Modelling sperm-mucus interactions across scales

The process of the sperm reaching the egg is the reason we are all here, but we often don't stop to think, why was it that particular sperm and not one of the billions of others? If we do, we usually assume that it was all up to chance and that the sperm that provided half of our genetic make up simply had about a one-in-a-billion shot of being the one. This, however, is not the complete story and, as experimental evidence shows, the female tract deploys a variety of biochemical and biophysical mechanisms to actively select the most viable sperm cells, allowing only this group the chance at fertilising the egg. Understanding the mechanisms at play is not only fundamental to our understanding of reproductive biology, but also crucial to effectively diagnosing and treating cases of infertility.

One key player in sperm selection is mucus: the complex fluid through which the sperm cells must swim. When we think of mucus, we often think of a slimy and gooey substance. The gooeyness is due to the fact that mucus in comprised of a network of elastic filaments suspended in water. Due to its small size, a sperm cell, rather than experiencing the gooeyness, instead experiences the network as a series of obstacles with which it must interact as it tries to swim. During fertile periods, the properties of the filament network change to allow healthy, viable sperm to pass, while filtering out the rest. It remains unclear, however, which network properties enable this remarkable differentiation between healthy and abnormal sperm cells. Developing a clear understanding of the underlying mechanics of sperm-filament network interactions could pave the way for the development of new diagnostics, based on synthetic artificial mucus environments, as well as new fertility treatments.

The goal of this project is to use mathematical modelling to quantify these sperm-network interactions and explore how they impact sperm selection. The models we develop will be able to examine how both the shape and swimming characteristics of individual sperm affect its ability to move through networks of different properties, as well as how the interactions affect the motion of multiple sperm and sperm populations at scales close to the female tract itself. To do this, we will develop two kinds of mathematical models. The first model will provide a microscopic description of the coupled motion of the sperm cells and filaments by resolving the details of the fluid flows generated by the swimming sperm, the bending and stretching of the network filaments, and the collisions between the sperm cells and network filaments. This model will allow us to explore in great detail how different network properties affect the motion of individual or small groups of sperm cells with different swimming characteristics and morphologies. The second model will describe the dynamics of sperm populations in the female tract at the longer time and larger length scales not accessible to the first model. This model will be derived using a rigorous coarse-graining methodology to systematically eliminate degrees of freedom from the more detailed model while still ensuring relevant effects are captured consistently. Using this model we can explore en masse sperm selection and link population-level differentiation with details of the sperm-mucus interactions.

We aim for these mathematical models to have the two-fold effect of pushing forward fields associated with applied mathematics such as scientific computing, fluid mechanics, non-linear partial differential equations, and multiscale analysis, but also providing important inroads of using mathematics to impact the biological sciences and medicine. A key aspect of our project is to interface with active fertility clinicians and reproductive biologists and explore with them how our models coupled with their laboratory techniques might be used in the future to enhance clinical data and provide better patient outcomes

Impact vision: Mathematical models are used widely in weather prediction and to predict financial markets. We envision a future where the predictive power of mathematical models is also used in healthcare to help diagnose diseases and improve patient outcomes. Our project aims to make in roads towards this vision in the context of fertility healthcare.

Impact on society: Infertility treatments are expensive, invasive, and often used without identifying the exact cause of infertility. We aim to couple our mathematical models to existing fertility diagnostics with the aim of increasing diagnosis accuracy and improving patient outcomes. To do this, we will collaborate with Dr Matt Tomlinson, the head of an NHS fertility lab, and Prof William Holt, a world leader in fertility research. We view this aspect of the project as the prototyping phase of a virtual mucus simulator, a software tool that can be used by clinical fertility labs to enhance fertility diagnosis. We plan to explain our vision of using mathematics in healthcare to the public through the Imperial Festival, an annual event showcasing the institution's research activities to a general audience.

Impact on people: The use of mathematical models in healthcare requires training junior mathematicians to work with clinical scientists. With this in mind, the PDRAs will work closely with Dr. Tomlinson and his team to couple the mathematical models with their lab data. This will become part of their larger training in numerics and data handling that will increase their job prospects. At the same time, the PRDAs will be encouraged to develop their own independent ideas. They will receive travel funds to attend conferences and develop international contacts. Throughout the project, they will receive careful guidance from EEK and PD and benefit from the Imperial College Postdoctoral Development Centre. We aim for training to also extend to postgraduates through courses we will teach as part of the multi-university TCC programme. We will also participate in the Imperial CDT in Fluid Mechanics across Scales and expose our own PhD students to the proposed research.

Impact on knowledge: Our project will provide new knowledge on the specific problem of sperm cell locomotion in filament networks, as well as the broader problem of modelling biological materials at various length- and time-scales. The new mathematical techniques that we plan to develop will find application in many other biological problems, including cancer cell motility in the extracellular matrix. Our project will provide new knowledge on using mathematical models in healthcare by working directly with clinicians and coupling our models with their data and lab techniques. We will publish our results in journals with strong interdisciplinary focus, as well as those in mathematical biology, applied mathematics, and fluid mechanics. We will also present our research at conferences serving these different communities. Additionally, we aim to bring together UK mathematicians and fertility researchers by leveraging funds to organise targeted workshops.

Impact on Economy: Coupling mathematical models with existing clinical techniques provides a clear path to new wealth creation. Dr Tomlinson is a co-founder of the start-up Pro-Creative Diagnostics which developed the computer assisted semen analysis (CASA) package Sperminator. The project will help bolster this UK-based start-up, through advertising its usage as part of an innovative project. Coupling our models with the data format provided by this software provides a direct route to their eventual usage as part of a bigger software package where simulations based on our models are run alongside video processing. We envision possible commercial activities to arise as a result of this project and plan on interfacing with Imperial Innovations which aids in the commercialisation of research emerging from Imperial.