Symmetric vs. asymmetric stem cell divisions: an adaptation against cancer?

Abstract

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two "hits", and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

Figure 1. Symmetric and asymmetric stem cell divisions.

In the asymmetric division model, a stem cell produces one differentiated cell and one stem cell. In the symmetric division model, a stem cell produces two differentiated cells or two stem cells.

Figure 2. The six different approximation regimes (Table 2) for solutions of system (2–3).

Plotted is the quantity (a) and (b) as a function of the frequency of symmetric divisions, , for three different values of (solid lines), together with the approximations given by the formulas in Table 2. Approximations , , and are best demonstrated in panel (a), where the quantity is plotted. Approximations , , and are best demonstrated in panel (b), where the quantity is plotted. The other parameters are , .

Figure 3. The reduction in the rate of double mutant production in stem cells with symmetric divisions compared to stem cells with asymmetric divisions only.

Plotted is the quantity in formula (4) as a function of the mutation rate, . The percentage of the stem cells in the whole population () is marked next to the lines. The other parameters are , .

Figure 4. The probability of double-hit mutant generation as a function of , the probability of symmetric stem cell divisions.

The results of numerical simulations are presented as points connected with dotted lines (standard deviations are included). Analytical results are given by solid lines (formula (11). The horizontal line represents the calculations for the homogeneous model. We ran batches of runs. The parameters are , , , .

Figure 5. The probability of double-mutant generation as a function of , the ratio of TA cells to the total number of cells.

As in Figure 4, the results of numerical simulations are presented as points connected with dotted lines (standard deviations are included), and the analytical results are given by solid lines (formula (11)). The horizontal lines represent the calculations for the homogeneous model. We ran batches of runs. Plotted is the probability of double-mutant generation as a function of , for purely symmetric () and purely asymmetric () models, for three different values of . The parameters are .

Figure 6. The probability of double-hit mutant generation in the symmetric division model.

The case of symmetrically dividing stem cells, same as in Figure 5.

Figure 7. The threshold fraction of stem cells corresponding to stem and TA cells contributing equally to double-hit mutant production.

The quantity , which corresponds to , is plotted as a function of the mutation rate, , for three different values of , and . For the fraction of stem cells above these values, stem cells have a higher contribution to the rate of double-mutant production compared to the non-stem cells. Thin dashed lines show the approximations of equation (8).

Figure 8. The immortal DNA strand hypothesis.

The probability of double-hit mutant generation is calculated for a particular set of parameters as a function of (the probability of symmetric divisions), according to formula (21. For the minimum corresponds to at (asymmetric divisions only), for and we have an intermediate minimum at and respectively, and for higher values of the minimum is reached for (symmetric divisions). Here, , , , , , and the parameter varies from to in increments of .

Figure 9. Why are symmetrically dividing stem cells produce mutants slower?

The weight of a typical symmetrically dividing mutant stem cell lineage, , relative to the weight of an asymmetrically dividing mutant stem cell lineage, , is plotted as a function of the number of stem cell divisions, . Here, , , and 20 batches of simulations were performed to calculate the mean and the standard deviation.

Figure 10. Stem cell division decision trees for the numerical algorithm.

(a) Divisions of wild-type stem cells. (b) Divisions of mutant stem cells. Stem cells are denoted by light circles with an “S” and TA cells by shaded circles with a “D”. One-hit mutants are marked with a star.