## 3 Results  
### Identification and Quantification of Residual Hydrophobic Mismatch  
To quantify residual hydrophobic mismatch for ChR2 in the POPC membranes, we obtained an extended simulation trajectory from MD simulations of the ChR2 homology model based on the C1C2 structure, embedded in a POPC lipid bilayer. The ChR2 homology model aligns closely with the recently solved X-ray structure of ChR2 (Figure 2A) with a RMSD of 1.17 A (Figure 2A) [39]. The most notable structural differences occur in the N-terminal domain and the loop between TM1 and TM2. The CTMD approach was then used as previously described [22; 27] to calculate the consequences of protein-membrane interaction, including membrane deformation and the free energy cost of the RHM. The analysis revealed significant residual hydrophobic mismatch in WT ChR2 (Table 1). Although membrane deformation had alleviated some unfavorable interactions, residues located at the cytoplasmic interface of TMs 2, 6 and 7 remained exposed to either polar or hydrophobic inappropriate environments due to the local adjacency to residues with diverse properties that prevented further adaptation of the membrane (see References [22; 27]) Consequently, Q73 on TM1 and Q210 on TM6 were found to face the hydrophobic interface of the membrane. This caused membrane thinning in the adjacent regions of both residues, leading to water penetration into the membrane and exposure of V269 to a polar environment (Figure 2B). Substantial RHM was also observed at N187 and V269. Notably, mutations at these positions have previously been shown to affect ChR2 function [32; 49]. The energy cost of residual hydrophobic mismatch across the bilayer was calculated upon mutagenesis at V269 and Q210 (Table 1). The RHM for Q73 was not calculated because it is located in a modeled loop connecting TMs 1 and 2, which is unresolved in the C1C2 chimera template. Initially, the RHM was calculated for the entire ChR2 homology model, comprising of RHM at residues 210, 269, 270, 69 and 73. As the residues in TM1 are in a modeled loop, RHM was also calculated leaving out the residues in TM1. Both sets of calculations resulted in the same general trends. First, mutation of V269 to serine or asparagine decreased RHM. The decrease in RHM can be directly attributed to the observation that replacement of the hydrophobic residue (V) with polar residues (S or N) eliminates the RHM energy penalty when water penetrates into ChR2 at this position. Similarly, mutation of Q210 to alanine also reduced the RHM energy penalty. Interestingly, the Q210A mutation also lowered RHM at the neighboring V269, as the elimination of the polar residue likely reduced water penetration. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**WT (kT)**} & **V295S (kT) (\% RHM** & **V269N (kT) (\% RHM** & **Q210A (kT) (\% RHM** \\  & **Decrease)** & **Decrease)** & **Decrease)** \\ \hline
12.1 & 7.7 (36\%) & 5.8 (52\%) & 3.1 (74\%) \\ \hline
7 & 3.7 (47\%) & 3 (56\%) & 2.3 (67\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Percent change of residual hydrophobic mismatch for channelrhodopsin-2 when compared to wild type protein, calculated with respect to the RHM of the entire protein. The average energy cost of RHM for WT channelrhodopsin-2 and select mutant constructs embedded in a POPC bilayer was calculated for the entire ChR2 homology model across the bilayer (top row) and leaving out TM1 residues modeled as being in a loop (bottom row). The relative rank of differences among the constructs is unchanged under the two conditions. These differences in RHM among constructs are consistent with the pattern of experimentally observed differences in the function of the constructs. Figure 2: Homology model comparison and structural context of hydrophobic mismatch. (**A**) Structural alignment of the ChR2 homology model (time) used for the calculations and the ChR2 X-ray structure (blue).