Patterns are ubiquitous in living systems and underlie the dynamic organization of cells, tissues, and embryos. Mathematical frameworks have been devised to account for the self-organization of biological patterns, most famously the Turing framework. Patterns can be defined in space, for example, to form stripes; in time, such as during oscillations; or both, to form traveling waves. The formation of these patterns can have different origins: purely chemical, purely mechanical, or a combination of the two. Beyond the variety of molecular implementations of such patterns, we emphasize the unitary principles associated with them, across scales in space and time, within a general mechanochemical framework. We illustrate where such mechanisms of pattern formation arise in biological systems from cellular to tissue scales, with an emphasis on morphogenesis. Our goal is to convey a picture of pattern formation that draws attention to the principles rather than solely to specific molecular mechanisms.

中文翻译：

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细胞和组织中时空模式的机械化学原理

模式在生命系统中无处不在，是细胞、组织和胚胎动态组织的基础。人们设计了数学框架来解释生物模式的自组织，其中最著名的是图灵框架。可以在空间中定义图案，例如形成条纹；及时，例如在振荡期间；或两者兼而有之，形成行波。这些图案的形成可以有不同的起源：纯化学的、纯机械的或两者的组合。除了这些模式的各种分子实现之外，我们还强调与它们相关的统一原理，跨越空间和时间的尺度，在一般的机械化学框架内。我们阐述了从细胞到组织尺度的生物系统中这种模式形成机制的出现位置，重点是形态发生。我们的目标是传达一幅模式形成的图景，引起人们对原理的关注，而不仅仅是特定的分子机制。