A Unified Model of Shoot Tropism in plants: Photo-, Gravi- and Propio-Ception — Supplementary Material

where s is the curvilinear abscissa along the organ, from the base s = 0 to the tip of the organ s = L and t is the time. νA(L, t) is the apical photoceptive term, readily transmitted all along the organ, and γC(s, t) is the proprioceptive term. Let now the initial conditions be a straight but tilted organ and the boundary conditions of a basal perfect clamping, : A(s, 0) = A(0, t) = A0 C(s, 0) = 0 (2) It is easy to see that the AaC model is in fact independent of space coordinate s. As the perception of the light is purely apical, each part of the organ receives a signal proportional to the same apical orientation at any time. Furthermore with the initial conditions in which the organ is straight, the curvature remains the same everywhere. Then by definition of the curvature, it comes that