The specification of SBML Level 1 is freely available from http://www.sbml.org/

Recent studies show that plant organ positioning may be mediated by localized concentrations of the plant hormone auxin. Auxin patterning in the shoot apical meristem is in turn brought about by the subcellular polar distribution of the putative auxin efflux mediator, PIN1. However, the question of what signals determine PIN1 polarization and how this gives rise to regular patterns of auxin concentration remains unknown. Here we address these questions by using mathematical modeling combined with confocal imaging. We propose a model that is based on the assumption that auxin influences the polarization of its own efflux within the meristem epidermis. We show that such a model is sufficient to create regular spatial patterns of auxin concentration on systems with static and dynamic cellular connectivities, the latter governed by a mechanical model. We also optimize parameter values for the PIN1 dynamics by using a detailed auxin transport model, for which parameter values are taken from experimental estimates, together with a template consisting of cell and wall compartments as well as PIN1 concentrations quantitatively extracted from confocal data. The model shows how polarized transport can drive the formation of regular patterns.Arabidopsis thaliana ͉ computable plant ͉ dynamical model ͉ pattern formation ͉ meristem I n the growing plant shoot, new leaf and flower primordia emerge at well defined positions, resulting in strikingly regular patterns (1). These phyllotactic patterns can be whorled (more than one new primordium develops simultaneously) or spiral (single primordia are created sequentially). Spiral phyllotaxis is often connected to the Fibonacci series because the numbers of parastichies (visible spirals) in each direction around the axis are commonly consecutive Fibonacci numbers. Also, consecutive primordia in the spiral often appear at a divergence angle close to the golden angle. The beautiful symmetries apparent in phyllotaxis and its connection to mathematics have inspired scientists to create theories and models to explain these patterns. One important finding from mathematical analysis and physical simulation (2, 3) is that many of the seemingly complex phyllotactic patterns and transitions found in plants can probably be explained to a large degree by any regular spacing mechanism superimposed on a gradually enlarging generative region. This finding is important because it suggests that the problem can be reduced to two potentially independent and smaller questions. The first question regards how meristem size is determined during plant development. The second question involves how a regularly spaced pattern of primordial position is specified. Traditionally, models have concentrated on the second question, and they can be divided into molecular and mechanical ideas (4-6). Because we investigate a model based on molecular experiments, here we discuss some molecular-based ideas in more detail. Schoute (7) first proposed the idea of lateral inhibition based on a diffusible chemical produced b...

ÐDetermining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers.