A general mathematical framework for modelling subnetworks of the nuclear auxin pathway

Auxins are a family of plant hormones involved in various processes across plant tissues and species. The Nuclear Auxin Pathway (NAP) consists of interacting transcription factors (ARFs) and repressors (Aux/IAAs), which govern an individual cells response to changes in auxin concentration. These components are present in all land plants, and many species possess multiple copies of each signalling component. We present a general framework for ODE-based models of NAP submodules with the flexibility to model the promotion and repression of target genes by any combination of transcriptional regulators. We analyse published data and show that auxin treatment in Arabidopsis thaliana roots triggers a range of characteristically distinct temporal response profiles--for both target genes and the signalling components themselves. Using our modelling framework, we recapitulate aspects of this behaviour by presenting examples of real and theoretical NAP subnetworks, and by analysing the effect that these network dynamics have on auxin-mediated transcriptional responses. This work demonstrates the utility of our modelling framework as a general-purpose tool for understanding the function of certain protein-protein and protein-DNA interactions through their effects on the NAP. This exploration of the rich dynamics of more complex signalling pathways promises to advance our understanding of the NAP.