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A developmental systems perspective on epistasis: computational exploration of mutational interactions in model developmental regulatory networks.

Gutiérrez J - PLoS ONE (2009)

Bottom Line: Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/- feedback) and associated control parameters, resulting in characteristic variational constraints.Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models.Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.

View Article: PubMed Central - PubMed

Affiliation: Grupo de Física y Astrofísica Computacional (FACom), Instituto de Física, Universidad de Antioquia, Medellín, Colombia. jayson.gutierrez@siu.udea.edu.co

ABSTRACT
The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/- feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.

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Average Mutational Trajectories with Respect to Fitness.Each plot summarizes the way in which successively accumulated mutations induce a fitness decline over each ensemble of networks modeled (average mutational trajectory). Black (dashed) line indicates a fitness decline in the absence of epistasis, which summarizes idealistic multiplicative effects among mutations (non-epistatic mutational trajectory, ). Red line indicates the calculated fitness decline. Average directionality of epistasis () and standard deviation (), average strength of epistasis (), and average mutational sensitivity () and standard deviation () were evaluated. A legend above a graphic “ANC: X TRs” reads Arbitrary Network Configuration with X Transcriptional Regulators (X = 5–8). Similarly, a legend “FNC: X TRs” reads Functional Network Configuration with X Transcriptional Regulators.
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pone-0006823-g002: Average Mutational Trajectories with Respect to Fitness.Each plot summarizes the way in which successively accumulated mutations induce a fitness decline over each ensemble of networks modeled (average mutational trajectory). Black (dashed) line indicates a fitness decline in the absence of epistasis, which summarizes idealistic multiplicative effects among mutations (non-epistatic mutational trajectory, ). Red line indicates the calculated fitness decline. Average directionality of epistasis () and standard deviation (), average strength of epistasis (), and average mutational sensitivity () and standard deviation () were evaluated. A legend above a graphic “ANC: X TRs” reads Arbitrary Network Configuration with X Transcriptional Regulators (X = 5–8). Similarly, a legend “FNC: X TRs” reads Functional Network Configuration with X Transcriptional Regulators.

Mentions: The first in silico mutational experiment was performed with the aim of characterizing the statistical behavior of the developmental propagation of combined mutational effects, and their possible impacts at the fitness level. Speciffically, I explored the way in which succesively accumulating mutations in a virtual embryo carrying a reference regulatory network impinged on the expression trajectories. A maximum of 10 mutations in each of the 15 networks of an ensemble were induced, whose fitness costs were evaluated as they accumulated; 2000 random mutational combinations were generated in each ensemble analyzed (for details on fitness calculations see Methods S2 and S3). The resulting average fitness decay tendency for each reference network, within an ensemble, was fit to the equation , where stands for the number of accumulated mutations, and the parameters and indicate average mutational insensitivity of the system, and average directionality of mutational interactions with respect to fitness, respectively [38]. Mutational effects on fitness reflecting independency would be observed for ; for a each successive mutation would tend to delay the fitness decline (positive epistasis); and for a each additional mutation would tend to accelarate the fitness decline (negative epistasis). The analysis of mutational trajectories (see Figure 2) over each ensemble of networks modeled show that the average tendency in the form successively accumulated mutations induce a fitness decline in arbitrary networks is clearly indicative of negative epistasis (red lines). In contrast, in functional networks mutations tend, on average, to compensate each other's effect as they accumulate, indicating positive or buffering epistasis. As mentioned above, the coefficients and capture the statistical behavior of the ensemble of networks modeled with respect to mutational insensitivity and directionality of mutations. Thus, they are important estimators that allow the comparisson of average effects between ensembles of arbitrary and functional networks, as well as between ensembles of networks exhibiting differing topological (structural) complexity. For example, the analysis indicates that the average mutational insensitivity in ensembles of arbitrary networks is greater than in those of functional ones (indicated by values closer to zero), thus corroborating the existence of a tight correlation between directionality of epistasis and average insensitivity [39]. It is also important to note that, comparatively, the average strength of epistasis () turned out to be larger in esembles of functional networks than in those of arbitrary networks. Finally, despite having found general tendencies regarding the statistical mutational behavior of the regulatory networks, no systematic relationship was observed between increasing network complexity and the epistatic nature of the regulatory networks. This observation contrasts with those results obtained in a recent study on epistatic interactions in simple network models [40], suggesting the existence of a general correlation between the average directionality of epistasis and network complexity (see below).


