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Semipermeable Membranes (Dialysis/Cellophane Membranes/Peptides/Activation Energy) LYMAN C

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Semipermeable Membranes (Dialysis/Cellophane Membranes/Peptides/Activation Energy) LYMAN C Proc. Nat. Acad. Sci. USA Vol. 69, No. 3, pp. 702-705, March 1972 On a Theory for the Passive Transport of Solute through Semipermeable Membranes (dialysis/cellophane membranes/peptides/activation energy) LYMAN C. CRAIG AND HAO-CHIA CHEN The Rockefeller University, New York, N.Y. 10021 Contributed by Lyman C. Craig, January 10, 1972 ABSTRACT It has been shown that thin-film dialysis the peptide or the membrane. This theory seemed reasonable can be performed in such a way that the limiting rate is the rate of entry of the solute into the membrane from the because of the high discrimination of the dialysis method, high-concentration side. The rate of diffusion, therefore, that appeared to be in the range of 2-3% of the Stokes reflects the probability of a molecule entering the pores on radius (3). the surface and does not depend on the resistance to Recently it has been discovered (5) that with peptides of diffusion offered by the internal structure of the mem- brane. The good correlation, so generally found, of the high charge density and with charges of the same sign, a order of escape times of given solutes with the order of free higher order of freedom from fixed charge on the membrane is diffusion rates is thus explained. The data from stretching required in order for dialysis rates to be independent of experiments with wet cellophane, in which the pore struc- charge. A method of covering any residual fixed charge has ture is distorted, are also explained. been developed; the charge is coupled with glycine amide with Soon after the method of thin-film dialysis was proposed as a the help of a water-soluble carbodiimide coupling agent. simple experimental way to study relative rates of diffusions Membranes so treated have reduced absorptive properties and, thereby, to permit estimations of Stokes radii, solute- and behave more ideally with highly charged solutes. It solvent behavior, and conformational change, preliminary seemed of interest to again investigate temperature, as well as studies (1) on the effect of temperature were also made. The salt, effects with these modified membranes. behavior of proteins approximated that expected on the basis RESULTS AND DISCUSSION of the theory that their relative rates of diffusion through membranes would occur in the same order as their free diffu- The effect of change of temperature on free diffusion coeffi- sion coefficients, but that differences would be greatly en- cients in various solvents has been thoroughly investigated by hanced due to the resistance of the membrane. This finding different workers, and was reviewed by Longsworth (6). implied that the membrane would carry no fixed charge, and Ideal spherical solutes follow the Stokes-Einstein equation indeed evidence was supplied that Visking dialysis casing rather closely: available at the time (2) did have a low, and apparently D KT/6wrrqr, (1) negligible, order of fixed charge. With increasing temperature, up to 40 50°, it was somewhat surprising to find that the in- where D is the diffusion coefficient, K is a constant, T is the creased rate of dialysis of certain test solutes approximated absolute temperature, tq is the viscosity, and r is the particle that shown by free diffusion (the Stokes-Einstein relation- radius. The uncertainty of hydration always must be consid- ship), i.e. directly proportional to change of absolute temper- ered with polar molecules, particularly with amino acids. For ature, but inversely proportional to the viscosity change of instance, glycine amide (7) diffuses considerably faster than the solvent. Above 50°, proteins known to undergo heat de- the dipolar ion. This is observed also with the dialysis method: naturation showed a much slower rate of dialysis, as would be the simple amides of the amino acids always dialyze more expected from an expanded molecule. rapidly than the free amino acids. This may be due to a hy- A preliminary study with carbohydrates of known confor- dration effect. mation and rigidity (3) strongly supported the theory of in- For particles that are not spherical, formulas analogous to creased selectivity, as compared to free diffusion, when com- Stokes' law for prolate and oblate elipsoids of revolution were parisons were at a given temperature, but the temperature co- derived by Perrin (8). These have been used for derivation of efficients were often too high for particular carbohydrates. frictional coefficients for the larger molecules, such as pro- These higher temperature coefficients were thought to be due to teins. Again there is the uncertainty of hydration effects, and changes in the hydration of either the solute or the membrane. it is not even certain that