Multilamellar Liposomes as a Model for Biological Membranes: Saturation Recovery EPR Spin-Labeling Studies

EPR spin labeling has been used extensively to study lipids in model membranes to understand their structures and dynamics in biological membranes. The lipid multilamellar liposomes, which are the most commonly used biological membrane model, were prepared using film deposition methods and investigated with the continuous wave EPR technique (T2-sensitive spin-labeling methods). These investigations provided knowledge about the orientation of lipids, their rotational and lateral diffusion, and their rate of flip-flop between bilayer leaflets, as well as profiles of membrane hydrophobicity, and are reviewed in many papers and book chapters. In the early 1980s, the saturation recovery EPR technique was introduced to membrane studies. Numerous T1-sensitive spin-label methods were developed to obtain detailed information about the three-dimensional dynamic membrane structure. T1-sensitive methods are advantageous over T2-sensitive methods because the T1 of spin labels (1–10 μs) is 10 to 1000 times longer than the T2, which allows for studies of membrane dynamics in a longer time–space scale. These investigations used multilamellar liposomes also prepared using the rapid solvent exchange method. Here, we review works in which saturation recovery EPR spin-labeling methods were applied to investigate the properties of multilamellar lipid liposomes, and we discuss their relationships to the properties of lipids in biological membranes.


Short Overview of Previous Applications of EPR Spin Labeling in Studies of the Properties of Multilamellar Liposomes
The major nitroxide, free radical, lipid spin labels, which were later used in membrane studies, were first synthetized between 1967 and 1971. Primarily, three classes of these spin labels were used: spin-labeled stearic acids with the nitroxide fragment attached to different carbon atoms of the acyl chain (n-SASLs, synthesis described in [1][2][3]); spinlabeled phosphatidylcholines with the nitroxide fragment attached at selected positions on the fatty acid chain (n-PCs, synthesis described in [1]); or the polar head group (T-PC, synthesis described in [4]), and spin-labeled cholesterol (Chol) analogs (ASL, synthesis described in [5], and CSL, synthesis described in [6]) (see Figure 1 for their structures). The nitroxide free radicals, first synthetized by Hoffman (1961) [7] and by Rozantsev and Neiman (1964) [8] and used as monitoring groups in lipid spin labels, are extremely stable in model membranes. In addition, the basic approaches to analyze the electron paramagnetic resonance (EPR) spectra of these spin labels are rather simple, and the same for all of the spin labels [9][10][11]. The lipid spin labels are easily introduced to model membranes, while the lipids are mixed for the preparation of multilamellar liposomes. All of these broadly expanded the applications of EPR spin labeling for membrane studies.
As indicated in the abstract, the conventional continuous wave EPR techniques using phospholipid (PL) and Chol analog spin labels provide basic insights about the organization model membranes, while the lipids are mixed for the preparation of multilamellar liposomes. All of these broadly expanded the applications of EPR spin labeling for membrane studies.
As indicated in the abstract, the conventional continuous wave EPR techniques using phospholipid (PL) and Chol analog spin labels provide basic insights about the organization and dynamics of lipids in lipid bilayer membranes. In this review, we indicate the first major publications describing the dynamic properties of the bilayers, such as the acyl chain flexibility gradient and rotational diffusion [1,12,13], lipid lateral diffusion [2,14], and PL flip-flop between the leaflets of the bilayer [4,15]; where the phase transition between gel and fluid phase membranes was investigated [16][17][18]; where the order and orientation of lipids in the bilayer were investigated [10,19,20]; and where the shape of the transmembrane hydrophobic barrier was established with the spin-labeling approach [21,22]. These investigations are reviewed in many papers [23][24][25] and book chapters [26][27][28][29]. Chemical structures of three classes of lipid spin labels used in membrane studies. Stearic acid spin labels (n-SASL-n-doxylstearic acid spin label); PL spin labels (n-PC-1-palmitoyl-2-(ndoxylstearoyl)phosphatidylcholine and T-PC-tempocholine-1-palmitoyl-2-oleoylphosphatidic acid ester); and Chol-analog spin labels (ASL-androstane spin label and CSL-cholestane spin label).

