l -Phenylalanine ammonia-lyase (maize, potato, and Rhodotorula glutinis)

ARCHIVES

OF

BIOCHEMISTRY

L-Phenylalanine Explaining

AND

the Kinetic

of Biochemistry,

(1977)

Ammonia-lyase (Maize, glutinis)

KENNETH Department

189, 102-113

BIOPHYSICS

Effects

Potato,

of Substrate Modification Relationships

R. HANSON The Connecticut Received

AND

Agricultural 06504 August

EVELYN Experiment

and Rhodotorula by Linear

Free-Energy

A. HAVIR Station,

New

Haven,

Connecticut

16, 1976

The action of phenylalanine ammonia-lyase [EC 4.3.1.51 on a series of para-substituted L-phenylalanines has been investigated. Multiple linear regression analysis has been used to relate the logs of k,,,, K,,,, and k,JK,,, to substituent parameters for electron withdrawal, hydrophobic bonding, and size. The inhibitory action of the enantiomeric nphenylalanines was also investigated. The results indicate that the rate-limiting step is not subsequent to the release of cinnamate from the enzyme. Explanations for the observed regression constants are discussed in terms of the influence of the substituent parameters on the dissociation constant for the bound substrate, the rate-limiting step, and intermediate steps such as the elimination process. The discussion utilizes a new theoretical treatment of the application of linear free-energy relationships to steadystate enzyme kinetics. It is shown that, in order to interpret structure-activity correlations in terms of rate and equilibrium constants for an unbranched catalytic sequence, a restricted model must apply. The reaction must have a single rate-limiting step so that quasi-equilibrium conditions prevail. In the QE-DS (quasi-equilibrium dominant-state) model, a single state of the enzyme-substrate complex is assumed to predominate. In the QE-FR (quasi-equilibrium fixed-ratio) model, changes in the enzyme substituents are assumed not to alter the ratio between the different forms of the enzyme-substrate complex prior to the rate-limiting step.

The theory of extrathermodynamic relationships allows organic reactions to be interpreted in terms of simpler model processes (l-3). The approach requires that chemical or physical equilibria be studied as a function of structure modificationeither ground-state equilibria defined by normal equilibrium constants or activation equilibria defined by rate constants. To a first approximation, the overall freeenergy change associated with an equilibrium may be treated as a linear combination of free-energy changes for individual model reactions. With well-chosen models, a further level of interpretation in terms of changes in molecular properties is possible. The kinetic constants for an enzymic reaction are, in theory, as susceptible to this type of analysis as other complex or-

ganic reactions (4-8). Indeed, data on interactions between drugs or agricultural chemicals and their biological targets can be ordered by structure-activity correlations (9-11). In this paper, the method is applied to the study of the reaction catalyzed by phenylalanine ammonia-lyase and the theoretical basis for interpreting the results examined. Phenylalanine ammonia-lyase catalyzes the anti elimination of NH3 and the (pro3&H of L-phenylalanine to yield trunscinnamate. The enzyme from many sources also acts on L-tyrosine to give truns-p-coumarate and both of these reactions are of physiological importance in higher plants. The reaction sequence is “ordered uni-bi” with cinnamate released before NH,+. Evidence has been pre102

Copyright All rights

0 1977 by Academic Press, Inc. of reproduction in any form reserved.

ISSN

OOEH%61

LINEAR

FREE-ENERGY

sented, by ourselves and others, that a dehydroalanine-containing electrophilic prosthetic group is present at the active site. If this group combines with the amino group of the substrate, the leaving group in the elimination step is the modified amino group. The aminated prosthetic group must be hydrolyzed after the release of cinnamate (for references, see 12, 13). An alternative view is that the modification of the amino group prior to N-C cleavage is achieved by coordination to a transition metal ion that is very firmly bound to the enzyme (14). The enzyme is, in principle, suitable for study because the substrate may be systematically modified by para substitution in the benzene ring. The results should provide information that can be integrated with other approaches to the study of the catalytic process. In addition, the kinetic data are of interest, as they bear on the metabolic role of the enzyme. The literature contains reports of the diverse metabolic effects of simple analogs of phenylalanine and tyrosine upon plant tissues (15). Some of these effects have been attributed to interactions with phenylalanine ammonia-lyase, yet the relevant kinetic information is exceedingly fragmentary. THEORETICAL

