Sequence Correlations in HP Model Proteins

Abstract: Amino acids that are in close contact in a protein structure tend to co-evolve, which gives rise to sequence correlations. Direct coupling analysis (DCA) is a method for predicting such contacts directly from sequence correlations, without assuming any prior knowledge of structures. To this end, sequence correlations are modeled using an Ising-like ansatz, whose couplings are determined through an inverse statistical-mechanical calculation. In this work, the problem of predicting contacts from sequence correlations is investigated in a minimal lattice-based protein model with only two amino acid types, hydrophobic (H) and polar (P). A structure for chain length 30 is considered, which is known from previous work to represent the minimum-energy state of 813 distinct HP sequences. Raw sequence correlations (covariances and Pearson correlations) are analyzed, and a DCA procedure is implemented. It turns out that the five largest couplings from the DCA calculation correspond to nearest-neighbor contacts in the known structure. Unfortunately, these five couplings are not well separated from the other ones. On the other hand, knowledge of this limited set of contacts is essentially sufficient to infer the entire structure of these HP sequences.