these formulas apply to the smaller When polypeptides of both the linear and the rigid cyclic molecules. In fact, Longsworth's data (6) are in quite good antibiotic types were studied, individual temperature co- agreement with the simpler Stokes-Einstein equation. efficients again appeared to be unpredictable (4), but were re- Although it is obvious that the restricted type of diffusion producible for each peptide. It was thought that the linear that results from thin-film dialysis is more complicated than peptides could easily undergo conformational change, but the free diffusion, it is helpful perhaps to think of it along the lines too-high temperature coefficients of the cyclic peptides were set forth in free diffusion studies. Thus, from the Stokes- again thought perhaps to reflect changes of hydration either of Einstein equation, the reciprocal plot shown in Fig. 1 can be 702 Downloaded by guest on October 1, 2021 Proc. Nat. Acad. Sci. USA 69 (1972) Passive Transport of Solute 703 constructed. The slope indicates the relative diffusabilities at TABLE 1. Comparative half-escape times (T/2) with highly the different temperatures and permits calculation of the acetylated membranes activation energy of diffusion. In thin-film dialysis, a straight-line escape plot (9) indi- T/2 (min) T/2 at cates ideal behavior, i.e., the rate of dialysis for the particular 20 00: T/2 membrane and assembly is proportional only to the concen- Membrane Solute at 200C at 400C at 400C tration gradient across the membrane. The half-escape time A 3H20 15 8.7 1.75 ±0.22 is, therefore, a measure of the rate of dialysis of the solute for 14CH30H 32 18 1.83 i 0.19 that membrane and cell that can be used for comparison with CH314COOH 52 29 1.80 ± 0.10 other solutes in the same membrane and cell. It is thus of B 3H20 11 7 1.51±0.16 interest to substitute the reciprocal of the half-escape time for CH314COOH 23 14 1.67 ± 0.06 the diffusion coefficient in the reciprocal plot for the study of [14CIUrea 40 26 1.56 ± 0.04 temperature effects. The reciprocal is required since a rate CH314COO-K+ 16 10 1.60 ± 0.12 constant is proportional to the reciprocal of the half-escape [14C]Glycine 23 13.5 1.71 ± 0.24 time. Such a plot of the logarithm of the reciprocal of the half- escape time against the reciprocal of the absolute temperature (Fig. 1) then provides a curve whose slope conceptually could membranes (4), the ratios of the half-escape time at 250 to give an estimation of the activation energy required for di- that at 400 of the relatively large solutes ribonuclease, cyto- alysis through the membrane. Hydration effects, as well as chrome c, and ovalbumin were 1.44, 1.42, and 1.48, respec- changes in conformation, would be included in this estimate. tively, in 0.01 N acetic acid. The expected ratio (Fig. 1) is Interaction with the membrane by adsorption would also be 1.44. On the other hand, very highly acetylated membranes, included if there were appreciable interaction. Whether or not which allow only very slow diffusion of small molecules such there is adsorption, however, can be easily determined by as urea, also show surprising adherence to the Stokes-Ein- a simple recovery calculation. stein equation (10). In Table 1, concentrations were deter- In spite of these complications, it seemed of interest to per- mined by scintillation counting of the labeled solutes (Tri-Carb form the experiments this way. We were surprised to find that Scintillation Counter in Bray's scintillation medium). The numerous solutes with the completely neutral membranes temperatures were 200 and 400, which, from Fig. 1, should have practically straight-line reciprocal plots over the tem- give a ratio of half-escape times of 1.73 if adherence to the perature range 4-40', with a slope in close agreement with Stokes-Einstein equation were followed. The agreement is that calculated from the Stokes-Einstein equation for free surprisingly good. These highly acetylated membranes are diffusion. The agreement of this slope with those for the di- more hydrophobic than the unacetylated ones and are con- peptide L-Leu-I-Tyr and the cyclic antibiotic gramicidin-SA diserably less flexible. in 0.1 M NaCl is shown in'Fig. 1. The data for the dipeptide From the data given for thin-film dialysis, it would appear were obtained from a membrane treated with glycine amide to that adherence to the Stokes-Einstein equation for rigid remove charge, and then acetylated to reduce its porosity. The solutes does not depend on the porosity, flexibility, or hydro-- data for gramicidin-SA were obtained from a more-porous phobicity of the membrane, provided it is free of fixed charge membrane, not acetylated but treated only with glycine and does not adsorb the solute. It also does not depend on the amide. A similar agreement has been obtained for tri- and size of the solute molecule, an observation coinciding with that tetraglycine in water.
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