Continuous Symmetry Breaking and Complexity of Biological Membranes

We consider domain-type patterns in biological membranes that possess an in-plane membrane order. Domains are inseparably linked to topological defects, and many features related to them can be guessed based on universal topological arguments. However, much more complex membrane patterns are typically observed. As possible generators of such configurations, we analyze two relatively simple and universal phenomena. Both are based on continuous symmetry breaking (CSB), which manifests ubiquitously in all branches of physics. We present the Imry–Ma argument which, in addition to CSB, requests the presence of uncorrelated random-field-type disorder. Next, we discuss the Kibble–Zurek mechanism. In addition to CSB it considers dynamical slowing when a relevant phase transition is approached. These approaches were originally introduced in magnetism and cosmology, respectively. We adapt them to effectively two-dimensional membranes and discuss their potential role in membrane structure formation.