Modelling the fluid mechanics of propulsion through a complex microenvironment

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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.