TY - JOUR T1 - Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks JF - bioRxiv DO - 10.1101/137091 SP - 137091 AU - Morgan Chabanon AU - Padmini Rangamani Y1 - 2017/01/01 UR - http://biorxiv.org/content/early/2017/05/12/137091.abstract N2 - Formation of membrane necks is crucial for fission and fusion. In this work, we aim to answer the following fundamental question: what is the relationship between spontaneous curvature and the Gaussian curvature at a membrane neck? We use the Helfrich model for lipid bilayers and solve the shape equation on catenoids to find the field of spontaneous curvature that will stabilize the membrane neck. 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. ER -