TRANSPORT PHENOMENA IN MEMBRANES EIGHTH SPIERS MEMORIAL LECTURE BY TORSTEN TEORELL Uppsala, Sweden First I want to express my sincerest gratitude for the great honour bestowed on me in inviting me to give this lecture in commemoration of the first secretary to the Faraday Society, Mr. Spiers, of whose biography I do not know very much. I do know, however, that the Faraday Society has ever since his days been a highly active and important body. My first contact with the Faraday Society can be dated back to 1937, almost twenty years ago, when a General Discussion was held on almost the same topic. It was concerned with “The Properties and Functions of Membranes, Natural and Artificial ”.I My own interest and the starting point of my work on membranes and their behaviour was a very definite one.I think it was rather typical of many biologists or medical research people like myself. As a research student I wanted to work on the problem of stomach ulcer formation and did some experiments on the cat’s stomach, on how its hydrochloric acid was produced and how its acidity was “ regulated ”. Soon it was possible to demonstrate that the gastric mucosal membrane, in some formal aspects at least, behaved exactly like a parchment membrane. It could exchange ions by dialysis across it and in that way it was possible for us to propose a hy- pothesis for the so-called “ acidity regulation ” of the stomach, which has since been tested in various medical quarters. The finding, that electrolyte transport processes in the stomach could be handled by something similar to Fick‘s diffusion law and that Nernst-Planck’s formulae for electrical potentials were applicable, encouraged me to proceed further.Like so many other youngsters in the thirties, we had a strong belief in the applicability of physical chemistry to biology and to medicine. Encouraged by great men like Hober and Michaelis, who incidentally were medical people, physico-chemical attacks were made on several biological problems, which were well described, but badly explained. Surface chemistry, solution theory, colloid chemistry, electrochemistry were employed, together with our enthusiasm, in our bold attempts to solve biological problems. For my own part, I must confess that the problem I started with, the riddle of the mechanism of the formation of the gastric acid, is as yet an unsolved problem, although there exist at least half-a-dozen unproven theories.GENERAL ASPECTS OF TRANSPORT IN MEMBRANES 1. IONIC ACCUMULATION-ACTIVE TRANSPORT The gastric acid secretion implied a problem of “ ionic accumulation ”, a term which was popular in the thirties. One spoke of accumulation phenomena in most living cells. It is well known that cells, for instance the red blood cells, do contain much more potassium than the environment, the blood plasma. Plant cells also contain much more potassium than the surrounding sea water or fresh water. In the red cells, which can be regarded as typical for the mam- malian organism, there is about sixteen times more potassium inside the cell than outside. The same is the case with nerves (fig. 1).Incidentally, the sodium which is the other main cation in the living body, is rich in the environment, but 910 TRANSPORT PHENOMENA I N MEMBRANES is depleted in amount inside the cells. Although one was fully aware that these phenomena of ionic accumulation were something peculiar to living things and were linked with metabolism, one attempted in various quarters to explain this peculiar potassium accumulation by the aid of ingenious physico-chemical models, worked out in theory or in practice. On this occasion I want to recall the pioneer work made by Osterhout, the great plant physiologist at the Rockfeller Institute in New York, who was wise enough to understand that collaboration with expert physical chemists (MacInnes, Shedlowsky, Longsworth) was a necessity for an analytical biologist.The ionic accumulation problem is not solved as yet, although I must admit that a great deal more is known about the phenomenological side A X O P L A S M 49 410 40 440 22 5 6 0 ecooo O l A L Y S A T t FIG. 1.-Diagram of giant axon of squid partly cut away in order to show the electric charge across the surface membrane. The approximate internal composition of a fresh fibre is shown for sodium, potassium, and chloride in mM, i.e. millimole per kg of water. The composition of the external fluid is also shown in mM (from Eccles 38). of it now than twenty years ago. One characteristic difference is that the problem has a new label. What was called “ionic accumulation” in the thirties is nowadays frequently named “ active transport ”, a term coined by the Dane, August Krogh.In order to create active transport Dean2 later suggested the existence of a “pump” and gave it the name sodium pump. In other words, the main attention which previously was focused on the potassium, accumulated inside the cell, was now instead turned to the sodium, which is supposed to be forced out of the cell. It is often said nowadays that one ion is transported across the membrane “ actively ” (i.e. the sodium ion), the other ions “ passively ”. A great deal of characterization of the so-called active transport in living material like the red cells, the frog skin and particularly in nerve, has been done in recent years. I want to recall that excellent work has been done in particular by Ussing in Copenhagen on frog skin, and on nerve by Hodgkin, Keynes and their col- laborators in Cambridge and several others. I feel that it is somewhat outside the programme of my lecture to enter into the phenomenology of active transport, although for the biologist it is a most interesting field, to which we cordially invite physical chemists to join us.2. SOME FEATURES OF LIVING MEMBRANES After this presentation of my angle of approach, it might be of some interest for those, who are not directly engaged in biological work, to get some ideas of the nature of a biological