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A kinetic model for glutamate dehydrogenase
I. theor. Biol. (1977) 66, 81-93
A Kinetic Model for Glutamate Dehydrogenase B. D. WELLS,? L. A. PARKS, I. TAM AND J. R. FISHERS Department of Chemistry and Institute of Molecular Biophysics, Florida State University, Tallahassee,Florida 32306, U.S.A (Received 10 February 1976, and in revisedform 17 May 1976)
A model for the glutamate dehydrogenase reaction has been obtained that contains the reported intermediates suggested by binding and equilibrium isotope exchange methods. Calculated steady state-initial velocity rates using this model are quantitatively consistent with a wide range of nonlinear experimental data in both directions. 1. Introduction
A number of approaches have been used in studying the mechanism of action of bovine liver glutamate dehydrogenase (EC 1.4.1.3) (GDH). Silverstein & Sulebele (1973) reported the formation of numerous enzyme-bound reactants using isotope exchange kinetics with the system at equilibrium. A number of alternate (random) pathways were identified. Recent binding studies also have detected several enzyme complexes (DiFranco & Iwatsubo, 1972; Fisher, 1973; DiFranco, 1974). Furthermore, detailed steady state kinetics have revealed extensive nonlinearity, particularly in the direction of glutamate oxidation (Barton & Fisher, 1972; Parks, 1973; Dalziel & Egan, 1972). These kinetic results require the presence of cycles in the mechanism (Wells, Stewart & Fisher, 1976). The intermediates detected in isotope exchange reactions and binding studies suggest that at least some of the needed cycles are the result of random (alternate) pathways. Recently Pal, Wechter & Colman (1975) have used affinity labelling to provide direct evidence for a second noncalaytic regulatory site on GDH. These results suggest that both ADP and NADH bind to this site and thereby provide a mechanism for generating cycles in addition to random pathways, The purpose of the research described here was to bring these kinetic and binding studies together in the form of a proposed mechanism. Furthermore 7 Present address: Department of Chemistry, Columbia University, New York, New York, 10027. 1 Deceased. T.R.
81
6
82
B.
D.
WELLS
ET
AL.
it was hoped that the resulting model would be quantitatively consistent with the extensive kinetic data that we have amassed (Barton & Fisher, 1972; Parks, 1973; Tam, 1972). 2. A Preliminary
Model
During the last several years we have been accumulating extensive steady state-initial velocity measurements with GDH over wide concentration ranges of substrates in both the forward (glutamate oxidation) and reverse (glutamate formation) directions. These results were routinely normalized (Barton & Fisher, 1972) in order to obtain an internally consistent set of data that can be treated with one model and set of rate constants. This data set involving 441 combinations of concentrations and over 2200 individual assays has been represented by two empirical equations (given below) which have been presented previously in slightly modified form (Barton & Fisher, 1972; Tam, 1972). The lower case letters are kinetic coefficients orward
direction
(1) d
___-1 if = a+b+c[D]+fi I II
III
L+ccl
[G] IV
f+g[D] v 1 __---__ + @j-fT[G] +J’[D][G] VI
+ k[D] VII
reverse direction
(2)
j+m-+-L+.____-
+
VIII
[DH] IX
[K] x
[K];DH] XI
+ &+ XII
~
____-
fi];K] XIII
+ [A];DH] XIV
+sCDH1 xv
vCDH1 + $WDHl ___ + t-K1 + ~CKIL-DHI + - LA1 CA1 XVI
XVII
XVIII
XIX
with values given in Table 1. Representation of data by equations composed of terms like those used in equations (1) and (2) does not prejudice the choice of models used for interpretation (Wells et al., 1976). This statement is based on the observation that second-site, co-operative and random pathway models give similar cycles and virtually identical mathematical functions. A model (Fig. 1) has been devised that is quantitatively consistent with equation (1) (Parks, 1973). When this model was used with the empirical
A MODEL FOR GLUTAMATE
83
DEHYDROGENASE
TABLE 1 Values (with standard deviations) of coeflcients Constant --- __ a
b : ; g h i
i k
Value
2*571tO.O5xlO-~ 1.36f0.26 x lo3 1~01f0~10x10~ 1%4f0.27 x 1O-8 1*27+0.10x lo-” 2.03f0.15 x LO2 5.42f1.02~ lo4 5.61 f0.96 x lo5 3.9810.71 x lo4 5.11 f0.32 x lo9 1*0x 10-z
in equations (1) and (2)
Constant I I?, n 0
P 4 r
s t 11 V W
Value 4~32~1O-~i2~8xiO-~ 1~56x10-9ztl~6x10-‘o 4*58x10-B+l~6x10-s 2.38 x 10-12f 1.1 x lo-= 1~08x10-~f2~0x10-~ 1~95x10-~0*7~9xIo-1~ 2.17 x 10-12f6.3 x lo-l3 1~73x10-~i1~0x10-3 3.76x10-4~9.0x10-5 1~63x10°15~7x10-1 6~30x10-bf1~0x10-5 5~llxlO-~i5~lX10-3
equation in the reverse direction
[equation (2)], it was found to be capable of accounting for some of the linear functions. However, three simple modifications allowed six of the 12 terms to be obtained (Fig. 2). These six terms (VIII, IX, X, XI, XIII, XVI) were predominantIy those needed for the linear regions with a-ketoglutarate and NADH. The enzyme intermediates in model 2 were compared to those found by Silverstein & Sulebeie (1973) using isotope exchange reactions and intermediates observed by others in binding studies (DiFranco & Iwatsubo, 1972). Since the intermediates found by isotope exchange were identified under conditions that could not have detected the presence of water at the catalytic site, we have assumed that water may or may not be present. The intermediates suggested by these other studies are shown in Fig. 2. It can be seen that we are suggesting four additional enzyme substrate complexes (EDAK, EAD, EAG and EAGD). Also it should be noted that several necessary
kinetic steps are included that involve events other than substrate or product
addition or elimination. However, one intermediate (EGDH) suggested by several research groups (Silverstein & Sulebele, 1973; DiFranco & Iwatsubo, 1972) is not present. Analysis of model 2 revealed that addition of this intermediate in level III forming a dead-end cycle could bring in terms XII and XIV [equation (2)]. This modification (Fig. 3) gives a model that accounts for all terms in the forward direction [equation (I)] and all of the linear terms in the reverse direction [equation] (2). However, all four nonlinear substrate
(NADH) inhibition terms in equation remain unaccounted for.
(2), (XV, XVII,
XVIII
and XIX)
84
B.
D.
WELLS
ET
AL.
FIG. 1. Model 1. A model to describe glutamate dehydrogenase kinetics in the direction of glutamate oxidation. The model consists of three levels (I, II and III). All the intermediates are described. An intermediate with a prime represents a kinetic step that does not involve substrate addition or product release. EAKDH = EGDW; G = glutamate; K = a-ketoglutarate: D = NAD; DH = NADH; A = ammonia; E = enzyme and W = water.
A MODEL
FOR GLUTAMATE
DEHYDROGENASE
85
FIG. 2. Model 2. Levels I and II of Model 1 have been interchanged and a cycle has been created by adding steps 13 and 14. The enzyme forms which are identical to those suggested by Silverstein & Sulebele (1973) are enclosed by boxes. See legend of Fig. 1 for details.
86
B. D. WELLS
ET
AL.
/A
FIG. 3. Model 3. The cycle added to model 2 has the enzyme forms identified. See the legend in Fig. 1 for details.
A
MODEL
FOR
GLUTAMATE
DEHYDROGENASE
87
FIG. 4. Model 4. The enzyme forms are included for the steps which were added to model 3. The encircled Roman numerals refer to the enzyme intermediates which give rise to the terms in equations (I) and (2). See Fig. I for details.
88
B. D. WELLS
ET
AL.
