Spatial dynamics of multistage cell lineages in tissue stratification

Abstract

In developing and self-renewing tissues, terminally differentiated (TD) cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit-amplifying) cell stages, which ultimately give rise to TD cells. As the tissue reaches a tightly controlled steady-state size, cells at different lineage stages assume distinct spatial locations within the tissue. Although tissue stratification appears to be genetically specified, the underlying mechanisms that direct tissue lamination are not yet completely understood. Herein, we use modeling and simulations to explore several potential mechanisms that can be utilized to create stratification during developmental or regenerative growth in general systems and in the model system, the olfactory epithelium of mouse. Our results show that tissue stratification can be generated and maintained through controlling spatial distribution of diffusive signaling molecules that regulate the proliferation of each cell type within the lineage. The ability of feedback molecules to stratify a tissue is dependent on a low TD death rate: high death rates decrease tissue lamination. Regulation of the cell cycle lengths of stem cells by feedback signals can lead to transient accumulation of stem cells near the base and apex of tissue.

Figure 1

Multistage cell lineage and tissue stratification. (A) A cartoon of general epithelia and relative locations of cells at different lineage stages (red, stem cells; yellow and green, TA cells, blue, TD cells). The connective tissue underlying the basal lamina is stroma. (B) One-dimensional coordinate along the apical-basal axis (z axis). The origin z = 0 is aligned with the basal lamina, and the top of epithelium, which moves due to the growth of the tissue, is denoted by z_max. (C) A schematic diagram of a single cell lineage and associated regulatory molecules. Cells proliferate, differentiate to the next lineage stage or undergo death. The terms A, G, and F represent secreted molecules, which are analogous to molecules ActivinβB, GDF11, and Follistatin in OE, respectively. The secreted molecules A and G inhibit the population of stem and TA cells, respectively (red barred arrow), and they are both inhibited by F (green barred arrow). (Gray arrows) Molecule production: A is produced by all cells, and G is produced by TA and TD cells.

Figure 2

Distribution of different cell types and molecule concentrations along the apical-basal axis in epithelia. (A) Cell volume fractions of each lineage stage, with color bars for the scales. (B) Normalized molecule concentrations of A and G. Parameters used are listed in Table S1 in the Supporting Material.

Figure 3

Correlation between permeability coefficients α_A and α_G with SF of stem cell and z_max. (A) (Blue) Permeability coefficients α_A and α_G in Eq. 8 (log scale) versus stratification factor (SF) defined in Eq. 9; (Green) permeability coefficients versus epithelium thickness. (B) Coefficients α_A and α_G versus SF with a fixed epithelium thickness. In the simulations, z_max is fixed to be 0.02 cm, which can be achieved by adjusting one of γ_A and γ_G. (C) α_A = α_G is varied from 10 to 100 with different binding rates (k_af = k_gf = 0, 0.01, 0.1). In these simulations, the epithelium thickness z_max is fixed to be 0.02 cm by adjusting γ_A. (D) Cell distributions with three sets of parameters with different coefficient values of α_A and α_G. The parameters associated with the above simulations are listed in Table S1 and Table S2.

Figure 4

Dynamics of epithelium thickness and dynamics of tissue stratification. Three cases are plotted: 1), rapid uptake of A and G in the stroma, with the intraepithelial binding with F; 2), slow uptake of A and G in the stroma, with the intraepithelial binding with F; and 3), rapid uptake of A and G in the stroma, without the intraepithelial binding with F. These cases are referred to in the figures as cases 1, 2, and 3 (and in panels A and B they are distinguished by colors green, red, and blue, respectively). The corresponding parameter sets are listed in Table S1 and Table S2. (A) Time versus the epithelium thickness (z_max) normalized by the steady-state thickness (z_ss). (B) Time versus the stem cell stratification measured by SF. (C) Distribution of cells for case 1. (D) Distribution of cells for case 2. (E) Distribution of cells for case 3.

Figure 5

Tissue stratification and thickness as functions of the death rate of TD cells. (A) Death rate of TD cells (d₂ in unit of per-cell cycle length) versus the thickness of the epithelium (z_max). (B) The value d₂ versus stratification factor (SF) of stem cells (blue) and TA cells (red). (C) Relationship between d₂ and the total stem cell (left) and TA cell (right panel) populations (arbitrary unit). (D) Cell distributions with d₂ = 0.01, 0.1, and 1. All other parameters are listed in Table S1 and Table S2.

Figure 6

Feedback on the cell cycle length of stem cells induces transient peaks of stem cell density. (A) Time course of stem cell distribution from the basal (z = 0) to apical direction is presented at four time points: 14, 21, 28, and 45 (cell cycles/ln 2). In each figure, the green-colored curve represents the stem cell density without any feedback on the cell cycle lengths (β = 0). The density of stem cells is graded monotonically from the basal lamina, with the stem cell niche established at T = 14. The red-colored curve is the stem cell density with molecule A regulating the cell cycle length of stem cells (β = 3). Two local maxima of stem cell density, one at the basal lamina, and the other at the apical surface, appear by T = 14, and the peak at the apical surface vanishes eventually, after T = 45. (B) Stem cell distributions at time points T = 14, 21, 28, and 45.