Tilt-Dependent Analysis of Diffuse X-ray Scattering from Oriented Stacks of Fluid Phase Lipid Bilayers

Recent simulations have indicated that the traditional Helfrich-Canham model for topographical fluctuations in fluid phase biomembranes should be enriched to include molecular tilt. Experimental evidence supporting the aforementioned enrichment is reported. The current work is a tilt-dependent analysis of the X-ray scattering from oriented stacks of fluid phase lipid bilayers. By analyzing several X-ray exposures from different DOPC samples, final single membrane mechanical moduli values of Kc = 8.4±0.6×10−13 ergs and Kθ = 90±7 mN/m are determined at 30 ◦C. The tiltdependent Kc-value is ∼20% greater than its tilt-independent analog, and therefore, it compares more favorably with Kc-values reported for some of the other experimental techniques as well as values determined from molecular dynamics simulations. The experimentally determined Kθ-value is between 10 and 20% greater than values reported from molecular dynamics simulations, more consistent than the corresponding Kc-values. As of yet, there is no other experimental technique that has determined the value of Kθ. The determined tilt-dependent and tilt-independent form factors are consistent, but the interpretation of the form factor within the tilt-dependent and -independent models is not identical. First, a tilt-dependent stacked bilayer free energy functional is hypothesized, based on a recent single membrane tilt-dependent free energy. Then, a tilt-dependent stacked bilayer electron density is posited, and a novel form factor / structure factor separation is derived. The height-height correlation function remains the most important statistical quantity for predicting the X-ray scattering from stacked bilayers. The tilt-dependent height-height correlation function is derived as well as an approximate analytic form for long in-plane length scales. Importantly, both the tilt-dependent and tilt-independent analytic approximations logarithmicly diverge for increasing in-plane length scales; both theories predict quasi-long range order of the height-height correlations. The theoretically predicted intensity is modified by several sample concerns including domain sizes and mosaicity and several experimental issues such as X-ray beam coherence, geometric broadening, and absorption of the incident and scattered X-rays. Measured scattering intensity from stacked DOPC bilayers are analyzed using both tilt-dependent and -independent models. The tilt-dependent model is shown to better account for the measurements, supporting the extension of the classic Helfrich-Canham model to include a tilt degree of freedom.