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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.

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Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals isgenerated, and their genotype determines their phenotype. Individuals aresubject to either truncation or stabilizing selection, and viableindividuals mate (if sexual) or divide (if asexual). Each gene in the nextgeneration has a small (3%) chance of having a mutation. (B) Eachmodel parameter was determined from genotype represented as a bit sequence.The model parameter value was calculated from the amount of complementaritybetween 2 different bit sequences with a length of 20 bits (figure shows 10bits for simplicity), representing the shapes of interacting surfaces in thebiomolecules. Black and red lines are graphical representations of theshapes these bit sequences represent; 1's indicate protrusions,0's indicate crevices. Each bit is weighted double that to itsright, and the strength of the interaction is scaled by the binary exclusiveOR (XOR) between the two bit sequences. A perfect fit in a bindinginteraction would have a low dissociation constant, while worse fits wouldhave corresponding looser binding. (C) Mutations may have specific effectsdepending on the location in the gene. Each gene had many separate bitsequences, one for each parameter in the model that the gene was involvedin, corresponding to the different quantitative effects of mutation. Forexample, a mutation in the enhancer or promoter sequence (E/P) would altergene expression levels, while mutations in the 5′ untranslatedregion or translation initiation site (UTR/SD) would alter translationrates. Mutations in the coding region that alter the binding site for CID onthe 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.
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pcbi-1000296-g002: Bridging genotype to phenotype to simulate evolution.(A) Flowchart of evolutionary model. A population of individuals isgenerated, and their genotype determines their phenotype. Individuals aresubject to either truncation or stabilizing selection, and viableindividuals mate (if sexual) or divide (if asexual). Each gene in the nextgeneration has a small (3%) chance of having a mutation. (B) Eachmodel parameter was determined from genotype represented as a bit sequence.The model parameter value was calculated from the amount of complementaritybetween 2 different bit sequences with a length of 20 bits (figure shows 10bits for simplicity), representing the shapes of interacting surfaces in thebiomolecules. Black and red lines are graphical representations of theshapes these bit sequences represent; 1's indicate protrusions,0's indicate crevices. Each bit is weighted double that to itsright, and the strength of the interaction is scaled by the binary exclusiveOR (XOR) between the two bit sequences. A perfect fit in a bindinginteraction would have a low dissociation constant, while worse fits wouldhave corresponding looser binding. (C) Mutations may have specific effectsdepending on the location in the gene. Each gene had many separate bitsequences, one for each parameter in the model that the gene was involvedin, corresponding to the different quantitative effects of mutation. Forexample, a mutation in the enhancer or promoter sequence (E/P) would altergene expression levels, while mutations in the 5′ untranslatedregion or translation initiation site (UTR/SD) would alter translationrates. Mutations in the coding region that alter the binding site for CID onthe 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 tosimulate evolution of the segment polarity network in response to selection on thepattern of en and wg expression (the phenotype). We present a diploid version of themodel that allows us to directly compare evolution and robustness in haploid anddiploid models. We also use a novel framework of deriving model parameter valuesfrom a digital genotype, which allows mutations to alter many gene properties (i.e.changes in expression level, stability and activity). Using these, we start withinitially viable identical founders and follow them through 2,000 generations ofevolution as shown in Figure 2A.We use the model to calculate phenotype (the en and wg pattern of expression) fromgenotype, apply truncation or stabilizing selection on the phenotype, using amultinomial 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 isgenerated, and their genotype determines their phenotype. Individuals aresubject to either truncation or stabilizing selection, and viableindividuals mate (if sexual) or divide (if asexual). Each gene in the nextgeneration has a small (3%) chance of having a mutation. (B) Eachmodel parameter was determined from genotype represented as a bit sequence.The model parameter value was calculated from the amount of complementaritybetween 2 different bit sequences with a length of 20 bits (figure shows 10bits for simplicity), representing the shapes of interacting surfaces in thebiomolecules. Black and red lines are graphical representations of theshapes these bit sequences represent; 1's indicate protrusions,0's indicate crevices. Each bit is weighted double that to itsright, and the strength of the interaction is scaled by the binary exclusiveOR (XOR) between the two bit sequences. A perfect fit in a bindinginteraction would have a low dissociation constant, while worse fits wouldhave corresponding looser binding. (C) Mutations may have specific effectsdepending on the location in the gene. Each gene had many separate bitsequences, one for each parameter in the model that the gene was involvedin, corresponding to the different quantitative effects of mutation. Forexample, a mutation in the enhancer or promoter sequence (E/P) would altergene expression levels, while mutations in the 5′ untranslatedregion or translation initiation site (UTR/SD) would alter translationrates. Mutations in the coding region that alter the binding site for CID onthe 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.
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Related In: Results  -  Collection

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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 isgenerated, and their genotype determines their phenotype. Individuals aresubject to either truncation or stabilizing selection, and viableindividuals mate (if sexual) or divide (if asexual). Each gene in the nextgeneration has a small (3%) chance of having a mutation. (B) Eachmodel parameter was determined from genotype represented as a bit sequence.The model parameter value was calculated from the amount of complementaritybetween 2 different bit sequences with a length of 20 bits (figure shows 10bits for simplicity), representing the shapes of interacting surfaces in thebiomolecules. Black and red lines are graphical representations of theshapes these bit sequences represent; 1's indicate protrusions,0's indicate crevices. Each bit is weighted double that to itsright, and the strength of the interaction is scaled by the binary exclusiveOR (XOR) between the two bit sequences. A perfect fit in a bindinginteraction would have a low dissociation constant, while worse fits wouldhave corresponding looser binding. (C) Mutations may have specific effectsdepending on the location in the gene. Each gene had many separate bitsequences, one for each parameter in the model that the gene was involvedin, corresponding to the different quantitative effects of mutation. Forexample, a mutation in the enhancer or promoter sequence (E/P) would altergene expression levels, while mutations in the 5′ untranslatedregion or translation initiation site (UTR/SD) would alter translationrates. Mutations in the coding region that alter the binding site for CID onthe 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 tosimulate evolution of the segment polarity network in response to selection on thepattern of en and wg expression (the phenotype). We present a diploid version of themodel that allows us to directly compare evolution and robustness in haploid anddiploid models. We also use a novel framework of deriving model parameter valuesfrom a digital genotype, which allows mutations to alter many gene properties (i.e.changes in expression level, stability and activity). Using these, we start withinitially viable identical founders and follow them through 2,000 generations ofevolution as shown in Figure 2A.We use the model to calculate phenotype (the en and wg pattern of expression) fromgenotype, apply truncation or stabilizing selection on the phenotype, using amultinomial 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