Fast Computation of the Fitness Function for Protein Folding Prediction in a 2D Hydrophobic-Hydrophilic Model

Protein Folding Prediction (PFP) is essentially an energy minimization problem formalised by the definition of a fitness function. Several PFP models have been proposed including the Hydrophobic-Hydrophilic (HP) model, which is widely used as a test-bed for evaluating new algorithms. The calculation of the fitness is the major computational task in determining the native conformation of a protein in the HP model and this paper presents a new efficient search algorithm (ESA) for deriving the fitness value requiring only O(n) complexity in contrast to the full search approach, which takes O(n2). The improved efficiency of ESA is achieved by exploiting some intrinsic properties of the HP model, with a resulting reduction of more than 50% in the overall time complexity when compared with the previously reported Caching Approach, with the added benefit that the additional space complexity is linear instead of quadratic

Long Proteins with Unique Optimal Foldings in the H-P Model

It is widely accepted that (1) the natural or folded state of proteins is a global energy minimum, and (2) in most cases proteins fold to a unique state determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic) model is a simple combinatorial model designed to answer qualitative questions about the protein folding process. In this paper we consider a problem suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P model have unique optimal (minimum energy) foldings? In particular, we prove that there are closed chains of monomers (amino acids) with this property for all (even) lengths; and that there are open monomer chains with this property for all lengths divisible by four.Comment: 22 pages, 18 figure

A Multi-Dimensional Width-Bounded Geometric Separator and its Applications to Protein Folding

We used a divide-and-conquer algorithm to recursively solve the two-dimensional problem of protein folding of an HP sequence with the maximum number of H-H contacts. We derived both lower and upper bounds for the algorithmic complexity by using the newly introduced concept of multi-directional width-bounded geometric separator. We proved that for a grid graph G with n grid points P, there exists a balanced separator A subseteq P$ such that A has less than or equal to 1.02074 sqrt{n} points, and G-A has two disconnected subgraphs with less than or equal to {2over 3}n nodes on each subgraph. We also derive a 0.7555sqrt {n} lower bound for our balanced separator. Based on our multidirectional width-bounded geometric separator, we found that there is an O(n^{5.563sqrt{n}}) time algorithm for the 2D protein folding problem in the HP model. We also extended the upper bound results to rectangular and triangular lattices

On a Generalized Levinthal's Paradox: The Role of Long- and Short Range Interactions in Complex Bio-molecular Reactions, Including Protein and DNA Folding

The current protein folding literature is reviewed. Two main approaches to the problem of folding were selected for this review: geometrical and biophysical. The geometrical approach allows the formulation of topological restrictions on folding, that are usually not taken into account in the construction of physical models. In particular, the topological constraints do not allow the known funnel-like energy landscape modeling, although most common methods of resolving the paradox are based on this method. The very paradox is based on the fact that complex molecules must reach their native conformations (complexes that result from reactions) in an exponentially long time, which clearly contradicts the observed experimental data. In this respect we considered the complexity of the reactions between ligands and proteins. On this general basis, the folding-reaction paradox was reformulated and generalized. We conclude that prospects for solving the paradox should be associated with incorporating a topology aspect in biophysical models of protein folding, through the construction of hybrid models. However, such models should explicitly include long-range force fields and local cell biological conditions, such as structured water complexes and photon/phonon/soliton waves, ordered in discrete frequency bands. In this framework, collective and coherent oscillations in, and between, macromolecules are instrumental in inducing intra- and intercellular resonance, serving as an integral guiding network of life communication: the electrome aspect of the cell. Yet, to identify the actual mechanisms underlying the bonds between molecules (atoms), it will be necessary to perform dedicated experiments to more definitely solve the particular time paradox. © 2017 Elsevier Ltd.The present results were partially obtained in the frame of state task of Ministry of Education and Science of Russia 1.4539.2017/8.9

Um algoritmo genético paralelo para o problema de dobramento de proteínas utilizando o modelo 3DHP com cadeia lateral

This work presents a parallel genetic algorithm (PGA) for the protein folding problem, using the 3DHP-SC model. This model has been sparsely studied in the literature due to its complexity. A new fitness function was proposed, based on the free-energy and compacity of the folding. Special genetic operators were developed, besides strategies to aid the algorithm in the search of protein conformations. Many experiments were done to adjust all the parameters of the system, including the basic parameters of the GA (mutation and crossover probability, and tournament size) and parameters of the special genetic operators and strategies. The effect of the energy matrix of the model in the performance of the algorithm was also studied. Moreover, a comparison with other evolutionary computation approach was done, to verify the performance of the proposed method. Since there is no benchmark available to date, a set of 25 sequences was used, based on a simpler model. Results show that the PGA achieved a good level of efficiency and obtained biologically coherent results, suggesting its adequacy for the problem.CNPqEste trabalho apresenta um algoritmo genético paralelo (AGP) para o problema de dobramento de proteínas, utilizando o modelo 3DHP-SC. Este modelo tem sido pouco abordado devido ao elevado grau de complexidade envolvido. Foi proposta uma função de fitness baseada na energia livre e na compacidade do dobramento. Operadores genéticos especiais foram desenvolvidos, além de estratégias para auxiliar o algoritmo no processo de busca de conformações de proteínas. Vários experimentos foram realizados para ajustar todos os parâmetros do sistema, incluindo os parâmetros básicos do AG (probabilidades de mutação e crossover, e o tamanho de torneio) e os parâmetros dos operadores especiais e das estratégias. O efeito da matriz de energias para o modelo no desempenho do algoritmo também foi estudado. Uma comparação com outra abordagem de computação evolucionária também foi realizada, a fim de verificar o desempenho do método proposto. Devido a não existir, até então, benchmarks para teste deste modelo, foi proposto um conjunto de 25 sequências baseado em outro modelo mais simplificado. Os resultados obtidos mostraram que o AGP alcançou um bom nível de eficiência e obteve dobramentos biologicamente coerentes, sugerindo a adequabilidade da metodologia proposta

Algorithms for string and graph layout

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 121-125).Many graph optimization problems can be viewed as graph layout problems. A layout of a graph is a geometric arrangement of the vertices subject to given constraints. For example, the vertices of a graph can be arranged on a line or a circle, on a two- or three-dimensional lattice, etc. The goal is usually to place all the vertices so as to optimize some specified objective function. We develop combinatorial methods as well as models based on linear and semidefinite programming for graph layout problems. We apply these techniques to some well-known optimization problems. In particular, we give improved approximation algorithms for the string folding problem on the two- and three-dimensional square lattices. This combinatorial graph problem is motivated by the protein folding problem, which is central in computational biology. We then present a new semidefinite programming formulation for the linear ordering problem (also known as the maximum acyclic subgraph problem) and show that it provides an improved bound on the value of an optimal solution for random graphs. This is the first relaxation that improves on the trivial "all edges" bound for random graphs.by Alantha Newman.Ph.D