Insights on raft behavior from minimal phenomenological models

Modulated and spiral surface patterns on deformable lipid vesicles

We investigate the behavior of two-dimensional systems that exhibit a transition between homogeneous and spatially inhomogeneous phases, which have spherical topology, and whose mechanical properties depend on the local value of the order parameter. One example of such a system is multicomponent lipid bilayer vesicles, which serve as a model to study cellular membranes. Under certain conditions, such bilayers separate into coexisting liquid-ordered and liquid-disordered regions. When arranged into the shape of small vesicles, this phase coexistence can result in spatial patterns that are more complex than the basic two-domain configuration encountered in typical bulk systems. The difference in bending rigidity between the liquid-ordered and liquid-disordered regions couples the shape of the vesicle to the local composition. We show that this interplay gives rise to a rich phase diagram that includes homogeneous, separated, and axisymmetric modulated phases that are divided by regions of spiral patterns in the surface morphology.

Pollen wall patterns as a model for biological self-assembly

We are still far from being able to predict organisms' shapes purely from their genetic codes. While it is imperative to identify which encoded macromolecules contribute to a phenotype, determining how macromolecules self-assemble independently of the genetic code may be equally crucial for understanding shape development. Pollen grains are typically single-celled microgametophytes that have decorated walls of various shapes and patterns. The accumulation of morphological data and a comprehensive understanding of the wall development makes this system ripe for mathematical and physical modeling. Therefore, pollen walls are an excellent system for identifying both the genetic products and the physical processes that result in a huge diversity of extracellular morphologies. In this piece, I highlight the current understanding of pollen wall biology relevant for quantification studies and enumerate the modellable aspects of pollen wall patterning and specific approaches that one may take to elucidate how pollen grains build their beautifully patterned walls.

Model of a raft in both leaves of an asymmetric lipid bilayer

We present a theory of inhomogeneities in the plasma membrane, or rafts, that can exist in both leaves of the plasma membrane. We note that although neither of the major phospholipid components of the outer leaf, sphingomyelin (SM) nor phosphatidylcholine (PC), evinces a tendency to form phases characterized by nonzero curvature, one of the major components of the inner leaf, phosphatidylethanolamine (PE), displays a strong tendency to do so whereas the other, phosphatidylserine (PS), does not. Therefore, we posit that the concentration difference of PS and PE couples to height fluctuations of the plasma membrane bilayer. This brings about a microemulsion in the inner leaf. Coupling of the concentration difference between PS and PE in the inner leaf and SM and PC in the outer leaf propagates the microemulsion to that leaf as well. The characteristic size of the inhomogeneities is equal to the square-root of the ratio of the bending modulus of the bilayer to its surface tension, a size which is ~100 nm for the plasma membrane. If the coupling between leaves were to be provided by the interchange of cholesterol, then our model raft would consist of SM and cholesterol in the outer leaf and PS and cholesterol in the inner leaf floating in a sea of PC and PE in both leaves.