Institute of Applied Mathematics, BioQuant and Interdisciplinary Center of Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany.
Magdeburg University, Institute for Analysis and Numerics, Magdeburg, Germany.
PLoS Comput Biol. 2018 Jul 3;14(7):e1006259. doi: 10.1371/journal.pcbi.1006259. eCollection 2018 Jul.
Chemical and mechanical pattern formation is fundamental during embryogenesis and tissue development. Yet, the underlying molecular and cellular mechanisms are still elusive in many cases. Most current theories assume that tissue development is driven by chemical processes: either as a sequence of chemical patterns each depending on the previous one, or by patterns spontaneously arising from specific chemical interactions (such as "Turing-patterns"). Within both theories, mechanical patterns are usually regarded as passive by-products of chemical pre-patters. However, several experiments question these theories, and an increasing number of studies shows that tissue mechanics can actively influence chemical patterns during development. In this study, we thus focus on the interplay between chemical and mechanical processes during tissue development. On one hand, based on recent experimental data, we develop new mechanochemical simulation models of evolving tissues, in which the full 3D representation of the tissue appears to be critical for obtaining a realistic mechanochemical behaviour. The presented modelling approach is flexible and numerically studied using state of the art finite element methods. Thus, it may serve as a basis to combine simulations with new experimental methods in tissue development. On the other hand, we apply the developed approach and demonstrate that even simple interactions between tissue mechanics and chemistry spontaneously lead to robust and complex mechanochemical patterns. Especially, we demonstrate that the main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory.
化学和力学模式的形成在胚胎发生和组织发育过程中是基础。然而，在许多情况下，潜在的分子和细胞机制仍然难以捉摸。大多数当前的理论假设组织发育是由化学过程驱动的：要么是一系列化学模式，每个模式都取决于前一个模式，要么是由特定化学相互作用自发产生的模式（如“图灵模式”）。在这两种理论中，力学模式通常被视为化学预图案的被动副产物。然而，一些实验对这些理论提出了质疑，越来越多的研究表明，组织力学可以在发育过程中主动影响化学模式。在这项研究中，我们因此专注于组织发育过程中化学和力学过程之间的相互作用。一方面，基于最近的实验数据，我们开发了新的机械化学模拟模型，用于演化组织，其中组织的完整 3D 表示对于获得真实的机械化学行为似乎是至关重要的。所提出的建模方法具有灵活性，并使用最先进的有限元方法进行数值研究。因此，它可以作为将模拟与组织发育的新实验方法相结合的基础。另一方面，我们应用所开发的方法并证明，即使是组织力学和化学之间的简单相互作用也会自发导致稳健和复杂的机械化学模式。特别是，我们证明了在纯粹化学理论框架中出现的主要矛盾可以使用机械化学图案形成理论自然而自动地解决。
