## 3 Results
### Identification and Quantification of Residual Hydrophobic Mismatch
Both Q210A and V269N had significantly increased ratios (Q210A:0.37 \(\pm\) 0.01; V269N: 0.33 \(\pm\) 0.01; Vm = \(-\)100 mV, pH 7.5) compared to (WT: 0.29 \(\pm\) 0.01), correlating to less inactivation under continuous illumination. The Q210N mutation had no effect on I\({}_{\text{ss}}\)/I\({}_{\text{p}}\) ratios. Apparent rate constants for decay and off kinetics were calculated. Decay kinetics were calculated by fitting ChR2 photocurrent traces from I\({}_{\text{p}}\) to I\({}_{\text{ss}}\) with a monoexponential or biexponential equation, respectively (Figure 5A). V269N had the largest effect on decay kinetics, resulting in accelerated inactivation. Q210A and the null mutant Q210N had no significant effect on decay kinetics (Figure 5B). A similar trend was observed for off kinetics, with V269N having accelerated rates and both Q210 variants not significantly altering kinetics (Figure 5C). Figure 4: Biophysical characterization of RHM-affecting mutants. (**A**) Representative steady-state current-voltage relationship of select mutants in Na\({}^{+}\) 6.0 solution. (**B**) Absolute reversal potentials determined at I\({}_{\text{p}}\) and I\({}_{\text{ss}}\) in Na\({}^{+}\) solutions at either pH 6.0 or 7.5. (**C**) Differences in E\({}_{\text{rev}}\) determined as noted. (**D**) Steady-state to peak current ratios, which are a measure of ChR2 inactivation. Values are reported as the average \(\pm\) SEM (n = 7–15). Statistically significant values are denoted with \({}^{*}\) (\(p<0.05\)). WT—blue; Q210A—red; Q210N—green; V269N—orange. Lastly, to determine whether RHM differences explain changes in the modulation of discrete transitions in the ChR2 photocycle, a four-state kinetic model was applied to fit experimental photocurrent traces. Theoretical fits were obtained by optimizing a set of nine parameters describing rates of transition and fundamental properties of the channel (Figure 6) (see Materials and Methods). The null Q210N mutant had the least effect on our parameters compared to WT (Table 3). Only the transition from O1 to O2 was slightly accelerated for this mutant. Both V269N and Q210A saw the largest change from the WT fits, having altered recovery and O2 -> O1 kinetics. Q210A also had a slower O2 to C2 rate while V269N had an accelerated O1 to O2 transition. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Construct** & \(\mathbf{I_{p}}^{7.5}\) & \(\mathbf{I_{ss}}^{7.5}\) & \(\mathbf{I_{p}}^{6.0}\) & \(\mathbf{I_{ss}}^{6.0}\) & \(\mathbf{I_{ss}}^{-1}\mathbf{p}^{7.5}\) & \(\mathbf{I_{ss}}^{-1}\mathbf{p}^{6.0}\) & \(\mathbf{I_{ss}}^{6.0}-\mathbf{I_{ss}}^{7.5}\) & \(\mathbf{I_{p}}^{6.0}-\mathbf{I_{p}}^{7.5}\) \\ \hline WT & \(4.30\pm 1.9\) & \(-9.84\pm 0.8\) & \(52.5\pm 2.7\) & \(24.6\pm 1.5\) & \(-14.1\pm 2.1\) & \(-27.8\pm 3.1\) & \(34.5\pm 1.7\) & \(48.2\pm 3.3\) \\ Q210A & \(9.39\pm 0.8\) & \(-6.20\pm 1.5\) & \(54.2\pm 2.6\) & \(20.1\pm 1.8\) & \(-15.6\pm 1.8\) & \(-34.1\pm 3.2\) & \(26.3\pm 2.4\) & \(44.8\pm 2.7\) \\ V269N & \(10.6\pm 0.4\) & \(-7.58\pm 0.7\) & \(75.0\pm 4.6\) * & \(13.2\pm 1.2\) * & \(-18.2\pm 0.8\) & \(-61.8\pm 4.8\) * & \(20.7\pm 1.4\) * & \(64.4\pm 4.7\) * \\ Q210N & \(-1.55\pm 2.2\) & \(-8.5\pm 1.6\) & \(45.3\pm 1.2\) & \(28.2\pm 1.3\) & \(-6.9\pm 2.7\) * & \(-17.0\pm 1.8\) * & \(36.7\pm 2.1\) & \(46.9\pm 2.5\) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of reversal potentials. The superscript denoted the pH of the solution used. Values are reported at the average \(\pm\) SEM (n = 7–15). Statistically significant values are denoted with * (\(p<0.05\)). Figure 5: Kinetic properties of RHM-affecting mutants. (**A**) Summary of exponential fitting of apparent rate constants. (**B**) Decay rate comparison of RHM-affecting and null ChR2 mutants. (**C**) Off rate comparison of RHM-affecting and null ChR2 mutants. Error bars represent the SEM (n = 7–15). Statistically significant differences are denoted by * (\(p<0.05\)). WT—blue; Q210A—red; Q210N—green; V269N—orange.