On the utility of a compartmental population kinetics model of intestinal epithelial stem cell proliferation and differentiation

Abstract

Background: The small intestinal epithelium is a dynamic system with specialized cell types. The various cell populations of this tissue are continually renewed and replenished from stem cells that reside in the small intestinal crypt. The cell types and their locations in the crypt and villus are well known, but the details of the kinetics of stem cell division, and precursor cell proliferation and differentiation into mature enterocytes and secretory cells are still being studied. These proliferation and differentiation events have been extensively modeled with a variety of computational approaches in the past.

Methods: A compartmental population kinetics model, incorporating experimentally measured proliferation rates for various intestinal epithelial cell types, is implemented for a previously reported scheme for the intestinal cell dynamics. A sensitivity analysis is performed to determine the effect that varying the model parameters has upon the model outputs, the steady-state cell populations.

Results: The model is unable to reproduce the experimentally known timescale of renewal of the intestinal epithelium if literature values for the proliferation rates of stem cells and transit amplifying cells are employed. Unphysically large rates of proliferation result when these parameters are allowed to vary to reproduce this timescale and the steady-state populations of terminally differentiated intestinal epithelial cells. Sensitivity analysis reveals that the strongest contributor to the steady-state populations is the transit amplifying cell proliferation rate when literature values are used, but that the differentiation rate of transit amplifying cells to secretory progenitor cells dominates when all parameters are allowed to vary.

Conclusions: A compartmental population kinetics model of proliferation and differentiation of cells of the intestinal epithelium can provide a simplifying means of understanding a complicated multistep process. However, when literature values for proliferation rates of the crypt based columnar and transit amplifying cell populations are employed in the model, it cannot reproduce the experimentally known timescale of intestinal epithelial renewal. Nevertheless, it remains a valuable conceptual tool, and its sensitivity analysis provides important clues for which events in the process are the most important in controlling the steady-state populations of specialized intestinal epithelial cells.

Fig. 1

Compartmental scheme for proliferation and differentiation of the small intestinal epithelium, based (with permission) on Figure 7 of ref. 30. Subscripted k’s represent differentiation rates; unscripted lowercase Greek letters (α, β, γ, δ, ζ) indicate proliferation rates; subscripted λ’s indicate cell loss rates. Colors match the scheme in Figure 7 of ref. 26. CBC: crypt based columnar cell; TAC: transit amplifying cell; AP: absorptive progenitor; EC: enterocyte; SP: secretory progenitor; EEC: enteroendocrine cell; TC: Tuft cell; GPP: goblet / Paneth progenitor; GC: goblet cell; PC: Paneth cell

Fig. 2

Schematic of hexagonal arrangement of crypts (red) and villi (blue) in mouse ileum. The dashed green triangle represents a unit cell of the 2-dimensional lattice, demonstrating one of several possible arrangements that show that each villus is supplied with cells from, on average, 2 crypts

Fig. 3

Time dependence of cell populations described by the compartmental population kinetics model in Fig. 1. Colors match those of Fig. 1. The left panels (a, c) show the results for the baseline and fast scenarios over the first 20 days, respectively; the right panels (b, d) show the same results over a longer timescale of 100 days. The y axes are displayed in a semilogarithmic format to better display separation between the different cell populations