Limits...
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.

Show MeSH

Related in: MedlinePlus

Fitness (in different units for each curve) versus GC usage for neutrality exponent  and three different population sizes.The curves have been shifted in the vertical direction so that their maxima coincide. We obtain  by cubic fits, which are plotted as dotted, dashed, and solid lines.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2865504&req=5

pcbi-1000767-g003: Fitness (in different units for each curve) versus GC usage for neutrality exponent and three different population sizes.The curves have been shifted in the vertical direction so that their maxima coincide. We obtain by cubic fits, which are plotted as dotted, dashed, and solid lines.

Mentions: Fitness clearly increases with . The variation of fitness with is weaker, but one can nevertheless notice it from the plot. This variation translates into the fact that, for fixed fitness function and population size , there is an optimal usage such that fitness is maximal, as predicted in Eq. (7). The existence of this optimal mutation bias is demonstrated in Fig. 3, where we plot the fitness of populations with constant and as a function of their usage. For each set of parameters, we obtained the optimal GC usage by cubic interpolation, as exemplified in Fig. 3, and plotted it versus . We found that is small for very small populations, large for intermediate populations, and the bias is almost absent () for very large populations (see Fig. 4). We obtained qualitatively similar results as long as the neutrality exponent is not too large or too small (in that case, the fitness landscape becomes almost neutral). The population size at which the optimal GC usage is highest increases with decreasing for small , while the opposite holds for large . Our numerical results are consistent with the optimal GC usage becoming less dependent on in the infinite population limit, see Fig. 3 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)

Fitness (in different units for each curve) versus GC usage for neutrality exponent  and three different population sizes.The curves have been shifted in the vertical direction so that their maxima coincide. We obtain  by cubic fits, which are plotted as dotted, dashed, and solid lines.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000767-g003: Fitness (in different units for each curve) versus GC usage for neutrality exponent and three different population sizes.The curves have been shifted in the vertical direction so that their maxima coincide. We obtain by cubic fits, which are plotted as dotted, dashed, and solid lines.
Mentions: Fitness clearly increases with . The variation of fitness with is weaker, but one can nevertheless notice it from the plot. This variation translates into the fact that, for fixed fitness function and population size , there is an optimal usage such that fitness is maximal, as predicted in Eq. (7). The existence of this optimal mutation bias is demonstrated in Fig. 3, where we plot the fitness of populations with constant and as a function of their usage. For each set of parameters, we obtained the optimal GC usage by cubic interpolation, as exemplified in Fig. 3, and plotted it versus . We found that is small for very small populations, large for intermediate populations, and the bias is almost absent () for very large populations (see Fig. 4). We obtained qualitatively similar results as long as the neutrality exponent is not too large or too small (in that case, the fitness landscape becomes almost neutral). The population size at which the optimal GC usage is highest increases with decreasing for small , while the opposite holds for large . Our numerical results are consistent with the optimal GC usage becoming less dependent on in the infinite population limit, see Fig. 3 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
Related in: MedlinePlus