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In 1962 I published in detail the experimental evidence that the sodium pump hypothesis is untenable because under carefully controlled condition, the minimum energy need for pumping sodium ion from frog muscle cells is from 15 to 30 times that of the maximum energy available. The evidence and conclusion deduced had remained unchallenged until a reporter from the Science magazine, Dr. Gina Kolata published in 1976 a review entitled "Water Structure and Ion Binding: A Role in Cell Physiology?" (Sience, vol. 192, p.1220, 1976). In this article she claimed that two scientists, A and B had produced "crucial experiments and calculations ....that provide strong evidence for the existence of pumps". This public report was surprising to me on two accounts.
Firstly, I and other scientists, including Dr. Raymond Damadian, Dr. Freeman Cope, Dr. Carlton Hazlewood, had each individually received and responded to Kolata's article in the Letters to the Editor Column of a later issue of Science (193: 528, 1976). Yet neither my response, nor my recollection of the content of Kolata's article indicate that she had in her article a section mentioned the so-called "crucial experiments and calculations". The question arose: Did Kolata send us an earlier version of the article (and we responded to it) but put in print later a different version containing this "crucial experiment and calculations"(and other related and unrelated statements)?
I raised this issue in my letter to Dr. Kolata dated June 21, 1996. She answered my letter on another issue (see below) but not on this point specifically. On November 5, 1996 I wrote her another letter addressing this issue once more and exclusively. Again I got no response. On February 5, I repeated my request once more, asking for a yes-or-no answer, this time in a letter with a return slip (which was duly acknowledged and returned to me ). But still no answer.Whatever the reason for her unwillingness to respond to my simple question, her statement in her article could very well have produced---unintentionally, I am sure--- the spurious impression that I was not able to rebut the "crucial experiments and calculations"---utterly contrary to the truth (see below).
Feeling at the time that I had already answered all the relevant questions she raised in the manuscript she made available to us, I went on to other work and was not to learn about this "crucial experiment and calculations" claim until twenty years later--- when a friend, Dr. Gerald H. Pollack brought it to my attention. Since Drs. B and A were once my graduate students, the fact that I did not respond promptly to these alleged "crucial experiments and calculations" might have been misconstrued as evidence that the en masse departure of my former graduate students from my laboratory (see home-page under "Absolute Power Corrupts Absolutely) was for purely scientific reasons----a misconception that could be made into a powerful weapon in the hands of those who would prefer that my NIH-supported work be stopped, as it was (see home-page).
Surprise number two from Kolata's article was B and A's alleged "crucial experiments and calculations "--- which had, in Gina Kolata's opinion, reversed my earlier refutation of the sodium pump theory. What are these experiments and calculations?
Neither B nor A had conducted any experimental studies on the energy need of the sodium pump while they were working in my laboratory. Could they have gone into this new field after they left my laboratory? To find an answer, I went to the Citation Index and did a thorough search for all B's and A's scientific publications. I could not find a trace of what could be conceivably regarded as the source of Kolata's "crucial experiments and calculations. I then wrote to all three: Kolata and my two former students.
B never answered my letter or another follow-up letter I sent later. Kolata did answer and here is what she wrote me in her letter dated July 16, 1996:
"I am sorry to say that I can no longer remember where I got that information about Dr. B and Dr. A's (real names here and below withheld by G.L.) conclusions. I'm especially chagrined because Dr. A and Dr. B never published their results and Dr. A says I never even interviewed them. In retrospect, that seems hard to believe, but I was very young then and maybe I really was so inexperienced that I included that statement about their work without calling either Dr. A or Dr. B ..."
This notwithstanding, what she wrote as Dr. A and Dr. B's "crucial experiments and calculations" could be seen as the center piece of her whole article. Dr. A's response in his letter to me dated June 28, 1996, corroborated the fact that Kolata did not interview Dr. A or B. However, Dr. A too could not provide me with a copy of what might have been the source of Kolata's "crucial experiments and calculations ". This is the main portion of what Dr. A wrote:
"When I was a postdoc at Cornell and Dr. B was one at Yale, the two of us, still fresh from the tumultuous experiences in your lab, wrote a manuscript on analyzing the Na+ efflux data in muscle--a sort of literature review--taking into account compartmentation effects. It was an attempt to show, among other things, that your apparently fast efflux data could be reconciled with a multicompartment membrane theory. (Remember, though, that I also considered the rates measured in your zero-degree experiments too high, as I discussed at length in my thesis.) Dr. B and I had fun writing the paper, and we sent it to J. Membrane Biology, I believe, where it was immediately rejected...We didn't try to publish it after this rejection. So I suppose that's what Gina Kolata was talking about there. But the big puzzle is: how did she know about it? I don't think that we sent the manuscript to Science, and I'm certain that we never published it. But we may have circulated it around to friends, etc. So maybe she heard about it in the grapevine. That's just conjecture, but it seems to be a plausible scenario. As for citing it, that's impossible: never having passed through the fire of peer-review, it doesn't exist, and so it isn't part of the literature--nothing for you to argue with. I don't have a copy of the paper, having thrown out the manuscript as useless junk over a decade ago..."
So the much touted "crucial experiments" were never performed.
Even though now Dr. A does not regard what he and Dr. B wrote to have value beyond that of "useless junk", he did mention in the letter cited above that he had already rejected the association-induction hypothesis while still in my laboratory, and that he has given "the reason for this rejection at length in his Ph. D. Thesis"---a thesis I had never read before because by the time he started writing his thesis, he was no longer my graduate student.
On my request, Dr. A sent me the relevant portion of his Ph.D. thesis. From this thesis, one gets a closer look at the materials which had led Dr. A to reject the AI Hypothesis and to launch him in his new-found faith in the membrane pump theory. Before going into the details of what he had to say in his Ph. D. thesis, let us first construct a bird-eye view of the whole problem of the hypothetical membrane pumps.
The sodium-pump hypothesis does not offer a basic molecular mechanism for the postulated pump. It is therefore nothing much more than just a name, a rephrasing of one arbitrarily chosen observation. I have clearly pointed out as far back as 1955 (J. Phys. Med., 34: 89, 1955, p.94, paragraph 2) and repeated many times afterward ("A Physical Theory of the Living State: the Association-Induction Hypothesis", Blaisdell, 1962, p. 216; "A Revolution in the Physiology of the Living Cell", Krieger, 1992, p. 17) that if a membrane pump is a mechanism offered in ernest to explain the asymmetrical distribution of a permeant ion, it cannot be limited to just one arbitrarily chosen ion (i.e., the sodium ion). Instead, "we must have 'pumps' for all these ions" which, like sodium ion, are also permeant and do not follow the prediction of the Donnan ratio according to the membrane pump theory ". Nor can one postulate pumps only for ions. Pumps must be postulated for nonelectrolytes, chemicals like sugars bearing no net electric charges; many of them also do not follow the equal distribution pattern predicted by the membrane theory--- from its basic tenet that a living cell represents a membrane-enclosed dilute water solution.
Thus while it is legitimate and meaningful to choose just one pump to disprove the membrane pump theory on energy ground--- as I did in 1962. To argue that the membrane pump theory is tenable energetically, one must take into account all the pumps which must be postulated. And then show that the total energy needs of all pumps added together is within the limit of the energy available. Doing anything less would have created the false impression that the membrane-pump theory is all right, while it is not.
In his hopeless and pathetic attempt to resurrect the membrane pump theory, Dr. A did just that. Instead of dealing with all the postulated pumps together, he limited himself arbitrarily to one pump, the sodium pump. At the time when he was preparing his Ph.D. thesis, there were at least 20 pumps already postulated and published (some of which are not single pumps but long lists of pumps like the various sugar pumps and various free-amino-acid pumps). Worse, this list of pumps was collected from the literature by nobody else than A himself. Later this list was printed and published in a review A co-authored with Ochsenfeld and myself ( Ann. NY Acad. Sci. 204: 6, 1973, Table 2 on page 9).
All these postulated pumps A had gathered from the literature are confined to pumps at the cell membrane or plasma membrane. As mentioned in linked page, lp6a(1), pumps are also needed at the membranes of the subcellular particles because the ion and nonelectrolyte distribution across their surfaces are also as a rule asymmetrical. One kind of such subcellular particles is the sarcoplasmic reticulum, (SR). In frog muscle cells, the SR has a total surface 50 times larger than the plasma membrane. Since the energy need of the membrane pump (otherwise the same), varies directly with the size of the surface area of the particle, a similar pump at the surface of the SR would consume 50 times more energy than that at the cell membrane (see Ling, "A Revolution in the Physiology of the Living Cell", Krieger, 1992, Malabar, Fl., p.19).
