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A sensitive method for determining preferential binding of substances to enzymes and biological membranes
4NALYTICAL
47, 337-347
BIOCHEMISTRY
A Sensitive
Method
Substances
(197%
for Determining
to Enzymes
and
JESPER Institute
of Medical
Biochemistry,
Biological
Binding
of
Membranes
V. M@LLER
University Received
Preferential
of Aarhus,
May
8000
Aarhus
C, Denmark
19, 1971
It is well known that many enzymic reactions and transport processes across biological membranes show a distinct substrate specificity. In order to gain insight into the nature of these processes it is desirable to have sensitive methods for the measurement of t.he binding of substrates to these systems. Since modern scintillation apparatuses are capable of registering radioactive disintegrations with a high degree of accuracy, it should be possible in a particular sample to measure the preferential binding of a radioactive substrate as compared to that of a related, but nonreacting substance labeled with a different isotope. In this way, errors in the determination of binding, which are due to pipetting errors or uncertainties in the estimation of distribution volume of free substrate, are eliminated. On the ot.her hand, experience shows that a quite considerable variation in the results may occur as a consequence of different degrees of quenching of the samples in the counting vials. In the present paper a systematic study of the factors that affect the channel ratio as measured by liquid scintillat.ion counting has been carried out,. It has been found that a change in the channel ratio of about 0.2% can be detect.ed when proper corrections for quenching have been applied. Finally, the applicability of the method is demonstrated by an esamination of the stereospecific binding of D-glucose to hexokinase. METHODS
Counting
Procedure
D- (3H,) -Glucose (800 mCi/mmole) , D- (““(2) -U-glucose (300 mCi/ mmole), and ~-(~~C~)-glucose (3 mCi/mmole) were obtained from The Radiochemical Centre, Amersham, and used as the sources of radioactivity throughout the experiments reported in this paper. Samples for count-
337 @ 1972 by
Academic
Press,
Inc.
338
.JESPER
I’.
MdLLER
ing were prepared by mixing 0.2 ml of a water solution, containing D- (3H) -glucose (approximately 5 pCi/ml) and D-(W) -glucose (approximately 1 &i/ml) with 10 ml of the scintillator fluid described by Bray (1). The samples were counted in a Packard liquid scintillation apparatus (model 3320) at- the following settings: Channel I, gain 45% and voltage discrimination 5-40V; Channel II, gain 25% and voltage discrimination 40-1OOV. In cases in which use was made of Channel III, the following settings were employed: gain 25% and voltage discrimination 7(rlOOV. The high-voltage knob of the apparatus was in a position so as t.o give a maximal number of counts by the factory-supplied tritium standard at 50% gain and 5-1OOV discrimination. Addit,ion of internal standard (0.1 ml of (3H)-toluene or (I%)-toluene, Packard) indicated that the efficiency of Channel I for tritium was 13%. The count of tritium in Channel II was about. 0.03% that of Channel I. The efficiency of Channel II for (“C) was 32%, and the transgression of (‘“C) counts in Channel I corresponded to about 48% of the counts in Channel II. Binding
Experiments
The binding of n-glucose to hexokinase (ATP: hexose 6-phosphotransferase, EC 2.7.1.1) has been measured by equilibrium dialysis. Yeast hexokinase (Boehringer-Mannheim, Germany) was supplied as a suspension of protein crystals (10 mg/ml) in 3.2 M ammonium sulfate. Prior to the binding experiments ammonium sulfate was removed by dialyzing the enzyme suspension for 3648 hr against 2 liters of 0.025 M phosphate buffer (pH 7.0), which was changed once. Visking dialysis tubing, having a circumference of 2 cm, was made pliable by treatment wit,h boiling water for 15 min, and water was removed from the casing as completely as possible before use. Solutions (0.75 ml) containing hexokinase (0.7 mg protein/ml) and different concentrations of n-glucose (O-O.5 mM), dissolved in the ph0sphat.e buffer mentioned above, were transferred t.o the inside of t,he bags. A small volume (0.05 ml) of either a radioactive mixture of u-(3H)-glucose (approximately 2 pCi/ml) and L-(I~C) glucose (0.25-0.3 &$‘ml) or D-(W)-glucose (0.25-0.3 #&‘ml) was mixed thoroughly with the contents of the bags. The bags were carefully knotted and submerged in 3 ml of a solution with a similar composition as that inside the bags, except that. the protein had been omitted. The test tubes were then shaken for 12-18 hr at 4”C, and at the end of the shaking period 50 ~1 of 50% (w/v) trichloroacetic acid was added to 500 ~1 of the solutions outside and inside the bags, and the samples were centrifuged for 10 min at 1OOOg.The radioactive content of the supernatants was determined as described in the previous section.
BINDING
TO
EKZYMES
AND
BIOLOGICAL
339
MEMBRANES
RESULTS
Counting
of Aqueous Solutions
The channel ratio of replicate samples, prepared by adding 0.2 ml of mixtures of tritiated and (“C)-labeled *ugars to 10 ml of the scintillator fluid, was examined on a number of occasions, and the results of a representative experiment. are given in Table 1. Each vial was counted 8 t.imes with the liquid scintillation apparatus preset. to give 900,000 counts. The average number of counts per minute in Channel I is given by the second column of Table 1, and the third column shows the mean values for the ratio of the counts registcrctl in Channel I and Channel II + the standard deviation between the results obtained in the individual countings. It is seen that the S.D. average,1 s: kO.006, which does not differ much from the value expected for statistical fluctuations in the emission of radioactive particles (kO.005). 01~ the other hand, there is a quite considerable difference between the average values of the individual vials. ChI/ChII t.hus varies from 2.525 to 2.567 with an S.D. of kO.015, and this difference cannot. be accounted for by statistical fluctuations, since the S.E.M. of ChI/ChII of the individual vials is kO.002. It seems probable that the different channel ratios observed between individual samples result from different quenching characteristics of t,he vials, which might occur for the following reasons: (1) errors in the dispensing of radioactive solution and scintillntor fluid, (2) presence of quenching impurities in the vial e, or (3) different speckal properties of the vials. We have considered these possibilities in turn. Figure 1A shows that the channel ratio is almost constant. when the volume of the radioactive mixture is changed from 140 to 220 ~1, and 1B demonstrates that Variation
TABLE 1 of Cbrmtirig Results it, I)ill‘erellt, Channel
Vial
No.
