Mathematical Biology and Ecology Seminar

Phenotypic variation is a ubiquitous feature of biological cell populations, even in genetically identical cells growing in uniform environments. Such variability can have profound consequences for population-level behaviour, particularly under stress, yet it is often neglected in classical modelling frameworks.

In the first part of this talk, I consider mathematical models of bacterial population growth that explicitly incorporate non-heritable variation in individual cell growth rates. I examine how phenotypic heterogeneity and environmental selection shape population growth and the dynamics of phenotypic subpopulations. We derive theoretical results for population growth rates and compare them with predictions from homogeneous models, identifying regimes in which variability qualitatively alters population outcomes.

 In the second part of the talk, I turn to self-generated chemotaxis, a collective process in which cells modify their chemical environment to guide movement. Using a hybrid discrete–continuum model that couples stochastic cell motion with a continuum description of the chemoattractant, I investigate how phenotypic variation in motility, sensing, and chemical degradation affects the robustness of collective migration. The results and tools developed have broader implications for collective behaviour in cell biology, ecology, and evolution.

Every population consists of individuals who vary in their traits, and each trait may, or may not, be associated with frailty or fitness. Variation in frailty and fitness traits makes population studies prone to selective depletion bias (SDB). The issue is widespread across scientific domains. When an ageing cohort exhibits declining mortality, is it individuals becoming healthier or selective depletion of the frail? In an epidemic, when growth in cumulative infections decelerates, is it individuals cautiously changing behaviour or selective depletion of the most susceptible? In microbial populations, when mutations increase population vulnerability to stress, it is individuals becoming more vulnerable or mutant populations having higher variance in fitness? In each case, the first explanation invokes individuals changing, while the second recognises that populations change due to selection on pre-existing variation. While the former are intuitive and widely adopted, explanations that rely on selective depletion are more neutral and less commonly considered due to cognitive biases and challenges in estimating all variation that matters. 

Remodelling selection (ReMS) is proposed as a general strategy of study design and analysis to address the SDB problem. I will show how the approach has been employed in specific case studies and how it has been formalised in general.

The acquisition and maintenance of the correct cellular pattern and tissue architecture is essential for organ function in multicellular organisms. Beyond generating the required cellular diversity, developing tissues need to attain the appropriate morphology. Tissue architecture is built through symmetry breaking instabilities such as folding, branching, buckling or budding. Studying single-cell responses alone is not enough to reveal the mesoscale physical and biochemical processes that regulate tissue organization and morphology over time and scale. In our lab we investigate how the interaction between the extracellular matrix (ECM) and tissues regulates processes during development and cancer, with a focus on ECM mechanical properties. While most research in this domain has concentrated on the ECM's elasticity as a primary determinant of cell and tissue behaviour, it is important to note that the ECM possesses both viscous and elastic properties. I will present our findings demonstrating that the passive viscoelastic properties of the ECM regulate tissue architecture and patterning both during development and cancer. Specifically, we show that ECM viscoelasticity influences the spatial and temporal organization of multicellular tissues in breast and intestinal organoids. Overall, our work highlights the critical role of viscoelasticity in driving morphological symmetry breaking instabilities, a fundamental process in morphogenesis and oncogenesis, and suggests ways of controlling tissue through ECM mechanics.

Evolution underlies the transformation of a normal cell to a cancer, yet learning the parameters defining this dynamic process from single-timepoint bulk samples is an open challenge. To understand how cancer cells evolve in vivo, we must rely on naturally occurring, heritable lineage tracing markers that encode the evolutionary history of a population of cells. Here, I shall introduce our work on identifying selectively neutral “epigenetic barcodes” and employing them as a molecular clock. By coupling this process with mathematical modelling and Bayesian inference, we characterised the evolutionary history of almost 2000 lymphoid cancers (Gabbutt et al., 2025). Across a broad range of cancer types, we demonstrated that tumour growth rates and malignancy ages differed by orders of magnitude. In 2 independent cohorts of patients with chronic lymphocytic leukaemia (CLL), a typically indolent and slow growing cancer, the inferred growth rates were highly prognostic. I shall further discuss recent work applying this approach to resolve the clonal relationship between acute myeloid leukaemia (AML) blasts and differentiated neutrophils in patients without bone marrow failure.