Computational optogenetics: empirically-derived voltage- and light-sensitive channelrhodopsin-2 model

Abstract

Channelrhodospin-2 (ChR2), a light-sensitive ion channel, and its variants have emerged as new excitatory optogenetic tools not only in neuroscience, but also in other areas, including cardiac electrophysiology. An accurate quantitative model of ChR2 is necessary for in silico prediction of the response to optical stimulation in realistic tissue/organ settings. Such a model can guide the rational design of new ion channel functionality tailored to different cell types/tissues. Focusing on one of the most widely used ChR2 mutants (H134R) with enhanced current, we collected a comprehensive experimental data set of the response of this ion channel to different irradiances and voltages, and used these data to develop a model of ChR2 with empirically-derived voltage- and irradiance- dependence, where parameters were fine-tuned via simulated annealing optimization. This ChR2 model offers: 1) accurate inward rectification in the current-voltage response across irradiances; 2) empirically-derived voltage- and light-dependent kinetics (activation, deactivation and recovery from inactivation); and 3) accurate amplitude and morphology of the response across voltage and irradiance settings. Temperature-scaling factors (Q10) were derived and model kinetics was adjusted to physiological temperatures. Using optical action potential clamp, we experimentally validated model-predicted ChR2 behavior in guinea pig ventricular myocytes. The model was then incorporated in a variety of cardiac myocytes, including human ventricular, atrial and Purkinje cell models. We demonstrate the ability of ChR2 to trigger action potentials in human cardiomyocytes at relatively low light levels, as well as the differential response of these cells to light, with the Purkinje cells being most easily excitable and ventricular cells requiring the highest irradiance at all pulse durations. This new experimentally-validated ChR2 model will facilitate virtual experimentation in neural and cardiac optogenetics at the cell and organ level and provide guidance for the development of in vivo tools.

Figure 1. Experimental protocols, empirical measures and construction of ChR2 model.

A. Empirical measures extracted from experimental measurements and used to constrain/optimize the model. These are five parameters capturing the amplitude and kinetics of ChR2 current: peak current, I_P; steady-state current, I_SS, activation time constant, τ_ON; inactivation time constant, τ_INACT; and deactivation time constant, τ_OFF; they were quantified for each cell under all described experimental conditions. Blue bar indicates light pulse duration. B. ChR2 model structure used in this study, adapted from , , with two closed states (C₁ and C₂) and two open states (O₁ and O₂), seven transition rates, of which two (k₁ and k₂) are light-dependent; see Table 1 for details. C. Experimental protocol with voltage clamp and optical pulse application for a total of 20 combinations per cell: 5 holding voltages ranging from −80 to −10 mV and 4 irradiances ranging from 0.34 to 5.5 mW/mm². Example traces (ChR2 current) are shown for selected 4 (out of 20) combinations. D. Recovery-from-inactivation experimental protocol (S1–S2 pulse protocol) for a total of 60 combinations of conditions per cell (3 irradiances, 4 holding voltages and 5 inter-pulse intervals), as indicated.

Figure 2. Inward current-voltage rectification for ChR2 in experiments (left) and in the model (right).

Experimental (A) and model (B) example traces for ChR2 current in response to 0.5 s light pulses, 470 nm, at specified irradiances and holding voltages. CD. Current-voltage (I–V) curves for the peak current (I_P). EF. Current-voltage (I–V) curves for the steady-state current (I_SS). GH. Ratio of I_SS/I_P as a function of voltage. Experimental data in C, E, and G are presented as mean±S.E., n = 7.

Figure 3. Light- and voltage-dependence of kinetic parameters in experiments (left) and in the model (right).

AB. Light dependence of τ_ON across four voltage values. CD. Voltage dependence of τ_ON across four irradiance levels. EF. Light dependence of τ_OFF across four voltage values. GH. Voltage dependence of τ_OFF across four irradiance levels. IJ. Light dependence of τ_INACT across four voltage values. KL. Voltage dependence of τ_INACT across four irradiance levels. Experimental data in A, C, E, G, I, and K are presented as mean±S.E., n = 5.

Figure 4. Kinetics of recovery from inactivation for ChR2 in experiments (left) and in the model (right).

AB. Experimental and model traces in response to S1–S2 protocol, 3 s inter-pulse interval, irradiance of 1.6 mW/mm² and holding voltages of −40 and −80 mV. CD. Light dependence of τ_R across four voltage values. EF. Voltage dependence of τ_R across three irradiance levels. GH. Ratio of the peak currents in response to S2 and S1, I_P2/I_P1, as function of inter-pulse interval, across four voltage values. IJ. Ratio of the peak currents in response to S2 and S1, I_P2/I_P1, as function of inter-pulse interval, across three irradiance levels. Experimental data in C and E were fits to the average curves, n = 4. Experimental data in G and I are presented as mean±S.E., n = 4.

Figure 5. Temperature dependence of ChR2 current.

A–D Experimental data, adapted from , showing the effect of temperature (22°C and 37°C) on τ_ON, τ_INACT, τ_OFF and I_SS/I_P for a range of voltages. E. Temperature scaling factors (Q₁₀ values), derived from the data in A–D. F. Summary of average Q₁₀ values (from E) used as constraints for the model optimization; optimized Q₁₀ values for the rate parameters of the model. G. Example model traces of ChR2 current for the specified voltage and irradiance values at 22°C and 37°C.

Figure 6. ChR2 current during the cardiac action potential via AP clamp.

A. Adult guinea pig ventricular cardiomyocytes after 48 h of viral infection with Ad-ChR2(H134R)-EYFP, green fluorescence indicates ChR2 expression; scale bar is 50 µm. Experimental (B–D) and modeling (E–F) traces for guinea pig ventricular cells. B. Optically-triggered action potential (50 ms pulse at 470 nm, 1.5 mW/mm²) used for the AP clamp; dotted line indicates the voltage clamp conditions upon application of the waveform; blue dots indicate the beginning and end of the optical pulse. C. Extracted I_ChR2 as the difference current from the total current traces (panel D) recorded in dark conditions and with a light pulse. E. Analogous optically-triggered action potential in a model of a guinea pig ventricular cell. F. The underlying I_ChR2 according to the model.

Figure 7. Optical excitation in human cardiac cell types.

A. Optically-triggered action potentials (10 ms pulse at 470 nm, 0.5 mW/mm²) in human ventricular, atrial and Purkinje cells. B. Underlying ChR2 current upon the action potential generation for the three cell types. C. Strength-duration curves for the three cell types. Squares show simulated values for optical excitation threshold in ventricular myocytes with a Purkinje formulation of I_K1.