THE PERMEABILITY
`OF
`NATURAL MEMBRANES
`
`by
`
`HUGH DAVSON
`D.Sc (Lond.)
`Scimti.fic Sta.ff, Medical Research Council, London;
`Honorary Research Associate,
`University College London
`and
`J. F. DANIELL!
`D.Sc. , Ph.D., A.R.I.C.
`Professor of Zoology, King's ·coUege, London
`
`With a Foreword by
`E. NEWTON HARVEY
`Prefessor of Physiology in Princewn University, U.S.A.
`
`CAMBRIDGE
`AT THE UNIVERSITT PRESS
`1952
`
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`

`

`Q H 5 i l
`. j)3'5"
`\<3..- 2-
`
`To
`SIR JACK DRUMMOND
`who first interested us in this field, and
`for whose encouragement we are
`so greatly indebted
`
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`

`PUBLISHED BY
`THE SYNDICS OF THE CAMBRIDGE UNIVERSITY PRESS
`London Office : Bentley House, N.w. -1
`American Branch: New York
`Agents for Canada, India, and Pakistan : Macmillan
`
`First Edition 1943
`Second Edition 1952
`
`First printed in Great Britain at the University Press, Cambridge
`Reprinted by offset-litlw
`by Lowe & Brydone Ltd, London
`
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`

`

`v
`27766
`
`CONTENTS
`
`Note. Readers primarily hiterested in conclusions can profitably
`omit reading Chapters II, III and IV
`
`Foreword by E. NEWTON HARVEY
`
`Pref ace to Second Edition
`
`Authors' Preface
`
`Chap. I Significance of Permeability Studies
`II Methods of Studying Membrane Permeability
`III Equilibrium Conditions of Cells
`IV Some Equations used in Permeability Studies
`V The Nature of the Process of Diffusion
`VI The Structure of the Plasma Membrane
`VII The Interpretation of Permeability Measurements
`VIII Permeability to Non-Electrolytes
`IX Permeability to Gases
`X Permeability to Water
`XI Permeability to Proteins and to Large Lipoid
`
`Jxn Molecules
`
`\'o XIII
`J
`
`IV
`~
`~ xv
`\)
`~
`~ XVI
`
`Permeability of Erythrocytes to Ions
`Permeability to Ions of Cells other than the
`Erythrocyte
`Permeability to Weak Electrolytes and Dyes
`Impedance and Potential Measurements and
`Permeability
`The Effect of Narcotic Substances on Per(cid:173)
`meability
`
`LINDA HALL LIBRARY
`KANSAS CITY, Me,
`
`PAGE
`vii
`
`ix
`
`xi
`
`1
`
`5
`
`18
`38
`48
`
`57
`72
`
`80
`
`105
`llO
`
`ll8
`
`126
`
`161
`
`184
`
`193
`
`231
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`

`vi
`
`CONTENTS
`
`Chap. XVII The Effect of Temperature on Permeability
`XVIII Haemolysis
`XIX Membrane Permeability in Relation
`Secretion
`xx The Kidney
`XXI Theories of Cell Permeability
`
`to
`
`Appendix A. The Theory of Penetration of a Thin Mem-
`brane, by J.F. DANIELLI
`
`References
`
`/11dex
`
`PAO&
`244
`
`249
`
`264
`
`274
`
`294
`
`324
`
`336
`
`357
`
`NOTE
`In places it has been necessary to include ~npublished results or
`calculations. Those by H.D. are marked **, those by J.F.D. tt
`
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`

`CHAPTER VIII
`
`PERMEABILITY TO NON-ELECTROLYTES
`
`By J. F. DANIELL!
`Bv non-electrolytes we refer to substances which, over the
`physiological pH range, exist in a non-ionic form only and which
`also penetrate in an unionised form. Other substances (weak acids
`and weak bases) penetrate in most cases mainly in the unionised
`form, but they present several special problems which make it
`preferable to deal with them separately.
`Within the group of non-electrolytes a wide diversity of
`chemical and physical characteristics is still possible. Consider
`the molecular ·series hexane, propyl alcohol, urea and glycerol.
`Hexane has an olive oil:water partition coefficient of about 500,
`whereas that of glycerol is 0·00007. Propyl alcohol and urea have
`intermediate values of about O· l and 0·00015. Thus there is a
`difference of ten million-fold between the relative "affinities" of
`
`Propyl alcohol
`CH,
`I
`CH1
`
`dH.OH
`
`Urea
`NH,
`
`Jo
`I
`NH,
`
`Glycerol
`CH1OH
`I
`CHOH
`
`dH,OH
`
`Hexane
`CH,
`I
`
`CH1 JH,
`
`I
`CH,
`I
`CH,
`I
`CH,
`
`hexane and glycerol for water and oil. It is not surprising that
`such enormous differences between molecules should lead to great
`differences in permeability, provided the membrane ·to be pene(cid:173)
`trated can distinguish between molecules by virtue of these specific
`characteristics. Thus in water the dominant variable . affecting
`the rate of diffusion on passing from one of the molecules to
`another is the molecular weight, so that the relative rates of
`penetration of a water layer are as l ·O : 0·83 : 0·83 : l ·02; i.e.
`there is very little difference between the rates. In diffusing
`through e.g. a collodion membrane between two water layers, the
`
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`

