Mathematical Modelling as a Proof of Concept for MPNs as a Human Inflammation Model for Cancer Development

<p><b>Left:</b> Typical development in stem cells (top panel A) and mature cells (bottom panel B). Healthy hematopoietic cells (full blue curves) dominate in the early phase where the number of malignant cells (stipulated red curves) are few. The total number of cells is also shown (dotted green curves). When a stem cell mutates without repairing mechanisms, a slowly increasing exponential growth starts. At a certain stage, the malignant cells become dominant, and the healthy hematopoietic cells begin to show a visible decline. Finally, the composition between the cell types results in a takeover by the malignant cells, leading to an exponential decline in hematopoietic cells and ultimately their extinction. The development is driven by an approximately exponential increase in the MPN stem cells, and the development is closely followed by the mature MPN cells. <b>Right:</b> B)The corresponding allele burden (7%, 33% and 67% corresponding to ET, PV, and PMF, respectively) defined as the ratio of MPN mature cells to the total number of mature cells.</p

Model calibration.

<p>A) Plateaus to the left show the amount of hematopoietic stem cells <i>x</i>₀ (upper plateau) and that for MPN stem cells <i>y</i>₀ (lower plateau) whereas the plateaus to the right show the amount of hematopoietic stem cells <i>x</i>₀(lower plateau) and MPN mature cells <i>y</i>₀ (upper plateau). B) Plateaus to the left show the amount of hematopoietic mature cells <i>x</i>₁ (upper plateau) and that for MPN mature cells <i>y</i>₁ (lower plateau) whereas the plateaus to the right show the amount of hematopoietic mature cells <i>x</i>₁ (lower plateau) and MPN mature cells <i>y</i>₁ (upper plateau). The yellow and purple boxes show our data used for calibrating (and validating) the model with further details in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183620#pone.0183620.s001" target="_blank">S1 Appendix</a>. Yellow boxes show our “no MPN cancer values”, and purple boxes show our “full blown” MPN values in the advanced myelofibrosis stage. Yellow position marker shows the number of hematopoietic stem cells as used by Dingli & Michor [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183620#pone.0183620.ref092" target="_blank">92</a>], and black position markers show the number of cells as used by Gentry et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183620#pone.0183620.ref086" target="_blank">86</a>].</p

The conceptual model.

<p>Light gray boxes (symbolized x₀, x₁, y₀, and y₁) illustrate the compartments of the basic model, and the black arrows the rates of the flows between these compartments. Here x₀ denotes the number of HSC, x₁ that of HMS, y₀ that of MPN SC, and y₁ the number of MPN MC. The light blue compartment (symbolized a) contains all dead cells and the light orange compartment (symbolized s) the inflammatory level, i.e. the immune response. Blue arrows from these represent related rates of flows. Red stipulated arrows going from the inflammatory compartment represent effects of the cytokines (or neutrophils when eliminating dead cells) modulating rates of the basic model. Two additional rates (depending on x₀ and y₀) appearing as red stipulated arrows represent the bone marrow niches symbiosis with the stem cells modulating the self-renewal rates. Note, stem cells leaving their respective compartments enter the corresponding mature cell-pools as multiplied by the progenitor amplification factor (A).</p

Investigation of increased inflammatory load at various onsets and durations.

<p>Blue curve is default parameters corresponding to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183620#pone.0183620.g003" target="_blank">Fig 3</a>, red dotted is a doubling of inflammatory load, full red curve is a doubling of inflammatory load in year 0–20, then back to default level, black dotted curve is inflammatory doubling from year 10, the full black is inflammatory doubling year 10–30. <b>Upper:</b> Increasing inflammatory load has a boosting effect on MPN MC (A) as well as on HMC (B). <b>Lower:</b> Displaying the results in terms of the clinically available quantity, total blood cell count, also shows a boosted effect with increasing inflammatory load (C). The allele burden of JAK2 mutated blood cells similarly shows that increased inflammation increases disease development (D). There is a clear effect of MPN promotion with increasing inflammatory load, earlier onset, and exposure time. Lowering inflammatory load makes disease progression less rapid. Maintaining a doubling (red dotted curve) shifts the allele burden curve to the left by two years. Shortening the exposure time of inflammatory load weakens the disease progression. The inflammation has a fast impact on the total number of blood cells, which typically changes by 25% within the first year after doubling or reducing the inflammatory load by 50%.</p