Minimum-energy vesicle and cell shapes calculated using spherical harmonics parameterization

Khaled, K., Howard, J. / Acknowledgements: Foo, J.J. Experimental Data, Soft Matter 7, 2138-2143, 2011

An important open question in biophysics is to understand how mechanical forces shape membraneboundedcells and their organelles. A general solution to this problem is to calculate the bending energyof an arbitrarily shaped membrane surface, which can include both lipids and cytoskeletal proteins, andminimize the energy subject to all mechanical constraints. However, the calculations are difficult toperform, especially for shapes that do not possess axial symmetry. We show that the sphericalharmonics parameterization (SHP) provides an analytic description of shape that can be used to quicklyand reliably calculate minimum energy shapes of both symmetric and asymmetric surfaces. Using thismethod, we probe the entire set of shapes predicted by the bilayer couple model, unifying work based ondifferent computational approaches, and providing additional details of the transitions betweendifferent shape classes. In addition, we present new minimum-energy morphologies based on non-linearmodels of membrane skeletal elasticity that closely mimic extreme shapes of red blood cells. The SHPthus provides a versatile shape description that can be used to investigate forces that shape cells.