The effect of radioactive contaminants on the estimation of binding parameters by Scatchard analysis

130

Biochimica et Biophysica Acta, 533 (1978) 130--139

© Elsevier/North-Holland Biomedical Press

BBA 37867 THE EFFECT OF RADIOACTIVE CONTAMINANTS ON THE ESTIMATION OF BINDING PARAMETERS BY SCATCHARD ANALYSIS

ERWIN M. REIMANN and MELVYN S. SOLOFF Departments of Biochemistry and Surgery, Medical College of Ohio, C.S. 10008, Toledo, Ohio 43699 (U.S.A.)

(Received August 26th, 1977)

Summary 1. When protein-ligand interactions are measured with a radioactive ligand, the presence of a radioactive contaminant that is not bound can lead to errors in the determination of the concentration of bound and u n b o u n d ligand, and consequently to errors in estimation of the dissociation constant (Kd). The extent of errors caused by a non-binding contaminant was determined by computer simulation for five types of protein-ligand interaction: first order dissociation, two classes of binding sites with different dissociation constants, displacement, negative cooperativity and positive cooperativity. For each type of reaction several values of Kd and several concentrations of binding sites were assumed. 2. The presence of a contaminant results in Scatchard plots which are convex upward instead of linear for the first order dissociation reaction. Scatchard plots normally are concave upward with three of the reactions studied: two classes of binding sites, displacement reactions and negative cooperativity. The contaminant causes a reduction in the concavity and in certain instances the plots may appear linear; with larger amounts of a contaminant they may be convex upward. The shape of the Scatchard plots for positive cooperativity is convex upward in either the presence or absence of a contaminant. Except for the displacement reaction the distortion of the shape of the Scatchard plots increases as the concentration of binding sites increases. 3. A contaminant, therefore, can cause distortions of the Scatchard plots which can lead to: (1) misinterpretations of the type of protein-ligand interaction, (2) overestimation of the dissociation constants, and (3) errors in calculation of the concentration of binding sites. In some instances as little as 1% contaminant may have a profound effect on the apparent affinity and number of binding sites.

131 Introduction The use of radiolabeled ligands to determine the thermodynamic parameters of protein-ligand binding reactions (notably hormone-receptor interactions) requires an exact knowledge of the specific activity and purity of the ligand. Labeling procedures, such as radioiodination, may produce a mixture of radioactive materials that cannot be distinguished readily from each other. Even when labeled ligands are prepared free of radioactive contaminants, the ligands may- undergo radiochemical decomposition upon storage. In either instance the contaminants might not bind to the protein, resulting in errors in the estimation of dissociation constants and concentrations of binding sites. In this report we describe the extent of such errors on several types of binding reactions: First order dissociation. This is the simplest case, where dissociation of the ligand • protein complex (L • P) to ligand (L) and protein (P) is a first order process. L . P ~ L + P First order dissociation with a mixture o f 2 classes o f binding sites. The sites differ in dissociation constant, where P1 and P2 are proteins with different affinities for L. L'PI~L+P1 L "P2 ~ L + P 2 Displacement. This reaction, which appears to describe cyclic AMP-dependent protein kinases [1,2], is referred to as a displacement reaction because the catalytic subunit (C) displaces the ligand. We assume that the total concentration of regulatory (R) and catalytic subunits are equal.

L'R+C~L+R.C

(1)

Cooperativity. Cooperativity is seen where the binding of a ligand molecule to one site increases (positive cooperativity) or decreases (negative cooperativity) the binding of ligand molecules to other sites on the same protein; n = the total number of ligand molecules bound.

Ln.P~nL+P Methods

The following equations were used to relate b o u n d and u n b o u n d ligand for the above reactions, where B is the concentration of b o u n d ligand, U is the concentration of u n b o u n d ligand, K, K1 and K2 are equilibrium constants for the dissociation reactions and R, R1 and R2 refer to the total concentration of binding sites. The Hill equation [3] was used to relate b o u n d and u n b o u n d ligand in cooperative reactions. The Hill coefficient (n) is < 1 for negative cooperativity and > 1 for positive cooperativity. First order dissociation B = R U / ( K + U)

(2)

132 First order dissociation w i t h 2 classes o f binding sites B = R I U / ( K ~ + U) + R2U/(K2 + U)

(3)

Displacement F r o m Eqn. 1, it follows t h a t g = L(R. C)/(L. R) C

(4)