membrane, the fundamental unit of transport in our human body. It is the membranes which regulate the transport in the body, e.g. the passage of foodstuffs of various kinds from the stomach and intestines to the blood, from the blood to extracellular fluids and the tissue cells.In the reverse direction, transport takes care of the metabolites, which have to be removed as waste pro- ducts or poisonous products from the body. The cell membranes are the systems in which the physico-chemically-minded biologist places the transport forces. These are invisible, unseen forces, which cannot be dissected by forceps or knives, but which nevertheless are as real as any dissection preparation on the anatomy table. Some recent electron microscope pictures, which have been taken at the Karolinska Institutet, Stockholm,3~ 42 of nerve sheets, etc., are given in fig. 2. This shows a tangential section (a). The membrane is far fromFIG. 2a.-Pile of 8 myelin lamellae isolated from the myelin sheath of osmium-fixed cat motor root fibres.Dow Latex calibration particles (2600A) have been added to determine the thickness of the shadowed lamellae (after Fernandez-Moran 42). FIG. 2b.-Ultrathin section through the myelin sheath of osmium-fixed nerve fibre of the mouse sciatic nerve. The dark lines represent the' principal period. Between these lines a faint line with dark dots is visible. The mean distance between the principal lines is in this specimen 113 A, the space between these lines therefore being 85-90 8, wide. (Electron micrograph kindly provided by Dr. F. S . Sjostrand 3). The thickness of the dark lines is 25A. [Toface page 10.T. TEORELL 11 homogeneous and it is more or less a " sandwiched " membrane, like an American seven-layer cake.In another projection (b) structures, submicroscopical structures, almost down to the molecular level can be seen. The black parallel lines are, for instance, roughly of the order of a few fatty acid molecules in length, about 25w. I think it is appropriate at this occasion to remind you that the surface chemists here in England, I may mention the schools headed by Sir Eric Rideal and by Prof. Neil Adam, anticipated layers of this type already in the thirties. FIG. 3.-Schematic diagram of medullated nerve fibre structure based on polarization optical analysis. (A) N = axon positively uniaxial as referred to axial direction. M = myelin sheath positively unixial as referred to radial direction. (B) Submicroscopic structure of the myelin sheath (after Schmidt) (after Frey-Wyssling 39).In particular, it was Danielli4 who offered the first pictures (in 1935) of layered membranes in which proteins and lipoids were interlaced. And people who worked with the polarization microscope observed phenomena, which could only be explained as due to well-orientated structures of proteins and lipoids (fig. 3). It is amazing to see now on photographs like Dr. Sjostrand's, what could only indirectly be inferred to exist ten years ago. Here the theoretical mind was in front of the experimentalists. The electrical activity in the nerve-the nerve signal-is, as is well known, an electrical event with frequency-modulated signals, called " spikes ", with a frequency of from say ten signals a second up to about 1000 c/sec. The spikes have constant amplitudes roughly of the order of 100mV.The secret of the electrical nerve communication signal is in fact a permeability process and thus a membrane problem. It is a question of ionic transport processes. These phenomena have been most ingeniously characterized, analysed and even partly synthesized by Hodgkin, Katz, Keynes and Huxley here in England. I want to point out that the electrical forces, which operate in the nerves or in many other cell membranes, have a gradient of the order of at least 100 V/cm. This is far more. than in any conventional electrophoresis machine, and the current density is far from a modest one; it is roughly 1 mA/cm2. In other words, appreciable amounts of material would be expected to be electrically transported and that is also the case.Here we have an important feature of the living body : a great deal of the transport forces are surely electrical in character, affecting not only ions but also other substances which are electrically charged like colloids. Even large suspended particles, like the leucocytes, are believed to be subject to elec- trical forces. I think the nerve signal is the most complex membrane process : it shows a rhythmical, self-sustaining process of a special character, far different from what we are used to in the model diffusion set up with a parch- ment or ionic exchange membrane clamped between Perspex gadgets, etc. But12 TRANSPORT PHENOMENA I N MEMBRANES nevertheless, I believe that the elementary parts, at the molecular level of these biological events, complicated as they are, do contain just the same fundamental elements as we can reveal by the model studies on simpler, well-defined systems. 3.SURVEY OF MEMBRANE “ PERMEABILITY PHENOMENA ” I should like to emphasize that the interest of a biologist in membrane pro- cesses or, as it is commonly called in physiology, “ permeability phenomena ”, is usually placed upon several aspects, but in particular on two, namely, the kinetics of transport (the rate of transport across the membrane), and the ionic distribution figures. The first kind of studies was not easy to perform earlier, but nowadays with the advent of radioactive tracers and refined analytical methods, etc., one has been able to study rate processes. It was much easier to determine equilibria of ion concentrations such as distribution studies of K to Na of the type noted above; this is probably the reason why the literature contains more data of this type.In table 1 I have listed these and some other permeability phenomena under five different headings. Any complete membrane theory ought to cover all these five aspects and explain them. Here I will restrict myself to commenting on only a few points concerning the aspects listed. TABLE 1 .