Computer Analysis of Spectra of Enzyme-Substrate and Enzyme-Inhibitor Complexes Involving Aspartate Aminotransferase*

spectrally


Dicarboxylic
acid inhibitors and the amino and keto acid substrates interact with aspartate aminotransferase (EC 2.6.1. 1) to form spectrally distinct enzyme-inhibitor and enzyme-substrate complexes.
The spectra of solutions of the enzyme and varying concentrations of inhibitor or substrate are analyzed by computer methods to obtain the spectra of the enzyme-inhibitor and enzyme-substrate complexes. Programs have been written which permit the computation of the pK, values and the dissociation constants of the complexes with the use of the spectral data at many wave lengths. The complete spectra of the individual ionic species of the complexes are drawn.
Comparison plots of the experimental spectral data and the calculated spectra can also be obtained. These computer methods are applied to four enzyme-inhibitor complexes and to complexes of the enzyme with its substrates and two pseudosubstrates.
Spectra of apoaspartate aminotransferase containing bound pyridoxal phosphate analogues have also been analyzed.
The methods generally used involve construction of linear plots relating the concentrations of inhibitor or of substrate to the changes in absorbance at one or two wave lengths.
Extinction coefficients for the complexes at these wave lengths are obtained as well as the formation or dissociation constants.
From measurements at various values of pH, the acid dissociat'ion constants of the complexes can also be determined.
Recently, computer methods have been developed which permit evaluation of both acid dissociation constants and formation constants of complexes using entire spectra measured at various pH values and at various concentrations of ligand (9). Wit.h such methods, complete spectra of individual ionic species of the complexes could also be obtained.
The present work represents an extension of this method to a pyridoxal 5'-phosphate-dependent enzyme, aspartate aminotransferase (EC 2.6.1.1). The extensive previous work of Jenkins et al. (1,2,(4)(5)(6) and of Fasella, Giartosio, and Hammes (7) on the spectral changes undergone by the enzyme upon addition of substrates, pseudosubstrates, and dicarboxylic acid inhibitors makes aspartate aminotransferase an ideal system for testing the computer method.
Models describing the various possible complexes between the enzyme and its substrates have been postulated. When the substrate pairs, glutamate-a-ketoglutarate or aspartate-oxaloacetate, are added to the enzyme, a number of enzyme species are found.
These include the pyridoxal and pyridoxamine forms of the enzyme, binary intermediate enzyme-substrate complexes, an abortive complex between the pyridoxal form of the enzyme and the keto acid, and possibly an abortive complex between the pyridoxamine enzyme and the amino acid. The computer method provides a means of determining the contribution of the various enzyme forms to the overall spectra and permits, for the first time, calculation of complete spectra of individual ionic species of the complexes with the use of spectral data at many wave lengths.
EXPERIMENTAL PROCEDURE nlateriuZsThe aspartate aminotransferase was donated by Dr. W. T. Jenkins as the highly purified cytoplasmic a+subform (10). The absorbance ratio AGo:A340 was 3.6 in 0.02 M acetate buffer, pH 5.4. Enzyme concentrations were obtained from the absorbance at 364 rnp at pH 8.0, with the use of the molar extinction coefficient of 8.20 X lo3 (5,11). One mole is that amount of enzyme containing 1 mole of bound pyridoxal-P.
Aspartic and glutamic acids were purchased from Nutritional Biochemicals.
Oxalacetic and a-ketoglutaric acids were obtained from Calbiochem, and succinic acid was a product of Mallinckrodt.
Pyridoxal-P and glutaric and a-methyl-DLaspartic acids were purchased from Sigma. erytkro-/%Hydroxy-DL-aspartic acid was prepared and donated by Dr. W. T. Jenkins. Of the pyridoxal-P analogues, Compounds I (12) and IV1 were 2. Absorption spectra of the two ionic forms of the 01ketoglutarate-aspartate aminotransferase complex (---), and of the two ionic forms of the enzyme-succinate complex (---).
0.2 kK2 intervals (1 kK = lo3 cm-l). Spectra were corrected for base line errors and for very small amounts of turbidity when necessary.
Spectra were obtained of solutions of apoaspartate aminotransferase and apoglutamate decarboxylase (prepared according to the procedure of Hunt'ley and Metzler (13)) with low amounts of turbidity increasing slowly with time. The difference spectra of the protein with and without turbidity were used to obtain standard plots. It was found that the absorbance due to turbidity increased linearly with wave number over the range 18.8 to 31.3 kK (532 to 320 mp). The parameters, intercept and slope, for the linear correction were calculated from the standard plots and the absorbance at 532 rnp (18.8 kK) of the sample protein solutions.
