Stem cell competition in the gut: insights from multi-scale computational modelling

Three-dimensional (3D) computational tissue models can provide a comprehensive description of tissue dynamics at the molecular, cellular and tissue level. Moreover, they can support the development of hypotheses about cellular interactions and about synergies between major signalling pathways. We exemplify these capabilities by simulation of a 3D single-cell-based model of mouse small intestinal crypts. We analyse the impact of lineage specification, distribution and cellular lifespan on clonal competition and study effects of Notch- and Wnt activation on fixation of mutations within the tissue. Based on these results, we predict that experimentally observed synergistic effects between autonomous Notch- and Wnt signalling in triggering intestinal tumourigenesis originate in the suppression of Wnt-dependent secretory lineage specification by Notch, giving rise to an increased fixation probability of Wnt-activating mutations. Our study demonstrates that 3D computational tissue models can support a mechanistic understanding of long-term tissue dynamics under homeostasis and during transformation.


Appendix1: Simulation of Wnt-mutants
We performed five simulations for each mutation scenario. In each simulation, the crypt configuration during the mutation event is replicated N times so that each SC can be mutated individually whereas the other SCs remain unchanged in the respective replicate. Hence one initial wild type configuration will yield to N individual mutation configurations. Afterwards each mutation configuration is simulated independently, thus 5N simulations have been performed as each SC in each configuration has been selected for mutation.
Videos A1a,b and A2 show examples of this kind of simulations for mutant1 and mutant2 cells, respectively. In these videos mutated SCs and their progeny are colored as following: SC (pink), PC (cyan), GC (black) and enterocytes (white). Videos A1a,b have the same initial configuration, but differ in the SC selected for mutation. In Video A1a the selected SC clone overtakes the crypt in approximately 13 weeks, while in Video A1b the selected SC clone vanishes after about 2 weeks. Both videos use a bottom view. In Video A2 the selected SC clone spreads very fast and overtakes the entire crypt in less than 3 weeks. This video uses a side view. Note, that in each simulation terminal differentiated wild type PCs may persists even after conversion.

Additional references in the Appendix:
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Appendix2: SC position as a competitive factor
In order to demonstrate the relevance of SC position regarding SC competition we simulated competition between wild type SCs and a mutated SC that is located at the very bottom of the crypt. Thereby, we checked the extent to which the mutated cell can balance an intrinsic competitive disadvantage Fig. A1 shows results of simulations assuming that the mutated cell has a changed cell growth time or a changed threshold position P1 of the Wnt-activity; the latter referring to a changed capability to activate Wnt-signaling at a given external Wntconcentration.

Fig A1. SC position balances mutation-associated competitive disadvantage.
A) Sketch of the simulated system. In all simulations the SC with the lowest position (magenta cell) becomes mutated. B) Phylogenetic tree of a selected simulation assuming that the mutated SC has a 4 hours longer cell growth time  than the wild type SCs. Vertices are colored according to the cell growth time of the dividing cells. After about 8 weeks the mutated SC clone (dark red) overtakes the niche. C,D) Ratio between simulated and expected probability of a mutation to become fixed assuming a mutated cell growth time  (C) and Wnt-threshold position P1 (D). The mutated SC at the bottom of the crypt has a competitive advantage until its growth time is set to about 1.2 times the value of wild type SCs, resulting a 3-4 hours longer cell cycle time. Alternatively, it can balance a change of threshold position P1 to 4. Reference parameter simulations are indicated by white stripes.

Appendix 3: Clonal competition in crypts with different shapes
In order to analyze the impact of the explicit crypt shape on clonal competition we generated a set of crypts with different length, width and curvature (Buske et al. 2011) and compared the results with those obtained for the crypt used throughout the study (here called: reference crypt). Fig. A2 shows an example of a short and broad crypt that contains approximately the same number of cells as the reference crypt. Model parameters of the broad crypt are given in Table A2.