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`
`Patterns of Nonelectrolyte
`Permeability in Human
`Red Blood Cell Membrane
`
`P. NACCACHE and R. I. SHA'AFI
`
`From the Department of Physiology, The University of Connecticut School of Medicine,
`Farmington, Connecticut 06032
`
`ABSTRACT The permeability of human red cell membrane to 90 different
`molecules has been measured. These solutes cover a wide spectrum of non-
`electrolytes with varying chemical structure, chain length, lipid solubility,
`chemical reactive group, ability to form hydrogen bonds, and other properties.
`In general, the present study suggests that the permeability of red cell membrane
`to a large solute is determined by lipid solubility, its molecular size, and its
`hydrogen-bonding ability. The permeability coefficient increases with increas-
`ing lipid solubility and decreasing ability to form hydrogen bonds, whereas it
`decreases with increasing molecular size. In the case of small solutes, the pre-
`dominant diffusion factor is steric hindrance augmented by lipid solubility. It
`is also found that replacement of a hydroxyl group by a carbonyl group or an
`ether linkage tends to increase permeability. On the other hand, replacement of
`a hydroxyl group by an amide group tends to decrease the permeability coeffi-
`cient.
`
`INTRODUCTION
`
`Recently, the permeability coefficients of a series of amide, ureas, and diols
`have been measured on human red cells (1). Based on these studies, it was
`postulated that there are three important variables which need to be consid-
`ered separately in understanding the permeation process across human red
`cell membranes. The first is a parameter describing lipid solubility, the second
`a parameter depending on molecular size, and the third a parameter which is
`concerned with the chemical nature of the solute. Although this conclusion is
`in general agreement with earlier studies of nonelectrolyte permeations in red
`cells, particularly by Jacobs and H6ber and
`rskov (See Danielli [2]), it is
`based only on the measurements of the permeability of human red cell mem-
`branes to 14 solutes. In order to extend this further and to gain a better under-
`standing of the parameter which is concerned with the chemical nature of the
`solute, we have measured the permeability of human red cell membranes to 90
`
`714
`
`THE JOURNAL OF GENERAL PHYSIOLOGY - VOLUME 62, 1973
`
`pages 714-736
`
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`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
`
`7'5
`
`molecules. These molecules cover a wide spectrum of nonelectrolytes with
`varying chemical structure, chain length, degree of branching, type of bond,
`chemical reactive group, position of reactive group, lipid solubility, ability to
`form hydrogen bonds, and other properties. In selecting among the various
`solutes we were guided by the excellent study of Wright and Diamond which
`deals with the measurement of the reflection coefficients of various nonelectro-
`lytes in rabbit gallbladder (3).
`
`MATERIALS AND METHODS
`
`Human blood obtained by venipuncture was used throughout this study, with
`EDTA as an anticoagulant. The blood was kept refrigerated at 4°C for at most 48 h.
`Both the isotonic buffer (whose composition in millimoles/liter was: NaCl, 150;
`KCI, 5.0; MgC12, 1.0; CaC12, 0.25; NaH2 PO 4, 1.0; Na 2HPO 4, 5; pH = 7.4) and the
`test solutions were prepared on the day of the experiment. The experiments were
`carried out at room temperature (19-24°C) and at pH 7.4. The solutes were obtained
`from Fluka (Fluka, AG, Basel, Switzerland), Merck (Merck Chemical Div., Merck &
`Co., Inc., Rahway, N. J.), Fisher (Fisher Scientific Co., Pittsburgh, Pa.), and East-
`man Kodak (Eastman Kodak Co., Rochester, N. Y.).
`The rate of water entry into the cells was measured by a modification of the
`hemolysis and stop-flow technique (4, 5). Changes in cell volume were measured by
`spectrophotometry at 540 nm using a Beckman. Model B Spectrophotometer (Beck-
`man Instruments, Inc., Fullerton, Calif.) which was connected to a Grass DC am-
`plifier (Grass Instrument Co., Quincy, Mass.) and paper recorder. The red cells were
`diluted 200 times in an isotonic phosphate buffer just before the start of each experi-
`ment. 0.2 ml of this suspension was then injected into the observation tube which
`contained 2.5 ml of the test solution under study. The time-course of the change in
`light transmission at 540 nm was recorded. The test solution contained 0.3 M solute
`under study. The final mixture in the observation tube contained 0.04% red cells,
`0.277 M test solute, and 0.024 M NaCI. The base line, determined with the isotonic
`buffer as a test solution, was checked every three runs. 5-10 control runs in distilled
`water were carried out at the start of each experiment and at various times during
`the course of the experiment. Permeability coefficients were calculated using the
`equations derived initially by Jacobs and later summarized by Stein (4, 6).
