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Commentary |
Department of Physiology and Biophysics, Medical Sciences Program, Indiana University School of Medicine, Bloomington, Indiana 47405-4401, USA
ABSTRACT
When a solute is dissolved in water at (T, pel),
the temperature and external pressure applied to the solution, the
water in the solution is altered as is pure liquid water at (T,
pel - 
H2Ol). The
liquid water and the water in the solution are in equilibrium when
H2Ol is the osmotic pressure of the water in
the solution. Every partial molar property of the water in the solution
at (T, pel), including its vapor pressure,
chemical potential, volume, internal energy, enthalpy and entropy, is
identical with the same molar property of pure liquid water at (T,
pel - H2Ol). This
elementary fact was deduced by Hulett in 1903 from a thought
experiment; he concluded that the internal tension in the force bonding
the water is the same in both solution and pure liquid water, in
equilibrium, at these differing applied pressures. Hulett's
understanding of osmosis and the means by which the water was altered
by the solute were neglected and abandoned. Competing ideas included
the notions that the solute attracts the water into the solution and
that the solute lowers the activity (or concentration) of the water in
the solution. These ideas imply that the solute acts on the solvent at
the semipermeable membrane separating the solution and water. Hulett's
theory of osmosis requires that the solute alter the water at the free
surface of the solution where the solute exerts an internal pressure on
the boundary of the solution retaining the solute. Fluid exchange
across the capillary endothelium is influenced, in part, by colloidal
proteins in the plasma. The role of the proteins in capillary fluid
exchange must be reinterpreted based on Hulett's view, the only valid
view of osmosis.—Hammel, H. T. Evolving ideas about osmosis and
capillary fluid exchange.
Key Words: capillary–interstitial fluid exchange • Hulett's theory • Starling's hypothesis • Starling's equation
FROM 1960 UNTIL his death in 1980, Professor Scholander and I began preparation for this lecture honoring August Krogh. Of course, we did not know then the circumstances that would become available. Few persons admired Krogh more than Scholander did. And no one, I believe, admires Pete Scholander more than I do.
During this lecture, I shall attempt to be a teacher and a provocateur. I hope to increase your understanding of osmosis with some old and some new ideas about the osmotic process. I will reexamine Starling's experiment (1) and suggest new mechanisms to account for fluid exchange across the capillary endothelium as blood flows from one end to the other. My suggestions will be incomplete; so I challenge the reader to search for additional mechanisms whereby to account for fluid exchange between a capillary and its surrounding interstitial fluid.
The story of osmosis is like a tapestry. There are many strands, many ideas in the story. Each idea is associated with a person or persons.
IDEA 1: SOLUTE ATTRACTS SOLVENT: KROGH
Appropriate for this lecture, I shall start with August Krogh. Reference is made to quotations about "The exchange of water through the capillary wall" on page 280 in Krogh's (2) classic Monograph The Anatomy and Physiology of Capillaries, 1959. His words summarize the widely accepted view of physiologists regarding the role of solutes (including colloids) in affecting the movement of water in aqueous solutions.
"The impermeability of the capillary wall for colloids forms the basis of the mechanism for absorbing isotonic solutions of crystalloids into the circulation, described in 1896 in the classical paper by Starling: `On the absorption of fluids from the connective tissue spaces'.
"To demonstrate the absorption of a salt solution, isotonic with the blood, from the tissue spaces directly into the capillaries, each of the surviving hind limbs of a dog was perfused with the dog's own defibrinated blood, which was made to circulate regularly through the leg. One of the legs was first made edematous by the injection of 1% NaCl solution, and it was found that, while the blood circulating through the normal leg remained practically unaltered, the blood circulating through the edematous leg gradually became more dilute by taking up the fluid from the edema.
"This absorption seemed very puzzling, since the initially high osmotic pressure of the outside fluid must cause water to pass from the blood into the tissue spaces, while the constantly higher hydrostatic pressure of the blood in the capillaries must set up a filtration of water and salts in the same direction. Starling showed that the explanation of the observed absorption lay in the osmotic pressure of the blood colloids."
Then Krogh adds, "It is unnecessary here to go into the question about the exact nature of osmotic pressure, which is still a debated problem, and I need only remind you that the term osmotic pressure expresses the attraction of the dissolved substances for the solvent fluid; ... " (italics added for emphasis).
For want of a better idea, Krogh (2) allowed that dissolved substances attracted solvent fluid across a solute barrier. Dutrochet (3) held the same view when he demonstrated osmosis for the first time (Fig. 1 ). Two rhetorical questions concern us: 1) Does solute attract solvent into its solution across a membrane permeable only to the solvent; and 2) If not, is it important to know the osmotic mechanisms causing solvent transport? The answer to the first question is certainly not. The effect of the solute on the solvent depends almost exclusively on the number of solute atoms, molecules, or ions dissolved in (and in random motion in) the solution. It is unimaginable how this fact could be reconciled with the notion that equal numbers of these widely differing solute entities could attract the solvent equally.
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IDEA 2: SOLUTE LOWERS SOLVENT CONCENTRATION: GUYTON AND MOST BIOLOGISTS
Guyton (5) answers the second question in his discussion of osmotic equilibria and fluid shift between the extracellular and intracellular fluids. He writes: "One of the most troublesome of all problems in clinical medicine is maintenance of adequate body fluids and proper balance between the extracellular and intracellular volumes in seriously ill patients. The purpose of the following discussion, therefore, is to explain the interrelationships between extracellular and intracellular fluid volumes and the osmotic factors that cause shifts of fluid between the extracellular and intracellular compartments." Continuing the quotation, "The basic principles of osmosis and osmotic pressure ... are so important to the following discussion that they are reviewed here."
Guyton then attempts to explain osmosis as follows: "Osmosis results from the kinetic motion of the molecules in the solution on the two sides of the membrane and can be explained in the following way: The individual molecules on both sides of the membrane are equally active because the temperature, which is a measure of the kinetic activity of the molecules, is the same on both sides. However, the nondiffusible solute on one side of the membrane displaces some of the water molecules, thereby reducing the concentration of the water molecules. As a result, the so-called total chemical activity of water molecules on this side is less than on the other side, so that fewer molecules strike each pore of the membrane each second on the solute side of the pore than on the pure water side, resulting in net diffusion of water molecules from the water side to the solute side."
So Guyton subscribes to two other ideas about the mechanism of osmosis: 1) solute lowers the water concentration in the solution, and 2) this lessens the activity of the water. Both ideas imply that the solute has its effect on the water in the solution at the membrane and they give no consideration to the solute concentration at the free surface of the solution. A solution has a free surface when it has a gas–liquid interface where the liquid is in equilibrium with external gases (including vapors from solution) and where the pressure of these gases is an external pressure applied to the free surface of the solution. A free surface is also a boundary where most or all of the solute and solvent molecules are reflected and contained within the solution. Later we will note how understanding the way solute alters the solvent at a free surface can lead to an understanding of how solvent is altered by solute in a solution without a free surface. Biologists are taught that solutes lower the concentration of water in an aqueous solution and pure water diffuses into the solution through a membrane permeable only to the water. Both of these notions are derivatives of G. N. Lewis's (6) teachings that solutes near the semipermeable membrane lower the fugacity and the activity of the water at the membrane so that water diffuses through the membrane down an activity gradient. Let us examine these two ideas carefully.
