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

Modeling and predicting all-α transmembrane proteins including helix–helix pairing

AbstractModeling and predicting the structure of proteins is one of the most important challenges of computational biology. Exact physical models are too complex to provide feasible prediction tools and other ab initio methods only use local and probabilistic information to fold a given sequence. We show in this paper that all-α transmembrane protein secondary and super-secondary structures can be modeled with a multi-tape S-attributed grammar. An efficient structure prediction algorithm using both local and global constraints is designed and evaluated. Comparison with existing methods shows that the prediction rates as well as the definition level are sensibly increased. Furthermore this approach can be generalized to more complex proteins

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

Approximation Algorithms For Protein Folding Prediction

We present a new polynomial-time algorithm for the protein folding problem in the two-dimensional HP model introduced by Dill [1], which has been recently proved to be NP-hard [2]. The model abstracts one of the dominant forces of protein folding: the hydrophobic-hydrophilic interaction. Thus, proteins are modeled as binary strings on the alphabet fH, Pg, representing chains of hydrophobic and hydrophilic monomers. The problem is to find, given a string s, the two-dimensional structure that minimizes a given energy function. Our idea is the following: describe a class of feasible structures by means of an ambiguous contextfree grammar (i.e. there is a bijection between the set of parse trees and a subset of possible structures); give a score to every production of the grammar, so that the total score of every parse tree (the sum of the scores of the productions of the tree) is an upper bound on the energy of the corresponding structure; apply a parsing algorithm to find the parse tree..