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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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Observed versus expected compositional classes of potentials types I to VI.Compositional classes correspond to set of sequences with a given fraction of  and  monomers. A given compositional class contains 18- monomers type . Expected number of sequences per compositional class are estimated by sampling, for a given potential ,  random sequences from genotype space. Error bars represent one standard deviation from the mean. Colors code each potential type according to Fig. 3 and Table 1.
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pcbi-1003946-g006: Observed versus expected compositional classes of potentials types I to VI.Compositional classes correspond to set of sequences with a given fraction of and monomers. A given compositional class contains 18- monomers type . Expected number of sequences per compositional class are estimated by sampling, for a given potential , random sequences from genotype space. Error bars represent one standard deviation from the mean. Colors code each potential type according to Fig. 3 and Table 1.

Mentions: Sequences can be classified according to their composition into classes. Compositional classes correspond to the frequency of the relative fraction of monomers across non-degenerate sequences induced by a given potential. In the case of maps composed of binary potentials, compositional classes distribute binomially. If all 2 sequences in the L18 model were non-degenerate, there would be 19 compositional classes, ranging from the unique two sequences composed of only one of the two monomer types (compositional classes 0 and 18 in Fig. 6; with 0 and 100 of monomer , respectively) to 48,620 sequences composed of 50 of each monomer (compositional class 9).


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

Ferrada E - PLoS Comput. Biol. (2014)

Observed versus expected compositional classes of potentials types I to VI.Compositional classes correspond to set of sequences with a given fraction of  and  monomers. A given compositional class contains 18- monomers type . Expected number of sequences per compositional class are estimated by sampling, for a given potential ,  random sequences from genotype space. Error bars represent one standard deviation from the mean. Colors code each potential type according to Fig. 3 and Table 1.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g006: Observed versus expected compositional classes of potentials types I to VI.Compositional classes correspond to set of sequences with a given fraction of and monomers. A given compositional class contains 18- monomers type . Expected number of sequences per compositional class are estimated by sampling, for a given potential , random sequences from genotype space. Error bars represent one standard deviation from the mean. Colors code each potential type according to Fig. 3 and Table 1.
Mentions: Sequences can be classified according to their composition into classes. Compositional classes correspond to the frequency of the relative fraction of monomers across non-degenerate sequences induced by a given potential. In the case of maps composed of binary potentials, compositional classes distribute binomially. If all 2 sequences in the L18 model were non-degenerate, there would be 19 compositional classes, ranging from the unique two sequences composed of only one of the two monomer types (compositional classes 0 and 18 in Fig. 6; with 0 and 100 of monomer , respectively) to 48,620 sequences composed of 50 of each monomer (compositional class 9).

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