Transfer of Drug Resistance Characteristics Between Cancer Cell Subpopulations: A Study Using Simple Mathematical Models

Abstract

Resistance to chemotherapy is a major cause of cancer treatment failure. The processes of resistance induction and selection of resistant cells (due to the over-expression of the membrane transporter P-glycoprotein, P-gp) are well documented in the literature, and a number of mathematical models have been developed. However, another process of transfer of resistant characteristics is less well known and has received little attention in the mathematical literature. In this paper, we discuss the potential of simple mathematical models to describe the process of resistance transfer, specifically P-gp transfer, in mixtures of resistant and sensitive tumor cell populations. Two different biological hypotheses for P-gp transfer are explored: (1) exchange through physical cell-cell connections and (2) through microvessicles released to the culture medium. Two models are developed which fit very well the observed population growth dynamics. The potential and limitations of these simple "global" models to describe the aforementioned biological processes involved are discussed on the basis of the results obtained.

Applied mathematics and nonlinear sciences in the war on cancer

“…However, it has only recently become known that resistant cells secrete factors that makes sensitive cells refractory to the treatment. This has been later incorporated into mathematical models [47,48]. In addition, new interaction phenomena have been observed between both cell subpopulations that cannot be explained using any of the previously existing models [49].…”

Interplay of Darwinian Selection, Lamarckian Induction and Microvesicle Transfer on Drug Resistance in Cancer

“…Most of the approaches presented in those works can be classified into mechanism-based models and data-driven prediction techniques. Mechanism-based models range from those consisting of sets of ordinary differential equations accounting for the cellular population dynamics along with the effects of chemotherapeutic agents 41,42 ; partial differential equations that consider the spatial heterogeneity of the tumor cell density and the intratumoral drug concentration 15,43–45 ; stochastic models which take into account the action of the tumor microenvironment in the adaptation of cell subpopulations and where the initial conditions do not completely determine the future configuration of the system 46–49 ; agent-based methods which can incorporate drug resistance at multiple levels 50,51 ; and molecular dynamics simulation which can capture the conformational changes and the fluctuation at the atomic scale of both the administered drugs and their targets 52,53 . Following a different rationale, data-driven prediction methods for identifying biomarkers involved in drug resistance have recently attracted considerable interest and comprise omics data-based node biomarker screening, static and dynamic network approaches for identifying edge and module biomarkers 54–57 .…”

Optimal control problems for differential equations applied to tumor growth: state of the art

“…There are many mathematical models that deal with the different aspects of the growth of a tumor. They use ordinary differential equations [2,6,13,54], partial differential equations [1,3,34], stochastic processes [38], game theory [52], etc.…”