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Proportionality between variances in gene expression induced by noise and mutation: consequence of evolutionary robustness.

Kaneko K - BMC Evol. Biol. (2011)

Bottom Line: Under such conditions, the two types of variances in the gene expression levels, i.e. those due to mutations to the gene regulation network and those due to noise in gene expression dynamics were found to be proportional over a number of genes.Experimental evidences for the proportionality of the variances over genes are also discussed.The proportionality between the genetic and epigenetic variances of phenotypes implies the correlation between the robustness (or plasticity) against genetic changes and against noise in development, and also suggests that phenotypic traits that are more variable epigenetically have a higher evolutionary potential.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Basic Science, Univ, of Tokyo, and Complex Systems Biology Project, ERATO, JST, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. kaneko@complex.c.u-tokyo.ac.jp

ABSTRACT

Background: Characterization of robustness and plasticity of phenotypes is a basic issue in evolutionary and developmental biology. The robustness and plasticity are concerned with changeability of a biological system against external perturbations. The perturbations are either genetic, i.e., due to mutations in genes in the population, or epigenetic, i.e., due to noise during development or environmental variations. Thus, the variances of phenotypes due to genetic and epigenetic perturbations provide quantitative measures for such changeability during evolution and development, respectively.

Results: Using numerical models simulating the evolutionary changes in the gene regulation network required to achieve a particular expression pattern, we first confirmed that gene expression dynamics robust to mutation evolved in the presence of a sufficient level of transcriptional noise. Under such conditions, the two types of variances in the gene expression levels, i.e. those due to mutations to the gene regulation network and those due to noise in gene expression dynamics were found to be proportional over a number of genes. The fraction of such genes with a common proportionality coefficient increased with an increase in the robustness of the evolved network. This proportionality was generally confirmed, also under the presence of environmental fluctuations and sexual recombination in diploids, and was explained from an evolutionary robustness hypothesis, in which an evolved robust system suppresses the so-called error catastrophe--the destabilization of the single-peaked distribution in gene expression levels. Experimental evidences for the proportionality of the variances over genes are also discussed.

Conclusions: The proportionality between the genetic and epigenetic variances of phenotypes implies the correlation between the robustness (or plasticity) against genetic changes and against noise in development, and also suggests that phenotypic traits that are more variable epigenetically have a higher evolutionary potential.

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Change in the variances after the switching of the fitness condition. After evolution under the fitness condition to favor xi >0 ("on") for all the target genes i = 1, 2, ... k(= 8) as studied already, the fitness condition was switched at a certain generation to favor xi >0 for i = 1, 2, .., k/2 and xi <0 for i = k/2 + 1, .., k (i.e., the fittest gene expression pattern was given by + + + + − − −−, instead of + + + + + + ++). The switching was applied after a sufficiently large number of generations when the fittest networks are evolved (i.e., with xi >0 for the target genes). The switch initially caused a decrease in the fitness, but after a few dozens of generations, almost all networks evolved to adapt to the new fitness condition if σ > σc. The values of the parameter and the procedure for computing the variances were identical with those in the previous cases. (i) The plot of the variances of the fitness, Vg versus Vip per generation after the switching of the fitness condition. The color represented the generation number from the switching. There was a correlation between the increase in both the variances after the switch, and then, there was a proportional decrease as adaptation to the new fitness condition progressed. (b)(c) The plot of (Vg(i) and Vip(i)) over all genes i at the generation 10, 20, and 30 for (b), and 60, 80, and 120 for (c). After the switch Vg(i) and Vip(i) increased up to 30-60 generations, while the ratio Vg(i)/Vip(i)approached unity for many genes. For generations >60, the variances decreased while the proportionality between Vg(i) and Vip(i) was regained.
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Figure 5: Change in the variances after the switching of the fitness condition. After evolution under the fitness condition to favor xi >0 ("on") for all the target genes i = 1, 2, ... k(= 8) as studied already, the fitness condition was switched at a certain generation to favor xi >0 for i = 1, 2, .., k/2 and xi <0 for i = k/2 + 1, .., k (i.e., the fittest gene expression pattern was given by + + + + − − −−, instead of + + + + + + ++). The switching was applied after a sufficiently large number of generations when the fittest networks are evolved (i.e., with xi >0 for the target genes). The switch initially caused a decrease in the fitness, but after a few dozens of generations, almost all networks evolved to adapt to the new fitness condition if σ > σc. The values of the parameter and the procedure for computing the variances were identical with those in the previous cases. (i) The plot of the variances of the fitness, Vg versus Vip per generation after the switching of the fitness condition. The color represented the generation number from the switching. There was a correlation between the increase in both the variances after the switch, and then, there was a proportional decrease as adaptation to the new fitness condition progressed. (b)(c) The plot of (Vg(i) and Vip(i)) over all genes i at the generation 10, 20, and 30 for (b), and 60, 80, and 120 for (c). After the switch Vg(i) and Vip(i) increased up to 30-60 generations, while the ratio Vg(i)/Vip(i)approached unity for many genes. For generations >60, the variances decreased while the proportionality between Vg(i) and Vip(i) was regained.

Mentions: (v) By the variation in the environmental condition, the fitness condition for the target genes varied accordingly. By switching the condition for the target genes from 'on' to 'off' after some generations, we verified whether the evolution of GRN copes with this environmental variation. When the condition was switched, both the variances of epigenetic and genetic origins, as well as ri = Vg(i)/Vip(i), increased to adapt novel environmental condition. Once the adaptation was achieved, the variances as well as ri decreased, to regain robustness (Figure 5).


