Method to improve the accuracy of membrane osmometry measures of protein molecular weight

Journal of Biochemical and Biophysical Methods, 26 (1993) 299-307 © 1993 Elsevier Science Publishers B.V. All rights reserved 0165-022X/93/$06.00

299

JBBM 00997

Method to improve the accuracy of membrane osmometry measures of protein molecular weight Gary D. Fullerton a R o b e r t J. Z i m m e r m a n a, Kalpana M. Kanal a, L. Jean Floyd a and Ivan L. C a m e r o n b a Department of Radiology and b Department of Cellular and Structural Biology, The University of Texas Health Science Center at San Antonio, San Antonio, TX (USA)

(Received 30 November 1992) (Accepted 22 January 1993)

Summary M e m b r a n e osmometry provides a simple method to determine protein molecular weight but accuracy is limited by nonideal behavior. Recent studies (Fullerton et al., Biochem. Cell Biol., in press) show that non-ideal osmotic response of protein solutions is described by the empirical equation, M s v / M s = R T p / A s x 1 / H + I, where M s = mass of solute, Msv = mass of solvent, R = the Universal gas constant, T = absolute temperature, p = solvent density, A s = solute molecular mass, H = osmotic pressure, and I = the nonideality parameter. This linear relation is used in this paper to demonstrate that m e a s u r e m e n t of molecular weight from the slope simplifies such measures and improves the accuracy relative to classical methods. The molecular weight of bovine serum albumin is measured with error less than 0.9%. The single dimensionless nonideality parameter, 1 = 4.05 +0.07, describes nonideal curvature in the typical H V = nRT diagram better than the customary second power virial expansion requiring 3 fitting constants. Analysis of eight data sets on four proteins from the literature shows that molecular weight calculated from the slope of the new equation agrees with chemical molecular weight within an R M S error of only 1.9%. Key words: Osmometry; M e a s u r e m e n t method; Molecular weight; Protein

Introduction Membrane osmometry is frequently used as a simple method to determine protein molecular weight [1,2]. Traditionally such measurements require a seCorrespondence address: G.D. Fullerton, D e p a r t m e n t of Radiology, T h e University of Texas Health Science Center at San Antonio, Floyd Curl Drive, San Antonio, T X 78284-7800, USA.

300

quence of measured osmotic pressures at concentrations approaching zero to correct for nonideal behavior. Nonideal response makes osmotic pressure, H, II=n /V x RTx

@

(1)

highly nonlinear. A nonideality factor, q~, is frequently used to describe this [1]. The factor is a nonlinear function of concentration increasing from 1.0 at low concentrations to 3.0 or greater at protein concentrations typical in biology. This factor is expressed as a second or third order polynomial expansion with three or four fitting constants to provide _+1% accuracy. To complicate matters, q~ is observed to change with solvent characteristics such as pH, cosolute salt species and cosolute salt concentration. This study evaluates the capacity of the empirical solute/solvent interaction corrected equation [3] M~,,/M s = S

x1/H+ I

(2)

to simplify the extraction of accurate molecular weight from osmotic pressure data. Molecular weight, As, is calculated from the slope, S, such that A, = RTp/S

(3)

As the relation is linear, all data points are equally useable and no extrapolation is necessary. Nonideality is described by the constant I. Thus, small changes in solvent composition that affect q~ are unimportant to the new method. Comparison of measured molecular weight with chemical molecular weight shows that measurement accuracy of + 1% is easily achieved.

Materials and Methods Sample preparation

A 150 mM sodium chloride (NaC1) stock solvent solution was made with distilled, deionized water. Known amounts (0.6, 0.7, 0.8, 0.9, and 1.0 g) of lyophilized bovine serum albumin (BSA) (Sigma, St. Louis, MO, 98-99% albumin) were added to glass vials. Ten ml of solvent (150 mM NaC1) were added to each vial to create solutions of approximately 6, 7, 8, 9, and 10% (w/w) protein. The BSA samples were filtered (0.45 tzM Acrodisc filters, Gelman Sciences, Ann Arbor, MI) into new vials and degassed in a vacuum ( - 96 kPa) for 7 min prior to osmotic pressure measurements. Final BSA sample concentrations were determined gravimetrically by drying an aliquot ( ~ 4 g) of each filtered solution. The aliquots were dried in a vacuum oven at 65°C until the mass stabilized ( ~ 3 days) and then transferred to a higher vacuum at 100°C for an additional day. The final dry mass was corrected to account for salt in the solvent by subtracting the mass of the amount of salt/unit volume of water f r o m the dry down residue to calculate protein mass, M s.

