Computational Solutions To The Protein Folding Problem

The protein folding problem attempts to predict the native, or folded, state of a protein in three-dimensional space, given its primary sequence of amino acids. One common approach for a solution is to treat each complex amino acid as a single sphere, or united atom, and to model each peptide linkage between residues by a virtual bond between spheres. Computational efforts being examined rely on two major assumptions: for any specific molecular conformation, a corresponding potential energy function can be computed, and the three-dimensional, folded state corresponds to the global minimum of this energy function. The optimization method being used to minimize the potential energy involves collecting a large number of conformers, each attained by finding a local minimum of the potential energy function from a random starting point. The information from these conformers is then used to form a convex quadratic global underestimating function for the potential energy of the known conformers. The minimum of this underestimator is used to predict the global minimum for the function, allowing a localized conformer search to be performed based on the predicted minimum. The new set of conformers generated by the localized search can serve as the basis for another quadratic underestimation. After several repetitions, the global minimum can be found with reasonable assurance. The conformer which lies at the global minimum represents the three-dimensional folded state of the molecule -- Author abstract.

A solution to the protein folding problem has eluded researchers for more than 30 years. The stakes are high. Such a solution will make 40,000 more tertiary structures available for immediate study by translating the DNA sequence information in the sequence databases into three-dimensional protein structures. This translation will be indispensable for the analy sis of results from the Human Genome Project, de novo protein design, and many other areas of biotechnological research. Finally, an in-depth study of the rules of protein folding should provide vital clues to the protein fold ing process. The search for these rules is therefore an important objective for theoretical molecular biology. Both experimental and theoretical ap proaches have been used in the search for a solution, with many promising results but no general solution. In recent years, there has been an exponen tial increase in the power of computers. This has triggered an incredible outburst of theoretical approaches to solving the protein folding problem ranging from molecular dynamics-based studies of proteins in solution to the actual prediction of protein structures from first principles. This volume attempts to present a concise overview of these advances. Adrian Roitberg and Ron Elber describe the locally enhanced sam pling/simulated annealing conformational search algorithm (Chapter 1), which is potentially useful for the rapid conformational search of larger molecular systems.

Since the first attempts to model proteins on a computer began almost thirty years ago, our understanding of protein structure and dynamics has dramatically increased. Spectroscopic measurement techniques continue to improve in resolution and sensitivity, allowing a wealth of information to be obtained with regard to the kinetics of protein folding and unfolding, and complementing the detailed structural picture of the folded state. Concurrently, algorithms, software, and computational hardware have progressed to the point where both structural and kinetic problems may be studied with a fair degree of realism. Despite these advances, many major challenges remain in understanding protein folding at both the conceptual and practical levels. Computational Methods for Protein Folding seeks to illuminate recent advances in computational modeling of protein folding in a way that will be useful to physicists, chemists, and chemical physicists. Covering a broad spectrum of computational methods and practices culled from a variety of research fields, the editors present a full range of models that, together, provide a thorough and current description of all aspects of protein folding. A valuable resource for both students and professionals in the field, the book will be of value both as a cutting-edge overview of existing information and as a catalyst for inspiring new studies. Computational Methods for Protein Folding is the 120th volume in the acclaimed series Advances in Chemical Physics, a compilation of scholarly works dedicated to the dissemination of contemporary advances in chemical physics, edited by Nobel Prize-winner Ilya Prigogine.

The protein folding problem refers to the correlation of a protein's amino acid sequence and its native three-dimensional structure which is essential for functionality. It still constitutes one of the major challenges in computational biology. One commonly studied model for the protein folding problem is the HP lattice model in which proteins are considered in a fairly abstract representation. However, the HP model proteins exhibit significant parallels to proteins occurring in nature. The solution of the HP lattice mode as a combinatorial optimization problem has been proven to be NP-complete, and there have already been developed various different approaches for efficient algorithms. We study an integer programming formulation of the problem. Starting with an analysis of this model, where we concentrate on symmetry issues, we show how the model can be consolidated by exploiting symmetry properties of the underlying lattice. The main focus lies in the development of specific components of a branch-and-cut framework for the computation of solutions for the HP model by means of integer programming methods. In order to understand the structure of the model, we perform a series of polyhedral studies from which we derive two main classes of cutting planes. Furthermore, we exploit the knowledge of folding principles which are also valid for HP model proteins for the development of related branching strategies. For the solution of a special class of instances, we present an implementation of a genetic algorithm for the generation of primal feasible start solutions. Finally, we document the performance of the methods developed for each of the four topics (model consolidation, primal method, branching strategy and cutting planes) within the branch-and-cut procedure. We present computational results for different types of lattices, where we both consider known benchmark instances from literature and random instances.

