Moduli Spaces of Polygons with Applications to Protein-Macrocycle Docking

Synthetic Macrocycles (MCs) are receiving increased attention for their potential as therapeutic agents. Beside their promise as therapeutics, MCs also have great mathematical interest due to their complex topological structure. However, for several reasons effective methods for modeling 3D complexes of MCs and their protein targets are lacking. MCs are too large and complex for current methods used for docking small non-cyclic drug molecules. They are also too flexible for methods of protein-protein docking. The goal of this project is to develop geometrical methods to efficiently model the compliant interaction of macromolecules, also known as the Flexible Docking Problem. Current methods are based on brute force direct computer simulations. The large size of the molecules and the confined nature of the space to be explored renders these impractical. The efficient exact analytical methodologies used in the software BRIKARD for macrocycle structure modeling and in the molecular docking suite CLUSPRO will be combined through the development of mathematical structures into a new docking protocol, capable of efficiently handling flexible ligand protein docking. The resulting software will find immediate use in the pharmaceutical industry in the area of macrocyclic drug design. Moreover, the connection between molecular flexibility and robotics offers a rich ground for creating simple models that will be used for outreach activities introducing high school students to basic ideas of robotics, flexibility and molecular modeling. At the heart of protein-macrocycle docking lies a global search for an energy minimum, a challenging problem due to high dimensionality of the search space, rugged energy landscape, and high cost of energy function evaluation. The non-trivial structure of macrocycle shapespace effectively precludes successful modeling of protein-macrocycle interactions using current methods. This obstacle will be overcome by describing conformational spaces corresponding to different degrees of molecular flexibility by appropriate manifolds. The search will be guided by introducing a Riemannian metric to properly weigh ligand-protein rotation-translations and cyclic ligand flexibility. Energetic terms will also be incorporated to account for steric interactions of the ligand and binding pocket. This will allow efficient sampling of low energy regions, avoiding high energy areas of the joint conformational space. The resulting hybrid method will begin with coarse grained global sampling to identify promising areas of protein-ligand shapespace, followed by medium-range adjustments and optimization using more detailed scoring functions, and, finally, targeted fine resampling to obtain high resolution structures. The docking framework created will be applicable to a broad spectrum of tasks including unconstrained ligand docking and protein loop modeling. Intellectual merits include: (i) understanding moduli spaces of polygons in Euclidean space R3 with fixed side lengths and angles, (ii) deriving proper weights for searches in the relative placement and compliant shape changes in a protein-ligand complex, and (iii) improvement of effectiveness of general docking protocols. The resulting software will be released as open source and made freely available through the widely used CLUSPRO server. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.