域边缘的模式定位
Pattern localization to a domain edge
摘要：
细胞内蛋白质模式的形成一般由反应扩散模型描述。对这种系统的研究可以追溯到图灵，他展示了当两种反应组分具有不同的扩散率（例如膜结合和胞质状态）时，模式如何从均匀的稳态中出现。然而，在自然界中，系统通常在异质环境中发展，其中上游蛋白质模式影响下游蛋白质模式的形成。这方面的例子是Cdc42在芽殖酵母中邻近先前芽位的极化，以及在巨胞饮作用中围绕PIP3结构域形成的肌动蛋白募集环的形成。这表明先前建立的蛋白质模式可以作为下游蛋白质的模板，并且这些下游蛋白质可以“感知”模板的边缘。这种边缘感测如何工作的机制仍然难以捉摸。在这里，我们展示和分析一个通用的和强大的边缘传感机制，基于两个组件的质量守恒反应扩散（McRD）模型。我们的分析是植根于最近开发的理论框架McRD系统，称为局部平衡理论。我们扩展了这个框架，以捕获由于模板的空间异质反应动力学。这使我们能够以图形方式构建反应动力学相空间中的固定模式。此外，我们表明，蛋白质模板可以触发区域质量重新分布的模板边缘附近的不稳定性，导致蛋白质质量的积累，最终导致在模板边缘的固定峰。我们表明，简单的几何反应零倾的形状预测时，这种边缘检测机制是可操作的。因此，我们的研究结果提供了指导，为未来的生物系统的研究，并为设计的合成模式形成系统。
英文摘要：
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g. membrane-bound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud-site in budding yeast, and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can 'sense' the edge of the template. A mechanism for how this edge sensing may work remains elusive. Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a two-component mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems, and for the design of synthetic pattern forming systems.
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