Date Published: December 4, 2014
Publisher: Public Library of Science
Author(s): Evandro Ferrada, Erich Bornberg-Bauer
Abstract: 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.
Partial Text: The implications of understanding the properties and organization of the sequence-structure map of proteins are broad, they range from explaining the diversity of known protein folds in the context of cellular physiology and their evolution , synthesize molecules of biomedical or industrial interest , to engineer polymers  and proteomes de novo.
In order to explore the impact of the potential on the architecture of the sequence-structure map of natural proteins, I concentrate on the L18 model and binary alphabets. The computational tractability of this model allows us to study exact statistics of a large sample of potentials.
A graph theoretic approach, inspired on the concept of genotype-phenotype map, provides a common quantitative framework to investigate the sequence-structure relation. According to this framework, viable genotypes are represented as nodes, and edges connect genotypes that differ in a single position along the sequence. The distinction of genotypes according to the phenotypes they map onto, induces subgraphs whose properties and distribution have important consequences for biology. These subgraphs can be characterized quantitatively in terms of the statistics of their expected sizes, diameters and distances. I refer to this detailed characterization of the sequence-structure map, as its architecture.