`
`RESULTS AND DISCUSSION
`
`Table I gives the values of the permeability coefficients for all the 90 solutes
`which have been studied along with the molecular weight, and the ether: water
`partition coefficient (kether). For each molecule the value of at least nine de-
`terminations on three different blood samples is given. The values of keth,, are
`taken from Collander (7). The molecules are ordered according to increasing
`number of carbon atoms. It is important to point out here that the present
`values of the permeability coefficients of water and the 14 molecules which
`have been previously determined are smaller than those reported earlier (1).
`This is due to difference in experimental method since the present technique
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`716
`
`THE JOURNAL OF GENERAL PHYSIOLOGY
`
`VOLUME 62
`
`973
`
`I
`TABLE
`VALUES OF PERMEABILITY COEFFICIENTS FOR VARIOUS NONELECTRO-
`LYTES IN HUMAN RED CELL MEMBRANES
`
`Name
`
`Partition coeffident
`(kether)
`
`Permeability coefficient
`(P X 10- cm/s)
`
`Water
`Sulfamide
`Methanol
`Formamide
`Nitromethane
`Urea
`Thiourea
`Two carbon atoms
`Ethanol
`Ethylene glycol
`Dimethyl sulphoxide
`Acetonitrile
`Acetamide
`Thioacetamide
`2-Iodoacetamide
`Methyl formamide
`Methyl urea
`Three carbon atoms
`Acetone
`n-Propanol
`IsoPropanol
`Ethylene glycol monomethyl ether
`1,2-Propanediol
`1,3-Propanediol
`Glycerol
`Dimethyl formamide
`Ethyl formamide
`Methyl acetamide
`Propionamide
`Acrylamide
`Ethyl carbamate
`Ethyl urea
`Malonamide
`Four carbon atoms
`Tetrahydrofuran
`n-Butanol
`Isobutanol
`tert-Butanol
`Diethyl ether
`Dioxane
`Ethyl acetate
`1,3-Butanediol
`1,4-Butanediol
`2-Butene-1,4-diol
`2-Butyne-1,4, diol
`Ethylene glycol monoethyl ether
`1,2,4-Butanetriol
`Diethylene glycol
`Thiodiglycol
`3-Methoxy-1,2-propanediol
`2,3-Dioxanediol
`n-Butyramide
`Isobutyramide
`
`0.003
`
`0.14
`0.0014
`
`0.00047
`0.0063
`
`0.26
`0.0053
`
`0.60
`0.0025
`
`0.0012
`
`0.62
`1.9
`0.64
`0.061
`0.018
`0.012
`0.00066
`0.024
`
`0.013
`
`0.64
`0.0041
`0.00030
`
`7.7
`6.9
`2.2
`10
`
`8.5
`0.042
`0.029
`
`0.20
`
`0.004
`
`0.019
`
`0.058
`
`915415
`0.01
`11.3540.41
`8.05-0.66
`6.1540.28
`23.8741.14
`0.0740.03
`
`8.764-0.34
`3.3840.07
`1.3040.09
`4.5840.38
`4.2040.29
`3.3940.18
`3.87
`11.3540.61
`1.830.05
`
`9. 7540.51
`6.35-0.18
`4.3840.21
`12.1540.62
`1.7940.10
`0.914-0.04
`0.584-0.04
`11.9040.94
`5.0240.33
`3.1840.42
`3.80-0.28
`3.6640.33
`8.3440.82
`0.254-0.02
`0.01
`
`6.9940.19
`4.1240.14
`2.8140.11
`4.6540.30
`11.174-1.00
`11.9440.58
`5.544-.33
`2.1740.10
`1.1540.04
`0.79±-0.08
`1.3340.13
`12.8240.80
`0.244-.03
`0.634-.04
`1.704-0.15
`1.0040.04
`0.01
`4.8840.08
`2.8540.12
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`
`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
`
`717
`
`T A B L E
`
`I-Concluded
`
`Name
`
`Partition coefficient
`(kether)
`
`Permeability coefficient
`(P X 10 cm/$)
`
`Dimethyl acetamide
`Methyl propionamide
`Succinimide
`Ethyl acetamide
`N-2-hydroxyethyl acetamide
`Succinonitrile
`n-Propyl urea
`Isopropyl urea
`Five carbon atoms