The book will discuss classes of proteins and their folding, as well as the involvement of bioinformatics in solving the protein folding problem. In vivo and in vitro folding mechanisms are examined, as well as the failures of in vitro folding, a mechanism helpful in understanding disease caused by misfolding. The role of energy landscapes is also discussed and the computational approaches to these landscapes.

1. Introduction. 1.1. Protein structure. 1.2. Structure determination. 1.3. Dynamics simulation. 1.4. The myth of protein folding -- 2. X-ray crystallography computing. 2.1. The phase problem. 2.2. Least squares solutions. 2.3. Entropy maximization. 2.4. Indirect methods -- 3. NMR structure determination. 3.1. Nuclear magnetic resonance. 3.2. Distance geometry. 3.3. Distance-based modeling. 3.4. Structural analysis -- 4. Potential energy minimization. 4.1. Potential energy function. 4.2. Local optimization. 4.3. Global optimization. 4.4. Energy transformation -- 5. Molecular dynamics simulation. 5.1. Equations of motion. 5.2. Initial-value problem. 5.3. Boundary-value problem. 5.4. Normal mode analysis -- 6. Knowledge-based protein modeling. 6.1. Sequence/structural alignment. 6.2. Fold recognition/inverse folding. 6.3. Knowledge-based structural refinement. 6.4. Structural computing and beyond

This book covers elements of both the data-driven comparative modeling approach to structure prediction and also recent attempts to simulate folding using explicit or simplified models. Despite the unsolved mystery of how a protein folds, advances are being made in predicting the interactions of proteins with other molecules. Also rapidly advancing are the methods for solving the inverse folding problem, the problem of finding a sequence to fit a structure. This book focuses on the various computational methods for prediction, their successes and their limitations, from the perspective of their most well known practitioners.

This book presents a new approach to the Protein Folding Problem. It starts with a clear description of what the protein folding problem involves. Then, it suggests non-conventional answers to some of the questions posed. In particular, it emphasizes the importance of hydrophilic interactions and hydrophilic forces, rather than the hydrophobic effects, for the stability of the native structure of proteins, as well for the speed of the folding process.

Inference for dynamic systems and conformational sampling for protein folding are two problems motivated by applied data, which pose computational challenges from a statistical perspective. Dynamic systems are often described by a set of coupled differential equations, and methods of parametric estimation for these models from noisy data can require repeatedly solving the equations numerically. Many of these models also lead to rough likelihood surfaces, which makes sampling difficult. We introduce a method for Bayesian inference on these models, using a multiple chain framework that exploits the underlying mathematical structure and interpolates the posterior to improve efficiency. In protein folding, a large conformational space must be searched for low energy states, where any energy function constructed on the states is at best approximate. We propose a method for sampling fragment conformations that accounts for geometric and energetic constraints, and explore ideas for folding entire proteins that account for uncertain energy landscapes and learning from data more effectively. These ingredients are combined into a framework for tackling the problem of generating improvements to protein structure predictions.

Protein folding and aggregation is the process by which newly synthesized proteins fold into the specific three-dimensional structures defining their biologically active states. It has always been a major focus of research in biochemistry and has often been seen as the unsolved second part of the genetic code. In the last 10 years we have witnessed a quantum leap in the research in this exciting area. Computational methods have improved to the extent of making possible to simulate the complete folding process of small proteins and the early stages of protein aggregation. Experimental methods have evolved to permit resolving fast processes of folding reactions and visualizing single molecules during folding. The findings from these novel experiments and detailed computer simulations have confirmed the main predictions of analytical theory of protein folding. In summary, protein folding research has finally acquired the status of a truly quantitative science, paving the way for more exciting developments in the near future. This unique book covers all the modern approaches and the many advances experienced in the field during the last 10 years. There is also much emphasis on computational methods and studies of protein aggregation which have really flourished in the last decade. It includes chapters in the areas that have witnessed major developments and are written by top experts including:computer simulations of folding, fast folding, single molecule spectroscopy, protein design, aggregation studies (both computational and experimental). Readers will obtain a unique perspective of the problems faced in the biophysical study of protein conformational behaviour in aqueous solution and how these problems are being solved with a multidisciplinary approach that combines theory, experiment and computer simulations. Protein Folding, Misfolding and Aggregation Classical Themes and Novel Approaches is essential reading for graduate students actively involved in protein folding research, other scientists interested in the recent progress of the field and instructors revamping the protein folding section of their biochemistry and biophysics courses.