CONSIDERATIONS

Individual reactions steps. A substituent effect on a particular equilibrium involving the interaction of enzyme and substrate can, to a first approximation, be factored into three types of effect, as in Eq. [l], where X represents the substituent and H the refernce reaction for the unsubstituted compound (e.g., 5): -RTln(KX/KH) = 6~’

or -RTln(12X/KH) = ~AG+xtr,nic

t11

+ ~AGhydrophobie + BAGstertc . Each free-energy term in the equation may be related to the free-energy change for a single model reaction or to a linear combination of changes for model reactions (2). In this study, a single model has been used for each type to provide values for substituent parameters r, r, and A. (a) Electron withdrawal, cr: The basic Hammett relationship for aromatic com-

103

RELATIONSHIPS

pounds, log (KX/KH) or log (FzX/hH) = pa, provides u values for thepara substituents based on the ionization of benzoic acid by setting p = 1 for that equilibrium (2, p. 173). As additional information about the equilibria under study is lacking, sets of u values based on other model reactions have not been employed (2, 16). The constant p is a measure of the difference between the reaction studied and the reference reaction. This reaction constant will be written in equations as a rather than p. (b) Hydrophobic bonding, n: The interaction of many aromatic compounds with enzymes has been found to be effectively modeled by partition between octanol and water (17). The relationship may be expressed in the form log (KX/KH) or log (AxI KH) = br, where b is a measure of the difference between the equilibrium under study and the water-octanol reference which defines the substituent rr values (b = 1). (c) Size, A: There is no agreed best model for assigning steric parameters for aromaticpara substituents. The PavelichTaft-Ingold relationship for separating polar and steric effects, log (KX/KH) or log (kX/kH) = p*cr* + SE,, yields a set of E, values from a suitable reference reaction (s = 1). For many groups, Es has been shown to correlate linearly with average van der Waals radii (18, 19). In this study, we have employed as a substituent parameter A the displacement, in angstroms, of the van der Waals surface of thepara substituent beyond that for hydrogen in phenylalanine (i.e., the sum of bond lengths and van der Waals radii less the corresponding value for hydrogen). The relationship log (KX/KH) or log (kX/kH) = ch differs from the expression for u and Z- in that there is no reference reaction for which c = 1. For individual equilibria, given the above relationships, Eq. 111may be written as 121: log (KX/KH)

or log (kX/kF’) = au + br + CA.

121

Multiple-step reactions. In studying enzyme catalysis, empirical constants, a, b, and c may be determined from the regression of the catalytic parameters log kCat,

104

HANSON

AND

log K,, and log (k,,,/K,) against o, n, and A values. (For convenience, relative values using L-phenylalanine as a reference are used in this paper.) It is not necessarily true that, if all of the individual steps are describable by Eq. [21, the empirical a values will be related only to the CJcontributions to individual steps, b to the GTcontributions, and c to the A contributions. It is shown in the Appendix that for this to be true for an unbranched reaction sequence the reaction must have a single rate-limiting step so that quasi-equilibrium conditions prevail. In addition, for the regression constants for log kcat and log K, to be so related, additional restrictions must apply. The less restrictive kinetic model assumes that essentially all of the enzyme substrate complex is in one dominant state. This will be referred to as the quasiequilibrium dominant-state model (the QE-DS mode1J.l The alternative is a quasiequilibrium fixed-ratio model (QE-FR model) in which the ratio of the states of the enzyme substrate complex prior to the rate-limiting step is independent of the substituent parameters. If structure-activity correlations are to be interpreted, it must be postulated that one or the other of these restricted models is valid (at least to a first approximation). If it is later shown kinetically that neither simplified model

HAVIR

librium assumption has frequently been made in enzyme kinetic studies. The elimination step for phenylalanine ammonialyase, which would be expected to be influenced by u and A, may be prior to the ratelimiting step (see Discussion). It is therefore not possible to assume initially that the QE-FR model applies, although in many discussions of structure-activity correlations the implicit assumption has been made that only the substrate-binding step and the rate-limiting step are influenced by modifications of the substrate. The strategy adopted in this paper, therefore, is to assume provisionally that the QE-DS model applies and to regard the QE-FR model as a limiting case which could be adopted if all three substituent parameters are considered to influence only substrate binding and the rate-limiting step. Applying the QE-DS and QE-FR models. The empirical regression constants a, b, and c are estimates of the

partial derivatives with respect to u, 7~, and h of log kcat, log K,, or log (k,,JK,). It is assumed that the reaction sequence is unbranched and that the rate-limiting step is either cinnamate release or prior to this step. For the QE-DS model, Eqs. [31151 give the regression constants of u and analogous expressions give those of rr and A.