`Isoamyl alcohol
`3-Pentanol
`Furfural
`Furfuryl alcohol
`Tetrahydrofurfuryl alcohol
`2,2-Dimethyl-1,3-propanediol
`1,5-Pentanediol
`Diethylene glycol monomethyl ether
`Monoacetin
`Pyridine
`Diethyl formamide
`Dimethyl propionamide
`n-Valeramide
`Isovaleramide
`Glutaronitrile
`Butyl urea
`Asymmetrical diethyl urea
`Six carbon atoms
`Cyclohexanol
`Cathechol
`1,4-Cyclohexanedione
`2,5-Hexanedione
`1,6-Hexanediol
`2,5-Hexanediol
`2-Methyl-2,4-pentanediol
`Pinacol
`Ethylene glycol, monobutyl ether
`Dipropylene glycol
`Triethylene glycol
`Diethyl acetamide
`Dimethyl butyramide
`Nicotinamide
`Seven carbon atoms
`2,2-Diethyl-1,3-propanediol
`Monobutyrin
`Diacetin
`Diethyl propionamide
`Diethylene glycol monobutyl ether
`Tetraethylene glycol
`Diethyl butyramide
`Nine or more carbon atoms
`Triacetin
`Tetraethylene glycol dimethyl ether
`Triethylene glycol diacetate
`
`0.031
`0.031
`
`0.32
`
`19
`
`0.055
`0.037
`0.041
`1.2
`
`0.17
`
`0.019
`
`0.45
`0.12
`
`0.51
`0.43
`
`0.035
`0.0031
`
`0.22
`
`1.1
`0.0024
`
`1.4
`0.061
`0.52
`
`14.734-0.37
`6.244-0.21
`1.7340.05
`8.344-0.24
`0.01
`3.4840.07
`0.624-0.08
`0.4040.04
`
`7.06-0.21
`1.75410.04
`6.6640.40
`5.87-0.73
`9.2340.13
`1.814-0.05
`1.644-.10
`4.944-0.16
`0. 794-0.08
`36.444-1.89
`7.694-.77
`8.8740.60
`4.0240.16
`4.1440.16
`4.894-0.08
`1.694-0.05
`1.7740.05
`
`4.444-0.23
`0.01
`2.314-0.16
`2.514-0.06
`2.26i0.06
`3.2540.14
`4.524-0.08
`4.914-0.08
`4.1040.37
`1.54-0.05
`0.104-0.03
`21.04-0.50
`5.824-0.30
`1.224-0.08
`
`2.664- .06
`19.804-0.70
`1.114-0.18
`6.5340.43
`9.764-0.12
`0.0740.01
`4.004-0.54
`
`4.654-0.47
`6.794-0.19
`25.640.87
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`718
`
`THE JOURNAL OF GENERAL PHYSIOLOGY · VOLUME 62
`
`1973
`
`tends to underestimate the values of permeability coefficients. We were quite
`aware of this and have discussed in previous papers the reasons behind this
`expected difference in the methods (8). It is only fair to say that it would have
`been an overwhelming task to measure the permeability coefficients of all
`these solutes by any other methods available. Moreover, the present technique
`does not change the order of permeation of the various molecules relative to
`each other (1). From consideration of each homologous series such as amides,
`ureas, and others, it appears that there are at least three important variables
`which need to be considered separately in understanding the permeation
`process of these solutes. The first is a parameter describing lipid solubility, the
`second a parameter dependent on molecular size, and the third a parameter
`which is concerned with the chemical nature of the solute. As has been pointed
`out earlier by Sha'afi et al. (1), this model is perforce empirical and its specific
`properties depend upon the exact nature of each of the parameters that has
`been selected. In order to have an overview of these factors affecting permea-
`tion, we have chosen ether: water partition coefficient to reflect the lipid solu-
`bility parameter along with molecular weight to reflect molecular size.
