Figure 5. Validation and prediction of leukemia development in independent cohorts.

As a validation of the state-transition mathematical model, critical points, and state-space geometry, we mapped data from two additional independent experiments into the state-space: cohort 1 and cohort 2. Cohort 1 consists of 7 controls and 9 CM mice (vCM1–9) sampled at the same frequency as the training cohort. Cohort 2 consists of 2 controls and 3 CM mice (vCM10–12) sampled sparsely in time. A) Leukemia trajectories (PC2) of validation cohorts projected into the state-space constructed with the training cohort. Critical points were estimated with the same procedure as the training data set. The locations in the transcriptome state-space correctly identify controls and states of leukemia, even in cohort 2 which does not include timepoints prior to CM induction. B) The frequency of cKit⁺ leukemia blasts increases rapidly after crossing c₂ transition point. C) The equation of motion of the transcriptome-particle in the quasi-potential is a stochastic differential equation which predicts trajectories of state-transition. One realization of a stochastic simulation is shown (controls black, CM induced mice in colors). Controls remain at the reference state ($c_1^{*}$) and CM induced mice transition from the reference state of perturbed hematopoiesis (c₁) to the leukemic state (c₃). D) Due to the stochastic nature of the biological processes and variability in RNA-seq data, we predict state-transition by considering the spatial-temporal evolution of the probability density (P(x₂,t)) given by numerically solving the Fokker-Planck equation with initial conditions and simulation parameters determined by the training cohort. E) The predicted (simulated) time to state-transition is calculated by integrating the probability density. The predicted time to develop leukemia is compared to the observed time to leukemia with a survival analysis for validation cohorts (cohort 1 and 2; CM n=12; Ctrl n=9). Survival curves for the training cohort is also shown (red dashed lines, CM=7; black dashed lines, Ctrl n=7). The observed and simulated time to AML are not statistically different from each other (p >> 0.05).