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

Abstract

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.

Keywords: Paneth cell specification; Wnt and Notch signalling; clonal competition; mouse small intestine; three-dimensional computational model.

Figure 1.

Crypt position controls clonal competition of SCs. (a) Sketch of the simulated system. SCs (red) are located at the bottom of the crypt being surrounded by PCs (green). Leaving the SC niche, SCs become committed either to the enterocytic (blue) or to the goblet lineage (yellow). The crypt position P is defined as the distance from the crypt bottom in cell radii (5 µm). (b) Typical phylogenetic trees of a wild-type crypt covering about one week (i) and 10 months (ii). Vertices are coloured according to the temporal position of the dividing SCs within the crypt. The root vertex (white circle) indicates the simulation start. The edges of the persistent clone are coloured in orange. An SC that is pushed to positions P > 2 often proceeds this movement until it reaches the border of the SC niche at position P = 5 and undergoes differentiation (arrows). (c) SCs at the very bottom of the crypt exhibit a competitive advantage, i.e. the ratio w(P)/f(P) (see text) is larger than one. Such a ratio was found for SCs at positions P < 3. Errors: s.d.

Figure 2.

PC distribution affects monoclonal conversion. (a) Simulated long-term cell distributions for an intrinsically defined average PC lifespan of four (i) and eight weeks (ii). A long lifespan enables the PCs to accumulate at the bottom of the crypt leading to a depletion of SCs at this region. Additional extrinsic, cell contact-dependent control of PC lifespan can ensure that the cells intermingle also for intrinsically defined PC lifespan of eight weeks (iii). (b) Typical phylogenetic tree for an intrinsically defined PC lifespan of eight weeks. (c) Box plot of simulated monoclonal conversion times for an intrinsically defined PC lifespan of four and eight weeks and contact-dependent control of PC lifespan (CON). The contact-dependent control leads to monoclonal conversion times that agree with experimental observations. For a direct comparison, pseudo conversion times (EXP) have been generated that fit experimental results by Snippert et al. [2]. More details are given in electronic supplementary material, appendix S4.

Figure 3.

Autonomous Notch provides a competitive advantage. (a) Sketch of the simulated competitive scenario. SC maintenance requires either C₁ = 2 (magenta SCs) or 4 (red SCs) Notch-ligand expressing neighbours. The SCs, which are less dependent on external Notch activation, have a competitive advantage. They take over the crypt in about 66% of the simulations. (b)(i) Sketch of the simulated system for C₁ = 0 (and C₂ = 0). PCs (and GCs) are no longer specified. In this case, the most competitive SCs originate from position P = 1 (ii, errors: s.d.). The time to monoclonal conversion (iii) decreases from about six weeks under wild-type conditions (CON) to less than three weeks. More details are given in electronic supplementary material, appendix S4.

Figure 4.

Fixation of Wnt-activating mutations depends on Notch. (a) For mutant1 SCs, the number of Notch-ligand-expressing neighbours required for SC maintenance C₁ was increased to values larger than 3. Mutant2 SCs in addition were assumed to be maintained outside the SC niche, to have a lower sensitivity to contact inhibition of growth (V_p* = 0.76 V_p, electronic supplementary material, table SA1) and to specify into PCs that lack a migration bias. (b) The fraction of cells produced by wild-type and mutant1 SCs. Shown are average cell-type fractions within the progeny of 10 wild-type and mutant SCs. (c) (i) The increased PC requirement (pink symbols: C₁ = 5, olive symbols: C₁ = 4) by mutant1 SCs led to a competitive disadvantage of them, which vanishes in the case of autonomous Notch (blue symbols: C₁ = 0). (ii) Mutant2 SCs (here: C₂ = 1) show a competitive advantage that becomes even larger in the case of autonomous Notch (C₁ = 0, C₂ = 0). All errors: s.d.

Figure 5.

Fixation of cell division-associated mutations depends on Notch. (a) Distribution of cell division events. Shown is the ratio between the probability p(P) to find a cell division event at position P and the fraction of SCs located at this position f(P). Cell division events are less frequent at positions P < 4 for wild-type and P < 2 in the case of autonomous Notch. (b) As a consequence, the distribution of division-associated mutations changes and thus also their fixation probability. For wild-type crypts (i), the sum over all division-associated mutations that became fixed out of n independent mutations (plain orange) reduces to about half the value (0.57) observed for random distributed mutations (striped orange, 1.00). Under autonomous Notch (ii), this sum increases to 0.86 (plain blue). Errors: s.d.