Charmel
I (cpm
x
1OP)
\‘iala I fChannel II i‘V = 13)
+ 0.007 + 0.006 jy 0.00s 2. .530 * 0.006
I
156.5
2.566
$2 3
159 II
2.567 2.544
4
157.:: 150. Cl 15i.U
5 6 7
8 9 10
157.1
157.3 15X.6 157.9 157
5
2.548
i
0.006
2.535 * 0.004 Y2.525 JI 0.006 2.326 + 0.006 ".545 * 0.005 2.535 * 0.005
+ S.11.
3-K)
E
.JES;PER
I-.
RIBLLER
A
6
0280 Y E ,” ; 2.60
/O-O-O-~
s -2L 2.40 v
-
2.60
-
2.40
-
2.20
CP
s
I
5
RADIOACTIVE
MIXTURE
(ml)
10
SCINTILLATOR
15
20
(ml)
FIG. 1. (A) Effect of volume of mixture of n-(3H)-glucose and D-(l’C)-ghCOSe on channel ratio. Scintillator, 10 ml Bray solution. (B) Effect of volume of Bray scintillator on channel ratio of 0.2 ml of mixture of n-(‘HI-glucose and D-(W)glucose.
ChI/ChII has a plateau value in the presence of 10 ml of scintillator solution. Thus, the proportion of radioactive mixture and scintillator solution routinely used (0.2 and 10 ml, respectively) is suitable for minimizing variations in the channel ratio. In fact, it may be calculated that the changes that might occur as a consequence of pipetting errors are less than + 0.OOl.l In other experiments a series of vials was counted in the usual way, after which the vials were thoroughly cleaned by scrubbing and rinsing with ethanol, detergent, tap water, and deionized water. The vials were then refilled with the same solutions previously used, and counted again. The results of a representative experiment are given in Fig. 2, from which it appears that there is a definite correlation between the channel ratio of t.he individual vials in the first and second count,ing. Therefore, the variability of the channel ratios apparently is not due to the presence of impurities, but probably results from dissimilarities in the spect,ral properties of the vials. The results of experiments of the type shown in Fig. 2 indicate that it should be possible to reduce the scatter in the values of the channel ratio hy using marked vials, t,he propert.ies of which might be established by preliminary count.ing. However, this would be a somewhat tedious method, and we have therefore sought to establish a quench correction procedure for the determination of the ratio of (3H) and (“C). To this end the third channel of the apparatus was put to use and set at 25% ‘The +0.15%
repeatibility (S.D.) and
of delivering tO.l% (S.D.),
200 ~1 of fluid respectively.
and
10 ml of scintillator
fluid
was
RlNT)IxG
1‘0
EI\‘ZTJIES
AXD
BIOLOGICAL
341
MEMBRAKl?s
.-it? 2.56 ; a 0 c-i I I
252
2.54
2.56
ChI/Chil
2.38
- l.Counting
FIG. 2. Relationship between channel ratio of same vials in two counting ments. Solid curve indicates line of identity.
experi-
gain and a voltage discrimination of XklOOV in order to measure the number of counts in the upper part of the (“C) -spectrum. Figure 3 illustrates the relationship between ChI/ChII and ChIII/ChII, and on the basis of these results the following regression equation is obtained: (ChI,‘ChII)
= (8.27 _+ 0.62) (ChIIf/ChII)
It is to be noted that virtually
+ (0.107 k 0.005)
none of the (3H) disintegrations
3.230
(1)
are
d-
3.220 0/ 3.210
OWO 0
,“/”
oo
O0
2 0
33.200 2 BOO,/
3.190
3180
-/000
asa
0
0
i
1 .3720
.3740
.3760
.3780
Chlll/ChU
FIG. 3. Relationship between ChI/ChII and ChIII/ChII of mixture of D-("H)glucose and D-(W-glucose (0.2 ml) in Bray scintillator (10 ml). Settings of the liquid scintillation spectrometer: Channel I, 45% gain, 5-40 V discrimination ; Channel II, 25% gain, 4@-1OOV discrimination; Channel III, 25% gain, 70-100 V discrimination.
registered in Channel II and Channel III, and therefore ChIII/ChII is independent of the amount of (“H) and (‘“(2) in the vials. ChIII/ChII can thus be used to measure variations in quenching in the face of changes in the ratio of (“H) and (“C). In this way a reduction in the variation of ChI/ChII of 20.670 to not more than ?O.L?% can be achieved. In addit.ion to the quenching phenomenon discussed above, the effect of the counting rate on the channel ratio must be considered. ChI/ChII of various dilutions of the same mixture of D- (3H)-glucose and D-(W)glucose, dissolved in water, has been determined in the usual way (Fig. 4). A decrease of ChI/ChII is observed which is approximately proportional to the counting rate of Channel I. This dependence of ChI/ChII on the counting rate is to be expected because of the resolving time of the apparatus. It appears from the figure that the reduction of ChI/ChII corresponds to a resolving time of about 3 psec.2 It is thus desirable that the counting rate be similar when accurate comparisons of the channel ratio of two se& of samples containing (3H) and (‘“C) are to be carried out, or elm a correction has to be made for the effect of counting rate on the channel ratio. Binding
Experiments
In this section the applicability of the method for determining changes in the channel ratio of (“H) and (‘“C) is illustrated by comparing the binding of D- (“H) -glucose and L- (“C) -glucose to hexokinase in the ab-
0.2
ChI
FIG. 4. Dependence of channel case on counting rate of Channel
ratio I.