Background for the Application of SR EPR for Membrane Studies
The EPR techniques used to determine the structure and dynamics of model and biological membranes are continuously being developed to better understand membrane functions. In the early 1980s, the saturation recovery (SR) EPR technique was introduced for membrane studies. Numerous T1-sensitive spin-label methods were developed that greatly contributed to our understanding of the lateral organization of lipids in lipid bilayers, and to providing detailed information about their dynamics as a function of depth [30][31][32][33][34][35][36]. All of this information can be obtained at the physiological conditions for membranes (multilamellar liposomes) prepared from vastly diverse lipids, also resembling Figure 1. Chemical structures of three classes of lipid spin labels used in membrane studies. Stearic acid spin labels (n-SASL-n-doxylstearic acid spin label); PL spin labels (n-PC-1-palmitoyl-2-(ndoxylstearoyl)phosphatidylcholine and T-PC-tempocholine-1-palmitoyl-2-oleoylphosphatidic acid ester); and Chol-analog spin labels (ASL-androstane spin label and CSL-cholestane spin label).

Background for the Application of SR EPR for Membrane Studies
The EPR techniques used to determine the structure and dynamics of model and biological membranes are continuously being developed to better understand membrane functions. In the early 1980s, the saturation recovery (SR) EPR technique was introduced for membrane studies. Numerous T 1 -sensitive spin-label methods were developed that greatly contributed to our understanding of the lateral organization of lipids in lipid bilayers, and to providing detailed information about their dynamics as a function of depth [30][31][32][33][34][35][36]. All of this information can be obtained at the physiological conditions for membranes (multilamellar liposomes) prepared from vastly diverse lipids, also resembling those forming the lipid bilayer portion of biological membranes. Here, we present a short theoretical background to show the applications of the SR EPR spin-labeling approaches to investigate model membranes.
The SR EPR technique to measure the electron spin-lattice relaxation times (T 1 s) of paramagnetic samples (including nitroxide spin labels) was developed by Hyde in the 1970s [37,38]. With this technique, the recovery of the EPR signal to the thermodynamic equilibrium is recorded at a weak observing microwave power, not disturbing the EPR signal, and after the termination of the high saturating pump microwave power pulse ( Figure 2a). The thermodynamic equilibrium is restored by the spin-lattice relaxation describing the interaction of the spin system with the "lattice" (close environment of spins). This recovery time is characterized by the spin-lattice relaxation time, T 1 . For convenience, the SR signal is recorded and analyzed as a "decay" curve ( Figure 2b), which describes the changes in the EPR spectrum amplitude, through the equation: I0n is the amplitude of the SR signal from each domain at the beginning of the recording, and T1n is the spin-lattice relaxation time in each domain (see Section 6 for more explanation).
For spin-labeled multilamellar liposomes, the SR EPR signals at the X-band (microwave frequency 9.4 GHz) are received on the central line (mI = 0; see Figure 2a) of the EPR spin-label spectrum. To obtain the correct T1 values, the samples must be thoroughly deoxygenated (see Section 3). In this approach, which is used to obtain T1 values for singleand multi-exponential SR signals, it is not necessary for the pump pulse to be a saturating pulse. This qualitative SR EPR approach allows discrimination of the membrane domains. The SR EPR spin-labeling approach can also provide quantitative information about the lipids in the membrane domains (giving data about the relative amounts of PLs and Chol in the discriminated domains). The necessary condition for the quantitative approach is that the pump pulse completely saturates all of the components of the SR signal (see [39] for details of this method). If pump power is high enough, the amplitude of the signal decreases to zero (this is the case described in the Figure). The recovery signal to thermodynamic equilibrium is recorded at the same field position with a weak observing microwave power. The time of the "recovery disabled" is needed to protect the detector. The recovery to the equilibrium state is Figure 2. (a) The schematic illustration of the SR EPR experiment. The saturating high microwave power pump pulse (located at the field position of the central line (m I = 0) of the spin-label absorption spectrum) of the electron spin system. If pump power is high enough, the amplitude of the signal decreases to zero (this is the case described in the Figure). The recovery signal to thermodynamic equilibrium is recorded at the same field position with a weak observing microwave power. The time of the "recovery disabled" is needed to protect the detector. The recovery to the equilibrium state is exponential, and is described by the equation, I(t) = I(eq) − I(eq)exp(−t/T 1 ). I(t) and I(eq) are the amplitudes of the absorption spectrum at time t and at equilibrium, respectively. As indicated, the saturating pulse completely saturates the signal; (b) Usually, the SR signal is recorded and analyzed as a "decay" curve, which describes changes in the recorded EPR spectrum amplitude through the equation, SR signal = [I(eq) − I 0 ]exp(−t/T 1 ). Here, I 0 is the amplitude of the signal at the beginning of the recording. I(t) and I 0 are the amplitudes of the SR signal at time t and at the beginning of the recording. T 1 is the spin-lattice relaxation time. For t = T 1 (t/T 1 = 1), the signal amplitude changes e times (SR signal decreases to 37% of its initial value). If the membrane domains are present with significantly different fluidities, the observed SR signal can be fitted to a multi-exponential function: I 0n is the amplitude of the SR signal from each domain at the beginning of the recording, and T 1n is the spin-lattice relaxation time in each domain (see Section 6 for more explanation).
