The mathematical foundation appropriate to computational developmental biology and more generally to “systems biology” may in the future strongly overlap with that of theoretical physics. For example, the growing tip of the plant Arabidopsis thaliana is one of many fascinating multiscale dynamical systems to be found in developmental biology. This tissue, called the Shoot Apical Meristem, gives rise through cell division and growth to the entire above-ground part of the plant. How does the shoot meristem remain dynamically stable over the life of the plant? How does it give rise to the phyllotactic pattern of flowers, leaves and branches that radiate outward from the stem? Modeling is now contributing to detailed molecular-level hypotheses about these biological questions. Relevant physics, and mathematics that is well known to physicists, can be applied at all stages of a computational approach to understanding this system. For instance, image analysis produces data on spatial and temporal patterns of gene expression. It raises problems of cell-tracking and geometric deformation solvable with nonlinear optimization methods from elastics and statistical physics. Multiscale dynamical models of cellular state, intercellular communication and tissue growth can be expressed as reaction networks coupled to elastic mechanical models of variable-structure systems. Such models can be used to explore hypothesized mechanisms both for meristem maintenance and for phyllotaxis. And fundamentally, all of these applications can be expressed in terms of a probabilistic version of creation and annihilation operators.

Joint work with Tigran Bacarian, Pierre Baldi, Ashish Bhan, Victoria Gor, Marcus Heisler, Henrik Jönsson, Elliot Meyerowitz, Alex Sadovsky, Bruce Shapiro, and Venu Reddy. Further information available at www.computableplant.org, or emj@uci.edu.