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Direct determination of the stoichiometry of charge transfer complexes
416
Biochimica et Biophysica Acta, 421 (1976) 416--419 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA Report BBA 21420
DIRECT DETERMINATION OF THE STOICHIOMETRY OF CHARGE T R A N S F E R COMPLEXES
DAVID C. TELLER* and DAVID A. D E R A N L E A U
Department of Biochemistry, University of Washington, Seattle, Wash. 98195 (U.S.A.) (Received October 13th, 1975)
Summary The stoichiometry of the charge transfer complex between N-acetyl-Ltryptophan and 1-methylnicotinamide chloride has been determined to be precisely 1:1 by direct measurement of the molecular weight of the complex. The result is of interest both in terms of a general method for determining the stoichiometry of charge transfer complexes, and in terms of the probable stoichiometry of specific charge transfer complexes between 1-methylnicotinamide chloride and the exposed t r y p t o p h y l side chains of certain proteins. In the latter case, the result provides experimental p r o o f for the assignment of extinction coefficients of specified magnitudes to the homomorphic model complexes which serve as the basis for the interpretation of results with proteins.
One of the key problems in using model c o m p o u n d s to assess the interaction o f light-absorbing probes with proteins and nucleic acids is the assignment of the correct stoichiometry to the model c o m p o u n d interaction. While many investigators have assumed a particular stoichiometry to explain their data, it can be shown that in general, it is not possible to uniquely determine the number of b o u n d molecules when an indirect method such as the absorbance of light is used to estimate the extent of the interaction [1 ]. This is particularly important in the case of charge transfer int, eractions with proteins, where the equilibrium constants k and the extinction coefficients e of a number of homomorphic models are used to estimate the exposure and relative surface geometry of aromatic side chains [2--4]. In the usual methods of analysis of charge transfer complexes, numerical estimates of k and e are obtained by fitting absorbance data to one of a number of straight line plots [5]. Generally speaking, the equations on which *To w h o m inquiries should be addressed.
417
these plots are based have been derived on the basis of 1:1 stoichiometry, and are therefore not applicable to higher order complexes. On the other hand, it has been pointed o u t that curved lines can be obtained from higher order complexes which are experimentally indistinguishable from straight lines in some cases, and that in the limit of very small or very large saturation fractions, straight lines will be obtained as a necessary condition in higher order complexation [6]. The problems of curve~fitting for multiple complexes can be made readily apparent by considering a complex in which n equivalent and independant binding sites exist on a donor D, each site having the same intrinsic association constant and extinction coefficient by definition. The observation equation for this system is [1] where A is the A/[D0 ] = n k e [ X ] / ( 1 + h [ X ] )
(1)
absorbance, [Do ] the total donor concentration (constant), and IX] is the free acceptor concentration (variable). Although h can usually be determined unambiguously from the slope and intercept of any of the straight-line forms of Eq. 1, it is clear that e cannot be uniquely obtained because only two parameters (slope and intercept) are available to fit an equation containing three unknowns. This situation occurs whenever an indirect method in which the molecules are not counted is employed to determine the constants (light absorbance or emission, NMR, ESR, etc., [1] ). The molecular weights of charge transfer complexes can be determined accurately by taking advantage of the fact that only the complex absorbs light in the charge transfer portion of the absorbance spectrum. The absorption scanning system of the analytical ultracentrifuge can thus be used in the appropriate wavelength region to obtain unambiguous molecular weights for complexes in which the donor and the acceptor are about the same size. Sedimentation equilibrium experiments were performed in a Beckman Model E Analytical Ultracentrifuge equipped with electronic speed control and absorbance scanning system. The scanning system was modified in such a fashion that graphs of absorbance vs. radial distance could be recorded directly on an XY plotter [7]. The experiments reported here were performed at 52000 rev./min and 20°C. The solvent sector of the double sector centrifuge centerpieces contained only 1-methylnicotinamide chloride (acceptor), while the solution sector contained the same concentration of the acceptor and 10- 3 M N-acetyl-L-tryptophan (donor). The partial specific volume of the acceptor was measured pycnometrically to be 0.727 +- 0.004 ml/g, and the partial specific volume of the donor was calculated from its atomic composition to be 0.726 ml/g [8]. The partial specific volume of the tryptophannicotinamide complex was taken as 0.727 ml/g. The charge transfer absorbance was monitored at 364 nm, using long solution columns to increase the concentration gradient. Fig. 1 shows the charge transfer absorbance as a function of radial distance for three samples. Graphs of the log absorbance vs. the square of the radial distance were essentially linear but calculation of point-by-point weight average molecular weights indicated slight non-ideality. The values of 1/Mw, r were plotted as a function of the absorbance for each sample and extrapolated to zero absorbance using linear least squares analysis
418
: -
~- I~---TTT-F-T "
,
.....
