Maxent-Stress Optimization of 3D Biomolecular Models

Knowing a biomolecule\u27s structure is inherently linked to and a prerequisite for any detailed understanding of its function. Significant effort has gone into developing technologies for structural characterization. These technologies do not directly provide 3D structures; instead they typically yield noisy and erroneous distance information between specific entities such as atoms or residues, which have to be translated into consistent 3D models. Here we present an approach for this translation process based on maxent-stress optimization. Our new approach extends the original graph drawing method for the new application\u27s specifics by introducing additional constraints and confidence values as well as algorithmic components. Extensive experiments demonstrate that our approach infers structural models (i.e., sensible 3D coordinates for the molecule\u27s atoms) that correspond well to the distance information, can handle noisy and error-prone data, and is considerably faster than established tools. Our results promise to allow domain scientists nearly-interactive structural modeling based on distance constraints

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

New Approaches to Protein NMR Automation

The three-dimensional structure of a protein molecule is the key to understanding its biological and physiological properties. A major problem in bioinformatics is to efficiently determine the three-dimensional structures of query proteins. Protein NMR structure de- termination is one of the main experimental methods and is comprised of: (i) protein sample production and isotope labelling, (ii) collecting NMR spectra, and (iii) analysis of the spectra to produce the protein structure. In protein NMR, the three-dimensional struc- ture is determined by exploiting a set of distance restraints between spatially proximate atoms. Currently, no practical automated protein NMR method exists that is without human intervention. We first propose a complete automated protein NMR pipeline, which can efficiently be used to determine the structures of moderate sized proteins. Second, we propose a novel and efficient semidefinite programming-based (SDP) protein structure determination method. The proposed automated protein NMR pipeline consists of three modules: (i) an automated peak picking method, called PICKY, (ii) a backbone chemical shift assign- ment method, called IPASS, and (iii) a protein structure determination method, called FALCON-NMR. When tested on four real protein data sets, this pipeline can produce structures with reasonable accuracies, starting from NMR spectra. This general method can be applied to other macromolecule structure determination methods. For example, a promising application is RNA NMR-assisted secondary structure determination. In the second part of this thesis, due to the shortcomings of FALCON-NMR, we propose a novel SDP-based protein structure determination method from NMR data, called SPROS. Most of the existing prominent protein NMR structure determination methods are based on molecular dynamics coupled with a simulated annealing schedule. In these methods, an objective function representing the error between observed and given distance restraints is minimized; these objective functions are highly non-convex and difficult to optimize. Euclidean distance geometry methods based on SDP provide a natural formulation for realizing a three-dimensional structure from a set of given distance constraints. However, the complexity of the SDP solvers increases cubically with the input matrix size, i.e., the number of atoms in the protein, and the number of constraints. In fact, the complexity of SDP solvers is a major obstacle in their applicability to the protein NMR problem. To overcome these limitations, the SPROS method models the protein molecule as a set of intersecting two- and three-dimensional cliques. We adapt and extend a technique called semidefinite facial reduction for the SDP matrix size reduction, which makes the SDP problem size approximately one quarter of the original problem. The reduced problem is solved nearly one hundred times faster and is more robust against numerical problems. Reasonably accurate results were obtained when SPROS was applied to a set of 20 real protein data sets

The Kinetics of helix unfolding: Molecular dynamics simulations with Milestoning

The unfolding process of a helical heteropeptide is studied by computer simulation in explicit solvent. A combination of a functional optimization to determine the reaction coordinate and short time trajectories between “Milestones” is used to study the kinetic of the unfolding. One hundred unfolding trajectories along three different unfolding pathways are computed between all nearby Milestones providing adequate statistics to compute the overall first passage time. The radius of gyration is smaller for intermediate configurations compared to the initial and final states suggesting that the kinetics (but not the thermodynamics) is sensitive to pressure. The transitions are dominated by local bond rotations (the ψ dihedral angle) that are assisted by significant nonmonotonic fluctuations of nearby torsions. The most effective unfolding pathway is via the N-terminal

Study of protein-DNA interaction using new generation data

Ph.DDOCTOR OF PHILOSOPH

Operations research: from computational biology to sensor network

In this dissertation we discuss the deployment of combinatorial optimization methods for modeling and solve real life problemS, with a particular emphasis to two biological problems arising from a common scenario: the reconstruction of the three-dimensional shape of a biological molecule from Nuclear Magnetic Resonance (NMR) data. The fi rst topic is the 3D assignment pathway problem (APP) for a RNA molecule. We prove that APP is NP-hard, and show a formulation of it based on edge-colored graphs. Taking into account that interactions between consecutive nuclei in the NMR spectrum are diff erent according to the type of residue along the RNA chain, each color in the graph represents a type of interaction. Thus, we can represent the sequence of interactions as the problem of fi nding a longest (hamiltonian) path whose edges follow a given order of colors (i.e., the orderly colored longest path). We introduce three alternative IP formulations of APP obtained with a max flow problem on a directed graph with packing constraints over the partitions, which have been compared among themselves. Since the last two models work on cyclic graphs, for them we proposed an algorithm based on the solution of their relaxation combined with the separation of cycle inequalities in a Branch & Cut scheme. The second topic is the discretizable distance geometry problem (DDGP), which is a formulation on discrete search space of the well-known distance geometry problem (DGP). The DGP consists in seeking the embedding in the space of a undirected graph, given a set of Euclidean distances between certain pairs of vertices. DGP has two important applications: (i) fi nding the three dimensional conformation of a molecule from a subset of interatomic distances, called Molecular Distance Geometry Problem, and (ii) the Sensor Network Localization Problem. We describe a Branch & Prune (BP) algorithm tailored for this problem, and two versions of it solving the DDGP both in protein modeling and in sensor networks localization frameworks. BP is an exact and exhaustive combinatorial algorithm that examines all the valid embeddings of a given weighted graph G=(V,E,d), under the hypothesis of existence of a given order on V. By comparing the two version of BP to well-known algorithms we are able to prove the e fficiency of BP in both contexts, provided that the order imposed on V is maintained