Not only do sodium ion, magnesium ion, sugars, free amino acids etc. etc., which are found in the natural environment of the living cells, require pumps; exotic solutes, including those synthesized and thus created for the first time by organic chemists in chemistry laboratories also as a rule distribute asymmetrically across cell membranes and thus need pumps. This need of pumps for man-made chemicals poses two difficult if not insurmountable problems for the membrane-pump theory: First, since the living cell's genome had never been exposed to these new molecules in past history, how could the cell evolve pumps in anticipation of their future synthesis by humans? Second, since there is no limit to the number of new chemicals organic chemists can create, how is the limited space of the plasma membrane and subcellular particle membrane accommodate an infinity of pumps?
In my computation of the maximum energy available to operate the sodium pump of poisoned frog muscle given in detail in 1962, the energy source was to a large extent limited to the energy in the so-called "high energy phosphate bonds" of ATP and phosphocreatine present initially in the muscle cells. I then used values of these energies available in the literature. However, Podolsky and Morales (J. Biol. Chem. 218: 945, 1956) and George and Rutman (Prog. Biophys. Biophys. Chem. 10: 1, 1960) have conclusively demonstrated that the high-energy-phosphate-bond concept itself is a mistake. There is no such high-energy to speak of.
The downfall of the high-energy phosphate bond concept was a tremendously important landmark event in the history of cell physiology and it has not been challenged since its publication. Among its many major impacts, it demands that the maximum energy available for the postulated sodium pump I estimated must be revised. As a result, the figure of 22,95 cal/kg/hr for the total available free energy of poisoned frog muscle as given in my original publications (Table 8.5, Ling "A Physical Theory of the Living State", 1962, pp. 202-203)--- as the sum of the contributions from the decomposition (and presumed usage to pump the sodium ion) of creatine phosphate (21.57 cal/kg/hr), of ATP (0.64 cal/kg/hr), of ADP (0.18 cal/kg/hr) and from the residual glycolysis producing lactate (0.56 cal/kg/hr)--- must now be replaced by the free energy from the residual lactate production alone. This, of course, amounts to a mere 0.56 cal/kg/hr. A reduction of the maximum available energy by a factor of a little over forty-fold (40 times) is the result.
With this corrected maximum available energy, the disparity between minimum energy need and maximum energy available would rise sharply from 30.6 times, 15.4 times and 18.0 times from the three sets of experiments performed in 1956 (Table 8.9, ibid) to 1224 times, 616 times, and 720 times respectively ( " A Revolution in the Physiology of the Living Cell, Krieger, 1992, pp. 12-16) (see below, however, for a two-fold reduction of these figures due to partial adsorption of intracellular sodium ion). All of these new facts ( and much more ) are what a scientist wishing in earnest to resurrect the membrane-pump theory must deal with. Sadly, A could not and did not do it. Therefore, what he did was not a serious scientific inquiry. To call it "useless junk" as he himself did, is not an exaggeration. Nonetheless, it is of at least record-keeping interest, to look deeper into what A himself has to say in his Ph.D. thesis, which was not thrown away as trash and remains a part of the existing literature.
But before that, I must review some other works I have published which are directly relevant to understanding my original computation of the excessive energy and which A set out to challenge in a way that has excited one reader at least (Kolata) to (unearned) ebullience.
When radioactive sodium ion became available, Levi and Ussing carried out and reported the historically first sodium-ion-efflux studies---efflux meaning outward flow or movement, while influx means inward flow. In this study these workers first immersed an isolated frog sartorius muscle---comprising some one thousand entirely similar long hair-like muscle cells--- in a Ringer's solution---a man-made complex salt solution in which isolated cells can be kept alive for some time--- containing radioactively-labeled sodium ion. They then proceeded to follow the time course of the loss of radioactivity (from the radioactively labeled sodium ion) from the muscle as it is being continually washed in a stream of Ringer's solution containing no radioactivity. The logarithm of the labeled sodium-ion concentration remaining in the muscle at different times after washing began (as ordinate) was then plotted against the time of washing (as abscissa). This semilogarithmic plot can be readily resolved into two "straight-line" fractions, one fast (with a steeper slope) and one slow (with a flatter slope). Levi and Ussing attributed the fast fraction to come from labeled sodium ion trapped in the space between the individual muscle cells or fibers (called the interfibrillar or extracellular space) and the slow fraction as representing labeled sodium ion emerging from within the muscle cells and referred to as the sodium-ion efflux. This assignment was soon accepted by almost all the workers in the field. Though not everyone.