Biology teachers present water concentration as the basis for osmosis. If adding solute to water always lowered the water concentration in the solution, then this idea could not be falsified without other evidence to the contrary. However, even one exception would negate the idea. Adding solutes to water usually does lessen the water concentration in the solution. This fact is illustrated by adding Na2SO4 to water (Fig. 2 ). However, adding either MgSO4 or NaF to water increases water concentration up to a certain concentration. Nevertheless, the water never diffuses from these solutions to pure liquid water where its concentration is lower. Adding these solutes to the water in any amount always increases the Osmolality of the water, regardless of the water concentration. Moreover, the water concentration of the Na2SO4 solution decreases as a curvilinear function of solute concentration whereas the Osmolality of its water increases as a linear (not curvilinear) function of solute concentration. So the water concentration idea is false and cannot explain osmosis.
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IDEA 3: SOLUTE LOWERS ACTIVITY OF SOLVENT: LEWIS
What about water activity? Lewis (6 , 9 ) defined water activity in two ways. As illustrated in Fig. 3 , he defined activity in terms of a term he designates as fugacity. For a real solution, fugacity of the solvent, fsolventl(T, pel, xsolventl), differs from vapor pressure of the solvent, psolventg(T, pel, xsolventl), where T and pel are the temperature and external pressure applied to the solution and xsolventl is the mole fraction of the solvent in the solution, nsolventl/nsolventl + nsolventl. Only for the ideal solution are fugacity and vapor pressure of the solvent identical. But no solvent in any solution is ideal; so what is fugacity of the solvent in a real solution? Lewis suggested, and many authors repeat his suggestion, that fugacity of the solvent is the `tendency of the solvent to evaporate from the liquid solvent' either from pure liquid solvent or from the solvent in the solution. This suggestion has no meaning. Since fugacity and vapor pressure of a real solvent differ and since the vapor pressure of the real solvent is an exact measure of the tendency of the solvent to evaporate from its liquid phase, then fugacity cannot mean what Lewis suggested. The fact is that the term fugacity has no physical content. Likewise, when Lewis defined the activity of the solvent in a solution as the ratio of the fugacity of the solvent in the solution to the fugacity of pure liquid solvent, he defined another term that has no physical content. Stating that the solute lowers the fugacity and the activity of the solvent in a solution does not explain how the solute does it.
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Lewis also defined solvent activity in a solution, asolventl, another way, namely, µsolventl(T, pel, nsolutel, nsolventl) - µsolventl*(T, pel) is equivalent to RT ln asolventl, where µsolventl(T, pel, nsolutel, nsolventl) is the chemical potential (i.e., partial molar free energy) of the solvent in a solution of nsolutel moles of solute dissolved in nsolventl moles of solvent at (T, pel), the temperature and external pressure applied to the solution. µsolventl*(T, pel) is the chemical potential (molar free energy) of the pure liquid solvent at the same temperature and applied external pressure. R is the universal gas constant and T is the absolute temperature. So Lewis defined solvent activities in pure liquid and the solution in terms of the chemical potentials of the solvent in pure liquid and the solution, respectively. The chemical potentials of the solvent in solution and pure liquid are its partial molar and molar free energies in the two states. This definition of solvent activity in the solution indicates nothing about the mechanism by which the solute lowered the chemical potential of the solvent in the solution. I repeat, stating that the solutes lower the activity of the solvent in the solution does not explain how the solute alters the solvent.
IDEA 4: SOLUTE ALTERS INTERNAL SOLVENT TENSION: HULETT
It seems clear by now that these first three ideas about osmosis
are nonsensical answers of the basic question, How do the solutes alter
the solvent in a solution? Solute molecules (crystalloids and colloids)
do not and cannot attract water molecules into an aqueous solution.
Water concentration at a rigid membrane has no effect on the movement
of water across the membrane. Fugacity and activity of water are phony
terms (meaning `marked by empty pretension') and do not explain water
flux. An understanding of the roles of solute molecules on the movement
of water across a solute barrier must be based on Hulett's theory of
osmosis. Suppose that the external pressure applied to the free surface
of a solution is pel. Suppose also that
pel = psolventg*(T,
pel), where
psolventg*(T, pel) is
the vapor pressure of the solvent at (T, pel).
That is, the solvent vapor is the only gas and its vapor pressure is
the only external pressure applied to the solution surface. Next,
suppose that the external pressure applied to the surface of pure
liquid solvent is psolventg*(T,
pel) minus solventl,
where solventl is the osmotic pressure of
the solvent at the free surface of the solution. Hulett
(10)
recognized that solute alters solvent at the free
surface of a solution at (T, pel) in the same
way that pure liquid solvent is altered at (T,
pel -
solventl). Equilibrium between the
solution solvent and pure liquid solvent is attained only when the
pressure applied to the pure solvent is less than the external pressure
applied to the solution by solventl, at the
same temperature.
Hulett's idea about osmosis applies to the solvent in a solution in equilibrium with all phases of the solvent, at a constant temperature. He expressed his idea as a thought experiment (Fig. 4 ). In Hulett's article, he omitted the mathematics depicted in this representation of his thought experiment. Nevertheless, his idea and his conclusions are inescapable. He thought of three columns. Column III is a vertical column of water vapor in a gravity field. z is the vertical coordinate for the x and y horizontal coordinates. In the enclosure, there is no vapor other than water vapor. At temperature T, the vapor pressure at z = 0 is known and can be designated as pH2Og*(0) = pH2Ol*(T, pH2Og*), i.e., the external pressure applied to the liquid water is the vapor of the pure liquid water at z = 0 to which the applied temperature and pressure are (T, pH2Og*). Knowing this value, the exact vapor pressure at z = h, pH2Og*(h), can be determined by applying Boltzmann's energy distribution principle which requires there be fewer vapor molecules at z = h because, in a gravity field, the molecules at h have more molar internal energy (i.e., potential energy) than at z = 0.
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Next, consider column II. Pure liquid water is held at h by a matrix; as, for example, is the water in the xylem vessels at the top of a 100 meter tall redwood tree. The weight of the vapor pressure of liquid water between z = 0 and h results in a pressure applied to the liquid water at h equal to pH2Og*(h) - (h - 0)/10 atm, since a 10 meter vertical freestanding column of water exerts a pressure of 1 atmosphere at its base. Thus, at 100 meters, the pressure applied to the water at the top of a redwood tree will be 10 atm below ambient pressure. A negative pressure applied to liquid water lowers the vapor pressure of the liquid water in accordance with a rigorous thermodynamic equation known as Poynting's relationship. Of course, this equation ensures that the liquid water at z = h is exactly the same as the vapor pressure in column III at z = h. Otherwise, water molecules would either evaporate from the top of column II and condense at the bottom of column III (or vice versa) and this would result in a perpetual flow of water between the two columns; a violation of the Second Law of Thermodynamics.