3. A Model for Glutamate Dehydrogenase We were very pleasantly surprised that the model based on kinetic data in the direction of glutamate oxidation could account for data in the back direction so well. All that remained was to modify model 3 to treat NADH inhibition. The recent direct evidence for a second site on GDH (Pal et al., 1975)led us to seriously consider NADH binding at such a site as a basisfor generating NADH inhibition terms. We assumedthat various intermediates (model 3) could bind NADH at this second site better than others. Furthermore it was necessaryto choose these intermediates in such a way that the needed terms could be obtained. For example, level I was arranged in a way that prevented terms from being dependent upon [A]. Hence this level yielded terms VIII, IX, X and XI in equation (2). Since term XV is also independent of [A] it could only come from this samelevel. We assumedthat complex EAG could bind NADH at a second non-catalytic site giving a dead-end branch. TABLE 2 Rate constants for model 4 Rate constant k+!; k-,
k, k-,
I;, k- c k13 Ii-13
k14 k-1, kd k-d x, k, XI km, L-R k-,
km k-2,
Rate Rate Rate Value? constant constant Value constant Value Value - ~- ..~~~___ ~~ 3.40~ 10-l k, imx 10’2 k, 140x 1O1’ k, 24xlx 102 4.20 103x 10’ k-6 2.10x 1010 k-o 1.00x 103 k-i, 4.20 x 10” k, 2.80 x lOI2 k, 2.00x 10’” 7.00~10~ k7 1 .oo x 108 km, 1~00x102 IL, 2aox 104 1.00x lOa k-, 1+IO>:10~ k,, 3.70x 10-Z k, 5.42~ 10” 7.70 x IO8 k8 1GOx10~ 4.15x 10-l km, km8 1GOx 10” A-- 12 2.54~10’~ 1.40 x lo5 k, 1.07x 107 kg 1~00x10’ k, 1.00x to7 2.20 x 107 1GOx IO8 k-, 5.42 x 10”’ km, 5.40x IO9 keg 3.30x lo* k, 2.00~10~ k, 6.00x 10’ k16 l%?Ox 106 6.30~10~ km, 140x lo9 ke, I~OOX 105 1.11 x10$ k-16 7.00 x 1O1’ k, 1.00x lo3 k17 l+Ox104 k, 1wx 10” 1.00x 105 k-z 7.00x 10” 1.00x 108 140x 106 k-17 k-t 1.73x IO’ k __ t* 540x lo2 k, 8.00 x 1O1’ ku 1GO x 10’0 3.00>: 104 k-1, 3Gox 102 kl, 8.90x log k--u 1%30X IO5 3.00x 1010 kz laox 10” k, 6.00~ lo4 4.45 x IO” h-1, 1.73 x 1010 k-3 1GOx 106 k -ir 2.20 x 107 1GOx IO” k-1, 1~00%108 1~00~10~ ki 2.20 x 10” k 7.40x IO-’ k4 3.10 ke, 1.85 x lo8 k:O,, 7.00 x 105 4.00 x 104 h-4 1mx 104 k, k, 2.00 x 104 1.57 x 10” 1.25 x 108 k,, 5.15x 10” k:, 1%)x 10G k-,“. 203x 1012 k-21 7.40x 10-l 1.00x 10” 1.00x 102 kn kzz km, 2.00 x 107 103Y. 106 k-m
$ The units are min-l
for first order rate constants and mollwl
min-’ for second order.
A MODEL
FOR GLUTAMATE
DEHYDROGENASE
89
Similarly a two-step dead-end branch was formed by NADH and secondarily cc-ketoglutarate binding to free enzyme (E) and giving terms XVIII and XIX. Only term XVII, which is quantitatively a very small function, was not obtained from this model (Fig. 4). Model 4 was obtained from model 3 by adding dead-end branches in such a way that either random pathway or second site models could serve as a basis for their formation. Since no such opportunity was found for term XVII and since it was the least significant feature of equation (2), it was ignored. Rate constants were assigned to model 4 (Table 2) so that 22 of the 23 kinetic coefficients (Table 1) were obtained with the proper numerical values. Also nine micro-reversibility equations and the equilibrium constant (6.26 x 10e5) for the reaction had to be satisfied. The values used for rate constants were within the ranges reported by Eigen & Hammes (1963). The largest second-order rate constant was 2.54 x IO’ ’ mol/l/min (4-25 x 10” mol/ I/s) and the slowest first-order rate constant was 3.7 x 10v2 min- l (6.2 x 1o-4 SC’). Using model 4, the rate constants in Table 2 and Remech (a computer program to calculate reaction rates, DeTar, 1969), reaction rates were
FIG. 5. Double reciprocal plot of velocity and NAD at two different glutamate concentrations. The velocity is expressed in terms of enzyme hexamer molecular weight (313000). Data from Barton & Fisher, 1972; Parks, 1973. All the data was collected at pH 8.0 in 0.1 M sodium phosphate buffer with 10e4 M EDTA. The line was calculated using model 4 and the rate constants in Table 2.