I began to have doubts about this assignment in the 1950's, long before I carried out the energy balance study mentioned above. One strong reason for my doubt was that the size of the fast fraction of labeled sodium ion leaving the muscle (25%) is much larger than what one can expect from the known size of the extracellular space (ca. 10%). This discrepancy led me to suspect that the true sodium-ion efflux from the cells is mixed with that from the extracellular space, making up a part of the fast fraction. If my suspicion is right, its implication would be that the conventional value for the efflux rate of sodium is underestimated by a big factor. This early idea has much to do with the choice of specific technique for measuring the sodium ion efflux in the energy balance study reported in 1962 (see below). In years following several new lines of approach to this problem have verified my early suspicion in an unambiguous way. Somet of these new lines of approach are summarized next:
Early in the 1950's, I put together an apparatus-assembly (the key component is a well-type gamma-scintillation counter) in which the "detector" encloses the radioactive sample and thus allows many more readings of the radioactivity emanating from the muscle within a given period of time than the older methods often used (see below). With a special adaption of this new apparatus, I studied the sodium-ion efflux from a single isolated muscle cell. The results showed that even though I was measuring efflux from a single cell (which has no interfibrillar or extracellular space; the radioactive fluid on the cell surface is washed away almost instantly and makes no contribution to the much slower "fast fraction") and hence free from the complication due to the presence of radioactivity trapped in the interfibrillar or extracellular space of whole muscles, the efflux curve remains curved and---like that from an intact sartorius muscle containing some one thousand muscle cells--- resolvable into the two straight-line fractions. This observation confirmed my suspicion that the sodium ion leaves (and enters) the cell at a much faster rate than widely believed, and is represented by the fast fraction measured from the single cell. I also gave reason and evidence why the slow fraction is, in fact, rate-limited by the (slower) rate of desorption of a part of the sodium ion in the cells which is not free but adsorbed on intra-cellular macromolecules, mostly proteins.
A new question arose: "How can I reconcile my finding with the earlier report of Sir Alan Hodgkin and Paul Horowicz (J. Physiol. (London) 148: 127, 1959) who showed that in their single-muscle-cell experiment, the entire sodium-ion-efflux curve in a semilogarithmic plot could be fitted to a single straight line? An answer for this apparent conflict was soon obtained, an answer---- which despite its interesting and intrinsic scientific value, might have caused fallout affecting me and those closely associated with me far beyond my understanding of how scientists should conduct themselves when faced with new findings which run against their prior positions (see Homepage under "Absolute Power Corrupts Absolutely").
In the technique used by Hodgkin and Horowicz, only a small part of the radioactivity in the single muscle fiber is "seen" by the detecting Geiger Counter placed at a distance below the muscle cell sample. As a result, they must wait a longer period of time to collect enough "counts" for each data point. Accordingly their data points are separated by long 10 minute intervals. With my more efficient setup I had no difficulty collecting a far larger share of the radioactivity emanating from the single muscle fibers and was therefore able to measure data points at 1 minute or even briefer intervals.
Confirming my suspicion that their apparent single straight line relation in the semilogarithmic plots might be an artifact arising from too few data points, I was able to show that if I deliberately removed from mmy own data all the data points except those at the 10 minute intervals--- which was curved and resolvable into two straight lines to begin with --- the remaining points now also fits a single straight line just like those of Hodgkin and Horowicz.