`PERMEABILITY TO NON-ELECTROLYTES
`
`81
`discriminating factor is molecular diameter, and again there
`would be very little difference between these four molecules.
`Fujita found with two different collodion membranes the following
`relative permeabilities for the last three of these substances:
`membrane (1) l·O, 1:0, 0·8; membrane (2) 1·0, 0·97, 0·21. On
`the other hand, with cell membranes the ratios would be, roughly,
`hexane greater than l ·O : propyl alcohol l ·O : urea 0·005 : glycerol
`0·0005. * The discrimination now is between molecules of different
`polar character, the least polar penetrating most rapidly, the
`most polar least rapidly. Bearing in mind these very large
`differences which may exist between different non-electrolyte
`molecules, we may now proceed to consider the permeability of
`a number of different types of membranes.
`The Permeability of the Erythrocyte. The earliest systematic studies
`of the permeability of erythrocytes to non-electrolytes are those
`of Griyns (1896) and of Hedin (1897), and it will be seen that,
`although their work was done so long ago, at a time when even
`the conception of the erythrocyte as a cell had first to be argued,
`their results are largely upheld by later work; in fact, it is worth
`pointing out that the work of Hedin was carried out under more
`strictly physiological conditions_ than most of the later investiga(cid:173)
`tions on non-electrolyte permeability.
`Quantitative work on the erythrocyte is comparatively recent,
`and is almost entirely based on the haemolysis technique. The
`quantitative analysis of times of haemolysis is almost entirely due
`to Jacobs and his colleagues. For many points we are still de(cid:173)
`pendent of qualitative evidence.
`Griyns first showed, by chemical methods, that urea added to
`chicken blood is equally distributed between cells and serum.
`He then, using the haemolysis method, showed that the following
`non-electrolytes did not penetrate the cell at all: amino acids,
`glucose, mannose, inositol, disaccharides. The following substances
`were shown to penetrate the cell: MeOH, EtOH, glycerol, ethers,
`urea, biuret, pyridine.
`Griyns was mainly interested in whether the substances pene(cid:173)
`trated the erythrocyte or not, and paid little attention to the
`actual rates at which this process occurred. However, he was able
`to draw the important conclusion that "substances with the same
`~ ~ere arc, of course, many cases ·where specific factors cause displacement
`•n this series.
`
`DD
`
`6
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`

`82
`
`PERMEABILITY TO NON-ELECTROLYTES
`
`chemical groupings behave similarly", which with modifications
`relating to the size of the molecules, and the distribution of the
`groups in them, may be upheld to-day.
`Hedin, using the method of freezing-point depression, and ox
`blood, obtained the results summarised in Table VII. He discusses
`his results in relation to Overton's theory of lipoid solubility, the
`more rapidly penetrating substances being the more lipoid soluble
`substances, with the exception of urea and ethylene glycol. He
`enunciates the rule that with polyhydric alcohols the rate of
`penetration decreases with the number of OH groups in the
`molecule. Thus already the principle of the importance of specific
`chemical groupings in regard to permeability had been brought out.
`
`TABLE VII. PERMEABILITY OF ox ERYTHROCYTES
`(HEDIN, 1897)
`
`Cane sugar}
`Dextrose
`Galactose
`Arabinose}
`Mannitol
`Adonitol
`Ethylene glycol}
`Glycerol
`Erythritol
`
`Amides l
`
`Urea
`Aldehydesj·
`Ketones
`Ethers
`
`Do not penetrate
`
`Penetrate only slightly within 24 hours
`
`Penetrate in the order given, times for completion of the
`process being a few minutes for ethylene glycol, less than
`2 hours for glycerol and greater than 28 hours for erythritol
`
`Penetrate too rapidly for rates to be compared
`
`Besides developing the above principle, the results of Kozawa
`(1914), using a haemolysis technique, led to the conception of
`real differences in permeability according to the species of
`erythrocyte studied. Thus with human erythrocytes he found the
`results shown in Table VIII. The erythrocytes of the ape (Macacus
`rhesus) behaved in the same way as human erythrocytes. It was
`
`TABLE VIII. PERMEABILITY OF HUMAN ERYTHROCYTES
`(KozAwA, 1914)
`
`Permeable to:
`
`Slightly permeable to:
`Impermeable to:
`
`Arabinose, xylose, galactose, mannose, sorbose,
`glucose, laevulose
`Adonitol
`lactose, ~lucoheptose,
`Cane sugar, maltose,
`methylglucoside, galactoside, glycine, alanine,
`mannitol, dulcitol
`
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`

