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Spectrophotometric studies of the quaternary structure of proteins
ARCHIVES
OF
BIOCHEMISTRY
Spectrophotometric
AND
BIOPHYSICS
Studies
1. Method HARVEY The Edsel B. Ford Institute
217-221 (1965)
110,
of the Quaternary
of Concentration-Difference F. FISHER2 for Medical Received
AND
Research, December
of Proteins’
Spectra
DALLAS Henry
Structure
G. CROSS
Ford Hospital,
Detroit,
Michigan
9, 1964
A method is presented for determining effects of concentration-dependent structural changes on environment of chromophoric residues of proteins. The theory for t,his technique of “concentration-difference spectra” is developed; t,he experimental methods required for application of that theory are described, and the theoretical effect.s of certain important experimental errors are considered. An experimental crit.erion for establishing the validity of a concentration-difference spectrum is proposed. Examples of application of the t,heory, method, and validity criterion to a dissociable protein system are demonstrated.
The various conformational kansitions undergone by protein molecules are frequemly classified as changes in secondary or tertiary structure (7). In addition to these changes, many protein molecules are capable of dissociat’ing into subunits, a process sometimes referred to as a change in quat’ernary structure (1). The quaternary structure of proteins has recently been reviewed by Reit’hel (10). The technique of ultraviolet)-difference spectroscopy has been employed extensively in studying the nature of all of t’hese processes (12). Certain proteins undergo specific association and dissociation react,ions under condit’ions where t,he only variable parameter is the concentration of the protein it’self. Examples of such systems are chymotrypsin (13) ; insulin (8) ; glutamic dehydrogenase (9) ; trypsin (2) ; hemoglobin (3) ; and hexokinase (11). The applicat#ion of the technique of ultraviolet-difference spec1 This investigation was supported in part by research grants from the National Institutes of Health (grant GM 05638-05) and the National Science Foundation (grant G 18628). z Present address: Veterans Administration Hospit,al, 4801 Linwood Boulevard, Kansas City, Missouri and University of Kansas School of Medicine, Department of Biochemistry, 39th and Rainbow Boulevard, Kansas City 12, Kansas. 217
tra t’o such concentrat’ion-dependent’ systems requires some extension of the technique. The t’heory and experimental procedure for such a method, together wit#h a consideration of, and criteria for, cert’ain important experimental errors, are described below. The application of t’his method to tfhe study of a concentratjion-dependent dissociation of a specific protein are described in an accompanying paper (4). THEORY
We define a “concentration-difference spectrum” as one between identical total weights of a protein in sample and reference cuvettes of identical cross-sectional area but different optical pathlengths, each filled with the same solvent, so t,hat#: C&8 = crb, ,
(1)
where c = protein concentration in mg/ml, and b = length of the optical path for the sample and reference cuvettes, respectively. Thus the two systems differ only in protein concentration and t’he resulting difference speckurn (corrected for solvent absorption) will reflect only those chromophore perturbations which are caused by changes in protein concentration.
218
FISHER
AND
FIG. 1. Scheme of experimental arrangement for concentration-difference spectra. [p] represents the protein concentration. Other symbols are described in the text.
The fundamental equation for concentration-difference spectra follows : Let AA(X) = A(X)
- AvO),
(2)
A-@(X) = Es(X) - E,(A),
(3)
where A is the absorbancy, and E is the extinction coefficient; and s and r refer to sample and reference cells, respectively. Then AA(X) = E,(X)c,b, - E,(X)c,b, .
(4)
Combining Eqs. (1) and (4), and using the definition of Eq. (3), we obtain:
AA(h) ~ cs b,
= AE(X).
This is the fundamental equation concentration-difference spectrum.