Results obtained with this method of turbidity correction were very similar to those obtained with a plot of log B against log wave length (14). The maximum correction at 320 rnp necessary in this study was 0.026 for a solution having an A of 0.545.
Spectra Required for ComputationsTo determine the pK,, dissociation constant, and spectra of the ionic forms of the enzyme-inhibitor complexes, the following spectra are necessary : (a) spectral measurements on solutions containing high concentrations of inhibitor at several pH values to obtain a pK; (b) spectra of the enzyme titrated with lower concentrations of inhibitor to obtain the inhibitor dissociation constant.
In the case of the enzyme-substrate complexes, spectra at several con-centrations of both the keto acid and the amino acid must be obtained.
Computer Programs-The programs used were written in FORTRAN IV language for use with the IRM 360/65 computer. The automatic graphing was done by the Cal-Comp Digital Incremental Plotter.
Enzyme-bound Pyridoxal-P Jnalogues-The apoenzyme of aspartate aminotransferase was prepared according to the procedure of Scardi et al. (15) with an adaptation described previously (11). The apoenzyme and an equivalent concentration of the pyridoxal-P analogue (approximately 5 X 10-S M) were incubated at room temperature in 0.01 M triethanolamine hydrochloride buffer, pH 8.3, for 15 min, sufficient time for complete binding.
Spectra of each enzyme-bound analogue were obtained at a number of different pH values. The pH was adjusted with an appropriate amount of either 0.5 M triethanolamine hydrochloride buffer or 0.5 RI acetate buffer.  I  I  I  I  I  I   I  I  I  I  I  I  I   22  24  26  26  30  32  34  WAVE NUMBER,  KK   IIK4 II   HPL  HL  HI'   SCHEME   I where L, HL, and HZL are the ionic forms of the dicarboxylic or keto acid. PL and HPL are the nonprotonated and protonated forms of the complex between the inhibitor and enzyme. Ke, K4, KS, and K7 are acid dissociat'ion constants, and Kg, a dissociation constant, is where Cp is the concentration where aH is the apparent hydrogen ion "activity" and is obtained with a pH meter. The concentrations of total enzyme, CtP, and total inhibitor, GIL, are given by Equations 5 and 6. values for Cp and CL are obtained by the computer through successive approximations.
The first estimate of CL is given by CL = CtLIP (7) and successive estimates of Cp and CL are obtained from Equations 5 and 6.
The trial value for Kg was determined from a plot of the reciprocal of the change in B at one wave length against the reciprocal of the inhibitor concentration. Data for these plots were obtained from titrations of the enzyme with inhibitor at one pH. Approximate values for K7 were obtained with Equa- where AA,,, is the absorption of HPL at X,,, at low pH, and AA is the absorption at the same wave length at a pH near the pK, of the complex.
The trial values of KT and Kg did not need to be extremely close to the final values computed and were adjusted by the computer with a modification of the grid method described by Nagano and Metzler (9). The molar extinction coefficients of the two ionic species (PL and HPL) were obtained by the method of least squares applied consecutively to the data at each experimental spectral point.
An example of the results obtained for different values of K, and Kg in the glutarate-enzyme complex is shown in Fig. 1. In Computer Analysis of Spectra qf Aspartate Aminotransferase Vol. 245, No. 10 this case, the original trial values were pK, of 8.81 and pKs of 1.39 (marked by X).
The numbers on the contour map are values of the sum of the squares of the deviations calculated for the various grid parameters.
Standard deviations of the absorbance values were calculated by dividing the values of squares of the deviations by the total number of experimental points minus the number of constants adjusted (degrees of freedom) and taking the appropriate square root (9).
These results were checked with a program which calculated these parameters by the method of steepest descent (16). The results calculated with either the grid program or the steepest descent method were very similar.
Comparison plots were also comput.ed to show the goodness of fit between computed spectra and experimental results (9).
