Gall2023 - Agent-based model of the intestinal epithelium
Model of the Month created by Dr Louis Gall – Advisor: Carmen Pin, AstraZeneca, Cambridge, United Kingdom
Original model – MODEL2212120002
Introduction
The functional integrity of the intestinal epithelium requires tight coordination between cell production, migration, and shedding along the crypt-villus axis [1]. Dysregulation of any one of these processes, e.g., due to disease or drug insult, can result in a loss of barrier integrity that leads to inflammation, susceptibility to infection, allergies, diarrhoea, malabsorption, and cancer.
To study how the intestinal epithelium maintains homeostasis and recovers from injury, we built a multi-scale, agent-based model (ABM) of the mouse intestinal epithelium [2]. This model allows for the quantitative simulation of disease- and drug-induced injury of the intestinal epithelium from protein-level effects acting on individual cells of the model.
Model
Our ABM simulates the spatiotemporal dynamics of individual cells in the crypt geometry, interacting physically and biochemically, undergoing division cycles (with individually modelled cell cycles using the model from [3]), and differentiating into mature epithelial cells. The cells form a representation of the intestinal crypt tissue that maintains homeostasis and recovers after injury. This stable, self-organising behaviour emerges in our model from the interaction of multiple signalling pathways (Wnt, Notch, BMP, ZNRF3/RNF43 and Hippo-YAP). These pathways allow the cells to sense their location and the local cellular composition (using this to modulate proliferation and differentiation to maintain the correct balance of cell types), respond to mechanical cues and control the dynamics of their cell cycle protein networks.
Figure 1 – Schematics of the small intestinal crypt composition and cell fate signalling pathways included in the agent-based model (ABM). A) Depiction of the crypt highlighting key signalling features and cell types in each crypt region. (B) Details of signalling pathways in the model. (C) Cell fate lineages and determination based on biochemical signalling. (D) Average composition of a simulated healthy/homeostatic crypt (over 100 simulated days), showing the relative proportion of cells at each position. See [2] for more details.
Results
To demonstrate the ability of our ABM to simulate the propagation of single-cell injury into disruption of the intestinal epithelium, we detailed three scenarios:
1) The targeted ablation of stem cells [4].
2) A CDK1 inhibitor.
3) 5FU-induced DNA and RNA damage [5].
These scenarios can be seen in the paper [2] and the BioModels submission.
Scenario 1 demonstrates how the feedback mechanisms regenerate the homeostatic form of the crypt after the cessation of injury, by efficiently restoring the stem cell population through signalling-induced dedifferentiation. Scenarios 2 and 3 demonstrate how a perturbation of intracellular cell cycle protein networks propagates to damage the entire intestinal epithelium. The CDK1 inhibitor prevents cells from entering M-phase or inducing mitotic death, while 5FU causes DNA and RNA damage that induces cell cycle checkpoint failure and cell cycle arrest. Ultimately, both drug mechanisms inhibit the regular progression of the cell cycle, preventing proliferation and/or causing apoptosis. This leads to a lack of crypt replenishment and migration to the villus (and subsequent loss of barrier integrity). Scenario 3 is described in Figure 2.
These simulations matched available experimental observations [4][5]. Using the spatial resolution of our ABM, we were able to incorporate a variety of data, including cell counts in regions of the crypt and villus, and simulated staining experiments matched to real-world Ki-67 and BrdU staining.
Figure 2 – Modelling 5-fluorouracil (5-FU) (50 mg/kg twice a day for 4 d) induced injury at several scales in mouse small intestinal epithelium. (A) A diagram showing the implemented mechanism in the agent-based model (ABM) to describe DNA and RNA damage and cell cycle disruption driven by 5-FU metabolites. (B) Predicted concentration (ng/ml) of 5-FU, FUTP, and FdUTP in plasma in mouse (pharmacokinetics model of 5-FU described in Gall et al., 2023). (C, D) Cell cycle protein dynamics and fate decision when 5-FU challenge starts (C) before or at the beginning of S-phase, leading to DNA damage and cell death at the G2-M-phase checkpoint, and (D) at the end of S-phase, resulting in not enough DNA damage, the cell finishes the cycle. (E) Predicted (solid line) and observed (dashed line) proportions of Ki-67-positive cells along the crypt axis at 6 hr, 1 d, 4 d, and 6 d during the 5-FU treatment period. Shadows depict the 95% confidence interval of our simulated staining results. (F, G) Predicted (lines) and observed (symbols) number of cells in the crypt (F) and villus (G). Vertical bars represent dosing times. Symbols represent cell counts from individual mice. See [2] for more details.
Discussion
Our work highlights the importance of novel modelling strategies to provide unprecedented insights into the biology of the intestinal epithelium with practical application to the development of safer drugs.
Agent-based models are the natural ontology of biological systems and allow researchers to integrate data across all scales, from the level of protein interactions to tissue-scale effects. For example, one could use single-cell data (obtained from, e.g., organoid and micro-physiological systems) to generate mathematical models of disease- and drug-induced injury on individual cells, which can then be inserted into individual cells of the ABM. The ABM can then extrapolate this single-cell insult into disruption of the entire intestinal epithelium and predictions of adverse effects.
References
[1] Gehart, H., Clevers, H. Tales from the crypt: new insights into intestinal stem cells. Nat Rev Gastroenterol Hepatol 16, 19–34 (2019). https://doi.org/10.1038/s41575-018-0081-y
[2] Gall L., Duckworth C., Jardi F., Lammens L., Parker A., Bianco A., Kimko H., David Pritchard M., Pin C. Homeostasis, injury, and recovery dynamics at multiple scales in a self-organizing mouse intestinal crypt. eLife 12:e85478 (2023) https://doi.org/10.7554/eLife.85478
[3] Csikász-Nagy A, Battogtokh D, Chen KC, Novák B, Tyson JJ. Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J. 2006 Jun 15;90(12):4361-79. https://doi.org/10.1529/biophysj.106.081240.
[4] Tan SH., Phuah P., Tan LT., Yada S., Goh J., Tomaz LB., Chua M., Wong E., Lee B., Barker N.. A constant pool of Lgr5+ intestinal stem cells is required for intestinal homeostasis. Cell Reports 34:108633 (2021). https://doi.org/10.1016/j.celrep.2020.108633 Cell Reports 34:108633
[5] Jardi, F., Kelly, C., Teague, C. et al. Mouse organoids as an in vitro tool to study the in vivo intestinal response to cytotoxicants. Arch Toxicol 97, 235–254 (2023). https://doi.org/10.1007/s00204-022-03374-3