Predicting clonal self-renewal and extinction of hematopoietic stem cells

Abstract

A single hematopoietic stem cell (HSC) can generate a clone, consisting of daughter HSCs and differentiated progeny, which can sustain the hematopoietic system of multiple hosts for a long time. At the same time, this massive expansion potential must be restrained to prevent abnormal, leukemic proliferation. We used an interdisciplinary approach, combining transplantation assays with mathematical and computational methods, to systematically analyze the proliferative potential of individual HSCs. We show that all HSC clones examined have an intrinsically limited life span. Daughter HSCs within a clone behaved synchronously in transplantation assays and eventually exhausted at the same time. These results indicate that each HSC is programmed to have a finite life span. This program and the memory of the life span of the mother HSC are inherited by all daughter HSCs. In contrast, there was extensive heterogeneity in life spans between individual HSC clones, ranging from 10 to almost 60 mo. We used model-based machine learning to develop a mathematical model that efficiently predicts the life spans of individual HSC clones on the basis of a few initial measurements of donor type cells in blood. Computer simulations predict that the probability of self-renewal decays with a logistic kinetic over the life span of a normal HSC clone. Other decay functions lead to either graft failure or leukemic proliferation. We propose that dynamical fate probabilities are a crucial condition that leads to self-limiting clonal proliferation.

Fig. 1.

Individual HSCs have distinct clonal life spans. (A–L) The %DT at different times after transplant of a single HSC. (A–F) Serial transplants were performed. At the indicated time points HSCs from the primary host (x) were transplanted into the secondary (○), and then the tertiary (△), and finally the quaternary (◆). Because secondary and higher transplants used several hosts per HSC clone, mean repopulation (±SD) is shown. In some instances the errors are too small to be discernible. The small errors reflect the similarities in repopulation kinetics of HSCs within a clone. Extrapolation of the curves to the right intersection with the time axis was used to estimate ”actual” life spans. Early data points for the HSC clones in A and B were published previously (10). (G–L) Clonal HSC life spans without serial transplants. These HSCs aged in the primary host.

Fig. 2.

Concerted repopulation kinetics of daughter HSCs within a clone. (A–D) The %DT for individual hosts at different times (horizontal axis) after transplant of single HSCs. (A–C) At the indicated time points, 5 × 10⁶ BM cells from the primary host (x) were transplanted into 2–3 secondary (○) hosts, and then into 4 different tertiary (△) hosts. Occasionally, the symmetry of repopulation levels is broken. For example, one mouse in B rapidly lost DT cells in blood at 18 mo after injection. This mouse died shortly thereafter, suggesting that the abrupt shift in %DT was pathological. (D) A total of 4 × 10⁴ BM cells from the primary host were transferred into 15 secondary mice.

Fig. 3.

Ballistic model of clonal aging. (A) Examples of how the function D(t) is derived from the interplay between the growth function D⁺(t) = bt and the decline function D⁻(t) = −at^α. Here, b was fixed and a was normalized to 1. Different values for α yield distinct life-span curves; e.g., for α = 1.6, the decline function (●) interacted with the growth function (▲) to generate a long life span (x). For α = 2.0 (decline function ○), we obtained a short life span (◇). (B) Parameter space of the prediction model. We tested 10⁷ variations of the parameters (b, a, α) by Monte Carlo simulation. For a and b we used a range of 1–10⁵ and 1 < α < 10 [α > 1 excludes linear D(t); α < 10, because large α quickly yields very short life spans (<1 mo)]. Shown are (b, a, α) that generate permissible configurations (1 < T < 1,000). (C) Frequency distribution of α: No permissible values were found for α > 3.52. (D) The shapes of the predicted (○) and the experimental data (x) match well.

Fig. 4.

A priori prediction of the life span of 27 HSC clones. The predicted (red) and actual (blue) life spans are shown (from Table S3). Axis units are months.

Fig. 5.

Simulating clonal HSC life spans. Two cell types are considered. HSCs can self-renew, be in a quiescent state (G₀), or differentiate into precursors and mature cells (DIF). In the simulator, the resting state is a by-product of asynchronous updating (39). The likelihood that a HSC divides into two daughter HSCs or into two DIF cells is determined by transition probabilities. Asymmetrical division scenarios were also considered and gave comparable results.

Fig. 6.

Simulations predict a logistic decline of self-renewal during the life span of HSC clones. (A–H) The simulated %DT (blue) after transplantation of a single HSC. All simulations were extended to 1,600 time points. (Insets) At the level of individual cells, the intrinsic fate probabilities as functions of division history (θ, horizontal axis) that yielded the blue curves. Red, probability of self-renewal (p_sn); green, probability of differentiation (p_diff). (A and B) Constant p_sn and p_diff; (C) p_sn and p_diff decline/increase linearly; (D) p_sn and p_diff decline/increase elliptically; (E) logistic change of p_sn and p_diff; (F) logistic p_sn with constant p_diff; (G) constant p_sn and increasing p_diff; (H) HSCs with high initial p_diff and low p_sn.