## 3 Results  
To define the relationship between the activity of the pyramidal neuron expressing ChR2 and the parameters of the light stimulus, we carried out experiments with a 10-light pulse train. We picked up the frequency at which the action potential (AP) was generated for each light stimulus (Figure 3). We considered the generation of action potentials because the membrane current changed at all frequencies used in this study. These results demonstrated a reduced number of AP with increasing frequency under blue light pulsing. The frequency at which the AP was generated for each light stimulus was in the range of 1-5 Hz. Further measurements were carried out at a frequency of 1 Hz. These results are similar to the data published previously [23], but the range of optimal stimulation frequency was more narrow in our experiments. The reason for this discrepancy requires further study. Figure 2: Photocurrents recorded using the whole-cell voltage-clamp technique at maximal intensity and light duration. t = 100 ms.  
We have studied the effect of the light pulse duration in the range of 1-5 ms, 10-50 ms and 100-500 ms on the amplitude of photocurrents at various LED intensities; the value of maximum intensity has been normalized to unity. Each point in Figure 4 represents the mean value of the measured amplitudes of the response to a 10-pulse train with fixed duration and intensity (see Figure 2). As shown in Figure 4, the dependency of the photocurrent amplitude on the light pulse is described by a right-skewed bell-shaped curve. The obtained dependency was identical for all light intensities used in the experiment. The obtained results agree with results published earlier [7, 24]. It should be noted that in the range of 1-20 ms, the value of this amplitude increases, while at higher values of pulse duration (30-500 ms), the amplitude decreases. An explanation for this fact  
Figure 4: Dependence of the membrane current amplitude for pyramidal neurons on the duration of light stimulation at different light intensities (the value of intensity maximum is taken as 1), time–light pulse duration, \(n=10\). Plots of mean values with error bars indicate the standard error (SE). To obtain these mean values, fourth-order polynomial smoothing over neighboring points was performed in GraphPad Prism 7. Figure 3: Action potential generation under blue light stimulation at different frequencies. may be based on the kinetic model of the ChR2 photocycle, in which three channel states (open (O), desensitized (D) and closed (C)) were considered [7]. The three states model was the first model describing a photocycle of channelrhodopsin-2. However, after the spectral analysis of ChR2 [25], an existence of four kinetic intermediate states (P\({}_{1}\), P\({}_{2}\), P\({}_{3}\) and P\({}_{4}\)) was indicated. Based on this information, four [24; 26] and six [27] state models have been developed. To explain our findings, we utilized the four-state model of ChR2 photocycle, which consists of two open states (\(O_{1}\to O_{2}\)) and two closed states (\(C_{1}\to C_{2}\)). Thus, the states defined by the spectral analysis can be interpreted as follows: \(O_{1}\to O_{2}\) corresponds to the states \(P_{2}\) and \(P_{3}\) (open states with the time constants of 1 ms and 10 ms, respectively) and state \(C_{2}\) (the time constant \(\sim\)5s) corresponds to the state \(P_{4}\) (dessentized). The state of \(C\) is the ground state of the channel and corresponds to \(P_{0}\). We suppose that the decrease of photocurrents after 30 ms is due to the transition in the \(P_{4}\) state, i.e., inactivation of ChR-2. We have also studied the time interval tau (\(\tau\)), which is needed to reach the maximum photocurrent (Figure 5) for different pulse durations (t) atmaximum intensities (I\({}_{\max}\)). We analyzed the relationship between \(\tau\) and light pulse duration (t) (Figure 6). According to dependence in the range of 10-30 ms, \(\tau\) corresponds to the light pulse duration. After t = 50 ms, the time \(\tau\) did not change.