0.4
0.6
0.6
1.0
(cpm=106)
of mixture
* The theoretical curves were calculated N/(1 - Nl’), in which N and N, refer respectively, and T is the resolving time
of n-(“H)-glucose
and
D-("c)-glU-
on the basis of the relationship: to the observed and true counting of the apparatus.
NO = rates,
BINDING
TO
ENZYMES
AND
BIOLOGICAL
343
MEMBRANES
sence of ATP. The binding experiments were carried out by equilibrium dialysis, using the same mixt,ure of D-(~H) -glucose and L- (14C)-glucose in all dialysis vessels as described under “Methods.” All vials were counted repeatedly until the statist,ical error was less than +O.l%. The channel rat,ios of the various samples were determined in duplicate and correrted for different degrees of quenching by measuring the channel rat.ios of vials containing the radioactive mixture and t.richloroacetic acid in the same proportion as used for deproteinizing the enzyme solutions. The presence of trichloroacetic acid in the samples resulted in a smaller slope of the correctirn curve than for that shown in Fig. 3. The regression equation in this case had the following form: (2) The corrected values of the channel ratios from the enzyme-containing solutions inside the bags ((ChI/ChII) i, and t,he dialyzate outside the bags ( (ChI/ChII) “) are given in the second and third columns of Table 2. Under t’he present conditions ChI/ChII for (“C) averaged 0.695, and the concentration of bound D-glucose relative to that, of free D-glucose was calculated from the following equation: (tihIII/ChII)
bound
n-glucose/free
= 1.33 (ChI/ChII)
+ 0.261
(ChI/ChII)i = (ChI/ChIIP
n-glucose
-
(ChI/ChII)u - 0.695
(3)
The subt,raction of 0.695 frotn (ChI/ChIIj” in the denominator was done to exclude the contribut)ion of L-(14C)-glucose to the counts of D-t3H)glucose in Channel I. It is apparent from the last, column of Table 2 that the binding of D-glucose calculated in this way decreases from about, 20% at kacer levels of D-glucose to less than 2% at concentrations of about 0.5 mM. The amount of D-ghCOse bound to the enzyme at, various aoncentra-
Binding
TABLK of o-Glucose Channel
Free D-glucose concn. (m&T) 0.004 0.015 0.055 0.238 0.472 U (ChI/ChII)‘: (ChI/ChIIp: *Calculated results given
2 by Hexokinase
rat,iosn
(ChI/ChII)’
(ChI/ChIIp
3.255 3.108 3.037 2.960 2.943
2.815 2.868 2.871 2.900 2.900
n-Glucose
bindingb
( yG)
20.3(16.0-22.6) 10.8 (9.9-12.5) 7.5 (7.0-8.0) 2.7 (2.4-2.9) 1.9 (1.6-2.6)
channel ratio of the fluid inside the bags, containing 0.7 mg protein/ml. channel ratio of dialyzates. as the ratio between bound D-ghCOSe and free n-glucose (eq. 3). The are the average and range of variation in 3 experiments.
344
.TESPER
V. MdLLER
tions of free n-glucose is shown in Fig. 5, together with results obtained by direct estimations of the binding of o-(%)-glucose in experiments carried out under the same conditions as those used for comparing binding of n-glucose and L-glucose. In the latter csperiments, no tritiated label was included in the samples, and the (14C)-radioactivity of trichloroacetic acid filtrates of the imler phase ( (cpm) i, and in the dialyeates ( (cpm) o ) was measured on the liquid scintillation counter, using a gain of 17.5% and a voltage discrimination of ,5-1OOV. The concentration of bound n-glucose, relative to that of free n-glucose, was then calculated according to the following equation: bolmd
u-glucose/free
~~-glu~cw
(cpm)’ = ~__
- (cpmP (cpm!cJ
It is seen from Fig. 5 that the results of the two dificrcnt ways of measuring binding of n-glucose are in agreement, although large variations in the individual experiments are apparent, cspc‘rially by direct estimation 0.018
0.016
-
.: 0.014
-
; ‘n m 0.012 E -2 ;jaJ 0.010
-
-
i
- 00080 0" : 0006cn b D 0.004 2 s 0.002-
0.1
0.2 Free
D-glucose
0.4
c.3 Concentration
05
(mM)
FIG. 5. Binding of n-glucose t.o hexokinase at different concentrations of free n-glucose as measured by channel ratio method (0) and directly on basis of ratio of n-glucose inside and outside the bags (A,). In the channel ratio method, bound DghCOSe was calculated according to equation 3 using a mixture of n-(%-glucosr and L-(‘T)-glucose. In the direct method bound n-glucose was calculated by equation 4 on the basis of measurements of counts per minute of n-(“C)-glucose in the protein fluids and dialyzates. Each point is the mean of 3 experiments, and the vertical bars represent mean deviation of the results obtained.
