Mechanisms responsible for the cell resting membrane potential

This chapter is vaguely relevant to Section E(i) of the 2017 CICM Primary Syllabus, which expect the exam candidate to "explain mechanisms of transport of substances across cell membranes". Though the words "resting membrane potential" never appear in the college grimoires, Question 14 from the second paper of 2017 dedicated 60% of the marks to this topic area. Specific areas of detailed knowledge expected by the examiners were an understanding of "selective permeability of the membrane, electrochemical gradients and active transport mechanisms". Beyond that, the trainees were only expected to "demonstrate awareness" of the Nernst equation and the Goldman-Hodgkin-Katz equation. 

The struggle to maintain some sort of exam relevance and topic focus has always been something of a challenge for this author, and this issue becomes more prominent wherever the attention from the college examiners is perceived to be mismatched with the apparent importance of the chapter topic. So it is with the resting membrane potential, which is fairly fundamental to virtually everything in medical biology. One would be justified in saying that the basic purpose of all life on Earth is to forcefully prevent ions from settling down to a nice electrochemical equilibrium on either side of a membrane. However, to protect exam candidates from this sort of talk, the important SAQ answers have been concentrated in this grey box. 

In summary:

 

If one needs an authoritative resource for this information, one should go to the official college textbooks. Chapter 1 of the 23^rd edition of Ganong's Review of Medical Physiology or Chapter 5 from Guyton & Hall (mine is the 13^th ed) both do an equally thorough job of explaining this concept. If this resource recommendation is for some reason unacceptable, the excellent article by Stephen Wright (2004) should probably be the next most important reference, as it is an earnest attempt to teach the teacher, i.e the article aims to describe to physiology instructors the best way to explain the resting membrane potential to undergraduates. Beyond that, Molecular Biology of the Cell (4th edition) has a section on this in Chapter 15 (section 4) by Harvey Lodish, which is available for free from the NIH. Lastly, if there is ample leisure time, Nicholas Sperelakis' Cell Physiology Source Book devotes an entire chapter to this issue (p. 219-242 of the 3^rd edition); this is probably the nearest thing to a single definitive reference, as it covers the topic in exhausting detail.

Definition of the resting membrane potential

The college examiner comments to Question 14 from the second paper of 2017 mentioned that "a good answer included a definition of the resting membrane potential". As usual, there is no official definition and most textbooks define it as 

"the voltage (charge) difference across the cell membrane when the cell is at rest."

In short, it is the charge difference between the inside and the outside of the cell.

The whole "at rest" component of the definition comes from the fact that most textbooks use this concept to segue into a discussion of action potential propagation, and so it becomes important to explicitly define this membrane potential as the "resting" state of an excitable cell, as opposed to the membrane potential of a cell which has just depolarised. 

So, what is the resting membrane potential of a typical cell? Everywhere you find a slightly different millivolt value. For example, elsewhere in this chapter the "default" value for the resting membrane potential of a "typical" cell is listed as being -90 mV.

This, of course, is wrong. The reason this fallacy is propagated here is largely because of the fact that Guyton & Hall use this value, and the CICM examiners will probably expect their exam candidates to quote from that official textbook. However, for the rest of us, it is important to acknowledge that there is a rather large range of different resting membrane potential values, depending on which cell one is looking at and on the extracellular fluid composition in its immediate microenvironment. Sperelakis (2001) offers a table of values in his textbook, which is reproduced here without any specific permission (and it is unclear which references these values come from). As you can see, the Guyton & Hall value (-90 mV) probably refers to the frog muscle myocyte, a favourite instrument of cell physiologists. Other textbooks (eg. Molecular Biology of the Cell, 4^th ed) use -70 mV, referring to the human neuron (usually a discussion of action potentials follows). 

Chemical gradients of ions across the cell membrane

As already discussed elsewhere, the composition of the intracellular fluid is significantly different to the composition of the extracellular fluid. The diagram below is borrowed from Ling et al (1984), and though the subjects were frog muscle cells, the general gist of this is probably generalisable. 

Let's just ignore the anions for a moment. Their time will come.  For now, let us say that because of the difference between intracellular and extracellular ion concentrations, there is a chemical concentration gradient between the two compartments.

