activity, or on Class II -SH groups, for which only phosphorylation activity is preserved. Labelling of the Class I groups requires solubilization of the membranes and subsequent reconstitution by precipitation with Mn2+ in order to remove contaminating peripheral proteins, which are also labelled. Control experiments with preparations in which the Class II groups are labelled demonstrate that the mobility and aggregation state of the enzyme in the reconstituted membranes are similar to those in the native membrane. Both the conventional maleimide nitroxide derivative and a new benzoylvinyl nitroxide derivative have been used for the labelling. The segmental mobility of the labels and the overall rotational diffusion of the labelled protein have been investigated using saturation transfer ESR spectroscopy. The benzoylvinyl spin-label derivative offers particular advantages for the study of the protein rotational mobility in that the segmental mobility is considerably reduced relative to that observed with the maleimide derivative. This is especially the case for the Class I groups, where the maleimide label exhibits pronounced segmental mobility. Comparison of the results from the two labels indicates that the integral of the saturation-transfer spectrum is much more sensitive to segmental motion than are the diagnostic line-height ratios. This fact allows a better level of discrimination between the two types of motion. The results from the benzoylvinyl nitroxide-labelled Class I groups suggest that the Na+/K+-ATPase is probably present as an (alpha beta)2-diprotomer (or higher oligomer) in the native membrane.     

Effect of phospholipid substitution on the mobility of protein-bound spin labels in sarcoplasmic reticulum

The influence of phospholipid environment upon the mobility of spin labels covalently bound to the Ca2+-transport ATPase (ATP phosphohydrolase [EC 3.6.1.3]) was studied by electron spin resonance spectroscopy in native and reconstituted sarcoplasmic reticulum membranes. Fragmented sarcoplasmic reticulum of rabbit skeletal muscle was covalently labeled with maleimide spin-labels of different chain length or with 4-(2-iodoacetamido)-2,2,6,6-tetramethylpiperidinooxyl, and the phospholipids were exchanged for dipalmitoylphosphatidylcholine or dioleoylphosphatidylcholine. With short-chain maleimide or iodoacetamide spin labels, the spectrum of the protein-bound label reflected the change in microenvironment caused by replacement of endogenous phospholipids with dipalmitoylphosphatidylcholine as a decrease in mobility. In contrast, after labeling with long-chain maleimide derivatives, there were no noticeable differences in the spectra before and after substitution with dipalmitophatidylcholine. Replacement of endogenous phospholipids with dioleoylphosphatidylcholine did not affect the spectra. The data indicate that increased viscosity in the environment of Ca2+-transport ATPase produced by replacement of sarcoplasmic reticulum lipids with dipalmitoylphosphatidylcholine reduces the mobility of short-chain maleimide spin labels covalently attached to the Ca2+-transport ATPase polypeptide.     

Studies on conformational transitions of Ca2+,Mg2+-adenosine triphosphatase of sarcoplasmic reticulum. II. Conformational characteristics of stabilized reaction intermediates as revealed by fluorescent and paramagnetic probes

Various reaction intermediates of sarcoplasmic reticulum Ca2+,Mg2+-ATPase were stabilized and accumulated by modifying a specific SH group or by using nucleotide analogs. Conformational changes of the Ca2+,Mg2+-ATPase during the catalytic cycle were studied in the stabilized intermediates by the use of fluorescent and spin probes, which were introduced at specific SH groups of ATPase, namely one highly reactive but functionally nonessential (SHN) and one essential for the decomposition of the E-P intermediate (SHD) [Kawakita, M., et al. (1980) J. Biochem. 87, 609-617]. The fluorescence intensity of N-(7-dimethylamino-4-methyl-3-coumarinyl)maleimide attached to SHD decreased by 2.5% upon addition of 10 microM AMP-P(NH)P provided that Ca2+ was also present. The AMP-P(NH)P-induced fluorescence change could also be detected by using other fluorescent probes such as N-[p-(2-benzimidazolyl)phenyl]maleimide and N-(1-anilinonaphthyl-4)maleimide. Moreover, labeling at SHN gave similar results. When SHN was labeled with N-[p-(2-benzimidazolyl)phenyl]maleimide, the fluorescence intensity also decreased by 2.5% upon addition of ATP only in the presence of Ca2+, where E-P formation took place. A conformational difference between ECa1-P X ADP and ECa1-P was suggested from saturation transfer ESR measurement of spin-labeled ATPase by using ADP beta S as an ADP analog to cause accumulation of ECa1-P X ADP beta S complex. Possible structural similarities among some of the intermediates are discussed based on these findings.     