(5) for a
TECHNIQUE
The experimental application of Eq. (5) can be conveniently discussed with reference to the schematic diagram shown in Fig. 1; the dotted lines should be disregarded for the moment. The shorter cell is used as the sample cell in a spectrophotometer, and is filled with a solution of protein in a suitable solvent. The longer cell, used as a reference cell, is filled with a solution of protein in the same solvent but at a concentration calculated from the equation: G = dhlb,
,
03)
which follows from Eq. (1) defining a concentration-diff erence spectrum. The differ-
CROSS
ence spectrum is then measured over the desired wavelength range. The difference spectrum of t’he same two cells in the same positions, containing solvent alone, is subtracted. Alternatively, a pair of matched tandem, partitioned cells may be employed as indicated by the dotted lines in Fig. 1. In this case the sample cell contains protein solut’ion in the solid line (left-hand) portion of the cell, while the dotted line (right-hand) portion is filled with solvent alone. Bot’h portions of the reference cell are filled with a protein solution diluted as indicated above. In either case the resulting concentrationdifference spectrum must be corrected for the differential protein light-scatter by some method such as that of Leach and Scheraga (fS3 The assignment of sample and reference cells shown here will produce a positive difference spectrum if a blue shift is produced by dilution. EFFECT
OF CONCENTRATION
ERRORS
Since AE represents a small difference between two large numbers, small deviations from the equality expressed by Eq. (1) will cause very large errors in the concentrationdifference spectrum. However, such errors, and AE itself, have quite different dependencies upon protein concentration; these differences, as discussed below, enable us to distinguish between them. While the following treatment is applicable to conventional difference spectroscopy (in which b, = b, and c, = c,), it becomes important primarily in concentration-difference spectra which are in general of an even smaller order of magnitude. Consider the case of a very small error in protein concentration, so that c8bs # crbr . 3 While the scatter-correction method of Leach and Scheraga (6) is the best procedure now available, it is generally agreed that it is not strictly accurate. Since the inaccuracies become more pronounced at shorter wave-lengths, they constitute the limiting factor in the interpretation of difference spectra low values of AE, such as concentration-difference spectra. A discussion of scattercorrections, together with a method of estimation of their contribution to difference spectra, will appear in a later paper in this series.
SPECTROPHOTOMETRIC
STUDIES
Assume first that: (7) Then, c, may be considered as the sum of two equal to concentrations : one, exactly (c&,)/b, , and a second term representing the small excess concentration: (8) where lie, (< cs. The differential written as
absorbancy
AA(X)
+
= E,(X)[c,b,
can now be
b&,1 -
E,(OG,
.
(9)
After rearranging terms and using the definition in Eq. (3), we obtain: AA(k)
=
AE(X)c,b, + E,(X)Gc,b, .
(10)
Returning to t’he initial assumption in Eq. (7), it is clear that we can equally well make the opposite assumption, that C*<--,
cr b, b,
(11)
whence Eq. (8) can now be rewritten as: cr b, c, = - 6c,. b,
(12)
Since this assumption produces only a change in sign of 6c, , we obt’ain an equation ident’ical t,o Eq. (10) except that the sign of the term containing 6c, is reversed. Removing the restrictions imposed by Eqs. (7) and (II), we can now write the equation for t)he general case :4 AA(h)
= AE(X)c,b, zt E,(X)Gc,b, .
Since AE << E, , and&<<
(13)
/c8 - c, /,itcan
4 Difference spectra must, by their nature, be smaller than the actual spectra from which they are derived. Concentration-difference spectra generally may be expected to be much smaller than conventional difference spectra. Therefore even a very small 6c will produce a very large change in AE and will be easily recognizable. For the same reasons, the effect of using either E, or E, in the &-containing term of Eq. (13) will be immeasurably small.
OF PROTEIN
STRUCTURE.
