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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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A two-dimensional caricature of a genotype network ().Sequences are represented as nodes. Edges are drawn between sequences that differ in 1 mutation. Degenerate sequences (1) are in grey, open squares. In this example,  = 192 nodes;  = 84 nodes;  = 0.43.  is composed of 3 genotype components ( = ()). Top left,  = 53; top right,  = 24; bottom,  = 7. Non-degenerate sequences in this example, fold onto 5 phenotypes represented by the neutral sets in colors blue,  = 12; green,  = 19; orange,  = 15; magenta,  = 23; and yellow,  = 15. Genotype components  and  are composed of more than 1 neutral network.  = {} and  = {}. Phenotype 1 (blue) can be found in genotype components  and :  = {}. Phenotype 2 (orange) can be found in all three genotype components:  = {}. Genotype component , is also a neutral network: .
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pcbi-1003946-g001: A two-dimensional caricature of a genotype network ().Sequences are represented as nodes. Edges are drawn between sequences that differ in 1 mutation. Degenerate sequences (1) are in grey, open squares. In this example,  = 192 nodes;  = 84 nodes;  = 0.43. is composed of 3 genotype components ( = ()). Top left,  = 53; top right,  = 24; bottom,  = 7. Non-degenerate sequences in this example, fold onto 5 phenotypes represented by the neutral sets in colors blue,  = 12; green,  = 19; orange,  = 15; magenta,  = 23; and yellow,  = 15. Genotype components and are composed of more than 1 neutral network.  = {} and  = {}. Phenotype 1 (blue) can be found in genotype components and :  = {}. Phenotype 2 (orange) can be found in all three genotype components:  = {}. Genotype component , is also a neutral network: .

Mentions: The non-degenerate fraction of sequence space induced by , can be treated as a network of genotypes () (Figure 1). Sequences are nodes, and edges are formed between pairs of sequences that differ in one point mutation (h(,) = 1). When two nodes in can be connected by a series of single point mutations, we say there is a mutational path () between them. The diameter of a graph corresponds to its largest .


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

Ferrada E - PLoS Comput. Biol. (2014)

A two-dimensional caricature of a genotype network ().Sequences are represented as nodes. Edges are drawn between sequences that differ in 1 mutation. Degenerate sequences (1) are in grey, open squares. In this example,  = 192 nodes;  = 84 nodes;  = 0.43.  is composed of 3 genotype components ( = ()). Top left,  = 53; top right,  = 24; bottom,  = 7. Non-degenerate sequences in this example, fold onto 5 phenotypes represented by the neutral sets in colors blue,  = 12; green,  = 19; orange,  = 15; magenta,  = 23; and yellow,  = 15. Genotype components  and  are composed of more than 1 neutral network.  = {} and  = {}. Phenotype 1 (blue) can be found in genotype components  and :  = {}. Phenotype 2 (orange) can be found in all three genotype components:  = {}. Genotype component , is also a neutral network: .
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g001: A two-dimensional caricature of a genotype network ().Sequences are represented as nodes. Edges are drawn between sequences that differ in 1 mutation. Degenerate sequences (1) are in grey, open squares. In this example,  = 192 nodes;  = 84 nodes;  = 0.43. is composed of 3 genotype components ( = ()). Top left,  = 53; top right,  = 24; bottom,  = 7. Non-degenerate sequences in this example, fold onto 5 phenotypes represented by the neutral sets in colors blue,  = 12; green,  = 19; orange,  = 15; magenta,  = 23; and yellow,  = 15. Genotype components and are composed of more than 1 neutral network.  = {} and  = {}. Phenotype 1 (blue) can be found in genotype components and :  = {}. Phenotype 2 (orange) can be found in all three genotype components:  = {}. Genotype component , is also a neutral network: .
Mentions: The non-degenerate fraction of sequence space induced by , can be treated as a network of genotypes () (Figure 1). Sequences are nodes, and edges are formed between pairs of sequences that differ in one point mutation (h(,) = 1). When two nodes in can be connected by a series of single point mutations, we say there is a mutational path () between them. The diameter of a graph corresponds to its largest .

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