Effect of cholesterol on structural and mechanical properties of membranes depends on lipid chain saturation

The effects of cholesterol on membrane bending modulus $K_{\text{C}}$, membrane thickness $D_{\text{HH}}$, the partial and apparent areas of cholesterol and lipid, and the order parameter $S_{\text{xray}}$ are shown to depend upon the number of saturated hydrocarbon chains in the lipid molecules. Particularly striking is the result that up to 40% cholesterol does not increase the bending modulus $K_{\text{C}}$ of membranes composed of phosphatidylcholine lipids with two cis monounsaturated chains, although it does have the expected stiffening effect on membranes composed of lipids with two saturated chains. The $B$ fluctuational modulus in the smectic liquid crystal theory is obtained and used to discuss the interactions between bilayers. Our $K_{\text{C}}$ results motivate a theory of elastic moduli in the high cholesterol limit and they challenge the relevance of universality concepts. Although most of our results were obtained at $30°\text{C}$, additional data at other temperatures to allow consideration of a reduced temperature variable do not support universality for the effect of cholesterol on all lipid bilayers. If the concept of universality is to be valid, different numbers of saturated chains must be considered to create different universality classes. The above experimental results were obtained from analysis of x-ray scattering in the low angle and wide angle regions.

Figure 1

H2 model fits (solid lines) to experimental form factors measured at $30°\text{C}$ (open symbols from oriented ORI samples and solid symbols from ULV samples). The lipid/cholesterol mixtures shown below the pure lipids had cholesterol mole fractions $c=0.3$. The data for pure lipids were from previous papers: DMPC [75], DOPC [61], diC22:1PC [16], and SOPC [76]. When the intensity is near zero, the raw data produce Gaussian distributions of apparent amplitudes that include some negative values of $\left|F\left(q_z\right)\right|$ that are shown in the figure; these are included in the H2 fitting to avoid biasing the model to overly large values of $\left|F\left(q_z\right)\right|$.

Figure 2

Total electron density profiles of DOPC with cholesterol mole fractions (a) $c=0$ and (b) $c=0.3$ versus distance $z$ from the center of the bilayer are shown as the thick curves labeled total. The contributions from the individual lipid components and cholesterol in the H2 model are shown only for negative values of $z$ with thinner lines labeled WC (water plus choline), (p) phosphate, (CG) carbonyl plus glycerol, $\left({\text{CH}}_2\right)$ methylene plus methine groups on the hydrocarbon chains, $\left({\text{CH}}_3\right)$ terminal methyl groups, and (Chol) cholesterol.

Figure 3

(a) Bilayer thickness $D_{\text{HH}}$ versus cholesterol mole fraction $c=N_{\text{Chol}}/\left(N_{\text{lipid}}+N_{\text{Chol}}\right)$. The $D_{\text{HH}}$ values for DOPC at $c=0.1$, 0.2, and 0.4 are from [77]. (b) Average travel of the chain methylenes along the bilayer normal $L=D_{\text{C}}/\left(n_{{\text{CH}}_2}+r\right)$.

Figure 4

Apparent area per lipid molecule $A_{\text{Lapp}}$ calculated from LAXS (solid symbols) and WAXS (open symbols) versus cholesterol mole fraction $c$.

Figure 5

Partial molecular area of lipid $A_{\text{Lpar}}$ and cholesterol $A_{\text{Cholapp}}$ versus cholesterol mole fraction $c$ for DMPC and DOPC. The data points $A_{\text{N}}$ obtained from Eq. (2) and the H2 model fit to the x-ray form factors. The solid lines are fits based on Eq. (12) in [39] to area per average molecule in Eq. (2). The dashed lines are the partial molecular areas of lipid obtained from the intercept at $c=0$ of the tangent to the black curve and the dotted lines (also in the inset for DMPC) are the partial molecular areas of cholesterol obtained from the intercept at $c=1$.

Figure 6

Wide angle $d$ spacing versus bilayer thickness $D_{\text{HH}}$.

Figure 7

Symbols show order parameter $S_{\text{xray}}$ from WAXS versus cholesterol mole fraction. The solid curves show the fits to the model: free $\text{cholesterol}+p$ free lipids $\iff$ complex [50]. The dotted lines show the fits to a refined model that also includes perturbation caused by the complex to the free lipid [6, 33].

Figure 8

Bilayer thickness $D_{\text{HH}}$ versus chain order parameter $S_{\text{xray}}$. The solid lines are linear fits for each lipid.

Figure 9

Bending modulus $K_{\text{C}}$ for bilayers of four lipids with cholesterol mole fraction $c$ at $30°\text{C}$.

Figure 10

Log of the bulk compression modulus $B$ versus water spacing $D_W^{\prime }$ between neighboring bilayers for SOPC, fitted with the solid straight line, and SOPC with mole fraction $c=0.3$ cholesterol, fitted with the dashed straight line. The arrows indicate the fully hydrated values of $D_W^{\prime }$.

Figure 11

Bending modulus $K_{\text{C}}$ versus relative temperature $T\text{−}{T}_{\text{M}}$ where the melting temperature $T_{\text{M}}$ for DMPC and DMPC/cholesterol is $24°\text{C}$ and for diC22:1PC and diC22:1PC/cholesterol is $13°\text{C}$. The cholesterol mole fraction was $c=0.3$ for the DMPC/cholesterol mixture and was $c=0.4$ for the diC22:1PC/cholesterol mixture.