Title: Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks,
Abstract: Formation of membrane necks is crucial for fission and fusion in lipid
bilayers. In this work, we seek to answer the following fundamental question:
what is the relationship between protein-induced spontaneous mean curvature and
the Gaussian curvature at a membrane neck? Using an augmented Helfrich model
for lipid bilayers to include membrane-protein interaction, we solve the shape
equation on catenoids to find the field of spontaneous curvature that satisfies
mechanical equilibrium of membrane necks. In this case, the shape equation
reduces to a variable coefficient Helmholtz equation for spontaneous curvature,
where the source term is proportional to the Gaussian curvature. We show how
this latter quantity is responsible for non-uniform distribution of spontaneous
curvature in minimal surfaces. We then explore the energetics of catenoids with
different spontaneous curvature boundary conditions and geometric asymmetries
to show how heterogeneities in spontaneous curvature distribution can couple
with Gaussian curvature to result in membrane necks of different geometries.