## 3 Results and Discussion
### Thermodynamics Parameters and Nature of the Binding Forces  
Entropy (\(\Delta S^{\circ}\)) and enthalpy (\(\Delta H^{\circ}\)), as the principal thermodynamic parameters involved in the interaction of compound **3** and BSA, are of significant importance as binding force determinants. Their importance arises from the fact that in such an interaction, the complex formation and the binding constant are highly temperature dependent. In principal, ligand-macromolecule binding can be a result of the involvement of one or more forces, including those that are hydrophobic, van der Waals forces, hydrogen bonding, and electrostatic forces. Former reports have recognized the various forces in protein/ligand binding, in line with the determined thermodynamic parameters [47; 48; 49]. Such measurements reveal three potential pathways through which a hydrophobic interaction is claimed if +ve entropy (\(\Delta S^{\circ}\)) and enthalpy (\(\Delta H^{\circ}\)) values, and hydrogen bonding and/or van der Waals forces could be the driving forces when \(-\)ve \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are observed. Additionally, electrostatic forces are deemed responsible when negative enthalpy (\(\Delta H^{\circ}\)) and positive entropy (\(\Delta S^{\circ}\)) are present. In the present study, the thermodynamic parameters of the compound **3**-BSA system were computed using Equations (6) and (7):  
\[\ln K=\frac{-\Delta H^{\circ}}{RT}+\frac{\Delta S^{\circ}}{R} \tag{6}\]  
\[\Delta G^{\circ}=\Delta H^{\circ}-T\cdot\Delta S^{\circ} \tag{7}\]  
where \(K\) is the association constant and \(\Delta G^{\circ}\) represents the free energy change. The gas constant and temperature in Kelvins are symbolized by \(R\) and \(T\), respectively. Accordingly, a plot of \(\ln K\) values against the reciprocal of the temperature (Figure 6) shall be used to compute the values of \(\Delta G^{\circ}\), \(\Delta S^{\circ}\), and \(\Delta H^{\circ}\).  
Based on the previously mentioned rules for the main binding forces, the results summarized in Table 2 revealed that compound **3**-BSA binding cannot be accounted for as a single intermolecular force model. Such values (Table 2) indicate a spontaneous interaction between compound **3** and BSA taking place via hydrogen bonding and electrostatic interactions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Temperature** & \(\Delta G^{\circ}\) & \(\Delta H^{\circ}\) & \(\Delta S^{\circ}\) & \(K\times 10^{\circ}\) & \(n^{\star}\) & \(r^{2}\) \\
**(T) (K)** & **(kJ-mol\({}^{-1}\))** & **(kJ-mol\({}^{-1}\))** & **(J-mol\({}^{-1}\)-K\({}^{-1}\))** & **(L-mol\({}^{-1}\))** & \\ \hline
288 & \(-32.98\pm 2.5\) & & & 9.65 \(\pm\) 0.95 & 0.947 \(\pm\) 0.018 & 0.9955 \\
298 & \(-34.04\pm 2.2\) & \(-0.72\pm 0.71\) & 105.09 \(\pm\) 5.32 & 9.32 \(\pm\) 1.20 & 0.946 \(\pm\) 0.019 & 0.9952 \\
309 & \(-35.19\pm 2.3\) & & & 8.92 \(\pm\) 0.97 & 0.945 \(\pm\) 0.018 & 0.9956 \\ \hline \end{tabular} \({}^{\star}\) All values are the average of three determinations.  
\end{table}
Table 2: Summary of the thermodynamic parameters for the compound **3**-BSA interaction along with binding parameters \(K\) and \(n\).  
Figure 6: An exothermic Van’t Hoff plot for compound **3**-BSA binding.