For spin-labeled multilamellar liposomes, the SR EPR signals at the X-band (microwave frequency 9.4 GHz) are received on the central line (m I = 0; see Figure 2a) of the EPR spin-label spectrum. To obtain the correct T 1 values, the samples must be thoroughly deoxygenated (see Section 3). In this approach, which is used to obtain T 1 values for singleand multi-exponential SR signals, it is not necessary for the pump pulse to be a saturating pulse. This qualitative SR EPR approach allows discrimination of the membrane domains. The SR EPR spin-labeling approach can also provide quantitative information about the lipids in the membrane domains (giving data about the relative amounts of PLs and Chol in the discriminated domains). The necessary condition for the quantitative approach is that the pump pulse completely saturates all of the components of the SR signal (see [39] for details of this method). The factors that affect the measured T 1 (in connection with the investigated system) are the structure of the nitroxide fragment, rate of motion of the nitroxide fragment (rotational diffusion), collisions with oxygen and other paramagnetic relaxation agents, dipole-dipole interaction with other paramagnetic agents, and local concentration of the spin labels. The factors that affect the measured T 1 (in connection with the SR EPR measurement) are the observing microwave power and microwave frequency. The text in bold indicates the factors discussed in this review.

Preparation of Multilamellar Liposomes and Handling Samples for EPR Measurements
The multilamellar liposomes form preferred models in membrane studies. Most often, they are prepared using the film deposition method from the dry film of lipids and spin-label mixtures formed on the bottom of the test tube after the evaporation of the solvent, the addition of the buffer, and vortexing (shaking) [33]. Their multilamellar structure allows for the tight packing of model membranes in the sample capillary used for EPR measurements (as compared with the packing of the unilamellar liposomes), which greatly increases the signal-to-noise ratio of EPR signals and allows the concentration of the lipid spin labels in the investigated samples to be decreased to the magnetically diluted condition. The multilamellar liposomes can be easily pelleted in Eppendorf test tubes and further pelleted in the TPX or Teflon capillaries used for EPR measurements [40]. That way, the concentration of lipids in the aqueous sample used for EPR measurements can be as great as~20% (wt/wt). The amount of water in these concentrated membrane suspensions is still high enough not to disturb the structure of the lipid bilayer [41]. Additionally, in the multilamellar dispersion, most liposomes have a diameter large enough that the effect of the membrane curvature on the properties of the inner and outer bilayer leaflets can be neglected.
The film deposition methods, especially when applied to form multilamellar liposomes containing high amounts of Chol, have some limitations. As it dries, the lipid mixture passes the solid-state intermediate conditions at which the solid-state demixing of Chol, in the form of Chol crystals, can occur [42]. The Chol molecules from these crystals do not participate in membrane formation after the addition of the buffer because of the very high kinetic barrier. The rapid solvent exchange (RSE) method was designed to prevent the lipids from demixing during liposome preparation, as happens during preparations using the film deposition method [42]. During the preparation of the multilamellar liposomes using the RSE method, the lipid solutions never pass through the solid state, ensuring compositional homogeneity throughout the membrane suspension. The apparatus and the method are described in detail in [43,44]. Briefly, the chloroform solutions of lipid mixtures with an appropriate lipid spin label are added into the vortexed buffer, and vortexed further under reduced pressure to rapidly remove the solvent. The multilamellar liposomes obtained using the RSE method can be pelleted and transferred to sample capillaries the same way as those prepared using the film deposition method. The absence of demixing artifacts in the multilamellar liposomes produced using the RSE method makes it possible to obtain reproducible and precise Chol saturation limits in the different membranes (Chol concentration at which the pure Chol bilayer domains (CBDs) start to form) and confirms that the formation of CBDs precedes the formation of Chol crystals in the lipid bilayer membranes [45,46]. As indicated in Section 6, the CBDs can be discriminated with ASL and CSL, using the SR EPR technique and molecular oxygen (O 2 ) or NiEDDA as the probe molecules.
