Department of Mathematics, Centre for Complexity Science, Imperial College London, London SW7 2AZ, UK
J R Soc Interface. 2018 Nov 14;15(148):20180454. doi: 10.1098/rsif.2018.0454.
The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.
胚胎形态的形成是一系列拓扑和信息对称破缺的结果。我们引入了向量反应扩散漂移（VRDD）系统，其中空间动力学的极限环是具有狄拉克 δ 型分布的形态发生素浓度。这与图灵反应扩散系统有根本的不同，因为 VRDD 产生了全系统的对称破缺。我们从具有单个组织轴（旋转对称）、双轴（镜像对称）和三轴（三维中没有对称操作符）的球形囊胚中发展出了“基本形式”。然后，我们引入了细胞分化的动力学，其中遗传调控状态被建模为有限状态机（FSM）。FSM 的状态切换基于作为动态变化的表观遗传信息的局部形态发生素浓度。我们使用 FSM 模型与 VRDD 系统相结合，在空间子域中分层生长复杂的形态。使用我们具有四层（拓扑、物理、化学和监管）的集成模拟模型，我们生成了类似生命的形态，如九头蛇。我们研究了连续和跳跃突变的基因型-表型映射。我们的研究可以在形态发生工程、软机器人和仿生设计中有应用。
