Action Potential Laboratory

Just as it is possible to simulate the flight of an airplane by solving the equations of flight (i.e., lift, drag, thrust, weight) and create a Flight Simulator, it is possible to simulate action potentials by solving the equations describing how the membrane potential is governed by voltage-dependent changes in Na⁺ and K⁺ channels (see equations below) and create an Action Potential Simulator.

When a depolarizing current is injected into a nerve cell, the resultant decrease in the membrane potential activates voltage-dependent Na⁺ channels. The activation of the Na⁺ channels in turn accelerates the depolarization process, producing the rising phase of the action potential. The depolarization associated with the rising phase of the action potential ultimately triggers the process of Na⁺ channel inactivation, which prevents further membrane depolarization and initiates the repolarization phase of the action potential. At the same time, the voltage-dependent K⁺ channels are activated, also contributing to the repolarizing the cell, and, in addition, producing the after hyperpolarization.

The basic equations used in the Action Potential Simulator are: $$V_m = \frac{1}{C_m}\int(I_{inj} - (V_m - E_{Na})g_{Na} - (V_m - E_K)g_K - (V_m - E_{l})g_{l})dt$$

where V_m is the membrane potential, C_m is the membrane capacitance, I_inj is the injected current, g_Na is the Na⁺ conductance, g_K is the K⁺ conductance, and g_l is the leakage conductance. The conductance of the Na⁺ channel is governed by an activation variable m and an inactivation variable h, g_Na = g_Namaxm³h and the conductance of the K⁺ channel is governed by a single activation variable n, g_K = g_Kmax n⁴

The default parameters are:

Maximum value of voltage-dependent Na⁺ conductance: 120 mS/cm²
Maximum value of voltage-dependent K⁺ conductance: 36 mS/cm²
Na⁺ equilibrium potential: 55 mV
K⁺ equilibrium potential: -75 mV
Current Injection: 28 nA/cm²

The resting membrane potential of the modeled neuron is -60 mV and the current injection is a 1-ms duration pulse starting at 5 ms with a default magnitude of 28 nA/cm². SNNAP Home Page.