Vinyl ketone reagents for covalent protein modification. Nitroxide derivatives suited to rotational diffusion studies by saturation transfer electron spin resonance, using membrane-bound Na,K-ATPase as an example

The reactivity of a series of substituted vinyl ketone nitroxides with an integral membrane protein, the Na,K-ATPase, is described. Increasing the electrophilicity of the conjugated double bond enhances reactivity markedly, with some spin labels showing higher reactivity than the conventionally used maleimide derivatives. The spectroscopic characteristics of the spin-labeled protein are also better suited for motional analysis by the saturation transfer electron spin resonance (STESR) method than with previous labeling procedures. The rotational correlation time, deduced from STESR experiments, is in the same range (100-300 microseconds) irrespective of the vinyl ketone derivative used, and the rotational mobility corresponds to an (alpha beta)2 or higher oligomer of the membrane-bound Na,K-ATPase.     

Conformational change in thrombospondin induced by removal of bound Ca2+. A spin label approach

The effect of removal of Ca2+ bound to thrombospondin (TSP) on the protein structure in solution has been investigated using ESR spin-label techniques. A maleimide spin label was selectively attached to the free thiol group presumably near the carboxyl-terminal domain in which Ca2+-binding sites are situated. The ESR spectra of spin-labeled TSP showed that the bound label undergoes a relatively fast rotational motion with an effective rotational correlation time in the nano-second time regimes. Removal of bound Ca2+ in TSP by dialyzing spin-labeled TSP from a Ca2+-containing buffer into an EDTA-containing buffer resulted in an increase in the mobility of the bound label by a factor of 2.3. The data suggest that EDTA chelation of bound Ca2+ in TSP induces a conformational change of TSP at least near the site of spin labeling.     

Heterogeneity of SH groups in sarcoplasmic reticulum.

The incorporation of [¹⁴C] N-ethylmaleimide reveals fast and slow-reacting sulfhydryl groups in sarcoplasmic reticulum. Two proteins react with the label: a fast-reacting glycoprotein recently isolated (Ikemoto, Cucchiaro and Garcia (1976) J. Cell Biol.$\text{70}$, 290a), and the Ca²⁺-ATPase. Labeling sarcoplasmic reticulum with a maleimide spin label gives a similar pattern. The spectra of maleimide-spin-labeled sarcoplasmic reticulum have both ‘strongly’ and ‘weakly’ immobilized components. Maleimide-spin-labeled purified Ca²⁺-ATPase, or sarcoplasmic reticulum labeled first with N-ethylmaleimide, and then with maleimide spin label, show spectra devoid of the ‘weakly’ immobilized component; the latter is enhanced in partially purified glycoprotein obtained from spin-labeled sarcoplasmic reticulum. This indicates that spectra from maleimide-spin-labeled sarcoplasmic reticulum do not reflect exclusively the state of the Ca²⁺-ATPase enzyme.     

Probing the helical tilt and dynamic properties of membrane-bound phospholamban in magnetically aligned bicelles using electron paramagnetic resonance spectroscopy

Wild-type phospholamban (WT-PLB), a Ca(2+)-ATPase (SERCA) regulator in the sarcoplasmic reticulum membrane, was studied using TOAC nitroxide spin labeling, magnetically aligned bicelles, and electron paramagnetic resonance (EPR) spectroscopy to ascertain structural and dynamic information. Different structural domains of PLB (transmembrane segment: positions 42 and 45, loop region: position 20, and cytoplasmic domain: position 10) were probed with rigid TOAC spin labels to extract the transmembrane helical tilt and structural dynamic information, which is crucial for understanding the regulatory function of PLB in modulating Ca(2+)-ATPase activity. Aligned experiments indicate that the transmembrane domain of wild-type PLB has a helical tilt of 13°±4° in DMPC/DHPC bicelles. TOAC spin labels placed on the WT-PLB transmembrane domain showed highly restricted motion with more than 100ns rotational correlation time (τ(c)); whereas the loop, and the cytoplasmic regions each consists of two distinct motional dynamics: one fast component in the sub-nanosecond scale and the other component is slower dynamics in the nanosecond range.     

Spin-labeling of adenosine triphosphatase in sarcoplasmic reticulum membrane and change in the state of the spin labels induced by deoxycholate.

