RESUMEN
BACKGROUND: Epicormic branches arise from dormant buds patterned during the growth of previous years. Dormant epicormic buds remain just below the surface of trees, pushed outward from the pith during secondary growth, but maintain vascular connections. Epicormic buds can be activated to elongate into a new shoot, either through natural processes or horticultural intervention, to potentially rejuvenate orchards and restructure tree architecture. Because epicormic structures are embedded within secondary growth, tomographic approaches are a useful method to study them and understand their development. RESULTS: We apply techniques from image processing to determine the locations of epicormic vascular traces embedded within secondary growth of sweet cherry (Prunus avium L.), revealing the juvenile phyllotactic pattern in the trunk of an adult tree. Techniques include the flood fill algorithm to find the pith of the tree, edge detection to approximate the radius, and a conversion to polar coordinates to threshold and segment phyllotactic features. Intensity values from magnetic resonance imaging (MRI) of the trunk are projected onto the surface of a perfect cylinder to find the locations of traces in the "boundary image". Mathematical phyllotaxy provides a means to capture the patterns in the boundary image by modeling phyllotactic parameters. Our cherry tree specimen has the conspicuous parastichy pair (2,3), phyllotactic fraction 2/5, and divergence angle of approximately 143°. CONCLUSIONS: The methods described provide a framework not only for studying phyllotaxy, but also for processing of volumetric image data in plants. Our results have practical implications for orchard rejuvenation and directed approaches to influence tree architecture. The study of epicormic structures, which are hidden within secondary growth, using tomographic methods also opens the possibility of studying genetic and environmental influences such structures.
RESUMEN
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems, which require an enzyme and substrate to bind several times in order to add multiple phosphate groups, can be bistable. Processive systems, in contrast, require only one binding to add all phosphate groups, and were recently shown to be globally stable. However, this global convergence result was proven only for a specific mechanism of processive phosphorylation/dephosphorylation (namely, all catalytic reactions are reversible). Accordingly, we generalize this result to allow for processive phosphorylation networks in which each reaction may be irreversible, and also to account for possible product inhibition. We accomplish this by first defining an all-encompassing processive network that encapsulates all of these schemes, and then appealing to recent results of Marcondes de Freitas et al. that assert global convergence by way of monotone systems theory and network/graph reductions (corresponding to removing intermediate complexes). Our results form a case study into the question of when global convergence is preserved when reactions and/or intermediate complexes are added to or removed from a network.