Introduction

The teaching of life sciences is traditionally organized into two parts: theory and lab practice ^1,2. At the undergraduate level, lab experiments to teach physiology and neurosciences are very expensive. Additionally, it is difficult to carry out experiments for intracellular recording with current and voltage clamp techniques. The need for space, expensive equipment, lab material and experimental animals for educational purposes is out of reach for most universities ³.

Diwakar et al. reported that in India an investment of around 20 million rupees (~267,900 USD) is required for a typical patch clamp configured for lab use, to which other costs such as the animals and facilities must be added ⁴. In Mexico, the presence of up to 50 students in each classroom makes this kind of lab practice impossible. One feasible alternative is the development of simulators for teaching. Indeed, simulated patients already form part of the learning environment in different disciplines of the medical field ^5,6,7 and virtual microscopy practices are employed in histology ⁸.

Teaching the basic principles of neuroscience is of special interest and can be greatly enhanced by incorporating realistic and interactive simulations of neuronal functioning ⁹. Single-neuron computer simulations began with the work of Hodgkin and Huxley ¹⁰. Several simulators are now available to realistically simulate neuronal networks, including GENESIS Simulation System ¹¹, NEURON Simulation Environment ¹² and NSL Neural Simulation Language. With the increasing capacity of computational performance, the simulation of the entire brain may ultimately be possible ¹³.

However, only a few neurosimulators have been adapted to a teaching environment. For example, Hernández and Zurek developed a module of teaching in NEURON, allowing students to examine the properties of biophysics in the axon by using the Hodgkin-Huxley model ¹⁴. A simulator capable of reproducing the classic Hodgkin and Huxley experiments was developed by Reyes-Lazalde et al. ¹⁵. The basic study of the passive properties of the axon and dendritic tree can be carried out with an interactive simulator developed for Windows^® environment ¹⁶. Brian, a program written in Phyton and found at http://brian.di.ens.fr, was developed for quickly coding models of spiking neuronal networks in everyday situations ¹⁷. iCell, an interactive cell modeling tool located at http://ssd1.bme.memphis.edu/icell/, integrates research and education for electrophysiology training. It consists of JAVA applets that represent models of a variety of cardiac cells and neurons and provide simulation data on the bioelectric activity of a single cell ¹⁸.

Traditional learning media, such as multimedia-based demonstrations, videos, reading and lectures, are passive environments and therefore limit the interactive experience of students ³. Contrarily, computer simulation enables active learning ³. The requirements are a computer room, software and an instructor. Several reports have described the pedagogical value of simulators ⁴. During a neuroscience course, a comparison was made between traditional teaching and active teaching aided by simulators, finding a greater understanding with the latter ³.

Ribarič and Kordaš tested the effectiveness of a software package for the study of cardiovascular physiology at the undergraduate level of a medical school. The software presented a new approach for teaching physiology, involving active learning and confronting students with multiple ways of simulating basic and clinical physiological phenomena ¹⁹. Reyes-Lazalde et al. obtained favorable results when employing software for teaching science ²⁰. Hence, virtual labs have shown their utility for learning science ²¹.

During the current pandemic, teaching at a distance has added new relevance to information and communication technology (ICT). In this ICT-induced thrust, there are novel types of teacher-student interactions and new pedagogical methods. Since all lab practices are now suspended, virtual labs provide an alternative. Due to the high costs of lab practices, the government of India has sponsored an initiative to develop virtual labs, including neurophysiology labs ⁴.

In the present work, simulators were developed for the teaching and learning of A-type potassium ion current in neurons. They will permit students to perform virtual experiments with a current and voltage clamp. With the help of an instructor, students will be able to appreciate the importance of the A-type potassium current (I_A) and how it modifies the train of action potentials (AP train), and discover other neuronal ion channels in addition to those described in the axon.

In 1961, Hagiwara et al. ²² recorded I_A for the first time in cells of the marine mollusk Onchidium verruculatum and identified it as a K⁺ current. The activation and inactivation of the current produces a characteristic “A” profile, which is the reason for the name ²³. The equilibrium potential of I_A is similar to that of the delayed rectifier and is activated with hyperpolarization. The capacity of I_A to trigger action potentials and excitability in various neurons has been extensively studied. The function of I_A in the AP train is to decrease the firing frequency ²⁴. Gustafsson et al. ²⁵ discovered the existence of I_A in CA3 neurons and found it to be decreased by 4-amonopyridine (4-AP), a convulsant, thus resulting in a marked increase in cellular excitability. In rat upper cervical ganglion neurons, I_A was characterized as being very rapidly activated at -60 mV potential, depending on the concentration of external K⁺. This activation was reduced with 4-AP ²⁶. In neostriatal neurons, Bargas et al. ²⁷ demonstrated that I_A is responsible for the delayed appearance of the action potential in response to near threshold depolarizing currents.

