Is protein folding problem really a NP-complete one ? First investigations

To determine the 3D conformation of proteins is a necessity to understand their functions or interactions with other molecules. It is commonly admitted that, when proteins fold from their primary linear structures to their final 3D conformations, they tend to choose the ones that minimize their free energy. To find the 3D conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a NP complete one. More precisely, to determine the backbone structure of the protein using the low resolution models (2D HP square and 3D HP cubic), by finding the conformation that minimize free energy, is intractable exactly. Both the proof of NP-completeness and the 2D prediction consider that acceptable conformations have to satisfy a self-avoiding walk (SAW) requirement, as two different amino acids cannot occupy a same position in the lattice. It is shown in this document that the SAW requirement considered when proving NP-completeness is different from the SAW requirement used in various prediction programs, and that they are different from the real biological requirement. Indeed, the proof of NP completeness and the predictions in silico consider conformations that are not possible in practice. Consequences of this fact are investigated in this research work.Comment: Submitted to Journal of Bioinformatics and Computational Biology, under revie

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

Protein folding in hydrophobic-polar lattice model: a flexible ant colony optimization approach

This paper proposes a flexible ant colony (FAC) algorithm for solving protein folding problems based on the hydrophobic-polar square lattice model. Collaborations of novel pheromone and heuristic strategies in the proposed algorithm make it more effective in predicting structures of proteins compared with other state-of-the-art algorithms

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