Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants

A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants

High Metallicity of the X-Ray Gas up to the Virial Radius of a Binary Cluster of Galaxies: Evidence of Galactic Superwinds at High-Redshift

We present an analysis of a Suzaku observation of the link region between the galaxy clusters A399 and A401. We obtained the metallicity of the intracluster medium (ICM) up to the cluster virial radii for the first time. We determine the metallicity where the virial radii of the two clusters cross each other (~2 Mpc away from their centers) and found that it is comparable to that in their inner regions (~0.2 Zsun). It is unlikely that the uniformity of metallicity up to the virial radii is due to mixing caused by a cluster collision. Since the ram-pressure is too small to strip the interstellar medium of galaxies around the virial radius of a cluster, the fairly high metallicity that we found there indicates that the metals in the ICM are not transported from member galaxies by ram-pressure stripping. Instead, the uniformity suggests that the proto-cluster region was extensively polluted with metals by extremely powerful outflows (superwinds) from galaxies before the clusters formed. We also searched for the oxygen emission from the warm--hot intergalactic medium in that region and obtained a strict upper limit of the hydrogen density (nH<4.1x10^-5 cm^-3).Comment: Typo corrected. The published version is available on-line free of charge by the end of 2008. http://pasj.asj.or.jp/v60/sp1/60s133/60s133.pd

Newton-Okounkov polytopes of Schubert varieties arising from cluster structures

The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes.Comment: 55 page

Isomorphisms among quantum Grothendieck rings and cluster algebras

We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum loop algebras. Consequently, we obtain a quantization of the monoidal categorification theorem of [Kashiwara-Kim-Oh-Park, arXiv:2103.10067]. We establish applications of these new ingredients. First we solve long-standing problems for any non-simply-laced quantum loop algebras: the positivity of $(q,t)$-characters of all simple modules, and the analog of Kazhdan-Lusztig conjecture for all reachable modules (in the cluster monoidal categorification). We also establish the conjectural quantum $T$-systems for the $(q,t)$-characters of Kirillov-Reshetikhin modules. Eventually, we show that our isomorphisms arise from explicit birational transformations of variables, which we call substitution formulas. This reveals new non-trivial relations among $(q, t)$-characters of simple modules.Comment: 60 page

Mathematical model studies of the comprehensive generation of major and minor phyllotactic patterns in plants with a predominant focus on orixate phyllotaxis

UTokyo FOCUS Press releases "Mathematics of leaves : Unusual Japanese plant inspires recalculation of equation used to model leaf arrangement patterns" https://www.u-tokyo.ac.jp/focus/en/press/z0508_00047.htm