The chemical dynamics of organ positioning in conifer development

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While math has long been used to describe plant patterns (e.g. the Fibonacci numbers observed in lateral organ arrangements, such as in pine cones), recent developments in molecular imaging have spurred a growing recognition in biology that many aspects of plant development are inherently quantitative (such as organ spacing, plant shape and architecture) and require mathematical theory to explain the underlying molecular mechanisms. Much of the new quantitative and mathematical work has been on the spatial distribution of the hormone auxin (a primary determinant of local growth) in the model plant Arabidopsis. Our work focuses on the unique dynamical aspects of developmental patterning and growth in conifer morphogenesis. Arabidopsis has two cotyledons (seed leaves'), which form in a planar arrangement; conifers have a variable number (frequently from 2 to 12), which form in a whorl on a domed geometry. Conifer cotyledons can therefore have much more complex spatial patterning (i.e. higher-order modes for growth catalyst patterns; more complex pattern selection to produce whorled morphogenesis). We have used reaction-diffusion (RD) models to characterize concentration patterning on surfaces in 3D which, coupled to local growth, represent the symmetry-breaking mechanism positioning the conifer whorls. We have studied the geometric dependence of patterning on experimentally-observed dome flattening, as well as expanding earlier theoretical ideas that whorled structures on domed geometries form in two stages a 1st stage to position the whorl, a 2nd stage to subdivide the whorl into cotyledons. Experimentally, we have found two such stages in spruce, and that they are separable by disruption of auxin transport. We now plan to incorporate the unique up-the-gradient' polar auxin transport (PAT) dynamics (discovered in Arabidopsis) into our 3D model. This addresses conifer geometry and local growth (which are not contained in any of the Arabidopsis models), and will also produce a new, continuous formulation of PAT (prior models are cell-based and discrete). Finite-element computations and mathematical analysis will be used to find the relative contributions of RD and PAT (on a growing domain) in conifer cotyledon formation (including dependence on particular reaction nonlinearities). Model dynamics will be refined by new 3D experimental data on auxin distributions. Benefits to field: advancing new mathematical techniques in plant science; training interdisciplinary scientists; leveraging recent large molecular and modelling efforts in Arabidopsis to understand conifers. Benefits to Canada: supporting Canadian expertise in mathematical, quantitative biology to gain quantitative understanding and control of the development of conifers, which are of central value to the country's ecology and economy (forestry is $20B of GDP, nearly 80% of forest tree species are conifers).