90
9.
D.
WELLS
ET AL.
I.3 x 10-4
4-3x10-4
Oo-
’
I
40
I
10-Z [GLUI
FIG. 6. Double reciprocal plot of glutamate (glu) and velocity at four NAD concen trations. See Fig. 5 for details.
IO2
[GLU]
,
FIG.
7.
Plot of reciprocal velocity versus glutamate at four NAD concentrations. See Fig. 5 for details.
r
[Kgl
10-3
.-I-. IO
.-
FIG. 8. Double reciprocal plot with a-ketoglutarate (Kg) at three different NADH and ammonia (A) concentrations. The fines are calculated with model 4 and the rate constants in Table 2. Data from Tam, 1972.
o+----;_____-~--.
92
B. D. WELLS __
.-__-
-
~_--.--
ET
AL.
.-___
-..
_____-____
3r---[NADH]
10-4
10-4
FIG. 9. Plot of reciprocal velocity and a-ketoglutarate NADH concentrations. See Fig. 8 for details.
(Kg) at two ammonia (A) and
IL>
-[Al
5x10-3
[Kg]
4x10-2
10-Z
5 x 10-2
10-2
5 x 10-3
I--l--I-l
2
3
4
IO~[NADH]
FIG. 10. Plot of reciprocal velocity and NADH concentration (Kg) and ammonia (A) concentrations. See Fig. 8 for details.
at three a-ketoglutarate
A MODEL
FOR
GLUTAMATE
93
DEHYDROGENASE
obtained theoretically for each experimental combination of reactant concentrations. The calculated values were compared statistically with experiment and gave a standard deviation of 12.0% in the forward direction and 13.8 in the reverse. Calculated lines and data points are compared in Figs 5-10. The fit obtained is very good considering that over 2200 experimental velocities are involved taken over a 4-year period by different investigators using different enzyme preparations. In ail cases the data were normalized to a standard assay condition in the direction of glutamate oxidation. This work was supported by National Institutes of Health grant No. GM-17506 and by contract No. E-(40-1)-2690 between the U.S. Energy Research and Development Administration and the Institute of Molecular Biophysics, Florida State University. REFERENCES BARTON, J. S. & FISHER, J. R. (1972). Biochemistry 10, 577. DALZIEL, K. & EGAN, R. R. (1972). Biochem. J. 126,975. DETAR, D. (ed.) (1969). Computer Programs for Chemistry, Vol. II, pp. 16-255. Academic Press. DIFRANCO, A. & IWATSUBO, M. (1972). Eur. J. Biochem. 30, 517. DIFRANCO, A. (1974). Eur. J. Biochem. 45,407. EIGEN, M. & HAMMES, G. (1963). A&J. Enzymol. 35, 1. FISHER, H. (1973). Adv. Enzymol. 39, 369. PAL, P. K., WECHTER, W. J. & COLMAN, R. F. (1975). Biochemistry 14, 707. PARKS, L. A. (1973). Ph.D. Dissertation, Florida State University, Tallahassee, SILVERSTEIN, E. & SULEBELE, G. (1973). Biochemistry 11,2164. TAM, I. (1972). Masters Thesis, Florida State University, Tallahassee, Florida. WELLS, B. D., STEWART, T. A. & FISHER, J. R. (1976). J. theor. Biol. 60,209.