301 The mass of the solution, Msol, as well as the dry residual mass, Mo, were measured. The mass of water, M w, was calculated using M w =Mso I - M d. The concentration of salt, X = Msalt/Mwater, measured separately during solvent preparation, was used to calculate the solvent mass. The solvent mass, M~v, equals the sum of water and salt, Msv = M w + Msalt = M w + M w X . The mass protein solute, Ms, was calculated using M s = M d - M w X to correct for salt. Then M s v / M s was calculated using Ms.,/M s = ( M w + M w X ) / ( M d - M ~ X )

(4)

The above procedures were repeated with a 150 m M potassium chloride stock solvent. Osmometry

The osmotic pressure measurements were made with an Osmomat 050 automatic colloid osmometer (UIC, Joliet, IL). A two layer m e m b r a n e / f i l t e r (supplied with the osmometer) with a 20 000 molecular weight cut-off was used. The samples had a p H of ~ 6.9 + 0.1 range, and were maintained at room temperature (24 _+ I°C range). The experiment began with the lowest ( ~ 6%) BSA concentration and proceeded to the highest ( ~ 10%) BSA concentration. The lowest concentration was selected to give a pressure measurement accuracy of 3 significant figures. To determine osmotic pressure, a typical 250-/zl sample was injected into the osmometer. Each BSA concentration was injected 6 times (with two osmotic pressure readings/injection) and required a total of approximately 1.5 ml of sample. The first reading at each concentration was discarded. The equilibrium time ranged from 2 to 4 min per injection. The osmotic pressure (n = 10) was read from the digital output in centimeters of solvent. The osmotic pressures for salt solutions (cm solvent) were converted to cm water by multiplying by the ratio of densities (1.0045). M s v / M s was plotted against the mean inverse of osmotic pressure, l / H , and the best fit calculated by linear regression. The molecular weight ( A ) was calculated from the slope of the regression using the following expression: A s = 84.8 x (273.15 + 24) x 1004.43/S

(5)

Results Detailed results of osmotic pressure measurements on BSA solutions in 150 m M sodium chloride for a single experiment (Expt. 1) are shown in Fig. 1 and Table 1. Additional measurements made in 150 m M sodium chloride and potassium chloride are not shown for brevity. The precision and accuracy of osmotic pressure measurements is on the order of 0.1%. Table 2 summarizes the regression

302 TABLE 1 Mean osmotic pressures of BSA solutions in 150 mM NaCI, 24°C, pH 6.9 Sample

Msv/M~ (g/g)

n

P (cm solvent)

P (cm H 2 0 )

ExplA ExplB ExplC ExplD ExplE

16.373 14.356 12.633 11.252 10.047

10 10 10 10 10

30.69 ± 0.15 36.17 ± 0.35 43.27 ± 0.44 52.79 ± 0.52 62.00± 0.13

30.83 ±0.15 36.33 ±0.35 43.46 ± 0.44 53.02 ± 0.52 62.27 ± 0.13

analysis of Ms,,/Ms as a function of 1/1I for the all experiments in either NaC1 or KCI solvents. The osmotic pressure of BSA at T = 24°C in both KCI and NaC1 is described by a single equation using the mean slope and /-value from the above analysis,

M~,,/M~= 381 x 1 / H +4.05

(6)

The molecular weight calculated from the slope of this equation is A s = 84.8 x 297.15 x 1004.4/381 = 66428 Da.

