ARC”,“ES
OF BIOCHEMISTRY
AND
BIOPHYSICS
Determination Constants THYGE Institute
168,
351-357(1975)
of Association
and Dissociation
for Bilirubin-Bovine FAERCH’
AND
of Medical Biochemistry, Received
Serum Albumin
J@RGEN
Uniuersity November
Rate
JACOBSEN
of Aarhus, Aarhus,
Denmark
5. 1974
The association rate constant for the binding of bilirubin to bovine serum albumin has been determined in a continuous-flow experiment. The value obtained is 0.9 x lo6 M- Is- I. Furthermore the dissociation rate constant is determined from the rate of the peroxidasecatalyzed oxidation of bilirubin in a bilirubin-albumin solution. This figure is 3.1 x lo-% I. Calculation of the apparent binding equilibrium constant from the two rate constants gives 2.9 x 107~- ‘. The above mentioned peroxidase oxidation has also been used for a direct estimation of the binding equilibrium constant giving 2.7 x 107~m’. A!1 experiments are carried out at 36°C and pH 7.4.
Bovine serum albumin binds 1 mol bilirubin at a high affinity site, and probably several moles more at weaker sites (1). The primary binding was studied by Blauer and King (a), using ORD. They estimated the binding constant at pH 5 but were not able to establish the co&ant at higher pH values. Wennberg et al. (3) determined the binding constant at pH 8.5 and did not observe gross changes when the pH was lowered to 7.5. The order of magnitude for the constant in his work is 108~-'. Krasner (4) has studied the binding of bilirubin to bovine serum albumin using a dialysis technique; he finds the binding constant 1.5 x 107~-1 at pH around 8. Chen (5) has recently reported the binding constant for serum albumin from a number of different species, among which is the cow. He uses quenching of the albumin fluorescence by bilirubin and obtains the value 2.2 x 107~-’ at 25°C in a phosphate buffer pH 7.4. The rate of association of BSA and bilirubin has been studied by Chen (6), with a stopped-flow technique using quenching of the protein fluorescence and ’ Present address: Aalborg mark.
Sygehus, Aalborg,
Den.
increase of the bilirubin fluorescence. He was not able to follow the primary binding, but described two relaxation steps. In the present work, the second-order rate constant for the association of BSA and bilirubin is determined in a continuous-flow experiment and the rate constant for the dissociation by an enzymatic method. From these two constants an equilibrium constant has been calculated. The equilibrium constant is in addition determined by the peroxidase method previously used for determination of the binding constant for bilirubin and human serum albumin (7). MATERIALS
METHODS
Crystalline bilirubin, horse radish peroxidase, type III, (80% impurities), and bovine serum albumin, fraction V. were all obtained from Sigma. The albumin was not defatted and contained 0.5 mol fatty acid/m01 protein measured by the method of Dole (8). The association process. A solution of bovine serum albumin is mixed with a solution of bilirubin sodium salt in the continuous-flow apparatus shown in Fig. 1. The reaction chamber of the equipment consists of two coaxial pipes, the inner delivering the albumin solution and the outer the bilirubin solution. The inner diameter of the pipes were 4 x 10 3 m and 8.3 x 10m3m, respectively. The flow was delivered by means of two 200 ml syringes giving a total of 23.4 ml/s. the
35i Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
AND
352
FAERCH
AND JACOBSEN
finns to ensure centration of pipe
The end of the inner
pipe
holes for the albumin
solution
W-photometer recorder
FIG. 1. The continuous-flow equipment. The inner pipe can be fixed in twenty positions by means of the measuring rail, the distance between each hole corresponding to 20 ms. The time from mixing to observation is calculated from the volume of the pipe and the flow rate. The flow was adjusted to ensure hydrodynamic turbulence. The mixing process was checked with the colour shift taking place within 1 mm bromthymolblue-base + H+ 4 bromthymolblue-acid, from the mixing point, corresponding to less than 3 ms. Thermostating ensured a temperature of 36°C in the reaction pipe. The equipment was manufactured in the workshop at the Institute of Medical Biochemistry, University of Aarhus. velocity of the reaction solutions being 0.43 m/s. The mixing process was checked by bromthymolblue-base the color shift taking + H+ - bromthymolblue-acid, place within 1 mm from the mixing point, corresponding to less than 3 ms. Thermostating ensured a temperature of 36°C in the reaction pipe. By changing the distance from the mixing point to the detecting point, it is possible to determine the extinction of the mixture in the range from 25 to 200 ms after mixing of the solutions. The extinctions were measured at 474 nm, where the difference in absorption between bound and unbound bilirubin is maximal (Fig. 2). Figure 3 shows the results obtained in a typical experiment. The lower horizontal level indicates the extinctions, E, at various times after mixing, ranging from 70 to 234 ms. The arrow shows the point where the flow was stopped, the absorption then increased to reach the final value, E,,, of the stable complex of bilirubin and albumin. The solid curve shows the experimentally found course of the absorption and the dashed curve is the theoretical course, assuming that there is only one step in the binding process. It is seen that the absorption change takes place in a slower rate than anticipated, indicating that the binding consists of more than one step. The solutions used were: 1.0 g bovine serum albumin or 2.0 g bovine serum albumin in 1500 ml 134 mM phosphate buffer at pH 7.35 (10, respectively 20
