Sloppy Model Analysis of Bifurcations in Biochemical Networks

The dynamic equations describing even simple biochemical networks have many parameters and exhibit a range of behaviors. Discovering and characterizing the bifurcation surfaces between these behavioral basins-of-attraction presents a substantial mathematical challenge, and closed-form solutions may not exist. Recent work has linked bifurcations to the renormalization group (RG), and the RG has been tied to sloppy analysis (or information geometry). This paper shows how sloppy analysis can apply directly to bifurcations, including the normal-form of all major types and multi-parameter multi-variable systems with no obvious simplifying reparameteriziation. The coarse-graining procedure employed allows analysis of either theoretical models or a data-driven approach. Sloppy analysis can therefore rapidly provide insight into otherwise difficult-to-characterize biochemical systems, and implies application to other forms of network analysis.