Computational model of cell positioning: directed and collective migration in the intestinal crypt epithelium

Abstract

The epithelium of the intestinal crypt is a dynamic tissue undergoing constant regeneration through cell growth, cell division, cell differentiation and apoptosis. How the epithelial cells maintain correct positioning and how they migrate in a directed and collective fashion are still not well understood. In this paper, we developed a computational model to elucidate these processes. We show that differential adhesion between epithelial cells, caused by the differential activation of EphB receptors and ephrinB ligands along the crypt axis, is necessary to regulate cell positioning. Differential cell adhesion has been proposed previously to guide cell movement and cause cell sorting in biological tissues. The proliferative cells and the differentiated post-mitotic cells do not intermingle as long as differential adhesion is maintained. We also show that, without differential adhesion, Paneth cells are randomly distributed throughout the intestinal crypt. In addition, our model suggests that, with differential adhesion, cells migrate more rapidly as they approach the top of the intestinal crypt. Finally, by calculating the spatial correlation function of the cell velocities, we observe that differential adhesion results in the differentiated epithelial cells moving in a coordinated manner, where correlated velocities are maintained at large distances, suggesting that differential adhesion regulates coordinated migration of cells in tissues.

Figure 1.

Initial cell condition for the model. (a) Seven cell types defined and their positions in the crypt. (b) Initial cell configuration in the two-dimensional lattice model. (c) Transitions of cell types in model D.

Figure 2.

The values of the entries in the matrix J(τ, τ′) in equation (2.3).

Figure 3.

Cell distribution from the simulations. In the two-dimensional lattice model, when differential adhesion is maintained, proliferative cells and differentiated post-mitotic cells do not intermingle: (a) scenario 1, (b) scenario 2. The black line depicts the sharp boundary between the proliferative and differentiated areas. When differential adhesion is removed from the model, differentiated cells intermingle with proliferative cells: (c) scenario 1, (d) scenario 2.

Figure 4.

Trajectories of cells. (a) The migration trajectories of cells moving from the bottom of the crypt to the top of the crypt when differential cell adhesion is maintained. (b) The trajectories of cells without differential cell adhesion show that, instead of staying at the bottom of the crypt, the Paneth cell (represented by dark blue dots) moves upwards when there is no differential adhesion. On the other hand, the proliferative cell in (b) stays at the bottom of the crypt and does not move upwards to the top of the crypt. The dot-to-dot distance equals 1 h. The colour of the dot corresponds to the cell type at that time point.

Figure 5.

Mean migration velocity of cells at different positions in the crypt. The results found in (a) scenario 1 (squares with dashed line, results from the two-dimensional lattice model (with differential adhesion); filled circles with dotted line: results from the two-dimensional lattice model (without differential adhesion)) and (b) scenario 2 (triangles with dashed line: results from the two-dimensional lattice model (with differential adhesion); asterisks with dotted line, results from the two-dimensional lattice model (without differential adhesion)) show that, with differential cell adhesion, cell velocity is increased. The average is taken over cells from 20 datasets.

Figure 6.

Spatial correlation of the cell velocity in cells with differential adhesion (circles) and cells without differential adhesion (squares). Comparison of cells with differential adhesion and without differential adhesion shows that the velocities of cells with differential adhesion are highly correlated; however, without differential adhesion, the spatial correlation of the velocity decreases when cell distance increases—(a) scenario 1; (b) scenario 2. Data are determined from cells in 20 datasets. The distance between cells, r, is normalized to the target cell diameter. Standard error (s.e.) bars are shown in the figure.

Figure 7.

Cell populations maintained in the model. Preserving cell homeostasis is of critical importance in fast-regenerating tissue such as intestine. (a) Cell populations of different types are maintained throughout the two-dimensional lattice model simulation when differential cell adhesion is considered. (b) However, when no differential cell is maintained, the population of proliferative cells is reduced.