Now, consider column I. The solute dissolved in the water in this
column has a concentration such that the equilibrium height of the
solution in column I is h. The only external pressure applied to the
water in the solution at its free surface at h is
pH2Og*(h). Hulett concluded that, due to an
internal positive pressure exerted by the reflected solute (molecules)
against the boundary of the solution at h, 1) the solute
must be pushing upward and holding the solvent of the solution at h and
2) the solvent must be opposing this solute pressure and the
cohesive force bonding the water in the solution in column I must be
altered exactly as is the cohesive force bonding the pure liquid water
in column II, caused by the lower pressure applied to it. In other
words, the internal tension in the cohesive force bonding the water in
the solution in column I at an applied pressure
pH2Og*(h) is exactly the same as the cohesive
force bonding pure liquid water at an applied pressure
pH2Og*(h) -
H2Ol(h), where
H2Ol(h) is the osmotic pressure of the water
in the solution at h. As illustrated in Fig. 4
, every partial molar
property of the water in the solution at (T,
pH2Og*(h)) is exactly the same as the same
molar property of pure liquid water at (T,
pH2Og*(h) -
H2Ol(h)). Hulett's explanation of how
the water in a solution is altered by the solute is inescapable; it
ensures that the vapor pressure of the water in the solution in column
I at every z, including z = 0, is exactly the same as the
vapor pressure of the pure liquid water in column II, and the same as
the vapor pressure in column III at the same z. Thus, there is no
violation of the `Second Law of Thermodynamics'. Note two important
facts. Hulett's theory attributes the osmotic pressure of the water in
a solution to the concentration of the solute at the free surface of
the solution at z = h. Hulett's theory requires that the
water in the solution at every z be subjected to the same internal
tension as is the water in the column of pure liquid water. This means
that the water on the two sides of the membrane have the same internal
tension. Both of these conclusions about the water in the solution
contradict the conclusions inferred from either of the three preceding
theories described above under Ideas I–III. These ideas attribute the
osmotic effect of the solute on the water in the solution to the
concentration of the solute at the membrane separating columns I and
II. They require that the internal tensions in the water on the two
sides of the membrane differ, i.e., water entered the solution from
column II and increased the pressure applied to the water in the
solution in column I, thereby altering its internal tension and
rendering it different from that in the pure liquid water. Hulett's
theory remains the only tenable theory explaining how the solutes alter
the water in a solution in equilibrium with pure liquid water at the
same temperature. Although Hulett's theory explains how solute alters
the solvent in a solution, without additional insights provided by a
kinetic theory of liquids, his theory does not predict accurately what
the osmotic pressure will be when only the moles of solute and solvent
are known. The other theories also fail to make this prediction.
Before proceeding further, we should inquire how a negative pressure applied to pure liquid water alters the internal tension in the force bonding the water in its liquid phase. Contrary to expectation, applying a negative pressure—a tension—to liquid water lessens the internal tension in the bonding force (8 , 11 , 12 ). For this reason, the vapor pressure of the liquid water is lowered when the pressure applied to it is diminished. The basic idea is simple. When the temperature and pressure applied to pure liquid water is (T, pel), the internal pressure exerted by the water molecules in the liquid against the liquid boundary is equal to RT/Vavail.H2Ol*(T, pel)), where Vavail.H2Ol*(T, pel) is the volume of space available for the motion of the centers of mass of the water molecules in a mole of liquid water at (T, pel). It equals the molar volume minus the molar hard-core volume, i.e., Vavail.H2Ol*(T, pel) = VH2Ol*(T, pel) - Vhard core H2Ol*(T, pel), where Vhard core H2Ol*(T, pel) is the space not available to the center of mass of a water molecule as it collides with others in a mole of liquid water. We should note that most collisions in liquid are high-order collisions, meaning that a molecule collides simultaneously with many other molecules of the same kind so that it is excluded from the volume of all those molecules with which it collides at the same time. For this reason, we can also understand how the hard-core volume of a mole of water vapor in which all collisions are first order, i.e., binary collisions, is 30.49 cm3; whereas the molar volume of liquid water is only 18.02 cm3 at 0°C and its molar hard-core volume only 14.92 cm3 (12) .
The internal tension in pure liquid water at (T,
pel) is the externally applied pressure minus
this internal pressure, i.e., 
H2Ol*(T,
pel) = pel -
RT/Vavail.H2Ol*(T,
pel). When the pressure applied to pure
liquid water is lessened from (T, pel) to (T,
pel - H2Ol), this
has little effect on the molar hard-core volume and has a pronounced
effect on the molar volume of available space. Consequently, the
internal tension is diminished to H2Ol*(T,
pel - H2Ol) =
[pel - H2Ol] -
RT/Vavail.H2Ol*(T, pel
- H2Ol). Thus,
H2Ol*(T, pel -
H2Ol) is always less than
H2Ol*(T, pel). That
is, H2Ol*(T, pel) -
H2Ol*(T, pel -
H2Ol) is always positive but less in
magnitude than H2Ol. For this reason, the
vapor pressure of liquid water is less at (T,
pel - H2Ol)
than at (T, pel). For the same reason and in
accord with Hulett's theory of osmosis, the internal tension and vapor
pressure of water in an aqueous solution are less than in pure liquid
water, both at the same (T, pel).
IDEA 5: INTERNAL WATER TENSION THE SAME INSIDE AND OUTSIDE THE PLANT CELL: DIXON
The logic of Hulett's thought experiment of 1903 was impeccable, but he was not the only one to arrive at equivalent theories. In the same year, Dixon (13) arrived at the same implications expressed in Hulett's theory, namely, that there can be no difference in the internal solvent tension across the semipermeable membrane. In Dixon's monograph (14) of 1914 entitled Transpiration and the Ascent of Sap in Plants, chapter 7, entitled `Osmotic pressure and leaf cells' and in the section `Pressure and tension in leaf cells', he reveals remarkable insight about the nature of these pressures within and without the cell of a plant leaf. He states: "The simultaneous presence of pressure and tension within these cells, at first sight, appears paradoxical, but a moment's consideration will show that it is quite possible for the solvent, water, to be in a state of tension, i.e., at a negative pressure, while the dissolved substances may be at a positive pressure and be active as a distending force in the cell.
"Even though by distinguishing between the pressure conditions of the solvent and of the dissolved substances it is easy to conceive how the water in a turgid cell may be in a state of tension, it appeared of interest to show in the following way that this peculiar state of affairs is possible."
Dixon proceeds to describe an experiment to demonstrate this state of affairs. In a later section of the same chapter entitled `Osmotic pressure balanced against gas pressure', Dixon describes a method (Fig. 5 , left) whereby he could apply gas pressure to leaves and stem of a plant or twig with only the cut end of stem protruding from the pressure vessel and extending into a container of water below. Dixon had the cylindrical wall of the vessel made of 1 cm thick glass so that he could safely apply gas pressures of up to 100 atm inside the vessel and observe wilting or flagging in the leaves of enclosed plant. He reasoned that when he applied sufficient gas pressure to a twig so as to cause water to leave it and cause the flask below stem to gain weight, then that pressure would equal the osmotic pressure of cells in the leaves. His reasoning was valid, but only when the twig had lost sufficient water to lose all its turgor pressure and wilted. In fact, the pressure at which water would just flow from the stem and enter the flask is the same as pbal in Fig. 6 and Fig. 7 , and is equal in magnitude to pxys, the xylem sap pressure in the twig. Apparently Dixon did not realize that he had already developed a method for measuring this important pressure for the study of water relationships in plants.
