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A cell-molecular based evolutionary model of tumor development driven by astochastic Moran birth-death process is developed, where each cell carriesmolecular information represented by a four-digit binary string, used todifferentiate cells into 16 molecular types. The binary string value determinescell fitness, with lower fit cells (e.g. 0000) defined as healthy phenotypes,and higher fit cells (e.g. 1111) defined as malignant phenotypes. At each stepof the birth-death process, the two phenotypic sub-populations compete in aprisoner's dilemma evolutionary game with healthy cells (cooperators) competingwith cancer cells (defectors). Fitness and birth-death rates are defined viathe prisoner's dilemma payoff matrix. Cells are able undergo two types ofstochastic point mutations passed to the daughter cell's binary string duringbirth: passenger mutations (conferring no fitness advantage) and drivermutations (increasing cell fitness). Dynamic phylogenetic trees show clonalexpansions of cancer cell sub-populations from an initial malignant cell. Thetumor growth equation states that the growth rate is proportional to thelogarithm of cellular heterogeneity, here measured using the Shannon entropy ofthe distribution of binary sequences in the tumor cell population. Nonconstanttumor growth rates, (exponential growth during sub-clinical range of the tumorand subsequent slowed growth during tumor saturation) are associated with aGompertzian growth curve, an emergent feature of the model explained here usingsimple statistical mechanics principles related to the degree of functionalcoupling of the cell states. Dosing strategies at early stage development,mid-stage (clinical stage), and late stage development of the tumor arecompared, showing therapy is most effective during the sub-clinical stage,before the cancer subpopulation is selected for growth.

An evolutionary model of tumor cell kinetics and the emergence of molecular heterogeneity driving Gompertzian growth