# Model-Based Phenotypic Signatures Governing the Dynamics of the Stem and Semi-differentiated Cell Populations in Dysplastic Colonic Crypts

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## Abstract

Mathematical modeling of cell differentiated in colonic crypts can contribute to a better understanding of basic mechanisms underlying colonic tissue organization, but also its deregulation during carcinogenesis and tumor progression. Here, we combined bifurcation analysis to assess the effect that time delay has in the complex interplay of stem cells and semi-differentiated cells at the niche of colonic crypts, and systematic model perturbation and simulation to find model-based phenotypes linked to cancer progression. The models suggest that stem cell and semi-differentiated cell population dynamics in colonic crypts can display chaotic behavior. In addition, we found that clinical profiling of colorectal cancer correlates with the in silico phenotypes proposed by the mathematical model. Further, potential therapeutic targets for chemotherapy resistant phenotypes are proposed, which in any case will require experimental validation.

## Keywords

Colorectal cancer Time delay model Bifurcation analysis Complex behavior Phenotypes## Notes

### Acknowledgements

This work was supported by the German Federal Ministry of Education and Research (BMBF) as part of the project e:Bio SysMet [0316171 to JV]. Julio Vera is funded by the Erlangen University Hospital (ELAN funds, 14-07-22-1-Vera-González and direct Faculty support).

### Compliance with Ethical Standards

### Conflict of interest

The authors declare no conflict of interest.

### Author Contributions

The initial idea, the mathematical model and the qualitative and numerical bifurcation analysis were developed by S. Nikolov. Mathematical simulations and in silico phenotypic signatures were computed by G Santos and J Vera. All the authors drafted the paper.

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