A developmental systems perspective on epistasis: computational exploration of mutational interactions in model developmental regulatory networks.

Gutiérrez J - PLoS ONE (2009)

Average Mutational Trajectories with Respect to Fitness.Each plot summarizes the way in which successively accumulated mutations induce a fitness decline over each ensemble of networks modeled (average mutational trajectory). Black (dashed) line indicates a fitness decline in the absence of epistasis, which summarizes idealistic multiplicative effects among mutations (non-epistatic mutational trajectory, ). Red line indicates the calculated fitness decline. Average directionality of epistasis () and standard deviation (), average strength of epistasis (), and average mutational sensitivity () and standard deviation () were evaluated. A legend above a graphic “ANC: X TRs” reads Arbitrary Network Configuration with X Transcriptional Regulators (X = 5–8). Similarly, a legend “FNC: X TRs” reads Functional Network Configuration with X Transcriptional Regulators.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2734181&req=5

pone-0006823-g002: Average Mutational Trajectories with Respect to Fitness.Each plot summarizes the way in which successively accumulated mutations induce a fitness decline over each ensemble of networks modeled (average mutational trajectory). Black (dashed) line indicates a fitness decline in the absence of epistasis, which summarizes idealistic multiplicative effects among mutations (non-epistatic mutational trajectory, ). Red line indicates the calculated fitness decline. Average directionality of epistasis () and standard deviation (), average strength of epistasis (), and average mutational sensitivity () and standard deviation () were evaluated. A legend above a graphic “ANC: X TRs” reads Arbitrary Network Configuration with X Transcriptional Regulators (X = 5–8). Similarly, a legend “FNC: X TRs” reads Functional Network Configuration with X Transcriptional Regulators.
Mentions: The first in silico mutational experiment was performed with the aim of characterizing the statistical behavior of the developmental propagation of combined mutational effects, and their possible impacts at the fitness level. Speciffically, I explored the way in which succesively accumulating mutations in a virtual embryo carrying a reference regulatory network impinged on the expression trajectories. A maximum of 10 mutations in each of the 15 networks of an ensemble were induced, whose fitness costs were evaluated as they accumulated; 2000 random mutational combinations were generated in each ensemble analyzed (for details on fitness calculations see Methods S2 and S3). The resulting average fitness decay tendency for each reference network, within an ensemble, was fit to the equation , where stands for the number of accumulated mutations, and the parameters and indicate average mutational insensitivity of the system, and average directionality of mutational interactions with respect to fitness, respectively [38]. Mutational effects on fitness reflecting independency would be observed for ; for a each successive mutation would tend to delay the fitness decline (positive epistasis); and for a each additional mutation would tend to accelarate the fitness decline (negative epistasis). The analysis of mutational trajectories (see Figure 2) over each ensemble of networks modeled show that the average tendency in the form successively accumulated mutations induce a fitness decline in arbitrary networks is clearly indicative of negative epistasis (red lines). In contrast, in functional networks mutations tend, on average, to compensate each other's effect as they accumulate, indicating positive or buffering epistasis. As mentioned above, the coefficients and capture the statistical behavior of the ensemble of networks modeled with respect to mutational insensitivity and directionality of mutations. Thus, they are important estimators that allow the comparisson of average effects between ensembles of arbitrary and functional networks, as well as between ensembles of networks exhibiting differing topological (structural) complexity. For example, the analysis indicates that the average mutational insensitivity in ensembles of arbitrary networks is greater than in those of functional ones (indicated by values closer to zero), thus corroborating the existence of a tight correlation between directionality of epistasis and average insensitivity [39]. It is also important to note that, comparatively, the average strength of epistasis () turned out to be larger in esembles of functional networks than in those of arbitrary networks. Finally, despite having found general tendencies regarding the statistical mutational behavior of the regulatory networks, no systematic relationship was observed between increasing network complexity and the epistatic nature of the regulatory networks. This observation contrasts with those results obtained in a recent study on epistatic interactions in simple network models [40], suggesting the existence of a general correlation between the average directionality of epistasis and network complexity (see below).

Bottom Line: Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/- feedback) and associated control parameters, resulting in characteristic variational constraints.Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models.Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.

View Article: PubMed Central - PubMed

Affiliation: Grupo de Física y Astrofísica Computacional (FACom), Instituto de Física, Universidad de Antioquia, Medellín, Colombia. jayson.gutierrez@siu.udea.edu.co

ABSTRACT
The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/- feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.

Show MeSH
Related in: MedlinePlus