Analytical model for long-distance tracer-transport in plants

Abstract

Recent investigations of long-distance transport in plants using non-invasive tracer techniques such as 11C radiolabeling monitored by positron emission tomography (PET) combined with magnetic resonance imaging (MRI) revealed the need of dedicated methods to allow a quantitative data analysis and comparison of such experiments. A mechanistic compartmental tracer transport model is presented, defined by a linear system of partial differential equations (PDEs). This model simplifies the complexity of axial transport and lateral exchanges in the transport pathways of plants (e.g. the phloem) by simulating transport and reversible exchange within three compartments using just a few parameters which are considered to be constant in space and time. For this system of PDEs an analytical solution in Fourier-space was found allowing a fast and numerically precise evaluation. From the steady-state behavior of the model, the system loss (steadily fixed tracer along the transport conduits) was derived as an additional parameter that can be readily interpreted in a physiological way. The presented framework allows the model to be fitted to spatio-temporal tracer profiles including error and sensitivity analysis of the estimated parameters. This is demonstrated for PET data sets obtained from radish, sugar beet and maize plants.