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Mathematical models to describe how leaders and followers drive cancer invasion
Reference persons TOMMASO LORENZI, KEVIN JOHN PAINTER
Description During cancer invasion, malignant cells spread from the primary site to infiltrate the surrounding healthy tissue, a process linked to an increased possibility of metastasis and a poorer prognosis. Recently, there has been significant interest in how ?phenotypic heterogeneity? within a cancer can drive its invasion. Rather than a homogeneous population of cells, cancers are typically structured into multiple subpopulations, where each subpopulation has a different phenotype: for example, one population may be much more proliferative, another may be more resistant to radiotherapy, etc. In the particular context of cancer invasion, much recent attention has focussed on ?follower-leader? structuring: cells at the leading edge lie on a spectrum between ?leader? to ?follower? subtypes, where the leader cells are localised at the forefront of invasion and guide the follower cells behind them.
Mathematical and computational modelling has become an increasingly popular and influential tool in order to understand the evolution of cancer growth. In the context of leader and follower driven cancer invasion, one recent modelling approach [1] has been to construct a system of ?structured integro partial differential equations (SIPDEs)?, a sophisticated class of mathematical models that can describe in detail both the complex spectrum of phenotypes within a cancer and the manner in which these are distributed through space and time as the cancer invades. Solutions to these systems show the formation of a phenotypically-structured travelling wave profile that bears high similarity to the above described leader-follower invasion seen in certain cancers.
A critical next step will be to connect these models more closely to known biology that regulates the behaviours of the different cell types. Recent work has identified that leader and follower cells engage in a ?signalling crosstalk?: a form of cell to cell communication that is mediated through the production and release of chemical factors, and thereby allow the different subpopulations to regulate each other?s behaviour [2]. For example, leader cells release factors that can allow follower cells to migrate, while follower cells release factors that allow leader cells to divide. This crosstalk, consequently, is believed to play a major role in the promotion of faster cancer invasion. The aim of this project will be to extend existing SIPDEs to include this critical biology, use mathematical and numerical analysis to explore how these factors promote invasiveness, and hence provide insights into the different ways these can be disrupted to slow or prevent cancer invasion.
References:
[1] T. Lorenzi, F.R. Macfarlane, K.J. Painter (2024). Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion. To appear in European Journal of Applied Mathematics. https://arxiv.org/pdf/2310.19933.pdf
[2] J. Konen et al (2017). Image-guided genomics of phenotypically heterogeneous populations reveals vascular signalling during symbiotic collective cancer invasion. Nature Communications. 8:15078. http://www.doi.org/10.1038/ncomms15078
Deadline 15/02/2025
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