Mathematical Modeling of Heterogeneity and Drug Response in Lung Cancer

Abstract

Technological advances have led to increasingly powerful and precise quantification of biological systems. These advances create a need for robust mathematical and computational approaches that are able to integrate complex data within rigorous theoretical frameworks. Within cancer, transcriptional profiling and drug efficacy screens have uncovered the significance of tumoral heterogeneity as a cause of relapse and drug resistance in patients. Furthermore, evidence suggests that distinct transcriptional programs can underlie cancer heterogeneity, and connecting drivers of transcriptional heterogeneity to drug response promises to lead to improved therapies. We develop computational approaches to identify master regulators of cancer heterogeneity, model drug response of heterogeneous populations, and quantify drug combination synergies. First, we develop a workflow to reconstruct master regulatory networks underlying cancer heterogeneity. Applied to small-cell lung cancer (SCLC), we find a network that stabilizes attractors for neuroendocrine and non-neuroendocrine SCLC subtypes. This revealed additional variant subtypes that become enriched in SCLC following drug-treatment. Investigating this, we identify and characterize a novel drug resistant neuroendocrine variant subtype. Simulation of an SCLC-specific regulatory network identifies ELF3 and NR0B1 as putative master regulators of this new variant subtype. Next we derive model of proliferation of heterogeneous cell populations, and show the variance of the populations drive the rate of rebound. Applied to non-small-cell lung cancer (NSCLC), we show quantification of this variance enables accurate prediction of time to relapse. Finally, we show that while distinct synergies of efficacy and potency arise from drug combinations, current methods for evaluating synergy fail to account for these different synergy types. We develop Multidimensional Synergy of Combinations (MuSyC) to decouple synergistic potency and efficacy. We show modern synergy metrics emerge as special cases of MuSyC, and highlight cases where these metrics cannot be applied or lead to biased results. We demonstrate the usefulness of MuSyC in mutant-EGFR NSCLC and mutant-BRAF melanoma. Taken together, these results represent progress toward rational design of interventions and drug combinations targeting heterogeneity and the emergence of resistance in cancer.