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Gel-exclusion chromatography on S1000 sephacryl: Application to phospholipid vesicles
ANALYTICAL
BIOCHEMISTRY
130, 47 1-474 (1983)
Gel-Exclusion Chromatography on Sl 000 Sephacryl: Application to Phospholipid Vesicles JACQUELINEA.REYNOLDS,'YASUHIKONOZAKI,ANDCHARLESTANFORD Department
of Physiology,
Duke
Universi&y
Medical
Center,
Durham,
North
Carolina
27710
Received November 15, 1982 Sephacryl S 1000 has an exclusion diameter of approximately 3000 A and is thus an appropriate gel exclusion medium for size analysis and fractionation of phospholipid vesicles. Calibration is conveniently carried out using polystyrene beads of known diameter eluted with a detergentcontaining buffer. Recovery of phospholipid vesicles of different sizes from SlOOO presaturated with lipid is greater than 95%, and diameters obtained from a calibration curve using the polystyrene beads are in good agreement with those obtained by negative contrast electron microscopy. KEY WORDS: chromatography; Sephacryl; phospholipid vesicles.
We have recently suggested in a preliminary communication (1) that gel-exclusion chromatography on Sephacryl SlOOO provides a quick and convenient method for determining the average size of phospholipid vesicles and for fractionation of heterogeneous populations of vesicles. In that work we calibrated the gel-exclusion column with phospholipid vesicle preparations of different sizes using a diameter determined by electron microscopy. Routine size analysis by this latter technique is tedious and can be subject to individual bias. The technique of sedimentation field flow (2) can be used for fractionation as well as size analysis but requires considerably more sophisticated instrumentation than gel-exclusion chromatography. Monodisperse microparticles ranging in diameter size from 500 to 10,000 A are frequently used as standards for light scattering, laser scattering, and scanning and transmission electron microscopy. These latex microspheres are also suitable for calibration of gelexclusion media designed for separation of very large molecules and small particles (e.g.,
Sephacryl SlOOO). We describe here a simple and reliable procedure for calibration of S 1000 using these microspheres and provide examples of the application of this gel-exclusion medium to phospholipid vesicle size analysis and separations. EXPERIMENTAL
PROCEDURES
Mutevials. All chemicals were standard reagent grade with the exception of (1) egg-yolk lecithin from Lipid Products, Nutley, England (2) sodium dodecyl sulfate from Gallard/Schlesinger, (3) [‘4C]octylglucoside from Research Products International, Elk Grove Village, Illinois, (4) S1000 Sephacryl Superfine from Pharrnacia, Piscataway, N. J., and (5) Polybead Polystyrene Monodisperse Latex from Polysciences, Warrington, Pennsylvania. Five sizes of Polybeads were used. Diameters supplied by the manufacturer were 570 f 60,lOOO -t 80, 1700 + 30,260O t 100, and 5000 + 60 A. Methods. Several different types of columns were packed with SIOOO as recommended by the manufacturer. Bio-Rad EconoColumns (0.7 X 50 cm) containing polyethylene support filters are routinely used by us
I To whom all correspondence should be addressed. 471
0003-2697183 $3.00 Copyright 0 1983 by Academic Press. Inc. All rights of reprcductton in any form reserved.
472
REYNOLDS.
NOZAKI.
for chromatographic applications involving lipids and lipid-protein complexes. Two glass columns of dimensions 0.9 X 25 and 0.8 X 55 cm were also used in these studies. Packing flow rates were 40 cm/h and the columns were allowed to stabilize at least 2 days at experimental flow rates before using. Sample loading and fraction volumes were l-2% of the total column volume. The effuent was monitored either by 90” light scattering using a microcell in a Perkin-Elmer MPF 44A or by absorbance at an appropriate wavelength in a microcell in a Cary 17D. Radioactivity was determined by liquid scintillation counting. All samples containing lipid were chromatographed on columns presaturated with egg-yolk lecithin. Several column volumes of aqueous buffer containing sonicated lipid vesicles were passed through the system until the eluant had the same phospholipid concentration as the buffer. The amount of lipid required for saturation depends upon the total surface area of support material, column walls, and exit tubing and can only be determined experimentally. Exchange of adsorbed lipid with lipid present in vesicular form is slow due to the low monomer solubility in aqueous media, and experiments using radioactive phosphatidylcholines showed no exchange during the course of the chromatographic procedure. Some caution should be exercised, however, in cases where vesicles contain mixtures of different lipids, and column effluents should be analyzed to insure that no compositional changes have occurred. Once the column has been saturated, aqueous buffers are used containing no lipid and recoveries under these conditions are routinely 95% or greater of the applied phospholipid vesicles or protein-lipid complexes. If columns are used with detergent after presaturation with lipid, part or all of the adsorbed lipid will be removed and the column must be resaturated. Sample and calibration data were plotted by use of the semiempirical equation of Acket-s(3) which we have used routinely for analysis of data on other gel filtration media (4).
