Phase transitions in tumor growth VII: The effect of periodic glucose pulses and privations in a cancer model

Tumor glycolysis is a self-organized nonlinear mechanism that can exhibit oscillations under certain conditions. Experimental evidence suggests that glycolytic oscillations may give certain advantages to cancer, including resistance to therapies. A previously developed oscillating glycolysis model was modified with the objective of theoretically evaluating the effect of pulses and periodic glucose deprivations in a frequency range that included values close to the autonomous frequency. The dynamics of the model before the perturbation were characterized. Then the model was perturbed with periodic pulses and deprivations of glucose. The dynamics obtained were characterized and compared with the model before the perturbation. The methods for the characterization of the dynamics were: stability analysis of the steady state, stroboscopic analysis and Lempel-Ziv index; while the cellular energy charge of the simulations was evaluated by the normalized ATP/ADP ratio. The results obtained indicate that periodic glucose pulses can lead to an increase in the energy charge. Surprisingly, sustained increases in glucose influx causes a decrease in the complexity of glycolytic oscillations, but cause increase in the cellular energy charge. On the other hand, periodically depriving the tumor microenvironment of glucose at high perturbation frequencies, regardless of the amplitude of perturbation, prevent the increase in the complexity of glycolytic oscillations and cause a decrease in the cellular energy charge of tumor cells. This strategy can increase the efficacy of antitumor therapies.