PM), and 9 mg bilirubin dissolved in 100 ~1 0.1 N NaOH, diluted to about 1500 ml, adjusted to pH 9.3 with 0.1 N HCl, and finally brought to 1500 ml (10 PM). The exact concentration was calculated from the final extinction in the reaction cuvette. For calculation of the results, the following symbols are used: b current bilirubin concentration b, bilirubin concentration in the mixing point p current albumin concentration p,, albumin concentration in the mixing point c current concentration of the bilirubin-albumin complex c, complex concentration at equilibrium. In a mixture of bilirubin and albumin the sum of bound and unbound bilirubin is constant: b+c=c,
(1)
The extinction measured, E, is the sum of the extinction from the free bilirubin and the extinction from the complex: E = EC + E,. From (I) the following
equation
(11) can be obtained:
RATE A 6x10’ -
CONSTANTS
353
FOR BILIRUBIN-ALBUMIN
Extinction Coefficient
FIG. 2. Photometric properties of bilirubin. Curve B shows the visible part of the spectrum of unbound bilirubin at pH 7.4. Curve C demonstrates the biliruhin spectrum after addition of an equimolar solution of bovine serum albumin. Curve C-B shows the difference between Curve C and B, with a maximum at 474 n. The extinction coefficients used were clsB ,,,,, = 52 x 10’ M cm- 1 for free bilirubin and c462”rn = 57 x lo3 ~-*crn~’ for the final bilirubin: bovine serum albumin complex, as determined by Chen (5). From these numbers the values at 474 nm could be calculated from the spectral curves. Supposing that one molecule of bilirubin associates with one molecule of albumin, p can be expressed by the following equation: p = po ~ (b, - b)
(IV)
pO is known from the weight of albumin dissolved in the starting solution, and b, is calculated from the extinction of the final complex, as the equilibrium concentration of unbound bilirubin is negligible. The rate constant for the second-order reaction can then be calculated from: FIG. 3. Continuous-flow experiment. Eight experiments corresponding to various times after mixing. The lower horizontal part of the curves shows the absorption of the mixture after the indicated time, E. When the flow is stopped (at the point marked by the arrows) the absorption increases to reach its final value, E,,, after lo-15 s. The dashed curve shows the theoretical course, supposing one second-order step, with the rate constant found in this work. all extinctions being taken at 474 nm. Using (Ia) in (II) one gets, as b = E,/c, : b = -.-F--E The nominator in equation (III) is derived from the continuous-flow experiment as the difference between the extinction determined during flow and the final extinction, obtained when a stable level is reached after the flow has been stopped (see Fig. 3). The determination of the denominator is described in Fig. 2.
k, = 3-T) 0
d log (plb)fdt
W)
0
The dissociation process. Unbound bilirubin can be oxidized by hydrogen peroxide with peroxidase as a catalyst (9). The proposed scheme for this reaction is shown in Fig. 4. The system has been used to determine the equilibrium constant for bilirubin-HSA (7). The principle is the following: Peroxidase and H,O, are added to a solution of bilirubin and albumin. The decrease in total bilirubin concentration is registered as a fall in absorption at 460 nm. The concentration of unbound bilirubin, b, is very low compared to the concentration of the complex, c, which means that the total bilirubin concentration is equal to c. From Fig. 4 it can be seen that the decrease in c per minute is proportional to the steady state concentration of b. By suitable choice of peroxidase concentration the oxidation process will be slow compared to the dissociation of the complex; in this case the steady state concentration of b equals the true equilibrium concentration. This is the basis for
354
FAERCH Albumm-Btllrubtn t
-
k-1
Bhrubbln
AND JACOBSEN carried out determined The velocity tional to the experiment, centration, known, and
t Album,” P
kl
iperoxodase)
H2”2
kP H20 4 X
FIG. 4. Scheme for the peroxidase catalyzed oxidation of bilirubin. Free bilirubin is degradated by hydrogen peroxide to a product with little extinction at 460 nm, while the albumin-bound bilirubin is protected against oxidation. the determination of the equilibrium constant, which has been described in more details elsewhere (7, 10, 11). The peroxidase catalyzed oxidation of bilirubin can also be used to determine the dissociation rate constant, k_, ; this has already been done for human serum albumin (12). If the symbols from Fig. 4 are used the following equations are valid: dbldt
= k-, c - k, x p x b - k, x b x [HFW]. (VI)
If steady-state condition is assumed, dbldt In this case (VI) can be rewritten to:
= 0.
km, x c = b x (k, x p + k, x [HRP]). As already stated the decrease in total bilirubin concentration per second u, is proportional to the concentration of unbound bilirubin, b:
in a cuvette and the degradation rate as the decrease in absorption at 440 nm. of the degradation of bilirubin is proporconcentration of bilirubin in the standard b,, , and the equivalent peroxidase con[HRP],,; both these concentrations are k, is calculated from: V 81 =
k, x b,, WRPI,,.
