Upper bounds for foldings in the FCC-HP protein model

Predicting the 3D native structure of a protein from its amino acid sequence is known as the protein folding problem. A wide range of simplified protein models have been introduced to approach this problem. The HP model is one of the most popular discrete models in which the number of neighbouring pairs (contacts) of hydrophobic(H) amino acids in the lattice is maximized. Upper bounds on the number of contacts are useful for measuring the quality of solutions produced by heuristic-based approaches and play an important role in approaches based on constructing hydrophobic cores. In, upper bounds have been derived for sequences that contain a given number of hydrophobic amino acids in the face-centered cubic (FCC) lattice based on rectangular grid. In this paper, we present a dynamic programming approach to determine upper bounds by using a similar approach but representing the FCC lattice based on triangular grid. Our results improve on the bounds presented in.