Derbidge Renatus, Baumgartner Stephan, Heusser Peter
Institute of Integrative Medicine, University of Witten/HerdeckeWitten, Germany; Research Institute at the Goetheanum, Science SectionDornach, Switzerland.
Institute of Integrative Medicine, University of Witten/HerdeckeWitten, Germany; Hiscia Institute, Society for Cancer ResearchArlesheim, Switzerland.
Front Plant Sci. 2016 Nov 25;7:1749. doi: 10.3389/fpls.2016.01749. eCollection 2016.
This paper presents a discovery: the change of the outline shape of mistletoe ( ssp. ) berries and during ripening. It was found that a plant organ that is usually considered to merely increase in size actually changes shape in a specific rhythmic fashion. We introduce a new approach to chronobiological research on a macro-phenotypic scale to trace changes over long periods of time (with a resolution from hours to months) by using a dynamic form-determining parameter called Lambda (λ). λ is known in projective geometry as a measure for pertinent features of the outline shapes of egg-like forms, so called path curves. Ascertained circadian changes of form were analyzed for their correlation with environmental factors such as light, temperature, and other weather influences. Certain weather conditions such as sky cover, i.e., sunshine minutes per hour, have an impact on the amplitude of the daily change in form. The present paper suggests a possible supplement to established methods in chronobiology, as in this case the dynamic of form-change becomes a measurable feature, displaying a convincing accordance between mathematical rule and plant shape.
槲寄生（亚种）浆果在成熟过程中轮廓形状会发生变化。研究发现，一个通常被认为只是体积增大的植物器官，实际上会以特定的节律方式改变形状。我们引入了一种在宏观表型尺度上进行生物钟学研究的新方法，通过使用一个称为拉姆达（λ）的动态形状决定参数来追踪长时间（分辨率从小时到数月）的变化。在射影几何中，λ作为一种度量蛋形轮廓形状相关特征的指标而为人所知，这种轮廓形状即所谓的路径曲线。对确定的昼夜形状变化进行了分析，以研究其与光照、温度等环境因素以及其他天气影响之间的相关性。某些天气条件，如天空覆盖率，即每小时的日照分钟数，会对形状的每日变化幅度产生影响。本文提出了一种对生物钟学既定方法的可能补充，因为在这种情况下，形状变化的动态成为一个可测量的特征，显示出数学规律与植物形状之间令人信服的一致性。