Determination of the binding equilibrium constant by peroxidase oxidation. The constant for bilirubin and human serum albumin has previously been determined by this method (7). The principle of the method is mentioned under the dissociation process and in Fig. 4. A series of experiments were carried out with constant bilirubin concentration, around 10 x 1Om6M, and varying concentrations of bovine serum albumin, resulting in a number of bilirubin/albumin ratios, ranging from 0.25 to 0.95, 67 mM phosphate buffer, pH 7.4 and 37°C were used. The oxidation velocity was measured and the concentration of unbound bilirubin calculated as described previously (10, 11). The results were plotted according to Scatchard (13) and the binding constant determined from the intercept on the ordinate. RESULTS
The results of the continuous-flow experiments are given in Table I. Three determinations were made with 5 PM bovine serum u = k, x b x [HRP], (VII) albumin and seven with an albumin concentration of 10 PM. In both cases the biliconsequently rubin concentration was 5 PM. The valk,xpxu +v ues for the association constant, k,, show (VIII) k-, = cxk,x [HRP] c’ approximately normal distribution. The algebraic mean and the error of the mean By rearrangement we obtain: was calculated as for a normal distribu1 1 k, XP tion. -=1 ___ (IX) +-. k-, x c V c x k, x k-, X(HRP] In Fig. 5 the results of the determinations of the oxidation velocities for differFrom the last equation it can be seen that a plot of l/u ent concentrations of peroxidase are plotvs l/[HRP] should give a straight line with an intercept on the ordinate which contains kk, as the ted according to equation (IX). The intercept on the ordinate is 1.96 x lo6 S.M-i; as only unknown parameter. the total bilirubin concentration, which The circumstances for determining the oxidation velocity, u, were the following: To a lo-mm cuvette equals the complex concentration, c, is 16.5 with 3.00 ml phosphate buffer, pH 7.4, containing 30.0 x lo- 6~, k _ 1is calculated to 3.1 x lo- 2 s- I. PM bovine serum albumin, 16.5 pM bilirubin, and 300 As described in the method section the PM H,O, small amounts of horse radish peroxidase slope of the line in Fig. 5 can be used to (HRP) was added to final concentrations ranging from estimate the association rate constant, k, , 0.8 to 160 nM. The velocity was registered as a from k-, and k,. The value of k- 1 has decrease in absorption at 460 nm. already been given and k, , determined as The slope of the line in Fig. 5 can be used for an described previously, is 2.2 x lo8 M-i s-i. additional estimation of k, , as k, can be determined The slope is 6.7 x 10m2s, p is 13.5 x 1O-6 M, from the following standard experiment: Bilirubin was oxidized by H,O, and peroxidase in and c, 16.5 x 10e6 M, which gives k, = 0.5 the absence of albumin (10). The oxidation was x 10s M- 1 s- 1 in good agreement with the
RATE
CONSTANTS
355
FOR BILIRUBIN-ALBUMIN
A LO-
1 .106 M'..,' v
30.
20.
1 [perwdase] , 25
I 50
/
FIG. 5. Plot l/u vs l/[HRP] according to equation IX. Results from experiment. The concentrations of bilirubin and bovine serum albumin were 16.5 x 1Om6M and 30.0 x 10m6 M, respectively. v was determined absorption at 460 rim/s. The correlation factor, 0.996, the intercept on the 10’ M- ‘s ‘, and the slope, 6.7 f 0.1 x lo- * se 1 were determined by linear the calculation of k - , and k ,. TABLE
.107 f"14
a peroxidase oxidation in the reaction mixture from the decrease in ordinate, 1.96 * 0.35 x regression. See text for
I
RESULTS OF CONTINUOUS-FLOW EXPERIMENTS Inital albumin concentration @,) (FM) 5.16 5.16 5.16 10.32 10.32 10.32 10.32 10.32 10.32
Extinction of complex at equilibrium at 474 nm (E,,)
0.252 0.252 0.204 0.271 0.278 0.280 0.280 0.336 0.336
0 k, = (0.9 * 0.55) lo8 M~‘s-’
1.5 0.59 2.0 0.69 0.82 1.14 0.79 0.15 0.26
Association rate constant (k I)n (M-k’) x x x x x x x x x
(Mean
106 106 10’ lo6 lo6 106 10’ 106 lo6 * SD).
result obtained by the continuous-flow experiment. The binding equilibrium constant for bilirubin and bovine serum albumin was calculated from k, , determined by continuous-flow, and k _ , , obtained from a peroxidase oxidation experiment, k l/k- 1 = K. The value is 2.9 x lo7 M-i. The peroxidase method may also be used to determine the binding constant directly if the enzyme concentration is kept relatively low (Fig. 4). Figure 6 shows a Scatchard’s plot derived from a series of peroxidase determinations. The intercept on the
FIG. 6. Determination of the binding constant from a Scatchard’s plot. Unbound bilirubin was determined by the peroxidase technique at different ratios bilirubin/albumin (=r). The intercept on the abscissa indicates the number of binding sites, n, and the intercept on the ordinate equals n x K,,,. The binding constant is 2.7 x 10’ M-‘.