Fragmented sarcoplasmic reticulum (SR) was reacted with a thiol-directed spin label, N-(1-oxyl-2,2,6,6,-tetramethyl-4-piperidinyl)maleimide, under various conditions. It was found that ATP inhibited the binding of the label to SR protein in the initial phase of the reaction, but as the incubation time was extended up to 18 h, the amount of label bound to SR protein in the control and ATP-containing samples became almost identical. The Ca2+-dependent ATPase control and ATP-containing samples became almost identical The Ca2+-dependent ATPase (ATP phosphohydrolase [EC 3.6.1.3]) of SR was protected by the presence of ATP during incubation with relatively low concentrations of spin label, irrespective of the total amount of label bound, although with increasing concentration of bound label the ATPase activity decreased. Deoxycholate slightly reduced the rotational freedom of the label bound to SR protein and decreased the initial rate of quenching of protein-bound nitroxide by ascorbate. From an analysis of these results, it was concluded that the binding of deoxycholate to protein decreases the accessibility of ascorbate to the protein-bound label.     

Antibodies against the 53 kDa glycoprotein inhibit the rotational dynamics of both the 53 kDa glycoprotein and the Ca(2+)-ATPase in the sarcoplasmic reticulum membrane.

The purpose of this study is to better define the relationship of the 53 kDa glycoprotein (GP-53) of the sarcoplasmic reticulum (SR) to other SR proteins. Towards that end the effects of antibodies against GP-53 on the rotational dynamics of maleimide spin-labeled proteins of SR of rabbit skeletal muscle were investigated. The labeling protocol used in this study provided 1.6 +/- 0.3 moles spin label incorporated per 10(5) g SR protein. Labeling specificity studies indicated that nearly 70% of the label bound specifically to the Ca(2+)-ATPase, with the remainder bound to GP-53. Using saturation-transfer electron paramagnetic resonance (ST-EPR), it was determined that the rotational mobility (i.e., the rate of rotation) of the spin-labeled SR proteins decreased greater than 5-fold upon preincubation of MSL-SR with an antiserum against the GP-53, while preincubation of MSL-SR with preimmune serum had no effect. Preincubation of MSL-SR with a monoclonal antibody against the GP-53 produced a 4-fold decrease in the rotational mobility of the MSL-SR proteins compared to control measurements. Further, these effects showed a marked calcium dependence: the decrease in the rotational mobility of the MSL-SR proteins preincubated with anti-GP-53 antibodies in 500 microM Ca2+ was 3-6-fold greater than that of MSL-SR preincubated with antibodies in 5 mM EGTA. While MSL was bound to both Ca(2+)-ATPase and GP-53, model calculations indicated that the decreases observed in the rotational mobility of the MSL-SR proteins caused by the anti-GP-53 monoclonal antibodies were too large to be accounted for by effects on GP-53 alone. The calculations suggest that the rotational rate of Ca(2+)-ATPase was also diminished by anti-GP-53 monoclonal antibodies, indicating an interaction between GP-53 and Ca(2+)-ATPase in the SR membrane.     

Spin label saturation transfer ESR studies of protein-lipid interactions in Photosystem II-enriched membranes

Saturation transfer ESR has been used to study the dynamic behaviour of lipids in the appressed regions of thylakoid membranes from pea seedlings. Four different phospho- and galacto-lipid spin labels (phosphatidylcholine labelled at the 12 or 14 C-atom positions of the sn-2 chain, phosphatidylglycerol labelled at the 14-position of the sn-2 chain, and monogalactosyldiacylglycerol labelled at the 12-position of the sn-2 chain) were used to probe the lipid environment in photosystem II-enriched membranes prepared by detergent extraction. The ESR spectra show that the majority of the lipid in these preparations is strongly motionally restricted. Values for the effective rotational correlation times of the labelled chains were deduced from the lineheight ratios and integrals of thhe saturation transfer ESR spectra. The effective rotational correlation times were found to be in the 10⁵ range, indicating a very low lipid chain mobility which correlates with the low lipid content of these preparations. Comparison of the effective rotational correlation times deduced from the different diagnostic regions of the spectrum revealed little anisotropy in the chain mobility, indicating that the dominant motional mode was trans-gauche isomerization. The effective rotational correlation times deduced from the spectral integrals were similar to those deduced from the lineheight ratios, consistent with the absence of any appreciable fluid lipid component in these preparations. The results also indicate some selectivity of interaction between the lipid species, with phosphatidylcholine exhibiting appreciably slower motion than either phosphatidylglycerol or monogalactosyldiacylglycerol.     

