Chapter 14 Electrical Potentials

Reinterpreting the resting membrane and activation potentials using the surface adsorption model.

As always, this is not medical advice, and reading this does not form a client relationship with me - your health is your responsibility.

Many have asked for my “thoughts” on things. The best place to start would be some of my older Substacks - especially the ones on supplementation (1 and 2). Also, please check out my IG story highlights. I have postponed consults for now; if you want to be added to my waitlist, please DM me on IG!

Today’s Substack will continue with Chapter 14, Electrical Potentials. Chapter 13 discussed cell volume control - swelling and shrinking. This chapter is of continued interest to me because I did research on the Hodgkin-Huxley model, also known as the conductance-based model which is a model that describes action potentials in neurons, for my chemical engineering masters. Action potentials are also required for the Ca-, and other-, oscillations I routinely discuss.

Summary:

Chapter 14 introduces the surface adsorption model of cell potential within the framework of the Ling fixed-charge hypothesis, elucidating its dependence on - temperature, the selective affinity of surface fixed charges for counterions (e.g., Na+ for K+) , external counterion concentration, and fixed-charge site density. Notably, this model accounts for the diverse ion sensitivities observed in different cell types and conditions. It further delves into the molecular events governing excitation and action potentials, emphasizing autocooperative changes in surface site affinities and depolarization-induced water permeability. These phenomena explain the early inward sodium current and delayed outward potassium current during action potentials and the all-or-none characteristic. Calcium as a cardinal adsorbant is highlighted, due to its importance in adsorption isotherms of potassium and sodium in muscle cells. Furthermore, it explains related phenomena like increased sugar permeability and transient local swelling. The following chapter extends the surface adsorption theory's relevance to mitochondrial potential.

My favorite sections of the book, section IV. A Reevaluation of Current Concepts in Physiology and Biochemistry and V. A Tentative Approach to Some Unsolved Problems in Biology and Medicine, including a look at oxidative phosphorylation, muscle contraction, cancer, etc. is coming up next!

14.1 Evidence Against the Membrane Theory of Cellular Electrical Potentials

The Hodgkin-Huxley neuron model is founded on the cell membrane theory, which questions its reasoning. As an aside, many do not understand this and is highlighted specifically with quantum mechanics. Models and theories can give and do give predictive power in which experiments can be tested to “prove” them. However, that does not mean our interpretation of how that mathematics came about, etc., is “correct.”

As a reminder, the cell resting potential is a mostly static voltage, where the action potential has to do with the dynamic voltage of the action potential that is electrochemical in nature. The static voltage has to do with the intracellular vs. extracellular charge asymmetry - what is in the cell is not held at neutral with what is outside of it.

The resting potential of frog muscle cells remained unchanged when external CI- were replaced with SO4-2. This observation suggested that Cl- had little effect on the resting potential. However, further studies revealed inconsistencies in this interpretation. For instance, experiments showed that the Cl- permeability of cell membranes could be higher than K+ permeability in some cases. In mammalian muscles, the Cl- conductance was significantly larger than the K+ conductance. Labeled CI- efflux experiments indicated much shorter time constants for Cl- efflux than K+ efflux. This further emphasized the significance of Cl- in membrane dynamics. Hodgkin and Katz modified the Hodgkin-Katz-Goldman equation by eliminating the chloride term, suggesting that Cl- distribution was already at equilibrium. However, this explanation was questioned, as many electrical potential differences, including resting potentials, are observed in equilibrium systems. Modifications like the above routinely happen in science instead of acknowledging the original theory was incorrect - see the infinity problem, also known as renormalization in quantum field theory. “The indifference of [the resting potential] to Cl-, and indeed to anions in general, in some cells, anit’se sensitivity to CI- in other cells, show quite clearly that the potential-generating systems among different types of cells, or even the same cell at different times, are quite selective. In some cases, they aMaxwell’sive for cations, and in other cases, for anions.”

The Hodgkin-Katz model of cellular potential, which suggests that the resting potential of cells depends on internal K+ concentration, was supported by some studies, including those by Baker, Hodgkin, Shaw (1961), Adrian (1956), and Hagiwara et al. (1964). However, done’s the same period (1950-1965), several other laboratories reported contradictory results: Tobias (1950), Falk and Gerard (1954), F. H. Shaw and colleagues (Shaw and Simon, 1955; Shaw et al., 1956), Koketsu and Kimura (1960), and Ichiji Tasaki and his co-workers (Tasaki and Takenaka, 1963, 1964; Tasaki et al., 1965) - these had to do with varying intracellular K+:Na+ while seeing no significant changes to the resting potential.