`
`Lipid Solubility
`It is evident from Table I that at least to a first approximation permeability
`coefficients increase with increasing kether. For example, in a given ho-
`mologous series, aside from the first members, increasing the number of CH 3
`groups results in an increase of both the permeability coefficients and kether
`This phenomenon, usually referred to as Overton's rule, has been observed in
`other systems and was one of the earliest indications of the lipid nature of cell
`membranes and of the key role of lipids as a diffusion barrier (3, 9).
`Kether has been chosen because its value is known for more solutes than the
`values for any other partition coefficients. In addition, we have found em-
`pirically as has been reported earlier, that the use of kether gives a better fit to
`our data. Ideally, one would like to know the value of the partition coefficient
`between water and membrane lipids in order to minimize experimental
`errors. The partition coefficients of nonelectrolytes have been studied by Hansh
`et al. (10) who found that aqueous solubility was the primary determinant of
`partition between water and a wide variety of organic solvents. They also
`showed that virtually any monofunctional organic liquid would serve equally
`well to represent the lipid phase in partition experiments with water. Since
`we are interested only in relative rates of permeation, kether will thus be a good
`index of the partition coefficient between water and membrane lipids.
`
`Violation of Overton's Rule
`Table II gives the chemical formula, the permeability coefficients, and kether
`for a few homologous series in which the only variable is the hydrocarbon
`
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`
`TABLE II
`VIOLATION OF OVERTON'S RULE BY THE SMALLEST MEMBER OF A
`HOMOLOGOUS SERIES
`
`Name
`
`Formula
`
`P X 10-
`
`ecm/s
`
`kether
`
`8.05
`
`0.0014
`
`4.20
`
`0.0025
`
`3.80
`
`0.013
`
`4.88
`
`0.058
`
`23.87
`
`0.00047
`
`1.83
`
`0.0012
`
`0.25
`
`0.0041
`
`OI
`
`I
`H-C--NH2
`
`O
`
`HSC-C-NH 2
`
`OI
`
`I
`HaC--CH 2 -C-NH 2
`
`OI
`
`I
`HSC- (CH 2) 2 -C-NH 2
`
`O
`
`H 2 N-C-NH 2
`
`OI
`
`I
`H3C-NH-- C-NH 2
`
`OI
`
`I
`H 3 C-CH2--NH-C-NH 2
`
`O
`
`Amide series
`
`Formamide
`
`Acetamide
`
`Propionamide
`
`Butyramide
`Urea series:
`
`Urea
`
`Methyl urea
`
`Ethyl urea
`
`Propyl urea
`
`H3C- (CH 2) 2-NH-C-NH 2
`
`0.62
`
`Butyl urea
`Alcohol series
`Methanol
`Ethanol
`Propanol
`Butanol
`Methyl-substituted amide series
`
`O
`
`HsC- (CH 2)3--NH--C--NH 2
`
`HaC- OH
`H3C-CH2-- OH
`H3C-(CH 2) 2--OH
`H3C- (CH 2 ) 3-OH
`
`Methyl formamide
`
`H-HC--NH-CH 3
`
`O
`
`Methyl acetamide
`
`H 3 C-C-NH--CH3
`
`Methyl propionamide
`Terminal diol series
`Ethylene glycol
`1,3-Propanediol
`1,4-Butanediol
`1,5-Pentanediol
`1,6-Hexanediol
`
`O
`
`H3 C-CH2 -C-NH-CH 3
`
`HO- CH 2 - CH 2 - OH
`HO- (CH 2) 3--OH
`HO- (CH 2 )4 -OH
`HO- (CH 2)- OH
`HO- (CH2) g-OH
`
`79
`
`1.69
`
`11.35
`8.76
`6.35
`4.12
`
`11.35
`
`3.18
`
`6.24
`
`3.38
`0.91
`1.5
`1.64
`2.26
`
`0.14
`0.26
`1.9
`7.7
`
`0.0053
`0.012
`0.029
`0.055
`0.12
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`720
`
`THE JOURNAL OF GENERAL PHYSIOLOGY
`
`· VOLUME 62
`
`· 1973
`
`chain length. Partition coefficients have been shown to increase regularly
`with the length of the hydrocarbon chain (7). It is clear that for the urea
`series, amide series, methyl-substituted amides, and terminal diol series, the
`relative permeability coefficient decreases up to the second or third member
`of each series, and only thereafter increases in accordance with Overton's
`rule. In the alcohol series, the permeability coefficient decreases regularly
`with increasing chain length from methanol to butanol in spite of a significant
`.r This behavior is contrary to what would be expected from
`increase in keth,
`Overton's rule. It is evident then that for small molecules of molecular weight
`under 75 the partition coefficient is not a good index of permeability and that
`Overton's rule is systematically violated.
