Modeling studies of heterogeneities in glycolytic oscillations in HeLa cervical cancer cells

Abstract

Previous experiments demonstrated that a population of HeLa cells starved of glucose or both glucose and serum exhibited a strong heterogeneity in the glycolytic oscillations in terms of the number of oscillatory cells, periods of oscillations, and duration of oscillations. Here, we report numerical simulations of this heterogeneous oscillatory behavior in HeLa cells by using a newly developed mathematical model. It is simple enough that we can apply a mathematical analysis, but capture the core of the glycolytic pathway and the activity of the glucose transporter (GLUT). Lognormal distributions of the values of the four rate constants in the model were obtained from the experimental distributions in the periods of oscillations. Thus, the heterogeneity in the periods of oscillations can be attributed to the di erence in the rate constants of the enzymatic reactions. The activity of GLUT is found to determine whether the HeLa cells were oscillatory or non-oscillatory under the same experimental conditions. Simulation with the log-normal distribution of the maximum uptake velocity of glucose and the four randomized rate constants based on the log-normal distributions successfully reproduced the time-dependent number of oscillatory cells (oscillatory ratios) under the two starving conditions. The di erence in the initial values of the metabolites has little e ect on the simulated results.

Oscillations and Dynamic Symbiosis in Cellular Metabolism in Cancer

“…On the other hand, their amplitudes of NADH fluorescence were nearly the same among these cells. These oscillations directly reflect enzymatic activities in the glycolytic pathway, thus can be a useful index for evaluating the Warburg effect in cancer cells ( 49 , 50 ). So far, glycolytic oscillations have not been reported in cancer patients or in healthy people, and thus it is challenging to observe their oscillations in vivo and to characterize them across human cancer types.…”

Modeling Cell Energy Metabolism as Weighted Networks of Non-autonomous Oscillators

“…In Amemiya et al (2019) constructed a model of cellular glycolysis to explain the glycolytic oscillations they had observed in HeLa cells. This model adopted an approach more similar to the mainstream discussed in the previous section.…”

“…The Amemiya et al (2019) model constructs glycolysis as two main processes: the phosphofructokinase 1 (PFK) reaction and the pyruvate kinase (PK) reaction. The former is modeled as the first step, converting glucose and ATP into intermediaries, while the second is the last reaction, converting these intermediaries into ATP and pools of NADH and other products.…”

“…This parameter can be compared to the time series of NADH fluorescence from a single cell in the Amemiya et al (2017) experiment, as NADH production in the cellular metabolic system is maximized when glycolysis and OXPHOS are able to act coherently. We provide this comparison in Figure 6, and this can be further compared to an equivalent output of the model in Figure 2 of Amemiya et al (2019). The Amemiya et al (2019) model considers just glycolysis, and is built on 7 autonomous differential equations tracking the change in quantities of a range of metabolites, relying FIGURE 5 | Surrogate tested coherence between groups of cells examined in Amemiya et al (2017), calculated with the coherence algorithm presented in Sheppard et al (2016).…”

“…We provide this comparison in Figure 6, and this can be further compared to an equivalent output of the model in Figure 2 of Amemiya et al (2019). The Amemiya et al (2019) model considers just glycolysis, and is built on 7 autonomous differential equations tracking the change in quantities of a range of metabolites, relying FIGURE 5 | Surrogate tested coherence between groups of cells examined in Amemiya et al (2017), calculated with the coherence algorithm presented in Sheppard et al (2016). Red coloring indicates groups of cells far from one another, 900-1, 200µm distance between their average positions, and blue close to one another, 300-400µm distance between their average positions.…”