The work just described was published originally in 1970 (Physiol. Chem. Phys. 2: 242, 1970). At that time A was working in my laboratory. Indeed, as indicated above, the key figure presented in this 1970 paper was reproduced in the 1973 review which A , Ochsenfeld and I myself coauthored (Ann. New York Acad. Sci., 204, pp. 17-18, Figs. 3 & 4, 1973). I bring this out here to leave no doubt that A at the time when he wrote his Ph. D. thesis knew that I have long regarded the conventional assignment (of the slow fraction as representing the sodium efflux from within the cells) as erroneous and much too slow, and that I believed that it is part of the fast fraction from the whole muscle which represents the true sodium ion efflux from within the cells. Three additional sets of investigations further and unanimously confirmed this early conclusion:
With a new centrifugation technique Ling and Walton first introduced in 1975 (Physiolo. Chem.Phys. 7: 215) a simple and quantitative way of removing all the extracellular space fluid from a frog sartorius muscle became available. Using this method Ling and Walton removed the labeled sodium ion caught in the extracellular space of labeled-sodium-loaded muscle before washing began. Despite the quantitative removal of what Levi and Ussing thought to be the sole source of the fast fraction of the sodium-ion efflux, the extracellualar-space fluid, a fast fraction (and slow fraction ) remains. This study confirms what we found under (1) and suggests that a major part of the fast fraction indeed comes from inside of the cells (Ling and Walton, Physiol. Chem.Phys. 7:501, 1975).
When frog muscle is exposed to a Ringer solution containing a low concentration of the metabolic poison, sodium iodoacetate (IAA), the muscle slowly deteriorates until it dies. In the course of this dying process, the total sodium ion concentration in the muscle cells rises slowly from its low value in normal cell ( ca. 25 millimoles per kilogram fresh muscle) to approach that in the outside Ringer solution ( ca. 100 millimoles per liter or 100 mM.)
Now if to the IAA-containing Ringer solution, we also added radioactively labeled sodium ion, and expose an isolated frog muscle for some time to this solution (call it solution A), followed by washing the radioactive isotope-loaded muscle in a Ringer solution containing only IAA but no radioactivity (call it Solution B), one can obtain a sodium-efflux plot of the poisoned muscle. If at the end of say one hour of washing in Solution B , one returns the muscle to the radioactively labeled -IAA containing solution A for a few more minutes, and then start washing it again in non-radioactive Solution B, one obtains a sodium-efflux plot of the muscle in a more advanced state of poisoning. The cycle of soaking and washing can be repeated again and again for a number of times, each time producing yet another efflux plot of the muscle in a more and more advanced state of poisoning until the muscle dies. All these plots can be resolved into a slow and a fast fraction. When all the efflux curves are plotted side by side and compared, one finds that neither the size nor the slope (i.e., rate of efflux) of the slow fraction changes much (at approximately 20-30 mM.) from the time the muscle was virtually normal until it was dead---in contradiction to the conventional assumption that it is the slow fraction which represents the intra-cellular sodium ion. Otherwise, the size of the slow fraction should gradually rise until it approaches the concentration of sodium ion in Solution A at around 100 mM.
In contrast, it was the fast fraction which steadily rose in size with each re-immersion in the labeled solution, and as the cells become closer and closer to death. When the cell dies completely, the labeled sodium ion in the fast fraction approached that of the sodium ion concentration in the radioactively labeled soaking Solution A. This experiment established once more that it is the fast fraction in the centrifuged muscle that represents the sodium-ion efflux. The next set of experiment confirms this conclusion in an even more quantitative manner (Ling, Walton and Ochsenfeld, J.Cell Physiol. 106:385, 1981).
If one exposes a small frog muscle fiber bundle (containing a few tens of muscle fibers or cells) for say exactly 3.0 minutes to a Ringer's solution containing labeled sodium ion and then remove the radioactivity caught in the extracellular space by the centrifugation method mentioned above, one can then do an efflux curve with closely placed data points. Each efflux curve obtained can be neatly resolved into a fast fraction and a slow fraction. In the semilogarithmic plot (done as usual), each fraction again appears as a straight line.
Now each one of these straight lines provides two sets of data to estimate how much labeled sodium has entered the cells (influx) during the initial 3.0-minute exposure to the radioactively labeled solution. One set of data comes from the slope of the straight line in the semilogarithmic plot, representing the rate of efflux (outward flow), but which must equal the rate of influx (inward flow) since the total Na+ concentration does not change during the experiment,--- only the (immeasurably small) concentration of radioactively labeled Na+ in the muscle fiber bundle changes. The other set of data comes from the extrapolated intercept on the ordinate of the straight line at washing time equal to zero.
The important point is this: only the fraction which truly represents the intracellular-extracellular exchange can yield two values that agree with each other. In contrast, the fraction which does not represent the true intra-, extra-cellular exchange will produce two values that disagree.