BINDING
TO ENZYMES
AKD
BIOLOGICAL
MEMBRANES
345
of D-glucose binding. Furthermore, the figure shows that, the binding of n-glucose approaches a saturation value at a concentration of free n-glucose of about 0.2 mdl. The dissociation constant for the interaction of o-glucose with the enzyme preparation as evaluated from a reciprocal l)lot of the result:: of Fig. 5 gives a value of 70 ,.J3. DISCUSSIOh-
The results presented in this paper demonstrate that it. is possible to reduce the S.D. of measurements of the channel ratio of t3H) and (‘“C) to 20.2% when correction is made for the different counting properties of the vials. It is therefore apparent that it should be possible by liquid scintillation counting to differentiate between two sets of samples having a slightly different. ratio of (“H) and (I%). The measurements on the binding of n-glucose to hexokina$e serve to illustrate the applicability and t’he calculations involved in using the method for practical purposes. It is seen from Table 2 that the range of binding is quite high at, low concentrations of n-glucose, but these variations probably result from various degrees of binding in the different. experiments rather than from inaccuracies in the estimation of the binding percentage. Thus, it was found that the SD. of the duplicate samples of the solutions was 50.17%. It appears probable that the method is most appropriate for cst,imation of binding in the range of l-5%). Womack and Colowick (21 have reported results on the binding of o-glucose to yeast hexokinase that were obtained by a dialysis technique (3) in which the rate of diffusion of D-(l’C)-glucosC across a cellophane membrane from a solution containing hexokinase and labeled n-glucose is taken as a measure of the concentration of free n-glucose. All the measurements were done on a single aliquot, the binding at various concentrations of D-ghCOS? being monitored by stepwise addition of unlabeled D-glucose. The most valuable feature of this method is that it is possible to conduct. a binding experiment within a short. period of time. However, it suffers from the drawback that a very small amount of radioactivity appears in the dialyxate, making it unsuitable for measuring low levels of binding. By contrast, the present method is capable of measuring a small degree of binding which may readily be the case in practice if limited amounts of enzyme are available, or when the binding process is characterized by a high dissociation constant. On the other hand, using the setup described here, a relatively long time period is needed to establish equilibrium between the solutions inside and outside the bag. However, it. should be possible to develop the procedure further by adding the pair of radioactive substances solely to the enzyme solution and by speeding up the rate of dialysis, e.g., by employing the thin
346
JESPER
I’.
M$LLER
film dialysis method of Craig (4). In this way substantial amounts of the radioactive substances would rapidly diffuse across the cellophane membrane, and it would not be necessary to await complete equilibration between the two phases, since the nonbonclecl compound could be used as reference substance to indicate the rate of dialysis of 100% free form. It is to be noted that the technique as out.lined here is primarily directed to measurements of binding to enzymes, involving no conversion of the ligand, but it may be possible to calculate the dissociation of a reactive substrate indirectly by measuring the displacement of an inert ligand in competition experiments. Finally, attention is drawn to the use of the channel ratio method to est,imate the specific binding of small molecules to cellular membranes or fractions thereof. This approach is of particular importance when studying the transport mechanism of compounds that are transported across cell membranes (5,6). A study assessing the specific retention of n-glucose by centrifuged specimens of human erythrocyte membranes has been published elsewhere (7). The use of the channel method in this case here obviated the difficulties in estimating the distribution volume of free n-glucose in densely packed membrane material. Furthermore, the earlier paper shows that lower degrees of binding (0.370) than those reported here for binding of n-glucose to hexokinase are detectable by this method. The requirements for detecting such small changes in the ratio of (3H) and (‘“C) between two different, sets of samples are: (1) The composition of the two samples, apart from that, of the radioactive compounds, should be identical, since the quench correct,ion curves may depend on t’he chemical composition of the samples (cf. regression equations 1 and 2). (9) The vials have to be counted repeatedly until the statistical error of the channel ratio has been reduced to a low level. (S) The counting rates of the samples should be similar, or else a correct’ion has to be applied for the effect of t’he counting rate on the channel ratio (Fig. 4). Besides, it should be emphasized that due consideration should be given to the possible existence of isotope effects (i.e., a different distribution volume of the (“H)- and (‘%)-labeled pair of compounds in question) when utilizing this method for assessing low levels of binding (7). SUMMARY
A systematic study of the factors affecting the channel ratio of a mixture of (3H) and (W) as measured by liquid scintillation counting has been carried out.. The variation in the estimation of the channel ratio by repeated counting of the same vial is shown not to exceed that expected from statistical fluctuations of the counting rate. However, variations between the channel ratio of different counting vials containing
the same solution of radioactivity and sciutillator fluid is larger than can be accounted for by statistical fluctuat,ions. A three-channel procedure is devised to correct for the different counting properties of the vials. Furthermore, the effect of the resolving time of the scintillation counter ou the channel ratio at different counting rates is noted. The calculations involved in the use of the method are demonstrated by an examination of the binding of u-glucose to hexokinase. Finally, the applicability of the method for determining low levels of slwific binding of substances to enzymes alid cellular membranes is discussed. ACKNOWLEDGMENTS The initial part of this study wascarried out during the tenure of a postdoctoral fellowship at the Department of Biological Chemistry, University of Manchester, England, sponsored by the Medical Research Council (grant G964/91B). My thanks are due to Dr. W. D. Stein for many helpful discussions on the subject. REFERENCES 1. BRAY, G. A., A?&. Biochena. 1, 279 (1960). 2. WOMACK, F. C., AND COLOWICK, S. P.. Ped. PTOC. 26, 557 (1967). 3. COLOWICK, S. P., AND WOMACK, F. C., J. BioE. Chem. 244, 774 (1969). 4. CRAIG, L. C., in “Methods in Enzymology” (C. H. W. Hirs, ed.), Vol. XI, p. 870. Academic Press, New York, 1967. 5. STEIN, W. D., “The Movement of Molecules across Cell Membranes,” p. 285. Academic Press, New York, 1967. 6. PARDEE, A. B., Science 162, 632 (1968). 7. MIdller, J. V., Biochim. Biophys. Acta 249, 96 (1971).