Proportionality between variances in gene expression induced by noise and mutation: consequence of evolutionary robustness.

Kaneko K - BMC Evol. Biol. (2011)

Change in the variances after the switching of the fitness condition. After evolution under the fitness condition to favor xi >0 ("on") for all the target genes i = 1, 2, ... k(= 8) as studied already, the fitness condition was switched at a certain generation to favor xi >0 for i = 1, 2, .., k/2 and xi <0 for i = k/2 + 1, .., k (i.e., the fittest gene expression pattern was given by + + + + − − −−, instead of + + + + + + ++). The switching was applied after a sufficiently large number of generations when the fittest networks are evolved (i.e., with xi >0 for the target genes). The switch initially caused a decrease in the fitness, but after a few dozens of generations, almost all networks evolved to adapt to the new fitness condition if σ > σc. The values of the parameter and the procedure for computing the variances were identical with those in the previous cases. (i) The plot of the variances of the fitness, Vg versus Vip per generation after the switching of the fitness condition. The color represented the generation number from the switching. There was a correlation between the increase in both the variances after the switch, and then, there was a proportional decrease as adaptation to the new fitness condition progressed. (b)(c) The plot of (Vg(i) and Vip(i)) over all genes i at the generation 10, 20, and 30 for (b), and 60, 80, and 120 for (c). After the switch Vg(i) and Vip(i) increased up to 30-60 generations, while the ratio Vg(i)/Vip(i)approached unity for many genes. For generations >60, the variances decreased while the proportionality between Vg(i) and Vip(i) was regained.
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Figure 5: Change in the variances after the switching of the fitness condition. After evolution under the fitness condition to favor xi >0 ("on") for all the target genes i = 1, 2, ... k(= 8) as studied already, the fitness condition was switched at a certain generation to favor xi >0 for i = 1, 2, .., k/2 and xi <0 for i = k/2 + 1, .., k (i.e., the fittest gene expression pattern was given by + + + + − − −−, instead of + + + + + + ++). The switching was applied after a sufficiently large number of generations when the fittest networks are evolved (i.e., with xi >0 for the target genes). The switch initially caused a decrease in the fitness, but after a few dozens of generations, almost all networks evolved to adapt to the new fitness condition if σ > σc. The values of the parameter and the procedure for computing the variances were identical with those in the previous cases. (i) The plot of the variances of the fitness, Vg versus Vip per generation after the switching of the fitness condition. The color represented the generation number from the switching. There was a correlation between the increase in both the variances after the switch, and then, there was a proportional decrease as adaptation to the new fitness condition progressed. (b)(c) The plot of (Vg(i) and Vip(i)) over all genes i at the generation 10, 20, and 30 for (b), and 60, 80, and 120 for (c). After the switch Vg(i) and Vip(i) increased up to 30-60 generations, while the ratio Vg(i)/Vip(i)approached unity for many genes. For generations >60, the variances decreased while the proportionality between Vg(i) and Vip(i) was regained.
Mentions: (v) By the variation in the environmental condition, the fitness condition for the target genes varied accordingly. By switching the condition for the target genes from 'on' to 'off' after some generations, we verified whether the evolution of GRN copes with this environmental variation. When the condition was switched, both the variances of epigenetic and genetic origins, as well as ri = Vg(i)/Vip(i), increased to adapt novel environmental condition. Once the adaptation was achieved, the variances as well as ri decreased, to regain robustness (Figure 5).

Bottom Line: Under such conditions, the two types of variances in the gene expression levels, i.e. those due to mutations to the gene regulation network and those due to noise in gene expression dynamics were found to be proportional over a number of genes.Experimental evidences for the proportionality of the variances over genes are also discussed.The proportionality between the genetic and epigenetic variances of phenotypes implies the correlation between the robustness (or plasticity) against genetic changes and against noise in development, and also suggests that phenotypic traits that are more variable epigenetically have a higher evolutionary potential.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Basic Science, Univ, of Tokyo, and Complex Systems Biology Project, ERATO, JST, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. kaneko@complex.c.u-tokyo.ac.jp

ABSTRACT

Background: Characterization of robustness and plasticity of phenotypes is a basic issue in evolutionary and developmental biology. The robustness and plasticity are concerned with changeability of a biological system against external perturbations. The perturbations are either genetic, i.e., due to mutations in genes in the population, or epigenetic, i.e., due to noise during development or environmental variations. Thus, the variances of phenotypes due to genetic and epigenetic perturbations provide quantitative measures for such changeability during evolution and development, respectively.

Results: Using numerical models simulating the evolutionary changes in the gene regulation network required to achieve a particular expression pattern, we first confirmed that gene expression dynamics robust to mutation evolved in the presence of a sufficient level of transcriptional noise. Under such conditions, the two types of variances in the gene expression levels, i.e. those due to mutations to the gene regulation network and those due to noise in gene expression dynamics were found to be proportional over a number of genes. The fraction of such genes with a common proportionality coefficient increased with an increase in the robustness of the evolved network. This proportionality was generally confirmed, also under the presence of environmental fluctuations and sexual recombination in diploids, and was explained from an evolutionary robustness hypothesis, in which an evolved robust system suppresses the so-called error catastrophe--the destabilization of the single-peaked distribution in gene expression levels. Experimental evidences for the proportionality of the variances over genes are also discussed.

Conclusions: The proportionality between the genetic and epigenetic variances of phenotypes implies the correlation between the robustness (or plasticity) against genetic changes and against noise in development, and also suggests that phenotypic traits that are more variable epigenetically have a higher evolutionary potential.

Show MeSH
Related in: MedlinePlus