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IDEA 6: DIXON'S COHESION THEORY EXPERIMENTALLY VERIFIED AND HIS THEORY OF TURGOR PRESSURE REDISCOVERED: SCHOLANDER AND HAMMEL
I describe this part of the story of osmosis because it reveals how Scholander and I became interested in osmosis. This interest also relates to August Krogh. In Bodil Schmidt-Nielsen's biography (15) of her parents entitled August & Marie Krogh: Lives in Science, she gives an account of how Scholander came to the United States. She writes: "While in the United States, August had arranged with Laurence Irving at Swarthmore College for Dr. Per F. Scholander to go to United States to work with Irving because of their common interest in diving mammals. Krogh was impressed with the brilliant Norwegian, who had been studying diving seals while working under the most primitive conditions in a cellar at the University of Oslo. Whenever Krogh saw real talent, he spared no effort. He recommended Scholander for a Rockefeller Fellowship, which was granted. In September 1939, however, Scholander received a letter from the foundation announcing that all fellowships had been canceled due to the war. Alarmed, Scholander asked Krogh, 'What do I do now?' Krogh did not want Scholander's talent to be wasted in Norway for the duration of the war. 'Board the first ship to America and pretend the letter has not reached you,' said Krogh. 'Once in America you will be taken care of.' Scholander worried, but told himself, 'If papa Krogh wants me to go, I will.' This he did and, as Krogh had promised, he got the fellowship."
In April 1953, I joined Scholander and flew to Frobischer Bay, Baffinland, Canada, to investigate how bony fishes avoid freezing in sea water at -1.8°C, since their body fluids should freeze at about -0.8°C. At that time, Scholander was also worried about Dixon's cohesion theory. It had never been experimentally verified and Scholander had doubts about its validity. When he returned to the Woods Hole Institution of Oceanography, where he worked, he investigated and discovered that in early spring the xylem sap in grape vines was under positive pressure. This reinforced his doubt about the cohesion theory. In 1960 I again joined a Scholander expedition to investigate the diving responses of Australian Aborigines who were diving for pearls in the Torres Straits. We took advantage of our location at the mouth of the Jardine River to inquire about another question, How do mangroves remove most of the salt in sea water as they transpire and how do they eliminate that salt which enters the xylem? Scholander made three independent efforts to test Renner's theory (16) (based on Dixon's cohesion theory) that the mangrove sucks nearly salt-free water into its roots by reverse osmosis. Scholander's experimental methods gave sap pressures of about +1 to -1 atm, not the -30 atm or less required by Renner's theory.
Soon after Scholander arrived at the Scripps Institution of Oceanography in late autumn of 1957 he began dreaming about a research vessel that would be designed to facilitate the researches of physiologists, biochemists, and neuroscientists. Scripps had no such ships in its fleet. By 1964, Scholander had some officials at the National Science Foundation persuaded that his plan was worthy of support. He also had formed a National Advisory Board (NAB)3to plan and govern the activities of this floating laboratory, which later became known as the R/V Alpha Helix. To demonstrate the feasibility of his ideas for a floating laboratory, he engaged a small converted harbor tug, the R/V Spencer Baird in the Scripps fleet, and sailed south to Magdalena Bay on the Pacific side of Baja California. I joined Scholander's expedition to continue studies of the local mangroves. Scholander wanted to show that reverse osmosis could account for the nearly salt-free xylem sap we had observed in Queensland, Australia. He removed the top part of a sapling mangrove and immersed the root system into sea water contained in an enclosed vessel, with the stem of the plant protruding through a pressure seal in the top of the vessel. Nitrogen gas from a N2 cylinder was admitted into the vessel so as to apply measured pressure to the sea water. Scholander expected that only when the gas pressure reached 30 atm or more would salt-free water flow out from the cut-off stem outside the vessel. Again, Scholander's experiment failed to confirm Renner's theory. Only sea water came out of the stem and at gas pressures of around 2 or 3 atm, not 30 atm. Only later was he able to demonstrate reverse osmosis in small mangrove plants grown hydroponically in sea water, thereby avoiding damage to the rootlets that are damaged by uprooting the plant from soil (17)
At this time, however, Scholander had to return to La Jolla, California, to meet with members of the NAB. He instructed Captain Hansen of the R/V Spencer Baird to sail around B.C. to La Paz, where Scholander planned to rejoin the ship, accompanied by some members of the NAB. As the ship was going around to La Paz, I asked Paul Fleischer, our gifted machinist, to make a small pressure vessel of a size sufficient to contain a mangrove twig with only a few leaves. When we arrived at La Paz and set up our shore camp, I was able to show that only when the N2 gas surrounding the entire twig in the pressure vessel reached 30 atm or more would xylem sap be pressed out of the cut end of the stem protruding through the pressure seal (Fig. 5 , right) (18) . Moreover, excess pressure caused sap to flow out of the stem. It was collected and found to contain no salt. Renner's theory was verified experimentally and a simple method was now available to measure xylem sap pressure in any twig from any plant. When Scholander returned to La Paz, he was accompanied by Wallace Fenn and Knut Schmidt-Nielsen. I met them at the airport and told them about these experiments, but Scholander was not convinced. After lunch on board the Spencer Baird, we took a small boat to the shore camp in a mangrove swamp and I demonstrated the method. After two hours of intensive interrogation, all were convinced that a new technique for investigating water stress in plants was available. Today, only a few plant physiologists 19-21) continue to doubt Dixon's cohesion theory and the pressure vessel technique that verifies the theory.
Wallace Fenn, a great respiratory physiologist in his time, suggested that the pressure vessel could be exploited to yield more information about water relations in the plant. From his experience with lung function, he had extracted valuable information about normal and pathological lungs by studying the pressure vs. volume relationships of the lung. This insight was applied to the plant twig (cf. Appendix A ). After the initial balancing pressure, at which the xylem sap returned and was maintained at the cut surface of the stem of a twig in the pressure vessel, measured, and recorded, an excess pressure was applied to the twig, causing sap to flow out. After collecting the sap and measuring the amount, a new balancing pressure was obtained. This step was repeated several times and the results were plotted as illustrated in Fig. 6 . These inverse balancing pressures vs. volume of xylem sap expressed from the twig can be used to obtain the intracellular osmotic pressures and turgor pressures of the average twig cell (also illustrated).
Results like these can be visualized and queried, as illustrated in Fig. 7 . A typical border parenchyma cell is illustrated in three degrees of hydration. The cell on the right in this figure has no turgor; it represents a cell in a twig from which sufficient xylem sap has been expressed so that its balancing pressure falls on the linear part of the curve in Fig. 6A . In this condition, the xylem sap pressure (the negative of the balancing pressure in the pressure vessel) equals the osmotic pressure in the intracellular sap, including both the cytoplasm and water vacuoles. The cell on the left illustrates a fully hydrated cell such that its xylem sap pressure is 1 atm and its osmotic pressure equals the turgor pressure within the cell. The middle cell illustrates a cell in a twig obtained from near the top of a transpiring tree in mid-afternoon. Its xylem sap pressure is -10 atm; its osmotic pressure is more than that of the left cell because it is partially dehydrated and it less then than that of the cell on the right because it is not fully dehydrated. Its turgor pressure is also midway between the fully hydrated cell and the dehydrated cell. As illustrated, the turgor pressure in each of these cells is the sum of the cell's osmotic pressure and the xylem sap pressure. When the xylem sap pressure is very negative, it can become equal in magnitude to the cells osmotic pressure, so that their sum becomes equal to zero and the turgor pressure becomes zero.
