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
Binary potentials as vectors of  values.Figure show a graphic representation of the 7 types of potentials described in Table 1. These potentials (type I-V, VII), correspond to the 6 non-redundant octants in the 3d representation of  coordinates. Potentials type VI, those with at least one  = 0.0, are represented by grey planes between octants.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g003: Binary potentials as vectors of values.Figure show a graphic representation of the 7 types of potentials described in Table 1. These potentials (type I-V, VII), correspond to the 6 non-redundant octants in the 3d representation of coordinates. Potentials type VI, those with at least one  = 0.0, are represented by grey planes between octants.

Mentions: Potentials can be represented as vectors. Due to the symmetry of the cube (), half of the space contains all possible non-redundant binary potentials. As suggested by previous studies, many properties of the potential energy function are determined by the proportion of repulsive, attractive and neutral interactions [39], [50]. I use this criterion to distinguish among 7 types of potentials, that correspond to the 6 non-redundant octants in the 3d -coordinates representation, plus any potential with at least one 0 (Table 1, Figure 3). The octant in black (Fig. 3), that corresponds to all-repulsive interactions (, , 0.0); is defined as potential type VII and, by definition, does not stabilize any conformation (see Eq. 1). The 245 potentials described above are an homogeneous sample from this space.


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

Ferrada E - PLoS Comput. Biol. (2014)

Binary potentials as vectors of  values.Figure show a graphic representation of the 7 types of potentials described in Table 1. These potentials (type I-V, VII), correspond to the 6 non-redundant octants in the 3d representation of  coordinates. Potentials type VI, those with at least one  = 0.0, are represented by grey planes between octants.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003946-g003: Binary potentials as vectors of values.Figure show a graphic representation of the 7 types of potentials described in Table 1. These potentials (type I-V, VII), correspond to the 6 non-redundant octants in the 3d representation of coordinates. Potentials type VI, those with at least one  = 0.0, are represented by grey planes between octants.
Mentions: Potentials can be represented as vectors. Due to the symmetry of the cube (), half of the space contains all possible non-redundant binary potentials. As suggested by previous studies, many properties of the potential energy function are determined by the proportion of repulsive, attractive and neutral interactions [39], [50]. I use this criterion to distinguish among 7 types of potentials, that correspond to the 6 non-redundant octants in the 3d -coordinates representation, plus any potential with at least one 0 (Table 1, Figure 3). The octant in black (Fig. 3), that corresponds to all-repulsive interactions (, , 0.0); is defined as potential type VII and, by definition, does not stabilize any conformation (see Eq. 1). The 245 potentials described above are an homogeneous sample from this space.

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