Modeling formation of membrane structures with Morpho

Membranes, such as those surrounding cells as well as organelles, play a key role in biology. These membranes often spontaneously form tubes or tethers to facilitate various biological functions. Often, complex networks of such tubes extend from vesicles and interact with other objects for structural and transport processes, such as osmosis or viral encapsulation. Numerical models have been created of the shapes of tubes using a Monte Carlo model (Kandy, Radhakrishnan) or by parameterizing the membrane as a curve and using azimuthal symmetry (Liese, Carlson). However, modeling the process of formation, without assuming azimuthal symmetry, is very challenging. Using Morpho, a programmable environment for shape optimization, we can model both the process of formation, and the shape as a three dimensional simplicial complex. By evolving the membrane from a flat configuration,imposing a deformation and periodically reminimizing the Helfrich energy, we can obtain snapshots of the membrane morphology and understand the energy landscape throughout the process of tubule formation. Prospects for using Morpho to model other membrane structures will also be discussed.