Detailed Programme - Travelling waves and bifurcations in mathematical biology, 25th April 2023, University of Nottingham

9:00 Arrival and coffee

9:30 Dan Nicolau Jr. (King’s College London)
"Sustained inflammatory oscillations due to topological collapse in cytokine networks preceding acute clinical crises"

Abstract: Cytokines mediate and control immune and inflammatory responses. Complex interactions exist between cytokines, inflammation and the adaptive responses in maintaining homeostasis, health, and well-being. Like the stress response, the inflammatory reaction is crucial for survival and is fine-tuned to be tailored to the stimulus and time. There is a substantial body of evidence that cytokine dysregulation is a feature of most chronic diseases, including (as well as lung disease) cancer, cardiovascular disease, immune-mediated inflammatory diseases such as rheumatoid arthritis, multiple sclerosis, Alzheimer’s disease and cystic fibrosis. Indeed, cytokine dysregulation appears to be a feature of the ageing process itself, particularly in individuals with unhealthy, ‘inflammaging’ phenotypes. In this talk, I describe recent work from our group that focusses on mathematical modelling of cytokine networks, in which regulation appears to be accomplished by negative feedback between different nodes, some with pro- and some with anti-inflammatory actions. These networks would seem to have a healthy native topology, characterised by a modular structure, while disease states (such as COVID) disturb this architecture, leading to sustained oscillations in cytokine levels. I will also discuss the potential clinical implications, should these hypotheses be proved correct -- in particular, the exciting possibility that we may be able to accurately and non-invasively predict clinical decline in patients with chronic lung (and other) diseases before they happen, i.e. to be able to treat people before they get sick.

10:30 Sonia Dari (University of Nottingham)
"Modelling the effect of matrix metalloproteinases in dermal wound healing"

Abstract: Understanding the biochemistry and pharmacology that underpins chronic wounds and wound healing is of high importance as there are over 2 million people in the UK suffering from chronic wounds. In particular, chronic wounds are susceptible to high levels of Matrix Metalloproteinases (MMPs), which are responsible for the modification and proliferation of healthy tissue. High concentrations of MMPs however cease to be beneficial and can lead to the destruction of the healthy tissue. In this talk, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe a hysteresis effect when apoptotic rates are varied, providing further insight into the management (and potential reversal) of chronic wounds.

11:00 Coffee

11:15 Philip Maini (University of Oxford)
"Modelling collective cell movement"

Abstract: Collective movement arises across multiple scales in nature. This talk will focus on the cell level, with application to biology, medicine and disease. It will be shown how coarse-graining a microscopic model inspired by angiogenesis, the process by which new blood vessels form in response to wound healing and cancer, results in a partial differential equation model that is different to the standard, phenomenological, "snail-trail" model used in the literature. It will then be shown how a simple hybrid agent-based model, combined with experimental validation, has led to new insights into collective movement in the cranial neural crest.

12:15 Blaine van Rensburg (University of Birmingham)
"Travelling waves driven by an inflammation-evolution feedback loop in inflammatory bowel disease"

Abstract: There is emerging evidence that somatic evolution (the evolution of cells within our bodies) impacts the progression of chronic diseases, as well as biological ageing, but it is difficult to study somatic evolution for several reasons including the long timescale over which it occurs. As such, there is an opportunity to use mathematical models to investigate the role of somatic evolution in chronic diseases and ageing. I will present results for a reaction-diffusion (RD) system which models the interaction between pro-inflammatory mutant cells and the immune system in the context of inflammatory bowel disease. I will also discuss a theorem, proved during the course of this project, concerning singular perturbations of RD systems which is also relevant to a more general class of RD systems which possess a timescale separation between different species.

12:45 Lunch break

13:30 Mohit Dalwadi (University College London)
"Emergent robustness of biological pattern formation in spatio-temporal morphogen variations"

Abstract: In biological systems, chemical signals termed morphogens self-organise into patterns that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How do cells decode these spatio-temporal patterns into signals in the presence of confounding effects caused by unpredictable or heterogeneous environments?

Through multiscale analysis, I will present a general theory of pattern formation in the presence of spatio-temporal variations, and show how robustness in the output manifests inherently from the same Turing bifurcations that generate the patterns. I will apply this theory to paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological morphogen variations. More broadly, I will show how the dynamics of pattern-forming systems with spatio-temporally varying parameters can be classified based on the bifurcations in their governing equations.

14:30 Celene Lee (University of Nottingham)
"Pattern formation in a nonlocal Lotka-Volterra system"

Abstract: We analyse the stability of the spatially-uniform, coexisting steady state of a diffusive nonlocal Lotka-Volterra (NLLV) system for two species in one spatial dimension, and include terms that model both nonlocal intraspecific and local interspecific competition. We find that the coexisting state of the system can lose stability once nonlocality is introduced. We use asymptotic and numerical analysis to find the neutral curve and also derive amplitude equations using weakly nonlinear analysis, which show that the bifurcation behaviour close to the neutral curve is consistent with numerical results. Finally, we construct the asymptotic solution in the limit of weak diffusivity and find that the leading order periodic solution consists of disjoint regions where either one or the other species is absent.

15:00 Coffee

15:15 Katerina Kaouri (University of Cardiff)
"Modelling the coupling of calcium signalling and mechanics in fertilization and embryogenesis"

Abstract: Calcium (Ca2+) signalling is one of the most important mechanisms of information propagation in the body. Moreover, the coupling between Ca2+ signalling and mechanical forces plays a crucial role. In embryogenesis, this mechanochemical coupling is critical but poorly understood; if it goes wrong embryo malformations occur, such as Spina Bifida and anencephaly. Also, earlier in development, at fertilization, an optimal pattern of Ca2+ waves and oscillations is associated with successful fertilization but monitoring Ca2+ damages the egg. Ca2+ waves are coupled to subtle movements (spasms) and flows in the egg cytoplasm and these can be detected non-invasively using high-speed cameras. Understanding the mechanochemical coupling in fertilization, can, thus lead to a new tool for choosing the best embryo in In-Vitro Fertilization treatments. I am going to present modelling work, in collaboration with experimentalists, that sheds some light into this fascinating Ca2+ world.

16:15 Closing remarks