lilF:
,,,,,tttt
1
_~-
_L.
--- .... " . . . . •
-~
' ....
x .......
/ !-' -a!
-~-.
:
. . . .
:-'
"
-T-
......." :
__1
.
-~--im
I. i1 ...
IlL
--":
...... i - - ~-uo _
......
I
........
!
.
. I
t R,R
!
! l|
11 . _ _ J
t ROR Radial
Distance
F i g . l . C h a r g e t r a n s f e r a b s o r b a n c e profiles at s e d i m e n t a t i o n e q u i l l b r i u m in t h e a n a l y t i c a l u l t r a c e n t r i f u g e . T h r e e s a m p l e s w e r e c e n t r i f u g e d at 52 7 6 2 r e v . / m i n f o r 2 0 2 6 rain. T h e c o n c e n t r a t i o n o f N - a c e t y l - L t r y p t o p h a n was 10 - 3 M. T h e m o l a r i t i e s of N - m e t h y l - n i c o t i n a m i d e w e r e 1 . 0 0 , 0 . 2 4 a n d 0 . 0 8 M for t h e t h r e e samples.
of the data. The weight average molecular weight calculated in this manner [ 7 ] was 420 + 26 g/mol, Because of the substantial pressure due to long columns and high speeds as well as a considerable density gradient of N-methylnicotinamide chloride, a second type of calculation was made. The solution density was calculated at each radial position using the compressibility of water and the redistribution N-methylnicotinamide chloride. The mass-average weight average molecular weight was then evaluated from the point-by-point molecular weights. A graph of 1/Mw,app vs. (Cb + Cm )/2 was extrapolated to C=O as shown in Fig. 2 for 5 samples. The molecular weight evaluated in this way was 394 -+ 21 g/mol. The experimental molecular weight obtained by either method is in good agreement with the molecular weight calculated by assuming the complex is composed of a single molecule each of both donor and acceptor viz., 418.92 g/mol. Thus the association constant and extinction coefficient for this o3°1
............
'
-
'
I 0
0
.~c~u o 2 ~ - ~ o
0'2~
................ O 1 AOSOr',bor~r..e
0
oo
~ 2
]
~ 3
....
: 4
'
(Graph , n o n e s )
Fig.2. R e c i p r o c a l a p p a r e n t w e i g h t - a v e r a g e m o l e c u l a r w e i g h t s g r a p h e d as a f u n c t i o n o f a b s o r b a n c e . T h e abcissa was t a k e n as t h e m e a n of t h e a b s o r b a n c e of t h e first a n d last d a t a points. T h e e q u a t i o n of t h e straight line is lO0/Mw,ap p = ( 0 . 2 5 4 ± 0 . 0 1 3 ) + ( 0 . 0 0 4 4" 0 . 0 0 5 ) A 3 ~ .
