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Diffusion of radioactive nonelectrolytes in saline-agar gels
ANALYTICAL
BIOCHEMISTRY
Diffusion
27,
of
381-386 (1989)
Radioactive
in Saline-Agar M. POLLAY, Department School
A. STEVENS,
Nonelectrolytes Gels’ AND
R. KAPLAN
of Surgery (Neurosurgery),
the University of Medicine and Veterans Administration Albuquerque, New Mexico 87106
of New Mexico Hospital,
Received January 16, 1968
The advantages associated with the use of agar gels as media for studying translational diffusion are primarily due to the rigidity of the gel columns. The solidity of the diffusion media has minimized the uncertainties associated with poor mixing and imprecise boundaries (10). This experimental method has been further enhanced by the use of radioisotopes which have improved the precision and ease of solute assay in thin gel sections (11). This present study, describes the use of a simple solution for obtaining a technique for measuring the diffusion coefficients of C14-labelgd nonelectrolytes in dilute salt solutions at a controlled pH and temperature., METHODS
Preparation of Dijfusion Media
The agar gel was prepared by adding 2.0 gm of purified agar (Difco 0560) to 100 ml of 155 mM NaCl at 90°C. The pH of the salt solution was adjusted to 7.4 by using NaOH or HCl as needed. The concentration of agar in this solution was assumed to be approximately 1.5% because of moisture in the agar and loss of this substance during the preparation of the solution (10). The agar-salt solution was cooled to 50°C prior to filling the diffusion chambers. The diffusion solution contained NaCl in the same concentration as the agar .gel (155 mM). The pH of the solution was adjusted, as discussed above, to 7.4 after the addition of the test solute. The following substances were added to the basic salt solution: inulincarboxy-C14, sucrose-C*4,. n-glucose-C14, 2-deoxyglucose-C14, creatinine,‘.l’kp., study h&s, been sup,ported in part by Public Health Service Grants NB06195~ and NB66269; National Institute of Neurological Diseases and Blindness. 381
@ 1969 by Academic Press, Inc.
332
POLLAY,
STEVENS,
AND
KAPLAN
Cl’, urea-CY4, and mannitol-0’. A sufficient amount of carrier was added to produce a final concentration of 1.0 n-&f. The specific activity of the solution was approximately 0.25pc/ml. Experimental
Method
The experimental arrangement is similar to that utilized by Schantz and Lauffer (10) and therefore will only be briefly described here. A modified 1.5 ml syringe barrel (B-D 18) was used for a chamber holding the solidified agar gel. The open face of the gel was placed through an opening in a covered specimen jar which contained 100 ml of the salt solution and radioactive solute. The agar gel face was placed in contact with the surface of the salt solution after the gel and solution reached thermal equilibrium (+ 0.5%) in a constant-temperature water bath. The solution was well stirred during the experimental period by a motordriven glass stirring rod. The periods of diffusion varied between 7 and 24 hours. At the termination of the diffusion period, the gels were extruded from the syringe and sliced at intervals of 1.0 mm to a depth of 2.0 cm. In all experiments, the accuracy of the slice depth was determined by weighing the slices in an analytical balance to the nearest 0.1 mg. Analytical
Methods
The gel slices as well as the pre- and postdiffusion samples of the radioactive solution (50 ~1) were added to scintillation counting vials containing 5.0 ml of purified Triton X-100 and 10.0 ml of toluene-base scintillation mixture (6.0 gm PPO and 150 mg POPOP per liter of toluene). Counting of samples was accomplished in a scintillation spectrometer at ambient temperature. The preset counting error was less than 0.5% (2 Q). Appropriate corrections were made for background and quenching when necessary. RESULTS
The computation of the diffusion coefficient (D) is based on the determination of solute (C,) distribution in the agar gel at time t and x distance from the initial solution-gel boundary and the application of Fick’s second law (5, 8, 9, 10). When the concentration in the initial layer of solution is maintained at a constant value (C,), the solution of this law is (5, 8) : c, = co jl-
2/&joyd&4
(1)
where y = x/da. Since Z/A Jo”e+ dy represents the error function of y, equation (1) may be written as:
NONELECTROLYTE
DIFFUSION
erf (x/&E)
IN
GELS
383
= 1 - C=/G
The distance x into the agar plug for the first slice was considered to be 0.05 cm since the average concentration C, (cpm/mg) in a thin gel section is essentially equal to the concentration at the midpoint of each gel slice. The subsequent measurement of x occurs at intervals of 0.1 cm. The precision of the gel slicing technique utilized in this study was supported by the small variation (< 1.0%) in weight of individual gel sections as compared to the mean weight of all sections. In addition, the thickness of each section, as calculated from its weight and the area of the gel face, was in close agreement with that of the expected slice depth (< 1.5%). The error function values corresponding to the 1 - Cz/CO data were obtained from a standard probability table (1). The data from a typical urea-P4 diffusion experiment were used to construct the graph in Ii’igure I. 1.5
r
UREA At=
- C ‘4
29,3+0
T=370C set
X (cm)
FIG.