47, 337-347
BIOCHEMISTRY
A Sensitive
Method
Substances
(197%
for Determining
to Enzymes
and
JESPER Institute
of Medical
Biochemistry,
Biological
Binding
of
Membranes
V. M@LLER
University Received
Preferential
of Aarhus,
May
8000
Aarhus
C, Denmark
19, 1971
It is well known that many enzymic reactions and transport processes across biological membranes show a distinct substrate specificity. In order to gain insight into the nature of these processes it is desirable to have sensitive methods for the measurement of t.he binding of substrates to these systems. Since modern scintillation apparatuses are capable of registering radioactive disintegrations with a high degree of accuracy, it should be possible in a particular sample to measure the preferential binding of a radioactive substrate as compared to that of a related, but nonreacting substance labeled with a different isotope. In this way, errors in the determination of binding, which are due to pipetting errors or uncertainties in the estimation of distribution volume of free substrate, are eliminated. On the ot.her hand, experience shows that a quite considerable variation in the results may occur as a consequence of different degrees of quenching of the samples in the counting vials. In the present paper a systematic study of the factors that affect the channel ratio as measured by liquid scintillat.ion counting has been carried out,. It has been found that a change in the channel ratio of about 0.2% can be detect.ed when proper corrections for quenching have been applied. Finally, the applicability of the method is demonstrated by an esamination of the stereospecific binding of D-glucose to hexokinase. METHODS
Counting
Procedure
D- (3H,) -Glucose (800 mCi/mmole) , D- (““(2) -U-glucose (300 mCi/ mmole), and ~-(~~C~)-glucose (3 mCi/mmole) were obtained from The Radiochemical Centre, Amersham, and used as the sources of radioactivity throughout the experiments reported in this paper. Samples for count-
337 @ 1972 by
Academic
Press,
Inc.
338
.JESPER
I’.
MdLLER
ing were prepared by mixing 0.2 ml of a water solution, containing D- (3H) -glucose (approximately 5 pCi/ml) and D-(W) -glucose (approximately 1 &i/ml) with 10 ml of the scintillator fluid described by Bray (1). The samples were counted in a Packard liquid scintillation apparatus (model 3320) at- the following settings: Channel I, gain 45% and voltage discrimination 5-40V; Channel II, gain 25% and voltage discrimination 40-1OOV. In cases in which use was made of Channel III, the following settings were employed: gain 25% and voltage discrimination 7(rlOOV. The high-voltage knob of the apparatus was in a position so as t.o give a maximal number of counts by the factory-supplied tritium standard at 50% gain and 5-1OOV discrimination. Addit,ion of internal standard (0.1 ml of (3H)-toluene or (I%)-toluene, Packard) indicated that the efficiency of Channel I for tritium was 13%. The count of tritium in Channel II was about. 0.03% that of Channel I. The efficiency of Channel II for (“C) was 32%, and the transgression of (‘“C) counts in Channel I corresponded to about 48% of the counts in Channel II. Binding
Experiments
The binding of n-glucose to hexokinase (ATP: hexose 6-phosphotransferase, EC 2.7.1.1) has been measured by equilibrium dialysis. Yeast hexokinase (Boehringer-Mannheim, Germany) was supplied as a suspension of protein crystals (10 mg/ml) in 3.2 M ammonium sulfate. Prior to the binding experiments ammonium sulfate was removed by dialyzing the enzyme suspension for 3648 hr against 2 liters of 0.025 M phosphate buffer (pH 7.0), which was changed once. Visking dialysis tubing, having a circumference of 2 cm, was made pliable by treatment wit,h boiling water for 15 min, and water was removed from the casing as completely as possible before use. Solutions (0.75 ml) containing hexokinase (0.7 mg protein/ml) and different concentrations of n-glucose (O-O.5 mM), dissolved in the ph0sphat.e buffer mentioned above, were transferred t.o the inside of t,he bags. A small volume (0.05 ml) of either a radioactive mixture of u-(3H)-glucose (approximately 2 pCi/ml) and L-(I~C) glucose (0.25-0.3 &$‘ml) or D-(W)-glucose (0.25-0.3 #&‘ml) was mixed thoroughly with the contents of the bags. The bags were carefully knotted and submerged in 3 ml of a solution with a similar composition as that inside the bags, except that. the protein had been omitted. The test tubes were then shaken for 12-18 hr at 4”C, and at the end of the shaking period 50 ~1 of 50% (w/v) trichloroacetic acid was added to 500 ~1 of the solutions outside and inside the bags, and the samples were centrifuged for 10 min at 1OOOg.The radioactive content of the supernatants was determined as described in the previous section.
BINDING
TO
EKZYMES
AND
BIOLOGICAL
339
MEMBRANES
RESULTS
Counting
of Aqueous Solutions
The channel ratio of replicate samples, prepared by adding 0.2 ml of mixtures of tritiated and (“C)-labeled *ugars to 10 ml of the scintillator fluid, was examined on a number of occasions, and the results of a representative experiment. are given in Table 1. Each vial was counted 8 t.imes with the liquid scintillation apparatus preset. to give 900,000 counts. The average number of counts per minute in Channel I is given by the second column of Table 1, and the third column shows the mean values for the ratio of the counts registcrctl in Channel I and Channel II + the standard deviation between the results obtained in the individual countings. It is seen that the S.D. average,1 s: kO.006, which does not differ much from the value expected for statistical fluctuations in the emission of radioactive particles (kO.005). 01~ the other hand, there is a quite considerable difference between the average values of the individual vials. ChI/ChII t.hus varies from 2.525 to 2.567 with an S.D. of kO.015, and this difference cannot. be accounted for by statistical fluctuations, since the S.E.M. of ChI/ChII of the individual vials is kO.002. It seems probable that the different channel ratios observed between individual samples result from different quenching characteristics of t,he vials, which might occur for the following reasons: (1) errors in the dispensing of radioactive solution and scintillntor fluid, (2) presence of quenching impurities in the vial e, or (3) different speckal properties of the vials. We have considered these possibilities in turn. Figure 1A shows that the channel ratio is almost constant. when the volume of the radioactive mixture is changed from 140 to 220 ~1, and 1B demonstrates that Variation
TABLE 1 of Cbrmtirig Results it, I)ill‘erellt, Channel
Vial
No.