When we were making these observations on mangroves, tall trees, desert plants, etc., an interesting question arose (18) : To what intracellular component do we attribute the turgor pressure: the solutes or the water? Plant physiologists writing textbooks on the subject were (and are) unanimous in their assertion that the water in the cell exerts the turgor pressure against the cell wall. This assertion is based on the flawed contention that the solutes in the cell lessen water concentration (as well as water activity) in the cell, and they lessen the chemical potential of the water in the cell. Thus, water enters the cell, presumably raising the water pressure in the cell, causing turgor pressure and thereby increasing its chemical potential sufficient to prevent further entry of water. Scholander recognized that this interpretation of turgor pressure was nonsense. He asked "how could the water pressure in the cell differ from the water pressure outside the cell membrane when the membrane was readily permeable to the water?" Of course, his question would have a ready answer if the solutes had an attraction for the water beyond the membrane; however, he dismissed this answer as nonsense as well. On reflection, we note that Scholander's view was nothing other than Dixon's view, a view that had long ago been abandoned by plant physiologists. When Scholander and I were preparing our monograph on osmosis (4) , we rediscovered not only Dixon's but also Hulett's view. Moreover, we found that other thoughtful persons had arrived at similar views regarding the nature of osmosis when a solution and its solvent are in equilibrium, including Noyes (24) , Herzfeld (25) , Duclaux (26) , and Mysels (27 , 28 ).
Figure 8 summarizes the differences between the conventional view and the Hulett and Dixon view. The conventional view is based on `water activity' and/or `water concentration', or even on `solute-water attraction'. Initially, when a solution and its solvent water are separated by a semipermeable membrane, allowing water to pass between them but not the solute, and their levels are the same (as illustrated on the left side of the upper panel), the conventional view holds that water diffuses from the pure liquid water into the solution. There is presumed to be no difference initially in the internal tension in the water on the two sides of the membrane: there is only a small pressure drop applied to the water in the pore causing it to pass through the pore. But water diffusion accounts for the transport of water across the membrane attributable to the initial lower water concentration and/or lower water activity. Finally, when the aqueous solution and water come into equilibrium, as illustrated on the right, the water pressure in the solution becomes equal to the osmotic pressure of the water in the solution, thereby raising its chemical pressure to equal that in the liquid water beyond the membrane. Note that a water pressure discontinuity exists at the solution side of the membrane according to the conventional view. Hulett, Dixon, and Scholander found this implication to be inexplicable.
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The Hulett, Dixon, and our view is represented in the bottom two panels of Fig. 8 . The water pressure is illustrated initially as less in the solution compared with the pure liquid water, as it would be if a negative pressure were applied to pure liquid water if it were to replace the solution on the solution side. Water rushes through the pores down a steep pressure gradient being pulled through pores by the altered water tension in the solution. In equilibrium, the water on the two sides of the membrane reveals identical internal tensions and flow ceases for this reason. There is, of course, a greater pressure applied to the membrane on the solution side, but this pressure is attributable to the solute molecules. They are reflected by the membrane; they change momentum and their time rate of change of momentum perpendicular to the membrane is a force. Per unit area, this force is the solute pressure that the rigid membrane opposes (cf. Fermi, 30).
IDEA 7: STARLING'S EXPERIMENT AND ITS CLASSICAL INTERPRETATION
So far we have been inquiring about the osmotic effects of the solute on the solvent when the solution solvent and pure liquid solvent are in equilibrium. I hope the reader is persuaded by now that only the Hulett and Dixon theory of osmosis remains tenable. However, equilibrium seldom pertains to fluids in biological systems. Fluids are commonly flowing either intermittently or steadily. Internal body fluids seldom have a free surface. Certain molecules, atoms, and ions are actively moved across cell membranes by protein transporters imbedded in the membrane. Thus, new insights derived from and in accord with the Hulett/Dixon theory become essential for understanding fluid exchange between fluid compartments that are separated by membranes or cell barriers partially or fully impermeable to certain micro solutes and colloids. Starling's experiment is an excellent example of a nonequilibrium situation where osmotic effects are operating (Fig. 9 ).
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Krogh's (2) account of Starling's (1) experiment quoted above is elegant, but it omitted several important details. Starling removed all the blood from a dog and divided nearly all of it into equal parts. He severed the femoral arteries and veins of the two hind legs, ran blood into their arteries, and collected the blood from their veins (Fig. 9) . He did this at least 12 times and as many as 24 times for each leg, so that the blood flow was intermittent, not a steady, continuous flow. The two legs were prepared differently in that the experimental leg was made edematous and nothing was done to the control leg. To make the experimental leg edematous, he writes that 1% to 1.05% NaCl was injected into the "connective tissue by means of a needle." He does not report how much salt solution was injected or in how many sites on the leg the solution was injected. When the blood was flowing into the femoral arteries, he maintained an arterial perfusion pressure of 65 to 85 torr, well below a normal pressure of 100 torr in a major artery in a dog. He assumed that the interstitial pressures in the experimental and control legs were equal and both negligible. A small amount of each dog's blood was set aside as a standard for comparison with the blood obtained after many passages through the experimental and control legs. After the experimental protocol was completed, Starling `estimated' the hematocrit and the concentration of the solid content of each blood sample taken after the last passage.
Starling believed that interstitial fluid (ISF) from the edematous leg was absorbed into the capillary blood during the multiple infusions, and this absorption was due only to the colloid osmotic pressure of the blood. Multiple perfusions of the control leg caused no reduction in the percentage of solids or in the hematocrit in this blood relative to the standard blood. In fact, these values increased a little in most cases relative to the standard blood. Multiple infusions of the experimental edematous leg reduced the percentage of solids by a little in all the dogs. The percentage of solids decreased by an average 3.0% relative to the control blood and by 4.3% relative to the standard blood. The hematocrit of the experimental blood was 6.3% less than in the control blood.
Starling concluded, "The importance of these measurements lies in the fact that, although the osmotic pressure of the proteids of the plasma is so insignificant, it is of an order of magnitude comparable to that of the capillary pressure; and whereas capillary pressure determines transudation, the osmotic pressure of the proteids of the serum determines absorption. Moreover, if we leave the frictional resistance of the capillary wall to the passage of the fluid through it out of account, the osmotic attraction (author's emphasis) of the serum for the extravascular fluid will be proportional to the force expended in the production of this latter, so that, at any given time, there must be a balance between the hydrostatic pressure of the blood in the capillaries and the osmotic attraction of the blood for the surrounding fluids (our italics for emphasis). With increased capillary pressure there must be increased transudation, until equilibrium is established at a somewhat higher point, when there is a more dilute fluid in the tissue-spaces and therefore a higher absorbing force to balance the increased capillary pressure. With diminished capillary pressure there will be an osmotic absorption of salt solution from the extravascular fluid, until this becomes richer in proteids; and the difference between its (proteid) osmotic pressure and that of the intravascular plasma is equal to the diminished capillary pressure."
Starling believed that the proteins in the blood caused the
osmotic attraction of the blood for the surrounding fluids. Thus,
Starling's classic paper set the stage for all subsequent
interpretations of the role of colloids in affecting the extravasation
and reabsorption of ISF from and to the capillary plasma. His
experiments have not been repeated or corroborated in detail, and his
interpretation of how the colloidal proteins function has not been
questioned. A modern interpretation of Starling's experiment, known as
Starling's hypothesis, differs little from his. Nearly every textbook
describing his experiment interprets it with a graphical representation
(Fig. 10
) or an equation known as Starling's equation:
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(x) is the volume of fluid filtering through
the capillary in unit time and unit length at x, Lp(x) is
the hydraulic conductivity of the capillary at x, S(x) is the
circumference of the capillary at x, Pinpl(x)
and PoutISF(x) are the hydrostatic pressures
inside and outside the capillary, respectively, at x,
e(x) is the reflection coefficient of the endothelium
for the colloids at x and where COPinpl(x) and
COPoutISF(x) are colloid osmotic pressures of
the fluids inside and outside the capillary. This equation is similar
to Renkin's Eq. 4 (32)
.