abscissa indicates that one bilirubin molecule is bound to bovine serum albumin at a high affinity site, and the intercept at the ordinate determines the binding constant, which is 2.7 x lOI M-l in good agreement
356
FAERCH
AND JACOBSEN
with the value obtained from the two rate constants. DISCUSSION
The time course of the change of the bilirubin absorption spectrum during the binding to bovine serum albumin was shown to be a second-order reaction as seen from Fig. 7 and from the observation that t, for the process is highly dependent the concentration. The kinetic of the reaction indicates that we have studied the first step in the binding process. The rate of the primary binding must be dependent of both the bilirubin and the albumin concentration in agreement with the findings. As can be seen from Fig. 3 the rate of the increase in absorption is slower than predicted from the second-order reaction. This means that at least one secondary relaxation step takes place after bilirubin has been bound to albumin. No quantitative estimation has been done on this slow step. The rate of the dissociation of bilirubin from albumin should preferably also have been studied by the continuous-flow method, this could theoretically be done by dilution of a bilirubin-albumin solution. Due to the high affinity of albumin for bilirubin such experiments give very minute differences in absorption, below the sensitivity of our instrument. It was therefore necessary to determine k _ 1by another technique. By the peroxidase method used we also were able to estimate k 1to compare
ACKNOWLEDGMENTS The authors wish to thank Professor R. F. Chen for sending prepublication information and Professor R. Brodersen for helpful discussion during the work. The skilful technical assistance of Eva Korsgaard is acknowledged. Thanks are also due to Ove S$nderskov for making the continuous-flow apparatus and to Frede Nielsen for the drawings.
7‘
logP/b1 006 i
yoi_ 002
with the value obtained from the continuous-flow experiment. As the binding process proceeds in more than one step the binding constant should be calculated from the product of the association rate constants divided by the product of the dissociation rate constants. In spite of that and of the use of different methods we find good agreement between the binding constant calculated from the two rate constants, 2.9 x 10’ M-l, and the equivalent figure determined by the peroxidase method, 2.7 x lo7 M-'. The value for the binding constant is further supported by the work of Chen (5), who gets 2.2 x 10’ M-l at 25” C and pH 7.4, and by Krasner (4), who obtains 1.5 x 10’ M-l under slightly different circumstances. Chen (6) has used stopped-flow measurements of the fluorescence of bilirubin and albumin to study the binding process; he finds two first-order reactions, but he is not able to follow any second-order process. The first-order reactions may be equivalent to the secondary change in absorbance we observed (Fig. 3). It remains, however, unexplained why Chen’s results do not show the initial second-order reaction, although the experimental conditions are similar in the two investigations, except that the albumin we have used contains fatty acid, while Chen has defatted the albumin prior to use.
/
FIG. 7. Log (p/b) = f(t). The figure shows the linear dependence of log (albumin/bilirubin) with time. This indicates second-order kinetic. See text for details.
REFERENCES 1. WENNBERG, R. P. (1971) Proc. Sot. Ped. Res. Atlantic City, N.J. 2. BLAUER, G., AND KING, T. E. (197O)J. Clin. Chem. 245, 372-381. 3. WENNBERG, R. P., AND COWGER, M. L. (1973) Clin. Chem. Acta. 43, 55-64. 4. KRASNER, J., GIACOIA, G. P., AND YAFFE, S. J. (1973) Ann. NY Acad. Sci. 226, 101-114. 5. CHEN, R. F. (1973) in Fluorescence Technique in
RATE CONSTANTS
FOR BILIRUBIN-ALBUMIN
Cell Biology (Thaer, A. and Sernetz, M. eds.), pp. 239-248, Springer Verlag, New York. 6. CHEN, R. F. (1974) Arch. Biochem. Biophys. 160, 106-112. 7. JACOBSEN,J. (1969) Fed. Eur. Biochem. Sot. Lett. 5, 112-114. 8. DOLE, V. P. (1956) J. Clin. Inuest. 35, 150-154. 9. BRODERSEN, R., AND BARTELS, P. (1969) Eur. J. Biochem. 10, 468-473.
357
10. JACOBSEN, J., AND FEDDERS, 0. (1970) Stand. Journ. Clin. Lab. Inoest. 26, 237-241. 11. JACOBSEN, J., AND WENNBERG, R. P. (1974) Clin. Chem. 20, 783-789. 12. BRODERSEN, R. (1974) J. Clin. Inuest. 54, 1353-1364. 13. SCHATCHARD, G., COLEMANN, J. S., AND SHEN, J. (1957) J. Amer. Chem. Sot. 79, 12-21.
