ANALYTICAL

BIOCHEMISTRY

82, 109-J 14 (1977)

Determination of the Donnan Effect in Equilibrium Dialysis and a Simple Method for its Correction PETER

SUTER

Department of Microbiology.

AND

JURG

P.

ROSENBUSCH’

Biozentrum, University of Basel, Klingelbergstrasse CH4056 Basel, Switzerland

70,

Received July 29, 1976: accepted May 23. 1977 Radioactive cesium ions have been used as indicators for the unequal distribution of electrolytes in two-compartment systems which contain nondiffusible macroions in one of the compartments. This method allows the precise determination of the Donnan ratio under conditions in which binding studies of small molecules to proteins are carried out. The corrections, which can be performed easily, are required for ligands whose affinities to proteins are low, particularly if electrostatic protein-ligand interactions preclude the use of high concentrations of diffusible ions. This is illustrated by the comparison of the Donnan equilibrium on the binding of succinate and of CTP to aspartate transcarbamylase from E. co/i.

The unequal distribution of electrolytes in two-compartment systems, arising from the presence of nondiffusible charged molecules such as proteins in one of the compartments, is textbook knowledge (1). It is well known that the Donnan equilibrium may affect the determination of ligand binding in equilibrium dialysis experiments and that this undesirable effect may in principle be prevented by increasing the concentration of diffusible electrolytes, or by choosing a pH close to the isoelectric point of the protein. These simple methods are not always applicable, however, particularly if the association of a ligand with a protein relies primarily on electrostatic interactions and if the protein precipitates near its isoelectric point. In such instances, equilibrium dialysis experiments could be performed at low concentrations of small ions, if a technique were available which allowed the evaluation of the Donnan effect. However, the determination by conventional techniques of protein charge, necessary for an indirect estimation of the resulting redistribution of electrolytes, is neither convenient nor accurate (2). We have therefore developed a method to quantitate the Donnan effect in equilibrium dialysis experiments directly, thus allowing the appropriate corrections of the results obtained. Using published data on the binding of two ligands to aspartate transcarbamylase (3,4), we illustrate that the redistribution of ’ To whom correspondence

should be addressed. 109

Copyright 0 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.

ISSN ooO3-2697

110 electrolytes ligands .

SUTER AND ROSENBUSCH

severely

affects the results obtained

EXPERIMENTAL

with weakly

binding

PROCEDURES

Aspartate transcarbamylase from E. coli was prepared according to the standard procedure (5) and checked for homogeneity and activity (6). Equilibrium dialysis experiments were performed at 22°C in multicavity cells (volume of 1 ml per half-cell; Chemical Rubber Co.) on a thermally insulated shaker, as described in detail elsewhere (7). In order to obtain complete recovery of radioactivity after dialysis experiments (98-lOl%), rubber washers were fitted between the two half-cells. The dialysis half-time of Cs+ ions was determined to be 30 min at 22°C. Determination

of the Donnan

Effect

Five hundred microliters each of buffer (40 mM potassium phosphate, pH 7.0, 2 mM 2-mercaptoethanol, and 0.2 mM EDTA, if not indicated otherwise) and of a protein solution (containing aspartate transcarbamylase in the same buffer at the concentrations indicated) were introduced into the two half-cells separated by a dialysis membrane (20/32, Union Carbide). CsCl was added to a final concentration,2 after equilibration, of 1 mM. Its specific activity was 15,000 cpm/pmol (13’Cs+ was obtained carrier-free as the chloride salt from the Eidg. Institut fur Reak; torforschung and introduced into the buffer compartment of the dialysis cell). After a 4-hr dialysis, 2.50 ~1 were withdrawn from both sides and counted either by liquid scintillation spectrometry in a Packard Tri-Car-b counter (counting error OS- 1% with counting times of 5- 10 min) or in a y-spectrometer. The ratio of the radioactivities, measured in the buffer compartment and in the protein-containing half-cell, directly yields the Donnan ratio. All experimental points obtained were used for the calculation of the means and their standard errors, as indicated in the legend to Fig. 1. Possible binding of cesium ions to the protein was assayed by a filter binding technique. Aliquots (500 ~1) of buffer with or without protein (500 pg) and containing cesium ions at the concentration and specific activity given above were filtered through nitrocellulose filter discs (25 mm in diameter; pore size, 0.05 pm; Sartorius 11310; pretreated for 10 min at 100°C in water). The filters were mounted on separate holders on two vacuum flasks which were connected in series to an aspirator. The pressure was 350 mm Hg. We found negligible binding (less than I mol of Cs+/mol (300,000 g) of aspartate transcarbamylase). This result 2 Nonradioactive CsCl was added because carrier-free cesium led to nonquantitative recoveries, due probably to adsorption to the walls of the Lucite cell and to the dialysis membrane.

