Modelling of Arabidopsis LAX3 expression suggests auxin homeostasis

•A single-cell model of the auxin responsive expression of the auxin inux transporter LAX3.•We identify conditions under which the model has bistability, and thus may act as a genetic switch.•Adding a decay term in the auxin signal we fit model parameters to match mRNA expression data.•The apparent rate of auxin signal decay suggests an endogenous auxin homeostasis mechanism.•The model with fitted parameters is still bistable, given a high enough rate of LAX3 auxin active inux relative to passive diffusion.

Emergence of new lateral roots from within the primary root in Arabidopsis has been shown to be regulated by the phytohormone auxin, via the expression of the auxin influx carrier LAX3, mediated by the ARF7/19 IAA14 signalling module ( Swarup et al., 2008). A single cell model of the LAX3 and IAA14 auxin response was formulated and used to demonstrate that hysteresis and bistability may explain the experimentally observed ‘all-or-nothing’ LAX3 spatial expression pattern in cortical cells containing a gradient of auxin concentrations. The model was tested further by using a parameter fitting algorithm to match model output with qRT-PCR mRNA expression data following exogenous auxin treatment. It was found that the model is able to show good agreement with the data, but only when the exogenous auxin signal is degraded over time, at a rate higher than that measured in the experimental medium, suggesting the triggering of an endogenous auxin homeostasis mechanism. Testing the model over a more physiologically relevant range of extracellular auxin shows bistability and hysteresis still occur when using the optimised parameters, providing the rate of LAX3 active auxin transport is sufficiently high relative to passive diffusion.