Teaching and learning the Hodgkin-Huxley model based on software developed in NEURON’s programming language hoc

Reading text-books and journal papers

Students are guided through readings and static figures found in text-books and journal papers, and also figures predesigned by the instructor, with the aim of understanding the behavior of different variables. However, this strategy does not allow any opportunities for interactively exploring new results arising from variations in the different neuronal conduction parameters [6, 7].

Experimental observation

Students carry out experiments to observe the temporal or spatial evolution of the variables. This strategy facilitates the understanding of concepts related to the properties of a specific neuron or neuronal circuit, but it depends on the conditions under which the experiments were performed [8, 9]. In addition, some neuronal electrophysiological phenomena are difficult to verify experimentally.

Computer simulations

Electrophysiological phenomena can be simulated through the use of software [1–5]. This offers multiple alternatives for modifying the electrical neuronal conduction properties, environmental conditions, and neuronal geometry, and for calculating and visualizing graphically the temporal or spatial evolution of the studied variables. Thus, computational simulation is an excellent option to overcome the difficulties present in the strategies mentioned above.

The need to use didactic software became evident during the development of a course of Neuronal Electrophysiology for undergraduate students in the Medicine program at Universidad del Norte (Barranquilla, Colombia). Such software must allow for the modification of the geometrical properties of a cylindrical axon, such as its length (L) and diameter (diam). The software must also permit the modification of neuronal biophysical properties such as the properties of a squid giant axon [10]; in this work, these are called “HH” properties.

Currently, there are several specialized software packages available for visualizing neural phenomena from different perspectives. These include NEST, which uses unicompartmental models [11], and NEURON and GENESIS, which use both uni- and multi-compartmental models, thereby providing a more realistic model [12–15]. Of these packages, NEURON is the most popular, with numerous papers published in prestigious journals in the neuroscience field [16, 17]. The literature clearly shows its efficiency in developing neuronal simulations with full control of the morphological and biophysical properties.

where Q ₁₀ is a measure of the increase in the opening and closing rates of the HH ion channels when the temperature (T) rises 10°C above the laboratory temperature, T ₀=6.3°C (internal temperature of the squid giant axon) [19].

The SENB software enables simulation of the propagation of action potential through a Hodgkin-Huxley type axon. SENB also allows the user to appreciate the effect of changing the geometric parameters (L and diam) of the axon, current stimuli parameters (NoStim, Amp, Dur, and Delay), active (GNa and GK) and passive (GL, Ra, and Cm) conduction parameters, temperature (T) of the axon environment, and internal and external ionic concentrations. The effects of changing these parameters can be observed in the temporal evolution of the membrane current and potential, the leak current, the sodium and potassium current, and the gating variables, as well as in the membrane resistance, the time and space constants, the sodium, potassium, and leak equilibrium potential, and the propagation speed of the action potential. The variables related to the parameters described above are explained in the Implementation section.

Users with programming experience can develop software using a combination of hoc (an interpreter with C-like syntax [20]) and Python [21], and can add new membrane properties with the compiled NMODL language [22]. For examples of these, refer to the web page in reference [23]. This software is aimed at special cases and for use by expert users, and thus does not facilitate teaching and learning processes. Note that there is a commercially available didactic software package, called “NEURON in action” [4], which is also based on the NEURON environment.

Tool performance

The SENB software was tested using examples from scientific literature. The first example compared the results for two different temperatures, T = 6.3°C (Figure 2a) and T = 25°C (Figure 2b). The second example compared repetitive spiking when four different long-lasting current steps of constant amplitude were injected into the axon (Figure 3), while the third example compared the results for two different stimulus frequencies, fe = 253.16 Hz (Figure 4a) and fe = 100.5 Hz (Figure 4b).

FIRST EXAMPLE: As T increases, the action potential spike becomes narrower and decreases in amplitude (Figure 2). This is to be expected, owing to the fact that the opening and closing rates of the potassium and sodium channels increase as T increases [19]. Then, both the time intervals for the sodium ions to enter the axolemma through voltage-dependent sodium channels and for the potassium ions to proceed to the extracellular environment through voltage-dependent potassium channels decrease. Thus, the curves of the gating variables and current densities are narrower.

SECOND EXAMPLE: A Hodgkin-Huxley axon stimulated with a long lasting current step of constant amplitude generates a response depending on the amplitude [25]. For a small amplitude, the response is a persistent sub-threshold depolarization (Figure 3A). If the current has just enough amplitude to exceed the spike threshold, a single action potential is generated (Figure 3B). When the amplitude is greater than the threshold, a train of spikes is generated, and the number of spikes in the train increases with the amplitude of the current (Figures 3C and 3D).

THIRD EXAMPLE: For a stimuli train with short length stimuli (Dur) and tintp greater than the refractory period, each stimulus generates an action potential. However, if tintp is less than the refractory period, each stimulus does not generate an action potential (Figure 4) [10, 26, 27]. To illustrate this phenomenon, Figure 4b shows the effect of applying a train of four stimuli with tintp = 13 ms and fe = 100.5 Hz, causing the propagation of four action potentials. Furthermore, Figure 4a shows the effect of applying a train of four stimuli with tintp = 5 ms and fe = 253.16 Hz, which causes the propagation of two action potentials.

SENB in the computer classroom

A virtual experiment was carried out to verify the role of SENB as a facilitator for learning processes related to the spread of nerve impulses along an axon. In this experiment, a group of 33 students were asked to observe how the temperature and passive and active conduction properties affect the formation and propagation of nervous impulses. A test revealing the level of understanding of concepts of electrophysiology was given to the students before and after the virtual experiment. A paired-sample t-test, executed using the IBM SPSS Statistic 20 software, yielded the following results: p−value<0,001 (${\overline{X}}_{\mathit{\text{before}}}=2.82$, σ _{b e f o r e} =1.13; ${\overline{X}}_{\mathit{\text{after}}}=4.63$; σ _{a f t e r} =0.53, with the grades in the range 0.00 to 5.00). Thus, the result of the test is statistically significant. The improvement in the results shows that SENB facilitates teaching and learning of the basic concepts of neuronal electrophysiology.

Why use SENB instead of the native NEURON GUI?

There are several reasons for using SENB instead of the native NEURON GUI in the teaching and learning of electrophysiology. First, the versatile current stimuli are easily modifiable. Second, the equilibrium potentials are calculated dynamically using the Nernst equation. Third, the electrophysiological variables can be visualized in the same window, and finally, several parameters of particular importance in electrophysiology analysis are calculated by default.