An integrative computational model for intestinal tissue renewal - PubMed (original) (raw)
doi: 10.1111/j.1365-2184.2009.00627.x. Epub 2009 Jul 20.
G R Mirams, A Walter, A Fletcher, P Murray, J Osborne, S Varma, S J Young, J Cooper, B Doyle, J Pitt-Francis, L Momtahan, P Pathmanathan, J P Whiteley, S J Chapman, D J Gavaghan, O E Jensen, J R King, P K Maini, S L Waters, H M Byrne
Affiliations
- PMID: 19622103
- PMCID: PMC6495810
- DOI: 10.1111/j.1365-2184.2009.00627.x
An integrative computational model for intestinal tissue renewal
I M M van Leeuwen et al. Cell Prolif. 2009 Oct.
Abstract
Objectives: The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.
Methods: At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.
Results: We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data.
Conclusions: We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis.
Figures
Figure 1
Normal colonic mucosa. (a) Microdissection image courtesy of the Department of Pathology, Ninewells Hospital, Dundee, UK. The circular structures correspond to cross‐sections of crypts of Lieberkühn. The space between these glands contains connective tissue (the lamina propria), blood vessels and lymphatics. (b) Schematic of a colonic crypt. The epithelial cells lining the crypts reside on a basement membrane. Murine and human intestinal crypts contain about 250 and 2000 epithelial cells, respectively (4, 20).
Figure 2
Schematic of our multiscale model for the dynamics of a colonic crypt. During a model simulation, the occurrence of cellular events (proliferation, differentiation, migration) is monitored at discrete time steps, tn. By coupling Wnt signalling, cell cycle, and mechanical models, we are able to predict the spatio‐temporal behaviour of every cell at time tn+1, given the state of the system at time tn (e.g. intracellular protein levels, cell position, Wnt stimulus, location of neighbouring cells) and the system parameters.
Figure 3
Schematic diagram of the mechanical model. Black points correspond to cell centres. Each pair of neighbouring cells (identified using a Delaunay triangulation) is attached by a spring. Solid lines represent the associated Voronoi tessellation, which is a partition of two‐dimensional space that assigns a polygon Pi to each cell centre ci such that all points in Pi are closer to ci than to any other cell centre. Five neighbouring cells surround the central cell i, highlighted in grey.
Figure 4
Predicted position‐dependent cell‐cycle times in the intestinal crypt. Distance along the vertical crypt axis is expressed in units of length L. The total height of the virtual crypt is 25. (a) Duration of the cell cycle as predicted by the WCC model alone (Wnt model + Cell‐cycle model). The curve corresponds to motionless cells exposed to a constant Wnt level. The predicted Wnt threshold for cell division is about 0.66. (b) Duration of the cell cycle as a function of cell position at division, as predicted by our multiscale crypt model (Wnt model + Cell‐cycle model + Mechanical model). Here, due to upward cell migration, cells are exposed to decreasing Wnt levels during their cell cycle. (c) Normalised Wnt stimulus as a function of height along the crypt axis.
Figure 5
Virtual dissection experiments. θ is the angle of section. (a) Vertical section of a cylindrical crypt and (c) corresponding dissection lines on the two‐dimensional rolled‐out surface. (b) Skewed section of the same crypt and (d) resulting dissection lines. The numbers in (c) and (d) represent the recorded cell positions along the dissection lines. In (c), there are labelled cells at positions 1, 2, 3, 4, and 5 along the dissection lines. In (d), the labelled cells are at positions 1, 2, 3, 5, 6 and 7, for the same crypt.
Figure 6
Virtual labelling‐index experiments. Data obtained from 250 crypt simulations performed with our DMC model. (a) Percentage of labelled cells per position along the dissection lines (Fig. 5c,d). Bullet points and crosses correspond to results obtained 40 min and 9 h after labelling, respectively. (b) True percentage of labelled cells as a function of distance from the virtual crypt base. Grey and black bars represent the results obtained 40 min and 9 h after labelling, respectively; whiskers show the corresponding variances. Height along the crypt axis is expressed in units of length L.
Figure 7
Clonal expansion in the crypt. Each column shows six snapshots from two independent in silico experiments performed with the Meineke et al. (columns I and II) and DMC (columns III and VI) model, respectively. At time t = 0 (see arrows in upper row), a single cell is stained with a blue dye. This label is transmitted from generation to generation without losing intensity, giving rise to a clonal population of blue‐stained cells. Row 2: t = 40 h; row 3: t = 100 h; row 4: t = 300 h; row 5: t = 800 h; row 6: t = 1340 h. Columns I and III show the clonal composition of the crypt. At time t = 0 (row 1), every cell in the crypt is regarded as a clonal population of size one and therefore given a different colour. Initially there are about 240 lineages. Columns II and IV highlight how the blue‐labelled populations evolve in time. Proliferative and differentiated cells are represented in yellow and pink, respectively. In column II, the stem cells, which are pinned to the base of the crypt, are highlighted in green. In the DMC simulation (columns III and IV), the population highlighted in blue eventually takes over the crypt (i.e. after 1340 h only one of the original lineages remains). As niche succession is a purely stochastic process, every stem cell has a probability 1/NS of becoming dominant, with _NS_the number of stem cells.
Figure 8
Dependence of cell size and geometry on cell adhesion. Simulation time = 800 h (the resulting crypts are shown in the Appendix). NN = DCM model; YN = area dependent cell–matrix adhesion only; NY = contact‐edge dependent cell–cell adhesion only; YY = contact‐edge dependent cell–cell adhesion and cell‐size dependent cell–matrix adhesion; EQ = values for hexagonal equilibrium lattice. The distance from the crypt base, y, is expressed in units of length L. (a) Average cell area as a function of cell position. (b) Average shape value (perimeter2/area) as a function of cell position.
Figure 9
Subcellular localisation of β‐catenin based on the Wnt model proposed by Van Leeuwen et al. ( 29 ) coupled to the cell‐cycle model by Swat et al. ( 30 ). Duration of the simulation = 630 h. Small crypts have been used here, to facilitate visualisation of β‐catenin's localisation. (a) and (b) show the model predictions according to Hypotheses I (purely competitive scenario) and II (two forms of β‐catenin), respectively. In (b), the rate of Wnt‐induced change of conformation of β‐catenin has been chosen such that cell–cell adhesion decreases with increasing Wnt. (c) Level of intracellular transcription complexes, CTi (nM). (d) Level of membrane‐bound adhesion complexes, CAi (nM).
Figure 10
Examples of available experimental data on intestinal tissue architecture and dynamics. (a) Intestinal crypt showing a ribbon of C_c_O deficient cells; image from (61), reproduced with permission. (b) Labelling indexes obtained 2 h (○), 24 h (•) and 48 h (□) after exposure to bromodeoxyuridine. For the corresponding methodology, see the Appendix. (c) Three‐dimensional rendered image of the surface of mouse colon. The nuclei (blue) are stained with DAPI and F‐actin (red) is stained with rhodamine phalloidin. Whole‐mount of tissue imaged using a multiphoton microscope. Scale bar = 60 µm. (d) Three‐dimensional rendered image of mouse colon stained for F‐actin showing the arrangement of the tube‐like crypt lumen. Whole‐mount of tissue imaged using a multi‐photon microscope. Scale bar = 60 µm. Images (c) and (d) courtesy of Dr. Paul Appleton, Näthke Lab, Cell and Developmental Biology, University of Dundee.
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