New
York:
Florida.
A Kinetic Model for Glutamate Dehydrogenase B. D. WELLS,? L. A. PARKS, I. TAM AND J. R. FISHERS Department of Chemistry and Institute of Molecular Biophysics, Florida State University, Tallahassee,Florida 32306, U.S.A (Received 10 February 1976, and in revisedform 17 May 1976)
A model for the glutamate dehydrogenase reaction has been obtained that contains the reported intermediates suggested by binding and equilibrium isotope exchange methods. Calculated steady state-initial velocity rates using this model are quantitatively consistent with a wide range of nonlinear experimental data in both directions. 1. Introduction
A number of approaches have been used in studying the mechanism of action of bovine liver glutamate dehydrogenase (EC 1.4.1.3) (GDH). Silverstein & Sulebele (1973) reported the formation of numerous enzyme-bound reactants using isotope exchange kinetics with the system at equilibrium. A number of alternate (random) pathways were identified. Recent binding studies also have detected several enzyme complexes (DiFranco & Iwatsubo, 1972; Fisher, 1973; DiFranco, 1974). Furthermore, detailed steady state kinetics have revealed extensive nonlinearity, particularly in the direction of glutamate oxidation (Barton & Fisher, 1972; Parks, 1973; Dalziel & Egan, 1972). These kinetic results require the presence of cycles in the mechanism (Wells, Stewart & Fisher, 1976). The intermediates detected in isotope exchange reactions and binding studies suggest that at least some of the needed cycles are the result of random (alternate) pathways. Recently Pal, Wechter & Colman (1975) have used affinity labelling to provide direct evidence for a second noncalaytic regulatory site on GDH. These results suggest that both ADP and NADH bind to this site and thereby provide a mechanism for generating cycles in addition to random pathways, The purpose of the research described here was to bring these kinetic and binding studies together in the form of a proposed mechanism. Furthermore 7 Present address: Department of Chemistry, Columbia University, New York, New York, 10027. 1 Deceased. T.R.
81
6
82
B.
D.
WELLS
ET
AL.
it was hoped that the resulting model would be quantitatively consistent with the extensive kinetic data that we have amassed (Barton & Fisher, 1972; Parks, 1973; Tam, 1972). 2. A Preliminary
Model
During the last several years we have been accumulating extensive steady state-initial velocity measurements with GDH over wide concentration ranges of substrates in both the forward (glutamate oxidation) and reverse (glutamate formation) directions. These results were routinely normalized (Barton & Fisher, 1972) in order to obtain an internally consistent set of data that can be treated with one model and set of rate constants. This data set involving 441 combinations of concentrations and over 2200 individual assays has been represented by two empirical equations (given below) which have been presented previously in slightly modified form (Barton & Fisher, 1972; Tam, 1972). The lower case letters are kinetic coefficients orward
direction
(1) d
___-1 if = a+b+c[D]+fi I II
III
L+ccl
[G] IV
f+g[D] v 1 __---__ + @j-fT[G] +J’[D][G] VI
+ k[D] VII
reverse direction
(2)
j+m-+-L+.____-
+
VIII
[DH] IX
[K] x
[K];DH] XI
+ &+ XII
~
____-
fi];K] XIII
+ [A];DH] XIV
+sCDH1 xv
vCDH1 + $WDHl ___ + t-K1 + ~CKIL-DHI + - LA1 CA1 XVI
XVII
XVIII
XIX
with values given in Table 1. Representation of data by equations composed of terms like those used in equations (1) and (2) does not prejudice the choice of models used for interpretation (Wells et al., 1976). This statement is based on the observation that second-site, co-operative and random pathway models give similar cycles and virtually identical mathematical functions. A model (Fig. 1) has been devised that is quantitatively consistent with equation (1) (Parks, 1973). When this model was used with the empirical
