Combined Population Dynamics and Entropy Modelling Supports Patient Stratification in Chronic Myeloid Leukemia

Abstract

Modelling the parameters of multistep carcinogenesis is key for a better understanding of cancer progression, biomarker identification and the design of individualized therapies. Using chronic myeloid leukemia (CML) as a paradigm for hierarchical disease evolution we show that combined population dynamic modelling and CML patient biopsy genomic analysis enables patient stratification at unprecedented resolution. Linking CD34(+) similarity as a disease progression marker to patient-derived gene expression entropy separated established CML progression stages and uncovered additional heterogeneity within disease stages. Importantly, our patient data informed model enables quantitative approximation of individual patients' disease history within chronic phase (CP) and significantly separates "early" from "late" CP. Our findings provide a novel rationale for personalized and genome-informed disease progression risk assessment that is independent and complementary to conventional measures of CML disease burden and prognosis.

Figure 1. Analysis Workflow.

Workflow outlining rationale and analytical pipeline. (a) Established clinical parameters classify CML patients in disease progression states regardless of genomic profile. (b) Combination of conventional scores, e.g. blast count, with patient gene expression (GEX) - derived genomic scores “CD34⁺ similarity” and “entropy” enables patient characterisation according to complementary scores at increased resolution. CD34⁺ similarity indicates disease history and progression risk, entropy is a quantitative measure of disorder or lack of GEX co-regulation. (c) Focus on CP patient progression risk assessment according to the CML population dynamic model by Dingli et al.. The model parameter CD34 ratio reflects cell population dynamics and is correlated with patient CD34⁺ similarity scores. Non-monotonic evolution of the model parameter entropy serves as alignment marker to map patient gene expression and disease time within CP. CP = chronic phase, AP = advanced phase, BC = blast crisis of CML.

Figure 2. Separation of population-based and mechanistic effects using stem and progenitor cell data from primary CML patients.

Genome-wide gene expression of 4 stem- and progenitor cell subpopulations (colours) across all phases of CML progression (shapes) in 12 patients and three healthy controls, represented by PCA-derived components 1, 2, and 3. PC: Principle Component, CP: chronic phase, AP: accelerated phase (by blast count criteria), AP_cyto: accelerated phase (by occurrence of additional clonal cytogenetic changes without increase in blast count), BC: blast crisis, HSC: hematopoietic stem cell, MEP: megakaryocyte-erythroid progenitor, GMP: granulocyte-macrophage progenitor, CMP: common myeloid progenitor. Data from GEO dataset GSE47927, by Copland M and Irvine DA.

Figure 3. Integrated tracking of CML disease progression stages from mixed-population clinical samples.

(a) Data points represent clinical samples of 42 CP (green), 9 AP (blue), 8 AP_cyto (purple), and 28 BC (red) patients. Each asterisk represents one patient. Differences between patients and corresponding disease stages are resolved by CD34⁺ similarity score in combination with blast count. (b) Data points as in a. Entropy of patient gene expression resolves differences in disease stages in combination with CD34⁺ similarity score.

Figure 4. Assessment of CP patient disease status and progression risk.

(a) Data points represent clinical samples of 42 CP patients (green asterisks) (GSE4170, Radich et al. 2006a). Normalized CD34⁺ similarity score combined with entropy of patient gene expression and simulated entropy maps CP evolutionary time intervals between model and patients. (b) 42 CP patients (green asterisks) as in a. plotted by observed entropy from clinical gene expression data and simulated entropy from the model converted to time (days after initial HSC mutation). Timespan covers ~6 years in accordance with the model.

Figure 5. Entropy-based separation of early vs. late chronic phase (CP) patients.

(a) Integrating CD34⁺ similarity score with entropy of patient gene expression and simulated entropy resolves differences in patient disease evolutionary time. 42 CP patients (asterisks) plotted by observed entropy from clinical gene expression data aligned by model-derived simulated entropy converted to disease time span (days). Time span covers ~6 years in accordance with the model. The red borderline separates “early” (T1) from “late” (T2) CP patients (light and dark green asterisks, respectively) at the simulated entropy minimum singularity at t = 1476 days (~4.04 years), and CD34⁺ similarity score = 0.403. b. T1 and T2 CP patient groups are significantly different in terms of gene expression (T1 vs. T2, FDR-adjusted p < 0.05). Progression towards advanced stage is highlighted by increasing differential gene expression compared to AP and BC, where the fraction of differentially expressed genes of T1-CP vs. AP (66.8%) > T2-CP vs. AP (32.3%), and T1-CP vs. BC (80.7%) > T2-CP vs. BC (46.14%).

Figure 6. Integrated concept for CML patient stratification and risk assessment during chronic phase (CP).

(a) Disease stage fractions (%) observed when patients are subdivided into CD34⁺ similarity quarters and low vs. high entropy, yielding eight sub-spaces. Graph represents disease stage fraction of each sub-space compared to all patients (42 CP (green), 9 AP (blue), 8 AP_cyto (purple), and 28 BC (red) patients, as in Fig. 3). (b) CML patient biopsy gene expression profiling enables differentiation of patients by CD34⁺ similarity and gene expression entropy. A population dynamic model for quantification of the evolution of hematopoietic cell types across CML serves to identify dynamics that are characteristic for disease status. Upon entropy-mediated alignment to time scale of disease evolution during CP, patient status can be matched to disease evolutionary time for risk assessment and personalized therapeutic intervention.