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For interstitial fluid to return to the venous end of a capillary, in accord with the Starling hypothesis and the Starling equation, the hydrostatic pressure in the plasma must decrease to less than plasma COP about midway along the capillary. This requirement by itself is problematic for three reasons. 1) Not all tissues in mammals have the same hydrostatic pressure profile in the plasma along their capillaries. For example, the mean arterial pressure in the lungs is less than half the systemic pressure. 2) Plasma COP can vary over a wide range with no ill effect. Hargens (33) found that humans cold acclimatized for four days increased their plasma COP by 16%. Hargens (34) also found that plasma COP was over 150 torr in tomcod and more than 75 torr in two other polar fishes, sculpin and Arctic char. 3) Schmidt-Nielsen (35) was puzzled by the fact that birds have arterial pressures double that of mammals, whereas their plasma COP is less than half that of mammals. These observations cannot be reconciled with Starling's hypothesis or equation.
IDEA 8: ANOTHER INTERPRETATION IS NECESSARY; I.E., ANOTHER THOUGHT EXPERIMENT, `SOLUTE DRAG' (36)
Remembering Hulett's theory of osmosis as applied to pure water in equilibrium with water in a solution, we are compelled to at least question Starling's hypothesis and its interpretation of the role of colloidal proteins. Moreover, both Fig 10 and Starling's equation are not representative of his experiment. Both representations assume that the blood flow was continuous through the capillaries of the dog's legs. It was intermittent; blood was passed through the legs 12 to 24 times before its solid content was assessed. Furthermore, in most representations, the COPinpl is assumed to be constant as the blood flows through the capillary. Even when allowance is made for the fact that the COPinpl of the plasma necessarily increases as a consequence of filtration at the arterial end of the capillary and then decreases at the venous end, no regard is given to the COPinpl differences, [COPinpl(x2) - COPinpl(x1)], along the length of the capillary blood. Only the difference between the COPinpl(x) of the plasma inside and the COPoutISF(x) of ISF outside the endothelium is credited with effecting fluid exchange.
Only the random motion of the colloidal proteins in the plasma and the ISF can effect fluid exchange. How can this account, in part, for fluid exchange? How can intermittent blood flow contribute to fluid exchange? If these considerations are insufficient, what other ideas are required to render a complete and satisfactory accounting for fluid exchange between plasma and ISF under all situations in the various tissues under widely differing levels of tissue activity? Clearly, more thought experiments are welcomed at this juncture.
When the concentration of a solute varies along an axis in a solution, the solute will diffuse along this axis and drag on the solvent through which it diffuses (36) . This idea is easily understood by considering a thought experiment (Fig. 11 ). Before time 0, a solution is maintained in a cylinder between two rigid semipermeable membranes, as illustrated in the upper panel. The membranes readily allow the solvent to flow into and out of the solution when the pressures applied by the two pistons to the pure liquid solvent on either side of the solution differ. For example, if pe,leftl exceeds pe,rightl, then solvent will flow into and out of the solution from left to right at a rate determined by the pressure difference and by the hydraulic conductivities of the two membranes. Note that the rigid membranes retain the solute in the solution. Due to the random thermal motion of the solute molecules within the solution, some are continually striking and being reflected by the membrane. These molecules change their momentum and exert a force perpendicular to the membrane, and the membrane opposes this solute pressure (30) .
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At time t = 0, the right membrane was carefully removed (Fig. 11
, lower panel). The solute molecules are no longer reflected by a
membrane, but they are still in random motion. They are now being
reflected by the solvent; they continue to exert a pressure, a pressure
against the solvent into which they are diffusing. Unless the pressure
applied to the left piston is instantly reduced to
pe,leftl -
solventl or the pressure applied to the
right piston is instantly increased to
pe,rightl +
solventl, solvent will flow from left
to right through the solution until the left piston presses against the
left membrane and the solute is distributed uniformly throughout the
solvent. solventl is the initial osmotic
pressure of the solvent in the solution and before t = 0.
Thus, when there is a solute concentration difference in a solution,
the solute diffuses down the difference from the highest to the lowest
concentration, drags on the solvent through which it diffuses,
and thereby exerts an osmotic effect on the solvent in proportion to
the greatest solute concentration difference,
Conc.solutel = [Conc.solutel(highest) -
Conc.solutel(lowest)]. Note especially that
1) the osmotic effect of solute drag is always due to the
diffusion of the solute from its highest to its lowest concentration in
the fluid through which the solute diffuses and 2) the
osmotic effect is immediate (there is no delay).
This thought experiment was experimentally verified by Hammel and Scholander (37) . Anyone with a colloid pressure osmometer can also verify it. For example, the COP of a standard colloidal solution was measured in a Wescor colloid osmometer model 4100. The membrane separating the upper and lower chambers of the osmometer is permeable to the saline solution but not to the colloid in the solution (Fig. 12 ). Two series of measurements of COP were made as a function of time for periods of several hours. In the first series, the drainage tube from the upper, colloidal solution chamber was shortened so that it ended 1 mm above the level of fluid in the drainage receiver provided with the instrument, as illustrated in Fig. 12 , waste collection system A. In this series, the COP of the standard solution remained unchanged for many hours; any variation in the measurement of COP was due to instrument drift. In the second series, the drainage tube for the colloidal solution ended below the level of the fluid in the receiver, as illustrated in Fig. 12 , waste collection system B; this is the arrangement provided by the manufacturer. The fluid in the receiver is a variable mixture of colloidal solution and saline solution that had been flushed through the upper and lower chambers of the osmometer. In the second series, the standard colloidal solution was flushed through the upper chamber at time zero and its COP was measured. The value of this first measurement was the same as the first measurement and all subsequent measurements in the first series. In the second series, the colloidal solution flushed through the upper chamber emptied into the receiver fluid, which differed markedly from the colloidal solution because this fluid was predominantly saline solution. Nevertheless, the initial measurements of COP in the two series were the same. In the first series, the colloidal solution had a free surface immediately above the receiver fluid. At this free surface, its colloidal molecules were reflected back into the solution; they exerted a pressure against this surface and altered the internal tension in the saline solution in which they were dissolved. This altered internal tension was transmitted to the saline in the lower chamber so that the pressure transducer in the instrument registered this altered tension as the COP of the colloidal solution. In the second series, the colloidal molecules were diffusing out from the end of the drainage tube and into the saline solution in the receiver. As they were diffusing out the end, the molecules were dragging on the saline fluid through which they diffused and altered its internal tension, the internal tension throughout the colloidal solution, and the saline below the semipermeable membrane. This situation is just like the situation depicted in Fig. 11B . Initially, the measurements of COP in the first and second series are the same. After a few hours the colloidal solution becomes diluted throughout so that its COP begins to decline.
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Returning to a consideration of Starling's experiment demonstrating
fluid exchange in resting muscle in a dog's leg, colloid drag on the
plasma likely was a small effect, depending only on the amount of
extravasation of protein free fluid out of the capillaries at their
arterial ends. As the plasma protein concentration increased, thereby
increasing the COPinpl(x), as blood flowed down
the capillaries, an axial colloid concentration difference,
[COPinpl(highest) -
COPinpl(lowest)]...COPinpl(highest - lowest), was generated so that the colloidal protein diffused
away from the site of highest protein concentration, dragging on the
plasma through which it diffused and thereby exerting an osmotic effect
proportional to COPinpl(highest -
lowest). In a resting muscle, this colloid effect may be small. In
an active muscle, extravasation of fluid will greatly increase and the
resulting colloidal effect will increase.
