Flexible protein folding by ant colony optimization

Protein structure prediction is one of the most challenging topics in bioinformatics. As the protein structure is found to be closely related to its functions, predicting the folding structure of a protein to judge its functions is meaningful to the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice model. Different from the previous ant algorithms for PFPs, the pheromones in the proposed algorithm are placed on the arcs connecting adjacent squares in the lattice. Such pheromone placement model is similar to the one used in the traveling salesmen problems (TSPs), where pheromones are released on the arcs connecting the cities. Moreover, the collaboration of effective heuristic and pheromone strategies greatly enhances the performance of the algorithm so that the algorithm can achieve good results without local search methods. By testing some benchmark two-dimensional hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed algorithm is quite competitive compared with some other well-known methods for solving the same protein folding problems

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

Exploring the HP Model for Protein Folding

We explore the HP model not only on the square lattice as originally proposed by Ken Dill, but we also use the triangular lattice. We find upper and lower bounds on the number of self-avoiding walks. In the square lattice, we get O(b^n) for some b in [2.414, 3]. We count the number of all self-avoiding walks of length up to 16 in the square and triangular lattices by exhaustively listing them. We use these lists of self-avoiding walks to study two HP sequences, one of length 11, and the other of length 16. We show that the diameter of the convex hull of a conformation can be used as an estimate of the energy of the conformation. Our examples demonstrate that the same holds true for the area of the convex hull. Both of these measures can be easily computed for a given conformation

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

New evolutionary approaches to protein structure prediction

Programa de doctorado en Biotecnología y Tecnología QuímicaThe problem of Protein Structure Prediction (PSP) is one of the principal topics in Bioinformatics. Multiple approaches have been developed in order to predict the protein structure of a protein. Determining the three dimensional structure of proteins is necessary to understand the functions of molecular protein level. An useful, and commonly used, representation for protein 3D structure is the protein contact map, which represents binary proximities (contact or non-contact) between each pair of amino acids of a protein. This thesis work, includes a compilation of the soft computing techniques for the protein structure prediction problem (secondary and tertiary structures). A novel evolutionary secondary structure predictor is also widely described in this work. Results obtained confirm the validity of our proposal. Furthermore, we also propose a multi-objective evolutionary approach for contact map prediction based on physico-chemical properties of amino acids. The evolutionary algorithm produces a set of decision rules that identifies contacts between amino acids. The rules obtained by the algorithm impose a set of conditions based on amino acid properties in order to predict contacts. Results obtained by our approach on four different protein data sets are also presented. Finally, a statistical study was performed to extract valid conclusions from the set of prediction rules generated by our algorithm.Universidad Pablo de Olavide. Centro de Estudios de Postgrad