Mitochondrial Membrane Potential Attracts Potassium⁈

[Travis]

A definitive account of the membrane 'pump' idea has been published by Gilbert Ling.

Ling, Gilbert. "History of the membrane (pump) theory of the living cell from its beginning in mid-19th century to its disproof 45 years ago--though still taught worldwide today as established truth." Physiological chemistry and physics and medical NMR 39.1 (2007): 1.​

It has been thoroughly destroyed by Gilbert Ling.

But why are higher concentrations of K⁺ found within the cell? and why does Na⁺ seem to be excluded. Why does this so-called "active transport" reversed upon the death of the cell. This has been explained in a few ways, but I think the the mitochondrial membrane potential (ψm) is what is directly responsible for this. This potential has been shown to attract positively-charged ions.

Logan, Angela, et al. "Assessing the mitochondrial membrane potential in cells and in vivo using targeted click chemistry and mass spectrometry." Cell metabolism 23.2 (2016): 379-385.​

The mitochondrial membrane potential is negative, generally around −150 mV.

The mitochondrial membrane potential (Δψm) is central to the organelle’s many functions. As electrons pass down the respiratory chain to oxygen, the difference in reduction potential drives proton pumping across the inner membrane, generating a proton electrochemical potential gradient comprising a pH gradient (∼0.8 pH units/50 mV, basic inside) and a Δψm (∼120–180 mV, negative inside); thus Δψm is by far the dominant component. ―Logan

This has has been accurately measured in a very interesting, and insightful, ways:

For this we direct probes to mitochondria using a triphenylphosphonium (TPP) lipophilic cation (Figure 1B). The large hydrophobic surface area of the TPP cation enables its rapid, several-hundred-fold accumulation into cells in response to the Δψ and from there into mitochondria in response to Δψm (Figure 1B). ―Logan

These authors used two positively charged molecules which were attracted to the negatively-charged mitochondrial membrane. These were immobilized on the membrane, and the two cations reacted with eachother forming a stable molecule. The selectivity was ensured by having an azido group on one molecule, and an alkyne groups on the other. This reaction is selective. The stable product is then simply measured by mass spectrometry.

Therefore every 1 mV Δψm increase accelerates mitochondrial MitoClick formation relative to that in the cytosol ∼800-fold at 120 mV and ∼80,000-fold at 180 mV. This leads to an 8% compounded increase in MitoClick formation per mV, making very small relative changes in Δψm easy to assess (Figure 1C). ―Logan

You might think that it would just as easily attract Na⁺ as K⁺since they both have the same charge. Gilbert Ling explains this partially by the fact that Na⁺ is actually bigger if you consider the hydrated radii—taking into account the ordered shell of water that surrounds it. Considering this associated water, this would actually give the K⁺ hydrate a higher charge/mass ratio and higher charge/volume ratio.

The 'membrane pump' theorists hypothesize any number of Rube Goldbergian approaches in which ATP, with the help of a high-energy phosphate bond (a misnomer), transfers energy to 'pump' sodium out of the cell. The reason they bring ATP into this is because it has been shown to raise the intracellular K⁺/Na⁺, but this could be explained in other ways. Also, ATPase activity has been shown on the cell membrane; but this is not a very selective reaction and it ATP spontaneously dissociates even in just plain water. The ATP/ADP equilibrium is pH-dependent.

So with a negative mitochondrial membrane potential (−ψm), which one would be expected to be more attracted to the mitochondria: Sodium or Potassium? Which would be expected to accumulate?

Potassium has a quicker electrophoretic migration time:

Beck, W., and H. Engelhardt. "Capillary electrophoresis of organic and inorganic cations with indirect UV detection." Chromatographia 33.7 (1992): 313-316.
​

It comigrates with ammonia. This is a consistent finding. Another study shows the same:

It is always the quickest to migrate towards a negative charge, even among a series of fifteen cations. Even with constant diffusion, you might expect a higher K⁺ concentration within the cell based on this principle alone. The negative membrane potential would constantly enrich the cell with K⁺ until the electron transport chain stops. This is cell death; only then Na⁺ becomes equilibrated.

