Table 1.
Listing of simulation parameters for this model.
In cases where parameters are drawn from literature, references are provided.
Fig 1.
A schematic illustration of the crypt’s structure and cell lineage classification.
Panel A) A cartoon of the intestinal crypt and the relative location of cells of different lineages. Panel B) A diagram of cell lineages. Stem cells give rise to terminally differentiated enterocytes, Goblet and Paneth cells, depending jointly on Wnt concentration as well as Notch expression of that cell’s neighbors. Only Paneth cells undergo apoptosis, since Goblet cells and enterocytes naturally undergo anoikis upon reaching the top of the crypt.
Fig 2.
Additional local Wnt production by Paneth cells leads to stem cell niche expansion.
Panel A) Ratio of each cell type of a typical crypt when local Wnt production capability is 100% and 150% for each Paneth cell, respectively. Color code for Panel A and Panel B: stem cell (red), Paneth cell (green), enterocytes (blue) and Goblet cell (yellow). Panel B) Snapshots of crypts at day 10 for different local Wnt production levels. Panel C) Plot of niche height as a function of different Wnt production rates at multiple times. Mean and standard deviation of an ensemble of 10 simulations is reported. Cases where the bar extends to the top indicate the niche is unstable and expands to occupy the entire crypt. Panel D) Indication of how the global and local Wnt influence the broad dynamics of the niche. Left column indicates the local Wnt production rates considered. G+L indicates that both global and local, Paneth cell derived Wnt are included while the right (L) column considers the setting where the global Wnt gradient is removed. “Stable” indicates a properly structured, steady state crypt results, “dies” indicates the niche (stem and Paneth cells) is completely lost, while “unstable” indicates the niche undergoes uncontrolled expansion. In no scenario is the niche stable both before and after the removal of the Wnt gradient, indicating in this setting Paneth cell derived Wnt cannot act redundantly.
Fig 3.
Role of BMP on niche homeostasis.
Panel A) Niche height as a function of different local Wnt production rates with BMP inhibition of proliferation considered. Mean and standard deviation of an ensemble of 10 simulations is presented. For the 400% production level, expansion continues in time until the niche completely overtakes the crypt. For the 100–300% cases, stability of crypt height has been verified with extended simulations. Panel B) Same as in (A) but with the global Wnt gradient removed. For low production rates, the niche is either completely lost or substantially smaller, but at higher rates (e.g. 200%), the niche height is only slightly impaired, indicating that at these levels the two Wnt sources can function redundantly. In all cases (in B), the niche heights at 5 days post removal represent steady state results.
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%).
Fig 5.
Diffusivity and degradation influence stem cell niche stability.
Panels A and B show the effect of reducing diffusivity or the strength of local Wnt degradation on niche dynamics. 0.3X and 0.1X each indicate the factor by which the relevant parameter is reduced. In A it is “D” that is reduced while in B, “d” is reduced.
Fig 6.
Influence of signaling noise on niche dynamics and stability.
Plot of stem cell niche height at steady state as a function of Wnt production rate and the amplitude of imposed noise (σ). Noise levels for the exogenous Wnt and BMP gradients are considered to be similar, so in each case we consider each to have noise amplitude of 0, 0.1, 0.2, and 0.4 respectively. Mean and standard deviation over an ensemble of 10 simulations at each production level and noise amplitude is reported. Cases where the bar extends to the top indicate the niche is unstable and expands to occupy the entire crypt.