Local sensitivity analysis of the “membrane shape equation” derived from the Helfrich energy
Abstract
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the “spontaneous curvature” term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich’s model. Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 21, 2020
- Source ID
- 10.1177/1081286520953888
Entities
People
- A Behzadan
- M Holst
- Padmini Rangamani
Organizations
- Air Force Office of Scientific Research
- California State University, Sacramento
- National Institute of General Medical Sciences
- National Science Foundation Division of Mathematical Sciences
- University of California, San Diego