Stochastic Hypothesis of Transition from Inborn Neutropenia to AML: Interactions of Cell Population Dynamics and Population Genetics

Abstract

We present a stochastic model of driver mutations in the transition from severe congenital neutropenia to myelodysplastic syndrome to acute myeloid leukemia (AML). The model has the form of a multitype branching process. We derive equations for the distributions of the times to consecutive driver mutations and set up simulations involving a range of hypotheses regarding acceleration of the mutation rates in successive mutant clones. Our model reproduces the clinical distribution of times at diagnosis of secondary AML. Surprisingly, within the framework of our assumptions, stochasticity of the mutation process is incapable of explaining the spread of times at diagnosis of AML in this case; it is necessary to additionally assume a wide spread of proliferative parameters among disease cases. This finding is unexpected but generally consistent with the wide heterogeneity of characteristics of human cancers.

Keywords: acute myeloid leukemia; branching process; clonal evolution; driver mutations; myelodysplastic syndrome; severe congenital neutropenia.

Figure 1

Dynamic stochastic model of impaired differentiation in granulocyte precursors. GCSF signaling occurs through its cognate receptor, GCSFR. It involves both proximal signaling networks consisting of signaling molecules such as Lyn, Jak, STAT, Akt, and ERK, and distal gene regulatory networks consisting of transcription factors. Together, these signaling networks promote proliferation, survival, and differentiation. In patients with severe congenital neutropenia, the earliest known mutation to contribute to transformation to secondary MDS or AML is a nonsense mutation in the GCSFR gene. This mutation leads to a truncated receptor, GCSFR delta 715.

Figure 2

Proliferating healthy cells in the bone marrow mutate at random times, possibly influenced by super-pharmacological doses of GCSF. As long as the cell population size is kept in check, genetic drift, and selection remove many of the mutants, whereas some mutants persist. When the population expands, new mutant clones become more easily established. At some point, a qualitative change in the proliferation rate occurs and the now malignant cell population starts rapidly expanding.

Figure 3

Summary of successive driver mutations in the natural course of the SCN → sMDS → sAML transition. (A) Counts N_i(t) of cells in successive mutant clones, under model as in Eq. 7 with A = 0.02, ε = 0.2, and k = 2. Straight lines with increasing slopes: counts of cells in successive mutant clones. Thick dashed line: Total mutant cell count. (B) Relative proportions n_i(t) = N_i(t)/Σ_jN_j(t) of cells belonging to successive mutant clones. Further details as in the Section “Mathematics of the Model.”

Figure 4

Cumulative distributions of the model-generated times at diagnosis of sAML. (A) Simulations under model as in Eq. 7 with A generated using Eq. 8, ε = 0.2, and k = 2. (B) Simulations under model as in Eq. 8 with A = 0.02, ε = 0.2, and k = 2.