Morphogenesis and mechanical instability of a prestressed tissue.

We consider the issue of whether purely mechanical properties of biological systems can, in principle, play a significant role in morphogenesis. As a simple example, we model a spherically arranged epithelium that is symmetrically prestressed under the action of cytoskeletal elements. A three-dimensional exact bifurcation analysis indicates the existence of a critical radius beyond which, for a physiologically attainable prestress, the spherical organoid is mechanically unstable and will buckle. We conclude that the purely mechanical aspects of biological tissues may indeed play a role in morphogenesis.

Estimation of the extent of the cutoff region from the spatial distribution of labelling and mitotic indices of intestinal crypts of a fixed length.

Current understanding of the pattern of proliferation within intestinal crypts involves the notion of a cutoff region introduced by Cairnie et al. (Exp. Cell. Res. 39, 539-553, 1965b). (Cells produced above the cutoff are non-cycling, whereas cells produced below the cutoff are cycling.) They contrasted the predicted distribution of proliferation in the extreme cases of a cutoff of width 0 (a sharp cutoff) with one eight cells wide (a slow cutoff) and concluded that the data were better explained by the latter. We have shown that crypt size variation artificially broadens the apparent distribution of proliferating cells in the crypt (Totafurno et al., Biophys. J. 54, 845-858, 1988). Here we show that the measurement and analysis of crypts of a specified height reduces this artifact. This work introduces the use of distance from the crypt base (in microns) to specify the location of cells within the crypt as an improvement over the cell position ordering traditionally used in the determination of the distribution of proliferating cells. We also show how to explicitly correct for several artifacts in the measurement of the labelling index. We conclude that cell proliferation within the crypt is more localized than previously realized; in fact, a cutoff as slow as eight cells wide is rejected.

Comparison of mesenteric with antimesenteric crypt and villus populations in the mouse jejunal epithelium.

Variation in the size and composition of crypts and villi along the length of the intestinal tract is well known. Here we investigate possible variation around the circumference of the intestine. This is a concern because most studies have ignored potential circumferential variation and its implications for experimental design in cell kinetic studies. We compared the crypt and villus populations of the mesenteric half with those of the antimesenteric half of proximal mouse jejunum. The branching crypt index and crypt and villus dimensions were measured. We found no evidence of differences in the branching crypt index, in the mean crypt and villus size, nor in the distribution of crypt and villus sizes between these two populations.

Theoretical analysis of the flow of cells over villi of the small intestine.

The flow of epithelial cells over villi of mouse small intestine is calculated from equations of cell number balance and irrotational flow. The influence of both villus geometry and crypt distribution about the villus base are studied. Specific, experimentally verifiable predictions are made.

Variation in crypt size and its influence on the analysis of epithelial cell proliferation in the intestinal crypt.

The standard model of epithelial cell renewal in the intestine proposes a gradual transition between the region of the crypt containing actively proliferating cells and that containing solely terminally differentiating cells (Cairnie, Lamerton and Steel, 1965 a, b). The experimental justification for this conclusion was the gradual decrease towards the crypt top of the measured labeling and mitotic indices. Recently, however, we have proposed that intestinal crypts normally undergo a replicative cycle so that at any time in any region of the intestine, crypts will be found to have a wide range of sizes. We show here that if this intrinsic size variation is taken into account, then a sharp transition between the proliferative and nonproliferative compartments of individual intestinal crypts is consistent with the labeling and mitotic index distributions of mouse and rat jejunal crypts. Thus there is no need to invoke the region of gradual transition from proliferating to nonproliferating cells as is done in the standard model. The position of this sharp transition is estimated for both the mouse and rat. Experiments to further test our model are suggested and the significance of the results discussed.

The crypt cycle. Crypt and villus production in the adult intestinal epithelium.

We propose a model for the growth of individual crypts that is able to account for the observed changes in the number of cells in crypts under normal conditions, after irradiation, and after 30% resection. Parameter values for this model are estimated both for mouse and man, and detailed predictions of crypt growth rates are made. This model does not predict a steady-state crypt size; rather it suggests that crypts grow until they bifurcate. We therefore propose a crypt cycle (analogous to the cell cycle) and present evidence that most if not all crypts in the adult mouse are cycling asynchronously and independently. This evidence consists of four experiments that indicate that branching crypts are randomly distributed over the intestinal epithelium, that the plane of bifurcation of branching crypts is randomly oriented with respect to the villus base, and that the size distribution of crypts is consistent with an expanding crypt population. We also report for the first time evidence of villus production in the adult mouse intestinal epithelium. We conclude that the crypt and villus populations in the adult mouse are not in a steady state.