`PERMEABILITY TO NON-ELECTROLYTES
`
`83
`found, however, that the erythrocytes of the ox, pig, rabbit,
`guinea-pig, goat, horse, camel and cat were all impermeable to
`the substances considered; dog cells were shown to be permeable
`to glucose. The important point was also made that isomeric
`sugars penetrate at different rates, and has since been confirmed
`by Wilbrandt (1938).
`
`TABLE IX. TIMES OF HAEMOLYSIS IN ETHYLENE GLYCOL AND
`GLYCEROL SOLUTIONS FOR DIFFERENT SPECIES {JACOBS, 1931)
`Time in seconds for 7 5 % haemolysis
`
`Species
`Rat
`Mouse
`Rabbit
`Guinea-pig
`Man
`Dog
`Cat
`Pig
`Ox
`Sheep
`
`(1)
`In NaCl
`4·20
`3·00
`3·00
`5·00
`8·35
`6·10
`2·65
`3·00
`3·80
`1-90
`
`(2)
`In glycol
`6·6
`8·6
`11·3
`15·7
`12·6
`28·6
`18·3
`16·7
`35·1
`24·1
`
`(2)-(1)
`(3)
`In glycerol --(-1)-
`19
`0·5
`39
`1·9
`2·2
`80
`196
`2-1
`43
`0·5
`1548
`3·7
`1222
`5·9
`1024
`4·6
`2325
`8·3
`1623
`11-7
`
`-,
`(3)-(1)
`-(-1)-
`3·5
`12·9
`21 ·8
`38·2
`5·1
`253·0
`459·0
`340·0
`612·0
`850·0
`
`Column (1) gives time ofhaemolysis in 0·02 M NaCl; column (2) that in ethylene
`glycol+0·02M NaCl; column (3) that in glycerol+0·02M NaCl
`
`TABLE X.
`
`(ULRICH, 1934)
`
`Species
`Ox, pig, rabbit, rat
`Mouse
`Mouse
`Guinea-pig
`
`Substance
`Hexoses mannitol
`Hexoses
`Sorbitol, mannitol, dulcitol
`Pentoses, glycine, alanine
`
`Penetration
`Not at all
`Not at all
`Rapid
`Penetrate
`
`Since Kozawa's work appeared, a great many investigators have
`made more detailed studies of the variation in permeability with
`species. In Table IX some results of Jacobs on the relative rates
`of penetration of ethylene glycol and glycerol into the cells
`of ten species are shown. The results are given in times of hae(cid:173)
`molysis, which are, very roughly, inversely proportional to
`permeability. The polyhydric alcohols and sugars have been
`studied from a species point of view by Ulrich (1934), whose
`results are shown in Table X. For the polyhydric alcohol,
`crythritol, the time~ in Table XI wer~ found for 75 % haemolysis. *
`• It will be seen later, when Davson's (1939) results on loss of potassium in
`non-elC<;trolyte solutions are discussed, that times of haemolysis of more than
`• few mmutes are sometimes of doubtful value.
`
`6-2
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`

