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Effect of regulatory architecture on broad versus narrow sense heritability.

Wang Y, Vik JO, Omholt SW, Gjuvsland AB - PLoS Comput. Biol. (2013)

Bottom Line: We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics.The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns.Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.

View Article: PubMed Central - PubMed

Affiliation: Centre for Integrative Genetics (CIGENE), Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway.

ABSTRACT
Additive genetic variance (VA ) and total genetic variance (VG ) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported VA /VG ratios from line-cross experiments is not well understood. Here we report how the VA /VG ratio, and thus the ratio between narrow and broad sense heritability (h(2) /H(2) ), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low VA /VG ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower VA /VG ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.

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Phenotypes derived from the cGP models.Graphical illustration of the phenotypes recorded for the five cGP models studied. Time courses (state variable on y-axis, time on x-axis) for the baseline parameter set are displayed for all five models. A. In the absence of external glucose all state variables (concentration of cAMP is shown) in the cAMP model [21] converge to a stable steady state (blue circle on y-axis). After addition of external glucose (5 mM added at time 50) we see a rapid change followed by a slow return to the original steady state. In addition to the original steady state, the extremal concentration (top blue circle) as well as the time to reach the extremum (blue line) was recorded as phenotypes. B. Metabolite concentrations (internal glucose (GLCi), glucose-6-phospate (G6P) and fructose-6-phospate (F6P) are shown) in the glycolysis model [20] all converge to a stable steady state, indicated by open circles. The steady state concentrations for 13 metabolites were recorded as phenotypes from this model. C. For the cell cycle model [22] we recorded the peak level and the time from bottom to peak as for the circadian model (Figure 1D), and in addition we recorded cell cycle events such as bud emergence at the time when [BUD] = 1 indicated by the black arrow. D. mRNA and protein concentrations (mRNA for Bmal1 (MB), Cry (MC) and Per (MP) are shown) in the circadian model [23] converge to a limit cycle. In addition to the period of oscillation (long blue line) for each of the 16 variables the peak level (open blue circle) as well as the time from bottom to peak (short blue line) were recorded as phenotypes. E. We used the base level, peak level, amplitude, time to peak, and time to 25%, 50%, 75% and 90% recovery of the action potential and calcium transient as cell level phenotypes of the action potential model [24]. An action potential is shown in the figure.
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pcbi-1003053-g001: Phenotypes derived from the cGP models.Graphical illustration of the phenotypes recorded for the five cGP models studied. Time courses (state variable on y-axis, time on x-axis) for the baseline parameter set are displayed for all five models. A. In the absence of external glucose all state variables (concentration of cAMP is shown) in the cAMP model [21] converge to a stable steady state (blue circle on y-axis). After addition of external glucose (5 mM added at time 50) we see a rapid change followed by a slow return to the original steady state. In addition to the original steady state, the extremal concentration (top blue circle) as well as the time to reach the extremum (blue line) was recorded as phenotypes. B. Metabolite concentrations (internal glucose (GLCi), glucose-6-phospate (G6P) and fructose-6-phospate (F6P) are shown) in the glycolysis model [20] all converge to a stable steady state, indicated by open circles. The steady state concentrations for 13 metabolites were recorded as phenotypes from this model. C. For the cell cycle model [22] we recorded the peak level and the time from bottom to peak as for the circadian model (Figure 1D), and in addition we recorded cell cycle events such as bud emergence at the time when [BUD] = 1 indicated by the black arrow. D. mRNA and protein concentrations (mRNA for Bmal1 (MB), Cry (MC) and Per (MP) are shown) in the circadian model [23] converge to a limit cycle. In addition to the period of oscillation (long blue line) for each of the 16 variables the peak level (open blue circle) as well as the time from bottom to peak (short blue line) were recorded as phenotypes. E. We used the base level, peak level, amplitude, time to peak, and time to 25%, 50%, 75% and 90% recovery of the action potential and calcium transient as cell level phenotypes of the action potential model [24]. An action potential is shown in the figure.

Mentions: The model of the complete cAMP signaling pathway in S. cerevisiae[21] taking the external glucose level as input was downloaded as SBML code (http://www.biomedcentral.com/content/supplementary/1752-0509-3-70-s1.xml) and integrated using PySCeS [25]. Genetic variation was introduced on association/dissociation and phosphorylation/dephosphorylation rates of signal proteins (see Figure S2 and Table S1). The initial steady state concentrations before adding external glucose, the peak values after adding glucose and the time taken to reach peak values of cellular proteins were recorded as phenotypes (see Figure 1A for phenotype illustration and Table S6 for phenotype descriptions).


Effect of regulatory architecture on broad versus narrow sense heritability.

