Statistical mechanics and kinetics of protein folding and aggregation

John Stephen Schreck

doi:10.17918/etd-3998

The self-assembly of amyloid proteins into fibrils is thought to be the cause of many diseases, including Alzheimer's disease, Huntington's disease, and prion-related disease (e.g. mad cow disease). Thus, understanding how certain proteins can form amyloid fibrils is essential, if cures are to be found. We start by exploring how individual proteins may transform from one conformational structure to another. For example, we study how an alpha-helix may change into to a beta-hairpin. We then study how amyloid proteins may join together to form aggregates of varying conformation and size. Overall, four main areas of these problems are studied in detail: protein structure change by equilibrium methods, protein aggregation at equilibrium with a fixed number of protein monomers in the system, protein aggregation in equilibrium with a variable number of monomers in the system, and finally the non-equilibrium aggregation of proteins into fibrils. For the systems studied at equilibrium, we focus on using methods from statistical mechanics. By describing a simple Hamiltonian that quantifies the interactions between residues in proteins, or proteins in aggregates, a transfer matrix can be used to solve the partition function of each system exactly. The transfer matrix used in our study of protein folding can take into account the long-range interactions found in beta-sheet structures. Once the partition function for either proteins or aggregates is calculated, various thermodynamical quantities can be derived and compared with experiments to test model predictions. We also introduce the aggregate and solvent phases, when studying protein self-assembly in the grand-canonical ensemble, which naturally introduces the chemical potentials of proteins and aggregates into the problem. For the non-equilibrium studies of protein aggregation, we use mass-action kinetic equations to calculate the concentrations of aggregates of all sizes as a function of time. We show that by taking into account all combinatorial ways two protein aggregates could join to form a larger aggregate, as well as all possible ways an aggregate could fragment into two pieces, certain calculated quantities can reliably predict the long-time average length distribution of the fibrils, as well as the total mass of protein found in the fibrils. Moreover, we are able to estimate how loosely-bound proteins are in aggregates. Overall, our studies of proteins allow us to gain a deeper understanding of the complicated processes involved in folding and aggregation.

Statistical mechanics and kinetics of protein folding and aggregation

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Statistical mechanics and kinetics of protein folding and aggregation

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