So we have a sub-threshold and supra-threshold voltage level. Current injected below the sub-threshold voltage regime, it goes up and then decays to resting state. Contrary, when you inject current at the supra-threshold regime, there is spike generation. After a specific magnitude of depolarizing current, the spike won't grow any bigger (battery prevents it from doing so as well as the "h" variable, check some sections below) but it will occur earlier.
Or else, what makes the membrane of the axon excitable? Or, what enables the membrane of the axon to create spiking activity, after a certain voltage threshold is reached? Why doesn't this happen to the dendrite? What is so unique in axon that enables it to "fire" such bursts of electricity (or, these boosts of action potential)? To answer these questions, Hodgkin and Huxley developed two techniques: the space clamp and the voltage clamp.
This technique means that you take a long axon and make it electrically isopotential, meaning that when you place inside the axon an axial low resistance (an axial electrode), all the points along the axon become isopotential, meaning in turn that there is no voltage drop (Prof. Segev definition: making the (long) axon effectively isopotential via the insertion of an axial conductive wire). So the space becomes "clamped" or shrinked because of the insertion of the low conductance axial electrode.
This is a most sophisticated method than the previous one. With this, you want to clamp/fix the voltage between the inside and the outside of the membrane of the axon. So you don't want the membrane to behave independently, as it wants normally to behave and generate a spike but you want to fix the voltage to a specific preset voltage and clamp it there. And why do I want to do this? Because I don't want the action potential to interfere. The voltage clamp technique, which is a fast-feedback system, enables the experimenter to dictate the desired voltage difference between the inside and the outside of the membrane. This electronic feedback system injects current exactly to counter-balance the excitatory, voltage-dependent membrane current that the membrane wants to generate. You "feel", using this feedback system, the current the axon wants to generate to blow a spike, then you inject through this system a counter-current, of the same amount but in the reverse direction so you fix the voltage. And because now you can fix the voltage between the two sides of the membrane, you can ask the question: "what is the current that flows between the two sides of the axonal membrane for this particular, fixed, clamped voltage"? Lesson slides, here.
So first let's clamp the voltage to a value, say -50mV (check lessons slides). Then we record the current needed to fix this voltage. By doing so, we first get a capacitative current, since we have a change in voltage (remember: C=dV/dt, we have a change in V). We keep having a constant voltage step and we see that we next have a resistive current so the system basically works as a passive RC circuit. Notice that we're talking about sub-threshold depolarizing voltage here. So, for sub-threshold depolarizing voltage clamp, the recorded membrane current is the current that flows via the "leak", or the passive conductance plus a small capacitative current at the start and at the end of the circuit (again, pls check the slides, they're quite self-explanatory). But what happens when we depolarize the cell further, to the supra-threshold regime?
So, HH represented mathematically the slow response (upstroke) with (1-exp(t)) to the power of 4 and the downstroke (fast-attenuation) as exp (-4t). Then they formed the following equation: the actual potassium conductance equals to the maximal conductance (conductance of total, absolute number of potassium channels) multiplied by the factor "n" (a voltage dependent parameter). The claim was that for a particular voltage clamp, "n" gets a value between 0 and 1. So at a very big voltage clamp, "n" gets near to 1. "n" depends on both voltage and time. It represents the proportion of K ion channels in an open stage. If n=1 then all the conductance (the maximal one) is available. They also tried to explain the power of 4 (check image below and quote at the bottom of it).
It's the period between 2 spikes, the gap or delay between the first and second. So the frequency is limited in axon.
- Conductance-based models
- The HH model
- Interactive Java applet of the HH mode
- Model DB
- HH model in NEURON
- HH model