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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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Plot of the distribution of the site Shannon entropy  calculated for the family of natural sequences of 1PGB (PF01053) in red and for the designed sequences in black.
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pone-0034228-g003: Plot of the distribution of the site Shannon entropy calculated for the family of natural sequences of 1PGB (PF01053) in red and for the designed sequences in black.

Mentions: We found (see Fig. 3) that the sequence populations generated for protein G at the design temperature had the closest variability compared to the corresponding family of natural sequences. Using the scheme just described we performed a design simulation for every stepping stone and hence generated a distribution of folding sequences for each of them. From now on we will refer to the stepping stones with their corresponding distribution of folding sequences as “islands". With the islands in hand a method is now required to characterize the probability of transition between islands. This method is described in the following section.


Analytic markovian rates for generalized protein structure evolution.

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

Plot of the distribution of the site Shannon entropy  calculated for the family of natural sequences of 1PGB (PF01053) in red and for the designed sequences in black.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0034228-g003: Plot of the distribution of the site Shannon entropy calculated for the family of natural sequences of 1PGB (PF01053) in red and for the designed sequences in black.
Mentions: We found (see Fig. 3) that the sequence populations generated for protein G at the design temperature had the closest variability compared to the corresponding family of natural sequences. Using the scheme just described we performed a design simulation for every stepping stone and hence generated a distribution of folding sequences for each of them. From now on we will refer to the stepping stones with their corresponding distribution of folding sequences as “islands". With the islands in hand a method is now required to characterize the probability of transition between islands. This method is described in the following section.

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