Simplified Lattice Models for Protein Structure Prediction: How Good Are They?

In this paper, we present a local search framework for lattice fit problem of proteins. Our algorithm significantly improves state-of-the-art results and justifies the significance of the lattice models. In addition to these, our analysis reveals the weakness of several energy functions used. A protein folds into a three dimensional native structure that has the minimum free energy. This structure is unique, stable and essential for its proper functioning. Knowledge about this structure is of paramount importance, since it can have an enormous impact on the field of rational drug design. The in vitro methods for Protein structure prediction (PSP) are slow and expensive. Computational methods have been used to solve this problem for more than thirty years. One of the challenges for solving PSP is the unknown nature of the energy function. Moreover, the all-atomic details of structures require huge computational power. For these reasons, researchers preferred to model the problem in a simplified way by restricting the locations of the amino acids of the proteins to discrete lattice points (cubic or face-centered) and search is guided by a simple energy function that considers the contact potentials (Miyazawa and Jernigan 1985; Berrera, Molinari, and Fogolari 2003; Lau and Dill 1989). A lattice L is a set of points in Z where the points are integral linear combinations of given N basis vectors. Two lattice points p, q L are said to be in contact or neighbors of each other, if q = p+~ vi for some vector ~vi in the basis of L. Every two consecutive amino acid monomers in the sequence are in contact (connectivity constraint) and two amino acids can not occupy same point in the lattice (self avoiding walk constraint). For any given protein sequence s, the free energy of a structure c is calculated by the following equation: