Kinetic Ising Model Study of Protein Aggregation

Abstract

Kinetic studies of protein aggregation processes based on the nucleation-polymerization (NP) mechanism and/or its variants are often formulated in terms of the law of mass action. Although these works have greatly enhanced our knowledge in the microscopic descriptions of fibril/aggregate formation (e.g., fragmentation and other secondary pathways), they have to inevitably deal with a huge number of filament species Fn (n=1 to 10∧3 ∼ 10∧4 or even more) as well as a number of kinetic parameters. Very often some kinetic assumptions for the species with a wide distribution of sizes and shapes would be needed in order to simplify the calculation. In contrast, starting from a phase-transition perspective, one is able to provide thermodynamic insight into the nucleation-controlled kinetic behavior. In this work, we propose to apply the kinetic Ising model to investigate the thermodynamics and kinetics of protein aggregation. At mean-field (MF) level, our model can offer thermodynamic interpretation to the lag time; in particular, it can explain the effect of temperature, concentration, and seeding on the change of kinetic profiles. Using four real proteins as examples, we show that the calculated fibril stability is consistent with experimental measurements. In addition, their kinetics can be classified according to a generalized scheme of the model. Our results suggest that protein aggregation could be studied within the framework of the Ginzberg-Landau phase transition theory.