## 3 Results
### Identification and Quantification of Residual Hydrophobic Mismatch
(**B**) The averaged membrane deformation around ChR2 is shown on a snapshot of the protein, with the residues where residual hydrophobic mismatch (RHM) occurs highlighted. The membrane deformations are shown in terms of the time averaged phosphate surface around the centered protein and water penetration. RMSD: Root mean square deviation  
These calculations thus added V269 to the cluster of adjacent polar and hydrophobic residues that are responsible for the large RHM penalties: Q210 (TM6), V269 and L270 (TM7), F69 and Q73 (TM1). As controls, energy penalty calculations were done for I95L and Q210N, two mutations that should not affect RHM. Indeed, neither of these null mutations changed the energy penalty compared to WT ChR2 (without TM1 contributions, compare the calculated energy penalty value for the WT: 7 kT, to those for I95L: 6.6 kT and Q210N: 6 kT). Differences of \(<\)1 kT are within thermal energy fluctuations and cannot be considered biologically significant  
Probing the Effects of Predicted RHM Changes with Experimental Measurements of Function for ChR2 Constructs  
In order to directly assess the functional effect of changes in RHM energy penalty on the functional properties of ChR2 constructs, we used two-electrode voltage clamp measurements. A trio of membrane-facing residues located at the cytoplasmic/TM interface (Q73, Q210, V269) were mutated to reduce RHM, in two cases by increasing the hydrophobic surface of the protein (Q73A and Q210A) and in once case decreasing it (V269N). Additionally, the two null mutants (Q210N and I95L) calculated to produce no change in RHM energy cost were also assayed. Functional expression of the mutants was tested in _X. laevis_ oocytes under voltage-clamp conditions. The results show reduced photocurrent for the Q73A, Q210A and V269N constructs, while Q210N produced increased photocurrent compared to WT (Figure 3). Q73A had currents \(<\)50 nA and was not analyzed further. I95L had no observable photocurrent under our experimental conditions. The functional effect of RHM on ChR2 selectivity was quantified by measuring reversal potentials (E\({}_{\text{rev}}\)) at I\({}_{\text{p}}\) and I\({}_{\text{ss}}\) in Na\({}^{+}\) solutions at pH 7.5 and 6.0 (Figure 4A) (see Materials and Methods). This allowed the determination of selectivity between Na\({}^{+}\) and H\({}^{+}\). Additionally, by measuring reversal potentials at the peak and steady-state currents we could monitor the progressive ion selectivity as ChR2 transitions between open states. A positive shift in I\({}_{\text{p}}\) E\({}_{\text{rev}}\) for V269N was observed at both pH 7.5 and 6.0 compared to WT. The shift was much larger at pH 6.0 than at pH 7.5, where the current is carried mostly by protons (pH 6.0) and not a mixture of Na\({}^{+}\) and H\({}^{+}\) (pH 7.5). In contrast, a hyperpolarizing shift in E\({}_{\text{rev}}\) for I\({}_{\text{ss}}\) was observed for this mutant only at pH 6.0 compared to WT (V269N: 13.2 \(\pm\) 1.2; WT: 24.6 \(\pm\) 1.5) (Figure 4B and C; Table 2). This indicated that the permeability of H\({}^{+}\) was increased at the beginning of ion conductance (I\({}_{\text{p}}\)) but then decreased over time (I\({}_{\text{ss}}\)) when compared to WT. Equally, when changes in E\({}_{\text{rev}}\) were considered, V269N becomes progressively less  
Figure 3: Representative photocurrent traces for RHM ChR2 mutants. Photocurrents were recorded in Na\({}^{+}\) solution at pH 7.5 at V\({}_{\text{m}}\) = \(-\)100 mV. Blue bar indicates illumination with blue light. WT—blue; Q73A—purple; I95L—yellow; Q210A—red; Q210N—green; V269N—orange. permeable for H\({}^{+}\) at pH 6.0. Interestingly, the control Q210A mutant had no observable effect on ion permeability. The null mutant did significantly alter the progressive ion selectivity at pH 7.5 and 6.0 but only to a small degree (Table 2). We also determined steady-state to peak current ratios that provide a measure of ChR2 inactivation during prolonged light exposure (Figure 4D).