Lattice models for photosynthetic membrane stacks
Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack play a key role in this ordering, as has been demonstrated by both empirical and computational methods. The architecture of thylakoid membranes, depending on physiological conditions, also may create circumstances for inter-layer interactions that instead disfavor the high protein densities of ordered arrangements. This dissertation introduces several statistical mechanical models for exploring the interplay between these opposing forces and for characterizing phases that reflect the periodic geometry of stacked thylakoid membrane discs. First, we propose a lattice model that roughly accounts for proteins' attraction within a layer and across the stromal gap, steric repulsion across the lumenal gap, and regulation of protein density by exchange with the stroma lamellae. Mean field analysis and computer simulation reveal a broken-symmetry striped phase disrupted at both high and low extremes of density. We expect that the widely varying light and stress conditions in higher plants explore the space of protein density and interaction strength broadly. The phase transitions we identify should thus lie within or near the range of naturally occurring conditions. Second, we expand upon this lattice description, allowing the thickness of each thylakoid's lumenal gap to fluctuate. This fluctuating-gap model introduces the possibility of mechanical control of photosynthetic function. We monitor how changing gap thickness affects mean protein occupation on both sides of the discs. Via mean field analysis and computer simulation we find even richer phase behavior for this model, featuring transitions that originate in long-ranged protein interactions mediated by lumenal gap fluctuations. These results suggest that compression or expansion of lumenal gaps could lead to sudden and dramatic changes in the population and spatial patterning of photosynthetic proteins. Taken together, the lattice models we have constructed and explored provide a framework for minimalistic modeling of the physics underlying structure and function of photosynthetic membranes.