Cluster connectedness and spanning clusters in percolation models of aggregated and crystalline proteins

Graph structures appear in countless biological phenomena at multiple scales, from chemical reaction networks to ecosystem-scale species interactions. Many molecular-scale physical phenomena are literal networks of physically interconnected entities, and benefit from being represented with a modeling framework based in graph theory. In this work, we present models for solvent channel architecture in protein systems, for both ordered (protein crystals) and disordered (protein aggregates) settings. We use stochastic spatial modeling via percolation theory to capture information about solvent accessibility and channel connectedness. Percolation theory deals with connectivity and criticality in random graphs/networks, with cluster connectivity providing information about pore structure, and criticality capturing important phase transitions in the systems under study. The random network framework investigated using percolation models enables us to address questions about in crystallo protein-ligand binding such as occurs in drug discovery fragment screening studies, and to comprehend formation and permeability of disease-associated protein aggregates such as occur in cataracts or plaques in neurodegenerative conditions.