A MODEL FOR GLUTAMATE
83
DEHYDROGENASE
TABLE 1 Values (with standard deviations) of coeflcients Constant --- __ a
b : ; g h i
i k
Value
2*571tO.O5xlO-~ 1.36f0.26 x lo3 1~01f0~10x10~ 1%4f0.27 x 1O-8 1*27+0.10x lo-” 2.03f0.15 x LO2 5.42f1.02~ lo4 5.61 f0.96 x lo5 3.9810.71 x lo4 5.11 f0.32 x lo9 1*0x 10-z
in equations (1) and (2)
Constant I I?, n 0
P 4 r
s t 11 V W
Value 4~32~1O-~i2~8xiO-~ 1~56x10-9ztl~6x10-‘o 4*58x10-B+l~6x10-s 2.38 x 10-12f 1.1 x lo-= 1~08x10-~f2~0x10-~ 1~95x10-~0*7~9xIo-1~ 2.17 x 10-12f6.3 x lo-l3 1~73x10-~i1~0x10-3 3.76x10-4~9.0x10-5 1~63x10°15~7x10-1 6~30x10-bf1~0x10-5 5~llxlO-~i5~lX10-3
equation in the reverse direction
[equation (2)], it was found to be capable of accounting for some of the linear functions. However, three simple modifications allowed six of the 12 terms to be obtained (Fig. 2). These six terms (VIII, IX, X, XI, XIII, XVI) were predominantIy those needed for the linear regions with a-ketoglutarate and NADH. The enzyme intermediates in model 2 were compared to those found by Silverstein & Sulebeie (1973) using isotope exchange reactions and intermediates observed by others in binding studies (DiFranco & Iwatsubo, 1972). Since the intermediates found by isotope exchange were identified under conditions that could not have detected the presence of water at the catalytic site, we have assumed that water may or may not be present. The intermediates suggested by these other studies are shown in Fig. 2. It can be seen that we are suggesting four additional enzyme substrate complexes (EDAK, EAD, EAG and EAGD). Also it should be noted that several necessary
kinetic steps are included that involve events other than substrate or product
addition or elimination. However, one intermediate (EGDH) suggested by several research groups (Silverstein & Sulebele, 1973; DiFranco & Iwatsubo, 1972) is not present. Analysis of model 2 revealed that addition of this intermediate in level III forming a dead-end cycle could bring in terms XII and XIV [equation (2)]. This modification (Fig. 3) gives a model that accounts for all terms in the forward direction [equation (I)] and all of the linear terms in the reverse direction [equation] (2). However, all four nonlinear substrate
(NADH) inhibition terms in equation remain unaccounted for.
(2), (XV, XVII,
XVIII
and XIX)
84
B.
D.
WELLS
ET
AL.
FIG. 1. Model 1. A model to describe glutamate dehydrogenase kinetics in the direction of glutamate oxidation. The model consists of three levels (I, II and III). All the intermediates are described. An intermediate with a prime represents a kinetic step that does not involve substrate addition or product release. EAKDH = EGDW; G = glutamate; K = a-ketoglutarate: D = NAD; DH = NADH; A = ammonia; E = enzyme and W = water.
A MODEL
FOR GLUTAMATE
DEHYDROGENASE
85
FIG. 2. Model 2. Levels I and II of Model 1 have been interchanged and a cycle has been created by adding steps 13 and 14. The enzyme forms which are identical to those suggested by Silverstein & Sulebele (1973) are enclosed by boxes. See legend of Fig. 1 for details.
86
B. D. WELLS
ET
AL.
/A
FIG. 3. Model 3. The cycle added to model 2 has the enzyme forms identified. See the legend in Fig. 1 for details.
A
MODEL
FOR
GLUTAMATE
DEHYDROGENASE
87
FIG. 4. Model 4. The enzyme forms are included for the steps which were added to model 3. The encircled Roman numerals refer to the enzyme intermediates which give rise to the terms in equations (I) and (2). See Fig. I for details.
88
B. D. WELLS
ET
AL.