In a series of studies on 23 small muscle fibers bundles in 8 sets of studies carried out between Oct. 27, 1977 and Nov. 23, 1977, the ratio of the intake of labeled sodium obtained from the intercept of the fast fraction over that from the slope of the fast fraction is close to unity or 100% from the fast fraction (107% + 3.6%) . In contrast, the same ratio from the slow fraction is far from unity or 100% at 481% + 39.5%. This work provided another set of unequivocal evidence that the true sodium ion efflux from frog muscle cells is that represented by the fast fraction (after removal of labeled sodium ion trapped in the extracellular fluid). (Ling, Physiol. Chem. Phys. 12: 215-232, 1980).
These four sets of independent studies taken together leave no doubt that the conventional assignment of the slow fraction to represent the sodium ion efflux is wrong. One consequence of this revolutionary discovery is that the true sodium efflux rate is at least ten times higher than what has been accepted by most muscle physiologists.
With this new understanding in mind, let us now go back to my original energy balance studies published in "A Physical Theory of the Living State: the Association-Induction Hypothesis" (Blaisdell, Waltham, 1962, Chapter 8).The first key issue here is how to estimate the minimum energy need for the postulated sodium pump. Obviously I could not do it the conventional way by estimating the rate of sodium efflux from the slope of the slow fraction. However, this was a decision to be made in the 1950's. All the important experiments to establish unequivocally that it is the fast fraction which represents the sodium ion efflux still belonged to the future. Nonetheless, I was already very sure that the slow fraction interpretation is wrong.
So I chose a conservative compromise, which is better than what I knew to be the wrong answer (i.e., from the slope of the slow fraction) and closer to what was not to be known with certainty until many years later. I also wanted to choose a compromise that even my opponents could not legitimately find fault with. Since the majority of workers at that time believed that the slow fraction represents the entire sodium efflux, I started from there. I exposed a small muscle fiber bundle for a finite length of time, say 3.0 minutes to a Ringer's solution containing labeled sodium ion. I then did a standard washout study and resolved the semilogarimic efflux curve obtained into a fast fraction and a slow fraction. I then extrapolated the slow fraction---which, I repeat, the majority of muscle physiologists at that time believed to come from the cells--- to zero time, which would, according to their belief, yield the labeled sodium ion initially present in the cells of the muscle fiber bundle. Since that initial radioactively labeled sodium could only have entered the muscle cells during the 3.0 minute of soaking in the labeled solution, dividing that amount of labeled sodium by 3.0 and the muscle-fiber-bundle weight yielded the rate of influx into a unit weight of muscle.
Since during the time of the experiment there was no significant change of the total sodium ion concentration, the influx rate and efflux rate must be equal at all times. Therefore the influx estimated from the slow fraction gives me an estimate of the sodium ion efflux rate. However, I also pointed out clearly that the method I chose for estimating the rate of sodium ion efflux is not the true initial Na+ but "deliberately underestimated initial Na22 content for the muscle fiber." (Line 6 from bottom of page 209 in the legend of Table 8.7 in "A Physical Theory of the Living State" 1962, see lp7a), implying clearly that the true efflux rate is even faster--- as subsequent studies, especially that under (1), (2), (3) and (4) have established without ambiguity. With these background material fully explained, let us now turn to Chris Miller's announced reasons given in his Ph.D. thesis for rejecting the AI Hypothesis and returning to the membrane-pump theory.
I put A's criticism into similar 6 subheadings as given by A himself:
In this, Miller pointed out that the sodium entry I determined by the intercept (i.e., influx rate) of the slow fraction does not agree with that determined by the slope of the slow fraction (i.e., efflux rate). This is truly weird.
First note that it was I who introduced the comparison of the efflux rate determined from the intercepts and from the slopes as a means of deciphering which fraction truly represents the sodium ion efflux. I was excited about this perception and in the early 70's I talked often about the intercepts and slopes etc. etc. during our weekly seminar and at other times to all my graduate and postdoctoral students including A. So much so, he was even a coauthor of the 1973 review in which the key figure of (1) experimentally establishing this point was reproduced which showed, like the others, that the slow fraction does not represent the sodium-ion efflux.
I never said that the efflux rate from the intercept of the slow fraction and from its slope should agree ---in fact I maintained precisely the opposite: that they should not agree (see (4) above).