Enzyme-Substrate Complexes-The spectral changes that occur upon the addition of both amino acid and keto acid substrates may be described as simply as possible by Scheme II. Jenkins (6,s) has reported that pH has no effect on the interconversions of the enzyme-substrate complexes and this was also found in the present study; therefore, only one ionic species has been considered in this scheme. PM is the pyridoxamine form of the enzyme, the spectrum of which does not change over the pH range of 5.0 to 9.0. Abortive complexes between amino acid and the pyridoxamine form of the enzyme do not appear to be formed with aspartate (6) The  Fig. 2 shows the protonated and nonprotonated forms of the complex of aspartate aminotransferase with a-ketoglutarate (solid lines) and with succinate (dashed lines). These spectra were plotted automatically, converting the absorption in wave length to wave number.

RESULTS
The spectra are interpolated between points to obtain a smooth curve. Similar spectra were obtained for the two ionic forms of the enzyme complexes with oxaloacetate and glutarate.
A comparison plot for the enzyme-inhibitor complex involving succinate is presented in Fig. 3. The solid lines were calculated with the results for K7, Kg, and the extinction coefficients obtained by the computer.
The points drawn in are the experimentally observed spectra. Very good agreement was obtained between the calculated and observed spectra over the wave length range studied for the two dicarboxylic acids, succinate and glutarate.
In Fig. 4, the calculated and observed spectra for the abortive complex with oxa1oacetat.e are shown.
In this case there is good fit between t.he two spectra in the region of the 429 rnp (23.3 kK) peak, but not in the region of the 364  5. Spectra of the complexes of aspartate aminotransferase with some substrates and substrate analogues.
Curve 1, erythrop-hydroxy-nL-aspartate (the scale is one-third that of the others) ; Curve 2, a-methyl-nL-aspartate; Curve 3, L-aspartate and oxaloacetate; Curve 4, L-glutamate and cr-ketoglutarate.  Table I. The st.andard deviation per absorbance point is included to give an idea of the goodness of fit obtained with each inhibitor. The deviation is higher with a-ketoglutarate and oxaloacetate than with glutarate and succinate because of the previously mentioned poor fit in the region of the 364 rnE.1 (27.5 kK) absorbing species. With the exception of the complex with oxaloacetate, the protonated forms of the complexes absorb at longer wave lengths than that of the free pyridoxal form of the enzyme.
Furthermore, the protonated forms of the enzyme-inhibitor complexes have higher extinction coefficients than that of the holoenzyme.
There is no appreciable shift in the absorption maxima of the nonprotonated form of the enzyme in the presence of the inhibitors. The inhibitors all cause a large increase in the pK, of the enzyme. The keto acids bind more tightly to the nonprotonated form of the enzyme than do the dicarboxylic acids.
The spectra of the enzyme-substrate complexes obtained with the aminotransferase with its normal substrates and some pseudosubstrates are shown in Fig. 5. These spectra are due only to the enzyme-substrate complexes, since the absorption due to abortive complexes and free enzyme have been subtracted from Analysis of Spectra oj Aspartate Aminotransferase Vol. 245, No. 10 the experimentally obtained spectra. Comparison spectra for the glutamate-oL-ketoglutarate system appear in Fig. 6. The fit with this substrate pair was good. The fit obtained in the comparison plots for the aspartate-oxaloacetate system was somewhat worse, and the value of standard deviation per absorbance point was higher than that obtained with glutamatecr-ketoglutarate.
A comparison plot for the data obtained with erythro-/I-hydroxyaspartate is presented in Fig. 7. The fit be-7- 6-11111111111III  III  I  I  I  I  I  I  1  I  550  500  450  400  360  360  340  320

Glutamate-a-ketoglutarate
Aspartate-oxaloacetate a-nn-Methylaspartate clythro-P-Hydroxy-nn-aspartate -tween the experimental and computed spectra is excellent. Excellent agreement was also obtained for the complex with amethylaspartate at both pH 7.6 and 8.8. This is consistent with the previous observation that there was no effect of pH on the distribution of the enzyme-substrate complexes with cymethylaspartate (7). The data obtained for the various enzyme-substrate complexes are presented in Table II. As was observed by Jenkins (8) Therefore, under the conditions used, there was essentially no free pyridoxamine form of the enzyme in the test solutions. It has been shown (11) that the pyridoxal-P analogues I to IV (see Fig. 8) bind to apoaspartate aminotransferase in an apparently normal fashion.