1.
Plot of r/d4%
vs. z from values obtained from a diffusion experiment
utilizing urea-W. The linearity of this plot supports, the concept that the measured diffusion is complying with Fick’s law (10). The diffusion eoeficient z) (em2/sec) for urea at 37°C as determined from the slope of this line (l/a) is 16.9 x 1O-scm2/sec. This value is uncorrected for the excluded volume of the gel and the obstruction of the gel itself to diffusion of the solute. This correction has been shown to be about 1.03 for salts, sugars, and other low molecular weight compounds (9, 10). The corrected coefficient is 17.4 X lo-6 cm2/sec at 37°C. The corrected diffusion coefficients for the nonelectrolytes determined at various temperatures are presented in Table 1. The values represent the
384
PoLL.0,
smNs,
AND
KAPLAN
mean f standard error of the mean (S.E.M.). The results at various temperatures are in close agreement with equation (3) :
where T = absolute temperature
(“C) and n = viscosity (centipoise).
TABLE1 Diffusion Coefficients Determined in Saline-Agar Gels Solute
Mann&l
SllrroSe Creatinine Urea Inlllin Glucme Z-Deoxyglucose
No. of experiments
5 22 26 37 5 25 37 5 25 37 5 37 25 37 5 25 37 25
4 2 2 6 4 4 6 4 6 4 4 4 4 4 4 2 4 2
Diffusion cce5eieat,~ D X 101 cm:/m
3.80 6.39 7.09 9.29 3.00 5.48 6.98 5.33 9.38 12.81 7.66 17.33 2.18 3.21 3.87 7.09 9.14 6.98
f 0.07 f 0.08 f 0.12 iO.13 f 0.01
f 0.15 f 0.09 f 0.08 f0.20 50.31 f 0.18 f 0.21 f 0.06 -I 0.10 f0.06 f 0.09 f 0.07 f 0.26
a All concentrations are 1.0 mM. * Corrected for excluded volume and gel obstruction. DISCUSSION In the past, diffusion
in agar gel has been shown
to be similar
to free
diffusion in water when appropriate corrections are made for gel obstruction and excluded volume of the gel (9, 10). The close agreement pctween the results of this present study and most previously reported values (Table 2) also supports the validity of equating the’ diffusion measured in saline-agar gels with free diffusion in water. In addition, this close agreement between diffusion coefficients of radioactive tracks and the unlabeled substances support the view of Curran et al. (4) that tracer flow can be used to predict flow of the bulk substance to an accuracy of a few per cent. This conclusion, however, is limited to solute concentration up to 200 mM.
NONELECTROLYTE
DIFFUSION
IN
385
GELb
In general, the diffusion coefficients determined at the low solute concentrations utilized in this study (1.0 mM) are slightly’greater than most values presented in the literature for more concentrated solutions. For practical purposes, however, the diffusion coefficients of nonelectrolytes in dilute aqueous solutions (< 0.25 M) can be considered constant. It should be noted that the diffusion coefficients for inulin and creatininc determined in this study are significantly greater than that found by TABLE 2 Diffiisiori Coeficients of W-Labeled Substances Compared with Literature Values for Unlabeled Compoundse Diihion coe5oient, cm~/8,0 x 10-s
Eubatance
Reference(a)
1.0
6.98
b
15.0 29.3 100.0 250.0 1.0 16.7 300.0 1.0 10.0 100.0 1.0
6.46 6.81 6.38 6.54 17.33
(3) (6, 7) (10)
18.15 15.39 9.14 9.12 8.96 3.21
64 10)
2.93 2.32 9.29
(12)
lMannito1
c 3.0 1.0
Creatinine
30.0 1.0
8.48 12.81
(2) h
10.0
9.85
(3,
Sucrose
Urea
Glucose Inulin
h
(2) (3)
(“10,
(2, 10) h
(3) b
o All values at 37°C. b Values for (Y-labeled compounds from Table 2. c Unspecified concentration of inulin-CF.
