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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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Distribution of expected size of clusters of sequences in genotype space for potentials type I-VI.For each sequence-structure map , generated by potential , plots present the expected size of sequence clusters  (), where x is:  or  (see main text). Panels present the relative distribution of  for potentials type I-VI. Distributions are normalized by , the non-degeneracy of sequence-structure map . Color code according to Fig. 3 and Table 1. Insets, relative distribution of expected size of genotype components (), normalized by the total number of non-degenerate sequences ( = ).
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pcbi-1003946-g008: Distribution of expected size of clusters of sequences in genotype space for potentials type I-VI.For each sequence-structure map , generated by potential , plots present the expected size of sequence clusters (), where x is: or (see main text). Panels present the relative distribution of for potentials type I-VI. Distributions are normalized by , the non-degeneracy of sequence-structure map . Color code according to Fig. 3 and Table 1. Insets, relative distribution of expected size of genotype components (), normalized by the total number of non-degenerate sequences ( = ).

Mentions: Figure 8 shows the distributions of and per type of potential. In order to compare maps generated by different potentials, I scale expected size by non-degeneracy (see legend of Fig. 8). Potentials type I, II and V, show genotype components that span on average 97, 99 and 93% of non-degenerate sequences, respectively (insets Fig. 8I, II, V). Note, however, that these distributions of expected size are generally due to the presence of a large genotype component. Figure S9 shows the distribution of the diameter () of genotype components per type of potential (see Models). While 60 to 90% of genotype components of potentials are composed of a single sequence ( = 0), all types of potentials show at least one large spanning genotype component ( = 18) (Fig. S9).


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

Ferrada E - PLoS Comput. Biol. (2014)

Distribution of expected size of clusters of sequences in genotype space for potentials type I-VI.For each sequence-structure map , generated by potential , plots present the expected size of sequence clusters  (), where x is:  or  (see main text). Panels present the relative distribution of  for potentials type I-VI. Distributions are normalized by , the non-degeneracy of sequence-structure map . Color code according to Fig. 3 and Table 1. Insets, relative distribution of expected size of genotype components (), normalized by the total number of non-degenerate sequences ( = ).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g008: Distribution of expected size of clusters of sequences in genotype space for potentials type I-VI.For each sequence-structure map , generated by potential , plots present the expected size of sequence clusters (), where x is: or (see main text). Panels present the relative distribution of for potentials type I-VI. Distributions are normalized by , the non-degeneracy of sequence-structure map . Color code according to Fig. 3 and Table 1. Insets, relative distribution of expected size of genotype components (), normalized by the total number of non-degenerate sequences ( = ).
Mentions: Figure 8 shows the distributions of and per type of potential. In order to compare maps generated by different potentials, I scale expected size by non-degeneracy (see legend of Fig. 8). Potentials type I, II and V, show genotype components that span on average 97, 99 and 93% of non-degenerate sequences, respectively (insets Fig. 8I, II, V). Note, however, that these distributions of expected size are generally due to the presence of a large genotype component. Figure S9 shows the distribution of the diameter () of genotype components per type of potential (see Models). While 60 to 90% of genotype components of potentials are composed of a single sequence ( = 0), all types of potentials show at least one large spanning genotype component ( = 18) (Fig. S9).

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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