Journal of Mathematical Biology

, Volume 75, Issue 5, pp 1171–1202 | Cite as

A kinetic model to study the regulation of \(\beta \)-catenin, APC, and Axin in the human colonic crypt

  • Brooks Emerick
  • Gilberto Schleiniger
  • Bruce M. Boman


The Wnt/\(\beta \)-catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between \(\beta \)-catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of \(\beta \)-catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer. We consider a regulatory function that promotes APC synthesis within the cell and its effect on the accumulation of the Wnt target protein, \(\beta \)-catenin. It is evident that an APC gradient exists along the crypt axis; however, the mechanism by which APC expression is regulated within the cell is not well known. We investigate the dynamics of an APC regulatory mechanism with an increased level of Axin at the subcellular level. Model output shows an increase of APC for a diminished Wnt signal, which explains the APC gradient along the crypt. We find that the dynamic interplay between \(\beta \)-catenin, APC, and Axin produces oscillatory behavior, which is controlled by the Wnt stimulus. In the presence of reduced functional APC, the oscillations are amplified, which suggests that the cell remains in a more proliferative state for longer periods of time. Increased Axin levels (typical of mammalian cells) reduce oscillatory behavior and minimize the levels of \(\beta \)-catenin within the cell while raising the levels of APC.


Colonic crypt APC regulation Wnt pathway Colorectal cancer Multiple timescale analysis 

Mathematics Subject Classification

92B05 92C37 92C40 92C42 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Brooks Emerick
    • 1
  • Gilberto Schleiniger
    • 2
  • Bruce M. Boman
    • 3
    • 4
  1. 1.Department of MathematicsTrinity CollegeHartfordUSA
  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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