AND TANFORD
The equation is Hydrodynamic
radius = 4) + &erff’( 1 - Kd),
where a0 and b. are constants of the gel filtration medium and Kd is the equilibrium constant for distribution between the gel pores and the fluid phase. erf-’ represents the inverse of the standard error function as tabulated for example in (5). When results are plotted in this way they should depend only on the properties of the gel and should be independent of column dimensions. Kd for any sample (standard or unknown) is obtained from: K ye-v,) d (K-V,) with V, the elution position of the sample, V. the void volume, and V, the total volume. RESULTS
Polystyrene beads of diameters from 500 to 5000 A tend to aggregate in aqueous media but can be readily dispersed by detergents. Therefore, for the purpose of calibration the columns were equilibrated in aqueous buffer containing various concentrations of sodium dodecyl sulfate. Polystyrene beads with diameters of 4000 and 5000 %,eluted in the void volume, and beads of 2600 A were barely included with a & of 0.017. The total volume was determined with either mercaptoethanol or [‘4C]octyl glucoside. Figure 1 (open symbols) shows the diameter of the polystyrene beads as a function of erf’ (1 - &). Polystyrene beads were also diluted by a factor of 50 from the supplied concentration of 2.5% solids into aqueous buffer and chromatographed on S 1000 in the absence of detergent (filled symbols in Fig. 1). Under these conditions the elution position was identical within experimental error with that observed when detergent was present in the eluting buffer. (We have previously shown that detergents have no measurable effect on gel-ex-
CHROMATOGRAPHY
elusion matrices of smaller pore size (4).) However, recovery of the beads from the column was poor due to selective adsorption of a portion of the polystyrene beads to the top of the column matrix. Aggregation and adsorption problems in the absence of detergent were more severe at increased ionic strength. Therefore, in general, calibration of SlOOO with polystyrene beads is best carried out with detergent present in the eluting buffer. Also shown on Fig. 1 are the elution data for cytochrome c (diameter = 30 A), human high density serum lipoprotein (diameter = 100 A), and a protein-lipid complex of apolipoprotein AI with egg-yolk lecithin (diameter = 90 A). These three substances were chromatographed in the absence of detergent on lipid presaturated columns. The exclusion limit of S 1000 is slightly larger than 2600 A, a result that agrees with the manufacturer’s stated exclusion diameter of approximately 3000 A. The upward curvature of the plot in Fig. 1 and the extrapolated negative intercept on the ordinate from the values of erff’ (I - &) greater than 0.5 suggest that the chromatographic medium consists of more than one distribution of pore sizes as described previously by Ackers (3) for artificially created mixtures. Figure 2 shows the elution profiles of polystyrene beads (diameter = 1700 f 30 A), eggyolk lecithin vesicles formed from mixed micelles of the lipid and octyl glucoside by the method of Mimms et al. (6), and a complex of apolipoprotein AI with egg-yolk lecithin that was homogeneous in analytical ultracentrifugation with a diameter of 90 A. In all three examples a 0.15-ml sample was loaded and eluted with a flow rate of 13 cm/h. Under these conditions, the band broadening appears to be similar to that of smaller pore size gels. For example, a column containing S200 superfine of identical dimensions and eluted at an identical flow rate showed a width at half-height for the apo AI-egg-yolk lecithin complex of 1.5 ml, comparable to the width at half height in Fig. 2 of 2 ml. It should be noted that these small analytical columns were
473
ON SIOOO SEPHACRYL
FIG. I. Calibration of Sephacryl SIOOO. 0.7 X 50-cm column, 0. I5 M NaCI, 0.02 M NaHC03, pH 80.0, +0.003 M sodium dodecyl sulfate, polystyrene beads. 0, No sodium dodecyl sulfate, polystyrene beads diluted X50, human serum high density lipoprotein 100 A, AI-egg-yolk lecithin complex 90 A, cytochrome c 30 A. 0, 0.9 X 25 and 0.8 X 55-cm columns, 0.20 M NaCI, 0.01 M Tris buffer, pH 7.5, 0.01 M sodium dodecyl sulfate, polystyrene beads.
