Critical Point for Membrane Bilayer Formation

Abstract

Unilamellar liposomes often are employed in investigations of lipid-protein interactions and the delivery of drugs in therapies for disease. Also, related lipid-containing nanoparticles have been developed as elements of a new class of mRNA vaccines. We show that only unilamellar films form in equilibrium lipid dispersions, at temperature values $\left\{{\text{T}}^{\ast }\right\}$ that depend on the identities of the lipids (e.g., ${\text{T}}^{\ast }\approx {29}^{\circ }\text{C}$ for DMPC). Thermodynamic analysis confirms that films at air-water surfaces can be used to monitor the properties of the lipid vesicles that form in the dispersion. When $\text{T}>{\text{T}}^{\ast }$, critical exponents describing film properties as T approaches ${\text{T}}^{\ast }$ are $\text{μ}\approx 1.4$ and $\text{v}\approx 0.7$, which are close to values for the interfacial tension and the correlation length of density fluctuations at fluid interfaces. These results, and observations that within the bilayer the lateral diffusion of fluorescent lipid probes demonstrates increases at ${\text{T}}^{\ast }$, suggest that unilamellar vesicles at ${\text{T}}^{\ast }$ are a transition state between two different multilamellar structures. We generalize the thermodynamic arguments to explain the linkage between lipid structures in the surface and bulk dispersion within more complex samples, showing that dispersions containing total lipid extracts of cell membranes have properties similar to those in dispersions containing single lipids. Information from various independent studies indicates that ${\text{T}}^{\ast }$ noted for bilayer membranes of a population of cells is identical to the temperature at which the growth or gestation of the cells occurs in vivo. Examples include whole-cell lipid extracts obtained from bacteria, and poikilothermic and homeothermic animals.

1. Introduction

It has long been recognized that lipids in cell membranes are arranged as a bilayer [1]. This has led to the development of unilamellar lipid vesicles (“liposomes” or “ULVs”) and related bilayer structures to study the behavior of lipid-associated proteins [2,3]. “Second generation liposomes” having modified surfaces are now employed therapeutically to deliver drugs and short RNA molecules to cells [4]. Among the latter are siRNA molecules used in cancer treatment and gene therapy (see, e.g., [5]).

Recently, considerable attention has been focused on using related, more elaborate, entities to move relatively long mRNA molecules into cells of potentially vulnerable persons as part of vaccination schemes against pathogens such as SARS, MERS and SARS-CoV-2 [6]. These schemes employ complex lipid-containing nanoparticles (frequently called “lipid nanoparticles,” or “LNPs”[6–8]) that contain cationic lipids not normally found in human membranes, as well as lipids whose head groups lose their charge once the LNPs reach targeted cells. The particles are formed from these lipids along with various polymer additives that create emulsions with mRNA molecules, devised so the mRNA molecules end up in the interiors of newly-formed LNPs. Among other functions, the LNPs have to protect their mRNA cargo against destruction by ribonucleases and other antagonists [7]. Studies are being carried out on possible use of mRNA cargoes in other therapies, e.g., to decrease the severity of heart failure [8]. Although the exterior borders of the LNPs contain only a single lipid leaflet (7), it will become apparent that there may be advantages to a cell if the lipid structures of the LNPs have physical properties like those of lipid bilayer vesicles, especially in how they respond to temperature.

Lipid bilayers also figure in complex cellular processes, a much-studied illustration of such a process being receptor mediated endocytosis (RME), in which the properties of the cell membrane -- including those of its bilayer core -- are critical elements [9,10]. Receptor mediated endocytosis is widely used by eukaryotes to deliver cargo-containing nanoparticles to cells [11]. However, although the lipid bilayer plays an important role in endocytosis, it usually is considered to be a uniform material whose structure is insensitive to temperature and other environmental variables. Also, its lipid concentrations are presumed to be spatially everywhere the same, even when the bilayer is composed of many components that may phase separate when endocytosis occurs. However, information obtained by using even simple liposomes as models must be treated with care, especially if the liposomes are produced by mechanical means, because their physical properties might differ from those of lipid membranes created by cellular processes.

During the 90+ years since the observations of Gorter and Grendal [1] were published, major advances have occurred in our understanding of many properties of biological membranes. However, despite increasingly sophisticated technological applications such as those mentioned in the previous paragraphs, important questions concerning the lipid bilayer concept remain unresolved. Several of these are subjects of this paper. As already mentioned, efforts to simulate the properties of cell membranes by using artificially prepared unilamellar phospholipid vesicles could be unreliable because non-biological methods used to prepare the vesicles may impose history-dependent properties that are absent in natural membrane biogenesis. A second, perhaps more profound, question is why the single lipid bilayer structure is ubiquitous in cell membranes. Additionally, do cell membranes possess unique properties that require metabolic activity by the cells to modify lipid composition when growth temperatures change? We address such questions in this paper by a simple equilibrium thermodynamic exposition of the assembly of unilamellar vesicles that arise from aqueous lipid dispersions containing typical membrane phospholipids. We show that, at thermodynamic equilibrium in the absence of external forces, the unilamellar bilayer of membrane lipids forms spontaneously at a temperature ${\text{T}}^{\ast }$ that depends on the composition of the lipids in their dispersion. Further, we show that ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$ when lipids are extracted from a physiological source, explaining the need for metabolic control of cell membrane lipid composition. We use the notation ${\text{T}}_{\text{cell}}^{\ast }$ to mean the gestation temperature of a multicellular organism or the growth temperature of a prokaryote or other unicellular organism, and present evidence that ${\text{T}}^{\ast }$ cell is equal to the critical temperature of unilamellar vesicle formation in water, ${\text{T}}^{\ast }$.

Studies showing that lipid bilayers assemble at physiologically significant temperatures are summarized in a review that contains supporting experimental data and inferences for biological phenomena [12]. We now show that the formation of unilamellar vesicles exhibit general attributes of critical phenomena for homogenous mixtures, with significant fluctuations of local supramolecular domains that give rise to physical attributes which, in the neighborhood of ${\text{T}}^{\ast }$, are dependent upon exponents of $\left({\text{T}}^{\ast }-\text{T}\right)$. We thus refer to $\left\{{\text{T}}^{\ast }\right\}$ as “critical temperatures” and the exponents as “critical exponents.” Here we present approximate values of these exponents for a typical bilayer-forming phospholipid, 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC), and then provide evidence that, more generally, critical bilayer assembly from total cell membrane extracts occurs over a wide range of organism-specific temperatures.

Results are presented in five sections. The first (Sec. 2) contains a discussion of a method for determining the surface pressure and surface concentration of lipid films arising at the air-water interface of an aqueous suspension of the lipids. Data obtained by this method for DMPC then are substantiated by thermodynamic analysis establishing that unilamellar vesicles uniquely form at ${\text{T}}^{\ast }$. We also use these data to derive values of related critical exponents. Section 3 extends the thermodynamic analysis to lipid mixtures and the generation of unilamellar vesicles from total lipid extracts of cell membranes. In particular, we demonstrate the equivalence between ${\text{T}}^{\ast }$ measured in films formed at the air-water interface and the value of ${\text{T}}^{\ast }$ pertaining to liposomes present in the lipid suspension. Moreover, evidence that the ${\text{T}}^{\ast }$ of cell membrane lipids reflects the gestation temperature of the organism from which they are obtained is reviewed. We then discuss, in Sec. 4, the miscibility of cholesterol and integral proteins within unilamellar phospholipid vesicles when $\text{T}={\text{T}}^{\ast }$. The data indicate that the presence of these materials, at least in moderate amounts, does not change ${\text{T}}^{\ast }$ of the lipid bilayer although other physical parameters can be affected. This leads us to discuss, in Sec. 5, how changes in phospholipid concentrations, in contrast to cholesterol and integral proteins, predictably change ${\text{T}}^{\ast }$. In Sec. 6 we examine lipid membrane transformations as the temperature is varied near ${\text{T}}^{\ast }$. Finally, in Sec. 7 (Discussion) we summarize and elaborate upon some principal results of the paper, and indicate how insights developed in this and related studies might be useful when designing LNPs to deliver mRNAs and drugs to the cells of human patients.

Over time, physical activity underlying bilayer membrane formation resulted in the existence of various rudimentary structures in which chemistry essential to life occurred. The consequences of this activity later became enshrined by evolution into the genetics of growing organisms. One of our goals is to focus attention on how physical rules might help one understand the properties of even more complex membranes. Some concepts and data discussed in this paper have previously been published but may be unfamiliar to readers because they appear in relatively old and/or inaccessible literature. Such information, included here because of its relevance to this and related studies, is fully identified by suitable references.

2. Thermodynamic analysis of unilamellar vesicles at the critical temperature ${\text{T}}^{\ast }$.

2.1. Background: Monitoring the temperature dependence of vesicle formation by observing phospholipid films at the air/water interface in equilibrium with bulk dispersions of lipid.

To understand the material presented in this Section, we first need to briefly review a technique previously developed to study the properties of bulk lipid dispersions. In principle, the equilibrium conditions for spontaneous formation of unilamellar vesicles from model phospholipids can be obtained from the temperature dependence of lipid solubility in aqueous dispersions [13]. However, this method is not feasible for biological membranes because of the low solubility of their lipids in water. Instead, we monitored the equilibrium monolayers that readily form at the air/water interface of aqueous dispersions of the lipids (i.e. saturated solutions) by measuring the surface pressure and surface film lipid concentration as a function of temperature. We will now show that this method provides conditions for the spontaneous assembly of unilamellar vesicles (ULVs).

Two previously reported studies of DMPC suspensions in water [14,15] provide the experimental basis for a thermodynamic description, which follows, of the assembly of unilamellar bilayers at the unique temperature ${\text{T}}^{\ast }$. Salient features of these studies appear in Figs. 1a and 1b, which we present here because they are necessary in order to understand the thermodynamic arguments that follow. Figure 1a shows, for the air-water interface of an aqueous suspension of DMPC, the dependence of surface pressure on temperature, $\text{π}$ vs T, between 22°C and 38°C. If the relative humidity (RH) is about 90 % (open points), when the temperature changes from 24°C to 29°C the surface pressure increases monotonically from $\text{π}\approx 0$ to a maximum of $\text{π}=45\text{mN}/\text{m}$. This is a reasonable value for a close-packed homogeneous phospholipid monolayer at the air-water surface in equilibrium with a dispersion of DMPC. However, when the vapor above the surface film is maintained at 100% RH, the $\text{π}$ - T relation for DMPC shown in Fig. 1a as closed points is obtained, and at 29°C the observed surface pressure, $\text{π}=\left({\text{γ}}_{\text{W}}-{\text{γ}}_{\text{F}}\right)$, is zero. Also, as seen in Fig. 1b, at 100% RΗ the film concentration at 29°C is that of a bilayer. $\text{π}=\left({\text{γ}}_{\text{W}}-{\text{γ}}_{\text{F}}\right)$, the film surface tension ${\text{γ}}_{\text{F}}$ equals the surface tension of water ${\text{γ}}_{\text{W}}$, and we infer that that under these conditions the bilayer is completely covered by a thin film of water.

Figure 1a.

The effect of relative humidity (RH) and temperature on the surface pressure, π, of surface films at the air-water interface in equilibrium with aqueous dispersions of DMPC. (○: ≈ 90% RH; ●: 100% RH). Each data point was obtained by equilibrating lipid at 23°C and rapidly heating to the indicated experimental temperature (<3 min). A specially-designed surface tension device, using a Wilhelmy plate in an enclosure for maintaining 100% RH, was employed to obtain these data. [15].

Figure 1b.

DMPC surface density (film concentration, mol/cm²) vs. temperature at 100% RH, obtained using aqueous dispersions of ³H-DMPC; area per molecule in the monolayer is 55 Ų/molecule. Data points pertain to separate experiments [14].

That the surface tension of the surface bilayer is equal to zero is predicted by theory [16]. The surface bilayer forms only when the combination of temperature and humidity is such that the chemical potential of water is the same in the vapor phase and the bulk dispersion. This allows the surface bilayer to form at the air-water interface, with polar groups oriented towards the vapor. An important aspect of the assembly of the surface bilayer assembly is its rapid rate of formation: the equilibrium surface bilayer forms within minutes once ${\text{T}}^{\ast }$ is attained. When the RH is less than 100% we infer that the surface bilayer transforms to a monolayer. Verification of this transformation is readily demonstrated by reducing the RH at 29°C, which results in π rising steadily from zero to 45 mN/m [15]. Although ${\text{T}}^{\ast }={29}^{\circ }\text{C}$ for DMPC, we note that the critical temperature for the formation of ULVs in the equilibrium aqueous dispersion varies markedly with acyl chain length, e.g., ${\text{T}}^{\ast }={44}^{\circ }\text{C}$ for DPPC and ${\text{T}}^{\ast }=7^{\circ }\text{C}$ for DOPC [14]. ${\text{T}}^{\ast }$ generally depends only weakly on lipid head group when $\text{T}={\text{T}}^{\ast }$ [17].

2.2. Critical exponents for surface pressure, $\text{π}$, and correlation length, $\text{ξ}$, of surface bilayers.

We now show ${\text{T}}^{\ast }$ also is the critical temperature for assembly of unilamellar vesicles. Consider, again, a suspension of DMPC in water. Water is present in association with hydrated polar groups and as solute within the hydrocarbon regions of the surface films and dispersed bilayers. Although the water of the hydrated polar groups may affect bilayer properties, it can be accounted for by the chemical potential of each phospholipid; moreover, the amount of water dissolved in the hydrocarbon regions of the dispersion bilayer and surface film is very low and may be disregarded for this discussion.

The following analysis is based on the temperature dependence of the surface pressure of the equilibrium monolayer, $\text{π}$ [18–20]. Let us first consider a simple (2-component) system of water and single-species lipid. We focus on the molar Helmholtz free energy ${\text{f}}_2$, the molar entropy ${\text{s}}_2$, and the molar energy ${\text{u}}_2$ when the phospholipid species is distributed at equilibrium between the surface film S and bulk lipid B. These quantities are related by

$$-\left({\text{f}}_2^{\text{S}}-{\text{f}}_2^{\text{B}}\right)=\text{π}{\text{A}}_2$$ (1)

$$\left({\text{s}}_2^{\text{S}}-{\text{s}}_2^{\text{B}}\right)={\text{A}}_2(\text{dπ}/\text{dT})$$ (2)

$$-\left({\text{u}}_2^{\text{S}}-{\text{u}}_2^{\text{B}}\right)={\text{A}}_2[\text{π}-\text{T}(\text{dπ}/\text{dT})]$$ (3)

where ${\text{A}}_2=1/{\text{Γ}}_2$ is the area/mole of the phospholipid in the surface film, ${\text{Γ}}_2$ being the surface concentration of the lipid (moles /cm²). These equations illustrate the significance of $(\text{dπ}/\text{dT})$ for revealing the presence of changes in state for both the surface film and bulk lipid phases. Moreover, since $\text{π}$ and $(\text{dπ}/\text{dT})$ are both zero for the surface bilayer at ${\text{T}}^{\ast }$, from Eqs. (1–3) one finds $\left({\text{f}}_2^{\text{S}}-{\text{f}}_2^{\text{B}}\right)=\left({\text{u}}_2^{\text{S}}-{\text{u}}_2^{\text{B}}\right)=\left({\text{s}}_2^{\text{S}}-{\text{s}}_2^{\text{B}}\right)=0$. That is, at ${\text{T}}^{\ast }$ the dispersed lipids have thermodynamic properties identical to those of the surface bilayer. The same logic applies to the monolayer films that form at the air/water surface when RH is 90%. Although in this case the monolayers are not in equilibrium with the saturated vapor phase and do not depend on the humidity, they are in equilibrium with the suspension of ULVs in the water. Consequently, as seen in Fig. 1a, at ${\text{T}}^{\ast }$ the equilibrium surface pressure for the monolayer is a maximum and $\text{dπ}/\text{dT}=0$, the only energetic distinction between the close-packed monolayer and surface bilayer being the work of forming the monolayer, $\text{π}{\text{A}}_2$. The molar entropies and molar enthalpies of the monolayer and the vesicles in aqueous suspension are identical. At ${\text{T}}^{\ast }$ the monolayer essentially is a leaflet of a bilayer. Measurements of monolayers provides a more convenient method to identify ${\text{T}}^{\ast }$ and associated thermodynamic properties because humidity control in the vapor is not required. Also, the monolayer data may be employed to evaluate the energetic properties of the equilibrium bilayers in the bulk aqueous phase at ${\text{T}}^{\ast }$.

Evidence that the surface bilayer appears to be a critical state structure is provided by the exponents that characterize surface phenomena of the DMPC film for values of T close to ${\text{T}}^{\ast }$. Studies of critical state phenomena of fluid interfaces, which are similar to our interface system, indicate that the region of the critical temperature can be characterized by two exponents of $\left(\text{T}-{\text{T}}^{\ast }\right)$, viz., $\text{μ}$ and $\text{v}$ [21,22]. The coefficient $\text{μ}$ describes how the interfacial tension, $\text{γ}$, decreases to zero at critical temperature ${\text{T}}^{\ast }$, and $\text{v}$ describes the divergence of the correlation length $\text{ξ}$, the region over which density fluctuations are correlated as the temperature of the systems varies. Specifically, it has been shown for fluid interfaces that $\text{γ}\sim {\left(\text{T}-{\text{T}}^{\ast }\right)}^{\text{μ}}$, where $\text{μ}=1.26$, and $\text{ξ}\sim {\left(\text{T}-{\text{T}}^{\ast }\right)}^{-\text{v}}$, where $\text{v}=0.63$ [22]. For a typical oil/water system, as the temperature increases to a value where complete miscibility of the oil in water occurs at the critical solution temperature, the interfacial tension approaches zero and the correlation length (related to the thickness of the oil/water interface) approaches infinity [21]. We infer from Fig. 1 that the behavior of the surface bilayer analogously involves the surface pressure tending to zero at ${\text{T}}^{\ast }\left({29}^{\circ }\text{C}\right)$, where the surface bilayer covers the entire air-water surface.

To evaluate the corresponding critical exponents for surface bilayer formation we use the data for 100% relative humidity (RH) shown in Fig. 1. As the temperature decreases from 35°C to 29°C, the surface film is transformed from a condensed monolayer (surface pressure, $\text{π}=45\text{mN}/\text{m}$, lipid concentration in the film, $\text{Γ}=3.2\times {10}^{-10}\text{moles}/{\text{cm}}^2$) to a bilayer ($\text{π}=0$, $\text{Γ}=6.4\times {10}^{-10}\text{moles}/{\text{cm}}^2$). For the intervening temperatures, where the surface film exceeds monolayer concentrations, regions of lipid as bilayer are in equilibrium with monolayer; as temperatures approach ${\text{T}}^{\ast }$ the monolayer concentration decreases while the amount of bilayer aggregate in the surface film increases. The decreasing surface pressure for this temperature range in Fig. 1a reflects only the decreasing concentration of monolayer because any bilayer structure present will not contribute to the measured surface pressure. The decrease in $\text{π}$, seen in the data of Fig. 1a between 29°C and 35°C, obeys the relation $\text{π}\sim {\left(\text{T}-{\text{T}}^{\ast }\right)}^{\text{μ}}$. The exponent $\text{μ}\approx 1.4$, obtained from the slope of the $\text{log}(\text{π})$ vs. $\text{log}\left(\text{T}-{\text{T}}^{\ast }\right)$ plot in Fig. 2, is notably close to the value of the critical exponent $(\text{μ}=1.26)$ for the fluid-fluid surface tension as the interface temperature approaches the critical temperature [22].

Figure 2.

Determination of the critical exponent $\text{μ}$ from the DMPC surface bilayer data shown in Fig. 1a. Measurements for the temperature range 29°C to 35°C were used. The slope of the plot of $\text{log}\text{π}$ vs. $\text{log}\left(\text{T}-{\text{T}}^{\ast }\right)$ yields $\text{μ}=1.4$. (The surface pressure π is analogous to $\text{γ}$, the interfacial tension of an oil-water interface.)