I
219
be seen that if we start with the system as specified in Eq. (11) and gradually increase c, , the true difference spectrum will change only very slightly, and always in the direction of increasing the absolute value of the optical density difference; while the absolute value of that contribution to the absorption caused by the imbalance of protein concentrations will change by a very large amount, and will, in fact, first decrease to the base line and t’hen event,ually change its sign. [That contribut,ion to a concentration-difference spectrum caused by scattered light will, for the general case considered here, also consist of two terms: t,he first, consisting of the true concentration-dependent difference in scatter, will remain constant in sign with small changes in protein concentration; while the second, consisting of the scatter of the amount. of protein corresponding to 6c, will behave as t,he corresponding absorption term containing 6c, and may carry eit*her sign. Fluorescence will cont,ribute to the spectrum in the same manner as does scattered light, that is, it too will consist of two terms. In order to determine the relative magnitude of such effects, both scat,tered and fluorescent light was monitored by installing a photomultiplier tube conrlected to a sensitive microphotometer in such a position t,hat it would receive scatt’ered light (or fluorescence) at 90” to the optical axis. The magnitude of the fluorescence was found to be very much smaller than bhe scatt’ered light, and can therefore, at least’ for t,he present experiments, be neglected. While in principle t,he amount of fluorescence and scat’tered light received by the phototubes of the spectrophotometer should be a function of the distance of the protein solution from t,he phototube, in practice this effect does not occur either with the Cary 11 or with t,he Cary 14 instruments. This was demonstrat’ed by placing a cuvet,te containing a solution of Ludox in the cell compartment at various dist’ances from the phototube. No change! in optical density was observed.] This relationship provides an important and useful criterion for determining whether various small peaks in a concentration-difference spectrum are due to a true
220
FISHER AR
AND CROSS
r
-‘,/I 0.02
I
(1) 1
o-
(2)
4) c: 1
I
I
-0.01 -
ao2 -A / II
240
I
260 280 300 WAVELENGTH (mu)
J
0
FIG. 2. Effect of a small imbalance in protein concentration on a concentration-difference spectrum. For both spectra, the sample cell contained 1.00 mg/ml protein in a cuvette with a pathlength of 1.000 cm. Both reference cells initially contained 0.1 mg/ml protein in a cuvette with a pathlength of 0.998 cm. For curve A, the protein concentration in the reference cuvette was decreased approximately 2.5y0. For curve B, the protein in the reference cuvette was increased approximately 2.5%. Both solutions were made up in 0.2 M phosphate buffer, pH 7.6. The differential absorption spectrum of these same two cells, filled with buffer alone, and placed in the same positions, was subtracted from each spectrum before correcting for scatter
from AA
us. log i plot.
The slope of both
scatter lines on this plot was 5.8. The spectra were run on a Cary model 11 spectrophotometer. The slit width varied from 0.08 to 0.15 mm. Enzyme and solvents were prepared as described previously (5).
concentration-difference spectrum or to concentration errors. A positive peak in a true difference spectrum will remain a positive peak when small additions of protein are made to either sample or reference cuvette, while a peak due to an imbalance of protein concentration will reverse its sign when small additions of protein are made to the cuvette with the lower protein concentration. (It is obvious that that portion of the absorption due to the &,-containing term of Eq. (13)
