  Zinc uptake in roots is believed to be mediated by ZIP (ZRT-, IRT-like
Proteins) transporters. Once inside the symplast, zinc is transported to the
pericycle, where it exits by means of HMA (Heavy Metal ATPase) transporters.
The combination of symplastic transport and spatial separation of influx and
efflux produces a pattern in which zinc accumulates in the pericycle. Here,
mathematical modelling was employed to study the importance of ZIP regulation,
HMA abundance and symplastic transport in creation of the radial pattern of
zinc in primary roots of Arabidopsis thaliana.
  A comprehensive one-dimensional dynamic model of radial zinc transport in
roots was developed and used to conduct simulations. The model accounts for the
structure of the root consisting of symplast and apoplast and includes effects
of water flow, diffusion, and cross-membrane transport via transporters. It
also incorporates the radial geometry and varying porosity of root tissues, as
well as regulation of ZIP transporters.
  Steady state patterns were calculated for various zinc concentrations in the
medium, water influx and HMA abundance. The experimentally observed zinc
gradient was reproduced very well. Increase of HMA or decrease in water influx
led to loss of the gradient. The dynamic behaviour for a change in medium
concentration and water influx was also simulated showing short adaptation
times in the range of seconds to minutes. Slowing down regulation led to
oscillations in expression levels, suggesting the need for rapid regulation and
existence of buffering agents.
  The model captures the experimental findings very well and confirms the
hypothesis that low abundance of HMA4 produces a radial gradient in zinc
concentration. Surprisingly, transpiration was found to be also a key
parameter. The model suggests that ZIP regulation takes place on a comparable
time scale as symplastic transport.