Hardly surprising. Keynes and Steinhardt's erroneous acceptance of the slow fraction as the true sodium efflux created their erroneously slow influx values.
Again wrong. It was shown long ago to be negligible compared to the total efflux (e.g., 0.1%) (Ling, Fed. Proc. Symposium 24: S-103, 1965, p. S-105, footnote).
Anatomically only the T-tubule is directly connected to the outside (Porter and Bonneville, An Introduction to the Fine Structure of Cells and Tissues, Lea and Febiger, Philadelphia, 1964) and the T-tubule makes up an insignificant fraction of the cell volume,( i.e., 0.4%) to accommodate the fast fraction of Na+ (Peachy, J. Cell Biol. 25:209, 1965; Hill, J. Physiol. 175:275, 1964) (see Physiol. Chem. Phys. 2: 242-248, 1970, p.246).
The speculation that the fast fraction comes from the SR is not only without supportive experimental evidence but in fact ruled out by the following two sets of facts considered together:
Ling and Walton studied the simultaneous efflux curves of both radioactively labeled Na+ and labeled K+ ion from the same muscles. After incubation of sartorius muscles in a Ringer's solution containing labeled Na+ ion from the start (total time of incubation in this radioactive ion was 18 hours at 25o C) but labeled K+ only for the last 25-40 minutes of incubation, the muscle was centrifuged to remove radioactively labeled ions in the extracellular space, washed in a stream of non-labeled Ringer's solution and the efflux curves plotted semilogarithmically as usual. Though freed of labeled ions in the extracellular space, the Na+ efflux curve continued to show the two-fraction profile as usual, while the K+ efflux is represented by a perfect straight line with a very gentle slope. There is no fast fraction at all in the K+ efflux curve (Ling and Walton, Physiol. Chem. Phys. 7:501, 1975).
If the fast fraction of Na+ came truly from the SR, then the membrane separating the T-tubule from the SR proper must be highly permeable to Na+ but impermeable to K+ altogether.
In that case, the part of the muscle cell surface near the T-tubule opening would become a permanent and exaggerated version of the cell surface normally seen only transiently during the passage of an action potential ( with transient high permeability to Na+ and low permeability to K+); and as a result, the (standing) resting potential would show great fluctuation along the length of the muscle fibers, with 90 mV-outside-positive potentials throughout most of the cell surface disrupted by periodic dips to 0 mV at points near the T-tubules openings--- which is totally contradicted by facts. No such periodic spatial fluctuations of resting potentials has been observed. (Ling and Gerard, J.Cell.Comp.Physiol.,34:383,1949; Nastuk and Hodgkin, J. Cell. Comp. Physiol. 35:39, 1950).
It might also be mentioned that if such spatially sharp difference in potential existed at all, it would create a wide-spread instability. The cell would be thrown into a continuous state of disorganized fibrillation and would soon die of exhaustion. Nature, as we know it, is much wiser than that.
This is true. In normal frog muscle, in the presence of an external sodium ion concentration of 100 mM, about half of the total intracellular concentration is adsorbed. The free fraction when expressed in micromoles per liter of cell water is about 18 mM. This reduction of free intracellular sodium ion concentration discovered in my laboratory long after the 1950's during which the energy balance study was made, would reduce the minimum energy need somewhat but this reduction is partly compensated by the increase in the sodium ion concentration gradient which increases the minimum energy need. However, even if we totally disregard this compensatory effect, the energy discrepancy from the recognition of the adsorption of intracellular sodium, would lower the minimum energy need of the sodium pump from between 600 times to 1200 times of the maximally available energy to between 300 times to 600 times. And that is only the discrepancy from considering just one ion, the sodium ion, at one kind of membrane, the plasma membrane alone.
This comment has no validity. The turn-over rate of the intra-, extra-cellular exchange of labeled Na+ goes on at a pace very fast (in minutes) while the time needed to lose the Na+ gradients altogether---never reached in any one of my experiments---would take many hours if not days. Consider this analogy. If at the end of a day, the water level in your reservoir has fallen 10%, how much energy you need to keep the water level at its original level depends not just on the difference of the water level at the beginning and end of the day, but even more importantly on how fast is the turnover rate of the water. If the turnover rate is very slow, say many days, then the energy needed to replenish the 10% loss is just that to move that amount of water. On the other hand, if the turnover rate is ten times, the energy would be ten times the total water content of the water reservoir. The 10% difference in the initial and final level is of lesser importance. But this is not the only point where, Miller went astray. He did not study the data carefully.
