Ultrastructural modeling of small angle scattering from photosynthetic membranes

The last decade has seen a range of studies using non-invasive neutron and X-ray techniques to probe the ultrastructure of a variety of photosynthetic membrane systems. A common denominator in this work is the lack of an explicitly formulated underlying structural model, ultimately leading to ambiguity in the data interpretation. Here we formulate and implement a full mathematical model of the scattering from a stacked double bilayer membrane system taking instrumental resolution and polydispersity into account. We validate our model by direct simulation of scattering patterns from 3D structural models. Most importantly, we demonstrate that the full scattering curves from three structurally typical cyanobacterial thylakoid membrane systems measured in vivo can all be described within this framework. The model provides realistic estimates of key structural parameters in the thylakoid membrane, in particular the overall stacking distance and how this is divided between membranes, lumen and cytoplasmic liquid. Finally, from fitted scattering length densities it becomes clear that the protein content in the inner lumen has to be lower than in the outer cytoplasmic liquid and we extract the first quantitative measure of the luminal protein content in a living cyanobacteria.