The provided code models the photocurrent kinetics of different variants of Channelrhodopsin-2 (ChR2), specifically ChRwt, ChETA, and ChR ET/TC. Channelrhodopsins are light-activated ion channels commonly used in optogenetics to control neuronal activity with precision. ChR2 variants have been engineered to have different activation and deactivation kinetics, which are crucial for their respective applications in neuroscience research. ### Biological Basis 1. **Channelrhodopsin-2 (ChR2):** - ChR2 is a light-gated ion channel found in the green alga *Chlamydomonas reinhardtii*. - Upon illumination with blue light, ChR2 opens, allowing cations (primarily Na+ and Ca2+) to flow into the cell, depolarizing the membrane potential. 2. **Kinetics of Photocurrent:** - Upon photoactivation, ChR2 opens rapidly and then stabilizes at a lower steady-state conductance while the light is on. - After the light is switched off, ChR2 channels undergo a deactivation process. 3. **Modeling Photocurrent Responses:** - The model in the code uses a bi-exponential function to capture the dynamics of photocurrent through the activation, steady-state, and deactivation phases of the ChR2 variants. - Parameters such as `Ipeak`, `Isteady`, `tau_act`, `tau_deact`, and `tau_off` are critical for describing the temporal dynamics of ChR2 opening (activation) and closing (deactivation). 4. **Key Parameters:** - **Ipeak**: Represents the peak photocurrent immediately following light onset. - **Isteady**: Represents the photocurrent level during prolonged light exposure, indicative of channel desensitization or adaptation. - **Tau Parameters**: - `tau_act`: The time constant for the rising phase of the photocurrent, corresponding to the speed of channel opening. - `tau_deact`: The time constant for the decay phase during continued illumination, reflecting channel desensitization. - `tau_off`: The time constant for current decay after the light is turned off, reflecting the speed of channel closing. 5. **Empirical Modeling:** - The code captures distinct kinetic profiles for different ChR2 variants by adjusting these parameters. - The `heaviside` function is used in the mathematical model to ensure that the photocurrent changes only within specified time windows (e.g., upon light-on and light-off events). Overall, this model allows researchers to simulate experimentally observed photocurrent responses for different ChR2 variants, providing insights into their functional characteristics and potential applications in manipulating neural activity in vivo.