Abstract
Kidney disease and renal disorders account for a significant proportion of health complications in mid-late adulthood worldwide. Many renal deficiencies are due to improper formation of the kidneys before birth, which are caused by disorders in the developmental process that arise from genetic and/or environmental factors. Mathematical modelling can help build on experimental knowledge to increase our understanding of the complexities of kidney organogenesis. In this paper, we present a discrete cell-based model of kidney development. Specifically, we model the tip of the developing ureteric tree to investigate the behaviours of cap mesenchyme cells which are required to sustain ureteric tip growth. We find that spatial regulation of the differentiation of cap mesenchyme cells through cellular signalling is sufficient to ensure robust ureteric tip development. Additionally, we find that increased adhesion interactions between cap mesenchyme cells and the ureteric tip surface can lead to a more stable tip-cap unit. Our analysis of the various processes on this scale highlights essential components for healthy kidney growth and provides insight into mechanisms to be studied further in order to replicate the process in vitro.
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Notes
This commonly used cellular interaction force gives a similar behaviour to a Lennard Jones type potential (used commonly in molecular dynamics). Moreover, it doesn’t exhibit unstable behaviour (cluster formation) when using a linear interaction force (Pathmanathan et al. 2009).
These seeds are predetermined and give rise to the same sequence of random numbers in a simulation regardless of which computer is used, ensuring our results can be replicated.
To exclude statistical outliers.
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Cook, B., Combes, A., Little, M. et al. Modelling Cellular Interactions and Dynamics During Kidney Morphogenesis. Bull Math Biol 84, 8 (2022). https://doi.org/10.1007/s11538-021-00968-3
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DOI: https://doi.org/10.1007/s11538-021-00968-3