T h e c o n c e n t r a t i o n of R • C = R -- L • R. If the t o t a l c o n c e n t r a t i o n of R and C are equal t h e n the c o n c e n t r a t i o n o f L • R and C will be equal. Substituting L • R for C and (R - - L • R ) f o r R • C into Eq. 4 gives: K = L(R --L" R)/(L" R)(L" R)

Substituting U for L and B for L • R gives: K = U(R -- B ) / B ~

Rearranging gives: K B 2+ U B - - UR = O

This quadratic e q u a t i o n has the following positive solution for B: B = (--U + x/U: + 4KUR)/(2K)

(5)

Cooperativity B = ( R U " ) / ( K + V")

(6)

Eqn. 2 can be c o n v e r t e d t o the f o r m : B/U = R/K--B/K

T h e Scatchard plot consists o f a plot o f B / U o n the y.axis vs. B on the x-axis [4]. F o r first o r d e r dissociation reactions the p l o t is linear with a y - i n t e r c e p t equal to R / K , a x - i n t e r c e p t equal to R, and a slope equal to --1/K. Scatchard plots f o r the o t h e r r e a c t i o n s result in non-linear plots [ 2 , 5 ] . Calculation o f the c o n c e n t r a t i o n o f b o u n d ligand n o r m a l l y is based on the a m o u n t o f r a d i o a c t i v i t y b o u n d and on the specific activity o f the ligand. A c o n t a m i n a n t can i n t r o d u c e errors into the e s t i m a t i o n o f the specific activity o f the ligand if it is calculated f r o m t h e t o t a l a m o u n t o f r a d i o a c t i v i t y (including radioactive c o n t a m i n a n t ) . T h e a m o u n t o f radioactive ligand will be in error whereas the t o t a l ligand c o n c e n t r a t i o n will be c o r r e c t if a s u f f i c i e n t a m o u n t of carrier ligand is a d d e d or if the c o n c e n t r a t i o n o f the ligand is m e a s u r e d b y a m e t h o d which distinguishes b e t w e e n the ligand and the c o n t a m i n a n t . In these instances the c o n t a m i n a n t results in an o v e r e s t i m a t i o n o f t h e specific activity and, accordingly, u n d e r e s t i m a t i o n o f the c o n c e n t r a t i o n o f b o u n d ligand. If B = b o u n d ligand and a = the f r a c t i o n o f the t o t a l radioactivity cont r i b u t e d b y the non-binding c o n t a m i n a n t , t h e n it can be s h o w n t h a t the decrease in B is equal t o a B and t h e a p p a r e n t b o u n d ligand (Bapp) is d e f i n e d as: Sap p =

B -- ~B

(7)

133 The decrease in B is reflected by an equal increase in U. Therefore the apparent u n b o u n d ligand (Uapp) is defined as: Uapp = U + ~B

(8)

From a large range of values for U we calculated Uapp using Eqn. 8 and B~pp using a combination of Eqn. 7 and Eqns. 2, 3, 5 or 6. The calculations assumed values for the dissociation constant, Kd, and for the concentration of binding sites (see figure legends) within the range of the most hormone-receptor reactions studied to date [6,7]. The values of a were 0, 0.01, 0.03, 0.1 and 0.3. In all of the figures, bound refers to Bap p and unbound refers to Uapp. No data were plotted when unbound ligand was less than 1 pM because this concentration would be below the level of detection in most protein binding assays. The calculations and plots were made with a Wang WCS-2200 computer equipped with a Model 2272 plotter. Results First o r d e r dissociation

In the presence of a contaminant the Scatchard plots are convex upward instead of linear. The slope and linearity become less as a increases (Fig. 1). For any given value of a the changes become more marked with increasing concentration of binding sites for a given Kd (compare Figs. 1A and B) or with decreasing Kd for a given concentration of binding sites (compare Figs. 1A and C). With a moderate a m o u n t of experimental variation the non-linearity of the plots might be undetected, resulting in underestimation of the slope and consequent overestimation of the Kd. The existence of a contaminant can be detected by a comparison of Scatchard plots obtained at concentrations of binding sites significantly above and below the Kd. Investigators can minimize the deviation in the slope and the curvature either by using concentrations of binding sites that are much lower than the Kd or by using concentrations of ligand which result in occupancy of 50% or more of the binding sites. A cont a m i n a n t also results in a reduction of the apparent concentration of binding sites, which is measured at saturating concentrations of ligand, in proportion to ~; e.g. when e = 0.3 the apparent concentration of sites is 30% less than the

C

I

B I I o z

0.05

0.10

•

5

10

0

0.05

0.10

BOUND

Fig. I . Seatchard p l o t s o f first order d i s s o c i a t i o n reactions w i t h 1 class o f binding sites. F o r A , B a n d C, R t = 0 . 1 , 1 0 a n d 0 . 1 n M , respectively; K d ffi 1, 1 a n d 0 . 0 1 , respectively. F r o m b o t t o m t o t o p in each panel, t h e fraction o f c o n t a m i n a n t ((~) is 0 . 3 , 0 . 1 , 0 . 0 3 , 0 . 0 1 a n d 0 .