(8 log keat/Wri = (a log ~+rlwnh0 lois Km,am,,,k = (a log KJW,i+ (8 log (k,,,lKm)l~~),~ = (a log k+rlau),r~-

applies or that the interpretations are incompatible with other facts, then the attempt to make sense of the observed structure-activity correlations can be abandoned. With respect to phenylalanine ammonia-lyase, the low turnover number (12) may indicate that a single step is rate limiting and therefore that quasi-equilibrium conditions prevail. The quasi-equi’ Abbreviations used: QE-DS, quasi-equilibrium dominant state; QE-FR, quasi-equilibrium fixed ratio; ES,, dominant state of the enzyme-substrate complex; ES,, state of the enzyme-substrate complex before the rate-limiting step; ES,, first enzymesubstrate complex; E, enzyme; S, substrate; Pr, product.

(a log M/dU),h. (8 log (J'IM)W,,. (8 lw~&W,~

In these equations, for the rate-limiting

[31 [41 - (a logP/au)~~.

k,, is the rate constant

step,

K, = k-,/k+,

(= kopflko,,)

is the constant for dissociation strate from the enzyme, P=

I51

of the sub-

r-1 IIKi 2

is the product of all intermediate ria where Ki = k-i/k+i,

equilib-

r-1 M=IIKi dfl

is the product of equilibria between the dominant states of the enzyme-substrate

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FREE-ENERGY

complex and the state before the rate-limiting step (ESd to ES,),

P/M

= I$

is the product of equilibria between the first complex and the dominant state of the enzyme-substrate complex (ES, to ESJ. For the QE-FR model, the equations with respect to u are as follows and similar equations apply for r and X. 63 log k,,,lauL,

= (a logk+,lacL.

161

(a log K,lau),,

= (a log a,/e,,,,.

171

63 log (Kcat/KnJla(TLh=

(a log k+&&* - 63 log K,l&r),,.

[g]

In this model, the relative proportions of the different states of the enzyme-substrate complex in quasi-equilibrium. are not important; however, if only one is dominant, then Eqs. [ll to [31 give [61 to [81 by making the P- and M-containing terms zero. Certain generalizations follow. (a) Changes in log PO, cannot be ascribed to changes in log K,. (b) Changes in log K, cannot be ascribed to changes in log K,,. (c) If changes in a substituent parameter alter both log Fz,,, and log K, so that the regression coefficients differ significantly from zero, then at least two steps in the reaction sequence must be influenced by the change. (d) Zero regression coefficients may arise because of a balancing of effects. However, for the QE-DS model, alterations of K+, only, or an equilibrium after ES, (the equilibrium constant appears in both M and P), will cause the regression coefficient for log K, to be zero, but not of K, only, or that for log kcat. Alterations an equilibrium prior to ESd (the equilibrium constant in P but not M), will cause the regression coefficient for log k,,, to be zero, but not that for log K,. (e) For the QE-DS model, if a single intermediate step in the reaction sequence is strongly influenced by changing a given substituent parameter, e.g., r, the equilibrium constant must be before or after the dominant intermediate. If the affected step is before ESd (e.g., if ESd = ES,), then (8 log k,,,ldcT),, = (a log k+,/arr),,. If the affected step is after

RELATIONSHIPS

105

E& (e.g.l ES, = ES,), then (a logK,l&r),, = 0 logK,l&r),*. (f, For the QE-DS model, if changes in k,,, and K, with respect to a given substituent parameter are attributed to k,, and K,, it is not implied that other substituent parameters do not influence other steps (in contrast to the QE-FR model). Negative cooperativity. An additional kinetic assumption must be mentioned. Phenylalanine ammonia-lyase exhibits a degree of negative cooperativity between the enzyme subunits (20,211. With L-phenylalanine and L-tyrosine, this is observed as an upward curve in the v against vl[Sl plots at values of v below 50% of the maximum. Experiments with inhibitors indicate that the curvature is not attributable to the presence of a mixture of different enzymes (20, 21). The curvature is much less noticeable for the other para-substituted phenylalanine studied. To allow interpretation of our structure-activity correlations, we have assumed that the complications engendered by subunit interactions can be avoided by analyzing only the limiting high substrate values for kcat and Km. The above assumption may be translated into postulates about subunit interactions given specific models. Richard et al. (22) have derived steady-state “structural” rate equations for such models, which are not to be confused with saturation functions (23). For phenylalanine ammonia-lyase, a partially concerted twoprotomer model is favored (21). The limiting k,,, at high substrate concentration is equal to the product of the intrinsic kCat and an interaction coefficient aBB which allows for the influence of one protomer in the B state on the rate constants for the other in the B state. The corresponding limiting K, is the product of the intrinsic K, and a factor composed of interaction coefficients and ratio terms. If the model is accepted, our assumption is equivalent to saying that aBB and the factor for K, are not significantly influenced by changing para substituents. The model employs simplifications which may or may not be appropriate, thus we cannot justify our assumption by such a translation; however, the model could be used as a starting point

