Dear Abhishek

This is a good question, and one that is rarely asked even if it is obvious and should be asked by all electrophysiologists at some point.

Simply speaking, in current-clamp, the recorded trace is a direct recording of actual membrane voltage and it is displayed in the 'correct' direction.

On the other hand, in voltage-clamp the displayed membrane current trace actually report the amplifier current injected to maintain the set membrane voltage. So what you read out as a trace is the compensatory opposite current to counter the physiological current.

It would therefore indeed be more accurate to invert the direction of the voltage-clamp recording, though this is not the convention, as you know.

Best regards

Jan

If "i" is inward current, which is assigned to be positive, "C" - membrane capacitance, "V" - membrane potential, "t" - time, and "g" - membrane conductance. Then, if we charge the capacitance, we have:

ΔV = i Δt C.

However, according to Ohm's law:

-i = g V.

In this case, more positive V increases outward current, or in our case makes inward current "i" more negative.

To simplify electrophysiological equations (to get rid of minus in the Ohm's law) the outward current current is assigned to be positive:

i = g V.

Consequently, the capacitance charging should be rewritten as:

ΔV = -i Δt C.

Now "-i" represents "minus outward" current, i.e. (-i) is still an inward current as it was before.

However, during the current clamp experiments researchers also do not like the minus, and use assumption that the inward current is positive, which allows to use the formula without minus, i.e.:

ΔV = i Δt C.

Thus, the assumption that inward current is positive is used only for convenience in the current clamp experiments. While in almost all other cases it is assumed to be negative, since this allows to use Ohm's equation without the minus.

Just to add to Jan's useful reply, a depolarizing current is always positive. In current clamp, you as experimenter get to be the one putting in the positive current, so you see it causing depolarization. In voltage clamp, as Jan said, the goal is to compensate for what is happening in the cell. When there is an inward current (from some channel or receptor opening on the cell), the voltage clamp puts in a negative current to cancel it out, to enforce the holding potential and prevent depolarization. You do not directly see the positive current entering the cell, but you can infer its presence from the negative current of the voltage clamp.

In fact, if you as experimenter want to step to a depolarized holding potential in voltage clamp, you would pass positive current, right? It is because of complicated things like this that is it better not to invert the voltage clamp trace to seek a more intuitive representation, but just leave it as it is.

Clear as mud, huh?

-Matthew

I respectfully disagree with Matthew.

Matthew wrote: "... a depolarizing current is always positive. ...When there is an inward current (from some channel or receptor opening on the cell), the voltage clamp puts in a negative current to cancel it out, to enforce the holding potential and prevent depolarization".

Again, if you are using membrane capacitance charging equation (ΔV = i Δt C), then inward (e.g., sodium) current is positive.

However, if electrophysiologists are analyzing equivalent electric circuitry of a cells with Ohm's law equation (i = g V), as well as in the voltage clamp experiments the inward current is negative. In this case more negative (hyperpolarizing) V makes the inward (sodium or calcium) current even more negative, and the outward (e.g., potassium) current less positive. Then, in a cell equivalent electric circuitry analysis the membrane capacitance charging equation changes the sign to negative (ΔV = -i Δt C).

There are differences between the membrane current and the electrode current.

In the current clamp mode the depolarizing current via an electrode is an inward current (you can call it positive if you use membrane capacitance charging equation: ΔV = i Δt C, but it is not a membrane current), which activates sodium current that is also an inward and depolarizing current, which produces the upstroke of the action potential. However, if the depolarizing sodium current would be considered "always positive" (which is correct for ΔV = i Δt C), then with more depolarized membrane potential and according to Ohm's law (i = g V) the sodium current (i_Na) would increase, but it is decreasing due to reduction of the driving force (V - E_Na).

Therefore, in this case inward and depolarizing sodium current is negative, which is described by equation:

i_Na = g_Na * (V - E_Na),

where the driving force (V - E_Na) is negative and conductance is positive.

In the voltage clamp, indeed, the current through the electrode is opposite to the sum of the membrane currents and the capacitive current. However, it is generally accepted to use the sign of the membrane current, not the electrode current.

E.g., during activation of inward sodium current by a depolarizing voltage step the amplifier injects via an electrode the fast depolarizing inward current to charge the membrane capacitance from -70 to -20 mV, e.g., and then outward current to compensate for additional depolarization caused by the activated inward sodium current and to hold the membrane potential at -20 mV. Thus, after reaching -20 mV the sum of the membrane and electrode currents is equal to zero to hold the membrane (i.e., capacitive) potential unchanged.

Therefore, in Axon Instruments' Clampex software the INWARD and depolarizing sodium CURRENT in the voltage clamp mode is depicted as a NEGATIVE current.

Thank you very much Jan Tønnesen, Anatoli Kabakov and Matthew Xu-Friedman for your detailed explanations. The doubt actually originated while reading one of the electrophysiology paper on Purkinje neurons and that is when I noticed this. I think this should be explicitly stated in textbooks/lectures while teaching !!