Data for the correlation length $\text{ξ}$ were obtained from the relative area of the surface occupied by bilayer as temperature was lowered from 35°C to 29°C. This area, which is proportional to the concentration of lipid present as surface bilayer [21] was obtained from measurements of the radioactivity of tritium labeled DMPC located at the air-water surface between vapor and bulk dispersion (Fig. 1b). The calculation of the critical exponent ν for the correlation length was obtained from $\text{ξ}\sim {\text{Γ}}_{\text{SB}}\sim {\left(\text{T}-{\text{T}}^{\ast }\right)}^{-\text{v}}$, where ${\text{Γ}}_{\text{SB}}$ represents the amount of bilayer in the surface film (‘SB’indicates surface bilayer). Quantitative data for ${\text{Γ}}_{\text{SB}}$ were obtained from Fig. 1b that shows the radioactivity of tritium-labeled DMPC at the air-water interface between vapor and bulk dispersion. But the data given in Fig. 1b pertains to the total amount of lipid in the surface film, $\text{Γ}={\text{Γ}}_{\text{SB}}+{\text{Γ}}_{\text{ML}}$, so the area occupied by monolayer (‘ML’) with concentration ${\text{Γ}}_{\text{ML}}$ must be subtracted to obtain ${\text{Γ}}_{\text{SB}}$. The procedure to do so entails selecting $\text{Γ}$ at temperatures between 29°C and 35°C in Fig. 1b, and corresponding values of $\text{π}$ in Fig. 1a. (From Fig. 1a we find the relation $\text{log}\text{π}=1.25$ $\text{log}\left(\text{T}-{\text{T}}^{\ast }\right)+0.649$, which provides the value of π for each of these temperatures.) Since the surface pressure represents only monolayer in the surface film, its concentration $\left({\text{Γ}}_{\text{ML}}\sim 1/\text{A}\right)$ is obtained from $\text{π}-\text{A}$ isotherms at each of the selected temperatures. The latter were obtained from the DMPC $\text{π}-\text{A}$ isotherm at 30°C [23] by using the temperature variation of the DMPC bilayer molecular area (0.31Ų /degree) [24]. Then ${\text{Γ}}_{\text{SB}}=\left(\text{Γ}-{\text{Γ}}_{\text{ML}}\right)$ was calculated, allowing us to obtain a relation between surface bilayer concentration and temperature, viz., $\text{log}{\text{Γ}}_{\text{SB}}=-0.7$ $\text{log}\left(\text{T}-{\text{T}}^{\ast }\right)+0.705$ (see Fig. 3). The above-described procedure yields $\text{v}\approx 0.7$, which is in close agreement with the value of the critical exponent $(\text{v}=0.63)$ determined for the correlation length of bulk fluid interfaces [22].

Figure 3.

Evaluation of the critical exponent $\text{v}$ from the amount of surface bilayer, ${\text{Γ}}_{\text{SB}}\text{moles}/{\text{cm}}^2$ (moles/cm²). Data over the range 29°C to 35°C in Fig. 1b for DMPC surface bilayer formation were used. The surface concentration ${\text{Γ}}_{\text{SB}}$ is analogous to the correlation length, $\text{ξ}$, for a fluid interface. Thus, to a good approximation we expect ${\text{Γ}}_{\text{SB}}\sim \text{ξ}$ where, as discussed by Rowlinson and Widom [22], $\text{ξ}\sim {\left(\text{T}-{\text{T}}^{\ast }\right)}^{-\text{v}}$. The slope of the plot shown here, $\text{log}{\text{Γ}}_{\text{SB}}$ vs $\text{log}\left(\text{T}-{\text{T}}^{\ast }\right)$, yields $\text{v}=0.7$.

2.3. Critical properties of equilibrium aqueous suspensions of DMPC at ${\text{T}}^{\ast }$; unilamellar vesicles form in the aqueous suspension only at ${\text{T}}^{\ast }$.

Confirmatory evidence that aqueous suspensions of DMPC give rise to unilamellar vesicles at the same temperature where surface bilayers form was obtained by cryo-transmission electron microscopy (Cryo-TEM). Figure 4a shows a previously unreported image of a field of unilamellar DMPC vesicles formed at 29 ± 0.1°C, which is ${\text{T}}^{\ast }$ for this material (see Methods). The vesicle walls are about 5 nm thick, and the diameters generally are 300–600 nm. As shown in Fig. 4a, sometimes vesicles are trapped within larger ones and occasionally one finds a smaller vesicle with a partially crumpled wall that is unstable as a unilamellar vesicle when squeezed between the walls of two other vesicles. Other images of the same preparation, not shown here, indicate that, overall, only about 30% are unilamellar; the bulk of the remaining structures are MLV’s (multilamellar vesicles) of varying wall thickness. (See Supplementary Material.) In contrast, when DMPC dispersions are equilibrated at 26°C or 38°C, no unilamellar vesicles are seen; only MLV’s with wall thicknesses of at least 2–5 bilayers (10–25 nm) are found, signifying that unilamellar vesicles form only at ${\text{T}}^{\ast }$ (see Fig. 4b). Although it may seem paradoxical that thermodynamics predicts that only the unilamellar state will be present at ${\text{T}}^{\ast }$ whereas both ULV’s and MLV’s appear, this result is consistent with the narrowness of the temperature range pertaining to the critical state: MLV’s form because, in experiments, temperatures cycle around ${\text{T}}^{\ast }\pm 0.1$ degree. (For dispersions studied at $\text{T}>\text{T}\ast$ (e.g., 38°C), water and lipid were separately warmed at the higher temperature before mixing to avoid inadvertent unilamellar bilayer formation when temperatures are transiently raised through a temperature range encompassing ${\text{T}}^{\ast }$.) We infer that the MLV’s forming at temperatures below and above ${\text{T}}^{\ast }$ represent different multilamellar structures, with the ULV as a transition state between the two.

Figure 4a.

Cryo-TEM images of DMPC vesicles formed under equilibrium conditions at ${\text{T}}^{\ast }={29}^{\circ }\text{C}$. All vesicles shown here have wall thicknesses of ~50 Å. The dark, thick images are of the lacey carbon grid onto which the DMPC suspension was pipetted.

Figure 4b.

Summary of the wall thicknesses of all observed DMPC vesicles formed at 26°C, 29°C and 38°C. (Key: black bar, ULVs 40–50 Å; stipled bar, 80–100 Å (two bilayers); unfilled bar, >100 Å (3–5 bilayers). Unilamellar vesicles are observed only at 29°C, which is ${\text{T}}^{\ast }$ for this material; none were observed at 26°C and 38°C.

3. Properties of multicomponent phospholipid mixtures at ${\text{T}}^{\ast }$.

3.1. Surface pressure vs. temperature behavior of phospholipid mixtures.

To demonstrate that the formation of ULV structures at ${\text{T}}^{\ast }$ is a general characteristic of phospholipid mixtures, we now examine a thermodynamic relationship establishing equilibrium between an aqueous suspension of a multi-component mixture of lipids and its monolayer at the air/water interface. A direct approach to the thermodynamic properties of phospholipid mixtures, including those of cell membranes, is obtained by using the Gibbs relation for the monomolecular surface films and the Gibbs-Duhem relation for the equilibrium lipid dispersed phase. Because of the very low solubility of phospholipids in water, as we did in the analysis of the DMPC study the interactions between the polar groups of the lipids and surrounding water are included in the chemical potentials of the lipids.

The Gibbs equation for lipid monolayers at the air/water surface may be written as

$$\text{dπ}={\text{S}}^{\text{S}}\text{dT}+\sum {\text{Γ}}_{\text{i}}\text{d}{\text{μ}}_{\text{i}}^{\text{S}}\text{i}=1,2,3,\dots \dots \dots ..\text{C}$$ (4)

where ${\text{S}}^{\text{S}}$ is the entropy/cm² of the surface film and ${\text{Γ}}_{\text{i}}$ is the surface concentration (moles/cm²) of the ith component of the film, with water within the film being component 1 and $\text{i}=2,3,\dots .$ representing the $(\text{C}-1)$ phospholipid constituents. The ${\text{μ}}_{\text{i}}^{\text{S}}$ are the corresponding chemical potentials. Also, the Gibbs-Duhem equation at constant atmospheric pressure for the lipid bulk aqueous suspension is

$$0={\text{S}}^{\text{B}}\text{dT}+\sum {\text{c}}_{\text{i}}\text{d}{\text{μ}}_{\text{i}}^{\text{B}}.\text{i}=1,2,3,\dots \dots ..\text{C}$$ (5)

Here, ${\text{S}}^{\text{B}}$ is the entropy/cm³ of the bulk lipid suspension and ${\text{c}}_{\text{i}}$ is the concentration (mol/cm³) of the ith component, including water, in the suspension. When surface film and bulk aqueous lipid suspensions are in equilibrium,

$${\text{μ}}_{\text{i}}^{\text{S}}={\text{μ}}_{\text{i}}^{\text{B}}={\text{μ}}_{\text{i}.}\text{i}=1,2,3,\dots \dots \dots .\text{C}$$ (6)

Thus, after dividing the terms in Eq. 5 by dT and inserting the resulting expression into Eq. 4 (also after dividing by dT), we obtain the following relationship between the lipid concentrations in the surface film and those in the equilibrium dispersion

$$\text{dπ}/\text{dT}=\left({\text{S}}^{\text{S}}-{\text{S}}^{\text{B}}{\text{Γ}}_1/{\text{c}}_1\right)+\text{Σ}\left({\text{Γ}}_{\text{j}}-{\text{c}}_{\text{j}}{\text{Γ}}_1/{\text{c}}_1\right)\text{d}{\text{μ}}_{\text{j}}/\text{dT}\text{j}=2,3,4\dots .\text{C}.$$ (7)

We now recall that the surface pressure is a maximum at $\text{T}={\text{T}}^{\ast }$ (even when RH <100% [14]), so $\text{dπ}/\text{dT}=0$ (see Fig. 1). We therefore can set both terms on the rhs of Eq. 7 equal to zero. Since $\left(-\text{d}{\text{μ}}_{\text{j}}/\text{dT}\right)$ equals the partial molar entropy, which always is positive, the coefficients in the sum are individually zero and we have $\sum {\text{Γ}}_{\text{j}}={\text{Γ}}_1/{\text{c}}_1\sum {\text{c}}_{\text{j}}$, so

$${\text{S}}^{\text{S}}/{\text{S}}^{\text{B}}={\text{Γ}}_1/{\text{c}}_1={\text{Γ}}_{\text{j}}/{\text{c}}_{\text{j}}=\sum {\text{Γ}}_{\text{j}}/\sum {\text{c}}_{\text{j}}\text{j}=2,3,4,\dots \dots ..\text{C}.$$ (8)

Thus, ${\text{S}}^{\text{S}}/\sum {\text{Γ}}_{\text{j}}={\text{s}}^{\text{S}}$ and ${\text{S}}^{\text{B}}/\sum {\text{c}}_{\text{j}}={\text{s}}^{\text{B}}$, which are the molar entropies (cal/moldeg) of the surface film and the ULVs in aqueous suspension, are equal. Therefore, the molar entropies, as well as the chemical potentials, of the monolayers and ULVs in suspension are identical at ${\text{T}}^{\ast }$. Furthermore, from Eq. 8, we obtain ${\text{Γ}}_{\text{j}}/\sum {\text{Γ}}_{\text{j}}={\text{c}}_{\text{j}}/\sum {\text{c}}_{\text{j}}$, so

$${\text{x}}_{\text{j}}^{\text{S}}={\text{x}}_{\text{j}}^{\text{B}}\text{j}=2,3,4,\dots \dots \dots \text{C}$$ (9)

where ${\text{x}}_{\text{j}}$ is the phospholipid mole fraction. Also, note that from Eqs. 8 there are $(\text{C}-1)$ relations among the ${\text{Γ}}_{\text{j}}/{\text{c}}_{\text{j}}$ lipid concentration variables, a property that will be used in the application of the Gibbs phase rule that follows in Sec. 3.2. (Recall that ${\text{Γ}}_{\text{j}}$ and ${\text{c}}_{\text{j}}$ are concentrations of the j^th lipid component in the surface film and bulk water, respectively.)