106

HANSON

AND

for studies of the influence of para substituents on negative cooperativity. MATERIALS

AND

METHODS

Amino acids. p-Fluoro-Land n-phenylalanines were a gift of Dr. D. C. Walton, College of Environmental Science and Forestry, SUNY, Syracuse, New York. The p-chloro-, p-bromo-, and p-iodo-mphenylalanines and 3-(2-thienylj-DL-alanine were resolved by treating the appropriate N-chloroacetyl derivatives of the m-compounds with carboxypeptidase A (Type II, Sigma) (24). Kinetic determinations. All kinetic measurements were performed on a Gilford 2400 recording spectrophotometer. The procedure for studying phenylalanine and tyrosine has been described (20, 25). The same methods were also used for the other substrates. Graphical analysis was used to obtain the limiting catalytic constants at high substrate concentration. The wavelengths used and the absorbancy (l-cm light path) of 1 pmol of the substituted truns-cinnamates in 3 ml of reaction mixture, pH 8.7, were as follows: F, 290 nm, 2.9; Cl, 290 nm, 5.0; Br, 290 nm, 14.8; I, 290 nm, 9.4; NO*, 320 nm, 4.8. As trans-p-bromocinnamate was not available for direct determination, its absorbancy was measured by treating known amounts (0.02-0.1 pmol) of p-bromo+phenylalanine with the enzyme from maize and measuring the change in absorbancy when the reaction had run to completion. The determinations with p-nitro-L-phenylalanine as a substrate were complicated by the strong absorbancy of this compound; however, at 320 nm, the substrate absorbancy at pH 8.7 was only 0.10 for 1 hmol in 3 ml. Changes in absorption spectra with pH introduced uncertainty into the determination of the pH optimum for this substrate, but the optimum is probably greater than pH 10. The inhibition constants for n-phenylalanine and its para-substituted analogs were determined by the same method used for n-phenylalanine (20). The departure from Michaelis-Menton kinetics was negligible over the range of substrate concentrations employed (0.8 to 6.7 mM) when inhibitor was present. In each case, the calculated maximum velocity was unchanged over the range of inhibitor concentrations tested (e.g., 0.1 to 6 mM). RESULTS

Table I shows K&,/k&,, K,, and K, values determined with the ammonia-lyase from three different sources. The K, values for the D enantiomers were determined using Gphenylalanine as the substrate, and the kinetics observed were, to a close approximation, those for competitive inhibition.

HAVIR

Table II shows the results of stepwise multiple linear regression analysis of the data in Table I [excluding 3-(2-thienyl)alanine]. Equations [91-[ill summarize the results using rounded numbers (see Discussion). As the number of data points must be appreciably greater than the number of explanatory variables for statistically meaningful results, only the experiments with the maize enzyme provided enough data to warrant multiple regression analysis. If the active sites of the enzyme from the three sources resemble each other sufficiently, however, examining all the data at once could provide information about the direct or indirect interactions between their common features and the para substituents. Table II shows (as do Eqs. [91-[ill) that, for each regression coefficient for the maize enzyme found to be significantly different from zero at the >95% level (boldface type), the significance has increased on using all of the data. The unconventional device of pooling the data can, in part, also be justified by direct comparisons between the results for the maize and potato enzymes. There was no correlation between corresponding log K, values, and, for this reason, the log (K,X/K,H) values were not handled as one set. A relationship between log K, for the Lamino acid and log K, for the n-amino acids were observed for the potato enzyme (r = 0.93, N = 5), but not for the maize enzyme. Inhibition experiments were not carried out with the enzyme from R. glutink. The arguments in this paper are based on statistical analyses using appropriate tests of significance. However, graphs were examined of the simple regressions of the logs of each catalytic parameter against the substituent parameter found to be most significant in the multiple regression equation (also selected by the stepwise regression program as the best single explanatory variable). Visual appraisal did not provide strong grounds for excluding any particular point from the data set. It was apparent that the correlations with u depend heavily on the OH and NO, substituent parameters. The use of other parameter values (e.g., cr+) for these

LINEAR

FREE-ENERGY TABLE

ACTION

OF PHENYLALANINE

AMMONIA-LYASE ALANINE,

puru substituent or analog

H OH F Cl Br I NOz 3-(2-Thienyl)-alanine

I

ON pr~-SUBSTITUTED AND

THEIR

(%

1.0 0.125* 0.73 0.37 0.24 0.37 0.316 1.40

L-PHENYLALANINES,

3-(%THIENyL)-L-

D ENANTIOMERS”

