title: Mathematical study for the mechanism of vascular and spot patterns by auxin and pin dynamics in plant development.
abstract: Inhomogeneous distribution of auxin is essential in various differentiation processes of plant development. Auxin transfer between cells by efflux carrier protein called PINFORMED (PIN) has been considered to be responsible for inhomogeneous distribution of auxin. Two major types of auxin distribution patterns are "spot" patterns and "passage" patterns, which are responsible for determining the position of the primordia of a leaf or flower in shoot apical meristem and formation of leaf veins, respectively. In this study, we studied the pattern formation of auxin distribution mediated by polarization of PIN using mathematical methods. We developed several different models which show possible interaction mechanisms between auxin and PIN on 2-dimentional hexagonal cellular lattice, (1) Basic auxin flux model, (2) auxin-dependent PIN degradation model and (3) auxin self-feedback model. We analyzed these models by numerical calculation and mathematical analysis. From intensive numerical calculations under different conditions, we found that some models show three different types of pattern formations in dynamics, (a) homogeneous, (b) passage and (c) spot pattern depending on parameter condition. We analyzed these models mathematically using approximation of 1-dimensional periodic space. We determined the conditions that passage and spot patterns are generated in each model, respectively. After these analyses, we propose possible mechanisms by which plants switch passage and spot patterns in different organs by small modification.
authors.affiliation: Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan; Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8503, Japan. Electronic address: y.hayakawa@riken.jp.
authors.forename: Yoshinori
authors.initials: Y
authors.lastname: Hayakawa
authors.affiliation: Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan.
authors.forename: Masashi
authors.initials: M
authors.lastname: Tachikawa
authors.affiliation: Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan; Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8503, Japan; Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Japan. Electronic address: mochi@riken.jp.
authors.forename: Atsushi
authors.initials: A
authors.lastname: Mochizuki
mesh_terms: D001692:Biological Transport / Q000502:physiology; D002352:Carrier Proteins / Q000378:metabolism*; D007210:Indoleacetic Acids / Q000378:metabolism*; D008954:Models, Biological; D063245:Plant Development / Q000502:physiology*; D010940:Plant Proteins / Q000378:metabolism*
chemical_list: D002352:Carrier Proteins; D007210:Indoleacetic Acids; D010940:Plant Proteins
keywords: Ordinary differential equation; Pattern formation; Plant morphogenesis