The validity of Eq. 9 has been tested with binary mixtures of tritium-labeled phospholipids under conditions of 100% relative humidity. Similar to measurements on DMPC, results indicate that, at the ${\text{T}}^{\ast }$ specific to a particular mixture, a surface bilayer forms with the same composition as the equilibrium bilayers in the ULV aqueous suspension [14]. For the same mixture with RH <100%, $\text{π}$ is seen to be a maximum at the same critical temperature. More generally, complex phospholipid mixtures dispersed in water show a maximum in their $\text{π}$-T relations whatever the value of the relative humidity (i.e., even when RH <100%). Moreover, the molar entropy, chemical potential and lipid compositions of the surface monolayer and bilayer in the aqueous ULV suspension are identical. We have seen these are the same conditions for the formation of unilamellar vesicles from single component phospholipids at ${\text{T}}^{\ast }$, as discussed above in Sec. 2.3.

3.2. The Phase Rule and its application to multi-component lipid systems at ${\text{T}}^{\ast }$.

To understand how pressure and lipid composition affect the critical temperature, ${\text{T}}^{\ast }$, we use the Gibbs Phase Rule to determine the number of independent intensive variables that must be specified to completely define conditions for equilibrium between a suspension of multi-component lipids vesicles and their monolayer at the air/water surface. The Phase Rule states that

$$\text{F}=\text{C}-\text{P}+2$$ (10)

where F is the number of independent intensive variables that can be arbitrarily varied in a system containing P phases and C components (lipid and water), temperature and pressure being two other independent variables. The lipid monolayer at the air/water surface at ${\text{T}}^{\ast }$ is a single, homogeneous phase, and therefore does not provide additional constraints for determining the number of independent variables [25]. In general, for an aqueous suspension of ULVs at the critical temperature, ${\text{T}}^{\ast }$, and constant pressure, there are two phases, ULV and water $(\text{P}=2)$. Also, although C components are present, as shown above there are $\left(\text{C}-1\right)$ relations (Eq. 8) among them as constraints on the number of independent variables and these must be subtracted from Eq. 10. Thus, since pressure (1 atm) and temperature (${\text{T}}^{\ast }$) are set, if the identities and ratios of the lipid components are fixed there is only one independent variable, specifically the concentration of any one of the lipid components, needed to completely determine the conditions (the concentrations of the other lipids) for unilamellar vesicle formation at the critical temperature ${\text{T}}^{\ast }$, regardless of the number of components in the lipid suspension.

The following are circumstances that illustrate situations one may encounter where the Phase Rule defines completely the equilibrium conditions for the formation of the critical state (see [20] for specific examples). Once the phospholipid composition of the dispersion is set, there is only one temperature, ${\text{T}}^{\ast }$, where ULVs form, ${\text{T}}^{\ast }$ being unique for the chosen lipid composition. For a two-component phospholipid mixture, the binary phase diagram for the presence of ULVs, i.e., ${\text{T}}^{\ast }$ versus composition, is a line where the choice of the concentration of one component defines the dependence of ${\text{T}}^{\ast }$ on lipid composition. With three phospholipid components at constant temperature (${\text{T}}^{\ast }$) and pressure, the lipid compositions that form ULVs will fall on a line in a ternary phase diagram in which the choice of the concentration of one component will automatically fix the concentrations of the other two components. Variations in the composition and number of components are common in biology and the phase rule shows that, for three or more components, more than one lipid composition of that mixture may yield the same ${\text{T}}^{\ast }$. As a corollary, different phospholipid mixtures with the same ${\text{T}}^{\ast }$, when combined, will form a new critical bilayer with ${\text{T}}^{\ast }$ unchanged. The temperature at which the surface pressure is maximal always indicates the critical temperature for complex phospholipid mixtures, where both the equilibrium surface film and suspended ULVs are homogenous. In the rare occasion that a second lipid phase arises in the vesicle, only one of the phases will exhibit a unique ${\text{T}}^{\ast }$ [20].

3.3. Evidence that critical points of cell lipid membranes occur at physiological temperature (gestation/growth temperatures of multicellular or unicellular organisms, respectively).

An earlier study of the equilibrium properties of total lipid extracts of bacterial and red blood cell membranes [26] suggested that ${\text{T}}^{\ast }$ equals ${\text{T}}_{\text{cell}}^{\ast }$, the latter being the gestation or growth temperature of the cellular source of a particular lipid extract, depending on whether the organism is multicellular or unicellular. To investigate the generality of these observations we have collected results of critical temperature measurements for dispersions of the total lipids obtained from other sources, viz., neural tissues of squid and rat [27], human myelin [28], and sea urchin Lytechinus pictus embryonic tissue membranes [29]. Table 1 shows ${\text{T}}^{\ast }$ for each of these preparations as a function of ${\text{T}}^{\ast }$ cell. For poikilotherms such as bacteria (e. g., E. coli and B. stearothermophilus), where membrane composition varies with temperature, a new growth temperature results in a change in ${\text{T}}_{\text{cell}}^{\ast }$. Various techniques were used to determine ${\text{T}}^{\ast }$, yet all of the lipid dispersions in water show ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$.

Table 1.

Comparison of critical temperatures, $\left\{{\text{T}}^{\ast }\right\}$, of total extracted phospholipids with physiological (growth or gestation) temperatures, {${\text{T}}_{\text{cell}}^{\ast }$}.

Phospholipid Source	${\text{T}}_{\text{cell}}^{\ast }$,°C	${\text{T}}^{\ast }$,°C (Ref.)
Prokaryotes
E. coli	20	19 ± 1 [26]
“	25	24.5 ± 1 [33]
“	29	29.5 ± 1 [33]
“	30	30 ± 1 [26]
“	32	32 ± 1 [33]
B. stearothermophilus	50	49 ± 1 [26]
“	59	58 ± 1 [26]
Eukaryotes
Squid (L. pealei) neural tissue
“ fin nerve	16	15 ± 1 [27]
“ optic lobe	16	15 ± 1 [27]
Rat forebrain	38	37 ± 1 [27]
“ cerebellum	38	37 ± 1 [27]
“ brainstem	38	37 ± 1 [27]
“ spinal cord	38	37 ± 1 [27]
Human cerebral white matter, myelin	37	37 ± 1 [28]
Human erythrocytes	37	37 ± 1 [26]
Sea urchin, blastula membrane	10	10 ± 0.6 [29]
“   “	16	16 ± 0.2 [29]
“   “	23	23 ± 0.4 [29]

Table 1also demonstrates the equilibrium status and relevance of the Phase Rule for cell membranes. For example, since for homeotherms the Phase Rule predicts that all membrane bilayers of the same organism normally will have the same ${\text{T}}^{\ast }$ regardless of their lipid compositions, it is understandable why the lipids of human myelin [30] and lipids of red blood cell membranes [31], having markedly different compositions, yield the same value of ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$ (see Table 1). Also, some of the lipid extracts included in Table 1 contain lipids from several membranes of the cell; e.g., E. coli extracts contain lipids from the double membranes that surround the cells. Although the two membranes of E. coli have different compositions, their mixture yields ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$, varying as the growth temperature is changed.

As indicated previously (Eq.6), equilibrium implies that the same physical state must exist in both the dispersion and cell membrane. This deduction is confirmed by Cryo-TEM studies of aqueous suspensions formed of whole-cell lipids extracted from E. coli that were grown at 32°C (see Methods): unilamellar vesicles were found in dispersions formed at 32°C (Fig. 5a), while at 38°C and 22°C only multilamellar structures were seen (Fig. 5b). As inferred from Cryo-TEM studies of DMPC (Fig. 4), cycling of the ambient temperature around ${\text{T}}^{\ast }$ yields MLVs in addition to unilamellar structures.

Figure 5a.

Cryo-TEM images of vesicles formed from total lipid extracts of E. Coli grown at 32°C, showing unilamellar vesicles whose bilayer membrane widths are 40–50 Å. Calibration bar (under lable) is 100 nm. (Additional images shown as Supplemental Material.)

Figure 5b.

E. coli grown at 32°C (see Fig. 5a). Summary of the wall thicknesses observed of vesicles formed at 22°C, 32°C and 38°C. Key: black bar, ULVs 40–50 Å; stipled bar, 80–100 Å (two bilayers); unfilled bar, >100 Å (3–5 bilayers). Unilamellar vesicles with wall thicknesses of 40–50 Å were seen only at 32°C. When lipid samples were prepared at 22 °C and 38 °C, no unilamellar vesicles were seen.

All of the systems heretofore examined have been maintained at constant atmospheric pressure in the analysis. In principle, changes in pressure will also affect the composition and critical temperature of the membranes. Growth of barophilic bacteria at constant temperature has been studied as a function of large variations in pressure [32]. Although the growth temperature is constant, as expected the lipid composition of the membranes varies with the applied pressure.

3.4. Diffusion anomaly in bilayers at ${\text{T}}^{\ast }$: further evidence for the critical state.

Further evidence that a phase change occurs in lipid bilayers when ${\text{T}}^{\ast }={\text{T}}^{\ast }$ previously was obtained by examining temperature dependent lateral diffusion coefficients of fluorescent lipid tracers (NBD-PE), determined from FRAP measurements of multilamellar layers of DMPC in contact with a pool of water [33]. As seen in Fig. 6, a large increase in the translational diffusion of the probes occurs when the sample temperature, T, is about 0.4 degrees below ${\text{T}}^{\ast }\approx {29}^{\circ }\text{C}$. The diffusion of the probes arises from interactions with lipid molecules whose positions essentially are fluctuating in the plane of the bilayer. These fluctuations intensify when T is close to the critical point, ${\text{T}}^{\ast }$. Evidence for enhanced intermolecular fluctuations in the region of ${\text{T}}^{\ast }$ also is seen in several other physical studies of giant unilamellar vesicles of DMPC: for example, at ${\text{T}}^{\ast }$ the bilayer compressibility modulus shows a minimum [34], and the bilayer bending elastic modulus is a maximum [35]. Although unusual, an increase in probe diffusion at a critical point has been found in other systems as well [36,37]. The 0.4 °C difference between ${\text{T}}^{\ast }$ and the temperature where the diffusion coefficient is maximal probably is due to the presence of the NBD-PE tracers.

Figure 6.

FRAP measurements of the lateral translational diffusion coefficient, D of the fluorescent lipid probe NBD-PE moving within a sample of DMPC multilayers. The maximum in D occurs at $\text{T}={28.6}^{\circ }\text{C}$, differing from ${\text{T}}^{\ast }\approx {29}^{\circ }\text{C}$, perhaps due to the presence of the probe molecules. Figure reproduced from Jin et al. [33].