`84
`
`PERMEABILITY TO NON-ELECTROLYTES
`
`TABLE XI. HAEMOLYSIS IN ERYTHRITOL SOLUTIONS
`
`Species
`Ox
`Rat
`Pig
`Rabbit
`Man
`Mouse
`
`Time for 75 % haemolysis
`8 hours
`6 hours
`5 hours
`3·5 hours
`1·75 hours
`Few minutes
`
`Jacobs & Glassman in a preliminary report (1937) give a brief
`account of results on species characteristics, the most important of
`which are summarised below. The permeabilities to glycerol, urea
`and thiourea of the erythrocytes of 9 species of elasmobranch,
`14 of teleosts, 2 frogs, 6 turtles, 4 snakes and 4 birds were com(cid:173)
`pared. The following generalisations may be made:
`
`BIRDS.
`
`FISHES.
`
`Ethylene glycol penetrates fastest. Urea and thiourea highly
`variable from species to species. Thiourea usually faster than
`urea.
`Glycol and glycerol penetrate very rapidly at nearly equal
`rates. Thiourea much slower, urea slowest.
`REPTILES. Urea relatively rapid, glycol next; thiourea much slower.
`Permeability to glycerol only slight.
`MAMMALS. Urea very rapid; ethylene glycol much slower and thiourea
`still slower.
`
`The most interesting features of the work so far described on
`species characteristics are first, that species may be grouped in
`accordance with their permeability to a given substance, e.g.
`glycerol; second, that many sp~cies show a specially high
`permeability to a given substance which is out of all proportion
`to its permeability to other substances; e.g. human cells are
`permeable to glucose, whilst rat and mouse cells are not at all
`permeable to glucose, but are more permeable to glycerol than
`are human cells: further, mouse cells are permeable to the poly(cid:173)
`hydric alcohols, sorbitol, mannitol and dulcitol, whilst human
`cells are not.
`So far enough has been said of species characteristics per se for
`the reader to appreciate how real and significant they are; in the
`later parts of this section further species characteristics will be
`brought out in relation to other phenomena of non-electrolyte
`penetration.
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`PERMEABILITY TO NON-ELECTROLYTES
`
`85
`
`The question of the relation of the rate of penetration of a
`substance with a low lipoid solubility to its molecular volume has
`been investigated by Mond & Hoffmann (1928) and Mond &
`Gertz (1929). More recently Hober & Orskov (1933) have made
`a more extensive study from the same point of view, and, as their
`results agree with those of Mond & Hoffmann, it will be sufficient
`to quote them alone.
`The method used was the haemolysis technique, and some of
`the results have been collected in Table XII. The figures in the
`table are values of t' = (t2 ~ t1) /t1 , where t1 = time of haemolysis
`in 0·02 M NaCl, and t2 = time of haemolysis in non-electrolyte
`+ 0·02 M NaCl. In this way differences in the fragility of the
`cells are to some extent discounted.
`
`TABLE XII. RELATIVE TIMES t' OF HAEMOLYSIS OF ERYTHROCYTE S
`IN SOLUTIONS OF DIFFERENT NON-ELECTROLYTES
`(SEE TEXT FOR
`DEFINITION OF t') (HOBER & bRSKOV, 1933)
`Species
`Acetamide
`Propionamide
`M.R.
`14·9
`Hl·5
`0-47
`Rat
`0·45
`Man
`0·90
`1-20
`Ox
`1·30
`1-70
`
`Ma Ion amide
`22•!)
`167
`102.5
`8£10
`
`Lactamide
`21
`18·4
`31·5
`72·0
`
`Species
`M.R.
`Rat
`Man
`Ox
`
`Species
`M.R.
`Rat
`Man
`Ox
`
`Species
`M.R.
`Rat
`Man
`Ox
`
`Urea
`13·7
`0·11
`0·3
`0·4
`
`MeOH
`8·2
`0
`0·12;1
`-0·19
`
`Glycol
`14·4
`0·94
`1·7
`16
`
`Methyl-urea
`18·5
`Hl
`2·3
`3·0
`
`Thiourea
`Hl·6
`31-7
`57
`119
`
`EtOH
`12·8
`0· 11
`0·3
`-0·05
`
`Glycerol
`20·6
`4·7
`60
`650
`
`PrOH
`
`BuOH
`
`0·45
`0·7
`0·41
`
`0·45
`0·3
`0·03
`
`Erythritol
`26·8
`1,500
`10,750
`Infinite
`
`Hober & Orskov conclude that the absolute value of the
`"Molecular Refraction", i.e. the volume of the molecule, is o~ly
`the determining factor when a given series of homologous sub(cid:173)
`stances is considered. The basis for this is clear from the table·
`in each group of homologous or chemically similar substances th;
`value of t' increases as the molecular volume increases. On the
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`