Wang Y, Vik JO, Omholt SW, Gjuvsland AB - PLoS Comput. Biol. (2013)

Phenotypes derived from the cGP models.Graphical illustration of the phenotypes recorded for the five cGP models studied. Time courses (state variable on y-axis, time on x-axis) for the baseline parameter set are displayed for all five models. A. In the absence of external glucose all state variables (concentration of cAMP is shown) in the cAMP model [21] converge to a stable steady state (blue circle on y-axis). After addition of external glucose (5 mM added at time 50) we see a rapid change followed by a slow return to the original steady state. In addition to the original steady state, the extremal concentration (top blue circle) as well as the time to reach the extremum (blue line) was recorded as phenotypes. B. Metabolite concentrations (internal glucose (GLCi), glucose-6-phospate (G6P) and fructose-6-phospate (F6P) are shown) in the glycolysis model [20] all converge to a stable steady state, indicated by open circles. The steady state concentrations for 13 metabolites were recorded as phenotypes from this model. C. For the cell cycle model [22] we recorded the peak level and the time from bottom to peak as for the circadian model (Figure 1D), and in addition we recorded cell cycle events such as bud emergence at the time when [BUD] = 1 indicated by the black arrow. D. mRNA and protein concentrations (mRNA for Bmal1 (MB), Cry (MC) and Per (MP) are shown) in the circadian model [23] converge to a limit cycle. In addition to the period of oscillation (long blue line) for each of the 16 variables the peak level (open blue circle) as well as the time from bottom to peak (short blue line) were recorded as phenotypes. E. We used the base level, peak level, amplitude, time to peak, and time to 25%, 50%, 75% and 90% recovery of the action potential and calcium transient as cell level phenotypes of the action potential model [24]. An action potential is shown in the figure.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC3649986&req=5

pcbi-1003053-g001: Phenotypes derived from the cGP models.Graphical illustration of the phenotypes recorded for the five cGP models studied. Time courses (state variable on y-axis, time on x-axis) for the baseline parameter set are displayed for all five models. A. In the absence of external glucose all state variables (concentration of cAMP is shown) in the cAMP model [21] converge to a stable steady state (blue circle on y-axis). After addition of external glucose (5 mM added at time 50) we see a rapid change followed by a slow return to the original steady state. In addition to the original steady state, the extremal concentration (top blue circle) as well as the time to reach the extremum (blue line) was recorded as phenotypes. B. Metabolite concentrations (internal glucose (GLCi), glucose-6-phospate (G6P) and fructose-6-phospate (F6P) are shown) in the glycolysis model [20] all converge to a stable steady state, indicated by open circles. The steady state concentrations for 13 metabolites were recorded as phenotypes from this model. C. For the cell cycle model [22] we recorded the peak level and the time from bottom to peak as for the circadian model (Figure 1D), and in addition we recorded cell cycle events such as bud emergence at the time when [BUD] = 1 indicated by the black arrow. D. mRNA and protein concentrations (mRNA for Bmal1 (MB), Cry (MC) and Per (MP) are shown) in the circadian model [23] converge to a limit cycle. In addition to the period of oscillation (long blue line) for each of the 16 variables the peak level (open blue circle) as well as the time from bottom to peak (short blue line) were recorded as phenotypes. E. We used the base level, peak level, amplitude, time to peak, and time to 25%, 50%, 75% and 90% recovery of the action potential and calcium transient as cell level phenotypes of the action potential model [24]. An action potential is shown in the figure.
Mentions: The model of the complete cAMP signaling pathway in S. cerevisiae[21] taking the external glucose level as input was downloaded as SBML code (http://www.biomedcentral.com/content/supplementary/1752-0509-3-70-s1.xml) and integrated using PySCeS [25]. Genetic variation was introduced on association/dissociation and phosphorylation/dephosphorylation rates of signal proteins (see Figure S2 and Table S1). The initial steady state concentrations before adding external glucose, the peak values after adding glucose and the time taken to reach peak values of cellular proteins were recorded as phenotypes (see Figure 1A for phenotype illustration and Table S6 for phenotype descriptions).

Bottom Line: We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics.The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns.Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.

View Article: PubMed Central - PubMed

Affiliation: Centre for Integrative Genetics (CIGENE), Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Ås, Norway.

ABSTRACT
Additive genetic variance (VA ) and total genetic variance (VG ) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported VA /VG ratios from line-cross experiments is not well understood. Here we report how the VA /VG ratio, and thus the ratio between narrow and broad sense heritability (h(2) /H(2) ), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low VA /VG ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower VA /VG ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.

Show MeSH
Related in: MedlinePlus