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

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

LightDock: a new multi-scale approach to protein–protein docking

Computational prediction of protein–protein complex structure by docking can provide structural and mechanistic insights for protein interactions of biomedical interest. However, current methods struggle with difficult cases, such as those involving flexible proteins, low-affinity complexes or transient interactions. A major challenge is how to efficiently sample the structural and energetic landscape of the association at different resolution levels, given that each scoring function is often highly coupled to a specific type of search method. Thus, new methodologies capable of accommodating multi-scale conformational flexibility and scoring are strongly needed. We describe here a new multi-scale protein–protein docking methodology, LightDock, capable of accommodating conformational flexibility and a variety of scoring functions at different resolution levels. Implicit use of normal modes during the search and atomic/coarse-grained combined scoring functions yielded improved predictive results with respect to state-of-the-art rigid-body docking, especially in flexible cases.B.J-G was supported by a FPI fellowship from the Spanish Ministry of Economy and Competitiveness. This work was supported by I+D+I Research Project grants BIO2013-48213-R and BIO2016-79930-R from the Spanish Ministry of Economy and Competitiveness. This work is partially supported by the European Union H2020 program through HiPEAC (GA 687698), by the Spanish Government through Programa Severo Ochoa (SEV-2015-0493), by the Spanish Ministry of Science and Technology (TIN2015-65316-P) and the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programaciói Entorns d’Execució Paral·lels (2014-SGR-1051).Peer ReviewedPostprint (author's final draft

FireDock: a web server for fast interaction refinement in molecular docking†

Structural details of protein–protein interactions are invaluable for understanding and deciphering biological mechanisms. Computational docking methods aim to predict the structure of a protein–protein complex given the structures of its single components. Protein flexibility and the absence of robust scoring functions pose a great challenge in the docking field. Due to these difficulties most of the docking methods involve a two-tier approach: coarse global search for feasible orientations that treats proteins as rigid bodies, followed by an accurate refinement stage that aims to introduce flexibility into the process. The FireDock web server, presented here, is the first web server for flexible refinement and scoring of protein–protein docking solutions. It includes optimization of side-chain conformations and rigid-body orientation and allows a high-throughput refinement. The server provides a user-friendly interface and a 3D visualization of the results. A docking protocol consisting of a global search by PatchDock and a refinement by FireDock was extensively tested. The protocol was successful in refining and scoring docking solution candidates for cases taken from docking benchmarks. We provide an option for using this protocol by automatic redirection of PatchDock candidate solutions to the FireDock web server for refinement. The FireDock web server is available at http://bioinfo3d.cs.tau.ac.il/FireDock/

Accounting for Large Amplitude Protein Deformation during in Silico Macromolecular Docking

Rapid progress of theoretical methods and computer calculation resources has turned in silico methods into a conceivable tool to predict the 3D structure of macromolecular assemblages, starting from the structure of their separate elements. Still, some classes of complexes represent a real challenge for macromolecular docking methods. In these complexes, protein parts like loops or domains undergo large amplitude deformations upon association, thus remodeling the surface accessible to the partner protein or DNA. We discuss the problems linked with managing such rearrangements in docking methods and we review strategies that are presently being explored, as well as their limitations and success

Dynamic control of selectivity in the ubiquitination pathway revealed by an ASP to GLU substitution in an intra-molecular salt-bridge network

Ubiquitination relies on a subtle balance between selectivity and promiscuity achieved through specific interactions between ubiquitin-conjugating enzymes (E2s) and ubiquitin ligases (E3s). Here, we report how a single aspartic to glutamic acid substitution acts as a dynamic switch to tip the selectivity balance of human E2s for interaction toward E3 RING-finger domains. By combining molecular dynamic simulations, experimental yeast-two-hybrid screen of E2-E3 (RING) interactions and mutagenesis, we reveal how the dynamics of an internal salt-bridge network at the rim of the E2-E3 interaction surface controls the balance between an “open”, binding competent, and a “closed”, binding incompetent state. The molecular dynamic simulations shed light on the fine mechanism of this molecular switch and allowed us to identify its components, namely an aspartate/glutamate pair, a lysine acting as the central switch and a remote aspartate. Perturbations of single residues in this network, both inside and outside the interaction surface, are sufficient to switch the global E2 interaction selectivity as demonstrated experimentally. Taken together, our results indicate a new mechanism to control E2-E3 interaction selectivity at an atomic level, highlighting how minimal changes in amino acid side-chain affecting the dynamics of intramolecular salt-bridges can be crucial for protein-protein interactions. These findings indicate that the widely accepted sequence-structure-function paradigm should be extended to sequence-structure-dynamics-function relationship and open new possibilities for control and fine-tuning of protein interaction selectivity

pDOCK: a new technique for rapid and accurate docking of peptide ligands to Major Histocompatibility Complexes

Background: Identification of antigenic peptide epitopes is an essential prerequisite in T cell-based molecular vaccine design. Computational (sequence-based and structure-based) methods are inexpensive and efficient compared to experimental approaches in screening numerous peptides against their cognate MHC alleles. In structure-based protocols, suited to alleles with limited epitope data, the first step is to identify high-binding peptides using docking techniques, which need improvement in speed and efficiency to be useful in large-scale screening studies. We present pDOCK: a new computational technique for rapid and accurate docking of flexible peptides to MHC receptors and primarily apply it on a non-redundant dataset of 186 pMHC (MHC-I and MHC-II) complexes with X-ray crystal structures. Results: We have compared our docked structures with experimental crystallographic structures for the immunologically relevant nonameric core of the bound peptide for MHC-I and MHC-II complexes. Primary testing for re-docking of peptides into their respective MHC grooves generated 159 out of 186 peptides with Ca RMSD of less than 1.00 Å, with a mean of 0.56 Å. Amongst the 25 peptides used for single and variant template docking, the Ca RMSD values were below 1.00 Å for 23 peptides. Compared to our earlier docking methodology, pDOCK shows upto 2.5 fold improvement in the accuracy and is ~60% faster. Results of validation against previously published studies represent a seven-fold increase in pDOCK accuracy. Conclusions: The limitations of our previous methodology have been addressed in the new docking protocol making it a rapid and accurate method to evaluate pMHC binding. pDOCK is a generic method and although benchmarks against experimental structures, it can be applied to alleles with no structural data using sequence information. Our outcomes establish the efficacy of our procedure to predict highly accurate peptide structures permitting conformational sampling of the peptide in MHC binding groove. Our results also support the applicability of pDOCK for in silico identification of promiscuous peptide epitopes that are relevant to higher proportions of human population with greater propensity to activate T cells making them key targets for the design of vaccines and immunotherapies.16 page(s

A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem

We formulate a doubly nonnegative (DNN) relaxation of the protein side-chain positioning (SCP) problem. We take advantage of the natural splitting of variables that stems from the facial reduction technique in the semidefinite relaxation, and we solve the relaxation using a variation of the Peaceman-Rachford splitting method. Our numerical experiments show that we solve all our instances of the SCP problem to optimality