TABLE 2 Summary of BSA results in salt solutions Sodium chloride solution Sample Conc. (%)

n

I (g/g)

Slope

r 2 correlation

At

Expl Exp2 Exp3 Exp4

5 4 4 5

3.96 4.18 4.07 3.95

380 368 375 384

0.999 0.999 0.998 0.999

66500 68500 67400 65800

6, 7, 6, 6,

7, 8, 7, 7,

8, 9, 8, 8,

9, 10 10 10 9, 10

Mean NaC1 solutions (n = 4) S.D. S.E.M.

4.04 0.11 (2.7%) 0.05 (1.2%)

67100 1167 (1.7%) 584 (0.9%)

Potassium chloride solution Sample Conc. (%)

n

[ (g/g)

Slope

r e correlation

As

Exp5 Exp6 Exp7 Exp8

5 5 5 5

4.20 3.93 3.72 4.37

380 393 395 370

0.999 0.999 1.000 1.000

66400 64300 64000 68300

6, 6, 6, 6,

7, 7, 7, 7,

8, 8, 8, 8,

9, 9, 9, 9,

10 10 10 10

Mean KCI solutions (n = 4) S.D. S.E.M.

4.05 0.29 (7.2%) 0.14 (3.5%)

65700 2007 (3.1%) 1004(1.5%)

Both solutions Combined mean (n = 8) S.D. S.E.M.

4.05 0.20 (4.9%) 0.07 (1.7%)

66 400 1672 (2.5%) 591 (0.9%)

303

Discussion

Accuracy of molecular weight The mean molecular weight and mean I-values for the sodium chloride solutions and for the potassium chloride solutions do not differ significantly. Combining data, we have eight independent measures of molecular weight and solute/solvent interaction parameter I. The mean molecular weight for BSA calculated from the slope is 66400 + 1672 S.D. (2.5%). The standard error of the mean (S.E.M.) is 591 or 0.9%. The molecular weight of bovine serum albumin calculated from the amino acid composition is 66 336, which indicates measurement inaccuracy of only 64 or 0.1%. This error is less than the mass of a single amino acid. The +0.9% experimental precision is, however, our best estimate of accuracy. In 1928 Adair [4] measured the osmotic pressure of sheep hemoglobin. His evaluation using the method of extrapolation to zero concentration resulted in a calculated molecular weight of 69 700 _ 3000. The same data was re-evaluated in 1977 by Ross and Minton [5] using recent thermodynamic relationships and multiple terms in the power expansion on concentration to give an improved measure of molecular weight of 68000. The chemical structure of hemoglobin yields a molecular weight of 64 312. Thus these two molecular weight measures are in error by 5388 (8.4%) and 3688 (5.7%), respectively. The interaction corrected plot of Adair's data [3] is linear and fits all 18 observations with an R 2 of 0.99979, a slope of 27.97 (S.E. of coefficient = 0.10) and

18 16 14 12 10

6

/

h 2 = 0.999

4

/

A s=

66500

2 0 0.00

0.01

0.02

0.03

0.04

1/= ( 1 / ¢ m H = 0 )

Fig. 1. The inverse osmotic pressure (1/~-) vs. inverse concentration (Msv/M s) of bovine serum albumin in 150 mM NaCl salt solution at pH 6.9 and 24°C was plotted. The correlation coefficient2 (R 2) of the best linear fit of the data and the molecular weight (A s) is also shown. The data used to make the plot are given in Table 1.

304 TABLE 3 Literature summary of selected proteins showing /-values and molecular weights Solute /3-Lactoglobulin Hemoglobin Hemoglobin BSA (all) BSA (dilute) Ovalbumin Ovalbumin Ovalbumin

I 1.30 4.35 1.70 3.57 3.72 - 1.45 1.19 0.98

Slope

r a

n b

Calc. mol. wt.

Chem. mol. wt.

% Error

Ref.