OF BIOCHEMISTRY
AND
BIOPHYSICS
Determination Constants THYGE Institute
168,
351-357(1975)
of Association
and Dissociation
for Bilirubin-Bovine FAERCH’
AND
of Medical Biochemistry, Received
Serum Albumin
J@RGEN
Uniuersity November
Rate
JACOBSEN
of Aarhus, Aarhus,
Denmark
5. 1974
The association rate constant for the binding of bilirubin to bovine serum albumin has been determined in a continuous-flow experiment. The value obtained is 0.9 x lo6 M- Is- I. Furthermore the dissociation rate constant is determined from the rate of the peroxidasecatalyzed oxidation of bilirubin in a bilirubin-albumin solution. This figure is 3.1 x lo-% I. Calculation of the apparent binding equilibrium constant from the two rate constants gives 2.9 x 107~- ‘. The above mentioned peroxidase oxidation has also been used for a direct estimation of the binding equilibrium constant giving 2.7 x 107~m’. A!1 experiments are carried out at 36°C and pH 7.4.
Bovine serum albumin binds 1 mol bilirubin at a high affinity site, and probably several moles more at weaker sites (1). The primary binding was studied by Blauer and King (a), using ORD. They estimated the binding constant at pH 5 but were not able to establish the co&ant at higher pH values. Wennberg et al. (3) determined the binding constant at pH 8.5 and did not observe gross changes when the pH was lowered to 7.5. The order of magnitude for the constant in his work is 108~-'. Krasner (4) has studied the binding of bilirubin to bovine serum albumin using a dialysis technique; he finds the binding constant 1.5 x 107~-1 at pH around 8. Chen (5) has recently reported the binding constant for serum albumin from a number of different species, among which is the cow. He uses quenching of the albumin fluorescence by bilirubin and obtains the value 2.2 x 107~-’ at 25°C in a phosphate buffer pH 7.4. The rate of association of BSA and bilirubin has been studied by Chen (6), with a stopped-flow technique using quenching of the protein fluorescence and ’ Present address: Aalborg mark.
Sygehus, Aalborg,
Den.
increase of the bilirubin fluorescence. He was not able to follow the primary binding, but described two relaxation steps. In the present work, the second-order rate constant for the association of BSA and bilirubin is determined in a continuous-flow experiment and the rate constant for the dissociation by an enzymatic method. From these two constants an equilibrium constant has been calculated. The equilibrium constant is in addition determined by the peroxidase method previously used for determination of the binding constant for bilirubin and human serum albumin (7). MATERIALS
METHODS
Crystalline bilirubin, horse radish peroxidase, type III, (80% impurities), and bovine serum albumin, fraction V. were all obtained from Sigma. The albumin was not defatted and contained 0.5 mol fatty acid/m01 protein measured by the method of Dole (8). The association process. A solution of bovine serum albumin is mixed with a solution of bilirubin sodium salt in the continuous-flow apparatus shown in Fig. 1. The reaction chamber of the equipment consists of two coaxial pipes, the inner delivering the albumin solution and the outer the bilirubin solution. The inner diameter of the pipes were 4 x 10 3 m and 8.3 x 10m3m, respectively. The flow was delivered by means of two 200 ml syringes giving a total of 23.4 ml/s. the
35i Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
AND
352
FAERCH
AND JACOBSEN
finns to ensure centration of pipe
The end of the inner
pipe
holes for the albumin
solution
W-photometer recorder
FIG. 1. The continuous-flow equipment. The inner pipe can be fixed in twenty positions by means of the measuring rail, the distance between each hole corresponding to 20 ms. The time from mixing to observation is calculated from the volume of the pipe and the flow rate. The flow was adjusted to ensure hydrodynamic turbulence. The mixing process was checked with the colour shift taking place within 1 mm bromthymolblue-base + H+ 4 bromthymolblue-acid, from the mixing point, corresponding to less than 3 ms. Thermostating ensured a temperature of 36°C in the reaction pipe. The equipment was manufactured in the workshop at the Institute of Medical Biochemistry, University of Aarhus. velocity of the reaction solutions being 0.43 m/s. The mixing process was checked by bromthymolblue-base the color shift taking + H+ - bromthymolblue-acid, place within 1 mm from the mixing point, corresponding to less than 3 ms. Thermostating ensured a temperature of 36°C in the reaction pipe. By changing the distance from the mixing point to the detecting point, it is possible to determine the extinction of the mixture in the range from 25 to 200 ms after mixing of the solutions. The extinctions were measured at 474 nm, where the difference in absorption between bound and unbound bilirubin is maximal (Fig. 2). Figure 3 shows the results obtained in a typical experiment. The lower horizontal level indicates the extinctions, E, at various times after mixing, ranging from 70 to 234 ms. The arrow shows the point where the flow was stopped, the absorption then increased to reach the final value, E,,, of the stable complex of bilirubin and albumin. The solid curve shows the experimentally found course of the absorption and the dashed curve is the theoretical course, assuming that there is only one step in the binding process. It is seen that the absorption change takes place in a slower rate than anticipated, indicating that the binding consists of more than one step. The solutions used were: 1.0 g bovine serum albumin or 2.0 g bovine serum albumin in 1500 ml 134 mM phosphate buffer at pH 7.35 (10, respectively 20
