Abstract
The polar transport of the plant hormone auxin has been the subject of many studies, several involving mathematical modelling. Unfortunately, most of these models have not been experimentally verified. Here we present experimental measurements of long-distance polar auxin transport (PAT) in segments of inflorescence stems of Arabidopsis thaliana together with a descriptive mathematical model that was developed from these data. It is based on a general advection-diffusion equation for auxin density, as suggested by the chemiosmotic theory, but is extended to incorporate both immobilization of auxin and exchange with the surrounding tissue of cells involved in PAT, in order to account for crucial observations. We found that development of the present model assisted effectively in the analysis of experimental observations. As an example, we discuss the analysis of a quadruple mutant for all four AUX1/LAX1-LAX3 influx carriers genes. We found a drastic change in the parameters governing the exchange of PAT channels with the surrounding tissue, whereas the velocity was still of the order of magnitude of the wild type. In addition, the steady-state flux of auxin through the PAT system of the mutant did not exhibit a saturable component, as we found for the wild type, suggesting that the import carriers are responsible for the saturable component in the wild type. In the accompanying Supplementary data available at JXB online, we describe in more detail the data-driven development of the model, review and derive predictions from a mathematical model of the chemiosmotic theory, and explore relationships between parameters in our model and processes and parameters at the cellular level.
Highlights
Auxin is a plant hormone endowed with a unique transport system
We present experimental measurements of long-distance polar auxin transport (PAT) in segments of inflorescence stems of Arabidopsis thaliana together with a descriptive mathematical model that was developed from these data
It is based on a general advection–diffusion equation for auxin density, as suggested by the chemiosmotic theory, but is extended to incorporate both immobilization of auxin and exchange with the surrounding tissue of cells involved in PAT, in order to account for crucial observations
Summary
Auxin is a plant hormone endowed with a unique transport system. Interest in auxin transport dates back to 1880, when Charles Darwin reported on a transmissible signal that is involved in the phototropy of Canary grass coleoptiles (Darwin and Darwin, 1880). Over the past few decades tremendous progress has been made in revealing the genes and their protein products involved in PAT, and we observed an increasing number of computational models aimed at understanding the role of the distribution of auxin in time and space, during growth and developmental processes These models rely largely on observed expression patterns of PAT genes instead of direct measurements of auxin fluxes (cf Kramer, 2008). The mathematical model of the dynamics of this system identifies individual PAT cells As this description is in between a macroscopic model that ignores cellular structure and a microscopic model that describes transport processes at the molecular scale, we call it a mesoscopic model for PAT. We will briefly comment on this problem in the Discussion, in particular with respect to the assumptions made by the MGGM model
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