52.76 52.69 27.97 28.58 28.24 42.29 42.35 42.34

0.9961 0.9993 0.99989 0.992 0.992 0.9997 0.99994 0.998

20 7 18 45 35 21 7 12

35911 31944 61815 65 352 66 232 44501 44806 45684

36630 32156 c 64 312 66336 66 336 44588 44588 44588

+ 1.96 - 0.66 3.90 - 1.48 - 0.16 - 0.20 0.50 2.45

[6] [7] [4] [8,9] [8] [10] [11] [12]

RMS error

1.87%

a Correlation coefficient. b Number of measurements. c Assuming solutions containing 6 M urea caused disassociation of tetramers into dimers.

an /-value of 1.70 (S.E. Y Est. = 0.52). (Note that the slope indicated here involves units of pressure expressed in cm of mercury. These measurements were made in aqueous solutions of KC1 (0.1 M), N a 2 H P O 4 (0.0613 M) and K H 2 P O 4 (0.00533 M) at a temperature of 0°C. The density of the solvent was p = 1.015.) The molecular weight of hemoglobin calculated from the slope is 61815 + 223 S.E. The error with respect to the chemical molecular weight is - 2 4 9 7 or an absolute error of 3.9%. This analysis shows that error is less than achieved with the two traditional methods on the same data set and data analysis is greatly simplified. An error of 3.9% in comparison with the precision of 0.4% suggests a systematic error in the Adair data set. The precision is comparable to our measurements on BSA, but the accuracy is worse by a factor of four. A possible source of inaccuracy is the Kjeldahl nitrogen determination method used by Adair to measure the hemoglobin concentration. It is unlikely that in 1928 Adair was aware of the porphyrin ring component of hemoglobin. The molecular weight of the protein components of hemoglobin (minus the porphyrin ring) is 61 898, in close agreement with the value calculated from the slope of Adair's data (61815). The porphyrin ring contains no nitrogen and does not contribute to the Kjeldahl measurement, but does contribute to the mass. This may be the source of systematic error. Table 3 shows re-evaluation of osmotic pressure data in eight studies from the literature [4,6-12]. These results include four proteins for which the chemical molecular weight is known. The root mean square (RMS) error is 1.87%. Only for hemoglobin in the study by Burk and Greenberg [7] does molecular weight change from the native value. The calculated molecular weight deviates by a factor of 2. Burk and Greenberg conducted their study in 6 M urea. They concluded that this highly effective denaturing agent splits the hemoglobin tetramer to form two dimers. We concur with this.

305

Precision and significance of I-value The mean of the/-value (expressed in g/g) for BSA in 150 mM sodium chloride is 4.04, and is 4.05 in 150 mM potassium chloride. These values are not significantly different. The overall mean for both solvents (n = 8) is I = 4.05 + 0.20 (4.9%) S.D. The S.E.M. is 0.07 (1.7%). The pH in these experiments was 6.9 + 0.1. The /-value is thus highly precise and reproducible with constant cosolute concentrations and conditions. Adair [4] measured the membrane potential in his experiments to allow calculation of the Donnan contribution to the osmotic pressure [13-16]. He calculated a pressure due to ionic redistributions induced by the protein charge, then subtracted this from the observed pressure to calculate a reduced pressure, Hp, due to the protein alone. A recalculation of I and S using this latter 'protein pressure' was done. The /-value shifted from 1.70 to 1.53, or a change of - 1 0 % . The molecular weight calculated from the slope, on the other hand, only changes from 61814 to 61768, or a change of 0.07%. Two important points are made from these observations. First, the slope and the molecular weight are independent of at least some of the perturbing influences of solvent characteristics. The second is that /-values reflect the influence of unequal ion distributions on opposite sides of the membrane induced by protein charge (Donnan equilibrium) [16]. A wide range of /-values and even one negative value are observed for ovalbumin in Table 3. Changes in /-values reflect changes induced by different solvent mixtures at different pHs. Systematic study of the factors influencing I and the importance in tissue hydration is outside the range of the present study. It is clear, however, that the interaction corrected osmotic pressure method provides the analytic tool for such a study. These observations suggest that changes in osmotic pressure with cosolute concentrations and pH as reported by many investigators are related to changes in the/-value or solute/solvent interaction caused by cosolute ion distributions. The exception is changes that induce aggregation or disruption of native structures, as demonstrated above with hemoglobin. The wide variation in /-values in Table 3 reflects variations due to the range of cosolute conditions used by different investigators. Any parameter influencing surface charge (pH, pK of protein, cosolute salt concentration) will cause I to change.

