A Statistical Mechanical Approach to Protein Aggregation

TL;DR

This paper introduces a statistical mechanical framework for modeling protein aggregation, enabling exact calculations of thermodynamic properties and providing insights into nucleation, phase diagrams, and fibril structures relevant to neurodegenerative diseases.

Contribution

It develops an exactly solvable model using Potts and transfer matrix methods to analyze protein aggregation and fibril formation, extending previous approaches.

Findings

Exact solutions for thermodynamic properties of protein aggregates

Phase diagrams illustrating aggregation behavior

Good agreement with experimental data on Aβ(1-40) and Curli fibrils

Abstract

We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for the understanding and treatment of neurodegenerative diseases and also for the development of bio-macromolecules as new materials. We write the effective Hamiltonian in terms of interaction energies between protein monomers, protein and solvent, as well as between protein filaments. The grand partition function can be expressed in terms of a Zimm-Bragg-like transfer matrix, which is calculated exactly and all thermodynamic properties can be obtained. We start with two-state and three-state descriptions of protein monomers using Potts models that can be generalized to include q-states, for which the exactly solvable feature of the model remains. We focus on n X N lattice systems, corresponding to the ordered structures observed in some real fibrils. We have obtained results on nucleation processes and phase diagrams, in which a protein property such as the sheet content of aggregates is expressed as a function of the number of proteins on the lattice and inter-protein or interfacial interaction energies. We have applied our methods to A{\beta}(1-40) and Curli fibrils and obtained results in good agreement with experiments.