Patterns in Biology: From Molecules to Cells and Organs
Tatsuo Shibata (Hiroshima Univ.)
Kaoru Sugimura1, Tadashi Uemura1, Atsushi Mochizuki2
1: Kyoto University 2: National Institute for Basic Biology
Dendrite is a neuronal process, which is specialized for receiving and processing synaptic or sensory inputs. Morphologies of dendritic trees are highly variable from one neuronal type to another and this diversity contributes to differential processing of information in each type of neurons. For instance, retinal ganglion cells and Drosophila class IV da neurons elaborate dendrites that uniformly cover their receptive field (this complete but non-redundant coverage is called Tiling). We previously showed that tiled da neurons regenerate space-filling patterns after severing branches (1, 2). This and other experimental data suggested that self-organization machinery controls development of space-filling dendrites. Our reaction-diffusion model that includes a cellular structure develops dendritic patterns autonomously. In addition the model also manifests the distinctive two feature of spatial regulation of neurons: tiling and regeneration. By the numerical analysis of the model we determined generalized conditions for branching. We also found that the spatial property of obtained patterns can be characterized by a statistic, branch alignment. Our preliminary analysis showed that the statistic reflects the distribution of activator inside of the cell. Therefore we may able to characterize neurons by the statistics and to predict internal distribution of activator from the external feature of neuronal branches.
1. Sugimura et al. Neuron (2004). 2. Sugimura et al. JNS (2003).
Takashi Miura (Kyoto Univ.)
Junction between skull bones is called skull suture, and it consists of thin undifferentiated mesenchyme which allows growth of skull vault. It develops complex interdigitated structure during development, which has noninteger fractal dimension. At later stage of life this tissue disappears intermittently. Although many molecular interactions has been known, how this structure is formed is not understood.
We show that known molecular interactions can be simplified to two-species reaction-diffusion model which can reproduce interdigitation of skull suture. From model predictions we found a novel structure and distribution of specific molecules. Moreover, by introducing time-dependent parameter, formation of fractal structure and disappearance of suture tissue can be reproduced by the same framework.
Koichi Fujimoto (University of Tokyo)
Morphogenetic evolution in animals and plants produces diversity and convergence. The comparative studies related with molecular network are rapidly developed. On the other hand, mathematical study of morphogenesis is limited in model organisms such as fruit fly, Drosophila melanogaster. Study of the convergence and the diversity in the evolution and the development (evo-devo) combined with morphogenetic dynamics, molecular networks, and mathematical analysis is of interest. We comparatively study a lot of artificial molecular networks with stripe pattern formation of a gene expression. The stripe leads to the segmentation in anterior-posterior direction in arthropod embryogenesis and is one of the hottest topics for molecular and morphogenetic study. We have collected such molecular networks by evolving them to generate the multiple stripes in computers. We classify pattern formation process to several types referred on the segmentation of arthropod, and found a specific network module such feed-forward loop or feed-back loop necessary for each developmental type. We mathematically analyze the function of the network modules relating with robustness of the segmentation, speed of the development, knockout response. We propose a unifying mechanism for the convergence and the diversity in the segmentation process of arthropod.