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Mutation bias favors protein folding stability in the evolution of small populations.

Mendez R, Fritsche M, Porto M, Bastolla U - PLoS Comput. Biol. (2010)

Bottom Line: This result is robust with respect to the definition of the fitness function and to the protein structures studied.This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT.To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran.

View Article: PubMed Central - PubMed

Affiliation: Centro de Biología Molecular Severo Ochoa, Consejo Superior de Investigaciones Científicas and Universidad Autónoma de Madrid, Madrid, Spain.

ABSTRACT
Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction.

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Optimal GC usage  versus population size  for neutrality exponent  and different values of the neutral thresholds  and , where the reference energy gap  and unfolding free energy  are those measured for the protein in the PDB.We simulated all nine combinations of the values  for either  of . We only show four combinations since all other curves are contained between them.
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pcbi-1000767-g006: Optimal GC usage versus population size for neutrality exponent and different values of the neutral thresholds and , where the reference energy gap and unfolding free energy are those measured for the protein in the PDB.We simulated all nine combinations of the values for either of . We only show four combinations since all other curves are contained between them.

Mentions: In the neutral limit , the selective pressure only affects the smallest stability variable, since . This tends to independent of and . Therefore, as discussed above, for large , the optimal is reached when , i.e. when the two selective pressures balance. The ML equations imply that at this point , so that the optimal does not depend on . The ML equations also imply that, in the large limit, (see Text S1), which means that the maximum stability and maximum fitness is attained at the value at which is minimum. This prediction is confirmed in Fig. 6 in the Text S1).


Mutation bias favors protein folding stability in the evolution of small populations.

Mendez R, Fritsche M, Porto M, Bastolla U - PLoS Comput. Biol. (2010)

Optimal GC usage  versus population size  for neutrality exponent  and different values of the neutral thresholds  and , where the reference energy gap  and unfolding free energy  are those measured for the protein in the PDB.We simulated all nine combinations of the values  for either  of . We only show four combinations since all other curves are contained between them.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2865504&req=5

pcbi-1000767-g006: Optimal GC usage versus population size for neutrality exponent and different values of the neutral thresholds and , where the reference energy gap and unfolding free energy are those measured for the protein in the PDB.We simulated all nine combinations of the values for either of . We only show four combinations since all other curves are contained between them.
Mentions: In the neutral limit , the selective pressure only affects the smallest stability variable, since . This tends to independent of and . Therefore, as discussed above, for large , the optimal is reached when , i.e. when the two selective pressures balance. The ML equations imply that at this point , so that the optimal does not depend on . The ML equations also imply that, in the large limit, (see Text S1), which means that the maximum stability and maximum fitness is attained at the value at which is minimum. This prediction is confirmed in Fig. 6 in the Text S1).

Bottom Line: This result is robust with respect to the definition of the fitness function and to the protein structures studied.This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT.To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran.

View Article: PubMed Central - PubMed

Affiliation: Centro de Biología Molecular Severo Ochoa, Consejo Superior de Investigaciones Científicas and Universidad Autónoma de Madrid, Madrid, Spain.

ABSTRACT
Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction.

Show MeSH