3. A Model for Glutamate Dehydrogenase We were very pleasantly surprised that the model based on kinetic data in the direction of glutamate oxidation could account for data in the back direction so well. All that remained was to modify model 3 to treat NADH inhibition. The recent direct evidence for a second site on GDH (Pal et al., 1975)led us to seriously consider NADH binding at such a site as a basisfor generating NADH inhibition terms. We assumedthat various intermediates (model 3) could bind NADH at this second site better than others. Furthermore it was necessaryto choose these intermediates in such a way that the needed terms could be obtained. For example, level I was arranged in a way that prevented terms from being dependent upon [A]. Hence this level yielded terms VIII, IX, X and XI in equation (2). Since term XV is also independent of [A] it could only come from this samelevel. We assumedthat complex EAG could bind NADH at a second non-catalytic site giving a dead-end branch. TABLE 2 Rate constants for model 4 Rate constant k+!; k-,
k, k-,
I;, k- c k13 Ii-13
k14 k-1, kd k-d x, k, XI km, L-R k-,
km k-2,
Rate Rate Rate Value? constant constant Value constant Value Value - ~- ..~~~___ ~~ 3.40~ 10-l k, imx 10’2 k, 140x 1O1’ k, 24xlx 102 4.20 103x 10’ k-6 2.10x 1010 k-o 1.00x 103 k-i, 4.20 x 10” k, 2.80 x lOI2 k, 2.00x 10’” 7.00~10~ k7 1 .oo x 108 km, 1~00x102 IL, 2aox 104 1.00x lOa k-, 1+IO>:10~ k,, 3.70x 10-Z k, 5.42~ 10” 7.70 x IO8 k8 1GOx10~ 4.15x 10-l km, km8 1GOx 10” A-- 12 2.54~10’~ 1.40 x lo5 k, 1.07x 107 kg 1~00x10’ k, 1.00x to7 2.20 x 107 1GOx IO8 k-, 5.42 x 10”’ km, 5.40x IO9 keg 3.30x lo* k, 2.00~10~ k, 6.00x 10’ k16 l%?Ox 106 6.30~10~ km, 140x lo9 ke, I~OOX 105 1.11 x10$ k-16 7.00 x 1O1’ k, 1.00x lo3 k17 l+Ox104 k, 1wx 10” 1.00x 105 k-z 7.00x 10” 1.00x 108 140x 106 k-17 k-t 1.73x IO’ k __ t* 540x lo2 k, 8.00 x 1O1’ ku 1GO x 10’0 3.00>: 104 k-1, 3Gox 102 kl, 8.90x log k--u 1%30X IO5 3.00x 1010 kz laox 10” k, 6.00~ lo4 4.45 x IO” h-1, 1.73 x 1010 k-3 1GOx 106 k -ir 2.20 x 107 1GOx IO” k-1, 1~00%108 1~00~10~ ki 2.20 x 10” k 7.40x IO-’ k4 3.10 ke, 1.85 x lo8 k:O,, 7.00 x 105 4.00 x 104 h-4 1mx 104 k, k, 2.00 x 104 1.57 x 10” 1.25 x 108 k,, 5.15x 10” k:, 1%)x 10G k-,“. 203x 1012 k-21 7.40x 10-l 1.00x 10” 1.00x 102 kn kzz km, 2.00 x 107 103Y. 106 k-m
$ The units are min-l
for first order rate constants and mollwl
min-’ for second order.
A MODEL
FOR GLUTAMATE
DEHYDROGENASE
89
Similarly a two-step dead-end branch was formed by NADH and secondarily cc-ketoglutarate binding to free enzyme (E) and giving terms XVIII and XIX. Only term XVII, which is quantitatively a very small function, was not obtained from this model (Fig. 4). Model 4 was obtained from model 3 by adding dead-end branches in such a way that either random pathway or second site models could serve as a basis for their formation. Since no such opportunity was found for term XVII and since it was the least significant feature of equation (2), it was ignored. Rate constants were assigned to model 4 (Table 2) so that 22 of the 23 kinetic coefficients (Table 1) were obtained with the proper numerical values. Also nine micro-reversibility equations and the equilibrium constant (6.26 x 10e5) for the reaction had to be satisfied. The values used for rate constants were within the ranges reported by Eigen & Hammes (1963). The largest second-order rate constant was 2.54 x IO’ ’ mol/l/min (4-25 x 10” mol/ I/s) and the slowest first-order rate constant was 3.7 x 10v2 min- l (6.2 x 1o-4 SC’). Using model 4, the rate constants in Table 2 and Remech (a computer program to calculate reaction rates, DeTar, 1969), reaction rates were
FIG. 5. Double reciprocal plot of velocity and NAD at two different glutamate concentrations. The velocity is expressed in terms of enzyme hexamer molecular weight (313000). Data from Barton & Fisher, 1972; Parks, 1973. All the data was collected at pH 8.0 in 0.1 M sodium phosphate buffer with 10e4 M EDTA. The line was calculated using model 4 and the rate constants in Table 2.