Many other experimental findings showed that electrical potentials shifted more rapidly than expected from significant changes in ion concentrations, suggesting the presence of an electrogenic (=produces electric activity in living tissue) Na+ pump that was not accounted for by passive ion movement. However, it's important to note that this electrogenic pump hypothesis was considered ad hoc and lacked testable predictions. It was challenged by the concept of an adsorbed state of cell K+ and was criticized as a form of Maxwell's demon. This hypothetical concept contradicts the laws of physics by sorting gases to create free energy de novo. The electrogenic pump was viewed as sorting Na+ and K+ to maintain a potential difference more significant than what physics would predict - another example of changing the math instead of one’s interpretation.

The resting cell is at times permeable to both Na+ and K+; as such, the all-or-none opening and closing of Na+ and K+ gates during an action potential does not follow.

The Hodgkin-Katz theory (resting potential) and the Hodgkin-Huxley (action potential) theory of cellular and action potentials rely on the assumption known as the independence principle. This principle posits that the cell membrane is a homogeneous and isotropic medium, and the diffusion of one ion within this medium is not influenced by the presence of other ions, whether of the same or different species. The Hodgkin-Katz-Goldman equation was developed based on this assumption. However, since 1952, doubts about the validity of the independence principle have emerged. Hodgkin and Huxley discovered that during the passage of an impulse, the observed influx of labeled K+ was only about 1/6 of what was calculated based on the independence principle. This led to the proposal of the long-pore model. Other studies further challenged the independence principle. For instance, experiments in squid axons demonstrated that alkali metal ions in the internal perfusing solution reduced the delayed current with varying degrees of effectiveness, contradicting the principle. Additionally, the conductance of both K+ and Na+ was shown to be reversibly depressed by low pH, with debates on whether this effecdoesn’tdirect through the gating process or a direct blockage of Na+ migration, posing challenges to the independence principle.

“The unequivocal establishment of the adsorbed state of cell K+ discussed in detail in Chapter 8 has disproved the membrane theory of cellular electric potentials. However, this does not by any means invalidate many of the important data acquired in past decades.” This is the crucial point; just because the interpretation is not necessarily “correct” does not mean we throw out all the math and experimental evidence.

14.2 Evidence for the Surface Adsorption Theory of Cellular Resting Potentials

Multiple experiments showed the resting cellular potential is dictated by what ions are adsorbed at the cell surface - see the section for further explanation of the experiments and their results.

14.3 Experimental Observations Not Explicable by the Membrane Theory but in Harmony with the Surface Adsorption Theory

Only a portion of the Hodgkin-Katz-Goldman equation has been experimentally verified, and this part is identical to the equation for cellular potential according to the Surface-Adsorption Model (SAM). This suggests that the observations supporting the Hodgkin-Katz-Goldman model are also consistent with the SAM. The SAM doesn't require intracellular K+ to exist in a free state. Instead, it suggests that intracellular ions, including K+, don't play an immediate role in determining cellular potential. This concept contradicts the membrane theory. The failure to demonstrate an expected relationship between external Cl- concentration and cellular potential contradicts the Hodgkin-Katz theory but aligns with the SAM. The SAM suggests that the surface sites on resting frog voluntary muscle cells are primarily anionic and exhibit no Cl- sensitivity - like charges, in this case, “-” and “-” repel.

14.4 The Molecular Mechanism of the Resting and Action Potentials

This is the Ca-oscillation at its core: “[D]uring excitation, in response to the removal of the cardinal adsorbent Ca2+, there is an electronic conformational change of the cell surface proteins: [the] surface anionic sites shifts transiently in an all-or-none manner from one state, in which K+ is preferred over Na+, to another, in which the relative Na+ preference is greatly increased. Concomitantly a transient depolarization of cell surface water occurs, creating an increase of nonspecific membrane conductance. The molecular event during the propagation of an action potential was described in terms of the indirect F-effect, and the transition from the resting to the active state is autocooperative in nature, with the inductive effect providing the major component of the nearest-neighbor interaction energy.” The indirect F-effect is an induction effect.

Ling puts forth an improved equation for the cellular resting potential (equation 14.8). This equation considers cooperative interactions between surface anionic sites, which are not considered in the simpler previous equation (equation 4.16). This is how theory and experiment should work as the experimental results match the predictions made by the equation:

1. When external K+ concentration increases, the resting potential falls with an ideal or near-ideal slope.

2. If external K+ concentration decreases below normal levels, the resting potential becomes constant at a low value rather than continually increasing.