134 6 r

10

A

C

5

0 o

5

10

o

5

o

10

s

i~

BOUND

Fig. 2. S c a t c h a r d p l o t s o f f i r s t o r d e r d i s s o c i a t i o n r e a c t i o n s w i t h 2 classes o f i n d e p e n d e n t b i n d i n g sites. T h e K d for the high affinity sites is 0 . 2 riM. F o r A, B a n d C, t h e K d f o r t h e l o w a f f i n i t y sites is 2, 2 a n d 20 n M , respectively; the c o n c e n t r a t i o n o f h i g h a f f i n i t y sites is 5, 1, a n d 1 riM, r e s p e c t i v e l y ; a n d t h e c o n c e n t r a t i o n o f l o w a f f i n i t y sites is 5, 9, a n d 9 n M , r e s p e c t i v e l y . F r o m b o t t o m t o t o p in e a c h p a n e l , ~ = 0 . 3 , 0 . 1 , 0 . 0 3 , 0.01 a n d O.

actual concentration of sites. This error is independent of the concentration of binding protein or Kd (Fig. 1). Thus, it is possible to calculate the actual number of binding sites if one knows the value of a.

Mixture o f 2 classes o f independent binding sites Scatchard plots for reactions consisting of two classes of independent binding sites normally are concave upward. The concavity increases as the concentration of low affinity (high Kd) binding sites increases relative to the concentration of high affinity (low Kd) binding sites and as the difference of Kd values between the two classes of sites increases {Fig. 2). The upward concavity of these plots decreases as a increases. The contaminant reduces the slope of the plots, especially at low levels of b o u n d ligand. Consequently, the Kd of both sites may be overestimated and the error in Kd for the high affinity site may be very large. At certain levels of contaminant the curves can appear to be essentially linear, thereby masking the presence of the high affinity binding protein. The portion of the Scatchard plot representing the lower levels of b o u n d ligand sometimes is extrapolated to estimate the number of high affinity binding sites. In such instances the presence of a contaminant would result in the overestimation of the number of high affinity sites and an underestimation of the affinity of these sites for the ligand. The errors in the estimation of the Kd and the concentration of binding sites increase as a increases. ~o

A

1o I

0

1o

C

• 0.5

1.0

. 0

0,5

1.0

0

.

.

. 0.5

1.0

~IOUND

Fig. 3. S c a t c h a r d p l o t s o f d i s p l a c e m e n t r e a c t i o n s . R t = 1 nM. K d = 0 . 3 , 0.1 a n d 0 . 0 3 in A, B a n d C, respec.

tively. F r o m b o t t o m to t o p in e a c h p a n e l , ~ = 0 . 3 , 0 . 1 , 0 . 0 3 , 0 . 0 1 a n d O.

135 2~

A

10

~

B

~5

o ce

0

0

05

1.0

0

5

10

0

5

10

BOUND

Fig. 4. Seatchard plots of the negative cooperativ~ty reaction. K d = 0.2 n M . For A, B and C, R t = 1, 10 and 10 n M , respectively; n = 0.8, 0.8 and 0.5, respectively. F r o m b o t t o m to top in each panel, ~ = 0.3~ 0.1,0.03, 0.01 and 0.

Displacement reaction The Scatchard plots are concave upward like those characterizing the preceding reaction. However, as e increases the plots become less concave upward (Fig. 3), and at high levels of contaminant they are convex upward. When ~ = Kd the plots become linear, thereby suggesting a first order dissociation instead of a displacement reaction.

Negative cooperativity The Scatchard plots are normally concave upward, as seen with 2 classes of binding sites and with displacement reactions [5]. The plots become less con. cave upward, however, as ~ increases and can become convex upward (Fig. 4). At intermediate levels of ~ the Scatchard plots tend to become linear (especially if n = 0.8 in Fig. 4B). The effect of ~ on the shape of the Scatchard plots is more pronounced at higher concentrations of binding sites (compare Figs. 4A and B) and as n decreases (compare Figs. 4B and C). As with the other reactions discussed, the apparent concentration of binding sites decreases in proportion to ~.