-VARIOUS IONIC PROCESSES IN MEMBRANE SYSTEMS, “ PERMEABILITY PHENOMENA ” 1. Ionic transport, “flux ”. Net flux, partial fluxes of different ion species. “ Influx ” and “ outflux ” of one ion species. Flux ratios. 2. Membrane potential. Potential components, “ mixed ” or total transmembrane potential.The diffusion potential. Conductances in steady state systems. Membrane rectification. Reactance properties, apparent capacitance and inductance. ‘‘ Flux equilibria ”, “ diffusion effects ”. 3. Electrical conductivity. 4. Ionic distribution equilibria. 5. Spatial distribution of the ions and the potential within the membrane. A type of membrane transport studies or permeability studies, which has become feasible in recent years, is the ‘‘ influx ” and “ outflux ” studies across membranes. One has to remember that what one usually measures is the net flux. This net flux in turn is composed of two independent streams, an influx and an ourflux across the membrane, which may be of an order of magnitude different from the net flux. One realizes nowadays that the higher potassium content inside many living cells may be due to the fact that the driving forces for the influx are different from those of the outflux.It is not any type of im- permeability. In many biological quarters even as late as ten years ago, one thought that the potassium somehow was “ trapped ” or “ sealed ” inside the red blood cells in the place where it was produced (in the bone marrow), and could not escape. Nowadays, however, it has been shown that we have a form of what I have called “ apparent impermeability ”, which is just a result of a steady state, an interplay of forces. It is also wise to stress the importance of the simple fundamental law valid here : the flux = (total driving force) x (concentration) x (the mobility),T. TEORELL 13 and that the driving force can be built up in superposition from chemical, electrical and hydrostatic components.It cannot be too strongly emphasized that steady states, i.e. zero net flux, sometimes do consist of a very rapid inflow and very rapid outflow of the same magnitude. Partial fluxes can also almost cancel one another and give a small resulting net effect. Fig. 4 represents a so-called charged mem- brane, to which I have devoted some studies (fig. 9a, b). According to the usual terminology this charged membrane would be described as poorly permeable under the conditions prevailing in the experiment. It is, however, very permeable, if one considers the partial processes, the influx and the outflux. (Membrunc cone) wk FIG. 4.-The influence of membrane charge w x upon the net flux, outflux and influx of the ions of a single electrolyte.The ionic mobilities are assumed to be identical (KCl). Note the small net flux at high wXvaIues (where, however, the influx and outflux may be very large or vanishing), thus a negative membrane becomes virtually anion impermeable and a positive membrane becomes cation impermeable (from Teorell7). After having considered the biological background, I now want to outline the present status of membrane research, mainly from the biologists’ point of view, and thereby describe the various types of system that have been investigated in the past and are being investigated now. In fig. 5 I have attempted to show the connections between different cases, which appear in different mathematical forms.The scheme is very incomplete and far from logical. It will only serve to demonstrate how I look upon the “ genealogy ” in membrane research and how the various systems are linked with each other. Furthermore this genea- logical tree is neither a chronological nor a historical one, although it would be very interesting to draw the sequence of how one research worker has depended on another-very few discoveries in this field have been of the type of mutations ! I have chosen the most difficult artificial diffusion transport systems at the bottom and then depicted various special cases upwards in the figure. It is not my intention to describe all the membrane transport “ families”, nor to describe in detail any particular “member ”. Some interesting cases I want, however, to pick out, in what follows in order to demonstrate that many peculiar phenomena which occur show similarity with what can be observed in14 TRANSPORT PHENOMENA I N MEMBRANES biological systems. The various " membrane transports " will now be presented in the following order : (a) uncharged membrane, (b) " fixed charge " membrane (= ionic membranes), (c) convection diffusion.I I _I -_ __ - - - ~ ~ - - - FIG. 5.--S;heme of3fferent type, of membrane transport phenomena.-Z = electric current ; 'u = rate of bulk flow; cox= sign (u) and charge (x> of the membrane ; S = different cation and anion species ; c1 and c2 = outside and inside solution con- centrations ; TMS refers to Teorell16 and Meyer and Sievers.17 SOME FEATURES OF UNRESTRICTED DIFFUSION ACROSS UNCHARGED MEMBRANES 1.THE KINETICS A typical system is a porous glass membrane or porcelain membrane or even a filter paper of a pore size of much larger radius than that of any of the solutes present, but small enough to secure a convection-proof diffusion layer. With a 1 : 1-valent electrolyte it can be shown, as was done by Behn in 1897,s that the flux of an ion, i.e. the amount transported in unit time across the unit area on membrane, follows an equation which in a compact form can be written as (Teorell, 1951,6s 19 1953 7) flux = $ = - Ku(c~~$ - ~ 1 ) .T. TEORELL 15 4 is an exponential function introduced already by Planck and signified as exp (+F/RT). Here + is the electrical potential, F, R, and T are, respectively, the faraday, the gas constant and the absolute temperature.The constant K is a complicated function of the prevailing concentrations and 5; u is the mobility, c1 and cq the concentration " inside " and " outside ". Incidentally, this general flux equation can be used to express possible equilibria between influx and outflux being respectively -KucZ[ and + Kucl. In the steady state one has zero net flux, and one obtains c y /cT as 4' or 58 loglo (cF/cy) in mV. This is a type of steady- state distribution, which I think was shown for the first time by myself9 in 1935 and I will return to it again later (the " diffusion effect "). Nowadays, it is frequently employed in biology to describe ionic equilibria in terms of the transmembrane potential (Hodgkin, Keynes, Ussing, etc.). In passing, it can be remarked that the diffusion across a homogeneous mem- brane consisting of a non-aqueous solvent, can be written in the same mathe- matical form as the general flux equation for electrolytes.In this case the 4 is identical with the partition coefficient instead of an electrical potential function ! 