DONNAN

c z c

EFFECT:

111

ASSAY AND CORRECTION

0.90 -

Lz 0.85 e

/ I

I

10

Protein

I 20

concentration

I 30

(mg/ml)

FIG. 1. Determination of the Donnan ratio as a function of protein concentration and the concentration of small buffer ions. VJs+ ions (1 mM; specific activity, 1.5 x 101 cpm/ pmol) were added to the compartment containing buffer before dialysis to equilibrium. Aspartate transcarbamylase was present at the concentrations indicated. The concentrations of the buffers (potassium phosphate, pH 7.0, containing 2 mM 2-mercaptoethanol and 0.2 mM EDTA) were: 40 mM (open symbols, the various shapes indicating different experiments); 40 mM, containing 0.1 M KC1 (closed squares); and 10 mM (closed triangles). The buffer strength of 40 mM phosphate, with no neutral salts added, corresponds to that used in a previous succinate binding study (3); the arrow “a” indicates the protein concentration used in those experiments. The binding of CTP to aspartate transcarbamylase (4) was determined at a low concentration of diffusible ions (IO mM phosphate), with the protein concentration indicated by arrow “b.” The bars shown indicate standard errors of the means. The points have been slightly spread along the x axis in the figure, so that they can be better distinguished. The true protein concentrations are given by the positions of the error bars. The lines represent the best fits to all experimental points obtained. They were computed by the least square method, using a standard program on a Hewlett-Packard 9810A desk computer. Note the expanded scale on the ordinate.

was confirmed by examining cesium binding over a concentration range of 2.5 to 1000 PM by a binding assay described previously (8). No binding was detected in these experiments, either. Procedure

for the Correction

of Experimental

Ligand Binding

Data

In equilibrium dialysis experiments, performed to determine ligandprotein interactions, the Donnan effect may be measured in tandem. For each experimental point, equilibrium dialysis is performed in duplicate. In one case, the radioactive tracer is the ligand, in the other, 137C~+. The result from the former assay yields the distribution of Iigand in the

112

SUTER

AND

ROSENBUSCH

TABLE

1

CALCULATIONS OF THE DONNAN EFFECT ON THE BINDING OF Two DIFFERENT LIGANDS TO ASPARTATE TRANSCARBAMYLASE WITH DISSOCIATION CONSTANTS DIFFERING BY A FACTOR OF 550” ParameteP

Llgands

(a) Ligand

Succinate

(b) Dissociation

constant

(cl Concentration

0.55 mhl

of phosphate

ions

Comments CTPe 1 PM

From Refs. 3 and 4

40 rnM

IO rnM

From Refs. 3 and 4

0.85

Determined from the distribution (cf. Fig. I).

(d) Donnan

ratio

0.92

(e) Ligand

charge

2.0

3.84

At pH 7.0; the charge of CTP is from Ref. IO.

0.85

0.55

From lines (d) and (e) accordmg

(0

Effective

Donnan

Ratio

(g) Enzyme

22.5 mglml (0.075 mM)

(h) Concentratmn

0.45 mhl

0.4 rnM

(0 robs.

2.4 sites

2.2 sites

W ~a.mmd

4.4 SlkS

(k) [L] bound,

(I)

of binding

sites

20 mg/ml (0.067 rnM)

predicted

0.33 rnM

[L]b free

(rn) [L]” free (II) [L]” total (0) [L] bound.

(9) [L] bound, (r)

From themass From Scatchard

plots in Refs. 3 and 4.

Chosen to obtain agreement between rohr expamentally (3) and the robn calculated in this table (cf. line p). I50 /kM

Calculated from lines (g) and (j) for succinate, from lines (g) and (i) for CTP.

2.3 PM

From Refs. 3 and 4.

0.85 rnM

1.3 pLM

Calculated

I.18 rnM

151 p&t

Sum of lines (k) and (m).

149 pLM

Difference

corrected

0.33 rnM

Underestimatedue

to Donnan

etTect

2.2 sites

and

from lines (I) and (f).

0. I8 rnM

- 45%

to Eq. [I].

of50,000daltonsperprotomer(6].

1.0 mhi

2.4 sites

ions

From Refs. 3 and 4.

ohs.

(P) rep.

of cesium

between

lines (II) and (I).

Ratio of lines (0) and (g) [cf. line (i)].

150 p4

Difference

between

lines (II) and (ml.

cl%*

Difference between lines (k) and (o), expressed as percentage of the correct figure (lines k or q).

n The computations have been performed on published data (Refs. 3 and 4). choosing m each case an experimental point from the Scatchard plot at a concentration of free ligand approximately twice that of the respective dissociation constant. Lines d-f and l-q dlustrate the procedure to correct experimental results step by step. * Abbreviations: [L], concentration of ligand; r, moles of ligand bound per mole of enzyme; b and p (superscnpts). values referring to the buffer or protein containing compartments. respectively: ohs., observed. e There are two classes of CTP sites, one with a K, = I @M, and a second with a K2 = 50 P’M (cf. Ref. 4). * This calculation is in agreement with the experimental observation (4) that the presence of 0. I M KCI does not appreciably affect CTP binding.

two compartments; the latter will give the Donnan ratio for univalent ions. Depending on the charge of the ligand, this ratio is converted to that appropriate for the ligand tested according to Eq. [l] (cf. Ref. 1). (m+b/m+p)il/Zi = (~~.-~lm-~)~“~j = constant, HI where m indicates the electrolyte

concentrations;

the superscripts b and p

DONNAN

EFFECT:

