Workshop on Pattern Formation and Functional Morphology, Thu, 10 Jan, 2008
Speaker: Richard Smith
Abstract
One of the most conspicuous examples of patterning in plants is phyllotaxis, which is the arrangement of plant organs about a central axis. On the side of a pine cone or in the head of a sunflower one can see intersecting rows of spirals, running in opposite directions, which create the visually striking effect of a lattice of organs. For over a century biologists and mathematicians have been searching for an explanation of this organ positioning. Computer scientists have joined this quest with simulations models to test a variety of hypotheses.
One attractive theory of phyllotaxis, upon which many previous simulation models are based, is that one or more diffusing inhibitors produced by existing organ primordia prevent the formation of new primordia nearby. This theory can be readily modeled within the framework of reaction-diffusion, which was originally proposed by Turing (1952) as a universal paradigm for biological pattern formation, including phyllotaxis. The reaction-diffusion mechanism fits nicely with the idea of genetic regulatory networks and is consistent with some patterning processes in animals.
Experimental results, however, suggest that quite different patterning mechanisms may be operating in plants. In a series of experiments aimed at understanding the processes involved in phyllotaxis, Reinhardt et.al. (2003) showed that organ initiation in Arabidopsis is triggered by the accumulation of an activator, the plant hormone auxin, rather than the absence of an inhibitor. Furthermore, polar transport of auxin, rather than diffusion, plays a central role in phyllotaxis regulation. This is fundamentally different from the reaction-diffusion model, in which cells depend on local self-enhanced production to create peaks in activator concentration. The transport model instead relies on the redistribution and concentration of the activator from surrounding tissues or from other more distant sources.
We constructed a simulation model of a growing shoot apex with realistic cell geometry to explore the hypothesis that actively transported auxin can indeed be responsible for the formation of phyllotactic patterns observed in nature. Consistent with experimental results, we consider polar auxin transporter molecules (PIN1 proteins) which are able to relocate preferentially to one side of a cell, thus polarizing the direction of auxin flux out of the cell. The exact mechanism of this localization is unknown; we have postulated a feedback mechanism according to which the PIN1 proteins relocate in response to the auxin concentration in neighboring cells. This assumption leads to a transport-based patterning mechanism which creates peaks in auxin concentration that determine the location of future organs. This model can create the correct spatial and temporal pattern of organ initiation sites. Furthermore, a variety of phyllotactic patterns observed in nature can be produced by varying model parameters. This model is also able to start patterns de novo and capture the effect of selected mutations and experimental manipulations.
Another patterning process in which the transport of auxin is thought to play a key role is leaf venation. Experimental work led Sachs (1981) to propose the canalization hypothesis to explain the emergence of veins in plant tissue. In this hypothesis, Sachs postulated that the auxin transport capacity of a cell membrane increases with auxin flux, causing preferred routes, or “canals”, of auxin flux to emerge. These canals eventually differentiate to form veins. We have extended previous simulations of canalization, performed on regular arrays of square cells, to a growing cellular model of a young leaf. Our simulations confirm that the canalization hypothesis is sufficient to explain the initial stages of vascular patterning in the developing Arabidopsis leaf. Our results also show that phyllotaxis and leaf venation can be explained within the same transport-driven model, by changing the rules for transporter localization and the growth dynamics of the underlying surfaces. This result is counterintuitive, because phyllotactic patterns are usually very different from venation patterns.
Lastly I will present a simulation of apical dominance that uses the canalization theory to implement the “traffic-jam” model for apical dominance proposed by Leyser (2006?). This model demonstrates an interesting aspect of auxin signaling mechanisms and demonstrates the diversity of possibilities that the transport patterning model possesses. This may shed some light on how this small molecule can be involved in so many different plant processes.
This work was done in collaboration with Przemyslaw Prusinkiewicz (University of Calgary), Ottoline Leyser (University of York), and the group of Cris Kuhlemeier (University of Berne).
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
This page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 05/02/24 - 08:11 CEST and this file (/specsem/ssqbm/participants/abstracts/index.php) was last modified on 12/18/12 - 11:01 CEST