## 3 Results and Discussions
### Kinetic Analysis  
To assess the impact on enzyme activity, the kinetic constants _Km_ and _kcat_ of the WT and mutants were measured. Luciferase activity was detected at 25 \({}^{\circ}\)C with gradually increasing substrate concentrations. The kinetic constants were determined using the Lineweaver-Burk graphical method (Table 2). Although the thermal stability of _Mut3_ improved, its affinity for the substrate luciferin decreased significantly (high _Km_). _Mut3_ (A485C-T518C) is located near the C-terminus, close to the conserved domain Ser-Lys-Leu (SKL), which is involved in the release of the product AMP during enzyme catalysis. The oxidation of luciferin is facilitated by the activating effect of AMP, which is crucial for the formation of the dioxetanone ring. The introduction of disulfide bonds increased the rigidity of this region, hindering the release of AMP and becoming the rate-limiting step in the enzyme-catalyzed reaction. Consequently, _Mut3_ exhibited lower affinity compared to the WT.  
The thermal stability of _Mut2_ was significantly enhanced; its substrate affinity increased by 1.97 times. Generally, an increase in the number of hydrogen bonds between side chains of residues improves intermolecular interaction forces [28]. The enzyme-substrate interactions of _Mut2_ were investigated. As the substrate luciferin approaches the active site, the region gradually closes to encapsulate the substrate. The WT luciferase had two residues, T347 and D441, which interacted with the substrate through two hydrogen bonds (Figure 6a). For _Mut2_, the introduction of artificial disulfide bonds increased the intermolecular force in this region. In this study, molecular docking analysis revealed that D-fluorescein can form additional hydrogen bonds with the surrounding amino acid residues A323, T347, and K534, thereby establishing strong interactions with the substrate within the catalytic pocket region (Figure 6b). These interactions likely contribute to enhanced substrate-binding stability. Furthermore, while the WT enzyme exhibited no  
\begin{table}
\begin{tabular}{c c c} \hline
**Luciferase** & _Km_ (\(\mathbf{\mu}\)**M**) & _Kcat_ (\(\mathbf{s^{-1}}\)) \\ \hline WT & 53.6 & 2.1 \\ \hline _Mut2_ & 27.2 & 4.2 \\ \hline _Mut3_ & 88.1 & 2.2 \\ \hline \end{tabular}
\end{table}
Table 2: Kinetic constants of WT and mutants’ enzyme.  
Figure 5: Thermal deactivation curves of WT luciferase and its mutants.  
\(\pi\)-alkyl interactions (Figure 6c), \(Mut2\) displayed \(\pi\)-alkyl interactions between D-fluorescein and residues D427 and R442. Additionally, a \(\pi\)-sulfur interaction was observed between D-fluorescein and residue H250 in \(Mut2\) (Figure 6d). The formation of these \(\pi\)-alkyl and \(\pi\)-sulfur interactions significantly strengthened the binding affinity of D-fluorescein to \(Mut2\), resulting in higher substrate affinity compared to the WT enzyme. The stability of a molecular docking conformation is inversely related to its binding energy; lower binding energy indicates a more stable conformation and a higher likelihood of interaction between the enzyme and substrate. In this study, the docking energies for WT, \(Mut2\) were \(-19.5\) kcal/mol and \(-23.4\) kcal/mol, respectively. The more negative docking energies of \(Mut2\) suggest stronger binding interactions with D-fluorescein compared to the WT enzyme. This finding may partly explain the decreased \(Km\) values observed for \(Mut2\) relative to the WT enzyme, indicating enhanced substrate affinity due to the optimized interactions within the catalytic pocket.