2. ELECTRICAL MEMBRANE POTENTIALS AT UNCHARGED POROUS MEMBRANES These can be described in a general way with Nernst-Planck's well-known equation or the Henderson equation, which is in a few special cases identical with the Planck one. The problem of potentials in homogeneous membranes (c' oil membranes") is a difficult one; it has recently been attacked in Gottingen by the Bonhoeffer school, which has contributed so much to modern membrane theory. 3. " CONCENTRATION PROFILES " Even in this, the simplest of all membrane systems with no membrane charge, accumulation phenomena inside the membrane can take place as was pointed (according to Teorell, J.Biof. Chem., 1936, 113, 735). The results conform reasonably well to the theoretically calculated curves (according to Planck-Plettig 8 or Teorell,6 eqn. (271, (28)). 0- out by Planck and Plettig 8 long ago. Fig. 6 shows what they anticipated theor- etically and which we have confirmed experimentally. This peculiar " concentra- tion profile " can be regarded as a " rudimentary " approach of the system towards a dynamic equilibrium of a type, which is presented in fig. 7 and which we have called the difusion @ect on ionic distribution9 Related effects have been called " harmony " by Staub.4116 TRANSPORT PHENOMENA I N MEMBRANES 4.DIFFUSION EFFECT The diffusion effect is something related to the Donnan effect where one ion, the ‘‘ active ” one, dictates the behaviour of all the other ions, the ‘‘ passive ” ones. In the genuine Donnan case the active ion is completely impermeable. In the diffusion effect all ions are permeable although to different degrees. It is interesting to note that one nevertheless gets the same type of ionic distribution (cp. fig. 7) as is generally regarded as characteristic of the genuine Donnan dis- tribution (which actually appears as a limiting case of the “diffusion effect ”). Intermediate Stea@ sfufe Membrane (0) FIG. 7.-Scheme illustrating the development of a “ diffusion effect ” upon the ionic distribution (uncharged membrane).(Top, left) : the experimental set up : the HC1 (the “ diffusing agent) ” is steadily supplied into ‘‘ inside ” (small volume) and diffuses across the membrane to ‘‘ outside ” (large volume). An electrical potential across the membrane results. (Top, right) : a hypothetical biological counterpart to the experiment (Below): the different stages in the development of the “diffusion effect” upon the distribution of the ‘‘ passive ” ions (K and Br). Black arrow6 indicate electrical flux, white arrows indicate the ‘‘ osmotic ” flux. In the final steady state these fluxes balance each other and the K and Br ions attain a ‘‘ flu, equilibrium ” (from Teorell7~ 9). It is especially worth pointing out that the diffusion effect system shows a transport of passive ions against their concentration gradients, i.e.ionic accumulation. This ionic accumulation model may have biological analogy, but I wish to emphasize that it exhibits no selectivity; potassium and sodium, for instance, are equally influenced in contrast to the behaviour of these ions in biological systems. 5. MEMBRANE RECTIFICATION, ETC. Returning again to the simple porous type of membranes one finds that they can exhibit electrical “ rectification effects ”, i.e. a difference in electrical con- duction according to the direction of the applied electrical current. This is due to re-arrangements of the ion gradients inside the membrane. This type of rectificationT. TEORELL 17 effect seems to appear in most biological tissues, and is probably complicated with fixed charges attached to the membranes ; they were described by Labes and Zain (1922),13 Blinks (1930),14 Cole (1939),14 Teorell (1948),15 see also fig, 8. Related phenomena are " anomalous " capacitance and inductance effects which often appear.lonic events in uncharged porous membranes must show peculiar transition phenomena, when the pores become increasingly smaller and the membrane turns into a micro-porous and finally into a homogeneous layer. Wilbrandt 10 in the early thirties had emphasized the necessity of reconciling the pore and homogeneous membrane effects. Danielli 11 (1936), in particular, appears to have been the (CO f h ode) I :\i FIG. 8.-Distribution of ions and potential within a (multi-)-membrane (cellophane surrounded by large, stirred volumes of 0.1 N HC1 and 0.1 N NaCl).Initial state (middle), steady state values after current flow (left and right). Points and crosses in the middle section are calculated values, the curves are all based on experimental values. The mV values were measured during a short interruption of the current flow (after Teorell 15). first one to attempt a quasi-thermodynamic treatment of thin and more or less thick homogeneous membranes in terms of activation energies, etc. In this respect Danielli pioneered the later general physico-chemical work by Eyring and others,l2 who with some success, have formally introduced their L' transition state theory " into the membrane realm. The kinetic approach, which I have chosen, and the more thermodynamical treatment are, of course, only different languages to describe the same phenomenon.For biologists, the kinetic approach is the preferable one as it is easier to transform into a rational experimentation. Thermodynamics is, on the other hand, less restricted. The formalism in the two different approaches can, of course, be shown to be closely related. THE BEHAVIOUR OF CHARGED MEMBRANES 1. THE GENERAL CONCEPTS OF THE FIXED CHARGE THEoRY.