3. A different pattern is observed in certain types of cells (e.g., cardiac Purkinje cells, HeLa cells, and pancreatic islet cells). Decreasing external K+ concentration causes the resting potential to fall, indicating autocooperative interaction among surface anionic sites - the behavior of resting potentials can vary between different cell types, depending on factors like the exchange rate of intracellular K+ and Na+.

4. It takes time for the resting potential to reach a new equilibrium, which coincides with the time it takes for the internal K+ concentration to adjust to the low external K+ concentration.

5. The resting potential is determined primarily by surface K+ adsorption rather than the total cell K+ content.

These align with the Surface Adsorption Model (SAM), which proposes that the behavior of resting potentials is strongly influenced by the interaction of ions with surface anionic sites on cell membranes.

The magnitude of the resting potential at a fixed level of K+ depends on external Ca+2. Higher concentrations of Ca+2 lead to an increased preference for KAutodidact’sface anionic sites, as observed in smooth muscle, liver cells, frog muscle, cardiac Purkinje fibers, and myelinated nerves. This is why we must consume sufficient Ca and why I continually question Mg supplementation without any thought about Ca intake! The increased K+ preference indicates increased structure, a higher resting potential, and things that should not be in the cell (e.g., heavy metals, “viruses,” etc.) are excluded.

The AI (Adsorption-Induced) hypothesis suggests that Ca+2 depletion lowers the affinity of the surface anionic sites for K+ and enhances the probability of Na+ entering the cell through adsorption-desorption routes. This leads to an increased influx of Na+ and simultaneous depolarization due to the high external Na+ concentration compared to K+ - this explains the K+ delayed outward current in the Hodgkin-Huxley model.

Puncturing, shearing, or damaging a cell leads to an activation potential that depends only on external Cl- concentration and not external K+ or Na+ concentration. “Thus the inside of the cell becomes more negative as external Cl- increases. These findings suggest that the activation process leads to a disappearance or decline of the concentration of fixed anionic sites at the height of the activition potential, and a transient appearance of fixed cationic sites spreading over the cell surface.”

14.5 Molecular Events Underlying Excitation

Figure 14.26 does a great job depicting the phase change that occurs during cellular activation.

“The functional cell surface is a two-dimensional matrix of proteins carrying fixed anionic sites in the form of an array of beta- and gamma-carboxyl groups, each set being under the influence of a cardinal site. In a resting cell, the cardinal site is occupied by a Ca+2, which allosterically controls the beta- and gamma-carboxyl groups, maintaining it at a relatively low value at which K+ is preferred over Na+. As a result, K+ is the predominant countercation at the cell surface.”

The cell surface model:

1. “The cell surface is semipermeable, meaning that it is most permeable to water

   but progressively less permeable to larger and more complex molecules.”

2. A “resting muscle or nerve cell surface, K+ is preferentially adsorbed over Na+ .” - like a K+ electrode.

3. “The cell surface potential shows no sensitivity to CI- because the resting surface

   sites are primarily anionic.”

4. “The cell surface potential shows no sensitivity to external Mg+2 concentration because beta- and gamma-carboxyl groups are isolated and not in

   pairs or clustered.”

5. “K+ entry shows competition and saturability because most K+ traffic is via the

   adsorption -desorption route.”

6. “Na+ entry is partly by the same adsorption-desorption route as for K+, and

   thus shows partial though much less favorable competition with K+, and partly

   by the saltatory route by jumping through the interstices. The saltatory

   route offers relatively high resistance to the passage of Na + and other

   cations because of the electric fields of the fixed beta- and gamma-carboxyl groups and a relatively low permeability to large hydrated ions through the polarized water.” - hydrated Na and larger than hydrated K.

7. “In muscle cells, the K+-adsorbing sites directly below the cell surface are

   hypothesized to be arrayed in rows parallel to the cell surface. A high activation energy for K+ migration between chains reduces outward K+ conductance. This then may account for the anomalous rectification phenomenon first observed by Katz, i.e., a greater resistance to outward K+ conductance than inward K+ conductance when muscles were in an external solution containing K+ at a concentration equal to that inside the cells. In other cases, these

   protein chains may be random or perpendicular to the cell surface (lower right

   corner of top of Fig. 14.26); in those cases, K+ may jump from one site to

   another, offering a high conductivity and hence normal

   rectification, as in many types of nerves. The same mechanism can also account

   for the much higher radial cytoplasmic resistance and membrane capacitance of

   muscle cells in comparison with nerve cells.”

“The order of selectivity of the resting surface sites is Rb+ > Cs+ > K+ > Na+.”

“The order of ion selectivity of the anionic site essential for the Na+ current is Li+ = Na+ > K+ > Rb+ > Cs+.”