## 3 Results and Discussion
### Molecular Game-Theoretical System for Sensing Hg\({}^{2+}\)  
According to the demonstration process of above-mentioned molecular game-theoretical system, both CoOOH and Hg\({}^{2+}\) competitively interacted with T33 to form the T-Hg\({}^{2+}\)-T-CoOOH ternary complex, resulting in the largest signal change (payoff from 2R = 1.0 to 2P = 0.3) of the whole system, suggesting that the T33-CoOOH complex sensitively senses Hg\({}^{2+}\). Under optimum conditions (100 nM T33, 4.69 \(\mathrm{\SIUnitSymbolMicro\text{g}}\)/mL CoOOH, 5 mM Tris-HCl, pH 7.4, Figures S5 and S6), the T33-CoOOH complex was used for detection of Hg\({}^{2+}\). As shown in Figure 5A, the fluorescence intensity gradually decreased with increasing concentration of Hg\({}^{2+}\) from 0 to 2000 nM. Similarly, the fluorescence quenching ratio (F0 \(-\) F)/F0 gradually increased with increasing concentration of Hg\({}^{2+}\) from 0 to 2000 nM (Figure 5B). Figure 5C shows the good linear relationship between the value of (F0 \(-\) F)/F0 and the Hg\({}^{2+}\) concentration in the range of 20 to 600 nM. The calibration equation was y = 0.00036x + 0.04076 with a correlation coefficient (\(R^{2}\)) of 0.995. The limit of detection was 7.94 nM according to the 3\(\sigma\) rule, which is below the maximum level (10 nM) of Hg\({}^{2+}\) permitted by the U.S. Environmental Protection Agency for drinking water. Compared with other previously reported Hg\({}^{2+}\) assays, our proposed approach has a much lower detection limit (Table S1). The result indicates that the molecular game-theoretical system based on T33 and CoOOH nanosheets can sensitively detect Hg\({}^{2+}\). Figure 5: (**A**) Fluorescence emission spectra of T33–CoOOH complex (100 nM4.69 \(\mathrm{\SIUnitSymbolMicro\text{g}}\)/mL) upon addition of various concentrations of Hg\({}^{2+}\) (from top to bottom: 0, 20, 80, 139, 198, 259, 320, 381, 441, 500, 600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, and 2000 nM); (**B**) The dependence of the fluorescence intensity changes (F0 \(-\) F)/F0 at 520 nm on the concentration of Hg\({}^{2+}\); (**C**) The linear relationship between (F0 \(-\) F)/F0 and the Hg\({}^{2+}\) concentrations in the range from 20 to 600 nM; (**D**) The selectivity of the T33–CoOOH complex (100 nM4.69 \(\mathrm{\SIUnitSymbolMicro\text{g}}\)/mL) for Hg\({}^{2+}\) assay (Hg\({}^{2+}\): 600 nM, other metal ions: 1.2 \(\mathrm{\SIUnitSymbolMicro\text{m}}\)). Buffer: 5 mM Tris-HCl, pH 7.4. To further evaluate the specificity of the T33-CoOOH complex under optimum conditions, we first investigated the responses of our method to Hg\({}^{2+}\) (600 nM) against other metal ions (Ag\({}^{+}\), Pb\({}^{2+}\), Cu\({}^{2+}\), Cd\({}^{2+}\), Mg\({}^{2+}\), Co\({}^{2+}\), Ba\({}^{2+}\), Be\({}^{2+}\), K\({}^{+}\), Ni\({}^{3+}\), and Ca\({}^{2+}\); each 1.2 \(\upmu\)M). As shown in the Figure 5D, the T33-CoOOH complex was highly selective for sensing Hg\({}^{2+}\), although the concentration of other interfering metal ions was much higher (two-fold) than that of Hg\({}^{2+}\). Zn\({}^{2+}\) exhibited a certain degree of interference. Zn\({}^{2+}\) may incorporate into CoOOH for formation of Zn-doped CoOOH [44; 45] and Zn-doped CoOOH may bind to thymines, probably by interacting with the Zn\({}^{2+}\) metal center with the deprotonated N3 imide of thymine and stacking the aromatic pendent group on the thymine nucleobase [46; 47]. A competition experiment in the presence of potentially competitive metal ions was also performed to further confirm the selectivity of this sensing system toward Hg\({}^{2+}\). As shown in Figure S7A, Hg\({}^{2+}\) can efficiently quench the fluorescence of this sensing system even if the other metal ions slightly affected the fluorescence intensity. As shown in Figure S7B, common anions did not remarkably affect the fluorescence change.