Bunim et al. (3). Welch and Sadler (12)) utilizing the solution to gel diffusion technique, found their resuIts for inulin also to be considerably greater than that previously presented in the literature. The low values reported by the earlier investigators for this substance may be due in part to the precipitation of inulin from the supersaturated solutions (1500 mgOJo) utilized in their experiments. There is no ready explanation for the low diffusion coefficients presented by Bunim et al. (3) fol creatinine, although the results of this present study are in line with those expected from its molecular weight.
386
POLLAY,
STEVENS,
AND
KAPLAN
SUMMARY
A simple solution to gel diffusion method utilizing radioactive tracers, has been described as a means of measuring the diffusion of certain biologically important nonelectrolytes in dilute. aqueous solutions. ACKNOWLEDGMENTS We wish to thank E. Estrada and R. Counsellor
for technical assistance.
REFERENCES 1. ALXUMOWITZ, M., AND STEGUN, I. A., in “Handbook of Mathematical Functions,” p. 1046. National Bureau of Standards. Washington, D.C., 1964; Dover, New York, 1965. 2. BBTJINS, H. R., in “International Critical Tables” (E. W. Washburn, ed.), Vol. V. McGraw-Hill, New York, 1929. 3. BUNIM, J. J., SMITH, W. W., AND SMITE, H. W., J. BioZ. Chem. 118, 667 (1937). 4. CURRAN, P. F., TAYLOR, A. E., AND SOLOMON, A. K., Biophys. J. 7, 879 (1967). 5. GEDDES, A. L., AND PONTIUS, R. B., in “Technique of Organic Chemistry” (A. Weissberger, ed.), Physical Methods, Part II, Chapter XVI, p. 896. Interscience, New York, 1966. 6. GOSTINQ, L. J., AND Moruus, M. S., J. Am. Chem. Sot. 71, 1998 (1949). 7. GRI~H, 0. M., AND MCEWEN, C. R., And. Biochem. 18, 397 (1967). 8. HIT~ECOCK, D. I., in “Physical Chemistry of Cells and Tissues” (R. Hober, ed.), Chap. I, p. 7. Blakiston, Philadelphia, 1945. (3. LAUFFEB, M. A., Biophys. J. 1, 295 (1961). 10. SCHANTZ, E. J., AND LAUFFER, M. A., Biochemistry 1, 658 (1962). 11. SMITE, T. C., CAMPBELL, A. D., AND HIJF, E. G., Med. CoZZ. Virg. Quart., Summer, 127 (19661. 12. WELCH, K., AND SADLER, K., Am. J. Physid. 210,652 (1966).
BIOCHEMISTRY
Diffusion
27,
of
381-386 (1989)
Radioactive
in Saline-Agar M. POLLAY, Department School
A. STEVENS,
Nonelectrolytes Gels’ AND
R. KAPLAN
of Surgery (Neurosurgery),
the University of Medicine and Veterans Administration Albuquerque, New Mexico 87106
of New Mexico Hospital,
Received January 16, 1968
The advantages associated with the use of agar gels as media for studying translational diffusion are primarily due to the rigidity of the gel columns. The solidity of the diffusion media has minimized the uncertainties associated with poor mixing and imprecise boundaries (10). This experimental method has been further enhanced by the use of radioisotopes which have improved the precision and ease of solute assay in thin gel sections (11). This present study, describes the use of a simple solution for obtaining a technique for measuring the diffusion coefficients of C14-labelgd nonelectrolytes in dilute salt solutions at a controlled pH and temperature., METHODS
Preparation of Dijfusion Media
The agar gel was prepared by adding 2.0 gm of purified agar (Difco 0560) to 100 ml of 155 mM NaCl at 90°C. The pH of the salt solution was adjusted to 7.4 by using NaOH or HCl as needed. The concentration of agar in this solution was assumed to be approximately 1.5% because of moisture in the agar and loss of this substance during the preparation of the solution (10). The agar-salt solution was cooled to 50°C prior to filling the diffusion chambers. The diffusion solution contained NaCl in the same concentration as the agar .gel (155 mM). The pH of the solution was adjusted, as discussed above, to 7.4 after the addition of the test solute. The following substances were added to the basic salt solution: inulincarboxy-C14, sucrose-C*4,. n-glucose-C14, 2-deoxyglucose-C14, creatinine,‘.l’kp., study h&s, been sup,ported in part by Public Health Service Grants NB06195~ and NB66269; National Institute of Neurological Diseases and Blindness. 381
@ 1969 by Academic Press, Inc.
332
POLLAY,
STEVENS,
AND
KAPLAN
Cl’, urea-CY4, and mannitol-0’. A sufficient amount of carrier was added to produce a final concentration of 1.0 n-&f. The specific activity of the solution was approximately 0.25pc/ml. Experimental
Method
The experimental arrangement is similar to that utilized by Schantz and Lauffer (10) and therefore will only be briefly described here. A modified 1.5 ml syringe barrel (B-D 18) was used for a chamber holding the solidified agar gel. The open face of the gel was placed through an opening in a covered specimen jar which contained 100 ml of the salt solution and radioactive solute. The agar gel face was placed in contact with the surface of the salt solution after the gel and solution reached thermal equilibrium (+ 0.5%) in a constant-temperature water bath. The solution was well stirred during the experimental period by a motordriven glass stirring rod. The periods of diffusion varied between 7 and 24 hours. At the termination of the diffusion period, the gels were extruded from the syringe and sliced at intervals of 1.0 mm to a depth of 2.0 cm. In all experiments, the accuracy of the slice depth was determined by weighing the slices in an analytical balance to the nearest 0.1 mg. Analytical
Methods
The gel slices as well as the pre- and postdiffusion samples of the radioactive solution (50 ~1) were added to scintillation counting vials containing 5.0 ml of purified Triton X-100 and 10.0 ml of toluene-base scintillation mixture (6.0 gm PPO and 150 mg POPOP per liter of toluene). Counting of samples was accomplished in a scintillation spectrometer at ambient temperature. The preset counting error was less than 0.5% (2 Q). Appropriate corrections were made for background and quenching when necessary. RESULTS
The computation of the diffusion coefficient (D) is based on the determination of solute (C,) distribution in the agar gel at time t and x distance from the initial solution-gel boundary and the application of Fick’s second law (5, 8, 9, 10). When the concentration in the initial layer of solution is maintained at a constant value (C,), the solution of this law is (5, 8) : c, = co jl-
2/&joyd&4
(1)
where y = x/da. Since Z/A Jo”e+ dy represents the error function of y, equation (1) may be written as:
NONELECTROLYTE
DIFFUSION
erf (x/&E)
IN
GELS
383
= 1 - C=/G
The distance x into the agar plug for the first slice was considered to be 0.05 cm since the average concentration C, (cpm/mg) in a thin gel section is essentially equal to the concentration at the midpoint of each gel slice. The subsequent measurement of x occurs at intervals of 0.1 cm. The precision of the gel slicing technique utilized in this study was supported by the small variation (< 1.0%) in weight of individual gel sections as compared to the mean weight of all sections. In addition, the thickness of each section, as calculated from its weight and the area of the gel face, was in close agreement with that of the expected slice depth (< 1.5%). The error function values corresponding to the 1 - Cz/CO data were obtained from a standard probability table (1). The data from a typical urea-P4 diffusion experiment were used to construct the graph in Ii’igure I. 1.5
r
UREA At=
- C ‘4
29,3+0
T=370C set
X (cm)
FIG.
1.
Plot of r/d4%
vs. z from values obtained from a diffusion experiment
utilizing urea-W. The linearity of this plot supports, the concept that the measured diffusion is complying with Fick’s law (10). The diffusion eoeficient z) (em2/sec) for urea at 37°C as determined from the slope of this line (l/a) is 16.9 x 1O-scm2/sec. This value is uncorrected for the excluded volume of the gel and the obstruction of the gel itself to diffusion of the solute. This correction has been shown to be about 1.03 for salts, sugars, and other low molecular weight compounds (9, 10). The corrected coefficient is 17.4 X lo-6 cm2/sec at 37°C. The corrected diffusion coefficients for the nonelectrolytes determined at various temperatures are presented in Table 1. The values represent the
384
PoLL.0,
smNs,
AND
KAPLAN
mean f standard error of the mean (S.E.M.). The results at various temperatures are in close agreement with equation (3) :
where T = absolute temperature
(“C) and n = viscosity (centipoise).
TABLE1 Diffusion Coefficients Determined in Saline-Agar Gels Solute
Mann&l
SllrroSe Creatinine Urea Inlllin Glucme Z-Deoxyglucose
No. of experiments
5 22 26 37 5 25 37 5 25 37 5 37 25 37 5 25 37 25
4 2 2 6 4 4 6 4 6 4 4 4 4 4 4 2 4 2
Diffusion cce5eieat,~ D X 101 cm:/m
3.80 6.39 7.09 9.29 3.00 5.48 6.98 5.33 9.38 12.81 7.66 17.33 2.18 3.21 3.87 7.09 9.14 6.98
f 0.07 f 0.08 f 0.12 iO.13 f 0.01
f 0.15 f 0.09 f 0.08 f0.20 50.31 f 0.18 f 0.21 f 0.06 -I 0.10 f0.06 f 0.09 f 0.07 f 0.26
a All concentrations are 1.0 mM. * Corrected for excluded volume and gel obstruction. DISCUSSION In the past, diffusion
in agar gel has been shown
to be similar
to free
diffusion in water when appropriate corrections are made for gel obstruction and excluded volume of the gel (9, 10). The close agreement pctween the results of this present study and most previously reported values (Table 2) also supports the validity of equating the’ diffusion measured in saline-agar gels with free diffusion in water. In addition, this close agreement between diffusion coefficients of radioactive tracks and the unlabeled substances support the view of Curran et al. (4) that tracer flow can be used to predict flow of the bulk substance to an accuracy of a few per cent. This conclusion, however, is limited to solute concentration up to 200 mM.
