Life at the Cell and Below-Cell Level. The Hidden History of a Fundamental Revolution in Biology
Gilbert N. Ling, Ph.D.
Pacific Press
ISBN 0-9707322-0-1

"Dr. Ling is one of the most inventive biochemist I have ever met."
Prof. Albert Szent-Györgyi,
Nobel Laureate

Chapter 10.

Ling's Fixed Charge Hypothesis (LFCH)
(p. 47-73)

As mentioned earlier, I began my training as a cell physiologist under Professor Ralph W. Gerard in the world-famous Department of Physiology at the University of Chicago. Like virtually all my peers, I was totally immersed in the belief that the membrane theory was the one and only guiding light. Naturally my first full-length publications (coauthored respectively with Prof. Gerard and W. Woodbury) are on the subject of "membrane potential,"95 a name and concept taken straight from the membrane theory.

Following a presentation of the "Sodium Pump Hypothesis" I gave at a departmental seminar49 p 124based solely on information gathered at the libraryI carried out some simple experiments of my own. My goal was to find out if the combined action of metabolic poisons and low temperature (0C) would promptly lower the concentration of K+ in frog muscles as the hypothesis would have predicted. The result was unforeseen, but also exciting. No change at all in the K+ concentration at the end of a five-hour-long experiment (see Table 8.4 and pp. 176-177 in Appendix 1 of Reference 49 for results of later more extensive confirmatory work). As I became more and more drawn into the new direction of research thus started, my doubts about the sodium pump hypothesis grew.

In the years following, I spent much time trying to dream up an alternative energy-saving mechanism to replace the hypothetical sodium pump. It was tough going. Years went by and I was getting absolutely nowhere. Then all of a sudden a possible solution dawned on me while I was browsing and mulling in the basement of the Welch Library of the Johns Hopkins Medical School in Baltimore. This new seminal idea, the centerpiece of what was later called Ling's Fixed Charge Hypothesis (LFCH),96 was also the first step toward the construction of the unifying theory of cell physiology, called the association-induction hypothesis (Al Hypothesis; AIH).98 The essence of this hypothesis will be presented here and in Chapters 11, 14 and 15.

The idea that intracellular K+ could be selectively adsorbed over Na+ was, to the best of my knowledge, first suggested by Herbert Roafand Benjamin Moore in 1908. However, as pointed out once already (and until the LFCH appeared), neither they nor anyone else had offered a quantitative molecular mechanism for this striking discrimination between a pair of ions so closely similar. Nor had anyone else suggested an explanation why proteinsthe most likely candidates inside the cells to offer the sites for the adsorption of K+can do the job in the living cell, but repeated attempts in the past to reproduce the phenomenon in vitro had all failed.99; 41 p 120 Nor had a molecular explanation been offered why this ability of selective adsorption (if correct) is promptly lost upon cell death. Ling's Fixed Charge Hypothesis represents the outcome of my first attempt to answer these questions.

10.1 A theory of selective accumulation of K+ over Na+

Three new theoretical concepts were introduced in the construction of a coherent theory of selective adsorption of K+ over Na+ and the closely related phenomena just mentioneda theory to be referred to later as Ling's Fixed Charge Hypothesis (LFCH). However, only one of the theoretical concepts described under (3) below represents what I mentioned above as the seminal idea.

(1) Enhancement of counter-ion (or neutral molecules) association with site fixation

This is a major new concept introduced in 1952not in the recognition of the existence of fixed charges, which had occurred long before100but in the theory of full associations of these fixed charges with free counterions like K+ and Na+. The incorporation of this basic concept distinguishes LFCH (and the association-induction hypothesis) from other "fixed charge hypotheses" of the past and present.101 Indeed, without full counter-ion association, selective adsorption of K+ over Na+ by the mechanism proposed below under (3) or by others suggested elsewhere later [14.1]would have been impossible.