Conclusions

The solute/solvent interaction corrected equation provides a simpler and more accurate method to measure molecular weight than previous osmotic methods. The isolation of solute/solvent interactions in the nonideality/-parameter should be useful in the study of protein hydration. With the carefully controlled measurement protocol described here for BSA, absolute error using a single experiment to measure the molecular weight of a globular protein is on the order of 2.5%. This

306 reduces to 0.9% with eight repetitions. M e a s u r e m e n t time for the protocol is 2 - 4 h. D a t a at lower c o n c e n t r a t i o n s are most i m p o r t a n t in the i n t e r a c t i o n corrected m e t h o d as they are in the classical methods. A l t h o u g h all data within the true solution r a n g e are useable, it is i m p o r t a n t that osmotic pressures for lower c o n c e n t r a t i o n s be accurate with at least three significant digits. T h e inverse plotting of data c o m p a r e d to t r a d i t i o n a l m e t h o d s amplifies the i n f l u e n c e of pressures at low c o n c e n t r a t i o n s . This also m e a n s , however, that distortions due to direct s o l u t e / s o l u t e i n t e r a c t i o n s as is visible at the highest c o n c e n t r a t i o n in A d a i r ' s data [3] do n o t greatly p e r t u r b calculations of S, I a n d A S. T h e data suggest a g e n e r a l f o r m u l a for B S A that may be of use to some investigators. T h e osmotic pressure for native B S A in 150 m M salt, p H 6.9, M s v / M ~ > I a n d 24°C is calculated with the empirical relation H(cm H20) = S / ( Ms,, / M ~ - I) = 381/( Ms,c / M ~ - 4.05)

(7)

Acknowledgements W e wish to give special t h a n k s to Jori Muckley for help in g a t h e r i n g a n d collecting data from the literature. W e would also like to t h a n k J o a n n e M u r r a y a n d Lucy R e i n a for m a n u s c r i p t p r e p a r a t i o n . This project was s u p p o r t e d in part by a g r a n t from G E Medical Systems, Milwaukee, WI.

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307 9 Scatchard, G., Batchelder, A.C., Brown, A. and Zosa, M. (1946) Preparation and properties of serum and plasma proteins. VII. Osmotic equilibria is concentrated solutions of serum albumin. J. Am. Chem. Soc. 68, 2610-2612. 10 Bull, H.B. (1941) Osmotic pressure of egg albumin solutions. J. Biol. Chem. 137, 143-151. 11 Guntelberg, A.V. and Linderstrom, K. (1949) Osmotic pressure of plakalbumin and ovalbumin solutions. Compt.-rend Lab. Carlsberg, Ser. Chim. 27, 1-25. 12 Marrack, J. and Hewitt, L.F. (1929) The osmotic pressure of crystalline egg albumin. Biochem. J. 23, 1079-1089. 13 Bull, T.E., Andrasko, J., Chiancone, E. and Forsen, S. (1973) Pulsed nuclear magnetic resonance studies on 23Na, 7Li and 35C1 binding to human oxy- and carbon monoxyhaemoglobin. J. Mol. Biol. Res. 73, 251-259. 14 Shinar, H. and Navon, G. (1984) NMR relaxation studies of intracellular Na + in red blood cells. Biophys. Chem. 20, 275-283. 15 Pettegrew, J.W., Woessner, D.E., Minshew, N.J. and Glonek, T. (1984) Sodium-23 NMR analysis of human whole blood erythrocytes and plasma. Chemical shift, spin relaxation, and intracellular sodium concentration studies. J. Magn. Res. 57, 185-196. 16 Donnan, F.G. (1911) Z. Elektrochem. 17, 572-581. As cited in: Ling, G.N. (1984) In Search of the Physical Basis of Life, Plenum Press, New York.