eluted at relatively high flow rates (13 cm/h) and that slower flow rates in general will improve the resolving power of gel-exclusion columns. However, in analyzing and separating lipid vesicle preparations it is desirable to minimize oxidative degradation and hydrolysis by carrying out all sample manipulations as rapidly as possible.
g effluent
FIG. 2. Elution profiles from Sephacryl SIOOO. 0.7 X SO-cm column, 0. I5 M NaCI, 0.02 M NaHC03, pH 8.0. A, 0.003 M sodium dodecyl sulfate, 1700 8, polystyrene beads. B, No sodium dodecyl sulfate, egg-yolk lecithin vesicles from octyl glucoside mixed micelles (Mimms et al. (6)), AI-egg-yolk lecithin complex (diameter = 90 A). The two complexes were chromatographed separately.
474
REYNOLDS.
NOZAKI.
To test the applicability of the bead calibration to measurement of vesicle dimensions, a comparison between column chromatography and electron microscopic analysis was made. Two preparations of egg-yolk lecithin vesicles were made from mixed micelles of lipid and n-dodecyl octaethylene glyco1 monoether using Amberlite XAD-2 nonionic polymeric adsorbent beads to effect detergent removal. Both preparations were heterogeneous with non-Gaussian distributions when examined by electron microscopy. Similarly, both preparations eluted from S1000 as asymmetric peaks with widths at half height of 8 ml (approximately one-half the column volume). This width is much greater than what can be attributed to normal spreading of a solute zone (3) (see Fig. 2, for example, where relatively homogeneous particles were chromatographed under identical conditions). A weight-average diameter was calculated from histograms obtained by negative strain electron microscopy and compared with the average diameter indicated by comparison of the eluted peak position with the calibration curve of Fig. 1. Vesicle preparation I was determined to have a weight average diameter of 1361 %, by electron microscopy and 1430 8, by chromatography on S 1000. Similar agreement was found for preparation 2 with corresponding diameters of 945 and 1070 8, from the two procedures. Given the inherent inaccuracy of determining an average peak position for a heterogeneous sample (multiple overlapping Gaussian bands) on gel-exclusion columns, this agreement is very satisfactory. DISCUSSION
The calibration data presented in Fig. 1 show reproducibility and essential superposition of results from different columns. In
AND TANFORD
addition, the results of Fig. 2 demonstrate that homogeneous samples elute from S 1000 with a nearly Gaussian distribution and band broadening comparable to that of smaller pore size gels, indicating the applicability of chromatography on S 1000 to determination of average size and size heterogeneity of individual lipid vesicle preparations. On the other hand, the multimodal nature of the elution curve (Fig. 1) makes the short columns used in the present study poorly suited for separation of vesicles into fractions of different size. The smallest vesicles reported are those formed by sonication (7) and they have a diameter of 2 10 A. These vesicles would elute according to the calibration curve of Fig. 1 with Kd = 0.3. Thus only 70% of the column bed would be available for separation of these vesicles from larger ones. Similarly, the separation between vesicle diameters of 1000 and 3000 8, would involve only 25% of the column bed. In preparative separations, then, much larger ratios of height to radius must be used for effective resolution. ACKNOWLEDGMENTS This work was supported by the Whitehead Medical Research Institute, U.S.P.H.S. Grants HL 30049 (J.A.R.), AM 04576 (C.T.), and National Science Foundation PCM79-20676.
REFERENCES I. Nozaki, Y., Lasic, D. D., Tanford, C., and Reynolds, J. A. (1982) Science 217, 366-367. 2. Kirkland, J. J., Yau, W. W., and Szoka, F. C. (1982) Science 215, 296. 3. Ackers, G. K. (I 970) Adv. Prot. Chem. 24, 343-447. 4. Nozaki, Y., Schechter, N. M., Reynolds, J. A., and Tanford, C. (1976) Biochemistry 15, 3884-3890. 5. Dwight, H. B. (1958) Mathematical Tables pp. 140143, Dover, New York. 6. Mimms, L. T., Zampighi, G., Nozaki, Y., Tanford, C., and Reynolds, J. A. (1981) Biochemistry 20, 833-840. 7. Huang, C. (1969) Biochemistry 8, 344-351.