`PERMEABILITY TO NON-ELECTROLYTES
`
`86
`other hand, for a given species, there is no correlation between
`the rates of haemolysis and the molecular volumes when sub(cid:173)
`stances belonging to different homologous series are used. The
`results of Hober & Orskov were extended to nine species and
`differences as striking as those described earlier were observed.
`
`Species
`Ox
`
`Rabbit
`
`TABLE XIII. (JACOBS et al. 193?)
`Time ofhaemolysis
`in seconds
`2169
`31
`58
`114
`38
`14
`l
`51
`5
`27
`82
`17
`7
`1·4
`
`Substance
`Glycerol
`Triethylene glycol
`Diethylene glycol
`ay Dioxypropane
`Ethylene glycol
`af3 Dioxypropane
`Propyl alcohol
`Glycerol
`Triethylene glycol
`Diethylene glycol
`ay Dioxypropane
`Ethylene glycol
`af3 Dioxypropane
`Propyl alcohol
`
`The results of Hober & Orskov made it quite clear that besides
`the molecular volume of the molecule and its lipoid solubility,
`there is at least one other factor of importance in determining
`the permeability of a membrane to a given substance. Hedin's
`finding that OH groups tend to slow the rate of penetration of
`a molecule has received ample confirmation in the study of the
`comp.~rative rates of penetration of sugars and their analogous
`polyhydric alcohols (with the exception in this case of the mouse
`erythr~yte). Further evidence of the importance of specific
`chemical groupings is given by the work just quoted of Hober
`& Orskov, and Fleischmann (1928) has shown that although
`glucose penetrates rapidly into the human erythrocyte, methyl
`glucoside does not penetrate at all, thus emphasising the im(cid:173)
`portance of the groups in the sugar molecule. Quantitative
`work on the effect of introducing OH groups into the propane
`molecule.has been published by Jacobs et al. (1935) and is shown
`in Table XIII, and it is seen that on introducing successive OH
`groups into this molecule the rate of penetration decreased with
`each group introduced. In the <;lihydroxy compound it is evident
`that the position of the OH group is important, the compound
`with its OH groups on adjacent ·(a.fJ) carbon atoms penetrating
`
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`

`PERMEABILITY TO NON-ELECTROLYTES
`
`87
`more rapidly than that with the OH groups at the ends of the
`molecule ( ixy) .
`Before proceeding with the remaining points of importance in
`relation to non-electrolyte permeability it would be useful to
`recapitulate the principles derivable from the work so far de(cid:173)
`scribed, as follows: apparently important variables are
`(a) Species characteristics,
`(b) Lipoid solubility,
`(c) Molecular volume,
`(d) Specific chemical groupings,
`(e) Position of the groups on the molecule.
`All of these factors, with one possible exception, are of funda(cid:173)
`mental importance in determining the rate of penetration of a
`sub,tance. The exception is molecular volume. The results we
`have given above show without doubt that, in any one homologous
`series, as molecular volume increases rate of penetration decreases.
`But many other properties of an homologous series vary in the
`same way as molecular volume, so that whilst it is of interest to
`observe this general parallelism between rate of penetration and
`molecular volume, a quantitative treatment is necessary before
`we can be sure whether this correlation is fortuitous or not.
`Conclusions on the Structu e of Red Cell Membranes. Many results
`are available to show that if a series of cells, such as (a) rat,
`(b) human, (c) ox erythrocytes, is considered, substances are found
`to penetrate the cells in different orders. For example, Hober &
`Orskov (1933) found that with acetamide the order of speeds is
`rat> man> ox, whereas with propyl alcohol the order is ox> man
`> rat. According to Jacobs et al. (1935) glycerol penetrates in the
`order rabbit> guinea-pig> rat> man> cat> ox; but with thiourea
`the order is cat> rat> rabbit> man> guinea-pig> ox. According
`to some authors the differences between such series are such that
`they can only be accounted for by a mosaic structure of the plasma
`membrane of at least some species; i.e. the membranes of these
`cells must consist of areas of different chemical properties. To the
`present writers this view does not seem to be well founded, since it
`is based on qualitative rather than on quantitative arguments.
`In Table XIV are given values of the permeability, temperature
`coefficient and of P Aft Qib+1o>11o for ox red cells. · The experimental
`data were taken from Jacobs et al. (1935) and the values of P
`calculated by the method of Jacobs (1934). For the substances
`
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`

