## 4 Discussion
The results presented here encourage the use of CaS nanostructures as a target cell cancer and metastasis therapy. The results presented in Figures 4 and 5 indicate that CaS nanostructures are capable of inhibiting the proliferation of cancer cells without affecting the survival and growth rate of normal cells and encourage further research in vivo. Many apoptotic chemical processes are dependent on Ca\({}^{2+}\) ion and H\({}_{2}\)S concentration [49; 50; 51; 52; 53]. We hypothesize that the release of calcium and sulfide ions from CaS is favored in the acidic environment found in cancer cells as opposed to the basic media in normal cells. This is further supported by thermodynamic considerations discussed below. The standard Gibbs free energies of formations \(\Delta G_{f}^{0}\), of H\({}_{2}\)S\({}_{(aq)}\), \(S^{-2}\)\({}_{(aq)}\), Ca\({}^{2+}\)\({}_{(aq)}\), and H\({}^{+}\)\({}_{(aq)}\) and CaS\({}_{(s)}\), are summarized in Table 4. Gibbs free energies of formation were obtained from the literature [52]. Using these values, we estimated that the dissolution of solid CaS\({}_{(s)}\) in water:  
\[\textbf{CaS}_{(s)}\rightarrow\textbf{Ca}^{2+}{}_{(aq)}+\textbf{S}^{-2}{}_{(aq)} \tag{3}\]  
is an endergonic reaction with a standard Gibbs free energy (\(\Delta G^{0}{}_{\rm{r}cm}\)) = 9.62 kJ/mol and is not a spontaneous process. The pH of normal and tumor cells depends on the tissue from where the sample is taken. The extracellular pH (pHe) of normal cells is slightly basic and ranges from 7.35 to about 7.8 [53]. The pKa of H\({}_{2}\)S and HS\({}^{-}\) is 7.04 and 11.96, respectively [52]. Thus, for pH values found in cancer cells, in the range of 6.2 to 7, we expect sulfide to exist predominantly as H\({}_{2}\)S, while for pH values between 7 and 11.96, we expect HS\({}^{-}\) to be the dominant sulfide-containing species. The reaction:  
\[\textbf{CaS}_{(s)}+\textbf{2H}^{+}{}_{(aq)}\rightarrow\textbf{Ca}^{2+}{}_{(aq )}+\textbf{H}_{2}\textbf{S}_{(g)} \tag{4}\]  
is exergonic with a \(\Delta G^{0}{}_{\rm{r}cm}\) of \(-\)109.7 kJ/mol and an equilibrium constant of the order of 10\({}^{19}\). In Equation (4), we have considered the H\({}_{2}\)S formed in the gas phase. The standard Gibbs free energy for the reaction is \(-\)103.58 kJ/mol with an equilibrium constant of the order of 10\({}^{18}\), if the H\({}_{2}\)S is formed in an aqueous solution. The sign and magnitude of \(\Delta G^{0}{}_{\rm{r}cm}\) for this reaction, either with H\({}_{2}\)S formed in the gas or aqueous phases, indicates that the formation of free calcium ions and hydrogen sulfide from CaS is a spontaneous process that releases a significant amount of energy in acidic media. Thus, the formation of Ca\({}^{2+}\) and H\({}_{2}\)S is thermodynamically favored in the acidic pH found in the extracellular fluid of cancer cells but is limited in the basic extracellular environment of benign cells. We propose that the difference in pH results in the selectivity of the CaS nanostructures to limit the growth and proliferation of breast cancer cells with little effect on the corresponding benign \begin{table}
\begin{tabular}{c c} \hline \hline
**Species** & \(\Delta G_{f}^{0}\) **(kJ/mol)** \\ \hline Ca\({}^{2+}\) & \(-\)553.6 \\ \hline S\({}^{2-}\) & 85.8 \\ \hline H\({}^{+}\) & 0 \\ \hline CaS & \(-\)477.4 \\ \hline H\({}_{2}\)S & \(-\)33.6 \\ \hline \multicolumn{2}{c}{**Thermodynamics in water (\(\Delta G_{f}\) (kJ/mol))**} \\ \hline CaS\({}_{(aq)}\rightarrow\) Ca\({}^{2+}{}_{(aq)}+S^{2-}{}_{(aq)}\) & 9.62 \\ \hline CaS\({}_{(s)}+\) 2H\({}^{+}\rightarrow\) Ca\({}^{2+}{}_{(aq)}+\)H\({}_{2}\)S\({}_{(g)}\) & \(-\)109.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The standard Gibbs free energy (\(\Delta G_{f}^{0}\)) of formation of probable species containing calcium and sulfide in an aqueous solution. cells. Calcium ion signaling in the cytosol can be grouped by their general mechanisms of movement: (1) Ca\({}^{+2}\) import into the cytosol (influx), (2) Ca\({}^{+2}\) export from the (sequestering), and (3) Ca\({}^{+2}\) buffering.