The basic handling of the multilamellar liposome samples is described in the first paragraph of this section. However, when the sample amount is very small, as for the multilamellar liposomes made from the total lipid extract of precious biological materials, some directions for handling can be useful. Introducing loop-gap resonators, especially for the SR EPR spectrometers, greatly reduces the active sample volume to a few microliters for X-band (microwave frequency 9.4 GHz) spectrometers, and to as little as 30 nL for Q-band (microwave frequency 34 GHz) and W-band (microwave frequency 94 GHz) spectrometers [47,48]. These approaches are described in [40]. Briefly, the preliminary work (before the EPR measurements) is performed for a convenient larger volume. After that, the samples are pelleted in Eppendorf tubes, and the pellet-still with a volume ten to a hundred times greater than that of the resonator's active sample volume-is transferred to a TPX or Teflon capillary, where it is again pelleted on the bottom of the capillary to the lens of the active region of the resonator [48,49]. More details are presented in [40], and schematically in Figure 3a for the TPX capillary.
some directions for handling can be useful. Introducing loop-gap resonators, especially for the SR EPR spectrometers, greatly reduces the active sample volume to a few microliters for X-band (microwave frequency 9.4 GHz) spectrometers, and to as little as 30 nL for Q-band (microwave frequency 34 GHz) and W-band (microwave frequency 94 GHz) spectrometers [47,48]. These approaches are described in [40]. Briefly, the preliminary work (before the EPR measurements) is performed for a convenient larger volume. After that, the samples are pelleted in Eppendorf tubes, and the pellet-still with a volume ten to a hundred times greater than that of the resonator's active sample volume-is transferred to a TPX or Teflon capillary, where it is again pelleted on the bottom of the capillary to the lens of the active region of the resonator [48,49]. More details are presented in [40], and schematically in Figure 3a for the TPX capillary.
The basic strategies used to equilibrate the sample with the appropriate air/nitrogen mixture when the measurements are performed at X-band and W-band with TPX, quartz, and Teflon capillaries are explained in [50], and schematically in Figure 3b for the TPX capillary.

Spin-Lattice Relaxation Rate as a Convenient Parameter of Membrane Fluidity
It is accepted that the spin-lattice relaxation rate (T1 −1 ) of lipid spin labels mainly depends on the rate of the rotation of the nitroxide fragment attached to the parent lipid molecule [51][52][53]. Thus, T1 −1 can be used as a convenient parameter to qualitatively describe the dynamics of the spin label (or, more specifically, the dynamics of the fragment of the parent lipid molecule to which the nitroxide fragment is rigidly attached). The measurements of T1 −1 must be performed for deoxygenated samples. The detailed fluidity profiles of acyl chains can be obtained by measuring the T1 −1 for n-PCs or n-SASLs with The basic strategies used to equilibrate the sample with the appropriate air/nitrogen mixture when the measurements are performed at X-band and W-band with TPX, quartz, and Teflon capillaries are explained in [50], and schematically in Figure 3b for the TPX capillary.

