A Brief Introduction to the Patch Clamp Technique and the Hodgkin–Huxley Equations

Patricia Martínez Díaz 

6. April. 2021

Hello and welcome back!

Now that we had explained some of the basics of electrophysiological modeling in the previous posts, this time I am going to talk about the Patch clamp technique and to further explain the equations that describe the action potential of an electrical cell, known as the Hodgkin-Huxley equations.  You might recall that Hodgkin–Huxley modeled the neuron of a squid’s giant axon. They did this by using an electrical analogue circuit of the cell membrane and also by applying Ohm´s law in order to calculate the voltages and currents in the circuit.

1. The Patch Clamp Technique

Hodgkin–Huxley recorded the action potential from inside of a nerve cell through an in-vitro experiment. One of the most popular methods used to study ionic currents is the patch clamp technique. During this assay, a tiny glass pipette suctions the cell membrane creating a “patch” and isolates the membrane, as seen in the image below. An amplifier is connected to the pipette and allows to record the current of the patch. A nice animation explaining the patch clamp technique can be seen in the following video.

Figure 1. The Patch clamp technique recording changes in ionic currents due to opening or closing of ionic channels. Obtained from: https://www.youtube.com/watch?v=mVbkSD5FHOw

2. An introduction to the Hodgkin-Huxley equations

Take a look at the following image:

– What do you see?

– Can you recognize all the elements in the circuit?

This is the electrical analogue circuit used to explain the voltage changes in the cell membrane caused by ionic gates kinetics and it is similar to the one proposed by Hodgkin–Huxley. It has 2 nodes, represented by the black points in the diagram, and 4 different paths arranged in parallel representing the currents of the sodium channel (INA), Potassium channel (IK), Leakage current (IL), caused by the experimental method itself, and the current through the cell membrane.

Using node analysis, it is possible to calculate the total transmembrane current (IInter), which is the sum of all the currents passing through each of the branches, as described in the following equation:

Figure 2. Electrical analogue of the cell membrane
ENa = 50 mV; EK= -88mV; EL=-54 mV; Cm= 1µF; GNamax= 120 mS; GKmax= 36mS; GL= 0.3 mS

Where ENa represents the Nerst potential of the sodium ion, EK for the Potassium ion and EL for the Leakage current. These values are more or less constant and can be obtained by looking at some papers in the literature. An interesting point of this equation is the conductance of the ionic channels, symbolized by the letter G. The electrical conductance is the measure of how easy the current flows through an object. In the previous equation  GNa represents the conductance of the sodium channel, G of the potassium channel and GL of the leakage current.

Additionally, when the membrane voltage (Vm) is known as well as the conductance Gx of an specific ion X, it is possible to calculate the current Ix.  However, you would still have to bear in mind that the conductance of the ionic gates is not constant and it changes throughout the time, meaning that sometimes the gate is close and sometimes it is open.  You can also see that when calculating the current passing through the capacitor, the current is equal to capacitance of the membrane times the derivative of the voltage with respect to time. This means that in order to solve our equation we will need to use some differential equation solving methods. In the following post we will talk about the conductance of the ionic channels and how to use these methods to solve our system.  Thanks for reading and until next time!

3. References

  1. Hodgkin AL, Huxley AF. Action Potentials Recorded from Inside a Nerve Fibre. Nature. 1939 Oct 1;144(3651):710–1.
  2. The Patch Clamp method. Available from: https://www.youtube.com/watch?v=mVbkSD5FHOw.
  3. Seemann G (2005) Modeling of electrophysiology and tension development in the human heart. ISBN: 3-937300-66-X

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