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, IP; steady-state current, ISS, activation time constant, τON; inactivation time constant, τINACT; and deactivation time constant, τOFF; 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 [9], [12], 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 (IP). EF. Current-voltage (I–V) curves for the steady-state current (ISS). GH. Ratio of ISS/IP as a function of voltage. Experimental data in C, E, and G are presented as mean±S.E., n = 7.
Table 1.
Model parameters.
Figure 3.
Light- and voltage-dependence of kinetic parameters in experiments (left) and in the model (right).
AB. Light dependence of τON across four voltage values. CD. Voltage dependence of τON across four irradiance levels. EF. Light dependence of τOFF across four voltage values. GH. Voltage dependence of τOFF across four irradiance levels. IJ. Light dependence of τINACT across four voltage values. KL. Voltage dependence of τINACT 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 τR across four voltage values. EF. Voltage dependence of τR across three irradiance levels. GH. Ratio of the peak currents in response to S2 and S1, IP2/IP1, as function of inter-pulse interval, across four voltage values. IJ. Ratio of the peak currents in response to S2 and S1, IP2/IP1, 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.
Table 2.
Light- and voltage-dependence of key ChR2 characteristics.
Figure 5.
Temperature dependence of ChR2 current.
A–D Experimental data, adapted from [30], showing the effect of temperature (22°C and 37°C) on τON, τINACT, τOFF and ISS/IP 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 IChR2 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 IChR2 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 IK1.