Tryptan Blue is probably the most common way to measure cell death. When a cell is living, it actively 'excludes' trypan blue. At cell death, it takes-it-up within. This can be visualized. Before I had seen the structure, I had hypothesized that it was negatively-charged. This turns-out to be true. Although it has a few amino groups, it has enough sulfonic groups to compensate—resulting in a net negative charge.

Anderson, Lucy M., and William H. Telfer. "Trypan blue inhibition of yolk deposition—a clue to follicle cell function in the cecropia moth." Development 23.1 (1970): 35-52.​

The observed activities of trypan blue in the cecropia follicle are in keeping with its chemical nature. Trypan blue is a disazo dye bearing free amino and sulfonic acid groups; it has a net negative charge. ―Anderson

Negatively-charged trypan blue molecules—and perhaps most, if not all, anions—are repelled during normal metabolism by the negative mitochondrial membrane potential. I can assure you that this is not a failure of an ATP-driven Trypan Blue membrane exclusion-pump (Trypan-ATPase⁈).

Jens Skou had won a Nobel Prize for isolating an enzyme that hydrolyzed ATP. It was found on the cell membrane. This enzyme was actually named before it had even been found based on it's presumed function, as a verb. It became a noun only later, after isolation. But a unicorn is also a noun; and just having purified enzymes does not necessarily mean that they do what you give them credit for within the cell. Standard enzyme assays cannot work with Na⁺/K⁺-ATPase because it needs a membrane to work. You cannot prove that this particular enzyme works in standard fashion.

Here are some quotes from his Nobel Lecture:†

The closest I could come was that A.I. Hodgkin and R.D. Keynes had shown that poisoning giant axons with dinitrophenol, cyanide or azide, decreased the active transport of sodium, suggesting that high energy phosphate esters are the substrate. ―Skou

Dinitrophenol also lowers the mitochondrial membrane potential. This would be expected to reduce the influx of K⁺.

Scaduto, Russell C., and Lee W. Grotyohann. "Measurement of mitochondrial membrane potential using fluorescent rhodamine derivatives." Biophysical journal 76.1 (1999): 469-477.​

...as a function of time as mitochondria are progressively deenergized by increasing concentration of dinitrophenol in the presence of TMRM. [...] ...in media containing 10 mM glutamate and 5 mM malate as substrates. Also added was either 0, 1.25, 2.5, 5, 10, or 20 M dinitrophenol to lower the membrane potential. ―Scaduto

This is a common finding:

Ionophores that dissipate the mitochondrial membrane potential, such as valinomycin (for potassium ions), p-trifluoromethoxyphenylhydrazone (FCCP, for protons), and dinitrophenol (DNP, for protons), ―Scaduto‡

By depolarizing mitochondrial (and in part plasma membrane) potentials with the protonophores 2,4-dinitrophenol and carbonyl... ―Piwnica§

And cyanide does the same by attaching to heme's iron centre, inhibiting the electrical reduction of oxygen and subsequent metabolism

Azide is an inhibitor of the electron transport chain:

Johnson, Lincoln V., et al. "Monitoring of relative mitochondrial membrane potential in living cells by fluorescence microscopy." The Journal of Cell Biology 88.3 (1981): 526-535.​

Examination of living cells by fluorescence microscopy after exposure to fluorescent probes reveals that cationic compounds such as rhodamines 3B, 6G, and 123, cyanine dyes, and safranine 0 are selectively accumulated by mitochondria (Fig . 1) [...] ...or cyanine dyes followed by mounting in medium containing inhibitors of electron transport such as azide, cyanide, antimycin A, or rotenone also leads to the release of fluorescent dye into the cytoplasm .

Notice that the only one which increases mitochondrial membrane potential also increases dye ingression. In this case, a positively-charged dyes were used. This is the reverse of the anionic trypan blue exclusion.