must correspond (except for sign) to the absorption spectrum of the protein itself. This provides an independent check on concentration imbalance.) Examples of both effects are shown in Fig. 2, which represent,s two concentrationdifference spectra of a protein wit,h a tenfold difference in prot’ein concentration and pathlengt’h. In curve A, the 6c, = 2.7 % of the nominal concentration. In curve B, the protein concent8ration in the reference cuvette has been increased by 2.7 % of the nominal concentration. Curve A is characterized by a large, broad positive peak with a maximum at 282 mp, by increasing positive absorption in the region below 250 mp, and by a series of small bumps. Curve B consists principally of a similar but negative large, broad peak and negative absorption below 250 mp. However, it will be noticed that the small bumps indicated by arrows (l), (a), (3), and (4) are positive peaks at identical wavelengths on both curves. The two spectra are interpretable on the basis of Eq. (13): the broad, reversible peak is due to the &,-containing term, whose magnitude and sign are very sensitive to even small changes in the prot’ein concentration of a given cell (since the term contains E, rather than AE) ; while the small peaks, indicat’ed by the arrows, are due to the AEc,b, term, and remain the same in sign and almost identical in magnitude despite small changes in protein concentration in either cell. This absence of reversibilit’y, then, is, in accordance with Eq. (13), a valid crit’erion for equating a given spectral peak with a concentration-dependent AE. [Since concentrat’ion difference spect,ra are of such ext,remely small magnitude, it is necessary to prove in each case that the observed spectral changes which do not reverse with the change in the sign of error concentration are neither instrument.al nor systematic errors of another kind. Evidence that such spectra are not due to general instrumental errors is provided by the following observations : a. The experimental technique itself is specifically designed to eliminate instrumental artifacts. The practice of subtracting the absorption of the identical cells filled
SPECTROPHOTOMETRIC
STUDIES
wit’h solvent alone from the spectrum obtained in the presence of the enzyme ensures that the difference spectrum finally obtained is due solely to the presence of enzyme. Each spectrum was rerun at a different slit-width to make certain that stray light’ anomalies were not influencing the spectrum. b. Displacement of the whole spectrum upward or downward on t,he optical density axis does not affect t.he spectrum, proving that irregularities in t’he slide wire are not responsible for the results. c. The same spectra have been run on a variety of spectrophotometers, including two different Cary 11 instruments, a Cary 14 instrument, and a Beckman DU spectrophotometer equipped with Gilford expanded scale linear-log absorbance recorder. The spectra were qualitatively similar on all four instruments, differing only in t,he limit,ations imposed by &ray light (particularly with the single beam Beckman instrument). The spectra therefore cannot be due to specific instrumental artifacts. d. Repeated retracing of t’he spectra insured that time-dependent changes were not occurring, and permitted valid dist’inction between random noise and true absorption signal. e. The same spectra have been run at least 20 times. The only difference from one run to another has been that which is clearly attribut’able to small dilution errors previously discussed which do not, affect the fine structure of the spectrum at) all, and are clearly random in nat’ure. f. Finally, the correlation of the wavelengths of the irreversible peaks obtained w&h t’heir larger counterparbs obtained from
OF PROTEIN
STRUCTURE.
I
221
pH and solvent perturbation spectra, and with those obtained from pertinent model compounds, as well as the invariance of such wavelengths from run to run, convince us that the spectra obtained, low in absolute magnitude though they may be, are indeed valid spectra, and are functions of the state of the enzyme alone and not due to experimental artifact.] REFERENCES 1. BERNAL, J. D., Discussions Faraday Sot. 26, 7 (1958). 2. CUNNINGHBM, L. W., TIETZE, F., GREEN, N. M., AND NEUR.~TH, H., Discussions Faraday Sot. 13,58 (1953). 3. FIELD, E. O., .~ND O’BRIEN, J. R. P., Biochem. J. 60, 656 (1955). 4. CROSS, D. G., AND FISHER, H. F., Arch. Hiothem. Biophys. 110, 222 (1965). 5. FISHER, H.F., MCGREGOR, L. L., SND POWER, U., Biochem. Biophys. Res. Commun. 3, 402 (1962). 6. LE.4cH, s. J., AND ScHER.4Ga, H. A., J. Am. Chem. Sot. 82, 4790 (1960). 7. LINDERSTR~M-LANG, K., “Lane Medical Lecture,” p. 58. Stanford Univ. Press, Stanford, California (1952). 8. ONCLEY, J. L., ELLENBOGEN, E., GITLIN, D., .~ND C;URD, F. R. N., J. Phys. Chem. 66, 85 (1952). 9. OLSEN, J. A., AND ANFIWEN, C. B., J. Biol. Chem. 197, 67 (1952). 10. HEITHEL, F., Advan. Protein Chem. 18, 123 (1963). 11. SCHACHMAN, H. K., Brookhaven Symp. Biol. 13, 49 (1960). 12. SCHER.~GA, H. A., “Protein Structure,” p. 217. Academic Press, New York (1961). 13. SCHWERT, G. W., J. Biol. Chem. 179,655 (1949).