BIOCHEMISTRY
130, 47 1-474 (1983)
Gel-Exclusion Chromatography on Sl 000 Sephacryl: Application to Phospholipid Vesicles JACQUELINEA.REYNOLDS,'YASUHIKONOZAKI,ANDCHARLESTANFORD Department
of Physiology,
Duke
Universi&y
Medical
Center,
Durham,
North
Carolina
27710
Received November 15, 1982 Sephacryl S 1000 has an exclusion diameter of approximately 3000 A and is thus an appropriate gel exclusion medium for size analysis and fractionation of phospholipid vesicles. Calibration is conveniently carried out using polystyrene beads of known diameter eluted with a detergentcontaining buffer. Recovery of phospholipid vesicles of different sizes from SlOOO presaturated with lipid is greater than 95%, and diameters obtained from a calibration curve using the polystyrene beads are in good agreement with those obtained by negative contrast electron microscopy. KEY WORDS: chromatography; Sephacryl; phospholipid vesicles.
We have recently suggested in a preliminary communication (1) that gel-exclusion chromatography on Sephacryl SlOOO provides a quick and convenient method for determining the average size of phospholipid vesicles and for fractionation of heterogeneous populations of vesicles. In that work we calibrated the gel-exclusion column with phospholipid vesicle preparations of different sizes using a diameter determined by electron microscopy. Routine size analysis by this latter technique is tedious and can be subject to individual bias. The technique of sedimentation field flow (2) can be used for fractionation as well as size analysis but requires considerably more sophisticated instrumentation than gel-exclusion chromatography. Monodisperse microparticles ranging in diameter size from 500 to 10,000 A are frequently used as standards for light scattering, laser scattering, and scanning and transmission electron microscopy. These latex microspheres are also suitable for calibration of gelexclusion media designed for separation of very large molecules and small particles (e.g.,
Sephacryl SlOOO). We describe here a simple and reliable procedure for calibration of S 1000 using these microspheres and provide examples of the application of this gel-exclusion medium to phospholipid vesicle size analysis and separations. EXPERIMENTAL
PROCEDURES
Mutevials. All chemicals were standard reagent grade with the exception of (1) egg-yolk lecithin from Lipid Products, Nutley, England (2) sodium dodecyl sulfate from Gallard/Schlesinger, (3) [‘4C]octylglucoside from Research Products International, Elk Grove Village, Illinois, (4) S1000 Sephacryl Superfine from Pharrnacia, Piscataway, N. J., and (5) Polybead Polystyrene Monodisperse Latex from Polysciences, Warrington, Pennsylvania. Five sizes of Polybeads were used. Diameters supplied by the manufacturer were 570 f 60,lOOO -t 80, 1700 + 30,260O t 100, and 5000 + 60 A. Methods. Several different types of columns were packed with SIOOO as recommended by the manufacturer. Bio-Rad EconoColumns (0.7 X 50 cm) containing polyethylene support filters are routinely used by us
I To whom all correspondence should be addressed. 471
0003-2697183 $3.00 Copyright 0 1983 by Academic Press. Inc. All rights of reprcductton in any form reserved.
472
REYNOLDS.
NOZAKI.
for chromatographic applications involving lipids and lipid-protein complexes. Two glass columns of dimensions 0.9 X 25 and 0.8 X 55 cm were also used in these studies. Packing flow rates were 40 cm/h and the columns were allowed to stabilize at least 2 days at experimental flow rates before using. Sample loading and fraction volumes were l-2% of the total column volume. The effuent was monitored either by 90” light scattering using a microcell in a Perkin-Elmer MPF 44A or by absorbance at an appropriate wavelength in a microcell in a Cary 17D. Radioactivity was determined by liquid scintillation counting. All samples containing lipid were chromatographed on columns presaturated with egg-yolk lecithin. Several column volumes of aqueous buffer containing sonicated lipid vesicles were passed through the system until the eluant had the same phospholipid concentration as the buffer. The amount of lipid required for saturation depends upon the total surface area of support material, column walls, and exit tubing and can only be determined experimentally. Exchange of adsorbed lipid with lipid present in vesicular form is slow due to the low monomer solubility in aqueous media, and experiments using radioactive phosphatidylcholines showed no exchange during the course of the chromatographic procedure. Some caution should be exercised, however, in cases where vesicles contain mixtures of different lipids, and column effluents should be analyzed to insure that no compositional changes have occurred. Once the column has been saturated, aqueous buffers are used containing no lipid and recoveries under these conditions are routinely 95% or greater of the applied phospholipid vesicles or protein-lipid complexes. If columns are used with detergent after presaturation with lipid, part or all of the adsorbed lipid will be removed and the column must be resaturated. Sample and calibration data were plotted by use of the semiempirical equation of Acket-s(3) which we have used routinely for analysis of data on other gel filtration media (4).
