An Ising/Potts Model Approach to Predicting Pathogen Case Fatality Rate and Vaccine Efficacy Based on Structural Motifs

Dating to the work of Bragg and Williams in the 1930s, characterizing system disorder with a single numerical value has proven to be an effective approach to predicting key properties. We demonstrate that it is possible to extend the concept of a Bragg-Williams order parameter (S) to pathogenic systems such as viruses and bacteria by examining the protein arrangement on the particle's outer surface. Underlying the methodology is the concept of structural motifs, which describe the nearest neighbor environment of each protein. For a fully ordered surface (S=1), the number of distinct motifs is limited and purely a function of the number of different proteins. Towards the other extreme (S=0), additional motifs become allowed, with the type and number of each dictated by S. A linear relationship between Case Fatality Rate and S² is obtained through Ising/Potts type models where each protein is represented by a distinct spin, and confirmed with experimental data across multiple viral families. Additionally, there is a robust correlation between vaccine efficacy and the order parameter difference between vaccine and corresponding pathogen.