`88
`
`PERMEABILITY TO NON-ELECTR.OLYTES
`
`glycerol, cxy dioxypropane, diethylene glycol, triethylene glycol, the
`value of P Afl Q~~+ioi,io should be approximately constant, but not
`for the other molecules, if the membrane is a homogeneous lipoid
`layer.* It will be seen that this is the case, so that the membrane
`of ox red cells behaves, to a first approximation, as a homogeneous
`lipoid layer. t t
`
`TABLE XIV. DATA FOR OX RED CELLS AT 20° c.
`p
`p MIQ~~+1oi110
`X 10-18
`l·lxlo-10
`10·6
`X 10- U
`8·5 X 10- 7
`7·8
`1·7 X 10- 7
`0·019 X iQ - 18
`0·209 X 10- 18
`2·0x 10-1
`0·405 X 10- 18
`82
`0·0017 X lQ - lo
`0·105 X 10- 18
`0·075 X 10-18
`0·033 X 10- 18
`
`Substance
`Propyl alcohol
`Urea
`Thiourea
`Glycol
`a.f3 Dioxypropane
`
`Glycerol
`a.y Dioxypropane
`Diethylene glycol
`Triethylene glycol
`
`Q10
`1·37
`1·86
`2·14
`2·92
`3·75
`
`3·65
`3·31
`3·42
`3·34
`
`0·17
`0·48
`1-16
`0·28
`
`On the other hand, in the case of red cells of man, rat and
`rabbit, it can be shown that a small part of the surface of the
`cell is specially adapted to allow passage of glycerol. Results of
`Jacobs et al. (1935) show that for these cells the Q,10 is about l ·2 for
`glycerol, and about l ·4 for urea. Consequently, if the membrane
`:were homogeneous, glycerol should penetrate these cells more ·
`rapidly than urea.* But in fact urea penetrates thirty-five times
`or more faster than glycerol. This can only be accounted for if
`3 % or less of the surface of these ceU5 is specially differentiated
`to permit passage of glycerol at a high rate. t t
`The Influence of the Medium on Permeability of Cells to Non-Electro(cid:173)
`lytes. So far as we are aware, no extensive systematic study of this
`aspect of non-electrolyte permeability has been described and
`most of what is known arises out of accidental discoveries. The
`principal work in this field is that of Jacobs and of Davson.
`Jacobs et al. (1935) mentioned that "acidity" of the medium
`causes, with a group of species, a marked retardation of the rate
`of haemolysis in glycerol solutions; the effect seems to be confined
`to this molecule. These authors do not define the pH at which
`In the description of the
`the effect of acidity shows itself.
`equilibrium conditions of the erythrocyte in Chapter m it was
`
`• See Chapter vu and Appendix A for the evidence and qualifications attending
`these statements.
`
`Novo Nordisk Ex. 2031, P. 14
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`PERMEABILITY TO NON•ELECTROLYTES
`
`89
`shown that the non-electrolyte suspension medium is acid and
`may have a pH of 5 or even less, so that the effect of acidity
`described by Jacobs et al. must show itself at even more acid
`reactions. Davson (1939d) has investigated the matter further and
`some representative results on the rabbit erythrocyte, using a
`phosphate buffer, are shown in Table XV, and it seems clear that
`the retarding influence of acidity begins at a pH of from 4·7 to
`4·5; however, in view of the importance of the ionic strength of
`the medium in these almost completely electrolyte-free suspensions
`of erythrocytes, it is questionable whether the pH of the medium
`alone is of much significance. The fact that the effect of acidity
`may be revealed by the "incautious breathing" of the investigator
`gives some idea of the difficulties encountered in a great deal of
`the work on penetration of non-electrolytes.
`
`TABLE XV. THE EFFECT OF THE pH OF THE MEDIUM ON THE RATE
`OF HAEMOLYSIS OF RABBIT RED CELLS IN ISOTONIC GLYCEROL SOLU(cid:173)
`TIONS (DAVSON, 1939d)
`Suspension medium
`0·32 Glycerol
`0·32 Glycerol buffer, pH 7·4
`0·32 Glycerol buffer, pH 6·8
`0·32 Glycerol buffer, pH 5·9
`0·32 Glycerol buffer, pH 5·5
`0·32 Glycerol buffer, pH 5·0
`0·32 Glycerol buffer, pH 4·75
`0·32 Glycerol buffer, pH 4·5
`
`Time of haemolysis
`30 sec.
`48 sec.
`41 sec.
`39 sec.
`34 sec.
`30 sec.
`53 sec.
`320 sec.
`
`Another influence of the medium on permeability is described
`by Jacobs & Corson (1934) in a short note. These authors state
`that minute traces of copper in the solution of glycerol causes a
`pronounced retardation in the rate of haemolysis of certain species
`of erythrocytes, attributable presumably to a slowing of the rate
`of entry of glycerol. The effect shown is with those species which
`show the effect of acidity: man, rat, mouse, guinea-pig, rabbit.
`It is inhibited by NaHCO3 •
`Davson (1939d), in a general study of the action of heavy
`metals, has shown that the effect of copper can be greatly increased
`bywashing thecellswith saline, this·action being due to the washing
`out of the bicarbonate and removal of the serum proteins from the
`system. Addition of NaCl or any alkaline buffer inhibits the action
`of copper, the pH at which this action begins being as acid as 4·5.
`These facts are shown in Tables XVI and XVII.
`
`Novo Nordisk Ex. 2031, P. 15
`Mylan Institutional v. Novo Nordisk
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`
`

