A recovery principle provides insight into auxin pattern control in the Arabidopsis root

Regulated auxin patterning provides a key mechanism for controlling root growth and development. We have developed a data-driven mechanistic model using realistic root geometry and formulated a principle to theoretically investigate quantitative auxin pattern recovery following auxin transport perturbation. This principle reveals that auxin patterning is potentially controlled by multiple combinations of interlinked levels and localisation of influx and efflux carriers. We demonstrate that (1) when efflux carriers maintain polarity but change levels, maintaining the same auxin pattern requires non-uniform and polar distribution of influx carriers; (2) the emergence of the same auxin pattern, from different levels of influx carriers with the same nonpolar localisation, requires simultaneous modulation of efflux carrier level and polarity; and (3) multiple patterns of influx and efflux carriers for maintaining an auxin pattern do not have spatially proportional correlation. This reveals that auxin pattern formation requires coordination between influx and efflux carriers. We further show that the model makes various predictions that can be experimentally validated.