The colonic crypt is a small finger-like invagination in the epithelial lining of the colon (right). Cells of different phenotypes make up the tissue of the crypt walls. Stem cells reside at the base and continually create daughter cells that migrate up the crypt until they are terminally differentiated and sloughed away near the top. Our model uses a degree of stemness (left) as a measure of cell-age and defines cell movement using non-linear diffusion. At steady-state, an abundance of proliferating cells (middle, blue curve) are kept above the stemness threshold and in the proliferating zone (left). Below this threshold, cells are differentiated (middle, red curve) and exit through the top. Each figure represents the steady-state output of the model under normal circumstances (no mutation). The paper is here.
Wnt Pathway Dynamics with APC and Axin Regulation
The Wnt Pathway is a cascade of chemical reactions within a cell that ultimately determines the destruction or accumulation of a proliferation promoting protein called beta-catenin. This figure shows a single trajectory in the phase space of a system of nonlinear differential equations that describes the interactions of three key proteins involved the Wnt pathway: beta-catenin, Axin, and APC. When the concentration of Axin is relatively small, the three concentrations become periodic in time. This indicates that a cell switches, periodically, between a proliferative and quiescent state. The paper is here.