OF
BIOCHEMISTRY
Spectrophotometric
AND
BIOPHYSICS
Studies
1. Method HARVEY The Edsel B. Ford Institute
217-221 (1965)
110,
of the Quaternary
of Concentration-Difference F. FISHER2 for Medical Received
AND
Research, December
of Proteins’
Spectra
DALLAS Henry
Structure
G. CROSS
Ford Hospital,
Detroit,
Michigan
9, 1964
A method is presented for determining effects of concentration-dependent structural changes on environment of chromophoric residues of proteins. The theory for t,his technique of “concentration-difference spectra” is developed; t,he experimental methods required for application of that theory are described, and the theoretical effect.s of certain important experimental errors are considered. An experimental crit.erion for establishing the validity of a concentration-difference spectrum is proposed. Examples of application of the t,heory, method, and validity criterion to a dissociable protein system are demonstrated.
The various conformational kansitions undergone by protein molecules are frequemly classified as changes in secondary or tertiary structure (7). In addition to these changes, many protein molecules are capable of dissociat’ing into subunits, a process sometimes referred to as a change in quat’ernary structure (1). The quaternary structure of proteins has recently been reviewed by Reit’hel (10). The technique of ultraviolet)-difference spectroscopy has been employed extensively in studying the nature of all of t’hese processes (12). Certain proteins undergo specific association and dissociation react,ions under condit’ions where t,he only variable parameter is the concentration of the protein it’self. Examples of such systems are chymotrypsin (13) ; insulin (8) ; glutamic dehydrogenase (9) ; trypsin (2) ; hemoglobin (3) ; and hexokinase (11). The applicat#ion of the technique of ultraviolet-difference spec1 This investigation was supported in part by research grants from the National Institutes of Health (grant GM 05638-05) and the National Science Foundation (grant G 18628). z Present address: Veterans Administration Hospit,al, 4801 Linwood Boulevard, Kansas City, Missouri and University of Kansas School of Medicine, Department of Biochemistry, 39th and Rainbow Boulevard, Kansas City 12, Kansas. 217
tra t’o such concentrat’ion-dependent’ systems requires some extension of the technique. The t’heory and experimental procedure for such a method, together wit#h a consideration of, and criteria for, cert’ain important experimental errors, are described below. The application of t’his method to tfhe study of a concentratjion-dependent dissociation of a specific protein are described in an accompanying paper (4). THEORY
We define a “concentration-difference spectrum” as one between identical total weights of a protein in sample and reference cuvettes of identical cross-sectional area but different optical pathlengths, each filled with the same solvent, so t,hat#: C&8 = crb, ,
(1)
where c = protein concentration in mg/ml, and b = length of the optical path for the sample and reference cuvettes, respectively. Thus the two systems differ only in protein concentration and t’he resulting difference speckurn (corrected for solvent absorption) will reflect only those chromophore perturbations which are caused by changes in protein concentration.
218
FISHER
AND
FIG. 1. Scheme of experimental arrangement for concentration-difference spectra. [p] represents the protein concentration. Other symbols are described in the text.
The fundamental equation for concentration-difference spectra follows : Let AA(X) = A(X)
- AvO),
(2)
A-@(X) = Es(X) - E,(A),
(3)
where A is the absorbancy, and E is the extinction coefficient; and s and r refer to sample and reference cells, respectively. Then AA(X) = E,(X)c,b, - E,(X)c,b, .
(4)
Combining Eqs. (1) and (4), and using the definition of Eq. (3), we obtain:
AA(h) ~ cs b,
= AE(X).
This is the fundamental equation concentration-difference spectrum.