`
`Molecular Size
`
`Fig. 1 shows the variation of In Prel/kether with molecular weight. According to
`irreversible thermodynamic consideration the permeability coefficient for a
`solute is given as follows:
`
`P = wRT = kx(f,
`
`, + fm),
`
`( )
`
`in which w is the permeability coefficient and has units of moles/dyne sec-
`ond, R is gas constant, T is absolute temperature, K 8 is the partition coefficient
`of the solute between membrane and external solution, and Ax is the path
`length through the membrane. Solute-water and solute-membrane frictions
`are denoted byfe andf, . Assuming k,,the,, to serve as a qualitative indicator of
`K,, the ratio P/keth,r should be inversely proportional to the sum of the fric-
`tional coefficient, Ax being assumed constant. There are four important con-
`clusions that can be drawn from Fig. 1 :(a) Steric hindrance has a consistent
`effect on the entire series including both hydrophilic and lipophilic molecules.
`(b) As evident from the slopes of the lines, the dependence on molecular weight
`varies considerably among various series. (c) Chemical factors are of great
`importance since each series falls on an entirely different curve. (d) The ratios
`Prel/kether of molecules that differ in chemical structure show no correlation
`with molecular weight when pooled together. The fact that we have plotted
`Prel/kether instead of P/kthe,, does not change any of these conclusions. In
`fact we have deliberately chosen Prel instead of P to eliminate Ax.
`We have also plotted the results using molar volume instead of molecular
`weight. Molar volume is a parameter which includes geometrical factors being
`equal to the molecular weight divided by the density of the pure compound.
`The molecular weight may be construed as a measure of molecular size based
`on a spherical model. Division by the density modifies the strictly geometrical
`interpretation by introduction of hydrogen-bonding ability because, as Pi-
`mentel and McClellan (11) have pointed out, hydrogen bonding generally
`increases the density and lowers the molar volume. The correlation of hydro-
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`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
`
`72 1
`
`1
`
`O ALCOHOLS
`x AMIDES
`A UREAS
`* GLYCOLS
`
`1
`
`100
`
`9
`
`30
`
`120
`10 40
`70
`MOLECULAR WEIGHT
`
`200
`
`FIGURE 1. Relation among relative permeability coefficient, partition coefficient
`and molecular weight for a series of alcohols, amides, ureas, and glycols in human red
`cells. The permeability coefficient is expressed relative to water. The code for the solutes
`is given below.
`
`Number
`
`Glycols
`
`Alcohols
`
`Amides
`
`Ureas
`
`1 Ethylene glycol
`2 Ethylene glycol monomethyl
`ether
`3 Diethylene glycol
`
`4 Diethylene glycol monomethyl
`ether
`5 Propylene glycol (1,2-pro-
`panediol)
`6 Ethylene glycol monoethyl
`ether
`7 Dipropylene glycol
`8 Triethylene glycol
`9 Diethylene glycol monobutyl
`ether
`10 Tetraethylene glycol
`11 Triethylene glycol diacetate
`12 Tetraethylene glycol diacetate
`
`Methanol
`Ethanol
`
`Formamide
`Acetamide
`
`Urea
`Methyl urea
`
`Isopropanol
`
`n-Propanol
`
`Dimethyl
`formamide
`Propionamide
`
`Ethyl urea
`
`tert-Butanol
`
`Butyramide
`
`n-Butanol
`
`Isovaleramide
`
`Isobutanol
`
`-
`
`-
`-
`-
`
`-
`
`-
`-
`-
`
`-
`
`-
`-
`
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`722
`
`THE JOURNAL OF GENERAL PHYSIOLOGY
`
`VOLUME 62
`
`1973
`
`gen-bonding ability with density is illustrated particularly effectively by the
`butanediol series in which the ability to form hydrogen bonds with other
`molecules decreases as the hydroxyl groups move closer and become able to
`form intramolecular hydrogen bonds. In these diols the density decreases as
`the ability to form hydrogen bonds with other molecules decreases. Substitution
`of molecular weight by molar volume does not alter any of the previous con-
`clusions.