Enzyme-bound I (E-I) and E-11 undergo spectral changes with changing pH in a manner similar t.o that found with the nat.ive enzyme. However, E-III and E-IV exhibit.ed absorption maxima at approximately 370 rnp (27.0 kK) at pH 8.3 and 5.0, and had no absorption at 429 rnp (23.3 kK) at pH 5.0. It was of interest to determine whether the latter two enzyme-bound analogues could be protonated at all. Since glutarate greatly increases the pK, of the native enzyme, it was thought that a similar shift in pK, would be observed with the enzyme-bound pyridoxal-P analogues. The spectral pK, values for the enzyme-pyridoxal-P analogues in the presence and absence of glutarate are presented in Table III. The pK, values for E-I and E-II were determined according to t.he method of Nagano and Metzler (9). Glutarate does cause a shift in the pK values of E-I and E-II of a magnitude similar to that observed with the pyridoxal-P enzyme. When glutarate was added to either E-III or E-IV at pH 5.0, there was an appreciable increase in absorption at 429 rnp (23.3 kK).
It was estimated that the pK, of the E-III glutarate complex was approximately 4.8 and the pK, of the E-IV glutarate complex was somewhat less then 4.8.

DISCUSSION
The computer methods described here enable the calculation of pK, values, dissociation constants, and spectra of enzymeinhibitor and enzyme-substrate complexes.
The results obtained when these methods were applied to aspartate aminotransferase agree well with most previously reported data. The pK, values and the dissociation constants for the complexes with glutarate and succinate are very similar to those reported by Jenkins (1, 2) using spectrophotometric titrations. The dissociation constants for the pseudosubstrates, P-hydroxyaspartate and ar-methylaspartate, obtained in this study are comparable to that of 3.8 x 10U4 M report.ed for ,&hydroxyaspartate (5) and 4.76 X low3 &I for nn-cr-methylaspartate (7). However, the dissociation constants obtained for glutamate, aspartate, a-ketoglutarate, and oxaloacetate are all lower than those reported previously (6,8,(18)(19)(20).
These differences may be due to differences in the reaction conditions used. Previous spectral studies had been conducted in pyrophosphate buffer, which has since been shown to interact with the enzyme-sub-strate complexes. 3 Kinet.ic studies (19) indicated that no abortive complex was formed with oxaloacetate at concentrations of 15 rnnf keto acid. However, these kinetic studies were conducted with a mixture of subforms of the enzyme in sodium arsenate buffer at 37".
The discrepancies obtained in the spectral changes upon binding keto acid to aspartate aminotransferase to form an abortive complex appear to be due to the buffer used. The results obtained in Tris buffer are fully consistent with the tnodel used to describe the formation of abortive complexes (Scheme I) and would indicate that the model is correct.
However, in triethanolamine buffer, the keto acids appear to be binding differently, and the simple model is not consistent with the data obtained in this buffer. The results obtained by analyzing the entire spectra indicate the importance of careful consideration of the reaction conditions. It appears that the dissociation constants and the spectral behavior of the abortive complexes may vary with certain conditions, such as buffer used. The unusual spectral behavior obtained with the keto acids in triethanolamine buffer would not have been observed with the one-wave length approach used by other investigators to determine dissociation constants.
Since the formation constants for the abortive complexes are low compared with those of the enzyme-substrate complexes, it was felt that these discrepancies would have little effect on the final spectra computed for the enzyme-substrate complexes. These methods of computer analysis have several advantages over previously described methods of analyzing spectrophotometric titrations of enzymes. The computer method utilizes data at many different wave lengths rather than just at one wave length.
It takes into consideration the spectral pK, values for both the pyridoxal form of the enzyme and the enzyme-inhibitor complexes.
The absorption spectra of the individual complexes can be computed. Fewer experimental spectra are needed to obtain all parameters required in a given model.
Comparison plots can be generated, thus providing a means of evaluating the model used.
The comparison plots and the low values of standard deviation per absorbance point obtained for the enzyme-inhibitor complexes would indicate that the spectra of the ionic forms of these complexes are reliable.
In each case, the spectrum of the HPL form is probably much more accurate than that of the PL form of the complexes.
Computer analyses can be extended to other studies of the aspartate aminotransferase system. For instance, some enzyme-inhibitor complexes of the enzyme in which pyridoxal-I' has been replaced with a pyridoxal-P analogue have been studied. Glutarate and a-ketoglutarate do form complexes with the enzyme-bound analogues. These complexes, like those with the native pyridoxal form of the enzyme, absorb at longer wave lengths and have a higher pK, than does the free enzyme-bound analogue.
The computer method can also be used to study the complexes of substrates and inhibitors with other enzymes.