(5) for a
TECHNIQUE
The experimental application of Eq. (5) can be conveniently discussed with reference to the schematic diagram shown in Fig. 1; the dotted lines should be disregarded for the moment. The shorter cell is used as the sample cell in a spectrophotometer, and is filled with a solution of protein in a suitable solvent. The longer cell, used as a reference cell, is filled with a solution of protein in the same solvent but at a concentration calculated from the equation: G = dhlb,
,
03)
which follows from Eq. (1) defining a concentration-diff erence spectrum. The differ-
CROSS
ence spectrum is then measured over the desired wavelength range. The difference spectrum of t’he same two cells in the same positions, containing solvent alone, is subtracted. Alternatively, a pair of matched tandem, partitioned cells may be employed as indicated by the dotted lines in Fig. 1. In this case the sample cell contains protein solut’ion in the solid line (left-hand) portion of the cell, while the dotted line (right-hand) portion is filled with solvent alone. Bot’h portions of the reference cell are filled with a protein solution diluted as indicated above. In either case the resulting concentrationdifference spectrum must be corrected for the differential protein light-scatter by some method such as that of Leach and Scheraga (fS3 The assignment of sample and reference cells shown here will produce a positive difference spectrum if a blue shift is produced by dilution. EFFECT
OF CONCENTRATION
ERRORS
Since AE represents a small difference between two large numbers, small deviations from the equality expressed by Eq. (1) will cause very large errors in the concentrationdifference spectrum. However, such errors, and AE itself, have quite different dependencies upon protein concentration; these differences, as discussed below, enable us to distinguish between them. While the following treatment is applicable to conventional difference spectroscopy (in which b, = b, and c, = c,), it becomes important primarily in concentration-difference spectra which are in general of an even smaller order of magnitude. Consider the case of a very small error in protein concentration, so that c8bs # crbr . 3 While the scatter-correction method of Leach and Scheraga (6) is the best procedure now available, it is generally agreed that it is not strictly accurate. Since the inaccuracies become more pronounced at shorter wave-lengths, they constitute the limiting factor in the interpretation of difference spectra low values of AE, such as concentration-difference spectra. A discussion of scattercorrections, together with a method of estimation of their contribution to difference spectra, will appear in a later paper in this series.
SPECTROPHOTOMETRIC
STUDIES
Assume first that: (7) Then, c, may be considered as the sum of two equal to concentrations : one, exactly (c&,)/b, , and a second term representing the small excess concentration: (8) where lie, (< cs. The differential written as
absorbancy
AA(X)
+
= E,(X)[c,b,
can now be
b&,1 -
E,(OG,
.
(9)
After rearranging terms and using the definition in Eq. (3), we obtain: AA(k)
=
AE(X)c,b, + E,(X)Gc,b, .
(10)
Returning to t’he initial assumption in Eq. (7), it is clear that we can equally well make the opposite assumption, that C*<--,
cr b, b,
(11)
whence Eq. (8) can now be rewritten as: cr b, c, = - 6c,. b,
(12)
Since this assumption produces only a change in sign of 6c, , we obt’ain an equation ident’ical t,o Eq. (10) except that the sign of the term containing 6c, is reversed. Removing the restrictions imposed by Eqs. (7) and (II), we can now write the equation for t)he general case :4 AA(h)
= AE(X)c,b, zt E,(X)Gc,b, .
Since AE << E, , and&<<
(13)
/c8 - c, /,itcan
4 Difference spectra must, by their nature, be smaller than the actual spectra from which they are derived. Concentration-difference spectra generally may be expected to be much smaller than conventional difference spectra. Therefore even a very small 6c will produce a very large change in AE and will be easily recognizable. For the same reasons, the effect of using either E, or E, in the &-containing term of Eq. (13) will be immeasurably small.
OF PROTEIN
STRUCTURE.