If the membrane was perfectly impermeable to ion transport, there would be no traffic possible and the sodium and potassium ions would politely stay on their side of the barrier. Unfortunately, the membrane is selectively permeable, and ions are able to make their way across. 

Membrane selectivity to ion diffusion

Without killing SEO by revisiting material available elsewhere on this site, it will suffice to say that the lipid bilayer of the cell membrane is a non-polar barrier and therefore quite effectively prevents the exchange of polar substances between the intracellular and extracellular environments. The cell membrane, therefore, maintains its permeability to ions by protein-facilitated diffusion; i.e. ion channels permit traffic of ion species across the membrane.

This is the next most important concept to absorb: the cell membrane is not a totally ion-impermeable structure, and controlled movement of ions across the membrane does occur. Though sodium channels do exist, they are few - and so typical animal cells are mainly permeable to potassium ions,  because of the presence of "leak channels".  These potassium channels are open at al times, at all membrane potential voltages (i.e. these are not voltage-gated channels), and they have no natural gating ligands, nor are they affected by any of the conventional potassium channel blockers. Lesage et al (2000) describe them in greater detail (in summary, they are dimeric two-pore-domain channel proteins, also known as K_2P channels, and there are about 15 families of them currently identified). 

Thus, the presence of these channels allows a continuous slow leak of potassium out into the extracellular fluid, along the chemical concentration gradient. 

Electrical gradient across the cell membrane

Before we brought ion channels into the discussion, the electrical neutrality on either side of the membrane was well maintained.

In other words, the equal concentrations of positive and negative ions on each side of the cell membrane means that the charge of each compartment is zero volts, and therefore there is no potential difference between the compartments.

Obviously, with potassium ions leaking across the membrane in one direction, it cannot stay that way.

As potassium ions leak out of the cell, they carry their positive charge with them. As a consequence of losing these potassium ions, the intracellular fluid becomes negatively charged relative to the extracellular fluid. Thus, the effects of the chemical concentration gradient across this semipermeable membrane also creates an electrical potential difference.

Equilibrium of electrochemical gradients across the cell membrane

Ordinarily, a leak of molecules across a membrane would culminate in equilibrium, i.e. where the molecules equilibrate into equal concentrations on either side of the membrane. However, this cannot happen in this case, because the potassium ions are positively charged. As they leak out of the cell, the intracellular fluid will become progressively more and more negatively charged, and some potassium ions will be attracted back into the cell by the forces of electrostatic attraction. There are, therefore, two opposing forces acting on potassium ions across this membrane. 

One might, therefore, imagine how the stream of potassium ions flowing out of the cell slows down and eventually becomes balanced with the flow of potassium ions back into the cell. One might even use the term electrochemical equilibrium to describe this balance. In fact, if one were inclined towards hardcore maths, one might be interested in some sort of formal mathematical representation of this equilibrium. At this stage, the groaning CICM exam candidate must make themselves familiar with the Nernst equation.

The Nernst Equation

This is the relationship of electrical and chemical forces acting on any ionic species across a semipermeable membrane. It is attributed to Walther Hermann Nernst, a bespectacled German scientist whose other achievements included developing some relatively ineffective chemical weapons for the Germans during World War I, and becoming one of the few scholars to receive a Nobel Prize while remaining officially recognised as a war criminal. 

One may find a more scientific discussion of the Nernst equation in the article by Stephen Wright (2004), which is free from those sorts of digressions. 

Basically, this version of the equation gives you a value (V_K) which is the potential difference (in volts) which opposes the force of a chemical concentration gradient for charged ions. [K] is used here because potassium is the ion of interest in this discussion. By substituting values for known constants and values (eg. the valence of potassium ions being 1+, and body temperature in Kelvin) one can simplify this equation into something which is hopefully more susceptible to being memorised by a half-crazed CICM exam candidate:

If one were to substitute commonly expected values for the intracellular and extracellular concentrations of potassium, we could work out what potential difference would be generated across a membrane. Wright (2004) uses a 10:1 gradient (i.e. 100 mmol intracellular and 10 mmol extracellular concentration) for illustration purposes; where the gradient is 10:1 the potential difference achieved at equilibrium is about 61 millivolts.  This potential difference is the "Nernst potential" for any given ion, and it increases whenever the ratio of concentrations increases (i.e. the greater the difference in concentration, the greater the Nernst potential required to maintain electrochemical equilibrium). 