419
system can be unambiguously obtained from the charge transfer titration data by setting n = 1 in eq. 1. The relevant charge transfer parameters (k, e) obtained under this condition are presented elsewhere [2]. The stoichiometries of a small number of crystalline intermolecular charge transfer complexes have previously been obtained from the composition of the crystals [ 5 ] . As near as we are aware, the present result is the first independent measurement of the stoichiometry of an organic charge transfer complex which does not depend on the obtention of suitable crystals. In addition, it forms the specific basis for the assignment of accurate extinction coefficients to model complexes involving the aromatic side chain of tryptophan and the 1-methylnicotinamide positive ion. The properties of such homomorphic complexes are the basis for the interpretation of similar charge transfer studies of proteins in solution. Supported b y NSF grant GB 18016 and NIH grant GM 13401. References 1 2 3 4 5
D e r a n i e a u , D . A . (19"/5) J. A m e r . C h e m . Soc. 9"/, 1 2 1 8 - - 1 2 2 4 H i n m a n , L.M., C o a n , C . R . a n d D e r a n i e a u , D . A . (19"/4) J. A m e r . C h e m . Soc. 9 6 , "/06"/--"/0"/3 D e r a n i e a u , D . A . , H i n m a n , L.M. a n d C o a n , C . R . ( 1 9 7 5 ) J. Mol. Biol. 9 4 , 5 6 7 - - 5 8 2 C o a n , C . R . , H i n m a n , L.M. a n d D e r a n l e a u , D . A . (19"/5) B i o c h e m i s t r y , in t h e p r e s s See f o r e x a m p l e Brlegleb, G. ( 1 9 6 1 ) E l e c t r o n e n - D o n a t o r - A c c e p t o r - K o m p l e x e , S p r i n g e r - V e r l a g , Berlin, o r F o s t e r , R. ( 1 9 6 9 ) " O r g a n i c C h a r g e T r a n s f e r C o m p l e x e s " , A c a d e m i c Press, N e w Y o r k 6 D e r a n i e a u , D . A . ( 1 9 6 9 ) J. A m e r . C h e m . Soc. 9 1 , 4 0 5 0 - - 4 0 5 4 "/ Teller, D.C. ( 1 9 " / 3 ) M e t h o d s E n z y m o l . 2 7 D , 3 4 6 - - 4 4 1 8 C o h n , E.J. a n d Edsall, J . T . ( 1 9 4 3 ) P r o t e i n s , A m i n o A c i d s a n d P e p t i d e s , R e i n h o l d , N e w Y o r k
Biochimica et Biophysica Acta, 421 (1976) 416--419 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA Report BBA 21420
DIRECT DETERMINATION OF THE STOICHIOMETRY OF CHARGE T R A N S F E R COMPLEXES
DAVID C. TELLER* and DAVID A. D E R A N L E A U
Department of Biochemistry, University of Washington, Seattle, Wash. 98195 (U.S.A.) (Received October 13th, 1975)
Summary The stoichiometry of the charge transfer complex between N-acetyl-Ltryptophan and 1-methylnicotinamide chloride has been determined to be precisely 1:1 by direct measurement of the molecular weight of the complex. The result is of interest both in terms of a general method for determining the stoichiometry of charge transfer complexes, and in terms of the probable stoichiometry of specific charge transfer complexes between 1-methylnicotinamide chloride and the exposed t r y p t o p h y l side chains of certain proteins. In the latter case, the result provides experimental p r o o f for the assignment of extinction coefficients of specified magnitudes to the homomorphic model complexes which serve as the basis for the interpretation of results with proteins.
One of the key problems in using model c o m p o u n d s to assess the interaction o f light-absorbing probes with proteins and nucleic acids is the assignment of the correct stoichiometry to the model c o m p o u n d interaction. While many investigators have assumed a particular stoichiometry to explain their data, it can be shown that in general, it is not possible to uniquely determine the number of b o u n d molecules when an indirect method such as the absorbance of light is used to estimate the extent of the interaction [1 ]. This is particularly important in the case of charge transfer int, eractions with proteins, where the equilibrium constants k and the extinction coefficients e of a number of homomorphic models are used to estimate the exposure and relative surface geometry of aromatic side chains [2--4]. In the usual methods of analysis of charge transfer complexes, numerical estimates of k and e are obtained by fitting absorbance data to one of a number of straight line plots [5]. Generally speaking, the equations on which *To w h o m inquiries should be addressed.