Spin-Lattice Relaxation Rate as a Convenient Parameter of Membrane Fluidity
It is accepted that the spin-lattice relaxation rate (T 1 −1 ) of lipid spin labels mainly depends on the rate of the rotation of the nitroxide fragment attached to the parent lipid molecule [51][52][53]. Thus, T 1 −1 can be used as a convenient parameter to qualitatively describe the dynamics of the spin label (or, more specifically, the dynamics of the fragment of the parent lipid molecule to which the nitroxide fragment is rigidly attached). The measurements of T 1 −1 must be performed for deoxygenated samples. The detailed fluidity profiles of acyl chains can be obtained by measuring the T 1 −1 for n-PCs or n-SASLs with nitroxide fragments located at different depths in the membrane, using the SR EPR technique. These profiles qualitatively show the same detailed features as the profiles obtained from the simulation of the EPR spectra obtained with a convenient continuous wave EPR technique using the microscopic order and macroscopic disorder model [54][55][56], which provides spin-label rotational diffusion coefficients, an actual quantitative measure of the membrane fluidity [57,58]. Figure 4 illustrates the similarities between both of the profiles, obtained from the simulation of the EPR spectra and from measurements of T 1 −1 , across the membranes of the multilamellar liposome dispersion of DMPC/Chol. nique. These profiles qualitatively show the same detailed features as the profiles obtained from the simulation of the EPR spectra obtained with a convenient continuous wave EPR technique using the microscopic order and macroscopic disorder model [54][55][56], which provides spin-label rotational diffusion coefficients, an actual quantitative measure of the membrane fluidity [57,58]. Figure 4 illustrates the similarities between both of the profiles, obtained from the simulation of the EPR spectra and from measurements of T1 −1 , across the membranes of the multilamellar liposome dispersion of DMPC/Chol. The simulation of the EPR spectrum is not an easy process, as it depends on many parameters (including the principal values of the g tensors and hyperfine tensors) that should be determined for the particular environment in which the spin label is located. Because of that, the spin-lattice relaxation rate measurements, which are straightforward and easy to obtain, are very promising and already used to describe the profiles of membrane fluidity across model membranes of multilamellar liposomes made of simple lipids [57][58][59], as well as across the membranes of multilamellar liposomes made of the lipid extracts from biological membranes [50,60,61] (see Figure 5), and across the domains in complex biological membranes [62,63]. The simulation of the EPR spectrum is not an easy process, as it depends on many parameters (including the principal values of the g tensors and hyperfine tensors) that should be determined for the particular environment in which the spin label is located. Because of that, the spin-lattice relaxation rate measurements, which are straightforward and easy to obtain, are very promising and already used to describe the profiles of membrane fluidity across model membranes of multilamellar liposomes made of simple lipids [57][58][59], as well as across the membranes of multilamellar liposomes made of the lipid extracts from biological membranes [50,60,61] (see Figure 5), and across the domains in complex biological membranes [62,63].  [64,65] it is assumed that the location of the acyl chain carbon atom in the membrane changes linearly with the position on the acyl chain (the maximal error is about +/−1.5 Å). We also assumed that nitroxide moieties in n-PC are located at the same Locations of spin labels for n-PCs are indicated by numbers and for T-PC by "T". Based on the data obtained from the neutron diffraction studies on phosphatidylcholine model membranes [64,65] it is assumed that the location of the acyl chain carbon atom in the membrane changes linearly with the position on the acyl chain (the maximal error is about +/−1.5 Å). We also assumed that nitroxide moieties in n-PC are located at the same depth as appropriate carbon atoms of the 2-chain of PC membranes [66]. It can also be concluded that a nitroxide moiety stays at the position determined by neutron diffraction for most of the time.
Adapted from [60], with permission of the Taylor and Francis Group.
As indicated above, and as illustrated in Figures 4b and 5, the T 1 −1 profiles provide excellent qualitative descriptions of the changes in membrane fluidity that occur after the additions of membrane modifiers. The results recently obtained in the Subczynski lab (not published) show a linear relationship between T 1 −1 and the rotational diffusion coefficients for the n-PC spin labels in the fluid-phase DMPC/Chol membranes of the multilamellar liposomes. The linearity is independent through the wide range of conditions, including the lipid environment, depth of membrane, local hydrophobicity, and anisotropy of rotational motion (independent of the order parameter). Thus, this linear dependence can be used as a calibration curve, allowing transformation qualitative profiles of T 1 −1 into quantitative profiles of spin-label rotational rates, which form a description of the membrane fluidity that is precise and easy to understand. Interestingly, a similar linear dependence between spin-lattice relaxation rates and rates of rotational motion was observed for a very different system, namely for various spin-labeled sites in the T4L protein (see Figure 2c in [67]).

Oxygen Transport Parameter as a Convenient Monitor of Membrane Fluidity
As shown in Section 4, the profiles of T 1 −1 can qualitatively describe membrane fluidity. As a result, the depth-dependent dynamics of the lipids forming the membrane can be acquired from the SR EPR measurements. All of these profiles are smooth and bell-shaped, which is the result of the cumulative effects of rotations that take place simultaneously at different positions along the chain. The movement of small molecules, such as O 2 , within the membrane is not affected by this cumulative effect. The molecular oxygen, a small and rather hydrophobic probe molecule, enters the vacant pockets transiently formed in the acyl chain matrix of membranes, moves with them, [68] and/or hops between the adjacent vacant pockets [69]. Because of that, the movement of O 2 is sensitive to the dynamics of the acyl chains, and to the structural nonconformability of the neighboring lipids (see [35] for further explanation).
