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,