Percolation theory is a mathematical formalism that deals with how connected clusters occur in random graphs/networks, and is used for modeling a wide array of problems involving disordered or porous media. It is a spatial stochastic process model possessing the important feature of criticality , referring to the ability of the model to capture behavior such as a phase change in which the system undergoes transition between states. It has been applied in modeling protein transport in membranes, behavior of photosynthetic reaction centers, and molecular condensates, to name just a few of its biophysical applications. In our work, we apply percolation theory to problems in protein crystallography. The process of crystal formation from concentrated protein samples is an obvious example of a phase transition, but there are other aspects of crystallization amenable to this modeling framework. In particular, we are interested in protein co-crystallization problems, in crystallo ligand binding, crystal packing problems, and solvent accessibility, all of which are connected to the porosity of the crystal and driven by spatial arrangement considerations. We explore the utility of percolation theory for capturing multiple phenomena that arise in crystallizing protein systems, and discuss related areas of application where percolation could prove a powerful modeling tool.
Lynch et al. (Sun,) studied this question.