Limits...
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.

Show MeSH
Ratio between expected size of sequence clusters for different types of potentials.(A) Ratio between the expected size of genotype components () and neutral networks () in black. Ratio between the expected size of genotype components () and neutral sets () in blue. (B) Ratio between the expected size of neutral sets () and the expected size of neutral networks (). Color code as in Fig. 3 and Table 1. The expected size of a cluster of sequence is calculated as the weighted average of sequences per cluster size (see main text).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4256021&req=5

pcbi-1003946-g010: Ratio between expected size of sequence clusters for different types of potentials.(A) Ratio between the expected size of genotype components () and neutral networks () in black. Ratio between the expected size of genotype components () and neutral sets () in blue. (B) Ratio between the expected size of neutral sets () and the expected size of neutral networks (). Color code as in Fig. 3 and Table 1. The expected size of a cluster of sequence is calculated as the weighted average of sequences per cluster size (see main text).

Mentions: The ratio of the expected size of different sequence clusters shows that genotype components are approximately 1,000 to 3,000 fold larger than the expected size of an average neutral set across potentials (/1,000–3,000) (Figure 10A). Although in general the expected size of an average neutral network follows a similar proportion, potentials type II and V, show large deviations, with genotype components: / 9,000 to 12,000 fold larger than the expected size of neutral networks. These ratios are particularly well conserved across potentials type V (Fig. 10A).


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

Ferrada E - PLoS Comput. Biol. (2014)

Ratio between expected size of sequence clusters for different types of potentials.(A) Ratio between the expected size of genotype components () and neutral networks () in black. Ratio between the expected size of genotype components () and neutral sets () in blue. (B) Ratio between the expected size of neutral sets () and the expected size of neutral networks (). Color code as in Fig. 3 and Table 1. The expected size of a cluster of sequence is calculated as the weighted average of sequences per cluster size (see main text).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g010: Ratio between expected size of sequence clusters for different types of potentials.(A) Ratio between the expected size of genotype components () and neutral networks () in black. Ratio between the expected size of genotype components () and neutral sets () in blue. (B) Ratio between the expected size of neutral sets () and the expected size of neutral networks (). Color code as in Fig. 3 and Table 1. The expected size of a cluster of sequence is calculated as the weighted average of sequences per cluster size (see main text).
Mentions: The ratio of the expected size of different sequence clusters shows that genotype components are approximately 1,000 to 3,000 fold larger than the expected size of an average neutral set across potentials (/1,000–3,000) (Figure 10A). Although in general the expected size of an average neutral network follows a similar proportion, potentials type II and V, show large deviations, with genotype components: / 9,000 to 12,000 fold larger than the expected size of neutral networks. These ratios are particularly well conserved across potentials type V (Fig. 10A).

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