PM), and 9 mg bilirubin dissolved in 100 ~1 0.1 N NaOH, diluted to about 1500 ml, adjusted to pH 9.3 with 0.1 N HCl, and finally brought to 1500 ml (10 PM). The exact concentration was calculated from the final extinction in the reaction cuvette. For calculation of the results, the following symbols are used: b current bilirubin concentration b, bilirubin concentration in the mixing point p current albumin concentration p,, albumin concentration in the mixing point c current concentration of the bilirubin-albumin complex c, complex concentration at equilibrium. In a mixture of bilirubin and albumin the sum of bound and unbound bilirubin is constant: b+c=c,
(1)
The extinction measured, E, is the sum of the extinction from the free bilirubin and the extinction from the complex: E = EC + E,. From (I) the following
equation
(11) can be obtained:
RATE A 6x10’ -
CONSTANTS
353
FOR BILIRUBIN-ALBUMIN
Extinction Coefficient
FIG. 2. Photometric properties of bilirubin. Curve B shows the visible part of the spectrum of unbound bilirubin at pH 7.4. Curve C demonstrates the biliruhin spectrum after addition of an equimolar solution of bovine serum albumin. Curve C-B shows the difference between Curve C and B, with a maximum at 474 n. The extinction coefficients used were clsB ,,,,, = 52 x 10’ M cm- 1 for free bilirubin and c462”rn = 57 x lo3 ~-*crn~’ for the final bilirubin: bovine serum albumin complex, as determined by Chen (5). From these numbers the values at 474 nm could be calculated from the spectral curves. Supposing that one molecule of bilirubin associates with one molecule of albumin, p can be expressed by the following equation: p = po ~ (b, - b)
(IV)
pO is known from the weight of albumin dissolved in the starting solution, and b, is calculated from the extinction of the final complex, as the equilibrium concentration of unbound bilirubin is negligible. The rate constant for the second-order reaction can then be calculated from: FIG. 3. Continuous-flow experiment. Eight experiments corresponding to various times after mixing. The lower horizontal part of the curves shows the absorption of the mixture after the indicated time, E. When the flow is stopped (at the point marked by the arrows) the absorption increases to reach its final value, E,,, after lo-15 s. The dashed curve shows the theoretical course, supposing one second-order step, with the rate constant found in this work. all extinctions being taken at 474 nm. Using (Ia) in (II) one gets, as b = E,/c, : b = -.-F--E The nominator in equation (III) is derived from the continuous-flow experiment as the difference between the extinction determined during flow and the final extinction, obtained when a stable level is reached after the flow has been stopped (see Fig. 3). The determination of the denominator is described in Fig. 2.
k, = 3-T) 0
d log (plb)fdt
W)
0
The dissociation process. Unbound bilirubin can be oxidized by hydrogen peroxide with peroxidase as a catalyst (9). The proposed scheme for this reaction is shown in Fig. 4. The system has been used to determine the equilibrium constant for bilirubin-HSA (7). The principle is the following: Peroxidase and H,O, are added to a solution of bilirubin and albumin. The decrease in total bilirubin concentration is registered as a fall in absorption at 460 nm. The concentration of unbound bilirubin, b, is very low compared to the concentration of the complex, c, which means that the total bilirubin concentration is equal to c. From Fig. 4 it can be seen that the decrease in c per minute is proportional to the steady state concentration of b. By suitable choice of peroxidase concentration the oxidation process will be slow compared to the dissociation of the complex; in this case the steady state concentration of b equals the true equilibrium concentration. This is the basis for
354
FAERCH Albumm-Btllrubtn t
-
k-1
Bhrubbln
AND JACOBSEN carried out determined The velocity tional to the experiment, centration, known, and
t Album,” P
kl
iperoxodase)
H2”2
kP H20 4 X
FIG. 4. Scheme for the peroxidase catalyzed oxidation of bilirubin. Free bilirubin is degradated by hydrogen peroxide to a product with little extinction at 460 nm, while the albumin-bound bilirubin is protected against oxidation. the determination of the equilibrium constant, which has been described in more details elsewhere (7, 10, 11). The peroxidase catalyzed oxidation of bilirubin can also be used to determine the dissociation rate constant, k_, ; this has already been done for human serum albumin (12). If the symbols from Fig. 4 are used the following equations are valid: dbldt
= k-, c - k, x p x b - k, x b x [HFW]. (VI)
If steady-state condition is assumed, dbldt In this case (VI) can be rewritten to:
= 0.
km, x c = b x (k, x p + k, x [HRP]). As already stated the decrease in total bilirubin concentration per second u, is proportional to the concentration of unbound bilirubin, b:
in a cuvette and the degradation rate as the decrease in absorption at 440 nm. of the degradation of bilirubin is proporconcentration of bilirubin in the standard b,, , and the equivalent peroxidase con[HRP],,; both these concentrations are k, is calculated from: V 81 =
k, x b,, WRPI,,.
