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The amino acid alphabet and the architecture of the protein sequence-structure map. I. Binary alphabets.

Ferrada E - PLoS Comput. Biol. (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Santa Fe Institute, Santa Fe, New Mexico, United States of America.

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.

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Potentials for the canonical HP and AB models.(A) General structure of a binary potential, composed of monomers  and . Potentials of the HP model (B), AB model (C), HP shifted (D), AB shifted (E).
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pcbi-1003946-g002: Potentials for the canonical HP and AB models.(A) General structure of a binary potential, composed of monomers and . Potentials of the HP model (B), AB model (C), HP shifted (D), AB shifted (E).

Mentions: A binary potential can be represented as a vector composed of 3 values, that describe 2 types of interactions (Figure 2A). First, those between the same type of monomers, or homomonomeric (i.e., ); and second, the heteromonomeric interaction (i.e.). The heteromonomeric interaction of a binary potential can be decomposed into ideal and excess parts [12], [30]. These parts describe the extent to which the potential favors two different hypothetical stages of the folding process. The ideal part represents an heteromonomeric interaction as in an ideal liquid. That is, as if there was no energetic contribution by the heteromonomeric interaction, and therefore it could just be approximated by the arithmetic mean of their homomonomeric values, as:  = (+)/2. In contrast, the excess part ( =  - ), aims to capture the contribution of the heteromonomeric interaction, and describe the extent to which the native conformation differs from an ideal mixture of amino acids, its additivity (). Here, I quantify the additivity of a given potential as:  = [E/E]+1 = /E.


The amino acid alphabet and the architecture of the protein sequence-structure map. I. Binary alphabets.

Ferrada E - PLoS Comput. Biol. (2014)

Potentials for the canonical HP and AB models.(A) General structure of a binary potential, composed of monomers  and . Potentials of the HP model (B), AB model (C), HP shifted (D), AB shifted (E).
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4256021&req=5

pcbi-1003946-g002: Potentials for the canonical HP and AB models.(A) General structure of a binary potential, composed of monomers and . Potentials of the HP model (B), AB model (C), HP shifted (D), AB shifted (E).
Mentions: A binary potential can be represented as a vector composed of 3 values, that describe 2 types of interactions (Figure 2A). First, those between the same type of monomers, or homomonomeric (i.e., ); and second, the heteromonomeric interaction (i.e.). The heteromonomeric interaction of a binary potential can be decomposed into ideal and excess parts [12], [30]. These parts describe the extent to which the potential favors two different hypothetical stages of the folding process. The ideal part represents an heteromonomeric interaction as in an ideal liquid. That is, as if there was no energetic contribution by the heteromonomeric interaction, and therefore it could just be approximated by the arithmetic mean of their homomonomeric values, as:  = (+)/2. In contrast, the excess part ( =  - ), aims to capture the contribution of the heteromonomeric interaction, and describe the extent to which the native conformation differs from an ideal mixture of amino acids, its additivity (). Here, I quantify the additivity of a given potential as:  = [E/E]+1 = /E.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Santa Fe Institute, Santa Fe, New Mexico, United States of America.

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.

Show MeSH