In the wake of the great theories of ionic dissociation of Arrhenius102 and of Debye and Hückel,103 it has been widely believed that monovalent ions of one electric charge in a dilute aqueous solution are fully dissociated from monovalent ions bearing the opposite chargeregardless if one species is fixed in space. (For illustrations of this deep-seated belief as late as 1961, see Figure 1 in Reference 104, Figure 5 in Reference 100; Figure 1 in Reference 105.) In harmony with this view of full ionic dissociation, the influential protein-chemist, K. U. Linderstrøm-Lang of the Carlsberg Laboratory in Stockholm described a protein molecule as an ellipsoid with electric charge uniformly smeared over its surface. Counterions in number matching the excess charges of the opposite polarity hover over the protein as a diffuse ion cloud.467 In his opinion, direct contact between proteins and counterions does not exist. My view to the contrary, to be reviewed next, was definitely running against the tide.

For the enhancement of counterion association in consequence of the spatial fixation of one species of ion,96 p 769 one of the two causes I gave in 1952 is the overlapping of the attractive electric field of neighboring fixed chargesthis field-overlapping is the microscopic foundation of what is known as the Law of Macroscopic Neutrality.97 pp 330-331 The result of this field-overlapping is not merely an increase of the adsorption energy of the ion [14.2(1)], enhancing its association with the fixed ion, but also the confinement of a dissociated counterion to within a much smaller space surrounding the fixed ions.96 p 769 This confinement reduces the entropy of dissociation of the counterion and strengthens its association with the fixed ion also.

The second cause I gave in 1952 is kinetic in origin (and nothing much more beyond that). Indeed, its specific detailed mechanisms are given for the first time here and now: While the chance of an anion and cation meeting and pairing may be assumed to be about the same whether or not one species is fixed in space, the number of effective collisions received from surrounding water molecules, which would tear apart the associated pair, is at least halved if one species is fixed and thus unmoved by the collision. The result is also an enhancement of association. Note that the first (field-overlapping) cause is restricted to particles carrying net electric charges (i.e., ions), the second (kinetic) cause does not suffer such a restriction and may therefore underlie all localized adsorption including the adsorption of ions and water.

The theory of enhanced counterion (and neutral adsorbent) association has been reiterated and discussed in my publications in years following.98 pp 17-28; 106 pp 152-155; 107 pp 39-41 importance in compelling close-contact association in living phenomena is put center-stage by the title of the general theory, association-induction hypothesis. Experimental confirmations on inanimate models of the predictions of this theory as applied to ions469; 98 pp 17-22; 107 p 40 and to water470 had been already in the literaturebefore the (only) theory for its explanation known to me (i.e., LFCH just reviewed) was published. One of these experimental studies will be summarized here.

Kern showed that the activity coefficient of Na+ in 0.0125 to 0.2 M Na salts of isobutyric acid (33) ranged from 0.90 to 1.00, indicating that 90% or more of the Na+ is free. When these isobutyric-acid monomers are joined end-to-end into the linear polymer, polyacrylic acid (-22-)n, and the carboxylic groups thus (not completely but substantially) fixed in space, the activity coefficient of Na+ at the same concentration range, fell to 0.168 to 0.315, indicating that from 68% to 83% of the Na+ is now associated with the carboxyl groups.469

(2) The salt-linkage hypothesis and a critical role for ATP

According to the LFCH, the negatively-charged β- and γ-carboxyl groups of isolated native proteins are largely engaged in salt-linkages with fixed cations (e.g., positively-charged ε-amino groups and guanidyl groups belonging respectively to lysine and arginine residues of intracellular proteins)108 and thus not free to adsorb cations like K+. In the LFCH, these β- and γ-carboxyl groups can be made available for adsorbing K+ ions by adenosinetriphosphate or ATP, when ATP occupies key controlling cardinal sites [14.3(3)].

In this early model, ATP serves its role by the same mechanism proposed earlier by Riseman and Kirkwood for keeping the contractile proteins like myosin from collapsing upon themselves and shortening, i.e., long-range electrostatic repulsion (transmitted through space).109 Later, in the association-induction hypothesis, I introduced a new (though related) mechanism (see [14.3] below). ATP is, of course, the end product of energy metabolism. Its critical role in maintaining selective K+ adsorption explains the loss of this ion upon cell death, when metabolism ceases and ATP regeneration comes to an end.

3) The 1952 electrostatic model for the selective accumulation of K+ over Na+ in living cells

Taking into account dielectric saturation110 (rapidly declining dielectric constant as one approaches an electrically charged site or ion, as illustrated in the inset of Figure 6) in the electrostatic interaction between a fixed anion and a free monovalent counter-cation, one can calculate the statistical probability of finding the counter-cation at different distances from the center of the negatively charged oxygen atom (of a β- and γ-carboxyl group) (Curve 2 in Figure 6).