The movement of O 2 within the lipid bilayer membranes is monitored using the indirect SR EPR technique, in which the collision rate between paramagnetic oxygen molecules and the nitroxide fragment of lipid spin labels is measured. Kusumi et al. [33] developed an accurate and convenient way to evaluate this bimolecular collision rate using the SR EPR spin-labeling approach through the introduced oxygen transport parameter (OTP), defined as: T 1 −1 (x, Air) and T 1 −1 (x, N 2 ) are the spin-lattice relaxation rates of the spin labels for samples equilibrated with air and nitrogen, respectively. x is the depth of the location of the nitroxide in the membrane; r 0 is the interaction distance between oxygen and the nitroxide (4.5 Å [70]); and p is the probability that an observable event occurs when a collision takes place. Thus, the OTP is the measure of the local oxygen diffusion-concentration product (D(x)C(x)) in the membrane around the nitroxide. This approach is quantitative because every collision of O 2 with the nitroxide fragment contributes to the change in the nitroxide spin-lattice relaxation time [71]. By placing the nitroxide fragment of lipid spin labels at different depths in the membrane, the profiles of the OTPs (and, thus, the profiles of the oxygen diffusion-concentration products) across the membrane can be obtained.
With the use of multilamellar liposomes, the OTP profiles were obtained across simple lipid bilayer membranes [34,35,72,73], as well as across the membranes of the multilamellar liposomes prepared from the total lipid extracts of biological membranes [60,61,[74][75][76], and those formed from membranes reconstituted with integral membrane proteins [77]. A lack of the cumulative effect mentioned above allows for more detailed profiles of the membrane fluidity to be obtained, which have much greater spatial resolution than the profiles of the acyl chain motion. The OTP profiles show the membrane property changes with atomic resolution. As shown in Figure 6, the OTP profiles can indicate abrupt changes (i.e., changes that occur a few times) in membrane fluidity occurring on the distance of one C-C bond in the acyl chain. The abrupt change, which was observed for the membranes saturated with Chol, was recorded for the fluid phase membranes, indicating that the vertical fluctuation of the lipids must be diminished, and the lipids aligned (see [78,79] for further explanation). The molecular dynamics simulation also confirmed that the saturation with Chol increases the vertical order and smooths the phosphatidylcholine bilayer surface [80]. indicate profiles were obtained with n-PC, and symbols (∆,▲,▼) indicate data were obtained with ASL and CSL. Symbols (∆,▲) are for data from the PL bilayer, and symbols (▼) are for data from CBDs. It should be noted that the positions of the nitroxide moieties of ASL and CSL in the CBD are shifted toward the membrane center. A "sinking" of Chol molecules in the CBD was evaluated in [75] as about four C-C bonds deeper compared to Chol in the surrounding phospholipid bilayer; (b) Profiles of the OTPs across membranes of multilamellar liposomes made of the total lipid extracts from cortical fiber cell membranes of eye lenses from the group of 61-70-year-old human donors. Symbols (•,▲) indicate profiles were obtained with n-PC, ASL, and CSL in the PL bilayer, and symbols (▼) are for data obtained with ASL and CSL from CBDs. The symbol (x) indicates an OTP in water. All profiles were obtained at 37 °C. At ages ranging from 60 to 70 years, human lens fiber cell membranes contain ~70% sphingolipids [81]. Approximate locations of the nitroxide moieties of the spin labels are indicated by arrows (numbers for n-PC and "T" for T-PC). Data points for (a) are adapted from [82] with permission of the Elsevier Science & Technology Journals and for (b) are adapted from [60] with permission of the Taylor and Francis Group.

