Contrasting the impact of cytotoxic and cytostatic drug therapies on tumour progression

Abstract

A tumour grows when the total division (birth) rate of its cells exceeds their total mortality (death) rate. The capability for uncontrolled growth within the host tissue is acquired via the accumulation of driver mutations which enable the tumour to progress through various hallmarks of cancer. We present a mathematical model of the penultimate stage in such a progression. We assume the tumour has reached the limit of its present growth potential due to cell competition that either results in total birth rate reduction or death rate increase. The tumour can then progress to the final stage by either seeding a metastasis or acquiring a driver mutation. We influence the ensuing evolutionary dynamics by cytotoxic (increasing death rate) or cytostatic (decreasing birth rate) therapy while keeping the effect of the therapy on net growth reduction constant. Comparing the treatments head to head we derive conditions for choosing optimal therapy. We quantify how the choice and the related gain of optimal therapy depends on driver mutation, metastasis, intrinsic cell birth and death rates, and the details of cell competition. We show that detailed understanding of the cell population dynamics could be exploited in choosing the right mode of treatment with substantial therapy gains.

Rapamycin Plus Doxycycline Combination Affects Growth Arrest and Selective Autophagy-Dependent Cell Death in Breast Cancer Cells

“…It has been described in many studies that mTOR inhibitors influence cell proliferation and drug sensitivity which could vary in a cell type-dependent manner. Tumour growth could be reloaded by the surviving cells since the inhibitory effect of the agents is rather cytostatic than cytotoxic [ 15 , 36 ]. In addition, there is growing evidence that combining mTOR inhibitors with chemotherapeutic agents (e.g., cisplatin, etc.)…”

“…Tumour growth, tumour mass reductions and tumour-free survival are the main goals during cancer treatments, which could have both cytotoxic and cytostatic effects [ 15 ]. After many drug administrations, which inhibit tumour cell proliferation, the surviving cells undergo autophagy as a transient bioenergetic adaptation mechanism.…”

Drug-induced resistance evolution necessitates less aggressive treatment

“…The function d i ( u, N ) models the pharmacodynamics of the drug dictating how the obtained concentration of the drug, which is represented by the control variable u , translates into cell death. Some drugs can also be cytostatic in nature, meaning that they decrease the birth rate instead of increasing the death rate, which can have important consequences [37] but nevertheless leads to the same mean-field growth as above. Finally, the pharmacodynamical effect may additionally depend on the total population size N .…”

Drug-induced resistance evolution necessitates less aggressive treatment

“…The function d i (u, N) models the pharmacodynamics of the drug dictating how the obtained concentration of the drug, which is represented by the control variable u, translates into cell death. Some drugs can also be cytostatic in nature, meaning that they decrease the birth rate instead of increasing the death rate, which can have important consequences [54] but nevertheless leads to the same mean-field growth as above. Finally, the pharmacodynamical effect may additionally depend on the total population size N. By definition, we concentrate on cases where d S (u, N) � d R (u, N) � 0 meaning that resistant cells have a selective advantage during treatment.…”