Journal of Mathematical Biology

, Volume 76, Issue 7, pp 1797–1830 | Cite as

Multi-scale modeling of APC and \(\beta \)-catenin regulation in the human colonic crypt

  • Brooks Emerick
  • Gilberto Schleiniger
  • Bruce M. Boman


Stem cell renewal and differentiation in the human colonic crypt are linked to the \(\hbox {Wnt}/\beta \)-catenin pathway. The spatial balance of Wnt factors in proliferative cells within the crypt maintain an appropriate level of cellular reproduction needed for normal crypt homeostasis. Mutational events at the gene level are responsible for deregulating the balance of Wnt factors along the crypt, causing an overpopulation of proliferative cells, a loss of structure of the crypt domain, and the initiation of colorectal carcinomas. We formulate a PDE model describing cell movement and reproduction in a static crypt domain. We consider a single cell population whose proliferative capabilities are determined by stemness, a quantity defined by intracellular levels of adenomatous polyposis coli (APC) scaffold protein and \(\beta \)-catenin. We fit APC regulation parameters to biological data that describe normal protein gradients in the crypt. We also fit cell movement and protein flux parameters to normal crypt characteristics such as renewal time, total cell count, and proportion of proliferating cells. The model is used to investigate abnormal crypt dynamics when subjected to a diminished APC gradient, a scenario synonymous to mutations in the APC gene. We find that a 25% decrease in APC synthesis leads to a fraction of 0.88 proliferative, which is reflective of normal-appearing FAP crypts. A 50% drop in APC activity yields a fully proliferative crypt showing a doubling of the level of stemness, which characterizes the initial stages of colorectal cancer development. A sensitivity analysis of APC regulation parameters shows the perturbation of factors that is required to restore crypt dynamics to normal in the case of APC mutations.


Colonic crypt APC regulation Wnt pathway Colorectal cancer Multi-scale model 

Mathematics Subject Classification

92C37 92C45 92C17 92C40 92D20 

Supplementary material

285_2017_1204_MOESM1_ESM.pdf (402 kb)
Supplementary material 1 (pdf 402 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Brooks Emerick
    • 1
  • Gilberto Schleiniger
    • 2
  • Bruce M. Boman
    • 3
    • 4
  1. 1.Department of MathematicsKutztown UniversityKutztownUSA
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  3. 3.Department of Biological SciencesUniversity of DelawareNewarkUSA
  4. 4.Center for Translational Cancer ResearchHelen F. Graham Cancer Center and Research InstituteNewarkUSA

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