Discrimination by the OTP Method and Its Applications in Model Multilamellar Liposomes
OTP is a sensitive characteristic of membrane fluidity. Often, the fluidity of coexisting membrane domains cannot be differentiated in a straightforward manner by measuring the spin-lattice relaxation time (T1 values of spin labels in coexisting domains are too close to allow fitting the SR EPR signal to the double exponential). However, in the presence of O2, the collision of oxygen with nitroxide fragments of these spin labels can affect the T1 differently in both domains. Even small differences in the membrane lipid packing can affect the oxygen concentration and oxygen diffusion, which affect the T1s differently in both coexisting domains. In the method developed by Ashikawa et al. [77], the differences in T1s from the spin labels located in these two membrane domains and recorded in the presence of O2 allowed for differentiation between the domains. This method is named Figure 6. (a) Profiles of the oxygen diffusion-concentration products (OTPs) across membranes of multilamellar liposomes made of egg sphingomyelin in the absence ( ,∆) and presence (•, , ) of a saturating amount of Chol. Symbols ( ,•) indicate profiles were obtained with n-PC, and symbols (∆, , ) indicate data were obtained with ASL and CSL. Symbols (∆, ) are for data from the PL bilayer, and symbols ( ) are for data from CBDs. It should be noted that the positions of the nitroxide moieties of ASL and CSL in the CBD are shifted toward the membrane center. A "sinking" of Chol molecules in the CBD was evaluated in [75] as about four C-C bonds deeper compared to Chol in the surrounding phospholipid bilayer; (b) Profiles of the OTPs across membranes of multilamellar liposomes made of the total lipid extracts from cortical fiber cell membranes of eye lenses from the group of 61-70-year-old human donors. Symbols (•, ) indicate profiles were obtained with n-PC, ASL, and CSL in the PL bilayer, and symbols ( ) are for data obtained with ASL and CSL from CBDs. The symbol (x) indicates an OTP in water. All profiles were obtained at 37 • C. At ages ranging from 60 to 70 years, human lens fiber cell membranes contain~70% sphingolipids [81]. Approximate locations of the nitroxide moieties of the spin labels are indicated by arrows (numbers for n-PC and "T" for T-PC). Data points for (a) are adapted from [82] with permission of the Elsevier Science & Technology Journals and for (b) are adapted from [60] with permission of the Taylor and Francis Group.

Discrimination by the OTP Method and Its Applications in Model Multilamellar Liposomes
OTP is a sensitive characteristic of membrane fluidity. Often, the fluidity of coexisting membrane domains cannot be differentiated in a straightforward manner by measuring the spin-lattice relaxation time (T 1 values of spin labels in coexisting domains are too close to allow fitting the SR EPR signal to the double exponential). However, in the presence of O 2 , the collision of oxygen with nitroxide fragments of these spin labels can affect the T 1 differently in both domains. Even small differences in the membrane lipid packing can affect the oxygen concentration and oxygen diffusion, which affect the T 1 s differently in both coexisting domains. In the method developed by Ashikawa et al. [77], the differences in T 1 s from the spin labels located in these two membrane domains and recorded in the presence of O 2 allowed for differentiation between the domains. This method is named the discrimination by oxygen transport method.
First, the discrimination by the oxygen transport method was used to discriminate the trapped lipid domain (slow oxygen transport domain) from the bulk plus boundary domain in the reconstituted membranes of bacteriorhodopsin and DMPC [77]. After that, it was used to discriminate raft domains [30] and CBDs [83]. Because the OTP profiles were obtained across these coexisting domains without their physical separation, few significant conclusions could be made. It is thought that the lipid-lipid interactions that form the liquid-ordered (l o ) phase domains within the surrounding liquid-disordered (l d ) bilayer may be responsible for the raft formation [84]. The OTP profiles across coexisting l o and l d phase domains [73] confirm that the properties of the l o phase domain (modeling raft domain) lie between those for the l d and the solid-ordered (s o ) phases [85]. However, at the Chol saturation limit, the properties of the l o phase to the depth of C9 are similar to those in the s o phase. At depths greater than C9, they are similar to those in the l d phase.