`

`PERMEABILITY TO NON-ELECTROLYTES
`
`90
`Jacobs had noticed that the time course of haemolysis in
`glycerol in the presence of copper is peculiar in that there is a
`marked auto-acceleration towards the end of the process. Davson:
`has found an explanation for this, attributing this effect to increase
`in alkalinity of the suspension medium, due to the h~emolysis
`itself. As alkalinity inhibits the action of copper, it will therefore
`accelerate the rate of penetration of glycerol. The alkalinity
`following haemolysis is due to the breakdown of the equilibrium
`distribution of anions, which for a cell in a non-electrolyte medium
`will be such as to cause the cell to be alkaline in respect to the
`suspension medium. Probably adsorption of copper on the
`haemoglobin released by },aemolysis is aiso an important factor
`in accelerating haemolysis.
`
`TABLE XVI. EFFECT OF WASHING OF ERYTHROCYTES ON THE
`INHII ITION OF PENETRATION OF GLYCEROL BY COPPER (DAVSON,
`1939d)
`
`Unwashed cells
`Unwashed cells
`Once washed cells
`Twice washed cells
`
`Suspension medium
`0·32 M Glycerol
`0·32M Glycerol l x 10-• M Cu
`0·32M Glycerol l x 10-•M Cu
`0·32 M Glycerol l x 10-• M Cu
`
`Time of haemolysis
`0 min. 35 sec.
`2 min. 55 sec.
`6 min. 30 sec.
`7 min. 25 sec.
`
`INFLUENCE OF REACTION OF THE MEDIUM ON THE
`TABLE XVII.
`INHIBITING ACTION OF COPPER ON GLYCEROL PENETRATION, AS
`SHOWN BY CHANGES IN TIME OF HAEMOLYSIS (IN SECONDS)
`(DAVSON,
`1939d)
`
`The time of haemolysis in glycerol alone was 30 sec.
`
`pH
`6·75
`· 4·75
`4·5
`
`Glycerol+ buffer
`41
`52
`320
`
`Glycerol+ buffer
`+10-•MCu++
`44
`53
`600
`
`Jacobs et al. (1937) have investigated the effect of small
`quantities of salts on the rate of haemolysis of ox cells in glycerol
`solutions and find a marked acceleration, which, however, they
`attribute chiefly to a change in the fragility of the cells due to
`anionic shifts. It is possible that other factors may be involved.
`A possible influence of salts and plasma proteins on penetration
`is revealed by Somogyi's (1928) results on the distribution of
`glucose between human plasma and cells; Somogyi's claims, that
`the passage of glucose from the cells to the suspension medium
`takes place within a minute or two, would give a permeability
`
`Novo Nordisk Ex. 2031, P. 16
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`PERMEABILITY TO NON-ELECTROLYTES
`
`91
`constant of the same order as that of glycerol, and yet erythrocytes
`of man are stable in pure glucose solutions for hours at room
`temperature. As most of the work on non-electrolyte permeability
`has been done with the haemolysis technique, which involves an
`enormous reduction of the salt content of the medium surrounding
`the cell, it seems that the thorough investigation of the influence
`of environment on permeability to non-electrolytes would not
`only be interesting, but absolutely necessary, before the exact
`significance of results obtained by the haemolysis technique will
`be clear.
`In concluding this description, it should be pointed out that
`we have not attempted to include all the published work on
`non-electrolyte permeability in this brief account, so that a certain
`amount of selection has been necessary; thus the voluminous
`literature on the vexed question of the distribution of glucose and
`amino acids between cells and serum has not been touched upon.
`Plant Cells. A very large amount of work has been done on the
`permeability of plant cells (including yeasts), but of this extremely
`little is published in a form suitable for quantitative treatment.
`The most outstanding work is that of the Finnish school of
