## 1 Introduction  
The eyespot region of the green algae Chlamydomonas reinhardtii contains two photoreceptor proteins, channelrhodopsin-1 (ChR1) and channelrhodopsin-2 (ChR2), which are implicated in the first committed step of the phototactic response [1; 2; 3]. ChR2 is a light-activated ion channel that conducts cations of multiple valencies down the electrochemical gradient [1; 2]. ChR2 is part of the microbial-rhodopsin family of membrane proteins found in archaea, algae and bacteria [4]. Its structure follows the common architecture of seven-helix transmembrane domains (TMD) that houses all-trans retinal bound through a protonated Schiff base to a completely conserved lysine residue on TM 7 (K257 in ChR2). Photoactivation of ChR2 with blue light (\(\lambda_{\text{max}}=470\) nm) isomerizes retinal to the 13-cis isoform to begin the photocycle reaction that leads to ion conductance [2]. The functional properties of ChR2 have made it a popular tool in the field of optogenetics in which excitable cells expressing photoactivatable ion channels are controlled by light. ChR2 activation can rapidly depolarize the membrane of excitable cells and induce neuronal spiking of action potentials with high temporal and spatial resolution [5]. ChR2 photocurrents rise to an initial transient peak (I\({}_{\text{p}}\)), which decays rapidly to a steady-state value (I\({}_{\text{ss}}\)) in a process known as inactivation [6]. Once illumination ends, I\({}_{\text{ss}}\) decays biexponentially to baseline, indicative of a two-step process [7]. Interestingly, even after long periods of recovery in the dark, ChR2 exhibits reduced peak currents on subsequent light pulses, which is referred to as desensitization [8]. There have been multiple attempts to generate a photocycle model that accurately recreates ChR2 photocurrents. Several kinetic three and four-state models have been developed to reproduce and quantify ChR2 photocurrents [9; 10]. The current models consist of two closed states and two open states (Figure 1) [11; 12; 13]. Here, the ground state C1 rapidly transitions to an initial high conducting O1 state. Under continuous illumination conditions, O1 decays to the lower-conducting O2 state. Once the light is turned off, ion conductance ends and O2 moves to the desensitized closed state C2. During sufficient time in the dark, C2 thermally converts back to C1. The ChR2 kinetic model is defined by the distribution of conformational states (O1, O2, C1, C2) with corresponding rates of transition and the ion conductance properties of these states. Molecular detail relating the timing of conformational changes during the photocycle to the resulting ion conductance is required for a better understanding that can lead to predictive modeling of ChR2 function. Indeed, compared to microbial-rhodopsin pumps, ChR2 undergoes much larger conformational changes in backbone structure prior to ion conductance [14; 15; 16]. The analysis of conformational rearrangements of the ChR2 molecule from spectroscopic measurements, spin-labeled electron paramagnetic resonance (EPR) experiments and molecular dynamic (MD) simulations has indicated activation-related movement of transmembrane segment (TM) 2 away from the bundle by over 3 A [16; 17]. This movement is also sensed by TM7 through an interhelical hydrogen-bonding network. The resulting reorientation of  
Figure 1: Channelrhodopsin-2 (ChR2) four-state model. Four-state kinetic model of ChR2 with two conducting (O1 and O2) and two non-conducting (C1 and C2) states. Each transition is represented by the corresponding rate parameter used in the kinetic model. The blue arrows represent light-assisted transitions. the gating residues E90, N258 and Y70 enables water penetration to the pore and subsequent ion conductance [15]. Given the substantial structural rearrangements of transmembrane segments (TMs) in the TMD associated with ChR2 function, it becomes important to evaluate the role and contribution of the local membrane environment in affecting channel mechanism.