`Recently, Lieb and Stein (12) have suggested that cell membranes should be
`treated as homogeneous membranes in which the permeability coefficient may
`be computed from an equation in which the only variables are molecular
`weight and the oil-water partition coefficient. In the case of bovine red cells,
`they have fitted permeability data obtained from hemolysis measurements to
`the equation
`
`P = P" mol wt ,
`
`(2)
`
`in which P is the permeability coefficient and P,, n, and p are adjustable con-
`stants, #/ the oil-water partition coefficient, and mol wtrel the molecu-
`lar weight, relative to methanol. Lieb and Stein obtained values of 1.4 for n
`and 6.0 for p. The least-squares fit to our data on human red cells in Table I
`was extremely poor. About 50 molecules were used for this analysis. These
`were the molecules which have known keth, r. The correlation is poor, as shown
`not only by the correlation coefficient of <0.4, but also by the very great
`scatter when the values predicted according to Eq. 1 are compared with the
`experimentally determined values. This is not surprising since Lieb and
`Stein's hypothesis has been already scrutinized and rejected by Sha'afi et al.
`(1), Smulders and Wright (13), and Dickson and Diamond (14).
`The lack of uniformity among solutes in Fig. 1 and the anomalous behavior
`of small hydrophilic solutes indicate quite clearly that no unitary hypothesis
`will serve to account for the behavior of all the solutes we have studied. The
`simplest and most straightforward explanation for these observations is to
`postulate that the red cell membrane behaves operationally as a mosaic struc-
`ture containing both lipid- and polar-region pathways. Neither pathway is ex-
`clusive, and for small lipophilic molecules such as methanol, both pathways
`are open. Steric factors are important to permeation by either route but not
`sufficient to account for all observations.
`The finding which appears to be most inconsistent with this general hy-
`pothesis is the observation reported by Macey and Farmer (15). These au-
`thors have shown that the compound phloretin significantly decreases the
`permeability coefficients for small hydrophilic solutes and exercises no effect
`on water transfer in human red cells. This would be quite inconsistent with the
`preceding hypothesis which postulates that small hydrophilic solutes permeate
`the membrane by the same polar-region pathways used by water. This ques-
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`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
`
`723
`
`tion has been recently investigated by Owen and Solomon (16), who have
`shown that phloretin exercises a general and far-reaching effect on the per-
`meability coefficients for both hydrophilic and lipophilic solutes. The rate of
`transfer of lipophilic solutes is increased by this compound, whereas the
`permeation of hydrophilic solutes is inhibited. In other words, the lipid solu-
`bility of a molecule determines whether its rate of permeation is inhibited or
`accelerated by phloretin. They have shown further that based on the kether for
`water, one would predict, in agreement with their finding, that phloretin
`should slightly increase the permeability coefficient to water. Accordingly, the
`initial finding of Macey and Farmer (15) is consistent with the two-pathway
`concept for red cell membranes.
`An alternate explanation which has been proposed by Stein (6) for the ob-
`served lack of uniformity and the anomalous behavior of small hydrophilic
`solutes is that the red cell membrane is homogeneous and that all molecules
`permeate by dissolving in the membrane fabric. The permeability coefficient
`for a given molecule is determined by its partition coefficient and molecular
`weight. According to this, the observed anomalies would then be the results of
`specialized membrane transport systems, such as facilitated transport (6).
