The Hodgkin-Huxley Model

one cell

This applet simulates the Hodgkin-Huxley Nerve Model for one cell. For information on the model equations go here

The program solves the equations and can plot all four variables of the model simultaneously. The time of integration is initially set to 40 ms but can be varied easily by changing the time value. Other parameters that can be changed are the time at which above-threshold external stimuli S1 and S2 are applied and the maximum conductance of each of the three currents. The gate variables range between 0 and 1 as described above, but they are rescaled in the plot to assist in concurrent visualization of gates and voltage.

When the program is run with the initial settings, it plots two activations produced by the two applied external stimuli, the first of which occurs after 5 ms and the second after 18 ms. When a stimulus is applied in the simulation, the voltage changes from its resting value of -60 mV to -45 mV. At this voltage the sodium activation gate m quickly opens, allowing the influx of sodium into the cell and thereby depolarizing it. As the membrane potential depolarizes, the slower sodium inactivation gate h closes, and the sodium current terminates (see the model equations, where the total current is proportional to the product mmmh ). By the time the sodium current has stopped, the much slower n gate has opened completely, generating an efflux of potassium ions that brings the cell membrane back to the rest state. The time course of the opening and closing of the gates as well as their relative speed can be seen when plotted along with the AP.

The timing for the stimuli S1 and S2 can be varied to observe how the AP changes. In particular, smaller intervals between S1 and S2 can yield interesting results if the second activation occurs before all the gate variables have time to recover completely. For example, by keeping S1 at 5 ms and changing the timing of S2 to 15 ms, the AP produced is a smaller one. If S2 is set to occur after 14 ms or earlier, no activation is produced. The explanation is simple: if a stimulus is induced very soon after an activation and the ionic gates have not had time to recover completely to their rest states, the application of a stimulus generates much less current than previously, resulting in either a smaller activation or no activation at all. This last effect is a property called refractoriness and is found in many excitable media.

With the Hodgkin-Huxley applet, we also can observe how the conductances affect the currents and consequently the AP. For example, decreasing the sodium conductance from 120 mmho/cm^2 to 70 mmho/cm^2 affects the time of rise the sodium current. If the sodium conductance is further decreased to 40 mmho/cm^2 it is no longer possible for the stimuli S1 and S2 to produce APs. We can conclude that a minimum sodium conductance is necessary to produce an activation. On the other hand, increasing the conductance too much can make the system auto-oscillatory. For example, if a single stimulus is applied, either by making S2 larger than the integration time or by setting it equal to S1, we can observe how the resting membrane potential is affected when gNa is increased. At 180 mmho/cm^2 we obtain a faster AP rise, but the resting membrane potential also is increased. When gNa is 188 mmho/cm^2 , the resting membrane potential is elevated above the threshold and the system becomes auto-oscillatory. In this regime, the larger gNa , the faster the oscillation frequency.

The chlorine conductance helps to bring the membrane potential back to the rest state following an activation. For example, in the previous case where gNa =188 mmho/cm^2 and gK =36 mmho/cm^2 , lowering gCl from 0.3 to 0.2 mmho/cm^2 suppresses the oscillations. A small negative gCl such as -0.01 mmho/cm^2 hyperpolarizes the cell by making it more negative during recovery.