Modelling Microtubule-Molecular Motor Systems

微管是自然界中普遍存在的细长细丝。它们形成纤毛的轴丝;在宏观尺度上驱动流体流动的毛发状细丝，通常在团藻等细胞的表面上发现。纤毛还排列在肺的上皮细胞上，可以协调它们的跳动来运输粘液，防止细菌进入体内。它们的运动是由分子马达驱动的，如动力蛋白，它沿着沿着微管长度移位，每个微管携带货物并对细丝施加切向力。这种强迫导致不稳定驱动的屈曲，其中微管表现出丰富而有趣的行为。我们的研究涉及微管的数学建模;具体来说，我们的目标是创建一个生物物理模型来描述微管变形，占分子马达的皮牛顿尺度效应。在该项目中，我们的目标是将其扩展到轴丝的模型，以生成纤毛的模型，并进一步扩展到考虑几个纤毛的耦合行为。尽管这个模型的细节水平，我们仍然可以通过使用GPU实现快速模拟。通过这些方法，我们的目标是阐明自然界中观察到的纤毛集体行为背后的过程。

Microtubules are long slender filaments that are ubiquitous in nature. They form the axoneme of cilia; hair-like filaments that drive fluid flow at a macroscopic scale, often found on the surface of cells such as Volvox. Cilia also line the epithelia in the lungs and can coordinate their beating to transport mucus, preventing bacteria from entering the body. Their motion is driven by molecular motors such as dynein, which translocate along the microtubule length each carrying cargo and exerting a tangential force on the filament. This forcing leads to an instability-driven buckling, where the microtubules exhibit a rich and interesting set of behaviours. Our research involves the mathematical modelling of microtubules; specifically, we aim to create a biophysical model to describe microtubule deformation, accounting for the piconewton scale effects of the molecular motors. Over the project we aim to extend this to a model of an axoneme, to generate a model of a cilium, and extend further to consider the coupled behaviour of several cilia. Despite the level of detail in this model, we can still achieve fast simulations by using GPUs. Through these methods, we aim to elucidate the processes behind the collective behaviours of cilia observed in nature.