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The membrane inclusions curvature equations

By Jean-charles Faugère, Milena Hering and Jeff Phan


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 non linear systems.

Year: 2011
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