A distinguishing feature of lipid (bilayer) membranes is their in-plane fluidity caused by free-flowing lipid molecules on the membrane surface. In continuum models for lipid membranes (e.g., the Helfrich–Canham model), fluidity manifests as invariance of the free energy to change in parametrization of the reference surface; a property termed reparametrization invariance. Two different parametric equations of the surface, related through a reparametrization, have identical equilibrium and stability properties. They can therefore be considered equivalent representations of the same surface. Since there are infinitely many ways to parametrize a surface, there are infinitely many equivalent representations for the surface. This highly redundant representation for a surface poses significant challenges to computations. For example, in computational studies using finite element analysis, extreme mesh distortion and spurious zero-energy modes are reported (Feng and Klug, 2006; Ma and Klug, 2008). In this work, by viewing reparametrization invariance as a form of gauge symmetry, we propose a gauge-fixing procedure for the case of topologically spherical membranes. We show that this procedure breaks gauge symmetry and tames the extreme redundancy of the system. We also demonstrate that this procedure is suitable for efficient numerical computations. We obtain accurate equilibrium configurations for the Helfrich–Canham model while circumventing computational issues noted above.

脂质（双层）膜的一个显着特征是它们在平面内的流动性是由膜表面上自由流动的脂质分子引起的。在脂膜的连续模型（例如，Helfrich-Canham模型）中，流动性表现为自由能不变，从而改变了参比表面的参数。一种被称为重新参数化不变性的性质。两种不同的参数方程式通过重新参数化关联的表面具有相同的平衡和稳定性能。因此，可以将它们视为同一表面的等效表示。由于有无数种方法可以对表面进行参数化，因此该表面有无数种等效表示形式。表面的这种高度冗余表示对计算提出了重大挑战。例如，在使用有限元分析的计算研究中，报告了极端的网格变形和虚假的零能量模式（Feng和Klug，2006年； Ma和Klug，2008年）。在这项工作中，通过将重新参数化不变性视为量规对称性的一种形式，我们提出了量规固定程序对于拓扑球形膜。我们表明，此过程破坏了量规的对称性，并驯服了系统的极端冗余。我们还证明了该程序适用于有效的数值计算。我们避免了上面提到的计算问题，同时获得了Helfrich-Canham模型的精确平衡配置。