At the very start of my Masters, my first experiments appeared to show that the histamine H3 receptor inhibited the release of GABA in the neocortex. It turns out, this was all lies. It was all lies because of series resistance, a concept I had vaguely heard of, but didn’t understand. If you’re just starting electrophysiology this post is for you. The hope is that by the end of this post, you will understand series resistance, and you’ll understand why it is extremely important to monitor it religiously, whether you’re performing voltage clamp or current clamp recordings.
Take Home Points
- The smaller your series resistance is relative to your membrane resistance, the closer the membrane potential will get to your command potential, given enough time. You should aim for your series resistance (after Rs compensation) to be less than 1/10th of your membrane resistance
- The membrane capacitor and the series resistances sets up a low-pass filter for your command voltage. Hence you will be able to voltage clamp faster signals when Rs and Cm are small
- Voltage clamp is never perfect, but it can be good enough. However, if Rs changes during your experiment, all currents you record will change with it, hence you must monitor it, and reject cells when it changes
In standard whole-cell voltage clamp, the goal is simple: hold the membrane potential of the cell at the command voltage (Vcmd) and tell the experimenter how much current that required, because it should be equal and opposite to any transmembrane current. However, there is one major thing that is stopping things going to plan: series resistance (Rs). Series resistance is the sum of all the resistances between the electronics in the amplifier and the inside of your cell, but in practice is made up of the resistance in the last dozen microns of the pipette and the junk that blocks up the hole between the pipette and the cell (good rule of thumb, your series resistance should be around 3x the open pipette resistance).
But why does series resistance matter? Because together with the resistance (Rm) and capacitance (Cm) of the membrane, it creates a voltage divider, that is, the voltage you are trying to apply to the cell is divided across Rs and the impedance presented by the combination of Rm and Cm. Even simpler yet, you can think of Rs as limiting the amount of current you can use to charge up the membrane. This means that the actual voltage you get inside the cell (Vout) is given by
Where Vm is the resting membrane potential. As you can see, if Rs is much smaller than Rm, then Vout approaches Vcmd, likewise, if Rs is massive, then Vout approaches Vm. This is where we can see the how the Rs < Rm/10 rule of thumb comes about. If we say Rs = Rm/10, then the above equation becomes:
Which simplifies to:
Which basically says Vout = Vcmd plus a tiny fraction of Vm. As Rs becomes a smaller fraction of Rm, the less Vm contributes to the final membrane potential.
But this voltage divider is a frequency dependent voltage divider, because capacitors let more current through when the voltage across them changes rapidly. And do you know the other word for a frequency dependent voltage divider? A filter, in this case a low-pass filter. The corner frequency of this filter is given by a pretty awful looking equation:
But if Rs is much smaller (about 10x less) than Rm, you can approximate the cut-off frequency of the filter with the much simpler
(A little helpful note, if Rs is in MΩ and Cm is in pF then the answer is in MHz).
To the right you see what this means. If we compare the ratio of the voltage across the cell membrane to the command voltage (Vout/Vin), we can see the effect of Rs on how good out voltage clamp is. Perfect voltage clamp would produce a horizontal line at Vout/Vin = 1, meaning that no matter how fast you tried to change the command voltage, the membrane potential would follow it perfectly. But instead what you see is what I described above: even at very low frequencies (e.g. constant voltages) when the series resistance is high the membrane potential does not even come close to the command voltage. You also see that as Rs increases, the filter becomes more aggressive, meaning that even relative slow voltage changes cannot be achieved. In the case illustrated, of an 100MΩ/100pF cell, when Rs is 40MΩ, you are beginning to fail to voltage clamp at the relatively glacial frequency of 10 Hz.
This may still seem relatively academic at this point, so let me really try to show you what this means. To the right you can see what happens when you try to voltage clamp a modeled synaptic current as Rs increases (the synaptic event is current based, rather than conductance, so it is the same no matter how bad the voltage clamp is). I have flipped the synaptic current, so they’re easy to compare. You see that even in the relatively ideal case of Rs = 10MΩ the measured current is a lot smaller than the real current. In part this is unfair because this current is instantaneously rising (and as the previous figure showed, fast changes are the enemy of any voltage clamp), so note how the decay of the current is relatively well captured in all cases. However, the point is, if you had been performing voltage clamp, and your Rs had changed from 10MΩ to 20MΩ, the current you would have measured would have dropped by about 15%. If you had been washing on a drug at the time, you might think that the drug caused that reduction (which is exactly what happened to me). Hence why I am always a lot more convinced by any long term voltage clamp experiment that shows Rs as a function of time, along with any other measurement (e.g. Fig 1 here).