Figure 6. A theoretical model for the selective adsorption of K+ over Na+ on a fixed oxyacid site presented in 1952 as part of Ling's Fixed Charge Hypothesis (LFCH) Computation takes into account the decrease of the dielectric constant of water (referred to in the Inset as "radial differential dielectric coefficient") when approaching an ion as illustrated in Inset. Theoretical curve (2) shows the probability of finding a monovalent cation (e.g., K+, Na+) associated with the fixed oxyacid anionpartially represented at extreme left of bottom section of the figureat distance (away from the center of the oxygen atom of the oxyacid group) indicated on the abscissa in Angstrom units. Note that only the hydrated K+ with its smaller radius shown in the bottom figure can enter the "shell of high probability of association" around the oxygen atom of the negatively-charged oxyacid group and becomes selectively adsorbed over the larger hydrated Na+ (the center of which stays largely out of the shell of high probability) also shown in the bottom part of the figure. (Ling,96 reproduced from Phosphorus Metabolism by permission of The Johns Hopkins University Press)


The bottom part of Figure 6 also shows the diameters of the smaller hydrated K+ and the larger hydrated Na+ ion.98 p 548; 111 Note that only the center of the smaller hydrated K+ can enter the "shell of high probability of association" around the fixed anion and become selectively adsorbed, but the hydrated Na+ is too large to do the same and is thus largely left out.

What is illustrated in Figure 6 is the first-of-its-kind quantitative molecular mechanism for the selective adsorption of K+ over Na+. Anticipating new developments to be described below in [14.1], I recast this mechanism in an adulterated but easier-to-parley lingo: Due to the different distances separating (the center of) the fixed anion and (the center of) the smaller hydrated K+, the electrostatic field strength experienced by a K+ is stronger than that by the larger hydrated Na+ The resulting preferential adsorption of K+ over Na+ on the β- and γ-carboxyl groups provides an energy-conserving, quantitative molecular mechanism for the selective accumulation of K+ over Na+ in living cells. (For a more detailed presentation of this theoretical model, see pp. 54-57 in Reference 98.)

In summary, proteins like myosin in muscle cells carry many β- and γ-carboxyl groups. Adsorption of ATP on the controlling cardinal site(s) {[14.3(3)]} on myosin enables these β- and γ-carboxyl groups to associate with (or adsorb) either K+ or Na+ Since the hydrated K+ is smaller than hydrated Na+, it is energetically more favorable for K+ to be adsorbed. Accordingly, K+ is selectively accumulated in the cell over Na+.

That said, I must add that this was how the LFCH (and the association-induction hypothesis) began in 1952. The proposed mechanisms are as valid today as then, as will be made clear in the next Section.

To be continued

"Life at the Cell and Below-Cell Level.
The Hidden History of a Fundamental Revolution in Biology":

Contents (PDF 218 Kb)
Preface (
PDF 155 Kb)
Answers to Reader's Queries (Read First!) (
PDF 120 Kb)

1. How It Began on the Wrong Foot---Perhaps Inescapably
2. The Same Mistake Repeated in Cell Physiology
3. How the Membrane Theory Began
4. Evidence for a Cell Membrane Covering All Living Cells
5. Evidence for the Cell Content as a Dilute Solution
6. Colloid, the Brain Child of a Chemist
7. Legacy of the Nearly Forgotten Pioneers
8. Aftermath of the Rout
9. Troshin's Sorption Theory for Solute Distribution
10. Ling's Fixed Charge Hypothesis (LFCH)
11. The Polarized Multilayer Theory of Cell Water
12. The Membrane-Pump Theory and Grave Contradictions
13. The Physico-chemical Makeup of the Cell Membrane
14. The Living State: Electronic Mechanisms for its Maintenance and Control
15. Physiological Activities: Electronic Mechanisms and Their Control by ATP, Drugs, Hormones and Other Cardinal Adsorbents
16. Summary Plus
17. Epilogue 

A Super-Glossary
List of Abbreviations
List of Figures, Tables and Equations
References (
PDF 193 Kb)
Subject Index
About the Author

"Life at the Cell and Below-Cell Level..."
"Gilbert Ling"