Maize GLl Et

107

RELATIONSHIPS

Potato K (mM

~2;;

Km fnm

0.27 0.029 0.69 0.48 0.36 0.62 0.96”

0.90 0.85 3.10 1.30 0.27 0.067

1.0

0.26 0.26

1.47

1.40

R. glutinis (T%

y;z/

c%

1.0 0.22 0.49 0.0776 -

0.65 0.20 0.80 0.76” -

1.20

1.45

0.57 0.48 0.14* 0.35

0.28h 0.80

0.38 0.44 0.081 0.90 0.80

1.10

0.66

1.7

0.15

a Blanks indicate that no experiment was performed and dashes that either the L-amino acid was not a significant substrate or the n-amino acid was not a signifcant inhibitor. The k,,, and K, values are limiting values at high substrate concentrations for the L-amino acids and the K, values are for the n-amino acids using Gphenylalanine as a substrate. All kinetic parameters listed were determined at pH 8.7. Satisfactory replicate values were obtained when the same constants were determined on separate occasions, e.g., for the potato enzyme and p-bromo-L-phenylalanine: k&/k& 0.14, 0.16, 0.12; K,, 0.28, 0.30, 0.25 mM. Several factors, however, make the values for the nitro derivative more difficult to determine: the sensitivity of the ultraviolet spectrum of the product to pH, the correction in the assay for the absorbancy of the substrate, and the sensitivity of the enzymes’ catalytic constants to pH. * The optimum pH differed from 8.7 when theparu substituent was OH (pH 7.7), Cl (7.6), Br (9.6), and NO1 (>lO). In the instances indicated, therefore, the constants were also determined at the optimum or, in the case of the nitro compound, at pH 10. The results given as the ratio (k&J/(kbt for phenylalanine at pH 8.7) and as the K,” (if determined) were: maize enzyme (OH, 0.14; NO,, 0.55 and 0.74 mM), potato enzyme (Br, 0.13 and 0.13 mM), R. glutinis (Cl, 0.083 and 1.24 mM).

substituents would change the magnitude but not the sign of the regression constants. Such extreme points, however, may be influenced by special factors other than those of the model reactions giving CT values. This difficulty has been encountered in other enzyme studies and we must therefore enter a caveat concerning the interpretation of correlations with V. To a limited extent, graphical presentation can also be used to examine the relationship of the data points to the second-best explanatory variable as the scatter about the fitted line for the best variable may be related to specific values of the second-best variable. Such a method is not equivalent to finding a least-square fit to both variables. 3-(2-Thienyl)alanine (Table I) cannot be included in our arguments based on multiple regression analysis because it is not a paru-substituted analog of phenylalanine. The five-membered ring (S in place of C= C) bears a close electronic resemblance to the benzene ring. In agreement with this,

spectrophotometric titration (procedure to be described elsewhere) showed that the pK, of 3-(2-thienyl)acrylic acid barely differed from that of cinnamic acid: 4.18 compared to 4.10. Despite this, Scat for enzyme from each source was markedly increased over the corresponding phenylalanine value. Likewise, the K, values were all high. The enhancement in Scat could be explained in more than one way, but, whatever the explanation, the results lend support to the view that there are common features in the influence of substrate modification on the catalytic process for the enzyme from different sources. DISCUSSION

Equations [61-191 summarize the results in Table II. The probability that the regression coefficients differ from zero is indicated as follows: omitted, <90%; no asterisk, 90-95%; *, 9599%; **, 99-99.9%; ***, >99.9%.

OF LOGS

F (1, 2)

(K,“/K,“) (inhibition by D enantiomers) Maize only (N = 6)

4.658 14 (
-0.724 10 (-5%) -0.567 5 (-1%)

1.193 12 (-5%) 1.023 24 (
0.421 5 (-10%) 0.431 3 (-10%)

Coefficient a

OF RELATIVE

(r1.238)

(kO.252)

(rtO.229)

(50.209)

(kO.335)

(t0.023)

(-eO.191)

of o (*SE)

CATALYTIC

1.935 17 (-5%)

-0.174 2 -0.168 1.5

0.377 5 (-10%) 0.199 3 (-10%)

0.216 5 (-10%) 0.042 0.1

Coefficient b

Calculated of TT (*SE)

(20.464)

(kO.134)

(+O.llS)

(?O.lll)

(kO.173)

(k-0.124)

II

0.308 2

-0.137 1.5 -0.216 4 (2.5%)

-0.308 4 (-10%) -0.197 5 (-5%)

