GreMuTRRR: A Novel Genetic Algorithm to Solve Distance Geometry Problem for Protein Structures

Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the protein structure one has to solve the Euclidean distance geometry problem given the incomplete interval distance data produced by NMR machines. In this paper, we propose a new genetic algorithm for solving the Euclidean distance geometry problem for protein structure prediction given sparse NMR data. Our genetic algorithm uses a greedy mutation operator to intensify the search, a twin removal technique for diversification in the population and a random restart method to recover stagnation. On a standard set of benchmark dataset, our algorithm significantly outperforms standard genetic algorithms.Comment: Accepted for publication in the 8th International Conference on Electrical and Computer Engineering (ICECE 2014

Protein structure determination via an efficient geometric build-up algorithm

Abstract Background A protein structure can be determined by solving a so-called distance geometry problem whenever a set of inter-atomic distances is available and sufficient. However, the problem is intractable in general and has proved to be a NP hard problem. An updated geometric build-up algorithm (UGB) has been developed recently that controls numerical errors and is efficient in protein structure determination for cases where only sparse exact distance data is available. In this paper, the UGB method has been improved and revised with aims at solving distance geometry problems more efficiently and effectively. Methods An efficient algorithm (called the revised updated geometric build-up algorithm (RUGB)) to build up a protein structure from atomic distance data is presented and provides an effective way of determining a protein structure with sparse exact distance data. In the algorithm, the condition to determine an unpositioned atom iteratively is relaxed (when compared with the UGB algorithm) and data structure techniques are used to make the algorithm more efficient and effective. The algorithm is tested on a set of proteins selected randomly from the Protein Structure Database-PDB. Results We test a set of proteins selected randomly from the Protein Structure Database-PDB. We show that the numerical errors produced by the new RUGB algorithm are smaller when compared with the errors of the UGB algorithm and that the novel RUGB algorithm has a significantly smaller runtime than the UGB algorithm. Conclusions The RUGB algorithm relaxes the condition for updating and incorporates the data structure for accessing neighbours of an atom. The revisions result in an improvement over the UGB algorithm in two important areas: a reduction on the overall runtime and decrease of the numeric error.Peer Reviewe

Distance-based protein structure modeling

Protein structure modeling can be studied based on the knowledge of interactions or distances between pairs of atoms, which is so-called distance-based protein structure modeling and this field includes problems of structure determination and refinement as well as analysis of protein dynamics. The distances for certain pairs of atoms in a protein can often be obtained based on our knowledge on various types of bond-lengths and bond-angles or from physical experiments such as nuclear magnetic resonance (NMR). The coordinates of the atoms and hence the protein structure can then be determined by using the known distances. However, it requires the solution of a mathematical problem called the distance geometry problem, which has been proven to be computationally intractable in general. On the other hand, due to insufficient distance data such as nuclear overhauser effect (NOE) data in NMR, the protein structures determined by conventional techniques usually are not as accurate as desired. Therefore, the uses of such protein structures in important applications including homology modeling and rational drug design have been severely limited. In this work, we have developed several efficient algorithms including theories for the solution of the distance geometry problem using a geometric build-up algorithm. We also introduced a knowledge-based method for protein structure refinement, in which we constructed a dedicated structural database for protein inter-atomic distance distributions and derived so-called mean force potentials to refine NMR-determined protein structures. We have participated in CASPR competition regarding comparative models and reported some substantial improvement using mean force potentials. Finally, an efficient and simple method called Local-DME calculations has been developed to study protein dynamics of NMR ensembles specifically

Algorithms for molecular geometry problems

Orientador: Carlile Campos LavorDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação CientíficaResumo: Neste trabalho, analisamos dois algoritmos da literatura para o "Molecular Distance Geometry Problem" (MDGP) e propomos um novo algoritmo que mantém a qualidade das soluções obtidas pelos dois anteriores e apresenta ganhos em termos de eficiência computacional. O MDGP consiste em determinar as posições dos átomos de uma molécula, no espaço tridimensional, a partir de um conjunto de distâncias entre eles. Quando todas as distâncias são conhecidas, o problema pode ser resolvido em tempo polinomial. Caso contrário, é um problema NP-difícilAbstract: In this work, we analyse two algorithms from the bibliography to solve the so-called "Molecular Distance Geometry Problem" (MDGP). Then, we propose a new algorithm that keeps the quality on the solutions obtained by both the previous ones and shows gains regarding computacional efficiency. The MDGP consists on the determination of positions of atoms in a molecule, on the tridimensional space, from a set containing distances among them. When all the distances are known, the problem might be solved in polynomial time. Otherwise, it is an NP-hard problemMestradoMatemática da ComputaçãoMestre em Matemática Aplicad

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Geometric Build-up Solutions for Protein Determination via Distance Geometry

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between atoms. To introduce the complexities of the MDGP we begin at its origins in distance geometry and progress to the specific sub-problems and some of the solutions that have been developed. This is all in preparation for a discussion of what is known as the Geometric Build-up (GBU) Solution. This solution has lead to the development of several algorithms and continues to be modified to account for more and different complexities. The culmination of this thesis, then, is a new algorithm, the Revised Updated Geometric Build-up, that is faster than previous GBU’s while maintaining the accuracy of the resulting structure

Sphere intersection in R^n and applications

Orientador: Carlile Campos LavorTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Calcular a interseção de esferas n-dimensionais no R^n é um importante problema com aplicações no cálculo de estruturas moleculares em biologia, sistema de posicionamento global (GPS), escalonamento multidimensional e geometria de distâncias. Neste trabalho, generalizamos resultados teóricos e métodos previamente propostos por Coope para o cálculo da interseção de esferas baseado na decomposição QR. Nosso principal resultado descreve a interseção de uma quantidade qualquer de esferas n-dimensionais, em que seus centros não são necessariamente afimente independentes. Também elaboramos um método para calcular a interseção de esferas e uma casca esférica, caso importante relacionado quando há incertezas nos dados do problema. Apresentamos possíveis aplicações para estes métodosAbstract: Finding the intersection of n-dimensional spheres in Rn is a relevant problem with applications in the calculation of molecular structures in biology, global positioning systems (GPS), multidimensional scaling and distance geometry. In this work, we generalize the theorical results and methods previously proposed by Coope for finding the intersection of spheres based on QR decomposition. Our main result describes the intersection of any number of n-dimensional spheres without the assumption that the sphere centers are affinely independent. We also developed a method to finding the intersection of spheres and a spherical shell, an important case related when there are uncertainties in the problem data. We present some possible applications for these methodsDoutoradoMatematica AplicadaDoutor em Matemática AplicadaCAPE