A saturation transfer electron spin resonance study on the break in the Arrhenius plot for the rotational motion of Ca2+-dependent adenosine triphosphatase molecules in purified and lipid-replaced preparations of rabbit skeletal muscle sarcoplasmic reticulum

By means of saturation transfer electron spin resonance spectroscopy the rotational motion of spin-labeled Ca2+-dependent ATPase molecules has been investigated for three kinds of preparations of rabbit skeletal muscle sarcoplasmic reticulum: MacLennan's enzyme (purified ATPase preparation), DOPC- and egg PC-ATPase (purified ATPase preparations in which endogenous lipids are replaced with dioleoyl and egg yolk phosphatidylcholine, respectively). The rotational mobility of the enzyme in these preparations is somewhat lower than that in the intact membrane, probably due to the reduced amount of lipids. For all the preparations, however, the Arrhenius plot for rotational mobility showed a break at about 18 degrees C, the same temperature at which a break in the Arrhenius plot for Ca2+-ATPase activity occurs. This result provides further evidence that the break in the Arrhenius plot is not related to a lipid phase transition but to a change in the physical state of the Ca2+-ATPase molecule existing in fluid lipids.     

Saturation transfer electron paramagnetic resonance on membrane bound proteins. II-Absence of rotational diffusion of the cholinergic receptor protein in Torpedo marmorata membrane fragments.

We have applied the technique of saturation transfer electron paramagnetic resonance to study the rotational diffusion of spin labeled membrane bound cholinergic receptors from Torpedo marmorata. Two different spin labels were used: a spin labeled maleimide derivative which binds covalently to proteins and a long chain spin labeled acylcholine which binds reversibly with a high affinity to the receptor protein. The maleimide spin label has a motion whose rotational correlation time is τ₂ > 10^?3 sec. The long chain spin labeled acylcholine indicates slightly more motion ($\text{τ}{}_2\text{? 10}{}^{\mathrm{?4}}\text{sec}$), but the nitroxide in this latter case is probably more loosely bound.     

Spin label study of slow molecular rotations of globular proteins using microwave saturation effects in electron paramagnetic resonance

Viscosity, temperature and ionic strength dependences of ESR microwave saturation parameters of spin labelled human oxyhemoglobin (Hb) and bovine serum albumin (BSA) have been studied. The piperidine and pyrrolidine nitroxyl derivatives of maleimide were used as covalent SH reagents for Hb and BSA and the same two derivatives of gamma-benzocarboline and spin labelled stearic acid were used as noncovalent spin probes for BSA. The effects of label binding tightness on ESR spectral parameters were considered. The rotational correlation times were determined using viscosity dependences of the separation of the outer hyperfine extrema and Stokes extrapolations at high viscosities. The ESR microwave saturation parameters of the spin labels were shown to depend just weakly on temperature (at constant eta/t) over the range 0-25 degrees and on g, A values but to be sensitive to protein rotational correlation times up to 10(-4) sec and also to the rotational anisotropy and to the relative motion of the spin label.     

Effect of the lipid environment on protein motion and enzymatic activity of sarcoplasmic reticulum calcium ATPase.

In order to investigate the roles of the physical states of phospholipid and protein in the enzymatic behavior of the Ca2+ -ATPase from sarcoplasmic reticulum, we have modified the lipid phase of the enzyme, observed the effects on the enzymatic activity at low temperatures, and correlated these effects with spectroscopic measurements of the rotational motions of both the lipid and protein components. Replacement of the native lipids with dipalmitoyl phosphatidylcholine inhibits ATPase activity and decreases both lipid fluidity, as monitored by EPR spectroscopy on a stearic acid spin label, and protein rotational mobility, as monitored by saturation transfer EPR spectroscopy on the covalently spin-labeled enzyme. Solubilization of the lipid-replaced enzyme with Triton X-100 reverses all three of these effects. Ten millimolar CaCl2 added either to the enzyme associated with the endogenous lipids or to the Triton X-100 soulbilized enzyme inhibits both ATPase activity and protein rotational mobility but has no detectable effect on the lipid mobility. These results are consistent with the proposal that both lipid fluidity and protein rotational mobility are essential for enzymatic activity.     