AND TANFORD
The equation is Hydrodynamic
radius = 4) + &erff’( 1 - Kd),
where a0 and b. are constants of the gel filtration medium and Kd is the equilibrium constant for distribution between the gel pores and the fluid phase. erf-’ represents the inverse of the standard error function as tabulated for example in (5). When results are plotted in this way they should depend only on the properties of the gel and should be independent of column dimensions. Kd for any sample (standard or unknown) is obtained from: K ye-v,) d (K-V,) with V, the elution position of the sample, V. the void volume, and V, the total volume. RESULTS
Polystyrene beads of diameters from 500 to 5000 A tend to aggregate in aqueous media but can be readily dispersed by detergents. Therefore, for the purpose of calibration the columns were equilibrated in aqueous buffer containing various concentrations of sodium dodecyl sulfate. Polystyrene beads with diameters of 4000 and 5000 %,eluted in the void volume, and beads of 2600 A were barely included with a & of 0.017. The total volume was determined with either mercaptoethanol or [‘4C]octyl glucoside. Figure 1 (open symbols) shows the diameter of the polystyrene beads as a function of erf’ (1 - &). Polystyrene beads were also diluted by a factor of 50 from the supplied concentration of 2.5% solids into aqueous buffer and chromatographed on S 1000 in the absence of detergent (filled symbols in Fig. 1). Under these conditions the elution position was identical within experimental error with that observed when detergent was present in the eluting buffer. (We have previously shown that detergents have no measurable effect on gel-ex-
CHROMATOGRAPHY
elusion matrices of smaller pore size (4).) However, recovery of the beads from the column was poor due to selective adsorption of a portion of the polystyrene beads to the top of the column matrix. Aggregation and adsorption problems in the absence of detergent were more severe at increased ionic strength. Therefore, in general, calibration of SlOOO with polystyrene beads is best carried out with detergent present in the eluting buffer. Also shown on Fig. 1 are the elution data for cytochrome c (diameter = 30 A), human high density serum lipoprotein (diameter = 100 A), and a protein-lipid complex of apolipoprotein AI with egg-yolk lecithin (diameter = 90 A). These three substances were chromatographed in the absence of detergent on lipid presaturated columns. The exclusion limit of S 1000 is slightly larger than 2600 A, a result that agrees with the manufacturer’s stated exclusion diameter of approximately 3000 A. The upward curvature of the plot in Fig. 1 and the extrapolated negative intercept on the ordinate from the values of erff’ (I - &) greater than 0.5 suggest that the chromatographic medium consists of more than one distribution of pore sizes as described previously by Ackers (3) for artificially created mixtures. Figure 2 shows the elution profiles of polystyrene beads (diameter = 1700 f 30 A), eggyolk lecithin vesicles formed from mixed micelles of the lipid and octyl glucoside by the method of Mimms et al. (6), and a complex of apolipoprotein AI with egg-yolk lecithin that was homogeneous in analytical ultracentrifugation with a diameter of 90 A. In all three examples a 0.15-ml sample was loaded and eluted with a flow rate of 13 cm/h. Under these conditions, the band broadening appears to be similar to that of smaller pore size gels. For example, a column containing S200 superfine of identical dimensions and eluted at an identical flow rate showed a width at half-height for the apo AI-egg-yolk lecithin complex of 1.5 ml, comparable to the width at half height in Fig. 2 of 2 ml. It should be noted that these small analytical columns were
473
ON SIOOO SEPHACRYL
FIG. I. Calibration of Sephacryl SIOOO. 0.7 X 50-cm column, 0. I5 M NaCI, 0.02 M NaHC03, pH 80.0, +0.003 M sodium dodecyl sulfate, polystyrene beads. 0, No sodium dodecyl sulfate, polystyrene beads diluted X50, human serum high density lipoprotein 100 A, AI-egg-yolk lecithin complex 90 A, cytochrome c 30 A. 0, 0.9 X 25 and 0.8 X 55-cm columns, 0.20 M NaCI, 0.01 M Tris buffer, pH 7.5, 0.01 M sodium dodecyl sulfate, polystyrene beads.
