The membrane inclusions curvature equations

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• 作者：Faug&egrave ; re ; Jean-Charles ; Hering ; Milena ; Phan ; Jeff
• 刊名：Advances in Applied Mathematics
• 出版年：2003
• 出版时间：November, 2003
• 年：2003
• 卷：31
• 期：4
• 页码：643-658
• 全文大小：230 K

文摘

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.