Fig. 7: Transition rates estimation for COCOC models, including fast gating rates.

Models were simulated with a COCOC topology, including fast rates that are considerably larger than the corner frequency of the low-pass filter (10 kHz). k₁₂ to k₄₃ were restricted to slower rates in the range of 0.1 ks⁻¹ to 10 ks⁻¹ and k₄₅, k₅₄ encompass the fast rates in the range of 10 ks⁻¹ to 1 Ms⁻¹. For this task, the regression architecture (Fig. 1B) was trained on dataset No. 6 (Table 1). The predictions were ranked according to the averaged error scores (RAE) for each model. A–C Excerpts of simulations using the ground truth and predictions of the best model (A), a selected model approximately below the median (B), and the worst model (C) are shown. They are accompanied by their respective 2D-histograms (2D_GT and 2D_Pr for the ground truth and prediction). The closed dwell-times are represented on the horizontal axis and the open dwell-times on the vertical axis, ranging from 0.01 ms to 100 ms. For computing the 2D-histograms, time series with a length of 10 million samples were used. Furthermore, using time series with a length of 1 million samples, the current distributions of ground truth and prediction are plotted together in the same graph. The red lines indicate the open (O) and closed (C) current amplitudes, spanning 2000 arbitrary units (AU), with an SNR = 5. In addition (inset), the segment of the time series between the vertical dashed blue lines is displayed with its corresponding idealization (black on gray). 100 simulations are computed with each predicted Markov model. The time series are idealized, and the 2D-histograms are generated. According to Eqs. 6, 7, the mean volume deviation and mean reference volume are then calculated, (\({\bar{V}}_{{{\rm{D}}}}({{\bf{G}}},{{{\bf{H}}}}_{1},\ldots ,{{{\bf{H}}}}_{100})\) and \({\bar{V}}_{{{\rm{R}}}}({{{\bf{H}}}}_{1},\ldots ,{{{\bf{H}}}}_{100})\), respectively). The volume differences are depicted in the 2D_GT and 2D_PR histograms, respectively. Furthermore, distribution of the rates of the 100 re-predictions are displayed in (D–F). The horizontal dashed lines frame the parameter range on which the NNs were trained. The diamond indicates the median as well as the 75 and 25 percentiles, while the whiskers denote the 10 and 90 percentiles. The orange dots connected with orange lines illustrate the ground truth as indicated in (A–C). F The green dots connected with green lines illustrate the predicted values upon which the re-estimation is based on. D–G Scatter plots indicate the output of the NN on the test dataset. The orange dashed lines and the red dashed lines indicate error scores (RAE) equal to 0.6 and 1.0, respectively. D, E Show the results for the overall worst predicted slow rates (k₃₂ and k₃₄), while F, G show the results for the fast rates (k₄₅ and k₅₄).