Limits...
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.

Show MeSH

Related in: MedlinePlus

Histogram of the ratio Vg(i)/Vip(i). (a)The variances Vg(i) and Vip(i) and their ratio were computed for each gene i, in the same manner as that adopted in Figure 2. Histogram of the  was computed and sampled for all genes i from 280 to 300 generations. σ = .001 (red +), .02 (green x), .03(blue *), .05(pink ▢), and .08(sky blue *) and .1 (black ○). (b) Temporal evolution of the histogram for the ratio Vg(i)/Vip(i) for σ = 0.1. The histogram was computed over all networks and for every 20 generations. We used the logarithmic scales for both axes, so that the values for abscissa shows : The histograms over generations 1-20, 21-40, 41-60,101-120, 181-200, and 281-300 were plotted with a different color for each network. With evolution, a peak was formed at Vg(i)/Vip(i) = ρ ~ 10-2.3. See Method for the choice of the parameters.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3045907&req=5

Figure 3: Histogram of the ratio Vg(i)/Vip(i). (a)The variances Vg(i) and Vip(i) and their ratio were computed for each gene i, in the same manner as that adopted in Figure 2. Histogram of the was computed and sampled for all genes i from 280 to 300 generations. σ = .001 (red +), .02 (green x), .03(blue *), .05(pink ▢), and .08(sky blue *) and .1 (black ○). (b) Temporal evolution of the histogram for the ratio Vg(i)/Vip(i) for σ = 0.1. The histogram was computed over all networks and for every 20 generations. We used the logarithmic scales for both axes, so that the values for abscissa shows : The histograms over generations 1-20, 21-40, 41-60,101-120, 181-200, and 281-300 were plotted with a different color for each network. With evolution, a peak was formed at Vg(i)/Vip(i) = ρ ~ 10-2.3. See Method for the choice of the parameters.

Mentions: We then plotted the histogram of ri over all genes i, sampled over a few sets of generations (see Figure 3a, plotted in log-scale for ri ). The figure showed that the peak at ρ was more prominent with an increase in σ. On the other hand, the broader distribution ranging between ri ~ ρ and 1 became more prominent as the noise level decreased, until the distribution around ri ~ 1 dominated at σ ~ σc.


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

Kaneko K - BMC Evol. Biol. (2011)

Histogram of the ratio Vg(i)/Vip(i). (a)The variances Vg(i) and Vip(i) and their ratio were computed for each gene i, in the same manner as that adopted in Figure 2. Histogram of the  was computed and sampled for all genes i from 280 to 300 generations. σ = .001 (red +), .02 (green x), .03(blue *), .05(pink ▢), and .08(sky blue *) and .1 (black ○). (b) Temporal evolution of the histogram for the ratio Vg(i)/Vip(i) for σ = 0.1. The histogram was computed over all networks and for every 20 generations. We used the logarithmic scales for both axes, so that the values for abscissa shows : The histograms over generations 1-20, 21-40, 41-60,101-120, 181-200, and 281-300 were plotted with a different color for each network. With evolution, a peak was formed at Vg(i)/Vip(i) = ρ ~ 10-2.3. See Method for the choice of the parameters.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Histogram of the ratio Vg(i)/Vip(i). (a)The variances Vg(i) and Vip(i) and their ratio were computed for each gene i, in the same manner as that adopted in Figure 2. Histogram of the was computed and sampled for all genes i from 280 to 300 generations. σ = .001 (red +), .02 (green x), .03(blue *), .05(pink ▢), and .08(sky blue *) and .1 (black ○). (b) Temporal evolution of the histogram for the ratio Vg(i)/Vip(i) for σ = 0.1. The histogram was computed over all networks and for every 20 generations. We used the logarithmic scales for both axes, so that the values for abscissa shows : The histograms over generations 1-20, 21-40, 41-60,101-120, 181-200, and 281-300 were plotted with a different color for each network. With evolution, a peak was formed at Vg(i)/Vip(i) = ρ ~ 10-2.3. See Method for the choice of the parameters.
Mentions: We then plotted the histogram of ri over all genes i, sampled over a few sets of generations (see Figure 3a, plotted in log-scale for ri ). The figure showed that the peak at ρ was more prominent with an increase in σ. On the other hand, the broader distribution ranging between ri ~ ρ and 1 became more prominent as the noise level decreased, until the distribution around ri ~ 1 dominated at σ ~ σc.

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