*3.2. Binding Constant and Number of Binding Sites*

The binding constants and binding stoichiometry are were determined using a double logarithmic regression plot derived from the equation: log (*F*0−*F*) *<sup>F</sup>* = log *K<sup>b</sup>* + *n* log[*Q*].

*K<sup>b</sup>* and *n* represent the binding constant and binding stoichiometry in the above equation. The representative plot for the binding constants at the three studied temperatures of the binary system BSA-ERL is given in Figure 1e. The binding constant was obtained from the intercept of the double log plot, and the binding stoichiometry from its slope is presented in Table 2. Thus, the binding stoichiometry value of ≈1 suggests a single class of binding site was involved in the BSA-ERL interaction. The binding constants for the BSA-ERL system were of the order of 10<sup>4</sup> M−<sup>1</sup> suggesting a moderate binding [45]. The binding constant at room temperature determined for the BSA-QUR system was of the order of <sup>≈</sup>(>10<sup>6</sup> ). The ternary system (BSA-QUR)-ERL had binding constants of the order of <sup>≈</sup>10<sup>2</sup> (Table 2).

The binding constant for the BSA-ERL system was studied at various temperatures since the binding constants are temperature-dependent. Therefore, the thermodynamic processes involved in the BSA-ERL interaction were also investigated using the van't Hoff equation and plot.

$$
\ln K\_b = -\frac{\Delta H^\circ}{RT} + \frac{\Delta S^\circ}{R}
$$

$$
\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ
$$

In the equation above, ∆*H*◦ is enthalpy change, ∆*S* ◦ is entropy change and ∆*G* ◦ is Gibbs free energy, *R* is the universal gas constant, and *T* is the temperature in kelvins (K).

The thermodynamic parameters ∆*H*◦ , ∆*S* ◦ and ∆*G* ◦ , were calculated from the van't Hoff plot for ln(*K<sup>b</sup>* ) vs. 1/*T* and are given in Figure 1f.

All the three parameters, enthalpy change, entropy change, and Gibbs free energy, given in Table 2, attained negative values. A negative Gibbs free energy indicates a spontaneous interaction. Furthermore, the BSA-ERL interaction is suggested by van der Waals force and hydrogen bonds based on negative enthalpy and entropy. Since the enthalpy was <sup>−</sup>260 kJ·mol−<sup>1</sup> whereas entropy was <sup>−</sup>0.79 kJ·mol−<sup>1</sup> , the BSA and ERL interaction indicate the interaction being enthalpy-driven, and the interaction had an unfavorable entropy.
