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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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Foldability as a function of a potential's additivity.Foldability was calculated using Eq. 2. Additivity, as described in Models. Values refer to the median foldability across non-degenerate sequences for a given potential. Shaded circles correspond to a single potential colored as defined in the legend (see Fig. 3 and Table 1). Black dots represent potentials type VI. Dashed lines illustrate additive potentials (; ).
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pcbi-1003946-g012: Foldability as a function of a potential's additivity.Foldability was calculated using Eq. 2. Additivity, as described in Models. Values refer to the median foldability across non-degenerate sequences for a given potential. Shaded circles correspond to a single potential colored as defined in the legend (see Fig. 3 and Table 1). Black dots represent potentials type VI. Dashed lines illustrate additive potentials (; ).

Mentions: Evidence from the theory of protein folding relates foldability to cooperativity or the non-additivity of interactions [15]. In the context of binary potentials, I measure additivity () as deviations of excess from the ideal part of the potential (see Models). Figure 12 presents the median across all non-degenerate sequences of each sequence-structure map, as a function of . In the case of a completely additive potential: (dashed lined at ).


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

Ferrada E - PLoS Comput. Biol. (2014)

Foldability as a function of a potential's additivity.Foldability was calculated using Eq. 2. Additivity, as described in Models. Values refer to the median foldability across non-degenerate sequences for a given potential. Shaded circles correspond to a single potential colored as defined in the legend (see Fig. 3 and Table 1). Black dots represent potentials type VI. Dashed lines illustrate additive potentials (; ).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g012: Foldability as a function of a potential's additivity.Foldability was calculated using Eq. 2. Additivity, as described in Models. Values refer to the median foldability across non-degenerate sequences for a given potential. Shaded circles correspond to a single potential colored as defined in the legend (see Fig. 3 and Table 1). Black dots represent potentials type VI. Dashed lines illustrate additive potentials (; ).
Mentions: Evidence from the theory of protein folding relates foldability to cooperativity or the non-additivity of interactions [15]. In the context of binary potentials, I measure additivity () as deviations of excess from the ideal part of the potential (see Models). Figure 12 presents the median across all non-degenerate sequences of each sequence-structure map, as a function of . In the case of a completely additive potential: (dashed lined at ).

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