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Analytic markovian rates for generalized protein structure evolution.

Coluzza I, MacDonald JT, Sadowski MI, Taylor WR, Goldstein RA - PLoS ONE (2012)

Bottom Line: A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism.The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution.Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Vienna, Vienna, Austria. ivan.coluzza@univie.ac.at

ABSTRACT
A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism. Such constraints can have multiple origins, in this work we present a model for constrained evolutionary trajectories represented by a markovian process throughout a set of protein-like structures artificially constructed to be topological intermediates between the structure of two natural occurring proteins. The number and type of intermediate steps defines how constrained the total evolutionary process is. By using a coarse-grained representation for the protein structures, we derive an analytic formulation of the transition rates between each of the intermediate structures. The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution. Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

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Schematic representation of the evolutionary process between the protein Immunoglobulin Binding Protein (1PGB) in blue on the left and the chain X of the 50's subunit of a secm-stalled E. Coli ribosome complex (2GYC) in red on the right.Between the two proteins we show a few of the 500 stepping stones generated with our procedure.
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pone-0034228-g001: Schematic representation of the evolutionary process between the protein Immunoglobulin Binding Protein (1PGB) in blue on the left and the chain X of the 50's subunit of a secm-stalled E. Coli ribosome complex (2GYC) in red on the right.Between the two proteins we show a few of the 500 stepping stones generated with our procedure.

Mentions: We consider two naturally occurring protein structures that represent the endpoints of the evolutionary process. We chose two proteins of equal length with substantial structural difference, for this purpose we used the Immunoglobulin Binding Protein (1PGB) and the chain X of the 50S subunit of a secm-stalled E. Coli ribosome complex (2GYC) (see Fig. 1). The secondary structure of the two proteins is represented by a string where each letter corresponds to a residue and the type of letter indicates if the amino acids is part of a helix (H), strand (E) or other (). Thus for the protein 1PGB we have: EEEEEEEEEEEEEEHHHHHHHHHHHHHHHEEEEEEEEEE (a pattern that we will refer to as 1PGB-E1 1PGB-E2 1PGB-H1 1PGB-E3 1PGB-E4), while 2GYC can be represented by: EEEEEHHHHHHHHEEEEHHHHHHHEE (which we will refer to as 2GYC-E1 2GYC-H1 2GYC-E2 2GYC-H2 2GYC-E3).


Analytic markovian rates for generalized protein structure evolution.

Coluzza I, MacDonald JT, Sadowski MI, Taylor WR, Goldstein RA - PLoS ONE (2012)

Schematic representation of the evolutionary process between the protein Immunoglobulin Binding Protein (1PGB) in blue on the left and the chain X of the 50's subunit of a secm-stalled E. Coli ribosome complex (2GYC) in red on the right.Between the two proteins we show a few of the 500 stepping stones generated with our procedure.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3367531&req=5

pone-0034228-g001: Schematic representation of the evolutionary process between the protein Immunoglobulin Binding Protein (1PGB) in blue on the left and the chain X of the 50's subunit of a secm-stalled E. Coli ribosome complex (2GYC) in red on the right.Between the two proteins we show a few of the 500 stepping stones generated with our procedure.
Mentions: We consider two naturally occurring protein structures that represent the endpoints of the evolutionary process. We chose two proteins of equal length with substantial structural difference, for this purpose we used the Immunoglobulin Binding Protein (1PGB) and the chain X of the 50S subunit of a secm-stalled E. Coli ribosome complex (2GYC) (see Fig. 1). The secondary structure of the two proteins is represented by a string where each letter corresponds to a residue and the type of letter indicates if the amino acids is part of a helix (H), strand (E) or other (). Thus for the protein 1PGB we have: EEEEEEEEEEEEEEHHHHHHHHHHHHHHHEEEEEEEEEE (a pattern that we will refer to as 1PGB-E1 1PGB-E2 1PGB-H1 1PGB-E3 1PGB-E4), while 2GYC can be represented by: EEEEEHHHHHHHHEEEEHHHHHHHEE (which we will refer to as 2GYC-E1 2GYC-H1 2GYC-E2 2GYC-H2 2GYC-E3).

Bottom Line: A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism.The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution.Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Vienna, Vienna, Austria. ivan.coluzza@univie.ac.at

ABSTRACT
A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism. Such constraints can have multiple origins, in this work we present a model for constrained evolutionary trajectories represented by a markovian process throughout a set of protein-like structures artificially constructed to be topological intermediates between the structure of two natural occurring proteins. The number and type of intermediate steps defines how constrained the total evolutionary process is. By using a coarse-grained representation for the protein structures, we derive an analytic formulation of the transition rates between each of the intermediate structures. The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution. Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

Show MeSH