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 difference 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 difference in the initial values of the metabolites has little effect on the simulated results.
Modeling studies of heterogeneities in glycolytic oscillations in HeLa cervical cancer cells
Note: This paper is part of the Focus Issue, “Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday.”
Takashi Amemiya, Kenichi Shibata, Yichen Du, Satoshi Nakata, Tomohiko Yamaguchi; Modeling studies of heterogeneities in glycolytic oscillations in HeLa cervical cancer cells. Chaos 1 March 2019; 29 (3): 033132. https://doi.org/10.1063/1.5087216
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