I told him about the Na⁺ + K⁺ activated crab nerve enzyme, and that it seemed to be part of the sodium pump. His reaction suggested to me that this was more important than surface spread enzmes. "Is it inhibited by ouaban"? he asked "What is ouabain" was my reply. He then told me that Schatzmann in Switzerland in 1954 had shown that cardiac gycosides, of which ouabain is the most water soluble, specifically inhibits the active transport in red blood cells. When Robert Post came to Aurhus after the conference I had the answer. The enzyme was inhibited by Ouabain, even if the sensitivity of the crab nerve enzyme is much lower than the sensitivity of the transport in red blood cells. ―Skou

Much has been made of ouabain on Na⁺/K⁺-ATPase. Skou cites this as an important step towards discovery in his Nobel Lecture, but it is a very weak inhibitor of this enzyme.

Erdmann, Erland, and Wilhelm Schoner. "Ouabain-receptor interactions in (Na⁺/K⁺)-ATPase preparations from different tissues and species Determination of kinetic constants and dissociation constants." Biochimica et Biophysica Acta (BBA)-Biomembranes 307.2 (1973): 386-398.​

3. Dissociation constants of the ouabain-receptor complex are 10- to 100- fold lower than the ouabain concentrations necessary for half-maximal inhibition of the (Na⁺/K⁺)-ATPase. The stoichiometry of [³H]ouabain-binding sites: phosphorylated intermediate varied between 4 (guinea pig kidney) and 1 (beef enzymes). It is assumed that the ouabain receptor and the ATP hydrolysing subunit are not tightly linked. ―Erdmann

Ouabain is a very old drug and its effects can probably be best explained as a mineralcorticoid antagonist. It is very similar to aldosterone and looks absolutely nothing like ATP, the substrate for Na⁺/K⁺-ATPase.

In early attempts to describe how ouabain influences sodium compartmentalization, some people have actually considered its effects on Na⁺/K⁺-ATPase. This was actually done despite its obvious similarity to aldosterone.

The I₅₀ for ouabain on Na⁺/K⁺-ATPase was determined to be around 10⁻⁷ (Erdmann↑). This varied slightly depending on the species. Considering that an 841% increase of renal Na⁺ retention had been induced (in a sheep) by an infusion of only 4(10⁻⁸) M ouabain per hour¶, it would appear that oubain has high-affinity hormonal effects than cannot be accounted for by its weak ATPase inhibition.

The enrichment of K⁺over Na⁺ in the cell can be satisfactorily explained by two simple observations: the negatively-charged mitochondrial membrane potential, and the quick K⁺ electrophoretic migration velocity.

All other changes in mitochondrial membrane potential lead to concentration changes of other, and larger, charged molecules within. This is easily determined when the solutes are dyes or fluorescent probes. It's only a matter of course to think the same thing would happen with potassium ions.

*Weston, Andrea, et al. "Factors affecting the separation of inorganic metal cations by capillary electrophoresis." Journal of Chromatography A 593.1-2 (1992): 289-295.
†Skou, Jens C. "The identification of the sodium-potassium pump." Chemistry 1 (1998): 997.
Chen, Lan Bo. "Mitochondrial membrane potential in living cells." Annual review of cell biology 4.1 (1988): 155-181.
§Piwnica, David, James F. Kronauge, and Mary L. Chiu. "Uptake and retention of hexakis (2-methoxyisobutyl isonitrile) technetium (I) in cultured chick myocardial cells. Mitochondrial and plasma membrane potential dependence." Circulation 82.5 (1990): 1826-1838.
¶Yates, N. A., and J. G. McDougall. "Interaction of exogenous ouabain and chronic mineralocorticoid treatment in the kidney of the conscious sheep." Clinical and experimental pharmacology and physiology 24.1 (1997): 57-63.

 

[mattyb]

Very great read, and extremely interesting. Well done.

But one questions remains for me. Let's say Na+ gets into the cell in too high of a concentration for some reason - how does the cell selectively eject the excess Na+ if it's clathrate size is too large to easily dissociate through the membrane?