Probe molecules moving within structures formed from total membrane lipids have an analogous diffusion anomaly at ${\text{T}}^{\ast }$. As seen in Fig. 7, multilamellar vesicles (MLVs) formed from total lipid extracts of E. coli grown at 25°C, 29°C and 32°C, and seeded with the same fluorescent phospholipid tracer, show diffusive behavior by FRAP measurements similar to that found in DMPC. Maxima appear at temperatures close to the growth temperatures of the bacteria from which the lipids were obtained, the lipid compositions of the cell membranes varying in concert with changes in the growth temperatures [33].

Figure 7.

Lateral diffusion coefficient D of the fluorescent probe NBD-PE as a function of temperature in multilamellar films of total membrane lipids obtained from E. coli preparations grown at $\text{T}={32}^{\circ }\text{C}$, 29 °C and 25 °C. The arrows indicate the temperatures at which the cells were grown. A maximum in D occurs at ${\text{T}}^{\ast }\approx {\text{T}}_{\text{cell}}^{\ast }$ for each lipid sample. Figure reproduced from Jin et al. [33].

Theoretical analysis of the formation of unilamellar vesicles (ULV) predicts that an MLV-ULV transition involves thermally generated Helfrich repulsive forces linked to out-of–plane bilayer undulations that overwhelm the van der Waals forces between multibilayers [38]. These undulations are observed over a wide range of temperatures and may differ from the lipid fluctuations that arise in the narrow region of the critical point at ${\text{T}}^{\ast }$. In-plane and out-of-plane fluctuations are coupled, and the influence of this coupling on critical behavior can be seen when out-of-plane undulations are suppressed [39,40]. DMPC and E. coli diffusion anomalies at ${\text{T}}^{\ast }$ were not perceptible when bilayers were confined, during pulsed field gradient (pfg) ³¹P NMR studies, to narrow spaces between parallel glass plates along which the bilayers were aligned [41].

4. Miscibility of cholesterol and integral proteins in bilayer vesicles at ${\text{T}}^{\ast }$.

4.1. Stability of ${\text{T}}^{\ast }$ when cholesterol is present in addition to phospholipid.

Much of the thermodynamic evidence for membrane critical state properties was obtained from prescribed mixtures containing only phospholipids, which show that ${\text{T}}^{\ast }$ will vary with phospholipid composition [20]. However, some of the lipid membranes represented in Table 1 include cholesterol, which is non-bilayer-forming. Also, some nerve preparations may contain significant amounts of myelin basic protein and/or proteolipids that co-extract with phospholipids. What might be the consequences of adding substances other than phospholipids to the samples?

To examine the effects of cholesterol on phospholipid bilayers at their critical temperatures, the surface pressures of films formed from egg yolk lipid (EYL) obtained from chicken oocytes, with and without cholesterol, are shown in Fig. 8 (see Methods). We presume, again, that a monolayer of pure phospholipid at ${\text{T}}^{\ast }$ closely represents a leaflet of a bilayer with the same entropy and internal energy as found in a corresponding equilibrium dispersion of ULVs; therefore, as shown below, measurement of the effect of cholesterol on the properties of a monolayer provides a measure of the interactions of cholesterol with lipids in the bilayer. Despite the fact that the egg yolk lipid mixture contains about 10 mole% cholesterol, its critical temperature, ${\text{T}}^{\ast }$, as seen in Fig. 8, is 38°C, which essentially is the same value of ${\text{T}}^{\ast }$ when cholesterol is removed. It also is the gestation and growth temperature for chicken embryos. However, although ${\text{T}}^{\ast }$ remains unchanged by the presence of this amount of cholesterol, the surface pressure at ${\text{T}}^{\ast }$ increases approximately 2 dyn/cm (mN/m). These observations indicate that at ${\text{T}}^{\ast }$ cholesterol is miscible in the phospholipid without affecting the basic bilayer structure. While only ~10 mole% cholesterol is present in the egg yolk lipids, the phenomenon is general: human RBC membranes, for example, contain much higher concentrations of cholesterol without affecting the relation ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$, as seen in Table 1.

Figure 8.

Equilibrium surface pressure, $\text{π}$, vs. T for monolayers that arise at the surfaces of aqueous dispersions of chicken egg yolk lipids. ○: total egg yolk lipids containing 10 wt % cholesterol; □ total egg yolk lipids with cholesterol removed. (Previously unreported data. See Methods for sample preparation.) The surface pressure was measured with a commercial, horizontal float film balance [27] in an enclosure filled with nitrogen at relative humidity = 90%. The maxima of the curves occur at ${\text{T}}^{\ast }$; arrow indicates ${\text{T}}_{\text{cell}}^{\ast }$ of chicken.

This phenomenon can be understood by first examining how the addition of cholesterol to the lipids increases the surface pressure of the monolayer, best explained by calculating the free energy of mixing. For a pure phospholipid monolayer maintained at constant temperature, the dependence of the surface pressure, ${\text{π}}^0$, on lipid composition is given by the Gibbs relation as

$${\text{π}}^0=\sum {\text{Γ}}_{\text{i}}^0{\text{μ}}_{\text{i}}^0\text{i}=1,2,3,\dots \dots \dots \dots .\text{C}$$ (11)

where ${\text{Γ}}_{\text{i}}^0$ is the concentration of the i^th phospholipid component and the notation “0” signifies the value in the absence of cholesterol. The symbol ${\text{μ}}_{\text{i}}^0$ represents the corresponding chemical potential. For the equilibrium between surface film and vesicles, ${\text{μ}}_{\text{i}}$ is identical in each phase and no separate notation is necessary to indicate whether the chemical potential is associated with either the surface or the vesicle dispersion phase (see Eq. 6, above).

For a monolayer of the mixture of egg yolk lipids (EYL) and cholesterol one has

$${\text{π}}^{\text{mix}}={\text{Γ}}_{\text{CH}}{\text{μ}}_{\text{CH}}+\sum {\text{Γ}}_{\text{i}}{\text{μ}}_{\text{i}}\text{i}=1,2,3,\dots \dots \dots ..\text{C}$$ (12)

where ${\text{Γ}}_{\text{CH}}$ is the concentration of cholesterol in the monolayer and ${\text{Γ}}_{\text{i}}$ is the concentration of the i^th phospholipid component in the cholesterol mixture. We have assumed that the concentrations of cholesterol and lipid components are constants within the films, as reflected by the coefficients ${\text{Γ}}_{\text{i}}^0$, ${\text{Γ}}_{\text{CH}}$ and ${\text{Γ}}_{\text{i}}$ in Eqs. (11) and (12). These equations thus can be used to obtain $\text{Δπ}=\left({\text{π}}^{\text{mix}}-{\text{π}}^0\right)$, the increase in surface pressure at ${\text{T}}^{\ast }$ when cholesterol is present in the monolayers and bilayers.

The total concentration of material in the monolayer is ${\text{Γ}}_{\text{T}}\left(\text{moles}/{\text{cm}}^2\right)={\text{Γ}}_{\text{CH}}+\sum {\text{Γ}}_{\text{i}}\approx \sum {\text{Γ}}_{\text{i}}^0$. An estimate for $\text{Δπ}$ is obtained by assuming that the area/molecule for cholesterol is 4 nm² and an average value for phospholipids is 6.5 nm². We thus find ${\text{Γ}}_{\text{T}}/\sum {\text{Γ}}_{\text{i}}^0=1.04$. Because $\text{μ}={\text{RT}}^{\ast }$ ln a, where ${\text{a}}_{\text{CH}}$ and ${\text{a}}_{\text{i}}$ are thermodynamic activities, and $\text{Γ}/{\text{Γ}}_{\text{T}}=\text{x}$, where ${\text{x}}_{\text{CH}}$ and ${\text{x}}_{\text{i}}$ are mole fractions, we find from Eq. (12) that

$$\begin{array}{l}\text{Δπ}={\text{RT}}^{\ast }{\text{Γ}}_{\text{T}}\left[{\text{x}}_{\text{CH}}\text{ln}{\text{a}}_{\text{CH})}+\sum {\text{x}}_{\text{i}}\text{ln}{\text{a}}_{\text{i}}-\sum {\text{x}}_{\text{i}}^0\text{ln}{\text{a}}^0\right].\end{array}$$ (13)

Upon introducing activity coefficients $\text{γ}=\text{a}/\text{x}$ and combining all terms containing ln $\text{γ}$, or ln x, we find

$$\begin{gathered} \text{Δπ}/{\text{Γ}}_{\text{T}}={\text{RT}}^{\ast }\left[{\text{x}}_{\text{CH}}\text{ln}{\text{γ}}_{\text{CH}}+\sum {\text{x}}_{\text{i}}\text{ln}{\text{γ}}_{\text{i}}-\sum {\text{x}}_{\text{i}}^0\text{ln}{\text{γ}}_{\text{i}}^0\right)] \\ +{\text{RT}}^{\ast }\left[{\text{x}}_{\text{CH}}\text{ln}{\text{x}}_{\text{CH}}+\sum {\text{x}}_{\text{i}}\text{ln}{\text{x}}_{\text{i}}-\sum {\text{x}}_{\text{i}}^0\text{ln}{\text{x}}_{\text{i}}^0\right] \end{gathered}$$ (14)

On the rhs of Eq. (14), the expression in the first bracket (that containing terms ${\text{RT}}^{\ast }\text{x}\text{ln}\text{γ}$) is the heat of mixing ${\text{ΔH}}_{\text{M}}$, and the second bracket (containing terms $\text{Rx}\text{ln}\text{x}$) is ${\text{ΔS}}_{\text{M}}$. Thus, the free energy, ${\text{ΔG}}_{\text{M}}$, of mixing cholesterol with ULVs of EYL becomes

$$\text{Δπ}/{\text{Γ}}_{\text{T}}={\text{ΔG}}_{\text{M}}={\text{ΔH}}_{\text{M}}-\text{T}\ast {\text{ΔS}}_{\text{M}}.$$ (15)

Finally, since we can calculate ${\text{ΔG}}_{\text{M}}$ from $\text{Δπ}$, only ${\text{ΔS}}_{\text{M}}$ needs to be evaluated to complete the thermodynamics of mixing cholesterol with monolayers and vesicles. While 36 phospholipids have been identified in chicken egg yolk [42], the mole fractions necessary to calculate ${\text{ΔS}}_{\text{M}}$ have not been established. However, we can estimate the maximum value of ${\text{ΔS}}_{\text{M}}$ by assuming that all phospholipid concentrations are equal. Using ${\text{x}}_{\text{CH}}=0.1$ and ${\text{x}}_{\text{i}}=0.9{\text{x}}_{\text{i}}^0$, from Eq. (14) we find that ${\text{T}}^{\ast }{\text{ΔS}}_{\text{M}}$ is negligible, being only 25 cal/mole, so ${\text{ΔG}}_{\text{M}}\approx {\text{ΔH}}_{\text{M}}$. From Fig. 8, at ${\text{T}}^{\ast }$ we find $\text{Δπ}=2\text{dyne}/\text{cm}$, ${\text{Γ}}_{\text{T}}\approx 2\times {10}^{-10}\text{mol}/{\text{cm}}^2$, and ${\text{ΔH}}_{\text{M}}\approx 160\text{cal}/\text{mol}$.

