Mathematical and Experimental Evidence That Differentiation of Leukemic Blasts in Acute Myeloid Leukemia Is Not Completely Blocked

Background: Hematopoietic stem cells precisely regulate self-renewal versus differentiation to balance the production of blood cells and maintenance of the stem cell pool. The canonical view of acute myeloid leukemia (AML) is that it results from a combination of molecular events in a hematopoietic stem cell that block differentiation and drive proliferation. These events result in the accumulation of primitive hematopoietic blast cells in the blood and bone marrow. We used mathematical modeling and an experiment to determine the impact of varying differentiation rates on myeloblastic accumulation in primary AML samples.

Model and Experiment: To examine the potential of varying degrees of perturbed differentiation to contribute to leukemic cell architecture, we generated a mathematical model using functional and hierarchical features of hematopoietic differentiation. This model demonstrates that there is a relationship between the ratio of the rate at which cells differentiate into a compartment from a more primitive compartment and the rate at which cells differentiate into a less primitive compartment (the amplification factor) and the fraction of the time a cell differentiates after it divides. Smaller differentiation fractions result in larger amplification factors. As the differentiation fraction declines toward 0.5, the amplification factor goes to infinity.

Since the more mature cell types are much more numerous than their progenitors, amplification factors must be quite large. Thus, the differentiation fraction is very close to 0.5, at least for some compartments. If, for some reason, the differentiation fraction is less than 0.5, then on average for every division the compartment grows, akin to leukemia.

Since the aggregate amplification factor from long-term stem cells to mature cells is roughly 10⁹, we expect 0.501 to be a typical value of the differentiation fraction in healthy hematopoiesis. This suggests that normal blood cell production must be on a knife's edge of being leukemic to work as it does. Given the large numbers of intermediate cells characteristic of leukemia, our model argues that the leukemic phenotype requires only a small reduction rather than a complete block in the delicate balance of differentiation. If this model of skewed differentiation (rather than blocked differentiation) is correct, that would mean that mature cell types would have a leukemic genotype.

We tested this by collecting peripheral blood samples from 12 patients with AML with abnormal cytogenetics such as t(8;21), inv 16, trisomy 8, 13q34 and MLL rearrangements or mutations such as FLT3-ITD and NPM1 and sorting the cells into several subpopulations including immature leukemic blasts, monocytes, neutrophils, and lymphocytes. We analyzed the isolated cell populations using interphase fluorescent in situ hybridization (FISH) or by sequencing to determine the identity and relative abundance of the leukemia-associated molecular aberrations. We found that all samples for which we were able to isolate neutrophils and myeloid blasts had (usually many) cells with abnormal cytogenetics or mutations at levels similar to those in the blast cell population, while as a control most of the purified T-cell subpopulations had either no or few abnormal cells detected. These findings contrast with the existing assumption that many of these abnormalities will lead to a full block in differentiation.

Conclusions: Our mathematical model shows that instead of the commonly held belief that AML results from a complete block of differentiation of the leukemic blasts, even a slight skewing of the fraction of cells that differentiate would produce an accumulation of blasts. Our experimental evidence confirms this model by showing that an incomplete block in differentiation is common in AML across different genetic driver lesions, thus changing an existing paradigm of AML biology. This, in turn, suggests that therapies aimed at increasing the differentiation fraction may be fruitful, but will require discernment of the specific actionable mechanisms underlying reduced or skewed differentiation in genetic subtypes of the disease. Our model will also be helpful in understanding the effect of therapeutic perturbation on hematopoiesis. This also warrants potential application to other hematologic malignancies characterized by different cells of origin and kinetics of disease progression.