The G. S. Watson Annual Lecture, 2007
Dr Bob Anderssen
Title: "Modelling Pattern Formation in Plants"
Presenter: Dr Bob Anderssen, Senior Principal Mathematician, CSIRO Mathematical and Information Sciences
Date: Tuesday, 29 May 2007, 4pm to 5pm, Room 3.03 - Applied Science 1 Building, La Trobe University, Bendigo
Abstract: The history of modelling pattern formation in biology can be traced back to Fibonacci and phyllotaxis. Such activities include modelling the shapes of leaves, the organization of the hairs on leaves, the arrangement of the petals on flowers and the stripes on animals, and the microscopic arrangement of the cellular structure within biological tissue. They can be viewed as representative inverse problems in biology, since, in such situations, one is aiming to recover from observations about the (two-dimensional) geometry of the pattern, information about three-dimensional structure and arrangements and/or the dynamics of the underlying developmental biology and genetics.
Just as in applied mathematics, where one works initially with some representative simplified model, biologists use model animal and plant systems (such as fruit flies, worms and Arabidopsis) to recover information about the dynamics of the underlying biology and genetics from observed properties (phenotypes) of the dynamics of the pattern format. Stereology and phyllotaxis represent appropriate model systems for explaining the role of mathematics in the information recovery involved.
An independent key and current inverse problem relates to how any specific pattern formation process should be modelled. A choice must be made between the averaging inherent in a macroscopic model and a cellular detail implicit in microscopic and molecular models. From a macroscopic perspective, Turing's seminal 1952 paper on morphogenesis represents the starting point for the various partial differential equation, reactor-diffusion, models that have been proposed and analysed for pattern formation in biology. Though such models can be adapted to simulate observed biological patterns, the molecular dynamics of the activator-inhibitor mechanisms, on which they are based, have yet to be confirmed biologically.
From a molecular perspective, it is the "genetics of geometry" that must be conceptualized and modelled. The decision-making involved will be illustrated using the modelling of phyllotaxis.