4.2. Similar invariance of ${\text{T}}^{\ast }$ when integral protein is present.

In Fig. 9 we show that the presence of about 1 wt% integral protein in a monolayer surface film of rat nerve lipids results in an increase in π over that in a pure lipid film. Significantly, though, no change in ${\text{T}}^{\ast }$ is observed. (${\text{T}}^{\ast }$ is identified from the maximum in the equilibrium surface pressure when the temperature is varied.) The 1.0 wt% integral proteins employed in these measurements (Fig. 9) were the fraction that remained in these neural samples after a multi-step protocol involving various solvents, and the purified lipids then were obtained by column chromatography [27].

Figure 9.

Equilibrium surface pressure vs. temperature relations for lipid extracts containing about 1wt.% protein, obtained from rat forebrain ●, compared with data from protein-free lipid extracts ○. Arrow indicates ${\text{T}}_{\text{cell}}^{\ast }\approx {37}^{\circ }\text{C}$, the gestation and core body temperature of the animal. (Figure from [27], modified and redrawn).

A much larger amount of integral protein normally is found in plasma membranes, yet the value of ${\text{T}}^{\ast }$ still is unaffected; for example, the membrane area occupied by integral proteins in RBC membranes is estimated to be 23% [43] but ${\text{T}}^{\ast }$ is found to be ${\text{T}}_{\text{cell}}^{\ast }$, the physiological temperature (Table 1). Similarly, a literature search of the properties of membranes that contain ion channels indicates that values of $\left\{{\text{T}}^{\ast }\right\}$ are close to those predicted by the gestation temperatures, {${\text{T}}_{\text{cell}}^{\ast }$}, of the animals from which they were derived (unpublished).

That cholesterol and cell-specific integral proteins both have no effect on ${\text{T}}^{\ast }$ suggests that other non-bilayer forming miscible material will behave similarly. Moreover, since integral proteins contain hydrophobic residues in the regions that span the bilayer, we expect that the proteins act as components of a regular solution, with ideal ${\text{ΔS}}_{\text{M}}$ and small positive ${\text{ΔH}}_{\text{M}}$. This is a reasonable assumption, considering that the protein domains that span the bilayer basically are linear hydrophobic chains that align with the oriented aliphatic chains of the bilayer. It has been shown that solutions of linear hydrocarbons with disparate chain lengths, such as of hexane and the 32-carbon n-dotriacontane, form ideal mixtures [44].

But this cannot explain the large increase in monolayer surface pressure noted in Fig. 9 due to the presence of integral protein--of an order of magnitude larger than that of cholesterol--especially since the weight fraction of protein in our studies was about one-fifth the weight fraction of cholesterol. However, we stress that the data in Figs. 8 and 9 were obtained from a surface monolayer, so protein segments that normally would be contained within the bilayer at ${\text{T}}^{\ast }$ might be exposed to the adjacent aqueous phase. Alternatively, the protein might be associated with hydrophobic lipid near the air-water interface. Such uncertainty complicates the physical interpretation of the data for lipid films containing integral proteins. Hydrophobic amino acids in water have positive free energies of mixing [45], due in part to a decrease in entropy. Thus, depending on the number of hydrophobic amino acids forced into the aqueous phase, the surface pressure of the lipid-protein film could be increased substantially. Although theoretical studies predict that molecular crowding can affect membrane structure and integral protein activity [46,47], we again stress that the values of ${\text{T}}^{\ast }$ seem to be unaffected by physiological amounts of cholesterol.

5. Calculating ${\text{T}}^{\ast }$ for mixtures of phospholipids from the internal energy of the components: A model for cellular adjustment of lipid composition in response to changes in ambient temperature.

We have shown in Sec. 3 that ${\text{T}}^{\ast }$ can vary with phospholipid composition. The following illustrative model shows how one can estimate changes in ${\text{T}}^{\ast }$ as a function of changes in phospholipid composition. The derivation of predicted values of ${\text{T}}^{\ast }$, which we have found to be close to experimental values [20], is based on unique properties of bilayer structure when $\text{T}\approx {\text{T}}^{\ast }$. For a vesicle containing a single lipid component, the amount of stored heat, q, can be determined from the relation $\text{q}=\text{m}\cdot \text{c}\cdot \left({\text{T}}^{\ast }-{\text{T}}_{\text{ref}}\right)$, where ${\text{T}}_{\text{ref}}$ is the temperature of a convenient reference lipid state in water, m is the mass of lipid in the vesicle (g/cm²), c the specific heat (cal/g-deg) and ${\text{T}}^{\ast }$ is the temperature at which ULVs form. The heat required to raise the temperature of the lipid to ${\text{T}}^{\ast }$, including latent heat of a gel-liquid transition, constitutes q for the lipid in the ULV. A vesicle formed from a two-component lipid mixture can be approximated as follows. Consider, for example, a vesicle composed of DMPC and DOPC which will have stored heat equal to ${\text{q}}_1+{\text{q}}_2={\text{q}}_{\text{final}}=\left({\text{m}}_1+{\text{m}}_2\right)\cdot \text{c}\cdot \left({\text{T}}_{\text{final}}^{\ast }-{\text{T}}_{\text{ref}}\right)$. (To simplify the calculation we assume that the specific heats of the phospholipids are equal and constant, that the latent heats of transition at ${\text{T}}^{\ast }$ are unchanged when lipid mixtures are formed, and that the mass fractions of the lipids are close to their mole fractions.) Thus, after mixing the lipids we find

$${\text{T}}_{\text{final}}=\left({\text{m}}_1\cdot {\text{T}}_1+{\text{m}}_2\cdot {\text{T}}_2\right)/\left({\text{m}}_1+{\text{m}}_2\right)\approx {\text{x}}_1\cdot \text{T}{\ast }_1+{\text{x}}_2\cdot {\text{T}}_2$$ (16)

where ${\text{x}}_1$ and ${\text{x}}_2$ are the mole fractions of the lipids.

How do values calculated by Eq. 16 and similar relationships compare with experimental observations reported in [20]? For an equimolar mixture of DOPC $\left({\text{T}}^{\ast }=7^{\circ }\text{C}\right)$ and DMPC $\left({\text{T}}^{\ast }={29}^{\circ }\text{C}\right)$ the calculated ${\text{T}}_{\text{final}}^{\ast }$ is 18°C, and the measured value is 14°C; for an equimolar mixture of DMPC and DPPC $\left({\text{T}}^{\ast }={44}^{\circ }\text{C}\right)$ the calculated ${\text{T}}_{\text{final}}^{\ast }$ is 36.5°C, in close agreement with the measured value of 35°C; for an equimolar mixture of DOPC, DMPC, and DPPC the calculated ${\text{T}}_{\text{final}}^{\ast }$ is 27°C compared to the measured value of 30°C. The slight difference between the calculated and measured values is reasonable, given the simplifying assumptions that were made. When lipids form ULVs, the stored heat of each lipid species in the critical state of a mixture is redistributed by molecular collisions to values commensurate with the equilibrium ${\text{T}}_{\text{final}}^{\ast }$. Integral proteins and cholesterol also contribute their heat of mixing to the system but the values are too small to alter ${\text{T}}^{\ast }$. (Values of ${\text{q}}_{\text{final}}$ are of the order of 10 kcal/mole for the lipids while ${\text{ΔH}}_{\text{M}}$ for cholesterol is of the order of 0.1 kcal/mole.) Since in Fig.9 it appears that the integral protein remaining in the rat brain sample does not significantly alter ${\text{T}}^{\ast }$, we infer that it also has a small heat of mixing with bilayer lipids at this temperature.

When single-cell poikilotherms like bacteria are located in an environment where the ambient temperature changes, a condition of stress arises that stimulates metabolism to modify membrane lipid composition so that the resulting ${\text{T}}_{\text{cell}}^{\ast }$ is the new growth temperature. The manner by which phospholipid composition adjusts to the new value of the ambient temperature depends on whether the temperature is increased, in which case phospholipids with saturated fatty acids (higher q bilayers) are added to the membranes, or whether the temperature is reduced, in which case phospholipids with unsaturated fatty acids (lower q bilayers) are added. The same concept applies to the thermal adaptation of archaea, where ${\text{T}}_{\text{cell}}^{\ast }$ can be at much higher temperatures than for bacteria and lipid chemistry is significantly different [48,49]. By maintaining their lipid bilayers in the critical state, the cells experience an essentially constant physical environment for membrane mediated biological activity, even if cell temperature varies over a relatively wide range. Although the phenomenon is readily understandable, the cell biology that leads to these lipid changes still is obscure.

6. Cell membrane assembly and stability at the critical temperature.

6.1. Changes in cell bilayers if T changes.

In cell membranes the same equilibrium constraints and potential structural instabilities exist as in unilamellar vesicles formed in dispersions. If the ambient temperature changes, the acyl chains of unicellular poikilotherms such as E. coli [50] and B. subtilis bacteria [51] and various eukaryotes -- e.g., the amoeba, D. discoideum [52] and the yeast, S. cerevisae [53] -- respond by synthesizing new lipid constituents [54]. At least for those organisms that have been tested, it has been found that these changes cause unilamellar membranes to form at new critical temperatures. The new lipid compositions are defined by the requirements of bilayer assembly at the growth temperature, ${\text{T}}_{\text{cell}}^{\ast }$, as seen with E. coli in Table 1. The normal temperature range for growth of a poikilotherm is relatively broad but has an upper limit beyond which lipid synthesis required for assembly is inhibited.

In contrast to poikilotherms, the growth temperature for mammalian cells is narrowly restricted. To see how mammalian cells respond to variations in ambient temperature, the effect of heating and cooling on the rate of erythrocyte hemolysis in fresh whole human blood, where lipid synthesis is absent, was studied [55]. At incubation temperatures of 37°C, 20°C and 4°C, no hemolysis was observed over a period of 30 hrs, and it is likely that cell viability was maintained by a supercooling behavior of the erythrocyte membranes. When the blood was heated above 37°C hemolysis occurred at a rate that increased as temperature was raised: for example, at 40°C about 1% of the original hemoglobin was found in solution after 30 hrs; at 45°C about 4% of the hemoglobin was released. The activation energy for hemolysis is ${\text{E}}^{\ast }=29\text{kcal}/\text{mol}$ at these temperatures [55].