90
9.
D.
WELLS
ET AL.
I.3 x 10-4
4-3x10-4
Oo-
’
I
40
I
10-Z [GLUI
FIG. 6. Double reciprocal plot of glutamate (glu) and velocity at four NAD concen trations. See Fig. 5 for details.
IO2
[GLU]
,
FIG.
7.
Plot of reciprocal velocity versus glutamate at four NAD concentrations. See Fig. 5 for details.
r
[Kgl
10-3
.-I-. IO
.-
FIG. 8. Double reciprocal plot with a-ketoglutarate (Kg) at three different NADH and ammonia (A) concentrations. The fines are calculated with model 4 and the rate constants in Table 2. Data from Tam, 1972.
o+----;_____-~--.
92
B. D. WELLS __
.-__-
-
~_--.--
ET
AL.
.-___
-..
_____-____
3r---[NADH]
10-4
10-4
FIG. 9. Plot of reciprocal velocity and a-ketoglutarate NADH concentrations. See Fig. 8 for details.
(Kg) at two ammonia (A) and
IL>
-[Al
5x10-3
[Kg]
4x10-2
10-Z
5 x 10-2
10-2
5 x 10-3
I--l--I-l
2
3
4
IO~[NADH]
FIG. 10. Plot of reciprocal velocity and NADH concentration (Kg) and ammonia (A) concentrations. See Fig. 8 for details.
at three a-ketoglutarate
A MODEL
FOR
GLUTAMATE
93
DEHYDROGENASE
obtained theoretically for each experimental combination of reactant concentrations. The calculated values were compared statistically with experiment and gave a standard deviation of 12.0% in the forward direction and 13.8 in the reverse. Calculated lines and data points are compared in Figs 5-10. The fit obtained is very good considering that over 2200 experimental velocities are involved taken over a 4-year period by different investigators using different enzyme preparations. In ail cases the data were normalized to a standard assay condition in the direction of glutamate oxidation. This work was supported by National Institutes of Health grant No. GM-17506 and by contract No. E-(40-1)-2690 between the U.S. Energy Research and Development Administration and the Institute of Molecular Biophysics, Florida State University. REFERENCES BARTON, J. S. & FISHER, J. R. (1972). Biochemistry 10, 577. DALZIEL, K. & EGAN, R. R. (1972). Biochem. J. 126,975. DETAR, D. (ed.) (1969). Computer Programs for Chemistry, Vol. II, pp. 16-255. Academic Press. DIFRANCO, A. & IWATSUBO, M. (1972). Eur. J. Biochem. 30, 517. DIFRANCO, A. (1974). Eur. J. Biochem. 45,407. EIGEN, M. & HAMMES, G. (1963). A&J. Enzymol. 35, 1. FISHER, H. (1973). Adv. Enzymol. 39, 369. PAL, P. K., WECHTER, W. J. & COLMAN, R. F. (1975). Biochemistry 14, 707. PARKS, L. A. (1973). Ph.D. Dissertation, Florida State University, Tallahassee, SILVERSTEIN, E. & SULEBELE, G. (1973). Biochemistry 11,2164. TAM, I. (1972). Masters Thesis, Florida State University, Tallahassee, Florida. WELLS, B. D., STEWART, T. A. & FISHER, J. R. (1976). J. theor. Biol. 60,209.
New
York:
Florida.