Effects of differential cell kill on the dynamic composition of heterogeneous tumors

Abstract

Three ecological models describing independent subpopulation growth, interactive competition for shared resources and endomitotic or inductive emergence of one population from the other are analyzed in an effort to describe the effects of environmental stress on the dynamic composition of artificial heterogeneous tumors (human colon adenocarcinoma cells) treated with Mitomycin C. A mathematical relationship for the dynamic composition of a heterogeneous tumor is derived for each model, and from these derived systems, isoclines for the composition trajectories are identified. Actual compositional dynamics of neoplasms perturbed from equilibrium by a therapeutic agent which displays differential cell kill are compared to similar dynamics of tumors which are mechanically displaced from equilibrium within the context of these theoretical structures. Each parameter in each model is identified with specific environmental stress effects, and the effects exerted upon the isoclines are identified. The biological mechanisms associated with theoretical stresses are discussed.