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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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Correlation between errors by noise and mutation over all genes. The frequency of errors by mutation versus noise plotted over all genes for 3 networks evolved at low noise σ = .1 > σc . The abscissa showed the number of events for which the expression of the gene is switched on or off by noise. Computation was carried out as follows: Taking an evolved network (with highest fitness), we simulated the gene regulation network(GRN) dynamics without noise for a sufficiently long duration and obtained the original value of x(i) for each gene i. (i) The GRN dynamics were then simulated in the same manner under the noise level σ = .1 for over 105 different runs, and the number of switch events (i.e., the runs in which x(i) changes its sign) was computed. (ii) We generated 105 networks by changing 50 paths randomly chosen from the original network, and simulated these GRNs without noise and computed the number of switch events for each gene i. Step (i) gives the number of error by noise, and step (ii) gives the error by mutation, for each gene i. The relations between these 2 errors were plotted for 3 original networks with a different color for each network.
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Figure 4: Correlation between errors by noise and mutation over all genes. The frequency of errors by mutation versus noise plotted over all genes for 3 networks evolved at low noise σ = .1 > σc . The abscissa showed the number of events for which the expression of the gene is switched on or off by noise. Computation was carried out as follows: Taking an evolved network (with highest fitness), we simulated the gene regulation network(GRN) dynamics without noise for a sufficiently long duration and obtained the original value of x(i) for each gene i. (i) The GRN dynamics were then simulated in the same manner under the noise level σ = .1 for over 105 different runs, and the number of switch events (i.e., the runs in which x(i) changes its sign) was computed. (ii) We generated 105 networks by changing 50 paths randomly chosen from the original network, and simulated these GRNs without noise and computed the number of switch events for each gene i. Step (i) gives the number of error by noise, and step (ii) gives the error by mutation, for each gene i. The relations between these 2 errors were plotted for 3 original networks with a different color for each network.

Mentions: The proportionality between the 2 variances implies the existence of a correlation between the noise- and mutation-induced changes in the gene expression statuses (see also Additional file 1, Figure S2 for the correlation in variances). Such a correlation was observed by computing the frequency of errors, i.e., changes in the on/off status of gene expression due to noise (without a change in the network) and as a result of mutation to the network (without adding the noise). The frequency of these 2 errors was highly correlated over genes for the GRN evolved at σ > σc (see Figure 4). In other words, genes that were switched on or off more frequently by noise were also switched more frequently by mutation. This was in strong contrast with the GRN evolved at σ < σc where no such correlation was observed (see Additional file 1, Figure S3). To sum up, the changeability of each gene expression level by noise and mutation was correlated, for a robust evolved system.


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

Kaneko K - BMC Evol. Biol. (2011)

Correlation between errors by noise and mutation over all genes. The frequency of errors by mutation versus noise plotted over all genes for 3 networks evolved at low noise σ = .1 > σc . The abscissa showed the number of events for which the expression of the gene is switched on or off by noise. Computation was carried out as follows: Taking an evolved network (with highest fitness), we simulated the gene regulation network(GRN) dynamics without noise for a sufficiently long duration and obtained the original value of x(i) for each gene i. (i) The GRN dynamics were then simulated in the same manner under the noise level σ = .1 for over 105 different runs, and the number of switch events (i.e., the runs in which x(i) changes its sign) was computed. (ii) We generated 105 networks by changing 50 paths randomly chosen from the original network, and simulated these GRNs without noise and computed the number of switch events for each gene i. Step (i) gives the number of error by noise, and step (ii) gives the error by mutation, for each gene i. The relations between these 2 errors were plotted for 3 original networks with a different color for each network.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Correlation between errors by noise and mutation over all genes. The frequency of errors by mutation versus noise plotted over all genes for 3 networks evolved at low noise σ = .1 > σc . The abscissa showed the number of events for which the expression of the gene is switched on or off by noise. Computation was carried out as follows: Taking an evolved network (with highest fitness), we simulated the gene regulation network(GRN) dynamics without noise for a sufficiently long duration and obtained the original value of x(i) for each gene i. (i) The GRN dynamics were then simulated in the same manner under the noise level σ = .1 for over 105 different runs, and the number of switch events (i.e., the runs in which x(i) changes its sign) was computed. (ii) We generated 105 networks by changing 50 paths randomly chosen from the original network, and simulated these GRNs without noise and computed the number of switch events for each gene i. Step (i) gives the number of error by noise, and step (ii) gives the error by mutation, for each gene i. The relations between these 2 errors were plotted for 3 original networks with a different color for each network.
Mentions: The proportionality between the 2 variances implies the existence of a correlation between the noise- and mutation-induced changes in the gene expression statuses (see also Additional file 1, Figure S2 for the correlation in variances). Such a correlation was observed by computing the frequency of errors, i.e., changes in the on/off status of gene expression due to noise (without a change in the network) and as a result of mutation to the network (without adding the noise). The frequency of these 2 errors was highly correlated over genes for the GRN evolved at σ > σc (see Figure 4). In other words, genes that were switched on or off more frequently by noise were also switched more frequently by mutation. This was in strong contrast with the GRN evolved at σ < σc where no such correlation was observed (see Additional file 1, Figure S3). To sum up, the changeability of each gene expression level by noise and mutation was correlated, for a robust evolved system.

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