6.2. Behavior of purified DMPC and DMPG.

Data for the lateral diffusion of NPD-PC in a multi-lamellar film of DMPC (see Fig. 6) provide an activation energy equaling ${\text{E}}^{\ast }=30\text{kcal}/\text{mol}$ when the temperature is varied over a range several degrees below ${\text{T}}^{\ast }$ (see Fig. 10). Not only is this value similar to that found for Hb leakage through RBC membranes at elevated temperatures, but it is close to the value found for the transition of extended lipid structures to unilamellar vesicles in a dispersion of a related material, DMPG.Na, where ${\text{T}}^{\ast }={31.5}^{\circ }\text{C}$ [17,56]. In this instance, when temperatures are below this value of ${\text{T}}^{\ast }$, a jelly-like, optically clear dispersion is observed that transforms to vesicles of ever-greater thickness as T is increasingly heated beyond ${\text{T}}^{\ast }={31.5}^{\circ }\text{C}$.

Figure 10.

Plot of ln D vs1000/T (degrees Kelvin) for evaluating the activation energy ${\text{E}}^{\ast }$ for diffusion of fluorescent probe NBD-PE in DMPC multilayers over the range $\text{T}={26}^{\circ }\text{C}$ to 28.6°C, from data shown in Fig. 6. One finds ${\text{E}}^{\ast }=30\text{kcal}/\text{mole}$ for the value of the activation energy. (Ordinate values represent a relative scale.)

Attempts to unravel the morphology of the DMPG·Na phase when T is below ${\text{T}}^{\ast }$ indicate a complex matrix with various interpretations that depend on the concentration and methodology used [57–60]. Despite the complexity of the physical state at $\text{T}<{\text{T}}^{\ast }$, these studies all report a transformation to vesicles when T is close to ${\text{T}}^{\ast }$. This transformation was first documented by suspending small polystyrene beads in the aqueous regions of the samples and following their motions by dynamic light scattering at different temperatures [17]. Since ${\text{E}}^{\ast }$ associated with the dissolution of the matrix also is 30 kcal/mol (Fig. 11) when unilamellar vesicles form in this material, these DMPC and DMPG.Na studies indicate that acyl chain energetics is more important in these samples than the relatively small contributions of phospholipid head groups. Moreover, their similarity to the value of ${\text{E}}^{\ast }$ found for RBCs at temperatures above ${\text{T}}_{\text{cell}}^{\ast }$ indicate that these values of ${\text{E}}^{\ast }$, and others of similar magnitude, are emblematic of energetics of phospholipid bilayer transformations that are widespread in biology. The expression relating D to E* is assumed to be of the form $\text{D}\sim \text{A}\text{exp}\left(-{\text{E}}^{\ast }/\text{RT}\right)$, where the variation of A with temperature is negligible and appears on a logarithmic scale as an irrelevant constant.

Figure 11.

Plot of ln D vs 1000/T (degrees Kelvin), over the range $\text{T}={29}^{\circ }\text{C}$ to 32°C, for evaluating the activation energy pertaining to the diffusion of polystyrene beads (dia = 1 micron) in aqueous dispersions of DMPG·Na. (The values of $\text{D}={\text{D}}_{\text{eff}}$ here were determined by dynamic light scattering; see Gershfeld et al. [17] for the definition of ${\text{D}}_{\text{eff}.}$). ${\text{T}}^{\ast }$ for these samples is approximately 30.5°C [17]. This plot yields ${\text{E}}^{\ast }=30\text{kcal}/\text{mole}$.

How do these concepts comport with properties of biological membranes? In general, supercooling at temperatures below ${\text{T}}_{\text{cell}}^{\ast }$, and a slow rate of cell damage at elevated temperatures greater than ${\text{T}}_{\text{cell}}^{\ast }$, allow for a robust physiological accommodation to temperature in homeotherms. The unilamellar bilayers that form spontaneously in vitro at ${\text{T}}^{\ast }$ from simple phospholipids, and from whole lipid extracts of cell membranes, to first order are spatially homogeneous. However, interactions with immobilized proteins, e.g., those tied to the cytoskeleton, may cause local heterogeneities in the lipid compositions of the cell bilayers. When ambient temperatures are not at ${\text{T}}^{\ast }$, cholesterol and integral proteins may be subjected to solution forces that lead to changes in their miscibility, as well as changes in protein structure.

6.3. Behavior of cells when $\text{T}\ne {\text{T}}^{\ast }$.

An example of membrane instability, for $\text{T}>{\text{T}}_{\text{cell}}^{\ast }$, has been reported for intact human red blood cells at temperatures elevated to 40 °C by vigorous exercise, whence lipid vesicles are shed, accompanied by morphological cellular changes [61]. Similarly, changes in membrane structure have been noted, when $\text{T}<{\text{T}}_{\text{cell}}^{\ast }$, in studies of giant plasma-derived membrane vesicles (GMPVs), often referred to as “blebs,” formed from the plasma membranes of cultured mammalian cells [62]. Such vesicles are optically homogeneous at ${\text{T}}_{\text{cell}}^{\ast }$ = 37°C, but upon cooling to 20°C visible phase-separation occurs. Consistent with this observation, optical studies of PtK2 cells, using STED (stimulated emission depletion microscopy) combined with FCS (fluorescent correlation spectroscopy), indicated that in the absence of cholesterol no stable aggregates or differing phases having sizes greater than the resolution limit of 20nm were found over the temperature range $\text{T}={27}^{\circ }\text{C}$ to close to 37°C, the latter being ${\text{T}}_{\text{cell}}^{\ast }$ [63,64]. The fluorescent analogs of cellular lipids examined in the latter studies exhibit modest degrees of fluctuating interactions, with relaxation times of several milliseconds for cholesterol-mediated reactions involving sphingolipids and yet shorter interaction times when other lipids are the binding partners.

7. Results and Discussion.

7.1. Results.

Among the principal results of the work featured in this paper are the following: a) Under equilibrium conditions, unilamellar bilayer vesicles (ULVs) form spontaneously from a lipid suspension only at a unique temperature, ${\text{T}}^{\ast }$, that depends on the lipid composition of the bilayers; b) ${\text{T}}^{\ast }$ has the properties of a critical temperature; c) Total membrane lipids extracted from a population of biological cells form ULVs in aqueous suspensions at ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$, where ${\text{T}}_{\text{cell}}^{\ast }$ is, respectively, the gestation or growth temperature of the multicellular animal or unicellular organism from which the cells were obtained, and d) As shown in the analysis presented in Sec. 3.1, membrane assembly at any particular ${\text{T}}^{\ast }$ can occur from many different phospholipid mixtures. These results all are substantiated by thermodynamic analysis.

7.2. Discussion.

The central theme of this paper is that there is a subtle, but distinct, change in state that occurs in a lipid bilayer membrane at a critical temperature, ${\text{T}}^{\ast }$, that depends on the phospholipid composition of the membrane. The importance of the critical bilayer state for living systems is clearly seen in simple unicellular organisms when rapid alterations of lipid composition occur in response to changes in ambient temperature so their membranes can conform to new critical state requirements. For homeotherms, though, changes in ambient temperature do not typically result in rapid metabolic responses of lipid accommodation; rather, supercooling generally maintains bilayer structure if temperatures are lowered below ${\text{T}}^{\ast }$, and relatively slow degradation of such structure occurs if temperatures are raised when $\text{T}>{\text{T}}^{\ast }$. These changes ultimately may result in cell membrane dysfunction or degradation, as is readily seen in red blood cells.

One concept of bilayer structure that emerges from the equilibrium experiments discussed in this paper is that the critical state at ${\text{T}}^{\ast }$ is characterized by transient lipid-lipid interactions, with molecular clusters that fluctuate in size and composition in an essentially homogeneous phase. The critical state persists when cholesterol and/or integral proteins are present, thereby allowing these essential constituents access to membranes having similar properties at ${\text{T}}_{\text{cell}}^{\ast }$, despite their having differing compositions. Our investigations thus yield insight into why, under normal circumstances, when $\text{T}\approx {\text{T}}_{\text{cell}}^{\ast }$, the phospholipid membranes of biological cells invariably contain single bilayer cores rather than lipid multilayers. Moreover, when the temperature of the cell is at ${\text{T}}_{\text{cell}}^{\ast }$, the unilamellar bilayer is the only intrinsically stable cellular lipid membrane structure.

Of course, the creation of cell membranes generally depends, in complicated ways, on cell metabolism and involves lipid intermediates and multiple proteins. This is well documented for bacteria [65] as well for multicellular organisms [66]. Moreover, membrane structure often shows features other than those captured in our analysis of the simplified lipid entities on which we have focused here: for example, the gram-negative bacterium S. typhimurium contains a two-membrane cell envelope in which the outer leaflet of the outer bilayer is composed mainly of glycolipids rather than phospholipids [67]. Additionally, cell membranes contain proteins that may form non-randomly distributed complexes, perhaps influenced by interactions with cytoskeletal elements as well as uneven effects of cellular mechanical stress. Since the time when early proto-membranes arose millions of years ago, the physical rules discussed in this paper probably modulated membrane formation while the genetic processes related to modern membrane biogenesis arose. By invoking these rules as adjuncts to thermodynamic analysis we have been able to shed light on several important biological relationships. The fact that ${\text{T}}^{\ast }$ for membrane lipid mixtures is the same as ${\text{T}}_{\text{cell}}^{\ast }$ for the cells from which the lipids are derived indicates that the same equilibrium structures and critical properties exist in cell membranes as in corresponding vesicles formed spontaneously from aqueous dispersions.

The properties of the ULVs are independent of the path followed for their formation. Related unilamellar films will arise spontaneously when the temperature, pressure and lipid composition are consonant with thermodynamic rules. When the total extracted lipids of a cell membrane form ULVs in aqueous suspensions at ${\text{T}}^{\ast }={\text{T}}_{\text{cell}}^{\ast }$, it can be assumed that the lipids in corresponding cell membranes are in a critical state (Table 1 and Fig. 5). For plasma membranes, a considerable number of phospholipid transfer proteins (PLTP) have been catalogued that bring specific phospholipids, synthesized in the endoplasmic reticulum, to the membranes [63]. It is immaterial whether delivery of phospholipids to the plasma membrane site is en masse or by discrete units, as long as the mole fractions of lipids bound to phospholipid transfer proteins equal the mole fractions in the membrane, perhaps corrected for differing PLTP and membrane partition coefficients of various components, i.e., ${\text{x}}_{\text{j}}\left(\text{PLTP}\right)={\text{x}}_{\text{j}}(\text{membrane})$, as appears in Eq. 9. An equivalent relation has been verified for phospholipids of differing water solubility that form ULVs at a characteristic ${\text{T}}^{\ast }$ [56].

