The membrane inclusions curvature equations

Abstract

We examine a system of equations arising in biophysics whose solutions are believed to represent the stable positions of N conical proteins embedded in a cell membrane. Symmetry considerations motivate two equivalent refomulations of the system which allow the complete classification of solutions for small N < 13. The occurrence of regular geometric patterns in these solutions suggests considering a simpler system, which leads to the detection of solutions for larger N up to 280. We use the most recent techniques of Gröbner bases computation for solving polynomial systems of equations. © 2003 Elsevier Inc. All rights reserved.