A Thermodynamic Model of the Formation of Protein Aggregates on a Matrix

The formation of pathological protein aggregates is associated with many neurodegenerative diseases. The aggregates can form by multilayer adsorption of ligands on a matrix in some cases; for example, the set of membrane protein receptors may act as a matrix. A thermodynamic model was developed to describe the formation of linear aggregates in which ligands are stacked. Cases where complexes of the same type or two different types form the stacks are considered. The model can be used to study pathological aggregation of various proteins and, primarily, amyloid β and its isoforms. The mean, variance, and entropy were calculated for a theoretical distributions of aggregate sizes. A comparison was made with other theoretical models of the formation of amyloid aggregates.