Charmel
I (cpm
x
1OP)
\‘iala I fChannel II i‘V = 13)
+ 0.007 + 0.006 jy 0.00s 2. .530 * 0.006
I
156.5
2.566
$2 3
159 II
2.567 2.544
4
157.:: 150. Cl 15i.U
5 6 7
8 9 10
157.1
157.3 15X.6 157.9 157
5
2.548
i
0.006
2.535 * 0.004 Y2.525 JI 0.006 2.326 + 0.006 ".545 * 0.005 2.535 * 0.005
+ S.11.
3-K)
E
.JES;PER
I-.
RIBLLER
A
6
0280 Y E ,” ; 2.60
/O-O-O-~
s -2L 2.40 v
-
2.60
-
2.40
-
2.20
CP
s
I
5
RADIOACTIVE
MIXTURE
(ml)
10
SCINTILLATOR
15
20
(ml)
FIG. 1. (A) Effect of volume of mixture of n-(3H)-glucose and D-(l’C)-ghCOSe on channel ratio. Scintillator, 10 ml Bray solution. (B) Effect of volume of Bray scintillator on channel ratio of 0.2 ml of mixture of n-(‘HI-glucose and D-(W)glucose.
ChI/ChII has a plateau value in the presence of 10 ml of scintillator solution. Thus, the proportion of radioactive mixture and scintillator solution routinely used (0.2 and 10 ml, respectively) is suitable for minimizing variations in the channel ratio. In fact, it may be calculated that the changes that might occur as a consequence of pipetting errors are less than + 0.OOl.l In other experiments a series of vials was counted in the usual way, after which the vials were thoroughly cleaned by scrubbing and rinsing with ethanol, detergent, tap water, and deionized water. The vials were then refilled with the same solutions previously used, and counted again. The results of a representative experiment are given in Fig. 2, from which it appears that there is a definite correlation between the channel ratio of t.he individual vials in the first and second count,ing. Therefore, the variability of the channel ratios apparently is not due to the presence of impurities, but probably results from dissimilarities in the spect,ral properties of the vials. The results of experiments of the type shown in Fig. 2 indicate that it should be possible to reduce the scatter in the values of the channel ratio hy using marked vials, t,he propert.ies of which might be established by preliminary count.ing. However, this would be a somewhat tedious method, and we have therefore sought to establish a quench correction procedure for the determination of the ratio of (3H) and (“C). To this end the third channel of the apparatus was put to use and set at 25% ‘The +0.15%
repeatibility (S.D.) and
of delivering tO.l% (S.D.),
200 ~1 of fluid respectively.
and
10 ml of scintillator
fluid
was
RlNT)IxG
1‘0
EI\‘ZTJIES
AXD
BIOLOGICAL
341
MEMBRAKl?s
.-it? 2.56 ; a 0 c-i I I
252
2.54
2.56
ChI/Chil
2.38
- l.Counting
FIG. 2. Relationship between channel ratio of same vials in two counting ments. Solid curve indicates line of identity.
experi-
gain and a voltage discrimination of XklOOV in order to measure the number of counts in the upper part of the (“C) -spectrum. Figure 3 illustrates the relationship between ChI/ChII and ChIII/ChII, and on the basis of these results the following regression equation is obtained: (ChI,‘ChII)
= (8.27 _+ 0.62) (ChIIf/ChII)
It is to be noted that virtually
+ (0.107 k 0.005)
none of the (3H) disintegrations
3.230
(1)
are
d-
3.220 0/ 3.210
OWO 0
,“/”
oo
O0
2 0
33.200 2 BOO,/
3.190
3180
-/000
asa
0
0
i
1 .3720
.3740
.3760
.3780
Chlll/ChU
FIG. 3. Relationship between ChI/ChII and ChIII/ChII of mixture of D-("H)glucose and D-(W-glucose (0.2 ml) in Bray scintillator (10 ml). Settings of the liquid scintillation spectrometer: Channel I, 45% gain, 5-40 V discrimination ; Channel II, 25% gain, 4@-1OOV discrimination; Channel III, 25% gain, 70-100 V discrimination.
registered in Channel II and Channel III, and therefore ChIII/ChII is independent of the amount of (“H) and (‘“(2) in the vials. ChIII/ChII can thus be used to measure variations in quenching in the face of changes in the ratio of (“H) and (“C). In this way a reduction in the variation of ChI/ChII of 20.670 to not more than ?O.L?% can be achieved. In addit.ion to the quenching phenomenon discussed above, the effect of the counting rate on the channel ratio must be considered. ChI/ChII of various dilutions of the same mixture of D- (3H)-glucose and D-(W)glucose, dissolved in water, has been determined in the usual way (Fig. 4). A decrease of ChI/ChII is observed which is approximately proportional to the counting rate of Channel I. This dependence of ChI/ChII on the counting rate is to be expected because of the resolving time of the apparatus. It appears from the figure that the reduction of ChI/ChII corresponds to a resolving time of about 3 psec.2 It is thus desirable that the counting rate be similar when accurate comparisons of the channel ratio of two se& of samples containing (3H) and (‘“C) are to be carried out, or elm a correction has to be made for the effect of counting rate on the channel ratio. Binding
Experiments
In this section the applicability of the method for determining changes in the channel ratio of (“H) and (‘“C) is illustrated by comparing the binding of D- (“H) -glucose and L- (“C) -glucose to hexokinase in the ab-
0.2
ChI
FIG. 4. Dependence of channel case on counting rate of Channel
ratio I.