Spin-labeling studies of beef-liver glutamate dehydrogenase.

Bovine liver glutamate dehydrogenase was spin labeled with a nitroxide derivative of parachloromercuribenzoate. The ESR spectrum was of the immobilized type and the labeling yield 0.6 mole of spin label bound per mole of protomer under standard conditions. The specific activity of the labeled enzyme was not modified but the activation by ADP abolished. Inhibition by GTP was not altered but the ESR spectrum showed that the bound spin label was further immobilized in the presence of GTP and NADPH. In the presence of the coenzyme NADPH, the labeling yield decreased to half its initial value. Such a protection effect was observed neither with NADH nor with ADP.     

Saturation transfer, continuous wave saturation, and saturation recovery electron spin resonance studies of chain-spin labeled phosphatidylcholines in the low temperature phases of dipalmitoyl phosphatidylcholine bilayers. Effects of rotational dynamics and spin-spin interactions.

The saturation transfer electron spin resonance (STESR) spectra of 10 different positional isomers of phosphatidylcholine spin-labeled in the sn-2 chain have been investigated in the low temperature phases of dipalmitoyl phosphatidylcholine (DPPC) bilayers. The results of continuous wave saturation and of saturation recovery measurements on the conventional ESR spectra were used to define the saturation properties necessary for interpreting the STESR results in terms of the chain dynamics. Spin labels with the nitroxide group located in the center of the chain tended to segregate preferentially from the DPPC host lipids in the more ordered phases, causing spin-spin interactions which produced spectral broadening and had a very pronounced effect on the saturation characteristics of the labels. This was accompanied by a large decrease in the STESR spectral intensities and diagnostic line height ratios relative to those of spin labels that exhibited a higher degree of saturation at the same microwave power. The temperature dependence of the STESR spectra of the different spin label isomers revealed a sharp increase in the rate of rotation about the long axis of the lipid chains at approximately 25 degrees C, correlating with the pretransition of gel phase DPPC bilayers, and a progressive increase in the segmental motion towards the terminal methyl end of the chains in all phases. Prolonged incubation at low temperatures led to an increase in the diagnostic STESR line height ratios in all regions of the spectrum, reflecting the decrease in chain mobility accompanying formation of the subgel phase. Continuous recording of the central diagnostic peak height of the STESR spectra while scanning the temperature revealed a discontinuity at approximately 14-17 degrees C, corresponding to the DPPC subtransition which occurred only on the initial upward temperature scan, in addition to the discontinuity at 29-31 degrees C corresponding to the pretransition which displayed hysteresis on the downward temperature scan.     

Effect of phospholipid substitution on the mobility of spin labels bound to the ATPase of sarcoplasmic reticulum

The mobility of spin labels covalently bound to the Ca2+-transport ATPase (ATP phosphohydrolase [EC 3.y.1.3]) was studied by electron spin-resonance spectroscopy in purified ATPase and reconstituted vesicles. The purified ATPase of sarcoplasmic reticulum of rabbit skeletal muscle was covalently labeled with maleimide spin-labels of different chain length and the phospholipids were exchanged for dipalmitoylphosphatidylcholine. The spectrum of the short-chain maleimide spin-label, bound to purified ATPase indicates reduced mobility after substitution of endogenous phospholipids with dipalmitoylphosphatidylcholine. With the long-chain maleimide derivative no difference was detected in the spectra, measured at 20-35 degrees C temperature before and after substitution with dipalmitoylphosphatidylcholine. Below 10 degrees C temperature the substitution with dipalmitoylphosphatidylcholine decreased the mobility of the prove, indicating that the microviscosity of environment in the vicinity of nitroxide groups was influenced by changes in the fatty acid composition. With both short and long chain spin-labels bound to purified ATPase adn sarcoplasmic reticulum vesicles the amplitude of weakly immobilized component sharply decreased in media containing 20-50% glycerol. Therefore, the mobility of covalently bound nitroxide group in short or long chain maleimide derivatives is also sensitive to the viscosity of the water phase.     

