Population dynamics of normal and leukaemia stem cells in the haematopoietic stem cell niche show distinct regimes where leukaemia will be controlled

Abstract

Haematopoietic stem cells (HSCs) are responsible for maintaining immune cells, red blood cells and platelets throughout life. HSCs must be located in their ecological niche (the bone marrow) to function correctly, that is, to regenerate themselves and their progeny; the latter eventually exit the bone marrow and enter circulation. We propose that cells with oncogenic potential-cancer/leukaemia stem cells (LSC)-and their progeny will also occupy this niche. Mathematical models, which describe the dynamics of HSCs, LSCs and their progeny allow investigation into the conditions necessary for defeating a malignant invasion of the niche. Two such models are developed and analysed here. To characterize their behaviour, we use an inferential framework that allows us to study regions in parameter space that give rise to desired behaviour together with an assessment of the robustness of the dynamics. Using this approach, we map out conditions under which HSCs can outcompete LSCs. In therapeutic applications, we clearly want to drive haematopoiesis into such regimes and the current analysis provide some guidance as to how we can identify new therapeutic targets. Our results suggest that maintaining a viable population of HSCs and their progenies in the niche may often already be nearly sufficient to eradicate LSCs from the system.

Figure 1.

A model of competition within the HSC niche. Normal haematopoiesis occurs through HSC production of progenitor cells (A) that differentiate to mature blood cells (D). Alongside, a pool of mature leukaemia cells (T) is maintained by self-renewing LSCs. Mature cells are able to leave the niche by migration into the bloodstream.

Figure 2.

Three different ways to sample over the two-dimensional parameter space of θ₁ and θ₂. (a) Random sampling draws from a multivariate uniform distribution. This is the most general (undirected) approach. (b) By subdividing the space using a LH, more even sampling of the space is obtained. (c) In contrast to the global approaches of (a) and (b), ABC sampling is targeted towards regions of acceptable model behaviour, as represented by the blue circles growing darker with each iteration. the advantage of such an approach is that time is not wasted searching through those areas of space that we are not interested in.

Figure 3.

(a) An example of how the results are presented, with a description of their meaning. (b) Comparison of different rates for healthy and leukaemia cell species.

Figure 4.

Dynamics of healthy and leukaemia stem cells that allow suppression of leukaemia to occur. For HSCs, self-renewal and symmetric differentiation should be controlled. For LSCs, no control is required. See figure 3a for explanation of the plots.