At this stage, it is important to mention that the magnitude of the actual ion flux across the membrane is actually quite small. The colourful diagrams might suggest that potassium ions are spraying wildly out of the cell, and the potassium "leak" channels at least imply that there is a measurable rate of  ions constantly diffusing out of the intracellular fluid, but in actual fact the molar mass of potassium making its way across those K_2P channels is so small that it cannot be measured by any conventional methods. The reason for this is the relatively large charge of each individual ion: each 1 mmol of monovalent  K⁺ carries approximately 100 coulombs of charge. Without going into excessive detail, one may summarise by saying that to generate a 60 mV potential difference across one square centimetre of cell surface, 6 × 10⁻¹³ mol of potassium ions need to cross the membrane - a quantity so small that no earthly instrument can measure it. 

In discussing this, we have so far focused on potassium ions as if they are the only ions getting across the membrane. Potassium is the largest contributor to the resting membrane potential, but there are plenty of other ions inside and outside the cell, and the cell membrane is (at least slightly) permeable to all of them. Because of this, the Nernst equation is an imperfect representation of the total electrochemical equilibrium at the cell membrane surface. It can only give us individual Nernst potentials for one ion at a time:

Ion species	Nernst potential
K+	- 94 mV
Na+	+ 60 mV
Ca2+	+ 130 mV
Cl-	- 80 mV

So, what is the overall effect of all these ions and their electrochemical concentration gradients? A much meatier equation is required, something which takes into account all the other ionic species.

The Goldman-Hodgkin-Katz Equation

Obviously, when you start talking about a selection of different ions, several additional factors will need to be taken into account:

• Valence of these extra ions
• The polarity of their electrical charge (so far we've been dealing only with positively charged potassium)
• Different concentrations of these ions on the inside and the outside of the cell
• Different membrane permeability for each ion species

To account for all of these, obviously some mutant version of the Nernst equation will be required. That is the Goldman-Hodgkin-Katz Equation. 

The main difference between this and the Nernst equation is the presence of additional ions and the addition of the P variable, which is the membrane permeability constant. If that permeability constant was zero for everything other than potassium, then all those other ions would mathematically disappear from the equation and it would revert to looking like a normal Nernst equation. 

Contribution of ionic species to the electrochemical equilibrium 

In fact, those other ions may as well disappear, for all the influence they exert on the resting membrane potential. The permeability of the membrane for potassium ions is orders of magnitude greater than for other ions.  For "normal" cells bathed in "normal" extracellular fluid, the ratio of potassium concentration is about 35:1, for which Guyton & Hall quote a Nernst potential of -94 mV.

Now, when you add the contribution from sodium (which has a Nernst potential of +61 mV), the combination of the two only gets you to an intracellular potential of -86 mV, i.e. it does not really budge. This is because the permeability of the membrane to sodium is so poor that sodium movement into the cell is minimal, compared to the movement of potassium out of the cell.

Guyton & Hall also mention that the Na⁺/K⁺ ATPase plays a minor role in the origin of the resting membrane potential. By pumping 2 potassium ions into the cell while pumping 3 sodium ions out, each time the pump cycles it removes a positive charge from the intracellular fluid, thereby increasing the negative intracellular potential. According to that textbook, the contribution of this phenomenon to the total resting membrane potential is the change from -86 mV to -90 mV, i.e. a fairly minor concentration. These numbers probably come from studies like Miura et al (1978). The investigators blocked the Na⁺/K⁺ATPase of canine Purkinje fibres using ouabain, and found that the resting membrane potential changed from - 83.6 mV to 78.8 mV as the result of this effect.

So, what about chloride? The apparent unfair focus on sodium and potassium in the discussion of electrochemical gradient seems to completely ignore the existence of chloride ions. This is actually quite reasonable. In most mammal cells there are no active chloride pumps, and the concentration of intracellular and extracellular chloride is distributed passively according to the Goldman-Hodgkin-Katz equation. Negative extracellular charge repels negatively charged chloride ions, and so one might expect there to be fewer of them inside the cell. This is true:  with a membrane potential of around -90 mV and an extracellular chloride concentration of around 100 mmol/L, the intracellular chloride concentration is expected to be around 5.0 mmol/L (Sperelakis, 2001- p.224).