## 1 Introduction
Such membrane-protein interactions have been shown to play central roles in the functional mechanisms of membrane proteins--from G-protein-coupled receptors (GPCRs) [18; 19; 20; 21] to transporters [22; 23; 24] and channels [25; 26]--but have not been addressed in the analysis of ChR2 function. Since the physical properties of membranes, such as thickness, curvature, compression modulus and specific composition have all been shown to affect the structure and function of the numerous membrane proteins studied, it seems essential to explore the role of membrane interactions of ChR2 in order to connect expected functional properties to diverse environments in various cells. The membrane-mediated regulation of proteins has been addressed quantitatively in terms of hydrophobic mismatch [21; 22; 27]. However, as the TM helix bundle of membrane proteins is highly asymmetric (with TM segments of dissimilar length and orientation), the evaluation of the mismatch is a complex task. Moreover, the conformational rearrangements associated with the various states of these proteins (active, inactive, desensitized) engender dynamic interaction with the lipid environment. Consequently, the hydrophobic mismatch that occurs when the membrane spanning regions of proteins do not position hydrophobic/hydrophilic regions in alignment with their counterparts in the bilayer is dynamic in nature, following the interfaces created in the protein states by deforming the bilayer so that the thickness of the hydrophobic portion of the lipid bilayer can match the hydrophobic core of the protein. This matching prevents the exposure of nonpolar (or polar) residues to the inappropriate part of the membrane and minimizes the energetic cost. If the adaptation of the membrane does not fully compensate the hydrophobic core, a residual hydrophobic mismatch (RHM) is established [19], which incurs additional energy costs [22]. In simple channels, such as the single, helical TMs gramicidin A channel, the hydrophobic mismatch can be remedied mostly by simple membrane deformations [28]. However, in more complex channels composed of multiple TMs the membrane adaptation is challenged by the radially asymmetric hydrophobicity of the interface surface, which also changes with the functional or oligomerization state of the protein. The recently developed computational approach--Continuum Theory-Molecular Dynamics (CTMD)--has been shown to account quantitatively for the effects of complex lipid deformations that occur with multiple TM helices [27]. Once the membrane deformation profile is established with CTMD for each conformational state of interest, the method also quantifies the solvent accessible area of unfavorably exposed residues due to RHM and calculates the resulting energy penalty [18; 22]. Because the CTMD method calculates the energy components in a specific structural context that identifies the residues producing the largest energy penalty, the results predict specific changes that can be introduced by mutagenesis to reduce (or increase) the RHM and show the dependence of RHM on the composition-dependent properties of the bilayer (e.g., thickness). Thus, the methodology can serve prospectively to identify residues critical to hydrophobic mismatch in different lipid environments and on this basis predict specific mutations that would increase/decrease the compatibility between the protein and the specific bilayer, thereby guiding mutagenesis experiments and choices of preferred membrane environments for activity. ChR2 has been successfully expressed in functionally diverse cell lines, each with unique membrane compositions [5; 29; 30; 31]. To further explore these membrane-protein interactions, we demonstrate the role of RHM as a mechanistically important component of ChR2 function. Through a combination of MD simulations, CTMD calculations and functional measurements, we have quantified the key contributions to RHM of residues within TM1 and TM7. For several decades, hydrophobic mismatch has been proposed to modulate TM protein function.