7.3. Significance and further study

Membrane bilayer structure is conserved throughout the totality of cellular architecture. Consequently, we believe the spontaneous assembly of unilamellar bilayers is a fundamental phenomenon worthy of continued investigation. Mechanisms have evolved to bring about the biogenesis of myriad complex membranes that carry out specialized functions, yet all these membranes have, as their pivotal elements, lipid bilayers. Not only should the study of the essential process of bilayer formation, and the consequences thereof, provide deeper understanding of normal biological function, it also might be useful in uncovering the etiology of various diseases that until now are lacking conclusive treatments. For example, puzzling changes in plasmalogen concentrations have been noted in the vicinity of Alzheimers Disease (AD) lesions, there being a decrease in ${\text{T}}^{\ast }$ in those regions [68]. Considering the widespread disability that AD and other brain diseases cause in aging human populations, it might be relevant to examine the extent to which similar events arise in tissues of patients suffering from other neurodegenerative disorders

In a related study that is based in part on an extensive literature search, we discovered that electrically excitable neural tissues often show decreases in the magnitudes of action potentials as the temperature is raised above ${\text{T}}^{\ast }$ of the cells being studied. Moreover, quantitative analysis indicates that activation energies associated with such changes have essentially identical values (Gershfeld and Nossal, unpublished). It would be of interest to find out whether other membrane-linked processes, such as the response to growth factors, are similarly affected by cell temperature. Studies also should be undertaken to determine to what extent temperature-induced membrane ion leak is the cause of the observed response rather than changes in the structure of physiologically relevant embedded proteins.

Novel instrumentation and protocols were used in order to acquire the data discussed in various Sections of this paper. One might usefully adopt some of these techniques, heretofore used in the studies of pure lipid samples, to investigate complicated membranes. For example, one could employ the diffusion of fluorescent probes (Sec. 3.4) to see how the presence, in the bilayer, of large amounts of cholesterol or different types of integral proteins, affect lipid microstructure. While the protocol mentioned in Sec. 4 indicated only minimal perturbation of ${\text{T}}^{\ast }$ when integral proteins are present, it utilized endogenous proteins that were obtained from the tissues that provided the lipids used for the measurements. Yet one might expect that these proteins are particularly compatible with the bilayers in which they normally are e mbedded. More generally, how do integral proteins at higher concentrations and exogenous proteins affect ${\text{T}}^{\ast }$?

Can information gleaned from such studies facilitate the design of complex lipid nanoparticle vesicles (LNPs) employed for the uptake and delivery of mRNAs, particularly since the membranes in these LNPs contain cationic and other unusual lipids? Likewise, how does an extended polymer matrix on the interior surface of the bilayer, e.g., of polyethylene glycol, affect ${\text{T}}^{\ast }$? In the Introduction (Sec.1), we listed other problems involved in creating LNPs to deliver relatively large mRNAs used in vaccines aimed at SARS-CoV-2 and other coronavirus diseases. Although LNPs generally are not equilibrium particles, the fusion of their bilayer components with intracellular bilayer membranes nonetheless may be facilitated if both membrane populations have the same ${\text{T}}^{\ast }$. Fewer, but similar obstacles need to be confronted when liposomes are employed to package relatively short, synthetic oligonucleotides and siRNA molecules used, e.g., for cancer therapy: Both secondary lipid vesicles and LNPs have to be strong enough to contain their cargo while circulating in the body, must have relatively long shelf lives as they await their use, and be stable against host immunity until they deliver their cargo to specific cellular targets, etc.; moreover, as previously mentioned, the membranes of LNPs employed as carriers for mRNA contain unnatural [73] charged lipids that change their ionization when inside cells. They also include a variety of neutrally charged “helper lipids” as well as lipids conjugated to polyethylene-glycol chains. Information enabling these components to be rationally chosen might facilitate work in this field.

Unfortunately, although broad categories of necessary LNP constituents have been identified, there often is little correlation between delivery efficiencies of in vitro and in vivo LNP vaccine constructs [69,70]. The design of productive LNPs and advanced liposomes still largely is empirical. However, the recognition that ${\text{T}}^{\ast }\approx {37}^{\circ }\text{C}$ for the human host may mean that monolayer and bilayer components of the exogenous membranes should be designed to have a similar value of ${\text{T}}^{\ast }$. Exogenous membrane then could be absorbed by existing cell membranes without changing ${\text{T}}_{\text{cell}}^{\ast }$; moreover, because at ${\text{T}}^{\ast }$ bilayer membranes demonstrate strong molecular fluctuations and other characteristics of phase transitions, the fusion of the lipid particles with endosomes may be enhanced (see comments about membrane behavior in Cheng and Lee [70] and Chaudhury et al. [7]). Since a modest degree of supercooling does not seem to affect bilayer structure and stability, perhaps the ${\text{T}}^{\ast }$ of the lipid bilayer components of LNPs and complex second generation liposomes should be designed to be slightly lower than ${\text{T}}_{\text{cell}}^{\ast }$. Whether and how these and related observations are technologically relevant should be further investigated. Not only may the properties of the bilayer be of importance in designing useful LNPs, but it recently has become evident that the properties of the core lipid bilayer also need to be better understood when designing liposomal carriers of anti-cancer drugs [71].

Finally, although in recent decades emphasis on genetic analysis and associated behavior of proteins has dominated biomedical and biophysical research, one should not overlook the importance of membranes on cell function and human health. For example, recent research has demonstrated that changes in the global temperature can lead to disruptions in food supplies due to the unavailability of various essential lipids [72]. In particular, it has been found that elevated ocean temperatures are likely to lead to decreases in the unsaturated fatty acids produced in phytoplankton, thereby affecting diets based on fish and other denizens of the sea because animals cannot make their own unsaturated lipids [73]. Even relatively small changes in ambient temperature can have profound environmental effects. Biophysical research and the increased knowledge that it produces − such as that described in this paper − likely will be of increasing relevance and importance.

Methods.

A. Cryo-TEM of membrane lipids [74]

Suspensions (0.01% w/w) of DMPC (Avanti) were prepared by vortex mixing dry lipid in distilled water at room temperature. Portions of the suspension were equilibrated at $\text{T}={26}^{\circ }\text{C}$ and ${\text{T}}^{\ast }={29}^{\circ }\text{C}$ (± 0.1°C). Additionally, a sample was incubated at 38°C but the lipid and water were heated separately at 38°C prior to mixing to avoid heating the sample continuously from room temperature through ${\text{T}}^{\ast }$, during which ULV’s might form. Suspensions were equilibrated for 48 hrs. at each temperature prior to use. A similar procedure was used to obtain relevant samples of E. coli lipids. For example, consider the case that the bacteria were grown at $\text{T}={32}^{\circ }\text{C}$: whole cell lipids were extracted by the method of Rose and Oklander [75] and a portion of the solution was evaporated under nitrogen [31], after which the dried lipids were suspended in water at a concentration of 0.01% (w/w) and vortex mixed at room temperature to produce a slightly turbid suspension. Portions of the suspension were incubated at 22°C and ${\text{T}}^{\ast }={32}^{\circ }\text{C}$. For incubation at 38°C, though, as done for DMPC, the lipids and water were heated separately at this temperature prior to mixing. Samples of the E. coli suspensions were equilibrated for 48 hrs at each temperature. Each step in forming the E. coli suspensions was performed under an atmosphere of nitrogen. To both the DMPC and E. coli suspensions, sodium azide (10^-4M) was added to inhibit bacterial growth.

Five microliters of each of the equilibrated suspensions were pipetted onto separate lacey carbon grids (EM Sciences, Fort Washington, PA) and left to adsorb for one minute. The grids were blotted with filter paper for 5 seconds, immediately plunged into liquid ethane at 110°K using a plunge-freezing device (Leica Reichert KF80), and then stored in liquid nitrogen until transferred to an electron microscope (Phillips CM120) via a cryo-transfer specimen holder (Gatan, Warrendale, PA). The holder maintained the sample grid at 104°K. The microscope was operated at an acceleration voltage of 120KV. Regions of vitreous ice on the grid were recorded, either on film in the low dose mode, or digitally with an energy filter (Gatan, Warrendale, PA). The micrographs were recorded at 5μm, under-focused to maximize the contrast of the vesicle walls.

The widths of vesicle walls were measured under 4-fold magnification using a graticule of 100 divisions /cm. The measurements were calibrated by using micrographs of a catalase crystal and a sample of tobacco mosaic virus (TMV), obtained under the same conditions that were used to obtain the vesicle micrographs. The catalase standard has lattice plane spacings of 87 Å; from 10 Cryo-TEM measurements of the sample a value of 80 ±10Å was obtained for the lattice spacings and the width of TMV was found to be the accepted value of 180 Å, independent of the degree of under-focusing (0–15 μm). This method for obtaining bilayer thickness was tested using published photomicrographs of ULV’s [76–78] in which ULV single bilayer thicknesses varied from 39–51 Å, in general agreement with the bilayer thickness that we obtained. Three grids were prepared for each temperature; all ULVs that were found on these grids (in approximately 15–20 fields) were measured. Four measurements of each vesicle were averaged to obtain the wall thickness.

B. Preparation of cholesterol-free egg yolk phospholipid (EYL) dispersions.

Two ml of the yolk from a chicken egg were dissolved in 10 ml of a 2-propanol-chloroform (2:1 v:v) solution and allowed to stand for 30 min. The mixture was vortexed and centrifuged, resulting in a clear solution with an extraneous pellet on the surface. The clear solution was evaporated under nitrogen and redissolved in chloroform. Thin layer chromatography, using a solvent of a mixture of choloroform, methanol and water in the ratio of 65:25:4, indicated the presence of phospholipids and cholesterol. The cholesterol in this solution was removed by column chromatography, using a Unisil column. The column was washed with chloroform, after which the chloroform solution of the egg yolk lipids containing unwanted cholesterol was placed on the top of the column. Three consecutive solvent washes then were used to remove the cholesterol: a) an initial wash of 5 ml chloroform, collected and tested by thin layer chromatography (tlc) to show that cholesterol, but not phospholipid, had been removed, b) a second wash of 5 ml methanol, tested by tlc to show that the wash contained phospholipids and perhaps a trace of cholesterol, and c) a final wash of 40 ml methanol, tested by tlc to establish that the wash contained only phospholipids. Surface pressure measurements were made, using the lipids in solution (c) and in the original extracted clear solution.

HIGHLIGHTS.

• Lipid films at air-water interfaces indicate status of vesicles in lipid suspension

• Bilayer phase changes occur at critical temperatures {${\text{T}}^{\ast }$} set by lipid composition

• Critical exponents for lipid films are similar to those of fluid interfaces

• ${\text{T}}^{\ast }$ of cell lipid bilayers equals the gestation/growth temperature of the cell source

• Experimental data are shown to agree with thermodynamic theory