# A stochastic model of corneal epithelium maintenance and recovery following perturbation

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## Abstract

Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called limbal epithelial stem cell hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process. Model analysis provides a set of constraints on the numbers of stem cells, division rates, and the number of division cycles required to maintain a healthy corneal epithelium. In addition, our stochastic analysis reveals noise reduction as the epithelium approaches its homeostatic state, indicating robustness to noise. Finally, recovery is analysed in the context of perturbation scenarios.

## Keywords

Chemical master equation ODE and stochastic model Corneal epithelium homeostasis and recovery## Mathematics Subject Classification

92C30## Notes

### Acknowledgements

The authors would like to thank Dr. John D. West (University of Edinburgh) for his valuable help in understanding the underlying mechanisms of the corneal epithelial maintaining process and the data provided. Eleni Moraki was supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (Grant EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh. Ramon Grima would like to acknowledge funding from BBSRC Grant BB/M025551/1. Kevin J. Painter would like to acknowledge Politecnico di Torino for a Visiting Professor position and funding from BBSRC Grant BB/J015940/1.

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