In the kidney nephron, blood flow is always high and the renal blood flow rate is much less variable than in muscle. As about 20% of the plasma entering the glomerulus by way of its afferent artery is filtrated out of the glomerulus into Bowman's capsule, the COP of the plasma increases from about 28 to 34 torr in humans. So the colloidal proteins in the blood in the efferent artery leaving the glomerulus diffuse down an axial concentration difference. They drag on the plasma through which they diffuse and they exert an osmotic effect determined by the difference [34 to 28] torr. The plasmas in the peritubular capillaries surrounding the proximal and distal convolutions and in the vasa recta are coupled to their surrounding ISF and to the fluid in the lumen of the proximal and distal convolutions and in the long loop of Henle, respectively. Thus, these plasmas pull the ISF into their capillaries and return most of the fluid entering Bowman's capsule to the circulating blood. In this assessment, the colloid effect is due to the difference in COP of the plasma entering and leaving the glomerulus, [34–28] torr, and not [COPinpl(x) - COPoutISF(x)] as computed conventionally. (See Appendix B for how pressures influence filtration of protein free plasma into Bowman's capsule.)
IDEA 9: INTERMITTENT FLOW (36)
When blood flow is continuous through a capillary, the
diameter of the capillary may vary somewhat as a function (x) along its
length due to fluid exchange, but at any x, its diameter will remain
constant in time. Depending on the amount of fluid exchanged at x, the
flow rate will diminish with increasing x when fluid is extravasated
and will increase as ISF returns to the capillary. Also, when
blood flow is continuous through a capillary, the combined hydrostatic
pressures in the plasma, Pinpl(x), and in
the ISF, PoutISF(x), are exerted
against the endothelium at x from the inside and outside, respectively;
they do not vary in time, although they are both functions of x. That
is, the steady-state hydrostatic pressure,
Pinpl(x), is highest at the arterial end, so
that the extravasation rate of fluid is greatest at this end and
extravasation continues as long as Pinpl(x)
exceeds PoutISF(x) by more than the
osmotic effects owing to the axial diffusion of the colloids and
microsolutes; the hydrostatic pressure in the capillary is least at the
venous end where ISF is returning to the capillary. However, in
continuous flow, the colloids return ISF to the capillary only when
there is a COPinpl(highest -
lowest), the maximum axial difference along x allowing the
colloidal proteins to diffuse down this difference and drag on the
plasma through which they diffuse. Axial concentration differences of
other solutes (ions, microsolutes, etc.) are also involved (see Idea 10
below). Note that axial differences of any plasma solute alter the
internal tension of the plasma water, as would an equivalent negative
pressure applied to this water, regardless of whether the plasma is
flowing or not and regardless of the direction of diffusion of the
solute, with or against the flow.
When the blood flow is intermittent, the hydrostatic pressure of the blood in the arterial end of a capillary varies from some value around 30 torr down to venous pressure. The capillary endothelium and its surrounding matrix are not rigid; they have some elasticity, meaning they will yield to the varying pressures applied to the inner and outer surfaces of the capillary endothelium as a function of time. Both the hydrostatic and colloidal pressures inside and outside a capillary are functions of time at x when capillary blood flow is intermittent. The variation of COPinpl(x, t) in time may be small but the variations of Pinpl(x, t) and PoutISF(x, t) in time may have an important effect on fluid exchange. For example, starting when the precapillary sphincter of a capillary has been constricted so that no blood is flowing, the hydrostatic pressure at its arterial end will be the same as at its venous end and the capillary diameters along the length of the capillary will be minimal because 1) the hydrostatic pressures inside and outside the capillary are the same and 2) the colloid pressure inside is greater than it is outside. When the precapillary sphincter dilates, Pinpl(x, t) increases and the elastic endothelium may increase a little in diameter over much of the length of the capillary owing to the entry of new blood into the capillary. At the same time, protein free plasma flows out of the capillary into the ISF as long as Pinpl(x, t) exceeds PoutISF(x, t) by the extent of all solute drag effects.
Once continuous capillary flow is established, any flux of ISF into the
capillary is due only to 1) the
COPinpl(highest - lowest)
resulting from extravasation of fluid from the capillary which, in a
resting muscle, may be small and 2) axial concentration
differences of other putative osmotically active substances in the
capillary plasma (see below).
When a well-oxygenated precapillary sphincter constricts again, the Pinpl(x, t) of its capillary rapidly drops to the venous pressure along the length of the capillary; since it will be momentarily less than PoutISF(x, t), ISF flows into the capillary especially at the arterial end. In this situation, PoutISF(x, t) may be sustained and continue to exceed Pinpl(x, t) for some time and along much of the length of this capillary due to extravasated fluid from adjacent capillaries, where flow continues. If intermittent flow in individual capillaries can be shown to make a significant contribution to capillary fluid exchange, the basis for it will need much more study.
IDEA 10: VARIABLE PLASMA pH (AS A FUNCTION OF x) ALTERS
DISSOCIATION OF PLASMA PROTEINS
AND
As blood flows from arteriole to venule end of a capillary, its pH will decrease in metabolizing tissue owing to an increasing concentration of CO2 and increasing concentrations of [H+] and [HCO2] in the plasma. We can safely assume that carbonic anhydrase (CA) in the endothelium insures that H+ and HCO3- ions are formed from CO2 nearly instantaneously and while the blood is still flowing in the capillary. The [H+] may also increase due to formation of lactic acid. The increasing H+ ion concentration as a function of x along the capillary will have two effects on fluid exchange. 1) A major effect, regardless of the flow rate, will be the maximal difference in the H+ ion concentration, [H+ (highest)] - [H+ (lowest)]. As the H+ ions diffuse down this difference—from the venule end toward the arteriole end of the capillary—they instantaneously drag on the plasma through which they diffuse, and thereby may pull ISF into the venous end of the capillary. More important, the diffusion of HCO3- ions from its highest to its lowest concentration within the capillary may also pull ISF into the capillary. However, axial diffusion of these ions can retard the outflow of plasma filtrate or return ISF into the capillary only if its endothelium is impermeable to these ions (cf. Fig. 5 in ref 8 ). The diffusions of these metabolic ions may be the principal means by which extravasation is retarded at the high pressure end of a capillary and interstitial fluid is drawn from outside into the plasma at the venous end of the capillary.
Is the capillary endothelium a barrier to H+ and HCO3- ion diffusion? I can only speculate that it is. It must be at least a partial barrier to HCO3- ion; otherwise, there would be no need for the CA enzyme in the endothelium to hasten HCO3- ion formation in the plasma. In any case, the HCO3- concentration is always higher in the ISF than in adjacent plasma. As CO2 diffuses in steady state through ISF to plasma, it has abundant time to hydrate and to equilibrate with HCO3- ions in the ISF, without CA. Assuming the endothelium is a barrier to HCO3- ion diffusion, then a typical difference in their concentrations in venous and arterial blood of about 2 meq/liter plasma in resting tissue in man (38) would cause an osmotic effect of 36 Torr owing to the axial diffusion of HCO3- ions from the venous end toward the arterial end of the capillary. In addition, the diffusion of dissolved CO2 through the pores in the endothelium at the venous end of the capillary will drag on the fluid through which it diffuses and pull some ISF into the plasma.
