Quantification of Transition Rates in B-Cell Acute Lymphoblastic Leukemia Identifies Structural Relationships between Cell States

Cancer stem cells (CSCs) are hypothesized to promote tumor progression through innate chemoresistance and self-renewal. Ostensible CSCs were first identified in acute myeloid leukemia and were found to have a CD34+/CD38- immunophenotype similar to hematopoietic stem cells. However, the isolation of CSCs from B-lymphoblastic leukemia (B-ALL) has proved more difficult. B-ALL cells with stem cell-like properties have been reported with variable immunophenotype, perhaps due to temporal variation of CD34 and CD38 expression in this setting. Thus, we hypothesize that cell state transitions between stem cell-like, hematogone-like, and naive B-cell-like leukemia subpopulations play a significant role in B-ALL disease progression. However, it is difficult to precisely quantify patient-specific rates of spontaneous cell state transitions between distinct immunophenotypic subpopulations (e.g. defined by CD34 and CD38 expression relative to neutrophils) from routinely collected clinical data.

Here, we develop a Markov chain mathematical model to quantify transition rates between four cell fates described by CD34 and CD38 flow cytometry markers. We employed an iterative, algorithmic search process using flow cytometry characterization of four B-ALL cell states with their normal counterpart appearing in parentheses: CD34+/CD38- (hematopoietic stem cells), CD34+/CD38+ (stage 1 hematogones), CD34-/CD38+ (stage 2 and 3 hematogones), and CD34-/CD38- (naïve B-cells). This numerical search procedure was used to derive patient-specific Markov matrices, describing the stochastic cell state transitions and resulting in estimates for cell state transition rates for each patient. Numerical Markov chain modeling training procedure was performed on flow cytometry data of a cohort of B-ALL patient samples of peripheral blood (N=46) and bone marrow (N=63) with matched clinical and molecular features such as BCR::ABL1 status, comprehensive genomic profiling, minimal residual disease (MRD) post-induction chemotherapy, and 3-year relapse. Critical to our goal of quantifying the evolution of state transition rates, we also obtained bone marrow measurements for a cohort of individuals in molecular remission (N=38). Analysis of Markov chain transition rates indicate a high degree of heterogeneity between patient-specific transition rates. Linear Discriminant Analysis (LDA), a supervised machine learning method, achieves an accuracy of 80% for predicting BCR::ABL1 status, and an accuracy of 84% (bone marrow) and 89% (peripheral blood) for disease state (cancer/remission) classification.

Markov matrices can be analyzed using matrix parameters that summarize the structural relationship between states within the model. For example, a reciprocity index is defined by the rate of incoming or outgoing transitions of each cell state. BCR::ABL1-positive and BCR::ABL1-like B-ALL patients correspond to a higher fraction of cells (x=0.682 for N=59 patients) in the stem-like CD34+/CD38- state (p<0.01) than BCR::ABL1-negative patients (x=0.190 for N=50 patients). This finding is explained by the difference in reciprocity rates: BCR::ABL1-positive/like patients have a lower rate of outgoing transitions from CD34+/CD38- (p < 0.01) and a higher rate of incoming transition toward CD34+/CD38- (p < 0.01) than BCR::ABL1-negative patients. Finally, comparison of Markov parameters for matched patients pre- and post-induction chemotherapy treatment quantifies the evolutionary selection pressures acting on transition rates induced by chemotherapy treatment. The approach described above provides supporting evidence that cell state transitions drive B-ALL disease progression.