Is there a possibility that ATPase still functions partially as theorized, but due to it's excessive energetic demands of this enzyme in controlling Na/K ratios, it is simply used as an ejection method for reducing intracellular Na, and that the overall ratio is still ultimately controlled by the membrane's own innate selectivity (based off clathrate size, not ATPase activity).

 

[Travis]

I don't think that the membrane can differentiate between these two. Much larger molecules flow through the cell membrane. Gilbert Ling, in the book that I have, used the hydrated radii to explain certain intracellular effects. He used it to explain how glutamate and aspartate residues have a greater affinity for K⁺ than Na⁺, and this affinity explains potassium's higher concentration within the cell. In the 60s, he was writing that the cell's proteins were like a "fixed charged system" — like an adsorbant, or an affinity-chromatography column designed for K⁺.

I would pull-up so quotes but my book does not have a Ctrl+F button . . ..but it does have an index and I'm a fast typer. Let me check . .

He says that K⁺ has a hydrated radius of 2.0Å and Na⁺ has one of 2.8Å. He has reference from 1939 for the person who had originally make these calculations.

This can explain why it travels faster than Na⁺ towards a negative charge during capillary electrophoresis.

 

[mattyb]

So are you saying that ions can freely dissociate through the cell membrane? (Ignoring all other factors). Can you point me towards some literature on this subject, because I am not able to find much other than your standard textbook-fair things that keep repeating that ions can't freely diffuse.

The rationale for why larger molecules (e.g. steroid hormones) can passively diffuse is different and doesn't necessarily apply to ions.

 

[mattyb]

I found one study that's somewhat on the topic of membrane-ion interactions, but I believe it's stating that ions incorporate into and interact with the lipid bilayer (and that bilayers may act as buffers), but they didn't touch on diffusion that much.

Effect of Sodium Chloride on a Lipid Bilayer

 

[Travis]

I think it's just a matter of semantics. You will hear talk about "selective accumulation," but it's really just "selective exclusion" by official accounts. If you read Skou's Nobel Lecture, you will see that the textbook idea is that both Na⁺ and K⁺ diffuse into the cell. The explanation centers around Na⁺ being pumped-out. So when they talk about "selective exclusion," they are really speaking about this.

Much larger molecules routinely cross the cell membrane.

The lipid bilayer is interesting, and nearly impermeable, but it cannot be continuous. There must be pores in the cell wall: Porin (protein) - Wikipedia

It has an inner pore diameter of 7Å at its narrowest point. It should be able to accommodate two hydrated Na⁺ ions side-by-side.

These are interruptions in the lipid bilayer.

The amino acid side-chains are numbered on the inner pore:

Looks like we've got arginines, tyrosines, and lysines at the very center of the pore; a slightly positively-charged interior — but still: it is generally-thought to routinely admit many things into the cell which are larger, and more charged, than sodium.

Cowan, S. W., et al. "Crystal structures explain functional properties of two E. coli porins." Nature 358.6389 (1992): 727-733.

 

[mattyb]

The sources I have found show that hydrated Na+ has a size as high as 8A, with many stating it to be around ~5A (average Na-O bond length of 2.5A). I don't know how reliable the ~2A figure is anymore. I don't know how reliable the techniques from the 1930s are compared to modern spectroscopy, I would need to speak to a old chemist to know how techniques have improved or worsen. And I believe hydrated sodium typically comes in pairs, correct? Other ions like hydrate calcium are even bigger than sodium and too wide for porin, so what about those?

I'm not convinced we have enough evidence to say that Na+ would diffuse via porin at this point. The positive residues in the interior of porin don't help this theory either. There are other ion channels to consider of course, though. But the existence of other ion channels makes me believe it to be slightly more likely that ATPase exists, and may have some functionality in Na/K exchange (although I still believe it's role in Na/K homeostasis is overestimated).

I still don't think repeating the mantra that larger molecules make their way in is evidence of anything. They are different, so let's keep our focus on ions.