-If we now turn from the uncharged to the charged membranes, i.e. membranes carrying a hxed ionic group in the matrix CL ionic membranes " according to Dean 2) we find that they show more complicated conditions which, however, lead to more inter- esting effects which may come still closer to the biological events (fig. 9).The fixed charged membranes seem to have become a rather popular research object18 TRANSPORT PHENOMENA I N MEMBRANES t t .ni @3-P,l f a2 \ f/anc& ) Donnun (Henderson) Donnon ?bid potenfW FIG. 9cr.-Diagram illustrating the basic concepts of the fixed charge theory (from Teorell 6 , 7). FIG. 9b.-The fixed charge theory applied to a single electrolyte. (A calculated case of HCI diffusing across a positive membrane, OX = 20, mobility ratio NH~VCI = 5.3). The diagram shows the course of the ion concentrations and of the electric potential. Note here that the total P.D. has the opposite sign to the interior membrane potential (42 - 41)~. Observe also the non-linear course of the total concentration, (Cl-), within the membrane. (In this particular case the variation of the potential ($2 - $ 1 ) ~ is approximately linear, which, however, is rather an exception) (from Teorell 6.7).T. TEORELL 19 since the advance of the synthetic ion exchange resins with cross-linked structures. It may be appropriate to recall that a chemical electrolyte character of these membranes was recognized clearly by Michaelis in the twenties. His work on " positive " and '' negative " membranes had a great influence on biological thinking. Michaelis regarded the effects produced by his dry collodion mem- branes as due to electrostatic repulsion and attraction of the diffusing ions. Michaelis' collaborator in 1935, Wilbrandt,lo suggested that the ionic distribution vis ci uis the membrane would be related to the Donnan distribution law. 70 s 8 e 5 0 4 FIG.10.-The variation of the ion concentrations at a charged membrane where the interior membrane potential is zero (cp. fig. 96). An actual counterpart would be a system as depicted with the arrangement : (1) 4 mN KCI + 2 mN NH4Cl ]I membrane w x = - 10 mN 11 2 mN KNO3. (2) The ionic mobilities of K+, N&+, C1- and N03- were assumed identical. In this case the respective concentration gradients inside the membrane signify direction and magnitude of the ion fluxes. Note that the K+ ions flow in the direction (2) -+ (l), i.e. from a lower to a higher Concentration. A simiiar situation would arise with any electrolyte mixture when the " membrane concentration " is high, relative to the bulk total concentration (from Teorell20). At about the same time I was working with the apparent transference numbers of Cellophane 40 and found that the so-called " concentration effect " shown by this membrane, a phenomenon observed and discussed in the early days of our century, especially by Beutner, could be linked with the somewhat high transfer- ence numbers I had obtained.This led to a provisional theory 16 in 1935 which aimed primarily at an explanation of the concentration effect on the membrane potential in terms of what at that time I called a " mixed potential ". This con- sisted of two membrane phase-boundary potentials of Donnan character and a Henderson potential between. A specific feature was the jumps of the spatial20 TRANSPORT PHENOMENA I N MEMBRANES distribution of concentration and the potential (cf. fig.9). Some time later Meyer and Severs 17 independently and at some length formulated an identical theory and also extended it to include oil membranes. Meyer and Severs like myself were at that time mainly interested in the electrical membrane potential and not until much later was a more extended theory formulated for the ion transport. Goldman 18 in 1943 integrated the Nernst-Planck differential equations for a charged membrane. His solution was, however, confined to the conditions inside the membrane and not its overall behaviour with the surrounding solutions. In 1951 6 and 1953 7 we therefore presented a somewhat fuller treatment of the problem, which led to a number of equations for the ionic fluxes, the electrical conductance and rectification, the membrane potential, and also for the “ profiles ” of concentrations and the electric potential. Certain simplifications had to be ’ introduced ; for instance, the activity corrections were disregarded and some very general approximations were made as to the influence of the bulk (water) movement.Extensions were later made by Schogl.20 On the whole it can be said that the same general formalism is valid for charged membranes as for uncharged ones in spite of the introduction of the “ double Donnan ” conception. We have previously shown that the condensed flux formula (for a cation), where u denotes the mobility and (1225 - CI), is equal to the difference in electro- chemical potential. This expression is also valid for a charged membrane; the only change lies in the significance of the constant K, which now will be still more complicated as it also takes care of the Donnan distributions (cf.Teorell,6 eqn. (4), ref. 7, p. 320, eqn. (5)). I am fully aware of the shortcomings of the fixed charge theory as regards the assumptions made, the mathematical procedures employed and the significance of the results. I am convinced that it will soon be superseded by more rigid and realistic treatments, but until that time the fixed charge conception may have fulfilled at least one useful purpose-to challenge other workers and thus stimulate new experiments and new theories. 