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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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Related in: MedlinePlus

Relationship between Vg(i) and Vip(i). As described in the Method section of the text, Vip(i) was computed as the variance of the distribution of Sign(xi) over 200 runs for an identical genotype, while Vg(i) was computed as a variance of the distribution of  over 200 individuals, where  was the mean over 200 runs. σ = 0.1 (a), 0.05 (b), 0.01 (c), and 0.001 (d). The plot of (Vg(i) and Vip(i)) for all genes i at the 300th generation: Target genes as red ▢, and nontarget genes as blue +.
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Figure 2: Relationship between Vg(i) and Vip(i). As described in the Method section of the text, Vip(i) was computed as the variance of the distribution of Sign(xi) over 200 runs for an identical genotype, while Vg(i) was computed as a variance of the distribution of over 200 individuals, where was the mean over 200 runs. σ = 0.1 (a), 0.05 (b), 0.01 (c), and 0.001 (d). The plot of (Vg(i) and Vip(i)) for all genes i at the 300th generation: Target genes as red ▢, and nontarget genes as blue +.

Mentions: Considering the possible generalization of Fisher's theorem [18,20], which states that the evolution speed is proportional to Vg, and applying it to the expression levels over genes, we may expect that the evolution speed of each gene expression level is proportional to Vg(i). Then, the proportionality between Vg(i) and Vip(i) over the genes can be expected from the proportionality between the evolution speed and Vip(i). Considering this, we examined the relationship between Vg(i) and Vip(i) for several values of noise levels (Figure 2). From the plots, we obtained the following findings:


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

Kaneko K - BMC Evol. Biol. (2011)

Relationship between Vg(i) and Vip(i). As described in the Method section of the text, Vip(i) was computed as the variance of the distribution of Sign(xi) over 200 runs for an identical genotype, while Vg(i) was computed as a variance of the distribution of  over 200 individuals, where  was the mean over 200 runs. σ = 0.1 (a), 0.05 (b), 0.01 (c), and 0.001 (d). The plot of (Vg(i) and Vip(i)) for all genes i at the 300th generation: Target genes as red ▢, and nontarget genes as blue +.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3045907&req=5

Figure 2: Relationship between Vg(i) and Vip(i). As described in the Method section of the text, Vip(i) was computed as the variance of the distribution of Sign(xi) over 200 runs for an identical genotype, while Vg(i) was computed as a variance of the distribution of over 200 individuals, where was the mean over 200 runs. σ = 0.1 (a), 0.05 (b), 0.01 (c), and 0.001 (d). The plot of (Vg(i) and Vip(i)) for all genes i at the 300th generation: Target genes as red ▢, and nontarget genes as blue +.
Mentions: Considering the possible generalization of Fisher's theorem [18,20], which states that the evolution speed is proportional to Vg, and applying it to the expression levels over genes, we may expect that the evolution speed of each gene expression level is proportional to Vg(i). Then, the proportionality between Vg(i) and Vip(i) over the genes can be expected from the proportionality between the evolution speed and Vip(i). Considering this, we examined the relationship between Vg(i) and Vip(i) for several values of noise levels (Figure 2). From the plots, we obtained the following findings:

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