Positive cooperativity The Scatchard plots are convex upward in the presence or absence of contaminants [5]. The maximum ratio of bound and u n b o u n d ligand is dramati0.2

\

Ai

B.l

21

2

I

0

0 0

.05

. 10

0

05

1,0

•

5

IZ

eW)UND

F i g . 5. S c a t c h a r d p l o t s o f the p o s i t i v e c o o p e r a t i v i t y s y s t e m . K d = 0 . 2 n M a n d n = 2. F o r A , B a n d C, R t = 0 . 1 , 1 a n d 1 0 n M , r e s p e c t i v e l y . F r o m b o t t o m t o t o p in e a c h p a n e l , ~ = 0 . 3 , 0 . 1 , 0 . 0 3 , 0 . 0 1 a n d 0 .

136 A

B

5

0 0,5

1.0

0

0,5

1.0

•

0

0S

BOUND

1,o

D

~I*

0.2:

OD 0.5

2

05

0 1,o

E1 o.,

0.2

~

~5

1,0

0

0.5

1.o

BOUND

Fig. 6. P l o t s o f

Bapp2/Uap p

vs. B a p p f o r d i s p l a c e m e n t ( A - - C ) a n d c o o p e r a t i v e r e a c t i o n s ( D - - F ) . F o r A, B

a n d C, R t = 1 n M a n d K d = 0 . 3 , 0 . 1 a n d 0 . 0 3 , r e s p e c t i v e l y . F o r D, E a n d F, K d = 1, R t = 1 n M , a n d the

Hill c o e f f i c i e n t = 0 . 5 , 1 a n d 2, r e s p e c t i v e l y . F r o m b o t t o m t o t o p in e a c h p a n e l , ~ = 0 . 3 , 0 . 1 , 0 . 0 3 , 0 . 0 1 a n d O.

cally reduced in the presence of a contaminant and there is a decrease in the apparent concentration of binding sites (Fig. 5). As with the other reactions, the decrease in b o u n d / u n b o u n d ligand due to a contaminant is greater with higher concentrations of binding sites. With higher concentrations of sites, a contaminant may cause the slope of the Scatchard plots to be zero over a broad range of bound ligand (Fig. 5C). This plot erroneously would indicate the absence of high affinity sites.

Plots of B2/U vs. B In the absence of a contaminant, plots of (Bapp)2/Uapp vs. Bapp are linear for displacement reactions [2]. Figs. 6A--C show the data of Fig. 3 plotted in this manner. As a result of the slightest a m o u n t of contaminant, the y intercept of these plots is reduced to zero and the curves are markedly convex upward. The concentration of binding sites has no effect on the shape of the curves for this reaction, in contrast to the results seen with first order dissociation. Although we do not present the plots here, the lack of effect of the concentration of sites can be illustrated by superimposing plots that are normalized by dividing both the x and y values by the concentration of total receptor sites. This approach can be used to verify experimentally the existence of a displacement reaction because the plots obtained with several concentrations of binding sites should be superimposable even in the presence of contaminant. As is observed with the first order dissociation reaction, the contaminant

137 has several effects: the Kd appears to increase when a increases; the error in slope is minimal when nearly saturating levels of ligand are present; and the decrease in apparent binding sites is directly proportional to a. The deviation from linearity of the plots of •/U vs. B for the displacement reaction increases as the Kd decreases (Figs. 6A--C). Depending on the Kd the plots obtained with the contaminant can mimic those seen either with no cooperativity (compare Figs. 6B and E), with negative cooperativity (compare Figs. 6A and D) or with positive cooperativity (compare Figs. 6C and F). Discussion If a preparation of a radioactive ligand contains a non-binding radioactive contaminant, the specific activity of the ligand and the concentration of the MODEL

TYPE OF PLOT

1 CLASS SITE

SCATCHARD

2 CLASSES OF SITES

SCATCHARD

DISPLACEMENT

~ = 0

SCATCHARD

B?U v s B

NEGATIVE COOPERATIVITY

SCATCHARD

POSITIVE COOPERATIVITY

SCATCHARD

Fig. 7. S u m m a r y o f t h e e f f e c t s o f c o n t a m i n a n t s o n binding plots.