Determination of the binding equilibrium constant by peroxidase oxidation. The constant for bilirubin and human serum albumin has previously been determined by this method (7). The principle of the method is mentioned under the dissociation process and in Fig. 4. A series of experiments were carried out with constant bilirubin concentration, around 10 x 1Om6M, and varying concentrations of bovine serum albumin, resulting in a number of bilirubin/albumin ratios, ranging from 0.25 to 0.95, 67 mM phosphate buffer, pH 7.4 and 37°C were used. The oxidation velocity was measured and the concentration of unbound bilirubin calculated as described previously (10, 11). The results were plotted according to Scatchard (13) and the binding constant determined from the intercept on the ordinate. RESULTS
The results of the continuous-flow experiments are given in Table I. Three determinations were made with 5 PM bovine serum u = k, x b x [HRP], (VII) albumin and seven with an albumin concentration of 10 PM. In both cases the biliconsequently rubin concentration was 5 PM. The valk,xpxu +v ues for the association constant, k,, show (VIII) k-, = cxk,x [HRP] c’ approximately normal distribution. The algebraic mean and the error of the mean By rearrangement we obtain: was calculated as for a normal distribu1 1 k, XP tion. -=1 ___ (IX) +-. k-, x c V c x k, x k-, X(HRP] In Fig. 5 the results of the determinations of the oxidation velocities for differFrom the last equation it can be seen that a plot of l/u ent concentrations of peroxidase are plotvs l/[HRP] should give a straight line with an intercept on the ordinate which contains kk, as the ted according to equation (IX). The intercept on the ordinate is 1.96 x lo6 S.M-i; as only unknown parameter. the total bilirubin concentration, which The circumstances for determining the oxidation velocity, u, were the following: To a lo-mm cuvette equals the complex concentration, c, is 16.5 with 3.00 ml phosphate buffer, pH 7.4, containing 30.0 x lo- 6~, k _ 1is calculated to 3.1 x lo- 2 s- I. PM bovine serum albumin, 16.5 pM bilirubin, and 300 As described in the method section the PM H,O, small amounts of horse radish peroxidase slope of the line in Fig. 5 can be used to (HRP) was added to final concentrations ranging from estimate the association rate constant, k, , 0.8 to 160 nM. The velocity was registered as a from k-, and k,. The value of k- 1 has decrease in absorption at 460 nm. already been given and k, , determined as The slope of the line in Fig. 5 can be used for an described previously, is 2.2 x lo8 M-i s-i. additional estimation of k, , as k, can be determined The slope is 6.7 x 10m2s, p is 13.5 x 1O-6 M, from the following standard experiment: Bilirubin was oxidized by H,O, and peroxidase in and c, 16.5 x 10e6 M, which gives k, = 0.5 the absence of albumin (10). The oxidation was x 10s M- 1 s- 1 in good agreement with the
RATE
CONSTANTS
355
FOR BILIRUBIN-ALBUMIN
A LO-
1 .106 M'..,' v
30.
20.
1 [perwdase] , 25
I 50
/
FIG. 5. Plot l/u vs l/[HRP] according to equation IX. Results from experiment. The concentrations of bilirubin and bovine serum albumin were 16.5 x 1Om6M and 30.0 x 10m6 M, respectively. v was determined absorption at 460 rim/s. The correlation factor, 0.996, the intercept on the 10’ M- ‘s ‘, and the slope, 6.7 f 0.1 x lo- * se 1 were determined by linear the calculation of k - , and k ,. TABLE
.107 f"14
a peroxidase oxidation in the reaction mixture from the decrease in ordinate, 1.96 * 0.35 x regression. See text for
I
RESULTS OF CONTINUOUS-FLOW EXPERIMENTS Inital albumin concentration @,) (FM) 5.16 5.16 5.16 10.32 10.32 10.32 10.32 10.32 10.32
Extinction of complex at equilibrium at 474 nm (E,,)
0.252 0.252 0.204 0.271 0.278 0.280 0.280 0.336 0.336
0 k, = (0.9 * 0.55) lo8 M~‘s-’
1.5 0.59 2.0 0.69 0.82 1.14 0.79 0.15 0.26
Association rate constant (k I)n (M-k’) x x x x x x x x x
(Mean
106 106 10’ lo6 lo6 106 10’ 106 lo6 * SD).
result obtained by the continuous-flow experiment. The binding equilibrium constant for bilirubin and bovine serum albumin was calculated from k, , determined by continuous-flow, and k _ , , obtained from a peroxidase oxidation experiment, k l/k- 1 = K. The value is 2.9 x lo7 M-i. The peroxidase method may also be used to determine the binding constant directly if the enzyme concentration is kept relatively low (Fig. 4). Figure 6 shows a Scatchard’s plot derived from a series of peroxidase determinations. The intercept on the
FIG. 6. Determination of the binding constant from a Scatchard’s plot. Unbound bilirubin was determined by the peroxidase technique at different ratios bilirubin/albumin (=r). The intercept on the abscissa indicates the number of binding sites, n, and the intercept on the ordinate equals n x K,,,. The binding constant is 2.7 x 10’ M-‘.