0.4
0.6
0.6
1.0
(cpm=106)
of mixture
* The theoretical curves were calculated N/(1 - Nl’), in which N and N, refer respectively, and T is the resolving time
of n-(“H)-glucose
and
D-("c)-glU-
on the basis of the relationship: to the observed and true counting of the apparatus.
NO = rates,
BINDING
TO
ENZYMES
AND
BIOLOGICAL
343
MEMBRANES
sence of ATP. The binding experiments were carried out by equilibrium dialysis, using the same mixt,ure of D-(~H) -glucose and L- (14C)-glucose in all dialysis vessels as described under “Methods.” All vials were counted repeatedly until the statist,ical error was less than +O.l%. The channel rat,ios of the various samples were determined in duplicate and correrted for different degrees of quenching by measuring the channel rat.ios of vials containing the radioactive mixture and t.richloroacetic acid in the same proportion as used for deproteinizing the enzyme solutions. The presence of trichloroacetic acid in the samples resulted in a smaller slope of the correctirn curve than for that shown in Fig. 3. The regression equation in this case had the following form: (2) The corrected values of the channel ratios from the enzyme-containing solutions inside the bags ((ChI/ChII) i, and t,he dialyzate outside the bags ( (ChI/ChII) “) are given in the second and third columns of Table 2. Under t’he present conditions ChI/ChII for (“C) averaged 0.695, and the concentration of bound D-glucose relative to that, of free D-glucose was calculated from the following equation: (tihIII/ChII)
bound
n-glucose/free
= 1.33 (ChI/ChII)
+ 0.261
(ChI/ChII)i = (ChI/ChIIP
n-glucose
-
(ChI/ChII)u - 0.695
(3)
The subt,raction of 0.695 frotn (ChI/ChIIj” in the denominator was done to exclude the contribut)ion of L-(14C)-glucose to the counts of D-t3H)glucose in Channel I. It is apparent from the last, column of Table 2 that the binding of D-glucose calculated in this way decreases from about, 20% at kacer levels of D-glucose to less than 2% at concentrations of about 0.5 mM. The amount of D-ghCOse bound to the enzyme at, various aoncentra-
Binding
TABLK of o-Glucose Channel
Free D-glucose concn. (m&T) 0.004 0.015 0.055 0.238 0.472 U (ChI/ChII)‘: (ChI/ChIIp: *Calculated results given
2 by Hexokinase
rat,iosn
(ChI/ChII)’
(ChI/ChIIp
3.255 3.108 3.037 2.960 2.943
2.815 2.868 2.871 2.900 2.900
n-Glucose
bindingb
( yG)
20.3(16.0-22.6) 10.8 (9.9-12.5) 7.5 (7.0-8.0) 2.7 (2.4-2.9) 1.9 (1.6-2.6)
channel ratio of the fluid inside the bags, containing 0.7 mg protein/ml. channel ratio of dialyzates. as the ratio between bound D-ghCOSe and free n-glucose (eq. 3). The are the average and range of variation in 3 experiments.
344
.TESPER
V. MdLLER
tions of free n-glucose is shown in Fig. 5, together with results obtained by direct estimations of the binding of o-(%)-glucose in experiments carried out under the same conditions as those used for comparing binding of n-glucose and L-glucose. In the latter csperiments, no tritiated label was included in the samples, and the (14C)-radioactivity of trichloroacetic acid filtrates of the imler phase ( (cpm) i, and in the dialyeates ( (cpm) o ) was measured on the liquid scintillation counter, using a gain of 17.5% and a voltage discrimination of ,5-1OOV. The concentration of bound n-glucose, relative to that of free n-glucose, was then calculated according to the following equation: bolmd
u-glucose/free
~~-glu~cw
(cpm)’ = ~__
- (cpmP (cpm!cJ
It is seen from Fig. 5 that the results of the two dificrcnt ways of measuring binding of n-glucose are in agreement, although large variations in the individual experiments are apparent, cspc‘rially by direct estimation 0.018
0.016
-
.: 0.014
-
; ‘n m 0.012 E -2 ;jaJ 0.010
-
-
i
- 00080 0" : 0006cn b D 0.004 2 s 0.002-
0.1
0.2 Free
D-glucose
0.4
c.3 Concentration
05
(mM)
FIG. 5. Binding of n-glucose t.o hexokinase at different concentrations of free n-glucose as measured by channel ratio method (0) and directly on basis of ratio of n-glucose inside and outside the bags (A,). In the channel ratio method, bound DghCOSe was calculated according to equation 3 using a mixture of n-(%-glucosr and L-(‘T)-glucose. In the direct method bound n-glucose was calculated by equation 4 on the basis of measurements of counts per minute of n-(“C)-glucose in the protein fluids and dialyzates. Each point is the mean of 3 experiments, and the vertical bars represent mean deviation of the results obtained.
