Fig 4. Downward Paneth cell migration is critical for the stability of stem crypt.

Panel A) Snapshots of typical crypts at Day 10 for four models. Color code for Panel A: stem cell (red), Paneth cell (green), enterocytes (blue) and Goblet cell (yellow). In all cases, Paneth cell migration is deleted so that they are subject only to the natural proliferative pressures. Model 1) Only the global Wnt gradient is present. Model 2) In addition to the global Wnt gradient, local Wnt production is included at the 100% level. Model 3) BMP inhibition of proliferation is added to Model 2. Model 4) Global Wnt and BMP gradients along with local Wnt production at the 200% level are included. Panel B) Results of an ensemble of 10 simulations for each model, niche height is reported at different times. Note that for models 1–3, stem cells are confined to the crypt base. In model 4 however, the stem cell population expands to reach the top of the crypt. In all cases, the Paneth cell population expands to the top of the crypt due to the lack of active migration. The provided color code indicates the model considered. Panel C) Spatial density of stem and Paneth cell along the z-axis at day 10. Black lines represent the populations for a control model with Paneth migration included (with 100% Wnt production and the BMP inhibition included) and the remaining curves are color coded as in (B). Panel D) Niche height as a function of different local Wnt production rates (100–400%) with reduced stem cell lifetime considered. Quasi steady state is reached for low local Wnt production rate (100–200%) while unconstrained expansion is observed for 300–400%. Panel E-F) Niche height as a function of different local Wnt production rates with reduced (E) and strengthened (F) drag force considered. The niche is stable for all cases with reduced (0.3X) drag. For enlarged (3X) drag, crypts are stable only for small local Wnt production rate (100–200%).