`Collander & Barlund. Fig. 25 shows the permeability of cells of
`Chara ceratophylla plotted against oil-water partition coefficient(cid:173)
`a form of graph originally due to Collander & Barlund (1933).
`The larger the oil-water partition coefficient, and the smaller the
`molecular volume, the more rapidly a molecule penetrates. Thii,
`work is based entirely.on chemical determination of the amount
`of penetrating substance which actually enters the cell sap, a fact
`which makes the work most reliable. From this diagram Collander
`(1937) concludes that "There is clearly a somewhat close
`concordance between the oil-water solubility of substances on the
`one hand, and their permeability constants on the other; this is
`not merely a general concordance, but, at least approximately, a
`direct proportionality .... On the other hand, the smallest mole(cid:173)
`cules obviously permeate faster than would be expected on account
`of their oil solubility alone .... It seems therefore natural to
`conclude that the plasma membranes of the Chara cells contain
`lipoids, the solvent power of which is on the whole similar to that
`of olive oil. But, while the medium-sized and large molecules
`penetrate the plasma membrane only when dissolved in the
`lipoids, the smallest molecules can also penetrate in some other
`
`Novo Nordisk Ex. 2031, P. 17
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`PERMEABILITY TO NON-ELECTROLYTES
`
`92
`way. Thus, the plasma membrane seems to act both as a selective
`solvent and as a molecular sieve."
`This view ofCollander's is based on qualitative arguments only.
`Danielli (Appendix A), from a theoretical study of the details of
`
`l•0r--------------,-.-M-cth_y_l _alco-hol _ _ _ _ _ _ _
`t Ethyl alcohol
`T_ricthyl
`u1thane auatc'
`Un:thylan •
`Anti~@Trimcthyl cittatc
`0
`-~
`0
`Monoc:i:~r;:e
`Propionam.idc •
`Prop. glycol O .... 0
`Formarrudc O
`O (g]~lyccrol ethyl cth r
`Acctarrudc O
`Glycol o
`00Glyccrol .!~~Y;~:
`Dimcthylun:a
`
`0,1 ...
`
`Cyanamidc
`
`I Diacetm
`
`0·01"'
`
`.
`
`Mclhylurea
`
`Lact!rude
`Urea o
`@urouopbln
`
`OMonacctin.
`
`OEthylun:a
`• Thiourea
`(I) Diethyl malonamide
`
`(),00 I ,. Mcthylolurca
`
`. . Glycerol
`
`• Dicyandiamide
`
`0 Malonarrudc
`
`0-0001 -
`Erythritol
`0
`
`I
`0·0001
`
`t
`I
`0·01
`0•001
`Partition coefficient
`
`0 MRn 22-30
`
`@ MRn>30
`O·I
`
`FIG. 25. Permeability (ordinates) of Chara to non-electrolytes (cm. per hr.)
`plotted against olive oil-water partition coefficients (Callander, 1937). Arrows
`are attached to permeability values which Collander & Barlund consider to
`be too low.
`
`the mechanism of diffusion across the plasma membrane, con(cid:173)
`cludes that there is no justification for plotting P against partition
`coefficients, so that the conclusions which Collander draws from
`Fig. 25 are not valid. Instead, one should plot* P Mi (in the case
`2500:r
`of rapidly penetrating molecules), and PM' e RT (in the case of
`slowly penetrating molecules), against partition coefficients. Then,
`
`• See p. 76 or p. 335 for explan_ation of these formulae.
`
`Novo Nordisk Ex. 2031, P. 18
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`PERMEABILITY TO NON-ELECTROLYTES
`
`93
`for a homogeneous lipoid layer, the points should lie between two
`lines distant by a factor of 5 from the average line. As can be seen
`from Figs. 26 and 27 the results of Callander & Barlund fall
`within these limits, and there is no differentiation between
`. molecules of different molecular volume. Herice it is concluded
`that the plasma membrane of Chara cells is possibly a homogeneous
`lipoid layer, to a first approximation. Thus,