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Expression of pattern in plants: combining molecular and calculus-based biophysical paradigms.

Pattern formation in plant meristems occurs across a broad scale. At the topographical level (large scale), tissue folding in the meristem is responsible for the initiation of new organs in specific phyllotactic patterns and also determines organ shape. At the cellular level (small scale), oriented cell division and microtubule-based cellulose reinforcement control cell pattern and growth direction. I argue here that structural specification at each scale is highly efficient if the pertinent gene activity is manifested in two complementary biophysical categories. At large scale, one category is the tendency of the formative tissue to fold with a certain spatial periodicity determined by its material properties (e.g., bending stiffness from cellulose content). This latent tendency is formalized in a differential equation for physical buckling. The second category at this scale comprises boundary conditions that specify how the latent tendency is manifested as topography: whether tissue humps occur as whorls or Fibonacci spirals. This versatile combinatorial format accounts for the relative stability of alternative organ patterning as well as alternative organ shaping (e.g., stamens vs. carpels). It also accounts for the structural shifts seen in normal development and after mutation or chemical/physical intervention. At small scale, the latent differential activity is the tendency for groups of dividing cells to co-align their cytoskeletons. The curvature of the surface opposes this tendency. The least curved part of a new primordium is its quasicylindrical midportion. There, by aligning microtubules and cellulose coherently around the organ, a new growth direction is set. Thus large-scale buckling produces curvature variation, which, in turn, affects the localization and orientation of the cytoskeleton. This scheme for the coherent production of diverse geometrical features, involving calculus at two structural levels, is supported by complex organogenetic responses to simple physical intervention. Also, many morphological alternatives, wild type vs. mutant, reflect single changes in parameters in this differential-integral format.