eluted at relatively high flow rates (13 cm/h) and that slower flow rates in general will improve the resolving power of gel-exclusion columns. However, in analyzing and separating lipid vesicle preparations it is desirable to minimize oxidative degradation and hydrolysis by carrying out all sample manipulations as rapidly as possible.
g effluent
FIG. 2. Elution profiles from Sephacryl SIOOO. 0.7 X SO-cm column, 0. I5 M NaCI, 0.02 M NaHC03, pH 8.0. A, 0.003 M sodium dodecyl sulfate, 1700 8, polystyrene beads. B, No sodium dodecyl sulfate, egg-yolk lecithin vesicles from octyl glucoside mixed micelles (Mimms et al. (6)), AI-egg-yolk lecithin complex (diameter = 90 A). The two complexes were chromatographed separately.
474
REYNOLDS.
NOZAKI.
To test the applicability of the bead calibration to measurement of vesicle dimensions, a comparison between column chromatography and electron microscopic analysis was made. Two preparations of egg-yolk lecithin vesicles were made from mixed micelles of lipid and n-dodecyl octaethylene glyco1 monoether using Amberlite XAD-2 nonionic polymeric adsorbent beads to effect detergent removal. Both preparations were heterogeneous with non-Gaussian distributions when examined by electron microscopy. Similarly, both preparations eluted from S1000 as asymmetric peaks with widths at half height of 8 ml (approximately one-half the column volume). This width is much greater than what can be attributed to normal spreading of a solute zone (3) (see Fig. 2, for example, where relatively homogeneous particles were chromatographed under identical conditions). A weight-average diameter was calculated from histograms obtained by negative strain electron microscopy and compared with the average diameter indicated by comparison of the eluted peak position with the calibration curve of Fig. 1. Vesicle preparation I was determined to have a weight average diameter of 1361 %, by electron microscopy and 1430 8, by chromatography on S 1000. Similar agreement was found for preparation 2 with corresponding diameters of 945 and 1070 8, from the two procedures. Given the inherent inaccuracy of determining an average peak position for a heterogeneous sample (multiple overlapping Gaussian bands) on gel-exclusion columns, this agreement is very satisfactory. DISCUSSION
The calibration data presented in Fig. 1 show reproducibility and essential superposition of results from different columns. In
AND TANFORD
addition, the results of Fig. 2 demonstrate that homogeneous samples elute from S 1000 with a nearly Gaussian distribution and band broadening comparable to that of smaller pore size gels, indicating the applicability of chromatography on S 1000 to determination of average size and size heterogeneity of individual lipid vesicle preparations. On the other hand, the multimodal nature of the elution curve (Fig. 1) makes the short columns used in the present study poorly suited for separation of vesicles into fractions of different size. The smallest vesicles reported are those formed by sonication (7) and they have a diameter of 2 10 A. These vesicles would elute according to the calibration curve of Fig. 1 with Kd = 0.3. Thus only 70% of the column bed would be available for separation of these vesicles from larger ones. Similarly, the separation between vesicle diameters of 1000 and 3000 8, would involve only 25% of the column bed. In preparative separations, then, much larger ratios of height to radius must be used for effective resolution. ACKNOWLEDGMENTS This work was supported by the Whitehead Medical Research Institute, U.S.P.H.S. Grants HL 30049 (J.A.R.), AM 04576 (C.T.), and National Science Foundation PCM79-20676.
REFERENCES I. Nozaki, Y., Lasic, D. D., Tanford, C., and Reynolds, J. A. (1982) Science 217, 366-367. 2. Kirkland, J. J., Yau, W. W., and Szoka, F. C. (1982) Science 215, 296. 3. Ackers, G. K. (I 970) Adv. Prot. Chem. 24, 343-447. 4. Nozaki, Y., Schechter, N. M., Reynolds, J. A., and Tanford, C. (1976) Biochemistry 15, 3884-3890. 5. Dwight, H. B. (1958) Mathematical Tables pp. 140143, Dover, New York. 6. Mimms, L. T., Zampighi, G., Nozaki, Y., Tanford, C., and Reynolds, J. A. (1981) Biochemistry 20, 833-840. 7. Huang, C. (1969) Biochemistry 8, 344-351.