`Even though there is some evidence derived from red cell studies which sup-
`ports this idea of facilitated transport systems for solutes such as glycerol and
`possibly even for urea (17, 18), we are unaware of any evidence to support this
`idea for all the deviant small molecules. The main argument Stein ad-
`vances in support of his hypothesis is to show on quantitative grounds that the
`presence in human red cell membranes of aqueous channels of average radius
`3.5 A will not account for the observed permeability coefficients. Using re-
`stricted-diffusion analysis formulated by Renkin (19), and assuming that the
`postulated channels have no special affinity to water molecules, Stein showed
`that permeability coefficients for nonelectrolytes calculated on the basis of 3.5
`A for the average pore radius would be much higher than those observed ex-
`perimentally. Granted that actual calculation of average radius, as pointed
`out earlier (by Sha'afi and Gary-Bobo (8)), may be completely invalid, this
`does not invalidate the concept of a polar route for solute permeation. In other
`words, Stein has merely shown that the observed permeability coefficients for
`various solutes in human red cells are inconsistent with a radius of 3.5 A, but
`this does not justify rejection of the polar-route concept.
`Another important geometrical factor which can be related to molecular
`size is the degree of branching in the molecules. The partition coefficients and
`permeability coefficients of isomers are summarized in Table III. Although
`there is no clear-cut apparent correlation between the degree of branching
`and the permeability coefficient, there are, however, two points which can be
`made. First, in the case of lipophilic solutes, the permeability coefficient de-
`creases with branching. It is conceivable that the observed decrease in perme-
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`TABLE III
`EFFECT OF BRANCHING ON THE PERMEABILITY COEFFICIENT (P) FOR
`NONELECTROLYTES IN HUMAN RED CELLS
`
`Name
`
`Formula
`
`n-Butanol
`
`HaC-CH2-CH 2-- CH2-OH
`
`kethe r
`
`7.7
`
`P X 10-6
`cm/s
`
`4.12
`
`Isobutanol
`
`tert-Butanol
`
`CH-CH 2-OH
`
`6.9
`
`2.81
`
`H3C
`
`H3C
`
`CHS
`
`HaC-C-OH
`/
`CHS
`
`2.2
`
`4.65
`
`n-Propanol
`
`H2C-CHr-CH2-OH
`
`1.9
`
`6.35
`
`Isopropanol
`
`Ha3CCH-OH
`
`0.64
`
`4.38
`
`CH3
`
`n-Valeramide*
`
`Isovaleramide
`
`0
`
`H 3 C-CH 2 CH 2-CH 2-C-NH 2
`0
`HaC
`
`-
`
`4.02
`
`CH-CH 2-- C-NH 2
`
`0.17
`
`4.14
`
`/
`H aC
`
`0
`
`n-Butyramide
`
`H3C--CH2-CH 2 -C-NH 2
`
`0.058
`
`4.88
`
`H3C
`
`O
`
`Isobutyramide
`
`CH-C-NH 2
`
`-
`
`2.85
`
`Hs C
`
`1,5-Pentanediol
`
`HO-CH 2-CH 2-CH 2--CH 2-CH 2 -OH
`
`0.055
`
`1.64
`
`2,2-Dimethyl-
`1,3-propanediol
`
`CH 3
`
`HO-CH2-C-CH 2 -OH
`
`-
`
`1.81
`
`CH 3
`
`* The permeability coefficient for n-valeramide is much too low.
`
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`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
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`TABLE II -Concluded
`
`Name
`
`Formula
`
`P X 10- i
`cm/.