-0.453 24 (<2.5%) -0.417 18 (-0.1%)

Coefficient c

(20.231)

(?O.lOS)

0.127

-0.086

-0.1612

0.048

(kO.089)

(?O.llO)

0.161

-0.036

(20.161)

(kO.099)

FOR

0.003

Constant d

PARAMETERS

of A (GE) (kO.092)

SUBSTITUENT

constants

TABLE AGAINST

regression

(+0.098)

PARAMETERS

0.95

0.72

0.92

0.75

0.88

0.61

0.89

R2

0.205

0.252

0.166

0.209

0.243

0.232

0.138

s

Regression

para-SuBsTITuTED

(-5%)

(40%)

(~5%)

F (3, 12) = 13 ((10%)

F (3, 12) = 10 (0.1%)

F (3, 3) = 11

F (3, 12) = 12 (-0.1%)

F (3, 3) = 7.6

F (3, 12) = 6.5(-l%)

F (3, 3) = 8

N-m)

statistics

F (m-l,

gross

PHENYLALANINES~

o Stepwise multiple linear regressions were performed using the widely available SPSS program (Statistical Package for the Social Sciences). R* (coefficient of multiple determination) is the variance explained by the regression. The standard error of estimate s describes the scatter of the dependent variable points about the fitted line. All of the intercept constants d differ from zero, the hydrogen reference point, by less than s. In the last column, m = number of constants in the regression equation = number of explanatory variables + 1, and N = number of data points. F (m-l, Nm) allows the null hypothesis that there is zero variance explained-by o, r, and A to be tested. The probability that an F value as large as that listed could occur in sampling a random population is given in parentheses. The F (1, N-m) statistic under each regression yields the probability that such a value would be observed if that regression coefficient were zero. If the probability listed is 99%, etc. The values of the substituent parameters for H, F, Cl, Br, I, OH, and NO, used in the regression calculations were o: 0.0, 0.062, 0.227,0.232, 0.180, -0.370, 0.778; TK 0.0, 0.15, 0.70, 1.19, 1.43, -0.61, 0.24; and A (in angstroms): 0.0, 0.59, 1.46, 1.76, 2.17, 1.32, 1.99.

log

Maize only (N = 7) F (1, 3) All data (N = 16) F (1, 12)

lois[(kt/K,“)/(k,“,t/K~H)l

Maize only (N = 7) F 0, 3) All data (N = 16) F (1, 12)

log Wn,“/K,H)

Maize only (N = 7) F (1, 3) All data (N = 16) F (1, 12)

logEltlkEgt)

REGRESSIONS

!i 53

2

$

2 2.

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FREE-ENERGY

RELATIONSHIPS

- 0.4”“*dX. - 0.3 dh.

HOal

=

0.4 dcr

d log @,a,),~,

=

0.4 do

=

1.2”da

+ 0.4 dr

=

l.O***dc

+ 0.2 dn - 0.2”dX.

d log (k,,JK,),,i,,

= -0.7”du.

d log (k,,t/K,),ll

= -0.6”“dc

d log (KJmaize

=

4.7 du

The equations show correlations with CT and h that are clearly significant and r may also be important as an explanatory variable. Apparently, changes in the para substituents perturb the kinetics rather than completely alter the system. If steps subsequent to the release of cinnamate in the normal catalytic sequence are rate limiting, kcat would be independent of such perturbations, as the rate expression for kcat would contain only rate constants for steps subsequent to cinnamate release (e.g., 26). As over lo-fold variations in kcat were observed, either cinnamate release or steps prior to this must be rate limiting. This possibility has been considered before, but only limited data were available (12, 27). The mechanisms of phenylalanine and histidine ammonia-lyases show many resemblances and it is therefore of interest that similar conclusions have been reached for that enzyme (28). With the 4nitro and 4-fluoro analogs of L-histidine, the k,,, values were reduced over lo- and 30-fold, respectively. Pre-steady-state kinetic experiments on L-histidine and the 4fluoro compound indicated that for both substrates the rate-limiting step was prior to the hydrolysis of the amino enzyme. The effects of modifying the substituent parameters are most conveniently discussed in reverse order. In each case, the question is asked: If the regression results are indeed significant, the results unbiased by unrecognized factors, and the QE-DS model applies, what is the simplest explanation for the observed results? AS adding the potato and R. glutinis results to those for maize did not substantially alter the regression results, most of the

+ 0.2 dr

Dal WI

(kcathnaize

d log

109

- 0.4”dh.

Wbl LIlaI

- 0.2”dX. - 1.9”dr.

