Molecular Pharmacology, Vol 9, 320-329, Copyright © 1973 by the American Society for Pharmacology and Experimental Therapeutics

Mathematical Simulation of the Interaction of Drugs That Inhibit Deoxyribonucleic Acid Biosynthesis

¹ Roswell Park Memorial Institute, New York State Department of Health, Buffalo, New York 14203
² Wellcome Research Laboratories, Research Triangle Park North (Carolina) 27709

A mathematical model was devised which could satisfactorily simulate the effects of combinations of inhibitors of DNA biosynthesis on the growth of L1210 leukemic cells in vitro. The model represents an open steady-state system regulated by a network of feedback controls. The behavior of the model was surprisingly insensitive to variations in the values of its 15 parameters, implying that it was the basic shape of the network which was responsible for the simulation. The presence of any one (or two) of the inhibitors caused pronounced changes in the concentrations of all the intermediate compounds in the resulting new steady state. Thus, in such a closely regulated system, the effects of a perturbation in one region will not be localized, but will be manifested throughout the entire system. Furthermore, it was predicted that such feedback regulation could lead to perplexing experimental results; for instance, extensive inhibition of a pathway within such a network could result in an increased, decreased, or even unchanged pool size of the product of this pathway. It was also observed that the inhibitor-induced process of passing from the original steady state to a new steady state was complex. Concentrations of intermediates need not change smoothly from one state to the other, but may overshoot, transiently move in a direction opposite to the final concentration, or undergo a damped oscillation. Attempts to deduce the effect of an inhibitor on such a system by consideration of the initial effects therefore may be misleading. Finally, experiments using the model indicated that the intensity of interaction of drugs in combination, whether antagonistic or synergistic, increased as the degree of inhibition of the system increased. Thus a combination which was mildly synergistic when studied at 50% inhibition became intensely so at 90% inhibition. This unexpected prediction has significance in the evaluation of studies in combination chemotherapy.

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