471156 Statistical Thermodynamic Modeling of Early Amyloid-β Oligomer Formation: Explicit and Implicit Incorporation of Hydrogen Bonding in a Self-Consistent Field Framework
To explore the configuration space of small Aβ oligomers, fully atomistic replica exchange molecular dynamics (REMD) simulations of Aβ were performed using the Gromacs (version 4.6.5) software package, the Charmm 36 force field and an explicit water model. An Aβ monomer was simulated using REMD at two different ionic strengths. In addition, an Aβ dimer was simulated at room temperature and physiological ionic strength. These simulations were used to derive an ensemble of conformations containing relevant structures for the monomer over a range of temperatures and ionic strengths as well as those for a dimer both during the process of binding and while bound.
A self-consistent field theory has been developed and implemented to model the thermodynamics of an arbitrary number of interacting Aβ molecules. The theory consists of formulating the appropriate thermodynamic potential for isolated Aβ molecules in a bath of solvent and ionic species in terms of the energy and entropy associated with all species. The theory captures the four most relevant physical properties of Aβ: these properties are the shape of the molecule, the characteristics of the protonatable sites, the hydrophobic nature of the constituent residues and the hydrogen bonding that can occur between donors and acceptors on the protein. Hydrophobicity and protein-protein hydrogen bonding are extremely important driving forces for protein structure and are both manifestations of the effects of hydrogen bonding. Hydrophobicity is captured implicitly in our model through the assignment of experimentally derived free energies of solvation to the solvent-exposed surface of the protein. These solvation energies reflect the disruption that different regions of the protein surface cause in the hydrogen bond network of water (that is, water-water hydrogen bonding) and the degree to which these regions form hydrogen bonds with water (protein-water hydrogen bonding). Protein-protein hydrogen bonding is captured in a separate term in the free energy which depends explicitly on the orientation of the donors and acceptors.
The theory was used to evaluate the most probable conformations of Aβ for isolated monomers and those in the process of dimerization. These conformations were then simulated using the same methodology as before thus establishing a feedback between the statistical thermodynamic model and molecular mechanics simulation to increase the resolution of the most significant part of configurational phase space. The complete, theoretical feedback-bolstered configurational ensemble was used as input in the theory which was applied to the process of Aβ trimer formation. In this study, the centers of mass of three Aβ monomers were assigned to positions in space and the theoretical model was used to calculate the properties of constrained equilibrium at those conditions. This procedure was repeated over a range of relative positions to elucidate the free energy landscape of the trimer formation process. As anticipated, it was found that the effects of hydrogen bonding as manifest through our implicit and explicit terms were significant determinants of the structure of the trimer.
This theory is capable of providing a rich description of the molecular organization and physics that guide Aβ interactions that cannot be determined experimentally. The unique flexibility of this theoretical framework to treat solution conditions and systems of arbitrary geometries makes this a promising tool in two important aspects. First, it can be used to further fundamental understanding of the Aβ oligomerization process and how this process depends on different factors. Secondly, this model can be used as an inhibitor design tool through the incorporation of inhibitors into the framework. Further work will extend this model to the treatment of the interactions of larger aggregate species in order to elucidate structural properties of these larger oligomers and characterize the thermodynamic pathways of their formation.