417
these plots are based have been derived on the basis of 1:1 stoichiometry, and are therefore not applicable to higher order complexes. On the other hand, it has been pointed o u t that curved lines can be obtained from higher order complexes which are experimentally indistinguishable from straight lines in some cases, and that in the limit of very small or very large saturation fractions, straight lines will be obtained as a necessary condition in higher order complexation [6]. The problems of curve~fitting for multiple complexes can be made readily apparent by considering a complex in which n equivalent and independant binding sites exist on a donor D, each site having the same intrinsic association constant and extinction coefficient by definition. The observation equation for this system is [1] where A is the A/[D0 ] = n k e [ X ] / ( 1 + h [ X ] )
(1)
absorbance, [Do ] the total donor concentration (constant), and IX] is the free acceptor concentration (variable). Although h can usually be determined unambiguously from the slope and intercept of any of the straight-line forms of Eq. 1, it is clear that e cannot be uniquely obtained because only two parameters (slope and intercept) are available to fit an equation containing three unknowns. This situation occurs whenever an indirect method in which the molecules are not counted is employed to determine the constants (light absorbance or emission, NMR, ESR, etc., [1] ). The molecular weights of charge transfer complexes can be determined accurately by taking advantage of the fact that only the complex absorbs light in the charge transfer portion of the absorbance spectrum. The absorption scanning system of the analytical ultracentrifuge can thus be used in the appropriate wavelength region to obtain unambiguous molecular weights for complexes in which the donor and the acceptor are about the same size. Sedimentation equilibrium experiments were performed in a Beckman Model E Analytical Ultracentrifuge equipped with electronic speed control and absorbance scanning system. The scanning system was modified in such a fashion that graphs of absorbance vs. radial distance could be recorded directly on an XY plotter [7]. The experiments reported here were performed at 52000 rev./min and 20°C. The solvent sector of the double sector centrifuge centerpieces contained only 1-methylnicotinamide chloride (acceptor), while the solution sector contained the same concentration of the acceptor and 10- 3 M N-acetyl-L-tryptophan (donor). The partial specific volume of the acceptor was measured pycnometrically to be 0.727 +- 0.004 ml/g, and the partial specific volume of the donor was calculated from its atomic composition to be 0.726 ml/g [8]. The partial specific volume of the tryptophannicotinamide complex was taken as 0.727 ml/g. The charge transfer absorbance was monitored at 364 nm, using long solution columns to increase the concentration gradient. Fig. 1 shows the charge transfer absorbance as a function of radial distance for three samples. Graphs of the log absorbance vs. the square of the radial distance were essentially linear but calculation of point-by-point weight average molecular weights indicated slight non-ideality. The values of 1/Mw, r were plotted as a function of the absorbance for each sample and extrapolated to zero absorbance using linear least squares analysis
418
: -
~- I~---TTT-F-T "
,
.....
lilF:
,,,,,tttt
1
_~-
_L.
--- .... " . . . . •
-~
' ....
x .......
/ !-' -a!
-~-.
:
. . . .
:-'
"
-T-
......." :
__1
.
-~--im
I. i1 ...
IlL
--":
...... i - - ~-uo _
......
I
........
!
.
. I
t R,R
!
! l|
11 . _ _ J
t ROR Radial
Distance
F i g . l . C h a r g e t r a n s f e r a b s o r b a n c e profiles at s e d i m e n t a t i o n e q u i l l b r i u m in t h e a n a l y t i c a l u l t r a c e n t r i f u g e . T h r e e s a m p l e s w e r e c e n t r i f u g e d at 52 7 6 2 r e v . / m i n f o r 2 0 2 6 rain. T h e c o n c e n t r a t i o n o f N - a c e t y l - L t r y p t o p h a n was 10 - 3 M. T h e m o l a r i t i e s of N - m e t h y l - n i c o t i n a m i d e w e r e 1 . 0 0 , 0 . 2 4 a n d 0 . 0 8 M for t h e t h r e e samples.
