## 3 Results  
We considered experimental patch-clamp data [15] from CHO (Chinese hamster ovary) host cells, stably expressing rat Kv10.1 channels, which exhibit a highly comparable electrophysiological behavior to human Kv10.1 channels [29]. The data provided comprises voltage-clamp measurements at three different temperature levels of 15, 25, and 35 \({}^{\circ}\)C. The dynamic behavior of the voltage-gated ion channels displays three main characteristics: activation, deactivation, and inactivation (Figure 3). In the case of the depolarization of the cell membrane, the Kv channel transits from the resting (closed) to the active (open) state. During prolonged depolarization, Kv channels switch to an inactivated state [30]. Figure 3 shows the whole-cell current response to applied voltage-step protocols for the determination of the activation, deactivation, and inactivation characteristics of the channel. In developing the dynamic behavior of the system, the three different stimulus signals, as shown in Figure 3, were used to provoke these activities. In addition, these activation, deactivation, and inactivation characteristics could also be stimulated alternatively by ramp, action potential (AP), and recovery protocols [15]. For model development, the dynamic behavior of Kv10.1 was considered at a temperature of 25 \({}^{\circ}\)C, which corresponds to standard experimental conditions in in vitro electrophysiological studies. The activation or opening is stimulated with appropriate depolarizing input voltage step functions. Nevertheless, the Kv10.1 response corresponds to the transient response of the system. Based on the experimentally measured response to given stimuli, we concluded that Kv10.1 behaves as a first-order system. We assumed all initial conditions as equal to zero and at a nominal voltage of 70 mV. It was possible to obtain an average model based on averaged data for all cells, as given in [21] for the Kv1.1 voltage-gated ion channel. We also considered a randomly chosen active cell with high-quality recording data from the database available via Channelpedia, a web-based freely accessible information management network and electrophysiology data repository [15]. The chosen cell ID is 9514 at 25 \({}^{\circ}\)C, and the host cell is CHO_FT; the species is rat. Input and output experimental data from patch-clamp measurements are given in Figure 3.  
Figure 4 shows the activation voltage step protocol to determine the opening or activation of the ion channel and the measured macroscopic ion current as input and output for system identification. We assumed a nominal operating point at an input voltage of 70 mV, based on the experimental design and input functions for inactivation and deactivation. Input-output data from the patch-clamp experiments for the nominal operating point are shown in Figure 5a. Time-domain experimental data were imported into the System Identification toolbox in MATLAB. The data were not preprocessed and, based on the measured output signal and input step signals, we adopted a first-order linear time-invariant system. A comparison between measured and simulated model output is shown in Figure 5b. The transfer function was estimated with one pole and null zeros in the continuous-time domain, the i/o delay was fixed to zero, and we set the initial condition to zero. The initialization method implies that the algorithm is used to initialize the numerator and denominator. Algorithms applicable only for estimating continuous-time transfer functions using time-domain data are the instrument variable (IV), state variable filters (SVF), generalized Poisson moment functions (GPMF), subspace state-space estimation (N4 SID), and a combination of all of the preceding (ALL) approaches [27; 28]. We chose to use the initialization method ALL. This method of systems modeling is known as black-box modeling. Figure 3: Dynamic behavior of the voltage-gated ion channel Kv10.1. Created with BioRender.