## 1 Introduction
Cell cycle interruption caused by CAP oxidizes histone mRNA and activates cell cycle checkpoints that halt the cells from undergoing further development [14]. The G1 phase in the cell cycle is the time in which cells physically grow and their organelles develop [19]. When this growth process is interrupted by CAP, cancer cells can no longer proliferate at an uncontrollable rate. \begin{table}
\begin{tabular}{c c c c} \hline
**Classification** & **Immunoprofile** & **Ki-67 Level** &
\begin{tabular}{c} **Example Cell Line** \\ **Used in This Study** \\ \end{tabular} \\ \hline Luminal A & ER\({}^{+}\), PR\({}^{+}\)/-, HER2\({}^{-}\) & Low & MCF-7 \\ \hline Luminal B & ER\({}^{+}\), PR\({}^{+}\)/-, HER2\({}^{+}\) & High & BT-474 \\ \hline HER2\({}^{+}\) & ER\({}^{-}\), PR\({}^{-}\), HER2\({}^{+}\) & High & SK-BR-3 \\ \hline Triple-negative & ER\({}^{-}\), PR\({}^{-}\), HER2\({}^{-}\) & Low & MDA-MB-231 \\ \hline \end{tabular}
\end{table} 
Table 1: Classification of Breast Cancer Cell Lines and Their Characteristics. Four different breast cancers and their categorization based on receptor type are listed. While studies show strong temporal correlations among CAP treatment, a decrease in cell proliferation, and an increase in cell death, several different theories of the CAP's mechanism of action exist due to the complex microprocesses involved in its ability to trigger cell cycle arrest and apoptosis. Our approach aims to bridge the gap in knowledge regarding these CAP-induced outcomes. Although the literature has implied correlations among cell signaling intermediates, cell proliferation, and cell death, the three have not been combined in a comprehensive _causal_ model thus far. A causal model is one that examines the relationships between potential causes and potential effects. Granger causality is a way to investigate causality between two variables in a time series, a sequence of data points that occurs in successive order over a period of time [20]. Granger causality tests whether a variable, the potential \"cause\", is helpful for forecasting, or predicting, the behavior of another variable, the potential \"effect\". By using empirical data sets to find patterns of correlation, the formulated vector autoregressive (VAR) model assumes the data-generating processes in any time series are independent variables. In a VAR model, each variable is regressed on all variables, including itself, at previous time points. Regression is a statistical method that attempts to determine the strength and character of the relationship between variables, revealing the temporal dynamics of a system of related parameters across time. A VAR model itself is made up of a system of equations that represents the relationships between the variables. The data sets are analyzed to see if they are correlated, verifying the usefulness of one variable to forecast another [20]. Therefore, according to Granger causality, if X \"Granger-causes\" Y, then past values of X should contain information that helps predict Y above and beyond the information contained in past values of Y alone [21]. In this study, Granger modeling was used to compare the individual effects of intracellular ROS, caspase activity (CA), Ki-67 expression, and G1 phase activity on cell proliferation and cell death after treatment with Canady Helios Cold PlasmaTM (CHCP). CHCP was developed at the Jerome Candy Research Institute for Advanced Biological and Technological Sciences (JCRI-ABTS) (U.S. Patent No. 9,999,462 B2 June 2018 [22]), and previous studies have demonstrated its anticancer effect on a variety of solid tumor cell lines including breast cancers [23,24]. The primary objective of this study is to identify causal versus correlational links of intracellular oxidative stress, CA, Ki-67 expression, and cell cycle to the death of breast cancer cells. The rationale for developing a computational causal model is that it can help answer questions on what variables need to be prioritized for future in vivo mammalian studies.