ASSAY

AND

CORRECTION

113

refer to the buffer and protein compartment, respectively; i represents a particular species of cations and j that of anions. Z is the charge of the respective electrolyte at the pH of the experiment. In this calculation, the activity coefficients may be assumed to be the same on both sides of the semipermeable membrane, and molar concentrations are taken to be equivalent to the molalities of the solution, a reasonable assumption at low ligand concentrations (1). To obtain the concentration of free ligand in the protein compartment, the concentration of ligand in the buffer compartment is multiplied by the appropriate Donnan ratio, calculated according to Eq. [l] from the observed ratio of cesium ions. The concentration of protein-bound ligand can be calculated as the difference between the total ligand concentration in the protein-containing half-cell, and the corrected concentration of free ligand in the same compartment. These calculations are demonstrated step by step in Table 1 (lines d-f and l-q). RESULTS

AND DISCUSSION

We have quantitated the redistribution of electrolytes occurring in a two-compartment system with increasing concentrations of aspartate transcarbamylase at different concentrations of diffusible ions (Fig. 1). From the basic equation describing the Donnan equilibrium (l), it is evident that the Donnan ratio depends on the protein concentration. Furthermore, the slopes should depend on the concentration of small electrolytes, and the intercepts of the lines should have a value of 1.0. The results, presented in Fig. 1, yield a value of 1.001 5 0.0104 (SD) for the intercept of the lines whose slopes clearly depend on the concentrations of diffusible ions. Thus, the addition of 0.1 M KC1 essentially abolishes the unequal distribution of diffusible ions, as anticipated (1). Consider now the binding of an unreactive substrate analog, succinate, to this enzyme which has been well characterized with respect to its structure and its binding properties (for a review, cf. Ref. 9). The interaction of succinate with the protein is due mainly to electrostatic forces (9), and its affinity to the enzyme is low (34). Since the addition of neutral salts further interferes with the binding of this ligand (our unpublished observation), a high concentration of diffusible ions cannot be used in equilibrium dialysis experiments. Therefore, we have now measured the Donnan ratio under the conditions used in earlier investigations of the association of this ligand with the enzyme, which yielded a value of four sites for succinate in aspartate transcarbamylase (3). If the redistribution of electrolytes is taken into account by correcting the published data with the appropriate Donnan ratio (cf. arrow “a” in Fig. 1, and Table I), a value of at least six sites is obtained. This result is in agreement with that of a recent investigation in which a filter binding

114

SUTER AND ROSENBUSCH

assay was used to study the association of succinate to this protein. This study yielded a value of 6.1 + 0.4 sites (8). We therefore conclude that the earlier result of four sites was, at least in part, an underestimation due to the effect of the Donnan equilibrium, as we have suggested previously (6). From Table 1, which shows the corrections step by step,- it can be seen that at an intermediate concentration of free ligand (approximately twice that of the dissociation constant of succinate from the complex), the observed value of r (moles of ligand bound per mole of enzyme) was too low by 45%. ,If the corresponding correction is performed for the association of CTP, a tightly binding effector of aspartate transcarbamylase, the correction is negligible (< 1%; cf. Table 1). This is so despite the high charge of CTP at pH 7.0 (10) and despite the low concentration of small ions employed in these experiments, since for tightly binding ligands, the concentration of free verws bound ligand is small. In contradistinction, the concentration of free ligand is very appreciable if its association with the protein is weak (cf. Table I), and the redistribution of electrolytes has therefore to be taken into account. The procedure described in this report thus provides a simple method to perform the necessary corrections of results obtained in a two-compartment system. ACKNOWLEDGMENT This investigation was supported by Grant No. 3.0920.73 from the Swiss National Science Foundation. The work forms part of a dissertation of P.S., submitted to the University of Base1 in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Phil. II).

REFERENCES 1. Tanford, C. (1961) Physical Chemistry of Macromolecules, pp. 225-227, Wiley, New York. 2. Tanford, C. (1961) Physical Chemistry of Macromolecules, pp. 425-428, Wiley, New York. 3. Changeux, J. -P., Gerhart, J. C., and Schachmann, H. K. (1968) Biochemistry I, 531-538. 4. Winlund, C. C., and Chamberlin, M. J. (1970) Biockem. Biqkys. Res. Commun. 40, 43-49. 5. Gerhart, J. C., and Holoubek, H. (1967) J. Bid. Ckem. 242,2886-2892. 6. Rosenbusch, J. P., and Weber, K. (1971) J. Biol. Chem. 246, 1644- 1657. 7. Rosenbusch, J. P., and Griffin, J. H. (1973) J. Bid. Ckem. 248,5063-5066. 8. Suter, P., and Rosenbusch, J. P., (1976) J. Bid. Ckem. 251, 5986-5991. 9. Jacobson, G. R., and Stark, G. R. (1973) in The Enzymes (Bayer, P. D., ed.), 3rd ed., Vol. 9, pp. 225-308, Academic Press, New York. 10. Alberty, R. A., Smith, R. M., and Bock, R. M. (1951) J. Biol. Ckem. 193,425-434.