The excess of Chol above the saturation limit of the l o phase of the PL bilayer forms pure CBDs. These domains can be discriminated only with the Chol analog spin label, ASL, using O 2 as a relaxation agent (see also Figure 6) [83]. The SR EPR signals of ASL from membranes contain these domains in the presence of O 2 ; they can be fitted satisfactorily only by double exponential functions, giving two OTP values. As shown [60], the values of the OTPs in the bulk domain (surrounding CBDs) do not change with an increased Chol content. In the CBDs, these parameters are very close to those in the surrounding environment when the CBDs begin to form; however, as the Chol content increases, the parameters become increasingly separate from those in the surrounding domain. The most probable explanation for these observations is that the CBDs are small, just above the Chol saturation limit, and the Chol exchange between the coexisting domains strongly affects the properties of the small domain. When the size of an individual CBD increases, at a greater Chol content, the influence of the bulk domain decreases. The major conclusion is that, with increased Chol content, the amount of Chol in a CBD increases, as does the size of an individual CBD [60].
In the recent publication [86], the authors, using AFM with the measured tip of the radius of 32 nm, were not able to discriminate the CBDs in the supported lipid membranes made of Chol/POPC mixtures, up to a Chol/POPC mixing ratio of 3/1. They concluded that CBDs in these supported lipid membranes are small, smaller than the surface of the discriminating AFM tip (~3000 nm 2 ).

Summary and Future Directions
The multilamellar liposomes are the model most often used to study the organization, dynamics, and properties of the lipid bilayer component of biological membranes. In addition, the EPR techniques, with the use of spin-labeling methods, have been applied extensively in these studies. The advancement of these techniques to the SR EPR technique [37,38] has allowed new information about the dynamics of lipids in membranes to be obtained. These investigations were possible because the spin-labeled multilamellar liposomes can be densely (tightly) packed in sample capillaries, allowing a good signal-to-noise ratio in the SR EPR measurements. In this review, we focus on recent developments that combine the RSE method of multilamellar liposomes' preparation, SR EPR spin-labeling methods, and spin-label oximetry to study the three-dimensional dynamic structure of lipid bilayers to better understand its function in biological membranes. This combination forms a unique approach that allows an extension of the established phase diagram for Chol/DMPC mixtures [45] to the one-phase region where the CBDs are detected (the structured liquid-ordered phase) and the two-phase region where the structured liquid-ordered phase of DMPC coexists with Chol crystals. The approach developed to discriminate membrane domains in multilamellar liposomes (i.e., discrimination by the OTP method) has been used successfully to discriminate domains in complex biological membranes [62,63,87,88], and was further developed to quantify lipids in these domains [39].
The routine analysis of SR EPR signals from spin-labeled membranes using multiexponential functions gives one, two, or-in some cases-three distinct spin-lattice relaxation rates for lipid spin labels, indicating that a membrane has one, two, or three distinct domains with distinct fluidities [33,73,83,88]. We think that the new way of analyzing the SR EPR signals of complex membranous systems using the stretched exponential function will allow more rigorous analysis of spin-lattice relaxation processes of lipid spin labels in membranes and parametrize the heterogeneity of membrane fluidity. This approach was first developed to analyze spin-label relaxation processes in complex biological membranes when one relaxation process (spin-lattice relaxations, due to the rotational diffusion of the spin labels) contributes to an exponential-like SR signal [89]. Recently, the second relaxation process, which contributes to the decay of SR signals, was included into the analysis, namely the Heisenberg exchange that occurs during collisions between the spin labels and O 2 [90]. The obtained fitting parameters allow evaluation of not only the distribution (heterogeneity) of the rotational diffusions of spin labels in investigated membranes, but also the distribution (heterogeneity) of oxygen diffusion concentration products within the membrane. This approach adds new insight into membrane fluidity descriptions. Although this approach was developed to analyze the SR signals from complex biological membranes, it was also used to analyze SR signals from multilamellar liposomes made of total lipid extracts from these biological membranes, giving new information about the heterogeneity of their organization and their dynamics [90,91].
SR EPR spin labeling, as presently developed, forms an exceptional tool to study the organization (formation of membrane domains) and dynamics (profiles of membrane fluidity) of model and biological membranes. Previously, these studies mainly focused on the qualitative description of membrane characteristics. The new achievements indicate that these characteristics can be described in more quantitative ways. Thus, the principal applications of SR EPR spin-labeling methods in investigations of model and biological membranes can be broadened to quantitative measurements of membrane properties.
Author Contributions: W.K.S., conceptualization, methodology, writing-original draft preparation, writing-review and editing, visualization, supervision, project administration, and funding acquisition; M.R., investigation, writing-review and editing, data curation, visualization, project administration, and funding acquisition; J.W., writing-review and editing, formal analysis, and visualization. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.