I
219
be seen that if we start with the system as specified in Eq. (11) and gradually increase c, , the true difference spectrum will change only very slightly, and always in the direction of increasing the absolute value of the optical density difference; while the absolute value of that contribution to the absorption caused by the imbalance of protein concentrations will change by a very large amount, and will, in fact, first decrease to the base line and t’hen event,ually change its sign. [That contribut,ion to a concentration-difference spectrum caused by scattered light will, for the general case considered here, also consist of two terms: t,he first, consisting of the true concentration-dependent difference in scatter, will remain constant in sign with small changes in protein concentration; while the second, consisting of the scatter of the amount. of protein corresponding to 6c, will behave as t,he corresponding absorption term containing 6c, and may carry eit*her sign. Fluorescence will cont,ribute to the spectrum in the same manner as does scattered light, that is, it too will consist of two terms. In order to determine the relative magnitude of such effects, both scat,tered and fluorescent light was monitored by installing a photomultiplier tube conrlected to a sensitive microphotometer in such a position t,hat it would receive scatt’ered light (or fluorescence) at 90” to the optical axis. The magnitude of the fluorescence was found to be very much smaller than bhe scatt’ered light, and can therefore, at least’ for t,he present experiments, be neglected. While in principle t,he amount of fluorescence and scat’tered light received by the phototubes of the spectrophotometer should be a function of the distance of the protein solution from t,he phototube, in practice this effect does not occur either with the Cary 11 or with t,he Cary 14 instruments. This was demonstrat’ed by placing a cuvet,te containing a solution of Ludox in the cell compartment at various dist’ances from the phototube. No change! in optical density was observed.] This relationship provides an important and useful criterion for determining whether various small peaks in a concentration-difference spectrum are due to a true
220
FISHER AR
AND CROSS
r
-‘,/I 0.02
I
(1) 1
o-
(2)
4) c: 1
I
I
-0.01 -
ao2 -A / II
240
I
260 280 300 WAVELENGTH (mu)
J
0
FIG. 2. Effect of a small imbalance in protein concentration on a concentration-difference spectrum. For both spectra, the sample cell contained 1.00 mg/ml protein in a cuvette with a pathlength of 1.000 cm. Both reference cells initially contained 0.1 mg/ml protein in a cuvette with a pathlength of 0.998 cm. For curve A, the protein concentration in the reference cuvette was decreased approximately 2.5y0. For curve B, the protein in the reference cuvette was increased approximately 2.5%. Both solutions were made up in 0.2 M phosphate buffer, pH 7.6. The differential absorption spectrum of these same two cells, filled with buffer alone, and placed in the same positions, was subtracted from each spectrum before correcting for scatter
from AA
us. log i plot.
The slope of both
scatter lines on this plot was 5.8. The spectra were run on a Cary model 11 spectrophotometer. The slit width varied from 0.08 to 0.15 mm. Enzyme and solvents were prepared as described previously (5).
concentration-difference spectrum or to concentration errors. A positive peak in a true difference spectrum will remain a positive peak when small additions of protein are made to either sample or reference cuvette, while a peak due to an imbalance of protein concentration will reverse its sign when small additions of protein are made to the cuvette with the lower protein concentration. (It is obvious that that portion of the absorption due to the &,-containing term of Eq. (13)
