Probing the rate of Ca2+-dependent neuroblastoma growth and drugs’ response using dynamic mathematical models

Intracellular Ca[Formula: see text] ([Ca[Formula: see text]]i) serves as a critical regulator of various cellular processes and plays a vital role in cellular growth, development, differentiation and apoptosis. Several studies have reported dysregulated [Ca[Formula: see text]]i expression under pathophysiological conditions, suggesting that modulating [Ca[Formula: see text]]i could be a potential therapy for regulating cellular responses. In this study, we extended the work of Wacquier et al. (2016) and predicted that [Ca[Formula: see text]]i oscillatory patterns in tumorigenic cells exhibit higher Ca[Formula: see text] amplitude compared to normal cells. The predicted Ca[Formula: see text] oscillatory pattern is then incorporated into the cell growth model of [16] to observe its effect in both normal and SK-N-SH cells. A combined deterministic model, integrating the outputs of Ca[Formula: see text] signaling and cellular growth model, is extended to a 15-day duration to observe the long-term effects of Ca[Formula: see text] oscillation on growth patterns. The figures of model simulations revealed the uncontrolled growth of SK-N-SH cells. The model is further modified to predict an optimal treatment protocol to consider the impact of different therapeutic drugs and Ca[Formula: see text] modulators. The model results demonstrated that combined chemotherapy treatments lead to improved outcomes compared to single chemotherapy. Similarly, the graphical representation of the growth patterns shows the sinusoidal behavior of the curves, indicating that the proposed chemotherapy does not completely eradicate tumorigenic cells but helps maintain the cell count at a reduced level. Our results also highlight the significant influence of Ca[Formula: see text] oscillation on cell count when considering chemotherapeutic treatments.