`
`kether
`
`2 -CH 8
`
`-
`
`5.02
`
`o1
`
`1
`
`H-C-NH-CH
`
`Ethyl formamide
`
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`
`Dimethyl formamide
`
`H-C-N
`
`0.024
`
`11.9
`
`O
`
`CH3
`
`CH3
`
`Ethyl acetamide
`
`Ethyl acetamide
`
`-CHg
`H 3 C--NH-CH2
`
`Dimethyl acetamide
`
`H
`
`CH3
`
`O
`II /
`-C-N
`
`CH 3
`
`8.34
`8.34
`
`14.73
`
`-
`
`-
`
`ability coefficient is the result of a decrease in the partition coefficient. There is
`no doubt that this is partially responsible for the observed differences, but not
`all, because (a) the solute isovaleramide has a much higher partition coefficient
`than n-butyramide and yet it is still less permeant and (b) the difference in
`permeability coefficients between the first pair of isomers is much higher than
`would be predicted on the basis of differences in partition coefficients. In
`water, Gary-Bobo and Weber (20) have found very little difference between
`the diffusion coefficients of butyramide and isobutyramide. Coupled with the
`finding that solubility in lipid solvent, as indicated by the partition coefficient,
`is not very sensitive to branching of a molecule, the above observation indi-
`cates that the discriminatory power of the red cell membrane is much greater
`than either bulk lipid solvent or bulk water. It appears, therefore, that the
`lipids in cell membrane are very much less fluid than lipid solvents or water
`and must be held in an organized structure so that they are less free to bend
`around a solute. This can be so if the hydrocarbon tails of membrane fatty
`acid residues are aligned in parallel and closely packed to each other. Second,
`in the case of the last two pairs, branching seems to increase permeability co-
`efficients. This increase cannot be due to differences in kethe, or molecular size
`since ethylformamide is certainly as lipid soluble as dimethyl formamide. This
`is also true for ethyl acetamideand dimethyl acetamide. For example, ethyl urea
`has a value for kether of 0.0041 whereas the corresponding value for dimethyl
`urea is 0.0031. The situation is quite clear when one examines the first three
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`I973
`
`isomers in the table. The solute tert-butanol obviously has a much lower par-
`tition coefficient than the other two isomers and yet it shows a higher permea-
`bility coefficient. One possible explanation for this behavior is that the presence
`of the dimethyl groups in the case of the amide series tends to decrease the
`ability of the latter group to form hydrogen bonds with external acceptors. As
`will be discussed later, the permeability coefficient for a molecule increases
`with decreasing ability to form hydrogen bonds. A similar explanation can be
`used in the case of tert-butanol. If the density of a solute in a given series can be
`taken as an index of the hydrogen-bonding ability of this solute, then such an
`explanation is quite reasonable. One piece of evidence which supports this
`idea is that the density of tert-butanol is less than that of n-butanol. Also the
`densities of dimethyl formamide and dimethyl acetamide are less than the
`densities of ethyl formamide and ethyl acetamide, respectively.
`
`Hydrogen-Bonding Ability
`
`The first systematic analysis of the possible role of solute hydrogen-bonding
`ability and its relation to permeation in membranes was carried out by Stein
`(6). In his book, he tried to correlate permeability coefficients for solutes to the
`number of hydrogen bonds, NH, the solute is able to form with water, and he
`found, in general, that when NH increases, the rate of penetration decreases. In
`addition, Diamond and Wright presented further evidence to support this con-
`cept (21). The results in the present study confirm this general hypothesis and
`show further that extreme care must be exercised when dealing with the effect
`of hydrogen-bonding ability of a solute on its rate of permeation. As will be
`discussed later, this interdependence is invariably violated in the case of small
`molecules both hydrophilic and lipophilic. In addition, this interdependence
`is often complicated by the dependence of permeability coefficients on lipid
`solubility since in general the smaller the NH the higher the partition coeffici-
`ent. However, a true dependence of the permeability coefficient on NH does in-
`deed exist. To show this, it is instructive first to compare the behavior of the
`molecule 1,3-propanediol with that of propionamide. These two molecules
`have very similar physical properties and the order of permeability coefficient
`is propionamide > 1,3-propanediol. The major difference lies in the altered
`hydrogen-bonding ability of the solute which results from the presence of a
`single amide group rather than two hydroxyls.
`Hydrogen-bonding ability is somewhat greater for amides than alcohols as
`illustrated by differences in NH . Franks and Ives (22) give this number as 2
`for the alcohol group, whereas the most likely value for the amide group is 3
`(23). Gary-Bobo et al. (24) have shown that a series of amides experiences
`greater friction than an analogous series of alcohols when diffusing across a
`nonporous cellulose acetate membrane; furthermore, the ratio of the frictions
`is about 3:2. If simple additivity of hydrogen-bonding ability is assumed as a
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`NACCACHE AND SHA'AFI Human Red Cell Membrane Permeability
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`727
`
`first approximation, it is apparent that the NH of the diols should be greater
`than that of amides. The density of 1,3-propanedio