INTERMEDIATE c~

HIGH r~

138 unbound ligand will be overestimated in binding assays. The effects of such errors on Scatchard plots for several different kinds of protein-ligand interactions are summarized in Fig. 7. In general, the contaminants cause the plots to appear more convex upward. If the curves are initially concave upward they may appear linear or convex upward; if initially linear the curves may appear convex upward. In certain instances as little as 1% contaminant may have a profound effect on the shape of the plots (Fig. 2A, 4B, 6A--C). Under some conditions the presence of a contaminant may result in an incorrect interpretation of the mechanism of interaction between protein and ligand. Thus, first order dissociation reactions may appear to demonstrate positive cooperativity as a result of a contaminant. First order dissociation reactions involving two classes of binding sites, displacement reactions and negatively cooperative reactions erroneously may give linear Scatchard plots in the presence of a contaminant. The linear plots would then be misinterpreted to indicate a simple first order dissociation reaction. As a general rule, the shape of the plot is most accurate when the binding sites are near saturation. Unfortunately, experimental error is often large in this region of the plot because the ratio of bound to total radioactivity is lowest. Even when the curvature of the Scatchard plot is affected minimally, the presence of a contaminant results in an overestimation of the Kd, Except for the displacement reaction this effect of the contaminant increases as the concentration of binding protein increases. To minimize such errors, one should conduct the binding studies at the lowest practical concentration of binding protein. However, the concentration of binding sites would still be underestimated. Distortions of binding curves comparable to those resulting from contaminants also occur when the ligand is inactivated during the incubation with a binding protein [8,9] or when a fraction of the bound radioactivity is lost during separation of bound and u n b o u n d ligand [10]. If the ligand is metabolized there is a reduction in binding with increasing incubation times, especially with low concentrations of ligand. However, a fixed concentration of preexisting contaminant does not alter the binding curves with time once a steady state has been achieved. By examining binding at different times one could, therefore, establish whether the contaminant was present initially or if was produced during the incubation. Errors in specific activity do not occur when the contaminant is produced by inactivation of the ligand during the course of the binding assay because the concentrations of labeled and unlabeled ligand decrease in parallel. Likewise, there is no error in specific activity if a portion of the bound radioactivity is lost during the separation step. In contrast, as shown here, the specific activity is overestimated when ligand preparations contain radioactive contaminants. A number of investigators have suggested that spare receptors could explain the observation that the apparent Kd measured in a binding reaction sometimes exceeds a drug or hormone concentration giving a half-maximal response. Because a contaminant can cause a gross overestimation of the K d in binding studies, the existence of spare receptors may be an incorrect conclusion when based on binding values obtained with contaminanted ligands. The error may be particularly great with radioiodinated hormones, which often are damaged in

139 the process of labeling. Our results point o u t some of the pitfalls in proposing reaction mechanisms and estimating binding parameters when preparations of a radioactive ligand contain radioactive contaminants. Unfortunately, investigators cannot easily correct for these errors. They must instead either scrupulously avoid the use of impure materials or else temper their interpretations of the data in light of the possibility of serious errors resulting from the presence of a radioactive contaminant. Acknowledgments This work was supported in part by grants AM 15611, AM 19231, HD 8406 and contract N01-CG-63983 from the National Institutes of Health. We thank Cindy Licata for the typescript. References 1 Reiman, E.M., Brostrom, C.O., Corbin, J.D., King, C.A. and Krebs, E.G. (1971) Biochern. Biophys. Res. Commun. 4 2 , 1 8 7 - - 1 9 4 2 Swillens, S., vanCauter, E., and D u m o n t , J.E. (1974) Biochim. Biophys. Acta 364, 250--259 3 Hill, A.V. (1910) J. Physiol. 40, iv--vii 4 Scatchard, G. (1949) Ann. N.Y. Acad. Sci. 5 1 , 6 6 0 - - 6 7 2 5 Schwarz, G. (1976) Biophys. Struct. Mechanism 2, 1--12 6 Cuatrecasas, P. (1974) Ann. Rev. Biochem. 4 3 , 1 6 9 - - 2 1 4 7 Birnbaurner, L., Pohl, S.L., and Kaumann, A.J. (1974) in Adv. Cyclic Nueleotide Res. (Greengard, P. and Robison, G.A., eds.), Vol. 4, pp. 239--281, Raven Press, New York 8 Lee, C.Y. and Ryan, R.J. (1973) Biochemistry 12, 4609 --4615 9 Desbuquois, B., Krug, F., and Cuatrecasas, P. (1974) Biochirn. Biophys. Acta 343, 101--120 10 Swfllens, S. and Dumont, J.E. (1975) Biochem. J. 149, 779--782