A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt

Abstract

We introduce a novel dynamic model of stem cell and tissue organisation in murine intestinal crypts. Integrating the molecular, cellular and tissue level of description, this model links a broad spectrum of experimental observations encompassing spatially confined cell proliferation, directed cell migration, multiple cell lineage decisions and clonal competition.Using computational simulations we demonstrate that the model is capable of quantitatively describing and predicting the dynamic behaviour of the intestinal tissue during steady state as well as after cell damage and following selective gain or loss of gene function manipulations affecting Wnt- and Notch-signalling. Our simulation results suggest that reversibility and flexibility of cellular decisions are key elements of robust tissue organisation of the intestine. We predict that the tissue should be able to fully recover after complete elimination of cellular subpopulations including subpopulations deemed to be functional stem cells. This challenges current views of tissue stem cell organisation.

Figure 1. Model of the murine small intestinal crypt.

a) Histological section. Expression of the functional stem cell marker Lgr5-LacZ (blue) is mainly restricted to a few cells at the crypt bottom Bar: 50µm. b) Example of a model network representing the BM of the crypt. The Gaussian (black) and Mean (red) curvature are highest at the crypt bottom. Wnt- activity is assumed to correlate with curvature and to adopt threshold values at position x_p and x_d (see text). c) Snapshot of a crypt simulation. Undifferentiated cells (red) and Paneth cells (green) are found intermingled at the crypt bottom, progenitors of enterocytes (blue) and Goblet cells (yellow) move upwards along the crypt axis. d) Steady state cell numbers over time. Colour code as in c). Black line denotes the total number of cells.

Figure 2. Steady state crypt.

a,b) Positional BrdU label index obtained a) 2h and b) 24h after labelling. Experimental data: red, Simulation data: black. Bottom: Snapshots of simulated crypts. Colour code as in Fig. 1. Saturated colour indicates cells labelled for proliferation activity. c),d) Experimental and simulated distribution of c) Paneth, and d) Goblet cells in the crypt. Experimental data (red) were taken from and , respectively. The insert in c) shows the simulated distribution of initial Paneth cell positions. A video showing an example of a steady state crypt simulation can be found in Video S1.

Figure 3. Clonal dynamics.

a),b) Snapshots of simulated cell clones (pink) at labelling initiation (t₀) and 7days later (t₁) for clones derived from a) an undifferentiated functional stem cell and b) an enterocyte progenitor. Colour code as in Fig. 1. c) Clonal expansion in LGR5-EGFP-IRES-creERT2 knock-in mice crossed with Rosa26-lacZ reporter mice 1, 15, 60 and 600 days after tamoxifen injection . The clones of LGR-5 expressing functional stem cells persist over long times. Bars: 50µm. d) Simulated clonal conversion in crypts: simulated data (black) and double exponential fit with time constants τ₁ and τ₂ (red). A video showing an example of a simulation of clonal conversion in a crypt can be found in Video S2.

Figure 4. Gain and loss of gene function studies.

Simulation results for crypt organisation following disturbed signalling. Colour code as in Fig. 1. Wnt++: Consitutive activation of Wnt in all cells leads to an expansion of the populations of undifferentiated and Paneth cells and a complete loss of Goblet and enterocyte progenitors. Wnt--: Reduced Wnt-signalling results in a complete loss of undifferentiated and Paneth cells. Notch++: Assuming constitutive active Notch-signalling in all cells completely suppresses the secretory lineages. Notch--: In contrast, a complete block of Notch-signalling results in full depletion of undifferentiated cells and the absorptive lineage.

Figure 5. Paneth cell distribution and numbers are affected by biomechanics as well as cell signalling.

a) Local fraction of Paneth cells in dependence of their migration force F_A ^Paneth. b) Local fraction of Paneth cells in dependence of their Notch-activation strength LP^Paneth. All other parameters of the model are fix (see Table 1). c) Average total number of Paneth cells as obtained in simulations changing F_A ^Paneth (pink squares, compare a)) and changing LP^Paneth (cyan squares, compare b)).