abscissa indicates that one bilirubin molecule is bound to bovine serum albumin at a high affinity site, and the intercept at the ordinate determines the binding constant, which is 2.7 x lOI M-l in good agreement
356
FAERCH
AND JACOBSEN
with the value obtained from the two rate constants. DISCUSSION
The time course of the change of the bilirubin absorption spectrum during the binding to bovine serum albumin was shown to be a second-order reaction as seen from Fig. 7 and from the observation that t, for the process is highly dependent the concentration. The kinetic of the reaction indicates that we have studied the first step in the binding process. The rate of the primary binding must be dependent of both the bilirubin and the albumin concentration in agreement with the findings. As can be seen from Fig. 3 the rate of the increase in absorption is slower than predicted from the second-order reaction. This means that at least one secondary relaxation step takes place after bilirubin has been bound to albumin. No quantitative estimation has been done on this slow step. The rate of the dissociation of bilirubin from albumin should preferably also have been studied by the continuous-flow method, this could theoretically be done by dilution of a bilirubin-albumin solution. Due to the high affinity of albumin for bilirubin such experiments give very minute differences in absorption, below the sensitivity of our instrument. It was therefore necessary to determine k _ 1by another technique. By the peroxidase method used we also were able to estimate k 1to compare
ACKNOWLEDGMENTS The authors wish to thank Professor R. F. Chen for sending prepublication information and Professor R. Brodersen for helpful discussion during the work. The skilful technical assistance of Eva Korsgaard is acknowledged. Thanks are also due to Ove S$nderskov for making the continuous-flow apparatus and to Frede Nielsen for the drawings.
7‘
logP/b1 006 i
yoi_ 002
with the value obtained from the continuous-flow experiment. As the binding process proceeds in more than one step the binding constant should be calculated from the product of the association rate constants divided by the product of the dissociation rate constants. In spite of that and of the use of different methods we find good agreement between the binding constant calculated from the two rate constants, 2.9 x 10’ M-l, and the equivalent figure determined by the peroxidase method, 2.7 x lo7 M-'. The value for the binding constant is further supported by the work of Chen (5), who gets 2.2 x 10’ M-l at 25” C and pH 7.4, and by Krasner (4), who obtains 1.5 x 10’ M-l under slightly different circumstances. Chen (6) has used stopped-flow measurements of the fluorescence of bilirubin and albumin to study the binding process; he finds two first-order reactions, but he is not able to follow any second-order process. The first-order reactions may be equivalent to the secondary change in absorbance we observed (Fig. 3). It remains, however, unexplained why Chen’s results do not show the initial second-order reaction, although the experimental conditions are similar in the two investigations, except that the albumin we have used contains fatty acid, while Chen has defatted the albumin prior to use.
/
FIG. 7. Log (p/b) = f(t). The figure shows the linear dependence of log (albumin/bilirubin) with time. This indicates second-order kinetic. See text for details.
REFERENCES 1. WENNBERG, R. P. (1971) Proc. Sot. Ped. Res. Atlantic City, N.J. 2. BLAUER, G., AND KING, T. E. (197O)J. Clin. Chem. 245, 372-381. 3. WENNBERG, R. P., AND COWGER, M. L. (1973) Clin. Chem. Acta. 43, 55-64. 4. KRASNER, J., GIACOIA, G. P., AND YAFFE, S. J. (1973) Ann. NY Acad. Sci. 226, 101-114. 5. CHEN, R. F. (1973) in Fluorescence Technique in
RATE CONSTANTS
FOR BILIRUBIN-ALBUMIN
Cell Biology (Thaer, A. and Sernetz, M. eds.), pp. 239-248, Springer Verlag, New York. 6. CHEN, R. F. (1974) Arch. Biochem. Biophys. 160, 106-112. 7. JACOBSEN,J. (1969) Fed. Eur. Biochem. Sot. Lett. 5, 112-114. 8. DOLE, V. P. (1956) J. Clin. Inuest. 35, 150-154. 9. BRODERSEN, R., AND BARTELS, P. (1969) Eur. J. Biochem. 10, 468-473.
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10. JACOBSEN, J., AND FEDDERS, 0. (1970) Stand. Journ. Clin. Lab. Inoest. 26, 237-241. 11. JACOBSEN, J., AND WENNBERG, R. P. (1974) Clin. Chem. 20, 783-789. 12. BRODERSEN, R. (1974) J. Clin. Inuest. 54, 1353-1364. 13. SCHATCHARD, G., COLEMANN, J. S., AND SHEN, J. (1957) J. Amer. Chem. Sot. 79, 12-21.
