Limits...
Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network.

Kim KJ, Fernandes VM - PLoS Comput. Biol. (2009)

Bottom Line: Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation.We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction.In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone.

View Article: PubMed Central - PubMed

Affiliation: Center for Cell Dynamics, Friday Harbor Labs, University of Washington, Friday Harbor, Washington, USA. kjkim@u.washington.edu

ABSTRACT
Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through "survival of the compatible": those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles.

Show MeSH

Related in: MedlinePlus

Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals is                        generated, and their genotype determines their phenotype. Individuals are                        subject to either truncation or stabilizing selection, and viable                        individuals mate (if sexual) or divide (if asexual). Each gene in the next                        generation has a small (3%) chance of having a mutation. (B) Each                        model parameter was determined from genotype represented as a bit sequence.                        The model parameter value was calculated from the amount of complementarity                        between 2 different bit sequences with a length of 20 bits (figure shows 10                        bits for simplicity), representing the shapes of interacting surfaces in the                        biomolecules. Black and red lines are graphical representations of the                        shapes these bit sequences represent; 1's indicate protrusions,                        0's indicate crevices. Each bit is weighted double that to its                        right, and the strength of the interaction is scaled by the binary exclusive                        OR (XOR) between the two bit sequences. A perfect fit in a binding                        interaction would have a low dissociation constant, while worse fits would                        have corresponding looser binding. (C) Mutations may have specific effects                        depending on the location in the gene. Each gene had many separate bit                        sequences, one for each parameter in the model that the gene was involved                        in, corresponding to the different quantitative effects of mutation. For                        example, a mutation in the enhancer or promoter sequence (E/P) would alter                        gene expression levels, while mutations in the 5′ untranslated                        region or translation initiation site (UTR/SD) would alter translation                        rates. Mutations in the coding region that alter the binding site for CID on                        the PTC protein (Red) would alter the ability of PTC to cleave CID.                        Similarly, the different active sites on the CID protein (green, blue,                        orange) could be specifically altered by mutations in the coding region.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2637435&req=5

pcbi-1000296-g002: Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals is generated, and their genotype determines their phenotype. Individuals are subject to either truncation or stabilizing selection, and viable individuals mate (if sexual) or divide (if asexual). Each gene in the next generation has a small (3%) chance of having a mutation. (B) Each model parameter was determined from genotype represented as a bit sequence. The model parameter value was calculated from the amount of complementarity between 2 different bit sequences with a length of 20 bits (figure shows 10 bits for simplicity), representing the shapes of interacting surfaces in the biomolecules. Black and red lines are graphical representations of the shapes these bit sequences represent; 1's indicate protrusions, 0's indicate crevices. Each bit is weighted double that to its right, and the strength of the interaction is scaled by the binary exclusive OR (XOR) between the two bit sequences. A perfect fit in a binding interaction would have a low dissociation constant, while worse fits would have corresponding looser binding. (C) Mutations may have specific effects depending on the location in the gene. Each gene had many separate bit sequences, one for each parameter in the model that the gene was involved in, corresponding to the different quantitative effects of mutation. For example, a mutation in the enhancer or promoter sequence (E/P) would alter gene expression levels, while mutations in the 5′ untranslated region or translation initiation site (UTR/SD) would alter translation rates. Mutations in the coding region that alter the binding site for CID on the PTC protein (Red) would alter the ability of PTC to cleave CID. Similarly, the different active sites on the CID protein (green, blue, orange) could be specifically altered by mutations in the coding region.

Mentions: In the following paragraphs, we describe extensions to this model that allow us to simulate evolution of the segment polarity network in response to selection on the pattern of en and wg expression (the phenotype). We present a diploid version of the model that allows us to directly compare evolution and robustness in haploid and diploid models. We also use a novel framework of deriving model parameter values from a digital genotype, which allows mutations to alter many gene properties (i.e. changes in expression level, stability and activity). Using these, we start with initially viable identical founders and follow them through 2,000 generations of evolution as shown in Figure 2A. We use the model to calculate phenotype (the en and wg pattern of expression) from genotype, apply truncation or stabilizing selection on the phenotype, using a multinomial sampling scheme to simulate random mating with a fixed population size (N = 200) and a per-gene mutation rate (μ) of 0.03.


Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network.

Kim KJ, Fernandes VM - PLoS Comput. Biol. (2009)

Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals is                        generated, and their genotype determines their phenotype. Individuals are                        subject to either truncation or stabilizing selection, and viable                        individuals mate (if sexual) or divide (if asexual). Each gene in the next                        generation has a small (3%) chance of having a mutation. (B) Each                        model parameter was determined from genotype represented as a bit sequence.                        The model parameter value was calculated from the amount of complementarity                        between 2 different bit sequences with a length of 20 bits (figure shows 10                        bits for simplicity), representing the shapes of interacting surfaces in the                        biomolecules. Black and red lines are graphical representations of the                        shapes these bit sequences represent; 1's indicate protrusions,                        0's indicate crevices. Each bit is weighted double that to its                        right, and the strength of the interaction is scaled by the binary exclusive                        OR (XOR) between the two bit sequences. A perfect fit in a binding                        interaction would have a low dissociation constant, while worse fits would                        have corresponding looser binding. (C) Mutations may have specific effects                        depending on the location in the gene. Each gene had many separate bit                        sequences, one for each parameter in the model that the gene was involved                        in, corresponding to the different quantitative effects of mutation. For                        example, a mutation in the enhancer or promoter sequence (E/P) would alter                        gene expression levels, while mutations in the 5′ untranslated                        region or translation initiation site (UTR/SD) would alter translation                        rates. Mutations in the coding region that alter the binding site for CID on                        the PTC protein (Red) would alter the ability of PTC to cleave CID.                        Similarly, the different active sites on the CID protein (green, blue,                        orange) could be specifically altered by mutations in the coding region.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2637435&req=5

pcbi-1000296-g002: Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals is generated, and their genotype determines their phenotype. Individuals are subject to either truncation or stabilizing selection, and viable individuals mate (if sexual) or divide (if asexual). Each gene in the next generation has a small (3%) chance of having a mutation. (B) Each model parameter was determined from genotype represented as a bit sequence. The model parameter value was calculated from the amount of complementarity between 2 different bit sequences with a length of 20 bits (figure shows 10 bits for simplicity), representing the shapes of interacting surfaces in the biomolecules. Black and red lines are graphical representations of the shapes these bit sequences represent; 1's indicate protrusions, 0's indicate crevices. Each bit is weighted double that to its right, and the strength of the interaction is scaled by the binary exclusive OR (XOR) between the two bit sequences. A perfect fit in a binding interaction would have a low dissociation constant, while worse fits would have corresponding looser binding. (C) Mutations may have specific effects depending on the location in the gene. Each gene had many separate bit sequences, one for each parameter in the model that the gene was involved in, corresponding to the different quantitative effects of mutation. For example, a mutation in the enhancer or promoter sequence (E/P) would alter gene expression levels, while mutations in the 5′ untranslated region or translation initiation site (UTR/SD) would alter translation rates. Mutations in the coding region that alter the binding site for CID on the PTC protein (Red) would alter the ability of PTC to cleave CID. Similarly, the different active sites on the CID protein (green, blue, orange) could be specifically altered by mutations in the coding region.
Mentions: In the following paragraphs, we describe extensions to this model that allow us to simulate evolution of the segment polarity network in response to selection on the pattern of en and wg expression (the phenotype). We present a diploid version of the model that allows us to directly compare evolution and robustness in haploid and diploid models. We also use a novel framework of deriving model parameter values from a digital genotype, which allows mutations to alter many gene properties (i.e. changes in expression level, stability and activity). Using these, we start with initially viable identical founders and follow them through 2,000 generations of evolution as shown in Figure 2A. We use the model to calculate phenotype (the en and wg pattern of expression) from genotype, apply truncation or stabilizing selection on the phenotype, using a multinomial sampling scheme to simulate random mating with a fixed population size (N = 200) and a per-gene mutation rate (μ) of 0.03.

Bottom Line: Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation.We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction.In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone.

View Article: PubMed Central - PubMed

Affiliation: Center for Cell Dynamics, Friday Harbor Labs, University of Washington, Friday Harbor, Washington, USA. kjkim@u.washington.edu

ABSTRACT
Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through "survival of the compatible": those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles.

Show MeSH
Related in: MedlinePlus