Manifold optimization methods for macromolecular docking
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Abstract
This thesis develops efficient algorithms for local optimization problems encountered in predictive docking of biological macromolecules. Predictive docking, defined as computationally obtaining a model of the bound complex from the coordinates of the two component molecules, is one of the fundamental and challenging problems in computational structural biology. Docking methods generally search for the minima of an energy or scoring function that estimates the binding free energy or, more frequently, the interaction energy, of the two molecules. These energy functions generally have large numbers of local minima, resulting in extremely rugged energy landscapes. Therefore, independently of the algorithm used for sampling the conformational space, virtually all docking algorithms include some type of local continuous minimization of the energy function.
Most state-of-the-art algorithms allow for the free movement of all atoms of the two molecules and rely on the minimization of the energy function to enforce structural constraints of the molecules. In contrast this thesis exploits the partial or complete rigidity of the molecules when defining the conformational space. As a result, the local optimization problems are formulated as optimization problems on appropriately defined manifolds. In the case of rigid docking, a novel manifold representation of rigid motions of a body is introduced that resolves many of the optimization difficulties associated with the commonly used manifold for this purposed , the so-called Special Euclidean group, SE(3). These difficulties arise from a coupling that SE(3) introduces between the rotational and translational move of the body. The new representation decouples these moves and results in a more appropriate and flexible optimization algorithm. Experimental results show that the proposed algorithm is an order of magnitude more efficient than the current state-of-the-art algorithms.
The proposed manifold optimization approach is then extended to the case of flexible docking. The novel manifold representation of rigid motions is combined with the so-called internal coordinate representation of flexible moves to define a new manifold to which the original manifold optimization algorithm can be directly extended. Computational results show that the resulting optimization algorithm is substantially more efficient than energy minimization using a traditional all-atom optimization algorithm while producing solutions of comparable quality.
It is shown that the application of the proposed local optimization algorithm as one of the components of a multi-stage refinement protocol for protein-protein docking contributes significantly to the refinement stage by helping to move the distribution of docking decoys closer to the corresponding bound structures.
Finally, it is shown that the approach of the thesis can be substantially generalized to address the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. This is a formulation used in a number of engineering applications other than molecular docking.
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Thesis (Ph.D.)--Boston University