The Membrane Inclusions Curvature Equations
Résumé
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 Groebner bases computation for solving polynomial systems of equations.