The intracellular sodium-ion concentration in the poisoned muscle remained essentially unchanging from its normal initial value of healthy muscles till at least the 6th hour after poisoning began, hovering between 20 to 30 micromoles per gram of muscle (while the external sodium ion concentration was at a steady 100 mM). From the 6th hour to the 8th hour, the sodium ion concentration in the cells rose to about 35 micromoles per gram but that is still well below the external concentration of 100 mM. Of the three sets of data presented, two sets lasted only 4 hours during which time there was no gradient degradation. Only the third set lasted till the 8th hour. But even at the 8th hour in the third set of experiments the overall electrochemical gradient was still over 100 mV outside positive (compared to between 120-130 mV outside positive at the very start of the experiment when the muscles were still normal). It is true that in this particular third set of experiment, there was such a decline of some 20% of the electrochemical gradient---like the 10% drop in water level of the water reservoir cited above--- and the energy need accordingly reduced by that percentage---as it was taken into account in my original calculations. And it was after this correction had been taken into account, that the minimum need of energy still exceeds the maximum available energy by a ratio of 1800%---a figure that is vastly made still larger later for reason given above.
To leave no doubt in the mind of the reader, consider another simple thought experiment. Suppose you are in a row boat on the open sea and suddenly something hit the boat and water is pouring in. To stay alive, you must bail out the water from the boat fast enough so that it would stay afloat. If A were right, your job should get easier and easier as the water level in the boat is rising higher and higher, and more and more of the water in the boat would leak back to the ocean outside by itself without your help. This is absurd. The truth is that no water can leak back from a lower level inside the boat to a higher level in the sea on its own. As long as the boat is still afloat, you must use approximately the same amount of energy to bail out the same amount of water. To be sure, it would cost a little less energy due to the lowering of the inside-outside level-difference, but that has already been taken into account in my calculations.
Similarly, the basic law of physics is incompatible with the idea that a positively charged ion like sodium could run "down" a 100 mV outside-positive electrochemical gradient, no more so than water can leak back from inside the still-afloat boat to the ocean outside or water can flow "down" from the bottom to the top of a hill.
There remain two other comments made by A in his Ph.D. thesis in defense of the membrane pump theory and against the AI Hypothesis. One was taken from another pair of my fleeing students, Palmer and Gulati which is briefly described and answered under linked page lp7 (6). The other concerning the electrical field effect at the cut end of muscles on K+ was answered in linked page lp7 (1).
A's conclusion that "Ling's energy calculation for the Na+ pump... is equivocal enough that it should not be taken as disproof of the membrane theory"(Ph.D. thesis, p. 36) was as presumptuous as a six-year-old shooting a BB gun at Mount Rushmore, and pronounces that he had toppled the Black Hills. The manuscript which he and B put together in fun and which he could be circulating around--- could not be much different from what he described as given "in details" in his Ph.D. thesis (see portion of his June 28, 1996 letter cited above) --- and why he himself has called the material he circulated around as "useless junk".
The fact that a reporter like Gina Kolata could be so completely captured by what Dr. A and Dr. B circulated around told me that I have to put the record straight. And that is what I have done here.
Thus the fact that Dr. A could get as far as he did was based on ignoring critical issues described under 2, including the important fact that ATP and phosphocreatine do not contain a package of so-called "high-energy bonds". This revelation raised the energy disparity by forty fold. His claim that I have overestimated the Na efflux rate is just as completely wrong as he was on virtually all the issue he raised with the only exception of the issue of bound sodium which does lower the estimated energy need for the hypothetical sodium pump but that only lowers the minimum energy need from 600-1200 times of that maximally available and thus impossible, to 300-600 times impossible.
There is little question in my mind that the mass exodus of my former students per se, aided by the kind of unfounded claims put out by A and B, and made worse by Gina Kolata's endorsement has contributed to the plight of legitimate cell physiology today.How much, no one can tell. Nevertheless, there is little doubt in my mind that A and all my other graduate students would have acted altogether differently if they did not see a total hopelessness in front of them to stick to the AI Hypothesis.You read my home page you should have some idea where the evilness really came from.