# Simple circuit question (cell membrane)

1. Nov 4, 2014

### Qroid

Hi all - I'm preparing a presentation that includes circuit diagram stuff, and it's been a very long time since I've done any of that.

For this circuit, http://alford.bios.uic.edu/Images/586 images/circuit model (i.e. a circuit model of an isolated patch of cell membrane), I read that "there can be no net current flow between the outside and inside, and the current across the parallel circuit components sums to zero" (paraphrasing).

First, is that right? If so, is it right at all times, or is it averaged over a long time? Can charge momentarily accumulate at the outside or inside?

Many thanks. Happy to clarify if I've made anything unclear.

2. Nov 4, 2014

### Staff: Mentor

What kind of file is that? My browser does not know how to open it.

3. Nov 4, 2014

4. Nov 4, 2014

### Staff: Mentor

Cell polarization and depolarization is common, and yes, there is no net flow of charge when averaged over time. There is definitely a flow of charge one way during polarization, and the opposite way during depolarization:

http://en.wikipedia.org/wiki/Depolarization

:-)

5. Nov 4, 2014

### Qroid

I'm confused about this line (quoting from http://lnc.usc.edu/~holt/papers/thesis/holt_thesis.pdf): "The total current through the membrane of any neuron must always equal zero, no matter what the neuron does, because of conservation of charge. However, current may enter at one point and exit at another." I take it to mean that at any moment in time, the net current through the membrane is zero.

Is this a direct result of the circuit diagram? For the given circuit (capacitor and resistor in parallel), does the capacitative current always equal the opposite of the current across the resistor?

6. Nov 4, 2014

### atyy

There is no net flow of total current across the cell membrane in the model, even without averaging. This is because current that flows into the cell across the resistor and battery will flow out through the capacitor. However, charge can accumulate on one side of the cell membrane, since there is no true charge that flows across the capacitor.

7. Nov 4, 2014

### Pythagorean

Conservation of charge is physics; charge is never created or destoyed in the universe, it just moves around, so if charge is leaving the cell or coming into it, it has to be accounted for.

And yes, the capacitive current is always equal and opposite, and since capacitor currents are modeled with a derivative, this actually allows us to construct a system of differential equations for describing the cell in a simulation!

8. Nov 4, 2014

### Andy Resnick

I'm not sure I understand what the first image is diagramming: there is a capacitance associated with the lipid bilayer (C_m) and a membrane potential V_m, then three parallel paths associated with Sodium, Potassium, and 'I' (maybe 'l' for leak?). The second image makes more sense- a membrane potential, membrane capacitance, variable ion conductances (sodium, potassium, chloride) and a leak path. The individual driving forces on an ion is depicted as an EMF. Sodium and potassium have opposite concentration gradients, so the driving forces (EMFs) for those ions are oppositely directed.

The net current flow is said to be zero because otherwise, there would be a buildup of charge on one side of the membrane- thus, sodium current is accompanied either by movement of an anion or counter-movement of another cation. Similarly, transcellular sodium transport can be accompanied by paracellular chloride transport.

Does that help?

9. Nov 4, 2014

### atyy

As I understand it, in these models the net current flow across the membrane is zero, and there is charge buildup on one side of the membrane. At steady state, there should be a non-zero potential across the points labelled "extracellular" and "intracellular", so there should be charge separation across the capacitor. Since one side of the capacitor is on the inside of the cell, and the other side is the outside of the cell, there is charge buildup on one side of the membrane.

10. Nov 6, 2014

### Andy Resnick

Yes- the transmembrane potential is not zero. From one perspective, that's the EMF driving ion transport when a channel/transporter is activated. From another (equivalent) perspective, the transmembrane potential results from concentration gradients across the membrane created by transporters, for example Na-K-ATPase.