One of the papers I've read in the past stated that potassium has a less stable hydration structure, meaning it may be able to more easily diffuse than other molecules - when the hydration structure would break (happens in picoseconds), there may be an opportunity for potassium to quickly diffuse into the cell before regaining a stable hydration structure. There may be something to explore in this idea, as sodium's hydration structure is supposedly more stable than potassium. So possibly the intracellular concentration of Na/K may be related to the stability of their hydration structures? This could possibly compliment the theory of cations being attracted to negatively charged cellular membranes (with K having faster transit) as a means of facilitating diffusion?

In this way I could see the negatively charged membrane facilitating both influx and efflux of cations, while hydration stability and negatively charged intracellular residues acting as absorbents (and possibly even minor contributions from facilitated transport via things like ATPase and ion channels) determining which ions are more likely to diffuse out and which ones stay put.

 

[Travis]

I just found a little modern study on the adsorption of K⁺ and Na⁺ onto synthetic polyglutamate.

The calculations show that sodium is hydrated more strongly than potassium; the experimentally measured difference in the hydration energies of the K-Cl and Na-Cl ion pairs (20.5 kcal/mol) is ∼60% of the calculated value (35.0 kcal/mol). We calculated the difference in binding energies of sodium and potassium ions to a single carboxylate as 2.3 kcal/mol. This is in the range of experimental and

ab initio values, which vary from ∼1.8 kcal/mol to ∼2.5 kcal/mol. We calculated the average equilibrium contact distances for cation-carboxylate oxygen pairs as 2.3 Å (sodium) and 2.6 Å (potassium), which are the same as reported in ref 11.

The ion pairs are loosly associated. A carbon–carbon single bond has a length of 1.54 Å. There is not one covalent bond listed with a length longer than these ionic dimers, except for I—I which is at 2.67 Å. I don't think that these are worth considering in most cases. They are loosely-held and weak associations.

I still don't think repeating the mantra that larger molecules make their way in is evidence of anything.

Except that it shows that the membrane has holes big enough to accommodate them. This is how pore-sizes are routinely estimated, by knowing the size of the molecules it permits.

The sources I have found show that hydrated Na+ has a size as high as 8A, with many stating it to be around ~5A (average Na-O bond length of 2.5A).

Where is it?

This study actully turns-out to be bad news for Gilbert Ling. Here are some quotes:

Accordingly, small cations such as sodium are expected to form contact ion pairs with carboxylate groups, while larger cations such as potassium are expected to be less strongly associated with the carboxylate side chains of proteins. This has recently been supported by several theoretical and experimental studies, [sic] demonstrating that sodium and potassium have different affinities for carboxylate groups. [...] ...including rationalization of the discrimination between sodium and potassium ions in biological environments such as ion channels and the operation of sodium and potassium pumps. ―Federov

In these studies, the different effects of potassium and sodium ions were attributed to the smaller carboxylate ion binding affinity of potassium ions relative to sodium ions resulting from the larger size of the potassium ions and the correspondingly lower charge density on the ion surface. The results of recent theoretical and experimental studies of different ions binding to a single carboxylate have also shown much weaker interactions of potassium ions than sodium ions with carboxylates. ―Federov

The main conclusions of our study are as follows: (i) Because of their lower charge density, potassium ions have much weaker affinity for the anionic side chains of R-PGA than do sodium ions and thus cannot effectively compete with water for the first solvation shell of the glutamates, ―Federov

The figure shows that the potassium ions have lower binding affinity for glutamates than water [sic]...―Federov

I've got Gilbert Ling's 1960 book. It's massive; it's 600 pages but I think I can find the relevant info.

He has determined experimentally that the affinity of a protein carboxyl group depends on it's c-value. This is a measure of polatity. At a c-value of ~2.5, the preference for either Na⁺ or K⁺ shifts. This is essentially the only ion pair in which the ion preference can be shifted.

He never says too much about what actually determines the c-value. As a measure of polarity, you would think that it could be caused by electron flow within the cell. At higher c-values, potassium is preferred.

