Mathematical Models of Cancer Evolution and Cure

You cannot cure what you do not understand. So how can mathematical modeling address this pressing issue? The advances in therapeutic success in multiple myeloma over the last decades have hinged on an an army of researchers identifying a critical genetic, epigenetic and biochemical signaling factors within of MM cells as well as the tumor microenvironment (TME). Unfortunately, despite these large scale efforts we do not yet offer our patients curative intent therapy. The inability to provide curative therapy, especially in the setting of HRMM, is characterized by evolving resistance to lines of sequential therapy as a result of alternating clonal dynamics following the failure of initial therapy to eradicate minimal residual disease (MRD). Recent results underline the importance of tumor heterogeneity, in the form of pre-existing genotypically (and phenotypically) distinct sub-populations that translate to drug-resistant phenotypes leading to treatment failure. This phenomenon of “clonal tides”, has been well characterized using contemporary molecular techniques demonstrating that clonal evolution progresses by different evolutionary patterns across patients. Thus, resistance to therapy is a consequence of Darwinian dynamics- influenced by tumor heterogeneity, genomic instability, the TME (ecosystem), and selective pressures induced by therapy. Such evolutionary principles can be analyzed and exploited by mathematical models to personalize therapeutic options for patients with MM. Currently available clinical decision support tools and physician acumen are not able to account for the shear amount of information available. Mathematical models, however, provide a critical mechanism(s) to account of the large number of aspects to help predict and manage MM- accounting for what we do not know. Models can be designed with the specific intent of characterizing intra-tumoral heterogeneity, changing ecosystems, and clinical parameters over time to create patient-specific clinical predictions much like hurricane prediction models. This can only be achieved by creating mathematical models parameterized by longitudinal data of a number of parameters. The novel application of mathematical models based on Darwinian dynamics can be imputed with data to 1) predict progression events (risk of progression to from smoldering to active MM), 2) relapse, and 3) predictions of clinical response of MM patients for the optimizing therapeutics for cure or optimal control of MM; thus, providing invaluable clinical decision support tools. Disclosures: Shain: Celgene: Consultancy , Speakers Bureau ; Amgen/Onyx: Consultancy , Speakers Bureau ; Takeda: Consultancy , Speakers Bureau ; Signal Genetics: Consultancy , Research Funding.

Cell-cell interactions and evolution using evolutionary game theory

Cancers arise from genetic abberations but also consistently display high levels of intra-tumor heterogeneity and evolve according to Darwinian dynamics. This makes evolutionary game theory an ideal tool in which to mathematically capture these cell-cell interactions and in which to investigate how they impact evolutionary dynamics. In this chapter we present some examples of how evolutionary game theory can elucidate cancer evolution.