The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-06-22 , DOI: 10.1140/epje/s10189-021-00086-x Andrei Zakharov 1 , Kinjal Dasbiswas 1
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Abstract
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress-dependent activity of myosin motors and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.
Graphic abstract
中文翻译：
模拟生物物质弹性片中机械化学图案的形成
抽象的
受发育组织和生物材料中活跃形状变形的启发，我们研究了两种通用的机械化学模型，其中薄弹性片的变形由化学信号的浓度梯度驱动，进而影响化学信号的浓度梯度。我们开发数值方法来研究耦合弹性变形和化学浓度动力学，并通过计算说明根据壳厚度、机械化学耦合强度和扩散率形成不同模式。在第一个模型中，片曲率控制收缩性抑制剂的产生，并且根据耦合中的阈值，会出现性质不同的模式。第二个模型基于肌球蛋白马达的应力依赖性活动，并演示了分子马达的浓度分布模式如何受到其产生的长程变形的影响。由于机械变形的传播通常比化学动力学（影响电机的分子电机或信号剂）更快，因此我们详细描述并实现了基于时间尺度分离的数值方法，以有效地模拟此类系统。我们表明，即使没有化学物质的扩散或平流传输，机械化学耦合也会通过弹性不稳定性导致不同系统中模式的远距离传播。
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