Protein docking refinement by convex underestimation in the low-dimensional subspace of encounter complexes

We propose a novel stochastic global optimization algorithm with applications to the refinement stage of protein docking prediction methods. Our approach can process conformations sampled from multiple clusters, each roughly corresponding to a different binding energy funnel. These clusters are obtained using a density-based clustering method. In each cluster, we identify a smooth “permissive” subspace which avoids high-energy barriers and then underestimate the binding energy function using general convex polynomials in this subspace. We use the underestimator to bias sampling towards its global minimum. Sampling and subspace underestimation are repeated several times and the conformations sampled at the last iteration form a refined ensemble. We report computational results on a comprehensive benchmark of 224 protein complexes, establishing that our refined ensemble significantly improves the quality of the conformations of the original set given to the algorithm. We also devise a method to enhance the ensemble from which near-native models are selected.Published versio

Optimization methods for side-chain positioning and macromolecular docking

This dissertation proposes new optimization algorithms targeting protein-protein docking which is an important class of problems in computational structural biology. The ultimate goal of docking methods is to predict the 3-dimensional structure of a stable protein-protein complex. We study two specific problems encountered in predictive docking of proteins. The first problem is Side-Chain Positioning (SCP), a central component of homology modeling and computational protein docking methods. We formulate SCP as a Maximum Weighted Independent Set (MWIS) problem on an appropriately constructed graph. Our formulation also considers the significant special structure of proteins that SCP exhibits for docking. We develop an approximate algorithm that solves a relaxation of MWIS and employ randomized estimation heuristics to obtain high-quality feasible solutions to the problem. The algorithm is fully distributed and can be implemented on multi-processor architectures. Our computational results on a benchmark set of protein complexes show that the accuracy of our approximate MWIS-based algorithm predictions is comparable with the results achieved by a state-of-the-art method that finds an exact solution to SCP. The second problem we target in this work is protein docking refinement. We propose two different methods to solve the refinement problem. The first approach is based on a Monte Carlo-Minimization (MCM) search to optimize rigid-body and side-chain conformations for binding. In particular, we study the impact of optimally positioning the side-chains in the interface region between two proteins in the process of binding. We report computational results showing that incorporating side-chain flexibility in docking provides substantial improvement in the quality of docked predictions compared to the rigid-body approaches. Further, we demonstrate that the inclusion of unbound side-chain conformers in the side-chain search introduces significant improvement in the performance of the docking refinement protocols. In the second approach, we propose a novel stochastic optimization algorithm based on Subspace Semi-Definite programming-based Underestimation (SSDU), which aims to solve protein docking and protein structure prediction. SSDU is based on underestimating the binding energy function in a permissive subspace of the space of rigid-body motions. We apply Principal Component Analysis (PCA) to determine the permissive subspace and reduce the dimensionality of the conformational search space. We consider the general class of convex polynomial underestimators, and formulate the problem of finding such underestimators as a Semi-Definite Programming (SDP) problem. Using these underestimators, we perform a biased sampling in the vicinity of the conformational regions where the energy function is at its global minimum. Moreover, we develop an exploration procedure based on density-based clustering to detect the near-native regions even when there are many local minima residing far from each other. We also incorporate a Model Selection procedure into SSDU to pick a predictive conformation. Testing our algorithm over a benchmark of protein complexes indicates that SSDU substantially improves the quality of docking refinement compared with existing methods

Optimization and machine learning methods for Computational Protein Docking

Computational Protein Docking (CPD) is defined as determining the stable complex of docked proteins given information about two individual partners, called receptor and ligand. The problem is often formulated as an energy/score minimization where the decision variables are the 6 rigid body transformation variables for the ligand in addition to more variables corresponding to flexibilities in the protein structures. The scoring functions used in CPD are highly nonlinear and nonconvex with a very large number of local minima, making the optimization problem particularly challenging. Consequently, most docking procedures employ a multistage strategy of (i) Global Sampling using a coarse scoring function to identify promising areas followed by (ii) a Refinement stage using more accurate scoring functions and possibly allowing more degrees of freedom. In the first part of this work, the problem of local optimization in the refinement stage is addressed. The goal of local optimization is to remove steric clashes between protein partners and obtain more realistic score values. The problem is formulated as optimization on the space of rigid motions of the ligand. Employing a recently introduced representation of the space of rigid motions as a manifold, a new Riemannian metric is introduced that is closely related to the Root Mean Square Deviation (RMSD) distance measure widely used in Protein Docking. It is argued that the new metric puts rotational and translational variables on equal footing as far local changes of RMSD is concerned. The implications and modifications for gradient-based local optimization algorithms are discussed. In the second part, a new methodology for resampling and refinement of ligand conformations is introduced. The algorithm is a refinement method where the inputs to the algorithm are ensembles of ligand conformations and the goal is to generate new ensembles of refined conformations, closer to the native complex. The algorithm builds upon a previous work and introduces multiple new innovations: Clustering the input conformations, performing dimensionality reduction using Principle Component Analysis (PCA), underestimating the scoring function and resampling and refinement of new conformations. The performance of the algorithm on a comprehensive benchmark of protein complexes is reported. The third part of this work focuses on using machine learning framework for addressing two specific problems in Protein Docking: (i) Constructing a machine learning model in order to predict whether a given receptor and ligand pair interact. This is of significant importance for constructing the so-called protein interaction networks, an critical step in the Drug Discovery process. The success of the algorithm is verified on a benchmark for discrimination between Biological and Crystallographic Dimers. (ii) A ranking scheme for output predictions of a protein docking server is devised. The machine learning model employs the features of the docking server predictions to produce a ranked list with the top ranked predictions having higher probability of being close to the native solution. Two state-of-the-art approaches to the ranking problem are presented and compared in detail and the implications of using the superior approach for a structural docking server is discussed