Modelling the fluid mechanics of propulsion through a complex microenvironment

微小的游动细胞，如精子和细菌，是地球上生命的基础。尽管如此，我们才刚刚开始了解这些细胞是如何起作用的——特别是，对于存放在子宫颈的数千万或数亿个精子如何以及为什么通过女性生殖道存活长达数天，以及一个精子如何偶尔与卵子受精以产生新生命，我们所知甚少。这一过程的许多方面正在逐渐被揭示：精子、子宫/输卵管和卵子之间的化学和生物信号，以及精子如何在这种流体环境中推动自己的物理原理。生物和物理方面相互作用——例如，化学信号可能导致尾巴快速移动，这取决于流体的性质，可能导致细胞在直线上移动得更快，或者陷入一种被称为“过度激活”的旋转运动中。我们将着重于通过数学建模来更好地理解这些物理方面。微小的游泳者还不到一根头发的宽度，他们所处的环境与我们日常生活中所习惯的环境非常不同。试管婴儿培养皿中的盐水中的精子受到的物理影响与在海里游泳的人非常不同：没有湍流，液体表现得像一种极其糖浆（“粘性”）的物质。这一点，再加上控制精子尾部运动的复杂机制，意味着很难建立现实的实验室模型。然而，可以建立数学模型；这个项目是关于开发这些模型的。我们将关注的主要挑战是精子必须通过的输卵管复杂的“迷宫般的”环境的影响，或者目前正在开发的基于微芯片的试管婴儿设备。由于意想不到的粘性效应发生在非常小的尺度上，边界非常重要，并以意想不到的方式改变细胞的游动方式。这些边界可能是微芯片迷宫的墙壁，精子游动的女性生殖道内部紧密相反的褶皱，或者是细菌居住的土壤颗粒中的孔隙。其影响非常难以理解；例如，科学家们花了大约50年的时间试图理解一个看似简单的现象：精子对显微镜载玻片固体边界的吸引力。一个关键的发展是最近的计算进步，它允许在模拟中精确地考虑细胞的形状，它的尾巴和边界本身。最近的研究结果表明，封闭的通道对引导细胞有显著的影响，而弯曲的通道壁可以根据细胞尾部跳动的细节来分离细胞。例如，如果我们可以设计一个微芯片迷宫，分离出一个“好”精子的丰富种群，这些精子形成适当，具有适合受精的游泳特征，并且可能具有未受损的DNA（低生育能力夫妇的常见问题），这将有助于生育治疗。但要开始利用这些影响，我们需要更系统地了解尾部运动、精子形状或“形态”以及通道形状如何相互作用以改变细胞轨迹。我们将通过构建一个数学模型来模拟复杂环境中的游动细胞来做到这一点。我们的模型将考虑流体特性，如粘度，以及细胞相对于壁面的位置和方向，如何与尾部波形相互作用，进而改变游泳运动。我们最近展示了这些影响是多么不可预测。然后，我们将利用这些发现来帮助开发可用于诊断不孕症和改善治疗的微芯片设备，并帮助了解精子如何到达卵子并使其受精的奥秘。

Microscopic swimming cells such as sperm and bacteria are fundamental to life on Earth. Despite this we are only beginning to understand how these cells function - in particular there is remarkably little knowledge of how and why the tens or hundreds of millions of sperm deposited at the cervix make their way through the female reproductive tract, survive for up to several days, and how one sperm may, very occasionally, fertilise the egg to produce a new life. There are a number of aspects of this process that are gradually being uncovered: chemical and biological signalling between sperm, womb/tubes and egg, and the physics of how sperm propel themselves through this fluid environment. The biological and physical aspects interact - for example chemical signals may cause the tail to move rapidly, which depending on the fluid properties could cause the cell to move faster in a straight line, or become trapped in a spinning motion known as 'hyperactivation'. We will focus on better understanding these physical aspects through mathematical modelling. Being less than the width of a hair in length, microscopic swimmers encounter an environment very different from that we are used to in day-to-day life. A sperm in salt water in an IVF dish is subject to very different physical effects from a person swimming in the sea: there is no turbulence, and the fluid behaves like an extremely syrupy ('viscous') substance. This, along with the complex mechanism controlling the movement of the sperm tail means that it is difficult to build realistic laboratory models. However, mathematical models can be developed; this project is about developing these models.The main challenge that we will be concerned with is the effect of complex 'maze-like' environments characteristic of fallopian tubes that sperm have to traverse, or microchip-based IVF devices that are currently in development. Because of the unexpected viscous effects occurring on very small scales, boundaries are very important, and change the way that cells swim in unexpected ways. These boundaries could be walls of a microchip maze, the closely-opposed internal folds of the female reproductive tract that sperm swim through or pores in a grain of soil inhabited by bacteria. The effects are remarkably difficult to understand; for instance scientists have spent around 50 years trying to understand a deceptively simple phenomenon: the attraction of sperm to the solid boundary of a microscope slide. A key development has been recent computational advances that allow the shape of the cell, its tail, and the boundaries themselves, to be taken into account accurately in a simulation. Recent findings show that enclosed channels have significant effects on guiding cells, and that curved channel walls can be used to separate cells based on the details of how their tails are beating. For example, it would be very beneficial if we could design a microchip maze to separate out an enriched population of 'good' sperm that are properly formed, have the right swimming characteristics to fertilise, and potentially have DNA which is not damaged (a common problem in subfertile couples) - this would assist fertility treatment. But to begin to exploit these effects, we need a much more systematic understanding of how the tail movement, sperm shape or 'morphology', and channel shape interact to alter cell trajectory. We shall do this by constructing a mathematical model that simulates swimming cells in complex environments. Our model will take into account how fluid properties, such as viscosity, and the position and orientation of the cell relative to the wall, interact with the tail waveform, which in turn changes the swimming motion. We recently showed how unpredictable these effects can be. We will then use these findings to help to develop microchip devices that can be used to diagnose infertility and improve treatment, and help understand the mystery of how sperm reach and fertilise the egg.