Scaling of lipid membrane rigidity with domain area fraction.

Biological membranes are highly heterogeneous in composition which in turn leads to local variations in the physical properties. Here we quantify how heterogeneity in stiffness determines the effective bending modulus, κeff, of model phase-separated membranes with coexisting soft fluid and rigid gel domains. We find that the temperature- and composition- dependent trends in membrane rigidity collapse onto a single curve, such that κeff directly scales with the area fraction of the rigid gel domains. Using no adjustable parameters, the measurements are found to agree with theoretical predictions for inhomogenous membranes and indicate that κeff is sensitive to the lateral distribution of the rigid phase within the membrane. This key finding confirms that the properties of heterogeneous membranes can be quantitatively predicted if the area fraction and properties of the individual phases are known.