I_A has been simulated with the aid of specialized programming languages for neuroscience. For example, it was simulated on a typical laterodorsal tegmental neuron with NEURON software ²⁸. To examine the role of I_A in excitability, network synchronization and epilepsy, Fransén and Tigerholm adopted a modified version of the model by Migliore et al., downloaded from the ModelDB ^29,30,31. However, there is no education simulator, to our knowledge, for I_A (http://sense- lab.med.yale.edu/senselab/modeldb/).

The relevance of I_A is evidenced by its participation in several regulatory mechanisms in neurons. The electrophysiological data reported depends on the recording techniques involved ³².

The aim of the present study was to generate educational software to facilitate the teaching and learning of I_A current in undergraduate and graduate programs. A series of simulators were grouped into three computer programs: I_A Current, I_A Constant-V Curves and I_A AP Train. With electrophysiological techniques, they reproduce I_A and allow for an unlimited number of virtual experiments.

Materials and methods

Three interactive computer programs were designed and developed to study I_A: I_A Current, I_A Constant-V Curves and I_A AP Train. For this purpose, the Visual Basic 6.0 programming language for Windows^® environment was adopted. The programs were compiled and made executable for Windows, from Windows 7 to Windows 10.

The programs act as simulators. To simulate a neuron, the Hodgkin-Huxley model ^{9,10,11,12,13,14,15} was employed (equations 1 and 2) and I_A was added in accordance with the model described by Connor et al. ²⁴ (equations 3, 4, 5, 6 and 7).

Where C_m is the membrane capacity per unit area (assumed constant), V is the membrane voltage, and g_Na, g_K, g_A and g_L are Na⁺, K⁺, I_A and leakage conductance, respectively. E_Na, E_K, E_A and E_L are the equilibrium potentials for Na⁺, K⁺, I_A and leakage, respectively. The equations utilized for Na⁺, K⁺ and leakage conductance and the corresponding velocities were those proposed by Hodgkin and Huxley ¹⁰, (see Hodgkin-Huxley equations for I_Na, I_K and I_L in Cronin ³³ and Sterratt et at. ³⁴).

The equations for I_A are ^24,34:

Where G_A is the maximum conductance of I_A, a is the activating particle and b is the inactivating particle ³⁴.

The kinetics of the activation curves a_∞(V) and b_∞ (V) (steady state) and time constants (_a(V) and (_b(V) are:

The parameters used in the model are: C_m = 1 μF cm^-2; E_Na, E_K, E_A and E_L = 50, -77, -80 and -22 mV, respectively; g_Na, g_K and g_L = 120, 20 and 0.3 mS cm^-2, respectively; g_A is variable, being selected by the simulators.

I_A AP Train program

This program is designed to reproduce the action potentials of neurons with an inward sodium current (I_Na), an outward K⁺ current (I_K) that does not inactivate (H-H type, Hodgkin and Huxley ¹⁰), and an outward potassium current that inactivates (I_A) (equation 1).

To start the integration, a fourth-order Runge-Kutta method with a step time of dt = 0.01 was used. An algorithm written in basic to solve differential equations with this method is found in Zill ³⁸.

Figure 1 illustrates the flow chart for the implementation of the models in Visual Basic^®.

Figure 1 Flow chart for implementing the models. For each simulator, the values of the variables and the stimulus pulse are entered. The program initializes the graph scales and the basal values of the model. The differential equations are solved simultaneously, and the results are presented graphically. The iteration time depends on the duration of the stimulus (dp). The user can exit the simulator at any time. 

Results and discussion

Three interactive computer programs (I_A Current, I_A Constant-V Curves and I_A AP Train) were designed and developed to reproduce the electrophysiology of I_A.

I_A Current program

A-type potassium current simulations

The user interface of the I_A Current simulator has two oscilloscope screens. One shows the macroscopic current traces of the I_A and the other illustrates the stimulus pulse in its voltage clamp mode.

The stimulus voltage to perform the simulations is in the range of -60 to -20 mV, with VH = -93 mV. In the neurons recorded by Connor and Stevens ³⁶, the activation time constant has values from 10-25 ms and the inactivation constant from 220-600 ms. These values vary according to the type of cell. In neurons of the hippocampus of the vertebrate central nervous system, the values are considerably lower. Experimental values from other neurons can also be employed. To simulate and replicate the experimental results in distinct neuronal systems, the user need only enter the time constants of different neurons.

The simulation of the experiments published by Connor and Stevens ^35,36 is depicted in Figure 2.

Figure 2 The simulation of the experiments carried out by Connor and Stevens were run to study the I_A. The voltage setting pulses are displayed on the lower oscilloscope screen. The upper screen portrays the currents traces corresponding to Vc = -60, -50, -40, -30 and -20 mV (the curves from baseline upwards). The VH was -93 mV and the rise time and decay current constants were 25 and 300 ms, respectively. 

Command voltage pulses of -60, -50, -40 and -20 mV were applied. As the command voltage becomes less negative, the amplitude of the current increases ³⁶. The I_A trace corresponding to each of the stimulus pulses is displayed on the upper oscilloscope screen. For each simulation, the value entered for the time constant was 25 ms for activation and 300 ms for inactivation.

