Abrupt transitions to tumor extinction: A quasispecies phenotypic model

Abstract

BackgroundThe dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i.e., proto-oncogenes and tumor suppressor genes), in genes responsible for genomic stability, and in house-keeping genes. Such mutations or loss of genes result into different phenotypes with increased proliferation rates and/or increased genomic instabilities. Also, lethal phenotypes with mutations or loss of house-keeping genes are present in our model.\n\nResultsDespite bifurcations in the classical deterministic quasispecies model are typically given by smooth, continuous shifts (i.e., transcritical bifurcations), we here identify an novel type of abrupt transition causing tumor extinction. Such a bifurcation, named as trans-heteroclinic, is characterized by the exchange of stability between two distant fixed points (that do not collide) involving, respectively, tumor persistence and tumor clearance. The increase of mutation and/or the decrease of the replication rate of tumor cells involves this catastrophic shift of tumor cell populations. The transient times near bifurcation thresholds are also characterized, showing a power law dependence of exponent -1 of the transients as mutation is changed near the bifurcation value.\n\nConclusionsAn abrupt transition involving tumor clearance has been identified with a phenotypic quasispecies cancer model. This result is discussed in the context of targeted cancer therapy as a possible therapeutic strategy to force a catastrophic shift by delivering mutagenic and cytotoxic drugs inside tumor cells. Our model also reveals a novel mechanism causing a discontinuous transition given by the stability exchange of two distant fixed points, which we name as a trans-heteroclinic bifurcation.