New models of gene transcriptional responses to auxin signalling in Arabidopsis are presented. This work extends a previous model of auxin signalling to include networks of gene-sets which may control developmental responses along auxin gradients. Key elements of this new study include models of signalling pathways and networks involving two Aux-IAA proteins (IAAs), auxin response factors (ARFs) and gene targets. Hypotheses for the gene network topologies which may be involved in developmental responses have been tested against experimental observations for root hair growth in particular. In studying these models, we provide a framework for the analysis of auxin signalling with multiple IAAs and ARFs, and discuss the implications of bistability in such systems. 2011 Elsevier Inc. All rights reserved.