Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks

The Noncompacted Folding of Proteins by Modified Elastic Net Algorithm

In this article, a protein sequence of length n is embedded in a two-dimensional lattice with m (>n) points. Thus the obtained minimal energy configurations are expected to have flexible shapes in contrast to the compact rectangular conformations. To fulfill this extension, the elastic net algorithm is modified to deal with the difficulty brought by the unsymmetrical relationship between amino acids and lattice points. New set partition strategy in the embedding phase is introduced, and two local search methods are applied to overcome the multimapping phenomena. Several HP benchmark examples with up to 48 amino acids are tested to verify the effectiveness of the proposed approach.

Optimal HP configurations of proteins by combining local search with elastic net algorithm

The prediction of protein conformation from its amino-acid sequence is one of the most prominent problems in computational biology. But it is NP-hard. Here, we focus on an abstraction widely studied of this problem, the two-dimensional hydrophobic-polar protein folding problem (2D HP PFP). Mathematical optimal model of free energy of protein is established. Native conformations are often sought using stochastic sampling methods, but which are slow. The elastic net (EN) algorithm is one of fast deterministic methods as travelling salesman problem (TSP) strategies. However, it cannot be applied directly to protein folding problem, because of fundamental differences in the two types of problems. In this paper, how the 2D HP protein folding problem can be framed in terms of TSP is shown. Combination of the modified elastic net algorithm and novel local search method is adopted to solve this problem. To our knowledge, this is the first application of EN algorithm to 2D HP model. The results indicate that our approach can find more optimal conformations and is simple to implement, computationally efficient and fast.

The simulation of the three-dimensional lattice hydrophobic-polar protein folding

One of the most prominent problems in computational biology is to predict the natural conformation of a protein from its amino acid sequence. This paper focuses on the three-dimensional hydrophobic-polar (HP) lattice model of this problem. The modified elastic net (EN) algorithm is applied to solve this nonlinear programming hard problem. The lattice partition strategy and two local search methods (LS(1) and LS(2)) are proposed to improve the performance of the modified EN algorithm. The computation and analysis of 12 HP standard benchmark instances are also involved in this paper. The results indicate that the hybrid of modified EN algorithm, lattice partition strategy, and local search methods has a greater tendency to form a globular state than genetic algorithm does. The results of noncompact model are more natural in comparison with that of compact model.

Unique optimal foldings of proteins on a triangular lattice

BACKGROUND

A problem for unique protein folding was raised in 1998: are there proteins having unique optimal foldings for all lengths in the hydrophobic-hydrophilic (hydrophobic-polar; HP) model? To such a question, it was proved that on a square lattice there are (i) closed chains of monomers having unique optimal foldings for all even lengths and (ii) open monomer chains having unique optimal foldings for all lengths divisible by four. In this article, we aim to extend the previous work on a square lattice to the optimal foldings of proteins on a triangular lattice by examining the uniqueness property or stability of HP chain folding.

METHOD

We consider this protein folding problem on a triangular lattice using graph theory. For an HP chain with length n > 13, generally it is very time-consuming to enumerate all of its possible folding conformations. Hence, one can hardly know whether or not it has a unique optimal folding. A natural problem is to determine for what value of n there is an n-node HP chain that has a unique optimal folding on a triangular lattice.

RESULTS AND CONCLUSION

Using graph theory, this article proves that there are both closed and open chains having unique optimal foldings for all lengths >19 in a triangular lattice. This result is not only general from the theoretical viewpoint, but also can be expected to apply to areas of protein structure prediction and protein design because of their close relationship with the concept of energy state and designability.

Exploring protein's optimal HP configurations by self-organizing mapping

Self-organizing map (SOM) has been used in protein folding prediction when the HP model is employed. The existing work uses a square-like shape lattice with l = m x n points to represent the optimal compact structure of a sequence of l amino acids. In this paper, a general l'-size sequence of amino acids is self-organized in a two dimensional lattice with l (> l') points. The obtained minimum configuration then has a flexible shape, in contrast to the compact structure limited in the lattice. To fulfil this extension, a new self-organizing map (SOM) technique is proposed to deal with the difficulty of the unsymmetric input and output spaces. New competition rules in the training phase are introduced and a local search method is applied to overcome the multi-mapping phenomena. Several HP benchmark examples with up to 36 amino acids are tested to verify the effectiveness of the proposed approach in this paper.