of the data. The weight average molecular weight calculated in this manner [ 7 ] was 420 + 26 g/mol, Because of the substantial pressure due to long columns and high speeds as well as a considerable density gradient of N-methylnicotinamide chloride, a second type of calculation was made. The solution density was calculated at each radial position using the compressibility of water and the redistribution N-methylnicotinamide chloride. The mass-average weight average molecular weight was then evaluated from the point-by-point molecular weights. A graph of 1/Mw,app vs. (Cb + Cm )/2 was extrapolated to C=O as shown in Fig. 2 for 5 samples. The molecular weight evaluated in this way was 394 -+ 21 g/mol. The experimental molecular weight obtained by either method is in good agreement with the molecular weight calculated by assuming the complex is composed of a single molecule each of both donor and acceptor viz., 418.92 g/mol. Thus the association constant and extinction coefficient for this o3°1
............
'
-
'
I 0
0
.~c~u o 2 ~ - ~ o
0'2~
................ O 1 AOSOr',bor~r..e
0
oo
~ 2
]
~ 3
....
: 4
'
(Graph , n o n e s )
Fig.2. R e c i p r o c a l a p p a r e n t w e i g h t - a v e r a g e m o l e c u l a r w e i g h t s g r a p h e d as a f u n c t i o n o f a b s o r b a n c e . T h e abcissa was t a k e n as t h e m e a n of t h e a b s o r b a n c e of t h e first a n d last d a t a points. T h e e q u a t i o n of t h e straight line is lO0/Mw,ap p = ( 0 . 2 5 4 ± 0 . 0 1 3 ) + ( 0 . 0 0 4 4" 0 . 0 0 5 ) A 3 ~ .
419
system can be unambiguously obtained from the charge transfer titration data by setting n = 1 in eq. 1. The relevant charge transfer parameters (k, e) obtained under this condition are presented elsewhere [2]. The stoichiometries of a small number of crystalline intermolecular charge transfer complexes have previously been obtained from the composition of the crystals [ 5 ] . As near as we are aware, the present result is the first independent measurement of the stoichiometry of an organic charge transfer complex which does not depend on the obtention of suitable crystals. In addition, it forms the specific basis for the assignment of accurate extinction coefficients to model complexes involving the aromatic side chain of tryptophan and the 1-methylnicotinamide positive ion. The properties of such homomorphic complexes are the basis for the interpretation of similar charge transfer studies of proteins in solution. Supported b y NSF grant GB 18016 and NIH grant GM 13401. References 1 2 3 4 5
D e r a n i e a u , D . A . (19"/5) J. A m e r . C h e m . Soc. 9"/, 1 2 1 8 - - 1 2 2 4 H i n m a n , L.M., C o a n , C . R . a n d D e r a n i e a u , D . A . (19"/4) J. A m e r . C h e m . Soc. 9 6 , "/06"/--"/0"/3 D e r a n i e a u , D . A . , H i n m a n , L.M. a n d C o a n , C . R . ( 1 9 7 5 ) J. Mol. Biol. 9 4 , 5 6 7 - - 5 8 2 C o a n , C . R . , H i n m a n , L.M. a n d D e r a n l e a u , D . A . (19"/5) B i o c h e m i s t r y , in t h e p r e s s See f o r e x a m p l e Brlegleb, G. ( 1 9 6 1 ) E l e c t r o n e n - D o n a t o r - A c c e p t o r - K o m p l e x e , S p r i n g e r - V e r l a g , Berlin, o r F o s t e r , R. ( 1 9 6 9 ) " O r g a n i c C h a r g e T r a n s f e r C o m p l e x e s " , A c a d e m i c Press, N e w Y o r k 6 D e r a n i e a u , D . A . ( 1 9 6 9 ) J. A m e r . C h e m . Soc. 9 1 , 4 0 5 0 - - 4 0 5 4 "/ Teller, D.C. ( 1 9 " / 3 ) M e t h o d s E n z y m o l . 2 7 D , 3 4 6 - - 4 4 1 8 C o h n , E.J. a n d Edsall, J . T . ( 1 9 4 3 ) P r o t e i n s , A m i n o A c i d s a n d P e p t i d e s , R e i n h o l d , N e w Y o r k