# Are living cells electrically neutral?

I found random scientific table which had a comment attached:

the cells must be electrically neutral.

Per my knowledge whole intracellular solution contains more electrons than protons (definition of negative charge) when cell rests and extracellular space is more or less electrically neutral, means it contains same number of protons and electrons at any time.

Could someone tell me whether my understanding is wrong or this comment below this scientific table I shared?

There are two ways to think about the "charge" of a cell. One way is by looking at all the chemical species inside the cell and calculating their sum charge. If you do this, you're going to get a neutral solution up to many decimal points of rounding error. Therefore, we don't really care or bother to do this. You'll get the same for the extracellular space, and really anywhere else you measure outside of a physics experiment. Electrical forces are incredibly strong, and when you get even modest charge separation the result is lightning.

In a table like is presented at your link, you can sum up some of the "major" anions and cations but you won't get anywhere near neutral; the comment is just making sure you don't think that based on the table there are no other charges there, we just don't care about them that much for membrane potential, they're boring and static. The reason we don't care about all the other ions so much when we calculate membrane potential is easy to see from the equations that actually tell us about membrane potential. Take the Goldman equation:

In this equation, you'll see we don't sum all charges inside and outside the membrane. Instead, we look at the ratio of concentrations of ions multiplied by their permeabilities through the membrane; anything that isn't permeable gets multiplied by zero and we ignore it entirely. The reason for this is that the potential across a membrane we measure isn't because there are measurably more or fewer positive or negative charges on either side, but that there is an imbalance in permeability of ions relative to their charge and concentration. Without any electrical forces involved, ions will tend to diffuse until their concentrations are equal on both sides of a membrane. However, if there is charge involved, the net diffusion is influenced by electrical forces such that for each ion there is some voltage at which the net movement of that ion is zero even though the concentration is not equal: that's the reversal potential for that ion calculated by the Nernst equation. The Goldman equation gives the weighted sum of all of those ions that can transit the membrane to give the overall equilibrium potential when there is zero net flow of charged ions.

I'll recapitulate the reference I quoted from Alberts et al here:

For a typical cell, 1 microcoulomb of charge (6 × 10^12 monovalent ions) per square centimeter of membrane, transferred from one side of the membrane to the other, changes the membrane potential by roughly 1 V. This means, for example, that in a spherical cell of diameter 10 μm, the number of K+ ions that have to flow out to alter the membrane potential by 100 mV is only about 1/100,000 of the total number of K+ ions in the cytosol.

Extrapolating from that, if we really only had the ion species in Table 11-1, what would that mean? Intracellularly, that table shows about 140.5 mM of net positive charge inside the membrane. 10 um sphere * 140.5 mM * 6 * 10^23 ions/mol = about 3.5 x 10^11 positive ions to move over 1.3 x 10^-5 square cm of membrane. 3.5 x 10^11 / (1.3 x 10^-5) / (6 x 10^12) = about 4500 volts to get to neutral - there aren't any biological voltages anywhere near that range.

Back to the title question:

Are living cells electrically neutral?

Yes, if we think about the summed charges inside the solution of a cell. However, if you look across the plasma membrane of a cell, you will find there is a miniscule charge separation at rest, principally because membranes are permeable to potassium ions and there are more positively charged potassium ions inside cells than outside of them (for most cells and solutions). Because a few more potassium ions flow out of the cell than flow in, there would be a little more positive charge flowing out than in if the voltage were zero; this creates a voltage across the membrane until there is a balance between charge and concentration gradients, and we say that most cells are electrically negative (in a typical range of -50 to -100 mV for mammalian cells). However, this is just charge sitting across the membrane that acts like a capacitor, you'll find positive charges sitting against the outside of the membrane as they get pulled toward the negativity inside the cell.

Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., & Walter, P. (2002). Ion channels and the electrical properties of membranes.

• Thank you for clearing out these misconceptions. Now I've understood that resting potential (~-70mV) what is commonly suggested by many sources, is potential difference across membrane (so charge difference in regions near membrane), which does not mean that whole cell is negatively charged. But, Could you elaborate more around why cell (let say at rest) is thought to be neutral at default? Why even small charge could not it have? Would it actually be similar to lighting phenomenon? Commented Sep 30, 2021 at 16:42
• @LashaBukhnikashvili I don't really know what to say besides what I've already written in this answer. It's not perfectly neutral, but it's so close you might as well consider it as such. There's just no process to create any substantial level of charge separation, biologically or otherwise. Commented Sep 30, 2021 at 16:45