Santos-Moreno, Tasiudi, Kusumawardhani, Stelling and Schaerli (Nature Communications 14, 2454, 2023) constructed the first directly experimental genotype networks of synthetic gene regulatory networks (GRNs): over twenty CRISPR-interference-based three-node GRNs in Escherichia coli, producing GREEN-stripe, BLUE-stripe, non-functional or oscillatory phenotypes, together with an ODE model ensemble covering the full genotype space. Their characterization of robustness and evolvability was necessarily genotypic, because phenotypes were coarse-grained into only three classes; they left the effect of varying gene number unexplored; and they did not validate their models on oscillatory experimental data. The open problem is to complete this framework quantitatively at the phenotypic level: define and compute phenotypic robustness and evolvability from the quantitative gradient and time-course data, determine how these properties depend on the number of genes in the network, and quantitatively validate the model ensemble's oscillatory dynamics predictions against experiments.

Background

A gene regulatory network (GRN) is a set of genes whose products regulate each other's expression, typically via transcription factors binding to DNA. A genotype network is a set of genotypes that all produce the same phenotype and are connected by small mutational steps, so that one can walk from any member to another without leaving the phenotype; such networks are thought to make populations robust to mutation while letting them reach neighborhoods of genotype space where novel phenotypes are accessible. Genotype networks were first predicted theoretically and confirmed experimentally for proteins and RNAs, but for GRNs the evidence was only comparative until Santos-Moreno et al. (Nature Communications 14, 2454, 2023) built them synthetically. Their system uses CRISPR interference (CRISPRi), in which a catalytically dead Cas9 protein guided by a small guide RNA (sgRNA) blocks transcription of a target promoter, so each network node represses other nodes by expressing an sgRNA against them. Three nodes mutually repressing one another and driving fluorescent reporters were characterized in E. coli across a gradient of the inducer arabinose: phenotypes were either a spatial GREEN-stripe or BLUE-stripe of reporter expression in the gradient, non-functional (NF) behavior, or sustained oscillations (the topology contains the classical repressilator, a three-node ring of repressions with delayed negative feedback). Guided by an ensemble of mechanistic ODE models estimated against the experimental data, the authors sampled the complete genotype space of single mutational steps (changing a promoter strength, an sgRNA identity, or adding/removing a repression) and computed genotypic robustness, defined as the fraction of one-mutation neighbors of a GRN that retain the same phenotype, and genotypic evolvability, defined as the number of distinct phenotypes accessible in a single mutation. They found each phenotype's genotype network to be one connected component, linked evolvability to specific motifs such as the incoherent feed-forward loop, and estimated the prevalence of order-dependent epistasis between pairs of changes at a few percent (model-predicted median prevalence of about 4.5% for functional GRNs), consistent with the few-percent prevalence reported for yeast. Three quantitative gaps were explicit in the paper itself. First, because phenotypes were coarse-grained into only three classes, only genotypic robustness and evolvability could be studied; phenotypic measures, expected to show subtle but important differences from genotypic ones (Payne and Wagner, Nature Reviews Genetics 20, 24-38, 2019), 'could be addressed in future studies' using the underlying quantitative data. Second, the effect of varying the number of genes (nodes) on these properties was left open, although abstract, purely computational genotype-phenotype maps had shown that adding levels of complexity enhances robustness and evolvability (Catalán, Wagner, Manrubia and Cuesta, Journal of the Royal Society Interface 15, 20170516, 2018). Third, the model ensemble was only minimally re-parameterized to describe the oscillatory genotype network, and 'we did not explicitly validate the models on oscillatory experimental data', so the quantitative accuracy of the oscillation predictions (which topologies oscillate, with what period and robustness to mutation) is unconfirmed. A related but separate strand, environment-dependent epistasis and higher-order (beyond-pairwise) interactions in synthetic GRNs, had already been assayed experimentally by the same laboratory in Baier, Gauye, Pérez-Carrasco, Payne and Schaerli (Science Advances 9, eadf1773, 2023), who measured pairwise and triplet combinations of mutations in a synthetic stripe-forming GRN across an inducer gradient and observed epistasis switching in magnitude and sign along the gradient.

Problem Statement

Extend the combined experimental and model-based characterization of synthetic GRN genotype networks of Santos-Moreno et al. (2023) from a qualitative, three-class genotypic description to a quantitative, phenotypic-level account, along the three linked directions the paper itself poses, which jointly constitute this objective: (1) Phenotypic robustness and evolvability: using the quantitative experimental data (fluorescence reporter gradients and time courses) and the model-ensemble simulations, define a finer phenotypic discrimination for the synthetic GRNs and compute phenotypic robustness and evolvability of the genotype networks under this representation, establishing whether and how they differ from the genotypic measures obtained under the three-class coarse-graining. (2) Gene-number dependence: extend the approach, experimentally and by model-based sampling of genotype space, to synthetic GRNs with varying numbers of genes (network nodes), and determine how robustness and evolvability of the genotype networks change with gene number, in analogy with the enhancement previously found for abstract multilevel genotype-phenotype maps. (3) Quantitative validation of oscillatory dynamics: validate the mathematical model ensemble on oscillatory experimental data, establishing the quantitative accuracy of its oscillation predictions, including which topologies oscillate and with what periods, amplitudes and mutational robustness. Together, the three directions determine whether the experimentally confirmed genotype-network picture (connectedness, motif-linked evolvability, moderate epistasis prevalence) survives quantitative phenotypic scrutiny and how it scales with network size.

References

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  2. Baier F, Gauye F, Pérez-Carrasco R, Payne JL, Schaerli Y. Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks. Science Advances 9, eadf1773 (2023). DOI: 10.1126/sciadv.adf1773. https://doi.org/10.1126/sciadv.adf1773
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