Alzheimer’s disease (AD) is the most common neurodegenerative disease and the sixth leading cause of death in the United States. One of the indications of AD is the presence of amyloid-β (Aβ) aggregates in the brains of those afflicted. Aβ is a small protein, usually 40 or 42 amino acids in length, with no known function or native conformation. This protein aggregates through diverse mechanisms to progress from monomers to soluble oligomers and ultimately insoluble fibrils. A significant body of evidence now suggests that soluble oligomers are the most cytotoxic species of Aβ aggregate. Due to the dynamic nature of these aggregates, it has proven exceedingly difficult to determine the structure of these toxic oligomers and predict the effect that varying solution conditions have on their stability and propensity to form. A statistical thermodynamics model has been developed to elucidate these relationships.
Aβ(1-42) was simulated using fully-atomistic replica exchange molecular dynamics (REMD) with GROMACS. Simulations were performed with NaCl concentrations ranging from 0 to 300 mM for a single monomer as well as for two monomers, which bound over the course of the simulation. We use an ensemble of approximately 106conformations taken from the simulations as input in a self-consistent mean field theory that explicitly accounts for the size, shape and charge distribution of both the amino acids in Aβ and all molecular species present in solution. The theory consists of writing the Helmholtz free energy functional of the system in terms of the entropy and energy associated with all species. Thermodynamic equilibrium expressions are derived from this functional for the probability of each Aβ conformation as well as the local density of all molecular species. Space is discretized in 3 dimensions to numerically solve these equations. The theory was applied in two distinct cases, one in which a single monomer was modeled and another in which two interacting monomers were modeled with the centers of mass of all conformations separated by a fixed distance. The latter case was iterated over a range of distances in order to capture a binding event with this thermodynamic treatment.
The solution of the model equations provides a prediction of the probabilities of the conformations of the Aβ dimer and the potential of mean force between two monomers during the dimerization process. The true power of the model is the unique accessibility that it has to this information at arbitrary ionic strengths and pH. Though this work focused on the interaction of Aβ monomers, the theory can be easily extended to predict the binary interaction of larger oligomer species. For these reasons, this model constitutes a reliable methodology to elucidate the structure of toxic oligomer species and a robust design tool for the development of oligomerization inhibitors.
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