2) The rising concentration of H+ ions as a function of x along the capillary will have another effect. Colloidal proteins in plasma have isoelectric points of less than 7.4. This means that as the pH of the plasma starts to decrease due to high rates of metabolism and CO2 production, fewer albumin and other protein molecules dissociate into polyanions and protons. That is, these proteins buffer the decrease in pH of the plasma by removing H+ ions from the plasma, and thereby lessening the osmotic effect of these proteins. This means that in metabolizing tissue, the colloid osmotic pressure of the plasma, COPinpl(x), lessens toward the venule end of the capillary. It also means that these colloids diminish the increase in the H+ ion concentration, and thereby diminish the return of ISF into the capillary caused by the diffusion of H+ ions from its highest to its lowest concentration in the capillary. On the other hand, the buffering action of the proteins enhances the formation and diffusion of HCO3- ions, increasing the osmotic effect of this metabolite and thereby enhancing the entry of ISF into the plasma due to its diffusion. An important feature of the osmotic effects of axial diffusion of the metabolites in a capillary is that they are load dependent. In other words, retardation of extravasation of fluid at the arterial end and the return of ISF to the venous end of a capillary are both increased by increased metabolism in the tissue. This feature is unlike the effect of intermittent flow on the return of ISF to the capillary, which will lessen as more capillaries are recruited for continuous flow in active tissue.
We need to inquire how bulk flow of blood through a capillary influences the osmotic effects due to diffusion of the colloidal proteins, CO2, H+, and HCO3- ions, and other metabolites down their respective maximal concentration differences within a capillary. The only requirement for the diffusion of these molecules and ions is that a concentration difference for each occurs in the plasma through which they diffuse. They instantly alter the internal tension of the fluid through which they diffuse. If the flowing plasma where these diffusions occur is still within the capillary, their effects on fluid exchange through the endothelial pores will be the same as when the plasma was stationary.
The amount of water in red cells flowing through the capillary of resting tissue increases from 322.8 ml/liter in arterial blood to 325.6 ml/liter in venule blood (38) , an increase of 0.9%. This increase may be attributed to a lowering of the colloid osmotic pressure of the plasma due to acidification of the blood by carbonic acid. The pH lessens from 7.19 in arterial to 7.167 in venous blood (38) . Thus, the metabolic production of carbon dioxide lessens the COPinpl by 0.9% from about 28 to 27.75 torr. Lactic and other metabolic acids in active tissue would lessen it more, allowing for return of a little more ISF to the venous end of a capillary as the plasma colloids diffuse toward the lessened COPH2Oplasma at the venous end. However, the increased diffusions of CO2, HCO3-, and H+ ions in active tissue remain the dominant causes for returning ISF to the plasma.
At present, Ideas 8–10 have not been experimentally tested to determine their relative contributions to fluid exchange between capillary plasma and its surrounding ISF. No doubt, other ideas will be required to attain a fully satisfactory account of capillary fluid exchange. It is also clear that any account of fluid exchange based on the flawed Ideas 1–3 does not and cannot explain how the exchange happens. It can be stated with certainty that the fully satisfactory account will be derived from Ideas 4 and 5, as these were applied to solvent and solutions in equilibrium. Here lies the challenge and the direction for more research.
CONCLUSIONS
1. Starling's hypothesis and Starling's equation are not acceptable interpretations of Starling's experiment. These interpretations do not apply to Starling's experiment and are invalid for three reasons. 1) Blood flow through all the capillaries was intermittent simultaneously, not continuous as is assumed in Starling's hypothesis and equation. b) Variation in colloid osmotic pressure of the plasma caused by fluid exchange is neglected in the Starling hypothesis and equation. c) When blood flow through a capillary is continuous and its protein concentration is unchanged, the colloidal proteins cannot affect fluid exchange across the capillary endothelium.
2. Part of the colloid effect involved in capillary fluid exchange must be attributed to the maximum colloid concentration difference along the axis of the capillary, i.e., [COPinpl(highest) - COPinpl(lowest)], down which the colloid diffuses. No colloid effect can be attributed to the colloid concentration difference across the endothelium, [COPinpl - COPoutISF].
3. Colloidal proteins drag on the plasma through which they diffuse and alter the internal tension in the plasma as would a negative pressure, in proportion to [COPinpl(highest) - COPinpl(lowest)] applied to the plasma.
4. Plasma is coupled to ISF, and is thereby pulled into the capillary.
5. Most of the colloid effect causing the return of ISF to the vasa recta and to the peritubular capillaries around a nephron can be attributed to the diffusion of the plasma proteins down their highest concentration difference as the colloidal protein molecules drag on the plasma through which they diffuse.
6. Some of the ISF returning to the capillaries of resting muscle may be attributed to those capillaries in which plasma flow is intermittent.
7. The colloidal proteins can effect fluid exchange in two ways: by a) dragging on the plasma through which they diffuse, whether flow is continuous or intermittent, or b) buffering the H+ ions from the dissociation and hydration of CO2.
8. As blood flows through the capillary, acidification of its plasma increases the H+ ion concentration owing to entry of CO2, formation of H+ and HCO3- ions, and (to some extent) the formation and dissociation of lactic acid, especially in highly active tissue. Thus, in metabolizing tissue, a difference in H+ ion concentration, [H+(highest)] - H+(lowest)], is generated. Regardless of blood flow rate, these H+ ions diffuse down their concentration difference, drag on the fluid through which they diffuse, and thereby pull ISF, to which the plasma is coupled, through pores in the endothelium and into the capillary. Corresponding axial differences in the bicarbonate concentrations in the plasma also act to return ISF to the capillary. Diffusion of these metabolic molecules and ions may be the dominant cause for returning ISF to the capillary owing to their combined osmotic effects.
APPENDIX A
After Wallace Fenn died in 1971, Mrs. Fenn wrote a letter to many of Dr. Fenn's friends requesting them to write "a short account of your contact with WOF as you knew him?" Eighty-seven of these letters were bound and printed, with the following title page:
WALLACE O. FENN
1893–1971
MEMORIES AND FACTS
FROM FRIENDS HERE AND ABROAD
Collected by
Mrs. Wallace O.
Fenn
The Medical School Print Shop
of the University of
Rochester
Rochester, New York
1976
On pages 178–179, Scholander's letter reads as follows:
P. F. Scholander, MD., Ph.D.
Director,
Physiology Research Laboratory
Scripps Institute of
Oceanography
University of California at San Diego
La Jolla,
California, 92037
In March 1964 Wallace and Knut Schmidt-Nielsen came to the Scripps Institution of Oceanography in La Jolla to advise on the construction of a special laboratory ship, which in due time materialized in the "Alpha Helix." I came to join them from an expedition in La Paz, Baja, California, where we were conducting an extensive study on osmotic relations in mangroves. After the meeting we all flew back together to the ship `Spencer F. Baird', which served as our base of operations at La Paz. Ted Hammel had just demonstrated that a small pressure chamber made for experiments on reverse osmosis in roots could be used to measure the negative sap pressure prevailing in mangroves, amounting to some 30–40 atmospheres. We were all fascinated by this early success and after seeing several demonstrations, Wallace prophetically stated that complete pressure-
0. The osmotic
pressure of the water in the solution is