Ulbl ml

comments on the regression coefficients apply equally to the maize enzyme alone or to all three enzymes. Substituent size, A. Table I shows that there is a cutoff in substrate binding when the substituents become too large. This is most noticeable for the R. glutinis enzyme, which will not accommodate Br, I, and NO,. The potato enzyme, however, will act on substrates with bulkier groups than L-tyrosine, which it does not bind, and the R. glutinis enzyme, which is less accommodating, acts on L-tyrosine. Size discrimination alone, therefore, does not account for the inability of the enzyme from some sources to bind L-tyrosine. The exclusion from the active site of L-tyrosine is of obvious metabolic importance, but the nature of the mechanism of exclusion is not apparent. The regression data apply only to compounds which are accommodated at the active site of the enzyme (including tyrosine). Unfortunately, although the regression coefficients clearly differ from zero, changes in substituent size are likely to alter the rate constants for almost any step in the catalytic sequence either by altering substrate alignment relative to the catalytic groups on the enzyme or by changing the structural energy of the protein in the various forms of the enzyme-substrate complex. If the main effects of these factors are upon the transition states rather than the ground states, the changes in the equilibrium constants for the intermediate steps may be small so that the partial derivative of log M and log PIM can be ignored. The analog of Eq. 131 then reduces = (8 log k+,/dA),, and the to (a log k,,,la&,

110

HANSON

AND HAVIR

regression results imply that increasing substituent size slows the rate-limiting step. The dissociation constant K, is atypical in that the structural energy of the protein only enters into one side of the equilibrium; thus, this constant may be more responsive to substituent changes. If the analog of Eq. [41 reduces to (a log Km/ the results imply ~&?I =(a log &/ax),,, an increase in substrate binding with increases in substituent size (up to the critical exclusion point). These would be the only available conclusions if the QE-FR model applied. The relationship between substituent size and substrate binding could be further examined by studying the binding of the L-amino acids to NaBH4inactivated enzyme. Hydrophobic bonding, 7~. It is reasonable to postulate that the regression coefficients of 7~for log K, and log K, reflect the responses of the dissociation constant a, to changes in rr. As the coefficients are of opposite sign (Eqs. [lo] and [121), it is unlikely that the aromatic ring of the inhibitor fits into the same position at the active site as the aromatic ring of the substrate. The same conclusion is suggested by the large differences in the coefficient of (+. Kinetic studies by Nari et al. (21) also indicate that the binding of n-phenylalanine differs from that of L-phenylalanine. They argue that n-phenylalanine will bind to only one of two protomers in the molecule and this inhibits both active sites. No hybrid complex is formed with D-phenylalanine on one protomer and its enantiomer on the active site of the other, but both protomers will bind the L-amino acid at their active sites. A further examination of the abilities of the several n-amino acids to protect the enzyme against inactivation by NaBH, (20) or NaBH$N (unpublished observations) would be in order. We consider it possible that the inhibiting effect of D-phenylalanine is associated with binding to a single regulatory site located on the twofold symmetry axis of the protein rather than with binding to an active site. The problem is of great importance as in uiuo compounds which in some way act like n-phenylalanine may serve to regulate the enzyme’s activity. Electron withdrawal, cr. The main influ-

ence of (T is likely to be on the elimination process and on substrate binding. There are many examples in the literature of (T influencing the binding of inhibitors to enzymes and Eq. [12] indicates such an influence for n-phenylalanine. If the elimination process is subsequent to the dominant intermediate, the partial derivative of log P/M may be relatively small so that (a log K,lac+Lx = (a log Ei’J&r),,. The results thus suggest that binding decreases with electron withdrawal. If (a log K,l~?cr),~ is interpreted in this way, then (a log &,J a~),, must reflect the influence of o upon the elimination process. Were C-H bond breaking rate limiting, it would be reasonable to equate the observed regression coefficient with (a log &/do),*, as has been done in studies of mandelate racemase (29) and yeast alcohol dehydrogenase (7, 8). The tritium isotope effect on k&Km for phenylalanine ammonia-lyase, however, is exceedingly small (30); thus, C-H bond breaking is probably associated with an equilibrium step prior to the rate-limiting step. If one assumes that this step is subsequent to the dominant intermediate, then a positive Hammett p for an equilibrium associated with a stepwise or concerted elimination process would tend to make (a log M/&T),, negative and therefore (a log k,,,/aa),, positive -as observed. In this context, it would be of interest to determine p for the elimination process itself by studying the influence of para substituents on log +K,. Radioactive substrates would be required as the equilibrium for Lphenylalanine strongly favors loss of ammonia (12, p. 22; 20). The regression results are least satisfactory with respect to the most important issue under investigation: the nature of the elimination process. [The alternative mechanisms for elimination may be discussed in terms of pathways over a freeenergy surface (12, pp. 31-33).1 A different approach to the study of electronic effects on the elimination is in progress. In collaboration with Dr. Charlotte Ressler, we have found that the phenylalanine analog 3-(1,4-cyclohexadienyl)-L-alanine (34) acts as a substrate for phenylalanine ammonia-lyase, but that k,,, is reduced from loto 40-fold depending on the source of the