2. I want now, however, to mention a few features of the consequences of the fixed charge theory which might have biological analogies. First it has been found that the peculiar uphill diffusion so characteristic for many biological membrane systems, i.e.diffusion or transport against the con- centration gradient, can be easily achieved in a fixed charge membrane as is demon- strated in fig. 11. We assume here a negative membrane (fixed charge density, w x = -lo), surrounded by KCl, NH4C1, and KNO3. Due to the Donnan dis- tributions at the membrane boundaries and the interaction of the driving forces in the interior, we obtain the unusual situation that the concentration gradient of the K ions (the full black curve) within the membrane is directed from the low concentration side towards the high concentration side. In other words, there exists an uphill transport of the K ions. Accordingly there need not be anything peculiar about movement against a concentration gradient.There is no “ active transport ” here ; it is an effect of the superposition of a few, well-defined driving forces. Another phenomenon at charged membranes related to the so-called “ diffusion effect ” of uncharged membranes mentioned earlier, is the development of similar steady state distributions of the ions present. Due to the effect of the fixed charges the mobility or transference numbers may be enhanced or decreased as com- pared with the free water situation in uncharged pores. This restriction upon one or several ions leads also to a distribution picture similar to the Donnan distribution. I think Netter21 in 1928 was the first to demonstrate that very pronounced Donnan-like ion equilibria ” could be obtained with Michaelis’ dried collodion membrane.The matter has been well investigated by Sollner 22 + = -Kdc24‘ - Cl),T. TEORELL 21 and collaborators working on the so-called permselective membranes developed in his laboratory. As an example of such distributions I refer to the following table from one of my own experiments (table 2). All ions present retain a dis- tribution ratio across the membrane of a similar order and conform to what can be calculated from the total trans-membrane potential. It is obvious that this ‘‘ equilibrium ” is not a genuine thermodynamic one ; it is ‘‘ gliding ” with time ! I should like to call this type ‘‘ time-variable or time-dependent equilibria.” The “ diffusion effect ” of uncharged membranes and these last mentioned distribution effects may perhaps be called ‘‘ flux equilibria ” (i.e.the influx of one ion con- stituent = the outflux, etc.) in order to distinguish them from the thermodynamical Donnan distribution. I want again to emphasize that these types of distribution equilibria do not show any selectivity, between, for instance, potassium and sodium. It might, however, be possible to get at least a temporary selectivity, if somebody could synthesize a suitable membrane matrix with selective ad- sorption properties (Skogseid 23 claimed some years ago that he had a resin with a pronounced K affinity). In this connection I should like to point out that there is no absolute necessity that the Donnan distribution at the membrane boundaries should be strictly obeyed. When in 1935 16 I first employed concentration jumps at the membrane- solution boundaries I chose for convenience the well-defined Donnan concentration jump.However, as far as I can see it is possible to introduce any ratio, specific for the individual solute species, provided it can be defined in some way or ex- perimentally justified. These ratios may not necessarily be the same or follow “ cellophane ” (1) initial state: 10 mM KCl 1 oXw-ZOmM (2) 1 mM HN4Cl (12 ml) * Note that CI- = K+ + NH4+. the same relationship at the “entrance” and “exit” sides of the membrane surface. I think we have here problems which need further amplification. A related case to be solved is where the fixed charge distribution within the membrane is ‘‘ skew ”, and not uniform as is usually postulated.TRANSPORT PHENOMENA INVOLVING BULK FLOW 1. INFLUENCE OF THE BULK FLOW (CONVECTION-DIFFUSION) We have now to deal with a still more complicated problem, where there is also a bulk movement within the membrane. Thereby we proceed to the field of electro-endosmotic phenomena. (Note that in fig. 5 in order to appreciate that the cases already treated, although common enough, were only ‘‘ branches ”, i.e. special cases, from a quantitative point of view, where the water transport was equal to zero (v = 0)).22 TRANSPORT PHENOMENA IN MEMBRANES A limitation in many of the kinetic formulas for transport in charged mem- branes or ionic membranes has been the neglect of the bulk movenient of the solu- tion which certainly occurs frequently, especially in biological structures.In most model experiments hitherto the water movement, for example in collodion or cellophane membranes, or even in the modern ion exchange resins, is fairly small and can as a first approximation be disregarded. Semi-permanent Porous Semi-permanent membrane membrane membrane 1 - 1 ‘- Thickness 6 V 8 e-- Cleo - -- Steady state . (Flux equilibrium) ’ C p RT-D FIG. 11 .