Uncoupling of Ca2+ transport in sarcoplasmic reticulum as a result of labeling lipid amino groups and inhibition of Ca2+-ATPase activity by modification of lysine residues of the Ca2+-ATPase polypeptide

Limited labeling of amino groups with fluorescamine in fragmented sarcoplasmic reticulum vesicles inhibits Ca2+-ATPase activity and Ca2+ transport. Under the labeling conditions used, 80% of the label reacts with phosphatidylethanolamine and 20% with the Ca2+-ATPase polypeptide. This degree of labeling does not result in vesicular disruption or in loss of vesicular proteins and does not increase the membrane permeability to Ca2+. Fluorescamine labeling of a purified Ca2+-ATPase devoid of aminophospholipids also inhibits Ca2+-ATPase activity, suggesting that labeling of lysine residues of the enzyme polypeptide is responsible for the inhibition of Ca2+-ATPase activity in sarcoplasmic reticulum. Fluorescamine labeling interferes with phosphoenzyme formation and decomposition in both the native vesicles and the purified enzyme; addition of ATP during labeling, and with less effectiveness ADP or AMP, protects both partial reaction steps. Addition of a nonhydrolyzable ATP analog protects phosphoenzyme formation but not decomposition. The inhibition of Ca2+ transport but not of Ca2+-ATPase occurs in sarcoplasmic reticulum vesicles labeled in the presence of ATP, indicating that the transport reaction is uncoupled from the Ca2+-ATPase reaction. The inhibition of Ca2+ transport but not of Ca2+-ATPase activity is also found in sarcoplasmic reticulum vesicles in which only phosphatidylethanolamine has reacted with fluorescamine. Furthermore, the extent of labeling of phosphatidylethanolamine is correlated with the inhibition of Ca2+ transport rates. The inhibition of Ca2+ transport is a reflection of the inhibition of Ca2+ translocation and is not due to an increase in Ca2+ efflux. We propose that labeling of phosphatidylethanolamine perturbs the lipid environment around the enzyme, producing a specific defect in the Ca2+ translocation reaction.     

State of aggregation of the (Ca2+ + Mg2+)-ATPase studied using saturation-transfer electron spin resonance

The state of aggregation of the (Ca2+ + Mg2+)-ATPase in the membrane of sarcoplasmic reticulum and in reconstituted membrane systems has been studied using saturation-transfer electron spin resonance (ST-ESR). Saturation-transfer ESR spectra show that in the sarcoplasmic reticulum, the ATPase is relatively free to rotate, with an effective rotational correlation time of approx. 33 microseconds at 4 degrees C, consistent with a monomeric or dimeric structure. The rate of rotation is observed to decrease with decreasing molar ratio of lipid to protein. In reconstituted systems, rotational motion of the ATPase on the millisecond time scale ceases when the lipids are in the gel phase. Addition of decavanadate, which causes the formation of crystalline arrays in negatively stained electron micrographs, results in only a small reduction in rotation rate for the ATPase in the membrane. The experiments are interpreted in terms of a short-lived (on the millisecond time scale) protein-protein interaction, with the formation of crystalline clusters of ATPase molecules which form and melt rapidly.     

Electron spin resonance and steady-state fluorescence polarization studies of lipid bilayers containing integral proteins

We derive equations that describe changes in the steady-state fluorescence polarization of the probe 1,6-diphenyl-1,3,5-hexatriene (DPH) or in the spectrum of electron spin resonance (ESR) nitroxide spin-labeled lipid probes as a function of the intrinsic molecule concentration in lipid bilayer membranes. We make use of an assumption used by us in an earlier paper. The equations are independent of any membrane model. They are valid when a DPH probe or a spin-labeled chain is equivalent to an unlabeled lipid hydrocarbon chain only as far as their general space-filling properties are concerned. We consider cases where the bilayer is either in a single homogeneous phase or in a two-phase region. We apply our equations to analyze ESR data from delipidated sarcoplasmic reticulum membranes and from egg yolk phosphatidylcholine bilayers containing Ca2+-ATPase, and DPH data from dipalmitoylphosphatidylcholine (DPPC) bilayers containing Ca2+-ATPase, both for T greater than Tc. The following conclusions were derived: (i) Ca2+-ATPase oligomers are "randomly" distributed, for the concentrations studied, in the fluid phase. (ii) There is no fixed stoichiometric ratio of "boundary" lipids and oligomers. (iii) Between 24k and 28k lipid molecules are able to surround each isolated oligomer composed of k Ca2+-ATPase monomers. Finally, we apply our equations to analyze DPH studies on DPPC bilayers containing Ca2+-ATPase for T less than Tc. We find that the results reported are in accord with the predictions of the model. In the Appendix, we show that an analytical expression for probabilities used by us is in very good agreement with the results of computer simulation.