must correspond (except for sign) to the absorption spectrum of the protein itself. This provides an independent check on concentration imbalance.) Examples of both effects are shown in Fig. 2, which represent,s two concentrationdifference spectra of a protein wit,h a tenfold difference in prot’ein concentration and pathlengt’h. In curve A, the 6c, = 2.7 % of the nominal concentration. In curve B, the protein concent8ration in the reference cuvette has been increased by 2.7 % of the nominal concentration. Curve A is characterized by a large, broad positive peak with a maximum at 282 mp, by increasing positive absorption in the region below 250 mp, and by a series of small bumps. Curve B consists principally of a similar but negative large, broad peak and negative absorption below 250 mp. However, it will be noticed that the small bumps indicated by arrows (l), (a), (3), and (4) are positive peaks at identical wavelengths on both curves. The two spectra are interpretable on the basis of Eq. (13): the broad, reversible peak is due to the &,-containing term, whose magnitude and sign are very sensitive to even small changes in the prot’ein concentration of a given cell (since the term contains E, rather than AE) ; while the small peaks, indicat’ed by the arrows, are due to the AEc,b, term, and remain the same in sign and almost identical in magnitude despite small changes in protein concentration in either cell. This absence of reversibilit’y, then, is, in accordance with Eq. (13), a valid crit’erion for equating a given spectral peak with a concentration-dependent AE. [Since concentrat’ion difference spect,ra are of such ext,remely small magnitude, it is necessary to prove in each case that the observed spectral changes which do not reverse with the change in the sign of error concentration are neither instrument.al nor systematic errors of another kind. Evidence that such spectra are not due to general instrumental errors is provided by the following observations : a. The experimental technique itself is specifically designed to eliminate instrumental artifacts. The practice of subtracting the absorption of the identical cells filled
SPECTROPHOTOMETRIC
STUDIES
wit’h solvent alone from the spectrum obtained in the presence of the enzyme ensures that the difference spectrum finally obtained is due solely to the presence of enzyme. Each spectrum was rerun at a different slit-width to make certain that stray light’ anomalies were not influencing the spectrum. b. Displacement of the whole spectrum upward or downward on t,he optical density axis does not affect t.he spectrum, proving that irregularities in t’he slide wire are not responsible for the results. c. The same spectra have been run on a variety of spectrophotometers, including two different Cary 11 instruments, a Cary 14 instrument, and a Beckman DU spectrophotometer equipped with Gilford expanded scale linear-log absorbance recorder. The spectra were qualitatively similar on all four instruments, differing only in t,he limit,ations imposed by &ray light (particularly with the single beam Beckman instrument). The spectra therefore cannot be due to specific instrumental artifacts. d. Repeated retracing of t’he spectra insured that time-dependent changes were not occurring, and permitted valid dist’inction between random noise and true absorption signal. e. The same spectra have been run at least 20 times. The only difference from one run to another has been that which is clearly attribut’able to small dilution errors previously discussed which do not, affect the fine structure of the spectrum at) all, and are clearly random in nat’ure. f. Finally, the correlation of the wavelengths of the irreversible peaks obtained w&h t’heir larger counterparbs obtained from
OF PROTEIN
STRUCTURE.
I
221
pH and solvent perturbation spectra, and with those obtained from pertinent model compounds, as well as the invariance of such wavelengths from run to run, convince us that the spectra obtained, low in absolute magnitude though they may be, are indeed valid spectra, and are functions of the state of the enzyme alone and not due to experimental artifact.] REFERENCES 1. BERNAL, J. D., Discussions Faraday Sot. 26, 7 (1958). 2. CUNNINGHBM, L. W., TIETZE, F., GREEN, N. M., AND NEUR.~TH, H., Discussions Faraday Sot. 13,58 (1953). 3. FIELD, E. O., .~ND O’BRIEN, J. R. P., Biochem. J. 60, 656 (1955). 4. CROSS, D. G., AND FISHER, H. F., Arch. Hiothem. Biophys. 110, 222 (1965). 5. FISHER, H.F., MCGREGOR, L. L., SND POWER, U., Biochem. Biophys. Res. Commun. 3, 402 (1962). 6. LE.4cH, s. J., AND ScHER.4Ga, H. A., J. Am. Chem. Sot. 82, 4790 (1960). 7. LINDERSTR~M-LANG, K., “Lane Medical Lecture,” p. 58. Stanford Univ. Press, Stanford, California (1952). 8. ONCLEY, J. L., ELLENBOGEN, E., GITLIN, D., .~ND C;URD, F. R. N., J. Phys. Chem. 66, 85 (1952). 9. OLSEN, J. A., AND ANFIWEN, C. B., J. Biol. Chem. 197, 67 (1952). 10. HEITHEL, F., Advan. Protein Chem. 18, 123 (1963). 11. SCHACHMAN, H. K., Brookhaven Symp. Biol. 13, 49 (1960). 12. SCHER.~GA, H. A., “Protein Structure,” p. 217. Academic Press, New York (1961). 13. SCHWERT, G. W., J. Biol. Chem. 179,655 (1949).