-A hypothetical case of a steady state arising from counter current (convection- diffusion). A single solute is confined between two membranes, permeable to the solvent but not permeable to the solute. A porous membrane, permeable to both solvent and solute, acts as a partition between two, stirred chambers. A constant flow of solvent is imposed on the system (open arrous), black arrow shows direction of diffusion.A perfectly satisfactory treatment of the important problem where electro- chemical potentials arising from concentration gradients and bulk movement co-operate has not yet been given. Promising approaches have, however, been attempted by several workers. Two different modes of approach have been employed, one the kinetic, e.g. by Schlogl209 24 a few years ago, and the other thermo- dynamic founded on the recently formulated laws for irreversible thermodynamics. I think it is appropriate to mention here a few important contributions such as those by Mazur and Overbeek,25 and by Schmid,26 who has also carried out experimental tests, those by Scatchard,27 Staverrnan,28 Lorenz 29 and most recently by Kirkwood,30 who have all derived interesting and biologically important results.It is striking to a biologist to be faced with the situation that such a highly theoretical and abstract treatment as Onsager’s so-called “ reciprocal relation ” can turn out to be of a fundamental importance for the explanation of the mechanisms of biological transport and communication problems. A special feature in these new theories on electrosmosis by Schmid, Schlogl, Staverman and others is that the old zeta potential, so often used to characterize the charge of particles or membranes, can be substituted by the fixed charge symbol, O J ~ , expressed in units of concentration,T. TEORELL 23 The essential new feature in the quantitative treatment of this convection transport in membranes is the appropriate introduction of a third driving force in the fundamental transport equations, besides gradients of chemical and electrical potentials.This is the effect arising from a gradient due to solvent (water) pressure. It may appear unconventional to speak of a pressure (hydrostatic) potential or in a more loose way of a “ water potential ”. But it nevertheless exists It is perhaps more evident if we make use of Hertz principles for convection- diffusion.31 Fig. 11 gives a simple example of a hypothetical case, where only a chemical potential and a hydrostatic potential co-operate. Here the creation of a characteristic unequal concentration distribution could be postulated, somewhat similar to what has been earlier demonstrated in the form of Donnan equilibria or “ diffusion effects ”, i.e.a kind of “ flux equilibrium ”. If by applying some force, the existence of which must be taken for granted, a constant bulk flow rate across this system could be produced, it can easily be shown that eventually a steady state would be attained (i.e. a flux equilibrium) where the concentration distribution could be equal to A similar relationship was valid for the result of the competitive behaviour between the chemical potential of ions and the electric potential. This was then written in the form : The difference is that instead of ($F), v, the linear bulk velocity, 6 the thick- ness of the membrane and D the diffusion coefficient are introduced. If the two equations are expressed logarithmically, it is easy to see from the dimensions that, in the first case ($F) expresses the electrical work ; in the second case (vS)/D sig- nifies the mechanical work.Each in turn is equal to the “ chemical ” work arising from the difference in concentrations, i.e. RT In (cy /@). In other words, the work terms balance one another in the ultimate steady state. For the present general case, where three driving forces are superimposed one therefore can write 7 c? US RTln- - mVF+ - = 0. c2” D Demonstrations of this type of steady-state distribution or flux equilibria seem to be rare. (L. Garby 32 working in our laboratory has carried out somewhat related experiments with heavy water, and Ussing33 has advanced a related theoretical reasoning for the behaviour of the frog skin.) Before finishing this section I should like to comment on a somewhat different case, i.e.when convection forces and electrochemical potentials appear simul- taneously in the charged membrane without a flowing electrical current. In such cases one can sometimes observe the phenomenon of anomalous osmosis, which has received much attention, since it was discovered long ago. In particular, I wish to recall the great biologist Jaques Loeb’s work some forty years ago. In modern days Sollner 34 and his collaborators have investigated this phenomenon thoroughly and they introduced the fixed charge conception in their explanations of this phenomenon. Quite recently a fine achievement was made by Schlogl24 from the Bonhoeffer group in Gottingen. He employed a principle rather similar to the one employed in the building-up of the quantitative fixed-charge membrane model and worked out the “ pressure profile ” at the membrane boundaries and within the membrane.I think he has been able to explain positive and negative anomalous osmosis very satisfactorily in that way.24 TRANSPORT PHENOMENA I N MEMBRANES 2. ELECTRO-ENDOSMOSIS AND RHYTHMICAL TRANSPORT PHENOMENA In the previous section we have touched upon some theoretical approaches to transport problems where three driving forces were simultaneously present. From an experimental point of view there exists a great literature under the label " electro-endosmosis ", describing all sorts of systems where these forces are -- ..... mE 6 -.- kQ 3 5 - 8 3.0- f0 2,s. 2.0. 0 8- L I I 1 ..... .... 0 30 GO 90 t20 MinnvlPs FIG.12.-Oscillatory phenomena during flow of constant electrical current. Experi- ments on a system 0.1 N NaCl I ( porous glass membrane 11 0.01 N NaCl; mA figures refer to different current densities in:mA-cm-2 (from Teorell 37). operating. I believe that the subject of electro-endosmosis deserves still more attention by the theoreticians and by the biologists. There is no doubt that living membranes are more or less " charged " (due to carboxyl-, amino- and other fixed groupings in the membrane matrix) and much evidence shows that flowing electrical currents can be produced, for instance, at the nerve action. One is therefore necessarily obliged to postulate the existence of electro-endosmotic phenomena in living tissues. Such a postulate implies that electrical events in these membranes have to be accompanied by simultaneous bulk (water) streaming.Only a very few biologists have so far paid attention to this possible effect (cf. Tobias,35 Hill36). This is to be regretted, but it can be explained by the great technical difficulties involved in