NONELECTROLYTE
DIFFUSION
IN
385
GELb
In general, the diffusion coefficients determined at the low solute concentrations utilized in this study (1.0 mM) are slightly’greater than most values presented in the literature for more concentrated solutions. For practical purposes, however, the diffusion coefficients of nonelectrolytes in dilute aqueous solutions (< 0.25 M) can be considered constant. It should be noted that the diffusion coefficients for inulin and creatininc determined in this study are significantly greater than that found by TABLE 2 Diffiisiori Coeficients of W-Labeled Substances Compared with Literature Values for Unlabeled Compoundse Diihion coe5oient, cm~/8,0 x 10-s
Eubatance
Reference(a)
1.0
6.98
b
15.0 29.3 100.0 250.0 1.0 16.7 300.0 1.0 10.0 100.0 1.0
6.46 6.81 6.38 6.54 17.33
(3) (6, 7) (10)
18.15 15.39 9.14 9.12 8.96 3.21
64 10)
2.93 2.32 9.29
(12)
lMannito1
c 3.0 1.0
Creatinine
30.0 1.0
8.48 12.81
(2) h
10.0
9.85
(3,
Sucrose
Urea
Glucose Inulin
h
(2) (3)
(“10,
(2, 10) h
(3) b
o All values at 37°C. b Values for (Y-labeled compounds from Table 2. c Unspecified concentration of inulin-CF.
Bunim et al. (3). Welch and Sadler (12)) utilizing the solution to gel diffusion technique, found their resuIts for inulin also to be considerably greater than that previously presented in the literature. The low values reported by the earlier investigators for this substance may be due in part to the precipitation of inulin from the supersaturated solutions (1500 mgOJo) utilized in their experiments. There is no ready explanation for the low diffusion coefficients presented by Bunim et al. (3) fol creatinine, although the results of this present study are in line with those expected from its molecular weight.
386
POLLAY,
STEVENS,
AND
KAPLAN
SUMMARY
A simple solution to gel diffusion method utilizing radioactive tracers, has been described as a means of measuring the diffusion of certain biologically important nonelectrolytes in dilute. aqueous solutions. ACKNOWLEDGMENTS We wish to thank E. Estrada and R. Counsellor
for technical assistance.
REFERENCES 1. ALXUMOWITZ, M., AND STEGUN, I. A., in “Handbook of Mathematical Functions,” p. 1046. National Bureau of Standards. Washington, D.C., 1964; Dover, New York, 1965. 2. BBTJINS, H. R., in “International Critical Tables” (E. W. Washburn, ed.), Vol. V. McGraw-Hill, New York, 1929. 3. BUNIM, J. J., SMITH, W. W., AND SMITE, H. W., J. BioZ. Chem. 118, 667 (1937). 4. CURRAN, P. F., TAYLOR, A. E., AND SOLOMON, A. K., Biophys. J. 7, 879 (1967). 5. GEDDES, A. L., AND PONTIUS, R. B., in “Technique of Organic Chemistry” (A. Weissberger, ed.), Physical Methods, Part II, Chapter XVI, p. 896. Interscience, New York, 1966. 6. GOSTINQ, L. J., AND Moruus, M. S., J. Am. Chem. Sot. 71, 1998 (1949). 7. GRI~H, 0. M., AND MCEWEN, C. R., And. Biochem. 18, 397 (1967). 8. HIT~ECOCK, D. I., in “Physical Chemistry of Cells and Tissues” (R. Hober, ed.), Chap. I, p. 7. Blakiston, Philadelphia, 1945. (3. LAUFFEB, M. A., Biophys. J. 1, 295 (1961). 10. SCHANTZ, E. J., AND LAUFFER, M. A., Biochemistry 1, 658 (1962). 11. SMITE, T. C., CAMPBELL, A. D., AND HIJF, E. G., Med. CoZZ. Virg. Quart., Summer, 127 (19661. 12. WELCH, K., AND SADLER, K., Am. J. Physid. 210,652 (1966).