My research broadly involves using mechanistic modelling to understand a wide range of emergent multiscale phenomena, with applications in biology and industry.
On this page I give a few examples of my research. Note that you can find a chronological list of my publications here, which is more likely to be kept up to date.
Cells in our body are continually making decisions - for example, when to divide or what to turn into - based on what is happening in their surroundings and what their neighbours are doing. Getting these decisions right is the basis for healthy function and development, but getting it wrong can lead to diseases such as cancer. To make the right decisions, cells need to decode signals containing information about their neighbours and their surroundings. However, these signals must travel through biological environments that are complex and continually varying, so they can get disrupted and become imprecise. Despite this interference, most biological systems are widely observed to be 'robust' to this type of disruption. That is, biological systems are remarkably good at interpreting these signals and making the right decisions. However, we still don't know why this robustness occurs for many systems in general, nor why it can be disrupted in a small number of cases. A lot of research is conducted in trying to understand these questions, since answering them would help us to improve targeted treatments and therapies for a wide range of diseases.
We are interested in understanding a universal (dynamic) robustness mechanism from dynamical systems theory in the context of biological signalling, with the goal of learning whether it can explain various biological observations of robustness. Specifically, when we refer to robustness we mean in terms of robustness of biological output to spatio-temporal variations in biological input. Additionally, the universal aspect is that the 'on-off' nature of many output decisions in biological signalling systems can be described mathematically via bifurcations. In general, we find that while the classic 'critical slowing' effect near bifurcations can generate dynamic robustness, the generated timescales are too quick to explain biological observations. However, by carefully accounting for the dynamic effects fundamental to spatio-temporal variations in input, we show that 'delayed bifurcation' effects that arise from dynamic crossings of bifurcations can generate dynamic robustness over the appropriate timescales.
More generally, we are also interested in understanding how cellular communication, via chemical signalling and other mechanisms, can lead to robust emergent decision making.
Some relevant work:
Cellular motility is widely studied in biophysics and beyond. One reason for this is that the individual motility of biological cells can lead to emergent and complex collective behaviours for groups of cells. That is, cellular motility can be considered a simple driver of emergent complex behaviour. We are interested in understanding motility across these different scales. We are interested in understanding how the rapid short-scale motion of microswimmers (e.g. rotating or yawing/pitching) can lead to emergent longer-scale trajectories in the presence of fluid flow. These types of problem can be considered active versions of the classic Jeffery's orbits for passive particles in fundamental fluid mechanics. Broadly, we find that active microswimmers can often be represented as effective passive particles in shear flow. Curiously, the shape of the effective passive particle seems to be different to the average shape of the rapidly moving particle in general.
In addition, we are also interested in understanding how communication via chemical signalling affects emergent complex behaviours in active matter.
Some relevant work:
Many biological and industrial applications involving fluid flow and mass transport (e.g. membrane filters and tissue scaffolds) take place within porous media, where the geometry of the system is complex. We are interested in addressing two main challenges in the modelling of such applications. First, it can be prohibitively computationally expensive to simulate the full geometry in these scenarios, and it is often more straightforward to use simplified representations of the flow and mass fields. We use hybrid asymptotic and computational methods to systematically determine the appropriate versions of the simplified representations that accurately reflect the microscale geometry.
Second, the change in the order of the partial differential equations used to model porous media flow and single-phase flow means that coupling these two types of flow problem can lead to interesting flow structures. We use technical asymptotic methods in combination with numerical simulations to understand the flow structures that can arise from this. For example, the standard problem of a porous medium within a Hele-Shaw cell involves ten asymptotic regions in space, and the sub-limit of a large Reynolds number (but small reduced Reynolds number) reveals an even more intricate boundary layer structure, with an additional eight nested asymptotic regions in space.
Some relevant work:
Filtration is a vital process in many industries, such as kidney dialysis, air purification, waste water treatment, and beer production. We use mathematical modelling to understand how design, manufacture, and operating procedure can increase filter performance. A key challenge in all this is that while the removal of contaminant occurs over the pore scale, it is incredibly computationally expensive to resolve models on this small scale over the much larger filter scale. Part of our research in this area involves systematically deriving averaged (homogenized) equations for filtration that can be solved efficiently, but still account for the behaviour on the pore scale.
In addition, we are also interested in improving chemical decontamination efforts. For example, in the decontamination of an oily toxic chemical agent by an aqueous cleanser within a porous medium, it is very difficult to mix the two phases to enhance contaminant removal. We use mathematical modelling to understand how one should choose a cleanser for this clean-up process given characteristics of the toxic agent.
Some relevant work:
A key goal of carbon recycling is to remove carbon dioxide from the atmosphere by converting it into clean and renewable energy sources. This can be done by creating 'cell factories', genetically modified bacterial colonies that consume carbon dioxide. The viability of the process and the products created are controlled by the specific enzymes the bacteria produce. While synthetic biologists can regulate bacterial enzyme expression, nonlinear reaction interactions mean that it is not well understood how to regulate expression to achieve a specific product. Moreover, in research laboratories these systems are tested with an abundance of feed gas, to determine the maximal viability of the microbial strain. However, the nutrient supply is limited when these laboratory experiments are scaled up for industrial production.
Our research addresses these two key challenges; we use multiscale modelling to determine which enzymes to target to achieve a given product, and how to upscale experiments effectively for industrial viability. The major challenges in engineering approaches to these problems are the disparities in the system length and timescales. While this can be a computational issue, it is the exact scenario in which multiscale approaches flourish. We exploit the extreme parameter ratios in these problems, using a hybrid approach where we couple asymptotic techniques such as homogenization and matched asymptotic expansions with numerical methods, and we interpret our results to provide testable predictions for experimentalists.
Some relevant work:
In this biotechnology, artificial body tissue is derived synthetically and used to repair or replace natural tissue. Its benefits include: bypassing graft-versus-host disease from donor tissue, providing a viable alternative to animal testing, and reducing the environmental footprint of eating meat. The process of growing artificial tissue takes place within a bioreactor and involves transporting nutrient-rich fluid to cells, which are placed within a porous scaffold (known as a tissue construct) to grow. A key challenge faced by tissue engineers is to ensure that the growing tissue cells receive enough nutrient. Since advection is the dominant nutrient transport mechanism in tissue engineering and the growth of tissue cells is generally mechanosensitive, understanding the flow field within a bioreactor is very helpful.
We use mathematical modelling to understand and improve nutrient delivery via advective and diffusive transport processes, which involves solving for the fluid flow within bioreactors. In general, mathematically determining the fluid flow within these systems can be computationally expensive, especially in bioreactors where the tissue construct is free to move (in an effort to mix the depleting nutrient), yielding a moving boundary problem. We use a wide range of asymptotic and numerical methods to significantly reduce the computational effort required to determine the fluid flow in such systems, often exploiting the slender geometry of common bioreactors.
Some relevant work: