A Lattice Statistical Mechanics Model of the Conformational and Sequence Spaces of Proteins

We develop theory to explore the relationship between the amino acid sequence of a protein and its native structure. A protein is modeled as a specific sequence of H (nonpolar) and P (polar) residues, subject to excluded volume and an HH attraction free energy ε. Exhaustive exploration of the full conformational space is computationally possible because molecules are modeled as short chains on a 2D square lattice. We use this model to test approximations in a recent mean-field theory of protein stability. Also, exhaustive exploration permits us to identify the “native” state(s) in the model, the conformation(s) of global free energy minimum. We then explore the relationship between sequences and native structures by (i) further exhaustive exploration of the full space of all sequences, for short chains, and (ii) random selection of sequences, for longer chains, in some cases exploring exhaustively only the fully compact conformations. The model has the following properties. For small ε, the chains are unfolded. With increasing HH attraction, molecules with certain sequences fold to a state with relatively few conformations that have (i) low free energy, (ii) high compactness, (iii) a core of H residues, and (iv) substantial secondary structure. The potential of a molecule to fold to this state is predicted largely by the composition, but for intermediate compositions it depends also on the specific sequence of residues. Some folding sequences have multiple native states; those native structures are broadly distributed throughout the conformational space. However, a most interesting prediction is that, even with only the H and P discrimination among residues in this model, a folding sequence is most likely to have only a single native conformation, a predominance that increases with chain length.