The simulations generate a classic I_A profile. This is a K⁺ output current that starts at hyperpolarized potentials and shows an ascending curve during activation until reaching a maximum, at which point it gradually descends during inactivation. With a new command voltage and VH, there are changes in the channel conductance (g_A) and consequently in the current and peak amplitude of the current. The data correspond to experiments carried out at 5 °C. The currents are very slow in gastropod neurons compared to those in the brain of rats or other vertebrates. I_A is presented directly without considering the total outward potassium current and I_K.

I_A conductance (g_A) simulations

The channel conductance (g_A) is obtained by dividing I_A by the voltage command (V_c). Figure 3 shows the same simulation conditions as Figure 2. The upper oscilloscope screen depicts the gA value in nS cm^-2. The trace duration is 1 s.

Figure 3 Simulations of gA with VH = -93 mV and pulses characterized by a voltage command of -60, -50, -40, -30 and -20 mV. The response is displayed on the upper oscilloscope screen. The trace with the smallest amplitude of conductance corresponds to -60 mV and the highest amplitude to -20 mV. 

Simulation for I_A equilibrium potential

One of the methods to determine the equilibrium potential of an ionic current is to perform voltage clamp experiments and find the command voltage where the current is zero. In the I_A Equilibrium Potential simulator, the equilibrium for the current was -63 mV (Figure 4). The current-voltage relation is not presented.

Figure 4 Simulation of the equilibrium potential. There was a lack of current at Vc = -63 mV. The upper lines correspond to Vc = -50 and -30 mV. 

Inactivation protocol simulation

To simulate the inactivation protocol, the I_A Inactivation Protocol program is provided with the interface depicted in Figure 5. The two oscilloscope screens on the left side show the current traces of I_A (upper) and the stimulation pulses (lower). The macroscopic I_A current is recorded in a neuron, beginning with a test depolarization at 0 mV and followed by the holding potential that varied from -90 to -50 mV.

Figure 5 Simulations with the inactivation protocol. The voltage holding (VH) was applied at -80, -70, -60, -50 and -40 mV, consecutively. The responses are displayed on the upper oscilloscope screen. The amplitude of the trace was greatest at -80 mV and least (2.6 nA) at -50 mV. 

As can be appreciated, the peak value of the current decreases as the holding voltage preceding the stimulus pulse becomes less negative. Figure 6 illustrates how the decline in the peak value follows the pattern of a decreasing curve, as reported by Connor and Stevens ³⁶. The maximum value of I_A was obtained with a holding potential of -90 mV, and a value near zero was found in the range of -50 to -40 mV.

Figure 6 Inactivation plot. The peak value of the current decreases as the VH becomes less negative, from -90 to -40, in decremental steps of 5 mV. These results replicate the experimental data ³⁶. 

Simulation of the activation and inactivation curves

Simulations of the activation and inactivation curves are based on the Hodgkin-Huxley model ¹⁰. Figure 7 shows an example of simulation. Curves a(V, ∞) and b(V, ∞) overlap between -30 and -20 mV.

Figure 7 Simulation of activation and inactivation curves for the I_A. The decreasing curve corresponds to inactivation and the increasing curve to activation. As the membrane potential becomes less negative, its activation is greater. The simulation is in agreement with the results of Connor et al. ³⁷. 

I_A Constant-V Curves program

This program allows the user to observe the voltage dependence of the opening and closing speed constants for I_A. In the first simulation, the values entered were those reported for gastropod cells (Figure 8).

Figure 8 Simulation carried out to portray the kinetics of the velocity constant α_m with respect to the voltage. 

I_A AP Train program

The Train IA program simulates a neuron with the sum of the currents I_A, I_Na and I_K. It reproduces action potentials when the neuron is stimulated by a current pulse lasting from 50-200 ms at an intensity of 8 nA cm^-2. A test simulation to study the effect of I_A on the AP train is shown in Figure 9.

Figure 9 Simulation of the effect of I_A on the AP train. With g_A = 50 mS cm^-2, it is clearly observed how this current hyperpolarizes the neuron and decreases the AP frequency ⁽³⁹⁾. Control action potentials (utilizing Na⁺ and K⁺ channels) in black, I_A action potentials in red. 

Two simulations were performed in a row with g_A set at 50 mS cm^-2. In the first, the AP was generated in a neuron with only Na⁺ and K⁺ channels (trace in black).

In the second, the AP was triggered in a neuron that also has A-type potassium channels (red line). Note how the time between APs increases in the second. Hence, I_A delays the appearance of the AP and the frequency of the AP train decreases.

Conclusions

The three interactive computer programs described herein were able to replicate the biophysical characteristics of I_A and provide a virtual reproduction of the electrophysiological processes involved in activating and inactivating an ion current.

The corresponding oscilloscope screens showed voltage-dependent curves. The I_A AP Train program simulates the influence of I_A on an AP train, revealing how it decreases the AP trip frequency in the trace. With this simulator, the effect can be observed of increasing or decreasing g_A (channel conductance), modifying time constants, and altering the kinetics of the speed constants, among other phenomena. The simulators should be considered a teaching tool and do not replace the professor.