Mathematical and computational analysis of the dynamics of polar transport of the plant hormone auxin.

Program

Part 1: Macroscopic PAT

Growth and development of (higher) plants takes a great deal of coordination between parts such as, for example, the shoot and the root system. Plants employ a complex system of chemical messengers to allow for this coordination and their responses to environmental factors such as gravity, light, temperature and pathogens. Over the past few years an increasing number of articles show that in addition to the chemical messengers plants show both short-distance and long-distance electrical signaling.

The plant hormone auxin (Indole-3-acetic acid, IAA) is one of these chemical messengers. It is synthesized in apical shoot meristems and leaf primordia, is transported in a basal direction by specialized parenchyma cells which reside in vascular bundles of leaves and vegetative and generative (inflorescence) stems. In the root, auxin is transported in the central cylinder towards the root tip, where the transport direction is reversed, and auxin is transported over a relatively short distance in an upward direction by root cap and epidermal cells.

It is this polar cell-to-cell transport of auxin that makes it quite special as compared to other plant hormones, which are transported through phloem sieve cells and xylem vessels. It is a very subtle system, that operates over long distances e.g. from the shoot to the root, but also over short distances thereby setting up gradients for example under the influence of environmental factors such as gravity and light, but also generating morphogenetic landscapes underlying pattern formation such as for example phyllotaxis. No wonder, that there exists a wealth of information in the literature as to auxin research. However, with the advent of molecular genetics and suitable model systems, in particular Arabidopsis thaliana, our insight in biosynthesis, transport, perception and transduction has substantially increased. That is, we are now at the stage that specific and deeper questions can be asked.

Over the past few years we have established a research program aimed at a deeper understanding of the dynamics of long-distance polar auxin transport (PAT). Our choice for studying long-range PAT comes from the fact that it is experimentally the most accessible part of PAT.

The most popular theory to explain long-range PAT is the so-called chemiosmotic theory. It describes cell-to-cell auxin transport through arrays of PAT cells by trans membrane diffusion, whereby specific auxin-export carriers placed polar in the plasma membrane at one side of the cell are responsible for the asymmetry or polarity of the auxin fluxes, and where the driving force of the PAT is generated by the proton-motive force. Furthermore, the transport of intracellular auxin in PAT cells is assumed to be by simple diffusion through the cytoplast; that is, it is not by directed intracellular transport mechanisms such as, for example, cytoplasmic streaming or vesicle transport.

Over the past few years molecular genetics of Arabidopsis thaliana has identified a class of putative auxin export-carriers, i.e. the so-called PIN proteins, whose intracellular position meets the predicted position by the chemiosmotic theory and correlates well with the direction of observed auxin fluxes. However, although a wealth of indirect evidence supports the chemiosmotic theory, a convincing proof that the theory is correct, and that the PIN proteins are the predicted carriers, was not available. We found that there are several reasons for this:

1. Although many polar auxin transport experiments had been published all of them lacked a well-defined quantitative experimental design suited for precise mathematical-model based analysis of observed intercellular auxin fluxes. We argued that this never could lead to unequivocal conclusions.
2. The assumed intracellular transport of auxin by simple diffusion had never been proven, because of a serious bottleneck, that is: thus far attempts to visualize intracellular auxin distribution and transport had failed.

The dots describe the program addressing ad 1, whereas ad 2 will be addressed in the Chara section.

• Development of a suitable experimental system. We adopted, with essential modifications, the classical donor-receiver assay, using inflorescence stem segments from Arabidopsis thaliana.
• Concomitant, the development of a macroscopic mathematical model of PAT to interpret macroscopic polar auxin fluxes through the experimental system. The model describes PAT by means of an advection-diffusion equation with extra terms that account for immobilization and exchange of auxin between arrays of PAT cells and the tissues surrounding them. The model has been built in such a way that it is not in conflict with the chemiosmotic theory but allows for alternatives.
• Implementing a high-speed computational platform that supports model simulation and Baysian parameter estimation from experimental data, using Markov chain Monte Carlo methods in collaboration with Prof. Dr. S. Portegies Zwart (Leiden Observatory).
• Investigation of auxin fluxes through our experimental system, using inflorescence stem segments from wild type and well-defined and characterized PAT mutants, such as PIN gene knockout mutants of A. thaliana. If in particular the PIN proteins were the sole auxin-anion efflux carriers responsible for the increased polar membrane permeability for auxin, we might expect that the pin mutants show a strong reduced or no PAT at all, because the velocity is virtually zero. Now, the concept of PAT velocity is only meaningful within the context of a mathematical model that describes PAT: it is by definition the strength (parameter) value of the advection part of the model. Such a model enables us to discriminate between the advection part (velocity) and other parameters that may influence the magnitude of the fluxes.
• The computational platform mentioned above was built to serve this goal.

Part 2: The role of auxin transport in Ginseng root and shoot architecture

Panax ginseng is an important medical herb that is widely cultivated in Korea, China and Japan. The root has been used as one of the most important traditional medicines in East Asia. Its use is rapidly expanding in Western countries as complementary and alternative medicine. It is estimated that the current world sales of various ginseng products are over 1 milliard US dollars.

Ginseng was formerly a wild plant but nowadays the ginseng roots available on the market comes from farms cultivating ginseng in fields. Field cultivation is a time-consuming and labor-intensive process: it takes 5 to 7 years from seedling to the final harvest. Beside the roots, also the above ground parts of the ginseng plant, like leaves and stems, are used for the production of ginseng products.

As mentioned earlier in the introduction, plants employ a complex system of chemical messengers to allow for the coordinated growth of roots and shoots. Since root architecture of ginseng plays such an important role in its economic value it is surprising to see that very little studies have been performed to better understand and improve root growth and morphology. The two main aspects that determine the price of ginseng roots are the number of lateral roots and the thickness of the main root (beside of course the amount of ginsenosides). The plant hormone auxin, and more particularly the polar auxin transport (PAT) of auxin, plays an important role in processes such as, branching, lateral root formation and secondary root growth.

In this project we will make use of our expertise in both measuring PAT and analyzing the obtained data through mathematical modeling from both stem and root tissue of ginseng plants with the ultimate goal of obtaining a better understanding of the role of auxin in the development of ginseng roots and shoots. Furthermore, the auxin transport capacity, as measured in stems, can be used as an indicator for plant fitness.