BINDING
TO ENZYMES
AKD
BIOLOGICAL
MEMBRANES
345
of D-glucose binding. Furthermore, the figure shows that, the binding of n-glucose approaches a saturation value at a concentration of free n-glucose of about 0.2 mdl. The dissociation constant for the interaction of o-glucose with the enzyme preparation as evaluated from a reciprocal l)lot of the result:: of Fig. 5 gives a value of 70 ,.J3. DISCUSSIOh-
The results presented in this paper demonstrate that it. is possible to reduce the S.D. of measurements of the channel ratio of t3H) and (‘“C) to 20.2% when correction is made for the different counting properties of the vials. It is therefore apparent that it should be possible by liquid scintillation counting to differentiate between two sets of samples having a slightly different. ratio of (“H) and (I%). The measurements on the binding of n-glucose to hexokina$e serve to illustrate the applicability and t’he calculations involved in using the method for practical purposes. It is seen from Table 2 that the range of binding is quite high at, low concentrations of n-glucose, but these variations probably result from various degrees of binding in the different. experiments rather than from inaccuracies in the estimation of the binding percentage. Thus, it was found that the SD. of the duplicate samples of the solutions was 50.17%. It appears probable that the method is most appropriate for cst,imation of binding in the range of l-5%). Womack and Colowick (21 have reported results on the binding of o-glucose to yeast hexokinase that were obtained by a dialysis technique (3) in which the rate of diffusion of D-(l’C)-glucosC across a cellophane membrane from a solution containing hexokinase and labeled n-glucose is taken as a measure of the concentration of free n-glucose. All the measurements were done on a single aliquot, the binding at various concentrations of D-ghCOS? being monitored by stepwise addition of unlabeled D-glucose. The most valuable feature of this method is that it is possible to conduct. a binding experiment within a short. period of time. However, it suffers from the drawback that a very small amount of radioactivity appears in the dialyxate, making it unsuitable for measuring low levels of binding. By contrast, the present method is capable of measuring a small degree of binding which may readily be the case in practice if limited amounts of enzyme are available, or when the binding process is characterized by a high dissociation constant. On the other hand, using the setup described here, a relatively long time period is needed to establish equilibrium between the solutions inside and outside the bag. However, it. should be possible to develop the procedure further by adding the pair of radioactive substances solely to the enzyme solution and by speeding up the rate of dialysis, e.g., by employing the thin
346
JESPER
I’.
M$LLER
film dialysis method of Craig (4). In this way substantial amounts of the radioactive substances would rapidly diffuse across the cellophane membrane, and it would not be necessary to await complete equilibration between the two phases, since the nonbonclecl compound could be used as reference substance to indicate the rate of dialysis of 100% free form. It is to be noted that the technique as out.lined here is primarily directed to measurements of binding to enzymes, involving no conversion of the ligand, but it may be possible to calculate the dissociation of a reactive substrate indirectly by measuring the displacement of an inert ligand in competition experiments. Finally, attention is drawn to the use of the channel ratio method to est,imate the specific binding of small molecules to cellular membranes or fractions thereof. This approach is of particular importance when studying the transport mechanism of compounds that are transported across cell membranes (5,6). A study assessing the specific retention of n-glucose by centrifuged specimens of human erythrocyte membranes has been published elsewhere (7). The use of the channel method in this case here obviated the difficulties in estimating the distribution volume of free n-glucose in densely packed membrane material. Furthermore, the earlier paper shows that lower degrees of binding (0.370) than those reported here for binding of n-glucose to hexokinase are detectable by this method. The requirements for detecting such small changes in the ratio of (3H) and (‘“C) between two different, sets of samples are: (1) The composition of the two samples, apart from that, of the radioactive compounds, should be identical, since the quench correct,ion curves may depend on t’he chemical composition of the samples (cf. regression equations 1 and 2). (9) The vials have to be counted repeatedly until the statistical error of the channel ratio has been reduced to a low level. (S) The counting rates of the samples should be similar, or else a correct’ion has to be applied for the effect of t’he counting rate on the channel ratio (Fig. 4). Besides, it should be emphasized that due consideration should be given to the possible existence of isotope effects (i.e., a different distribution volume of the (“H)- and (‘%)-labeled pair of compounds in question) when utilizing this method for assessing low levels of binding (7). SUMMARY
A systematic study of the factors affecting the channel ratio of a mixture of (3H) and (W) as measured by liquid scintillation counting has been carried out.. The variation in the estimation of the channel ratio by repeated counting of the same vial is shown not to exceed that expected from statistical fluctuations of the counting rate. However, variations between the channel ratio of different counting vials containing
the same solution of radioactivity and sciutillator fluid is larger than can be accounted for by statistical fluctuat,ions. A three-channel procedure is devised to correct for the different counting properties of the vials. Furthermore, the effect of the resolving time of the scintillation counter ou the channel ratio at different counting rates is noted. The calculations involved in the use of the method are demonstrated by an examination of the binding of u-glucose to hexokinase. Finally, the applicability of the method for determining low levels of slwific binding of substances to enzymes alid cellular membranes is discussed. ACKNOWLEDGMENTS The initial part of this study wascarried out during the tenure of a postdoctoral fellowship at the Department of Biological Chemistry, University of Manchester, England, sponsored by the Medical Research Council (grant G964/91B). My thanks are due to Dr. W. D. Stein for many helpful discussions on the subject. REFERENCES 1. BRAY, G. A., A?&. Biochena. 1, 279 (1960). 2. WOMACK, F. C., AND COLOWICK, S. P.. Ped. PTOC. 26, 557 (1967). 3. COLOWICK, S. P., AND WOMACK, F. C., J. BioE. Chem. 244, 774 (1969). 4. CRAIG, L. C., in “Methods in Enzymology” (C. H. W. Hirs, ed.), Vol. XI, p. 870. Academic Press, New York, 1967. 5. STEIN, W. D., “The Movement of Molecules across Cell Membranes,” p. 285. Academic Press, New York, 1967. 6. PARDEE, A. B., Science 162, 632 (1968). 7. MIdller, J. V., Biochim. Biophys. Acta 249, 96 (1971).