Pauling, Linus. "A Molecular Theory of General Anesthesia." (1961).
Fedorov, Maxim V., Jonathan M. Goodman, and Stephan Schumm. "To switch or not to switch: the effects of potassium and sodium ions on α-poly-L-glutamate conformations in aqueous solutions." Journal of the American Chemical Society 131.31 (2009): 10854-10856.

 

[Travis]

So possibly the intracellular concentration of Na/K may be related to the stability of their hydration structures?

Absolutely. I can see no other way. Sodium is actually smaller, so it would have a higher charge/volume volume ratio and would be expected to migrate faster. But this is not seen. Also, sodium is lighter so would have a higher charge/mass ratio. Magnesium has a much higher charge/mass ratio than potassium yet migrates slower towards a negative charge.

What correlates the most with electrophoretic migration? From:

• Weinberger, Robert. Practical capillary electrophoresis. Academic Press, 2000.

Since mobility depends on a solute’s charge/size ratio, the buffer pH is the most important experimental variable. The impact of pH on mobility, corrected for EOF, is illustrated in Figure 3.2 (1)

For this statement to be true, he must take the ion plus the entire hydration shell to be the "size." From:

• Nightingale Jr, E. R. "Phenomenological theory of ion solvation. Effective radii of hydrated ions." The Journal of Physical Chemistry 63.9 (1959): 1381-1387.

The below elements are presented in order of their migratory speeds.

Hydrated Radii
K⁺ = 3.31Å
Ba²⁺ = 4.04Å
Sr²⁺ = 4.12Å
Ca²⁺ = 4.12Å
Na⁺ = 3.58Å
Mg²⁺ = 4.28Å

Hydrated Volume
K⁺ = 18.98 ų
Ba²⁺ = 34.5 ų
Sr²⁺ = 36.60 ų
Ca²⁺ = 36.60 ų
Na⁺ = 24.01 ų
Mg²⁺ = 41.03 ų

Hydrated Charge/Volume Ratio
K⁺ = .0527 e⁺/ų
Ba²⁺ = .0579 e⁺/ų
Sr²⁺ = .0546 e⁺/ų
Ca²⁺ = .0546 e⁺/ų
Na⁺ = .0416 e⁺/ų
Mg²⁺ = .0487 e⁺/Å

Slight anomalies, but the trend is there. Temperature can also have an effect on the hydrated radii:

Qualitatively, this suggests that these ions which possess a minimum hydration at low temperatures tend to become more highly hydrated as the structure of water is destroyed by the increase in thermal energy at the higher temperatures. ―Nightingale

And he goes on to describe how some ions are affected differentially by temperature. This means that temperature could theoretically change the elution order of ions, or their relative electrical mobilities.

He actually made an interesting discovery in this paper. The hydrated radii is directly proportional to the B-coefficient, a measure of viscosity:

Viscosity B-Coefficient: The significance of the present set of hydrated radii, other than as a measure of the relative sizes of the ions as determined by transport processes, is best illustrated by their relation to the B-coefficient in the Jones-Dole equations for the viscosity of strong electrolytes. ―Nightingale

It's a perfect correlation (and the B-coefficient is also nearly perfectly proportional to the entropy of hydration.)

But his data for hydrated radii were just estimates, most of them. They were based on extrapolations from known radii. So perhaps the migratory speed is perfectly-proportional to the charge/size ratio at any one given temperature. It may be more accurate to determine the hydrated radii directly from electrophoretic migratory speeds? This actually appears possible by equating the Stokes–Einstein equation with the electrical mobility equation. After cancelling terms and rearranging, you end-up r = q/6πημ. The hydrated radius would then be a function of viscosity and electrical mobility, and vice versa. This does make sense considering the Nightingale paper.

 

[BigYellowLemon]

This thread is great, please keep it up.

 

[Travis]

It attracts everything else! (That is to say, it attracts every positive cation of high charge/mass ratio including stains of all types in such a reliable manner that's they're even used to measure cell vitality and . . . the mitochondrial membrane potential itself.)