Unraveling the Control of Cell Cycle Periods during Intestinal Stem Cell Differentiation

Abstract

During differentiation, intestinal stem cells (ISCs), a prototypical adult stem cell pool, become either secretory transit-amplifying cells, which give rise to all secretory cell types, or absorptive transit-amplifying cells, which give rise to enterocytes. These cells exhibit distinct cell cycle dynamics: ISCs cycle with a period of 24 h and absorptive transit-amplifying cells cycle with a period of ∼12 h, whereas secretory transit-amplifying cells arrest their cycle. The cell cycle dynamics of ISCs and their progeny are a systems-level property that emerges from interactions between the cell cycle control machinery and multiple regulatory pathways. Although many mathematical models have been developed to study the details of the cell cycle and related regulatory pathways, few models have been constructed to unravel the dynamic consequences of their interactions. To fill this gap, we present a simplified model focusing on the interaction between four key regulatory pathways (STAT, Wnt, Notch, and MAPK) and cell cycle control. After experimentally validating a model prediction, which showed that the Notch pathway can fine-tune the cell cycle period, we perform further model analysis that reveals that the change of cell cycle period accompanying ISC differentiation may be controlled by a design principle that has been well studied in dynamical systems theory-a saddle node on invariant circle bifurcation. Given that the mechanisms that control the cell cycle are conserved in most eukaryotic cell types, this general principle potentially controls the interplay between proliferation and differentiation for a broad range of stem cells.

Figure 1

The proliferative dynamics of intestinal stem cells (ISCs) and transit-amplifying (TA) cells. (A) A schematic illustration of the intestinal crypt, which is divided into two regions: the stem cell niche and TA zone. ISCs reside in a niche at the base of the crypt where they are supported by Paneth cells. The TA cells reside above the ISCs in the TA zone, which comprises a heterogeneous population of TA cells: absorptive TA cells (aTAs) proliferate, whereas secretory TA cells (sTAs), do not proliferate. Different TA cells can be marked by their expression of ATOH1, with sTAs expressing high levels of ATOH1 and aTAs expressing low ATOH1. Both cell types are derived from ISCs. (B) The influence diagram of the current model. Solid shapes with names represent the model components; arrows indicate activation; solid circle heads indicate repression. The model consists of four interacting modules. To see this figure in color, go online.

Figure 2

The simplified models suggest that ATOH1 might contribute significantly to the control of cell proliferation. (A) Representative CDK activities of three slowly-cycling cells. (B) Representative CDK activities of three rapidly cycling cells. (C) A classification tree. Nodes in which slowly cycling cells dominate are labeled as Slow; those in which rapidly dividing cells dominate are labeled Fast; nodes associated with arrested nodes are labeled Arrested. (D) A variable-importance calculation with a random forest (RF) analysis. Values are scaled from 0 to 100, for which predictors with a value of 0 are dispensable for classification and values of 100 indicate the most important model components or parameters. To see this figure in color, go online.

Figure 3

Experimental observations confirm the significant role of ATOH1 in controlling cell proliferation. (A) Representative crypt images from time-course confocal microscopy of an FUCCI2 (fluorescent ubiquitination-based cell cycle indicator)-derived enteroid. The arrow indicates a single cell that is traced to estimate the duration of the G1 phase of the cell cycle. Scale bar represents 10 μm. (B) The distribution of G1 phase durations obtained from FUCCI2 cells in control enteroids. (C) The distribution of G1 phase durations obtained from cells in Atoh1-KD enteroids. (D) Cells from control enteroids have a significantly longer G1 phase than Atoh1-deficient FUCCI enteroids (p < 0.0001). Error bars represent standard error. To see this figure in color, go online.

Figure 4

Bifurcation analysis revealed that a SNIC bifurcation controls ISC proliferation (A). A one-parameter bifurcation analysis showing the control of CDK by CCS. The solid curve indicates stable steady-state solutions, whereas the dashed curve indicates unstable steady states. Circles indicate the minimal and maximal amplitudes in oscillatory solutions of CDK. (B) A two-parameter bifurcation diagram showing how CCS and ATOH1 control the dynamics of CDK. The plane is separated into three distinct regions: one oscillatory and two nonoscillatory regions. The positions of different cells on this map determine their proliferative dynamics. (C) ISCs, aTAs, and arrested cells plotted on a two-parameter bifurcation diagram. ISCs and aTAs reside within the oscillatory region, whereas the arrested cells lie outside this region. (D) A three-dimensional (3D) plot of ISCs, aTAs, and arrested cells, with a third parameter, $R_{Ato}^{CKR}$. To see this figure in color, go online.

Figure 5

The model predicts three types of proliferation changes in response to STAT pathway activation. (A) The change in intestinal stem cells (ISCs) in response to activation of the STAT pathway. By elevating CCS, activation of the STAT pathway moves the ISCs rightward. Solid circles show the ISCs before STAT activation; open circles of identical colors show these ISCs after activation of the STAT pathway. Each arrow represents the trajectory of an individual cell following STAT activation. (B–D) Time series simulations of cells before and after STAT activation (dotted line); a cell that remains arrested after activation (B), a cell that begins to proliferate upon activation (C), and a third cell that proliferates faster after activation (D). To see this figure in color, go online.