The Amino Acid Alphabet and the Architecture of the Protein Sequence-Structure Map. I. Binary Alphabets

The correspondence between protein sequences and structures, or sequence-structure map, relates to fundamental aspects of structural, evolutionary and synthetic biology. The specifics of the mapping, such as the fraction of accessible sequences and structures, or the sequences' ability to fold fast, are dictated by the type of interactions between the monomers that compose the sequences. The set of possible interactions between monomers is encapsulated by the potential energy function. In this study, I explore the impact of the relative forces of the potential on the architecture of the sequence-structure map. My observations rely on simple exact models of proteins and random samples of the space of potential energy functions of binary alphabets. I adopt a graph perspective and study the distribution of viable sequences and the structures they produce, as networks of sequences connected by point mutations. I observe that the relative proportion of attractive, neutral and repulsive forces defines types of potentials, that induce sequence-structure maps of vastly different architectures. I characterize the properties underlying these differences and relate them to the structure of the potential. Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence. I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins. I discuss implications of these observations for the architecture of the sequence-structure map of natural proteins, the construction of random libraries of peptides, and the early evolution of the natural amino acid alphabet.Author Summary: If we were to design a proteome, what types and what proportion of amino acids would we use in order to optimize properties such as the diversity of sequences and structures, their robustness to mutations, or their ability to fold efficiently? Here, I use simple models to study the sequence-structure map of proteins from a design and evolutionary perspective. These models can be used to explore all sequences and structures, as a function of the types of interactions encoded by the sequence. I study the range of possible binary interactions between monomers, which include natural and artificial amino acids. The results indicate that different amino acid compositions induce vastly different sequences-structure maps. I classify and study the properties of these maps and relate their features back to the type of energy interactions. I compare these observations to the types of interactions observed in natural amino acids. My observations provide insights for our current view of the sequence-structure map of natural proteins, guiding principles for the construction of random libraries of peptides, and suggests constraints for the early evolution of the natural amino acid alphabet.