measurements of small volume changes of the living structures. I believe that such studies would be interesting, however, because our recent studies on electro-endosmotic " cell " models have revealed some possibilities of obtaining rhythmicaI or oscillating membrane phenomena (Teorell37). I must confine myself to describing only a few experimental facts. The model was roughly built up according to the scheme AgCl electrode ] 0.1 N NaCl I porous glass membrane 1 0.01 N NaCl ] AgCl electrode.T.TEORELL 25 Constant currents were applied across the electrodes and the whole set-up per- mitted simultaneous recording of the membrane potential, the electrical mem- brane resistance and the water-pressure difference across the membrane. A typical result obtained is demonstrated in fig. 12. The striking feature of these experiments is the appearance of rhythmical variations of the variables mentioned. Perhaps the alternation of the inward and outward movements of the water is the most conspicuous event, Damped oscillations and, under certain conditions, even undamped trains of oscillations could be achieved over rather extended periods. This system behaves in a somewhat similar way to an electronic “ relaxation ” oscillation and it is possible to formulate a theory relating to the “membrane oscillation ” on an analogous basis (to be published).Another remarkable feature can also be mentioned, namely, that this type of system applied to mixtures of alkali ions could exhibit a preferential or selective ion transport as can be seen in table 3. TABLE 3 Initial set up : 50 KCl - 5 KCI (l) 50 NaCl - 5 NaCl (2) (2000 ml) I (12ml) Conc. in mM. ; 25 mA cm-2 time [Klz “alz [KIzhNah 0 5.2 6.4 0.8 1 80’ 1.1 5.3 0.2 1 time tK21 [Lilz tKlz/ILi12 0 4.7 5.8 0.81 80’ 0.7 5.0 0.14 230” 0.2 4-0 0.05 It is, of course, tempting to think that these phenomena of rhythmicity and ion selection could be somehow related to actual living systems like the nerve, which displays just these features. I think however, that this should be attempted with the greatest caution.Much more work is required from the physico-chemical as well as from the biological side before one dares draw significant analogies. I am now at the close of my survey of membrane transport processes. We know a great deal more now than we did nineteen years ago when the Faraday Society last discussed these subjects. I hope that the tradition founded during Mr. Spiers’ secretaryship in the Faraday Society to assemble people of different view-points for a General Discussion on a subject of a common interest will persist and that we can meet again in a co-operative spirit. Co-operation with physical and chemical experts is what we in the biological fields need and appreciate. A meeting of this type to form a general discussion is indeed one of the boldest attacks against the secrecies of the Living Nature.Problems like “ facilitated diffusion ” and “ active transport ” and many other phenomena still await conquest. The descriptive terms of the biologist must be exchanged and translated into the well-defined and unambiguous language of the physicists and chemists. It may, however, be wise to remember that whatever the number of conditions we include in our research and formulas, we shall always be dealing with approximations, if we take the Living Nature as a standard. I believe that Michael Faraday, who was a humble man, felt that limitation of the human mind quite often! 1 The Properties and Functions of Membranes, Natural and Artificial, Trans. Faraday 2 Dean, Chem. Rev., 1947,41, 503. 3 Sjostrand, personal communication.4Danielli, J . Gen. Physiol., 1935, 19, 19; J. Cell. Comp. Physiol., 1936, 7, 393. SOC., 1937, 33, 91 1.26 TRANSPORT PHENOMENA IN MEMBRANE 5 Behn, Ann. Phys. Chem., 1897, 62, 54. 6 TeorelI, 2. Elektrochem., 1951, 55, 460. 7 Teorell, Progress of Biophysics (London, 1953), 3, 305. SPlettig, Ann. Phys. (ser. 5), 1930, 5, 735 (cf. Planck, Sitzungsber. Preuss. Akad. 9 Teorell, Proc. Nut. Acad. Sci., 1935, 21, 152 ; J. Gen. Physiol., 1937, 21, 107. 10 Wilbrandt, J. Gen. Physiol., 1935, 18, 933. 11 Danielli, in The Permeability of Natural Membranes, by Davson and Danielli 12 Zwolinski, Eyring and Reese, J. Physic. Chem., 1949, 53, 1426. 13 Labes and Zain, Arch. Expt. Path. Pharmakol., 1926,125,1,53 ; 1927,126,284,352; 14 Cole and Curtis, J. Gen. Physiol., 1941, 24, 551 ; (cf. Guttman and Cole, J. Gem 15 Teorell, Nature, 1948, 162, 961 ; Arch. Sci. Physiol., 1949,3, 205. 16 Teorell, Proc. Soc. Expt. Biol. Med., 1935, 33; 282. 17 Meyer and Sievers, Helv. chim. Acta, 1936, 19, 649, 665, 987; 1937,20, 634. 18 Goldman, J. Gen. Physiol., 1943, 27, 37. 19 Teorell, Abstr. Comm. XVIZI Znt. Physiol. Congress (Copenhagen, 1950), p. 481. 20 Schlogl, 2. physik. Chem., 1954, 1, 305 ; Schlogl and Schodel, ibid., 1955,5, 372, 21 Netter, Pjziigers Arch., 1928, 220, 107. 22 Sollner, J. Electrochem. Soc., 1950, 97, 139 ; J. Plz-vsic. Chem., 1945, 49, 43 ; Ann. 23 Skogseid, Noen derivater av polystyrol og deres anvendelse ved studirim av ioneut- 24 Schlogl, Z. physik. Chem., 1955, 3, 73. 25 Mazur and Overbeek, Rec. trav. chim., 1951, 70, 83. 26Schmid, Z. Elektrochem., 1950, 54, 424; 1951, 55, 229. Schmid and Schwarz. 27 Scatchard, J. Amer. Chem. SOC., 1953, 75, 2883. 28 Staverman, Trans. Faraday Soc., 1952, 48, 176. 29 Lorenz, J. Physic. Chem., 1952, 56, 775 ; 1953, 57, 341. 30 Kirkwood, Ion Transport Across Membranes (Acad. Press, N.Y., 1954), p. 119. 31 Hertz, Physik. Z., 1922, 23, 443 ; 2. Physik, 1923, 19, 35. 32 Garby, Nature, 1954, 173, 444. 33 Ussing, Advances in Enzymology, 1952, 13, 21. 34 Sollner, Dray, Grim and Neihof, Ion Transport across Membranes (Acad. Press, N.Y., 1954), p. 144. 35 Tobias, Modern Trends in Physiology and Biochemistry (ed. Barron, Acad. Press, N.Y., 1952), p. 310; cf. articles by the same author on related subjects in J. Cell. Comp. Physiol., 195 1-55. Wiss. P1iysik.-Math. KI. 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