Hatakeyama Tetsuhiro S, Kaneko Kunihiko
Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan.
Phys Rev E. 2017 Mar;95(3-1):030201. doi: 10.1103/PhysRevE.95.030201. Epub 2017 Mar 24.
The robustness of spatial patterns against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. This robustness is analytically explained as a result of the scaling properties of the buffered system, which also lead to a reciprocal relationship between the wavelength's robustness and the plasticity of the spatial phase upon external perturbations. Finally, we explore the relevance of this reciprocity to biological systems.
空间模式对扰动的鲁棒性是生物体发育过程中不可或缺的特性，生物体需要适应不断变化的环境。尽管针对这种鲁棒性的具体机制已进行了广泛研究，但对于在反应扩散系统中实现鲁棒性的一般机制却知之甚少。在此，我们提出一种缓冲反应扩散系统，其中由缓冲分子介导的化学物质的活性状态有助于反应，并证明模式波长的鲁棒性是由缓冲分子的动力学实现的。这种鲁棒性可通过缓冲系统的标度性质进行解析解释，这也导致波长的鲁棒性与外部扰动时空间相位的可塑性之间存在相互关系。最后，我们探讨了这种相互关系与生物系统的相关性。
