Protein Aggregation as a Phase Transition Process

Abstract

In this model we attempt to mimic the aggregation pattern found in real proteins using a modified Ising model. Similar to a Blume-Campel model, we restrict the proteins to occupy discrete lattice points and define a pairwise interaction depending on the configuration of the protein (as in the Potts model). We define three specific conformational states: native, intermediate and unfolded and consider the aggregation process as a series of second-order phase transitions. In this framework we can analyze the zeros of the partition function analytically continued onto the complex plane, specifically the Yang-Lee and Fisher zeros. Using combinatorial arguments we can simplify the partition function and predict the occurrences of phase transitions as a function of the interaction potential and protein density.