Practical indistinguishability in a gene regulatory network inference problem, a case study

Determining mechanistic models of gene regulation, especially underlying phenotypic variation, is a central goal of both mathematical biology and modern evolutionary biology. Progress has been made by analyzing high-throughput sequencing data, yet several challenges, involving both common characteristics of experimental data and the model development process, remain that limit the discovery of general principles. Even the highest-quality experimental data come with challenges. There are always sources of noise, a limit to how often we can measure the system in time, and it is impossible to measure all the relevant states that participate in the full underlying complexity. Additionally, there are usually sources of uncertainty in the underlying biological mechanisms, which give rise to multiple competing model structures. To underscore the need for further analysis of structural uncertainty in modeling, we use a meta-analysis across six journals covering mathematical biology and show that a huge number of mathematical models for biological systems are developed each year, but model selection and comparison across model structures appear to be less common. We then walk through a case study involving inference of regulatory network structure involved in a developmental decision in the nematode, Pristonchus pacificus, which exhibits an evolutionary novelty of mouth-dimorphism (predator vs. bacterivore). We first perform a careful study of the practical indistinguishability of a model structure, or the ability to uniquely infer the structure given the data, across a wide range of synthetic data regimes by refitting both the true model structure and several misspecified models. We then fit 13,824 distinct regulatory network models to gene expression data from three experimental conditions to determine which regulatory features are supported by the data. We discover model sets, or collections of models with shared regulatory network features that best fit the data, for each of the three experiments we considered and identify a regulatory network in the intersection of the three model sets. This model describes the data across the experimental conditions and exhibits a high degree of positive regulation and interconnectivity between the key regulators, eud-1, sult-1, and nhr-40. While the biological results are specific to the molecular biology of development in Pristonchus pacificus, the comparative modeling framework introduced here can be applied to other systems of gene regulation in an evolutionary developmental (evo-devo) context.