Of course, not only does Rs effect the current you end up recording, but it has big effects on the amount of unclamped voltage generated by any transmembrane current. To the right you see the size of the EPSP our synaptic current would produce in the absence of voltage clamp. In a perfect world this would be a flat line, i.e. the voltage would be clamped. But when Rs = 40MΩ, you can see that the EPSP produced is nearly half the size of the unclamped potential, i.e. this is not voltage clamp at all, but really some weird thing half way between current clamp and voltage clamp.
Finally, it’s worth mentioning that series resistance compensation allows us to minimize all of these effects (but not remove them). Specifically, if you have a real Rs of 20 MΩ, and then you perform series resistance compensation to 75%, then your series resistance will appear to be 5 MΩ. It’s also important to remember that in large cells, you run into space clamp problems, where you are unable to voltage clamp distal parts of the cell (you can think about the distal sites being behind another series resistor, this time formed by the resistance down the cytoplasm of the dendrite), but that is a whole other story.
For me, voltage clamp is no different that most science: you are not measuring perfectly and your measurements are just an approximation of the real thing. The important thing is to know when the approximation is good, and when it is bad, e.g. Voltage clamp recordings from cereballar granule cell (Cm = 5 pF, Rm = 1000MΩ) give you a good approximation of transmembrane current. But even if those good cases, when Rs changes, even a constant transmembrane current will appear to change, and that is really bad.
Below you can adjust the properties of your voltage clamp system, and see how good you voltage clamp should be.
Take Home Points
- A combination of the pipette capacitance and the series resistance sets up a low-pass filter for membrane voltages
- This filter works at a much higher frequency that the filter effecting voltage clamp
- Again, you should monitor it, as it can change the features of the voltages you are trying to measure
People often forget about the effect of Rs on current clamp recording, outside of bridge balance (which I very much hope you understand, but if you don’t, the simple thing is that when you inject current, it falls across the series resistor, meaning that you record a voltage that is the sum of the transmembrane voltage and the voltage across the series resistance. Bridge balance subtracts that voltage). But in a fashion very similar to in the voltage clamp case, series resistance effects the nature of filter that messes with your ability to record cellular properties. However, in current clamp, the capacitor that is involved is the capacitance formed by the pipette (Cp). Essentially, in current clamp, Rs limits how quickly the cell can charge Cp, which limits your ability to monitor fast voltage changes. The other resistance that is important is the input impedance of the amplifier, which I have labelled Rp. This represents how much current the circuitry in your amplifier draws.
Because the capacitor in question is much smaller (Cp < Cm), the frequencies where this filter starts to kick in are much higher, but action potentials are pretty fast voltage transients. As you can see in the figure to the right where we plot the ratio of the recorded voltage to the actual membrane potential (Vout/Vm), in the case where Rs = 100 MΩ, even signals around 100 Hz are being filtered, which will really filter action potentials (remember, the frequency components that make up the action potential are much faster than the rate at which action potentials occur). Furthermore, as Rs and Rp are in series they forms a voltage divider. Note how even at very low frequencies, where Rs is very high, the curve doesn’t quite reach 1? That shows that we are not even recordings the resting membrane potential accurately. Don’t believe me, need more proof?
Here we see how series resistances effects the ability to record a simple action potential. Clearly, even a relatively modest series resistance start to effect the ability to record action potentials. Likewise, the resting membrane potential is slightly depolarized as Rs gets very high. Potentially the Rp I have included in the model is a bit low, but it’s not massively too low. Moreover, the point remains, Rs, Cp and how much current your amplifier draws creates a filtering system, and if Rs changes, the filter changes. Your amplifiers capacitance neutralization is there to minimize this effect, but it only works if everything is set correctly (and it still only minimizes the effect).
So long story short: In voltage clamp, series resistance prevents your amplifier from charging the membrane capacitor, and in current clamp, series resistance stops your cell from being able to charge the capacitance of your pipette. These things are bad, but what is worse is when it changes over time. So monitor your series resistance constantly throughout your experiment.