LINEAR

FREE-ENERGY

enzyme (manuscript in preparation). It appears that replacing the aromatic system by the less effective electron sink afforded by a double bond, slows the reaction. The elimination step for histidine ammonialyase probably lies on a continuum of possible mechanisms for the two enzymes. It is therefore of interest that coordination of the imidazole of L-histidine to a divalent metal ion at the active site is thought to assist C-H bond breaking because the metal acts as an electron-withdrawing substituent (35). Klee et al. (28) report that, although L-[P-2HJhistidine and its para fluoro derivative show significant isotope effects on &, electron withdrawal in the corresponding nitro compound labilizes the P-hydrogen to such an extent that C-H bond breaking is no longer partially rate limiting and an isotope effect is not observed. The above discussion illustrates both the utility and limitations of the linear free-energy approach to the study of enzyme-substrate interactions. There is no guarantee that observed correlations are interpretable; however, with simpler systems in which the rate-limiting step involves a chemical transformation, and especially if a single explanatory variable suffices, the QE-FR model is likely to seem appropriate. The results are attributed to changes in k,,, and R, only. With a complex system, such as that investigated here, the QE-DS model may be a useful approximation to the true situation. Assignments of the influence of (+, rr, and h upon individual reaction steps depend upon the choice of simplifying assumptions. Acceptance of the model, however, does not require that a complete assignment be made. In studying enzyme kinetics with metabolically significant compounds, resolution into separate contributions by (+, 7~, and A represents an important gain in information and the QE-DS model may be used to justify this resolution.

111

RELATIONSHIPS APPENDIX

THE

QE-DS MODEL

Let the equilibrium constant K be a continuous function of the substituent parameters u, n, and A definable by three distinct model reactions. If there is a linear combination of free-energy terms, K has the form exp (eu + f71-+ gh + h). The partial derivatives of log K with respect to (T, V, and A in Eq. [131 are, therefore, identical to the constants e, f, and g: d log K = (a log K/&&

dcr

+ (a log K/&T),*

dm

+ (d log K/ah),,

dh.

Let all of the equilibrium and rate constants in an enzymatic process have the above properties. If A stands for kcat, K,, or kcatlKm, what conditions must the kinetic model satisfy so that the partial derivatives in Eq. 1141are constants independent of (T, z-, and A? d log A = (a log A/&T),,

dv

+ (a log A/&T),*

dr

+ (d log A/dA),,

1141 dh.

Hansch et al. (4) examined the simple modelE +SeESeEPr=E +Prwhere ES + EPr is rate limiting and the binding step is a quasi-equilibrium. The next order of complexity is to consider a quasi-equilibrium model with multiple intermediates between the binding step and the rate-limiting step. The general case may be approached through a specific model. In the following, step 5 is rate limiting so that all steps prior to this are in equilibrium. In Eqs. [151-1171, the terms are grouped to allow special consideration to be given to the rate-limiting and substrate-binding steps. By writing k-,/k+, = Ki, the use of reciprocals is avoided. If

E+s3c3,Sc3,33~,~ ES, 4 _ . . + E + Pr, then:

log kc,, = log k+, - log[(&+

[131

1,&s + l)% + 11.

log Km = log K, + log &K,K, - !og [(JK2 + l)K, + 1% + 11. log (k,,,/K,) = log k,, - log K, - log K&K,.

112

HANSON

AND

From the above, the general model yields Eqs. [18]-1201, where k,, is the ratelimiting step, P is the product and N is a nested function in the brackets above:

of a, to a,-, as

log 1Z,,t = log k,, - log N. log Km = log K, + log P - log N. log (Iz,atlKd

= lois k+r - log $1 - log P.

WI [19]

PO1

The partial derivatives with respect to (+, rr, and A of log K,, and log a, are constants by definition, and the partial derivatives of log P are likewise constants because log P is the sum of log K terms. However, as long as there are two separate terms in the expression for N, the partial derivatives of log N will not be constants but will be functions of N and therefore of all of the explanatory variables. It follows that only the partial derivatives of log (k,,JK,) are constants. For this to be valid for log kCat and log K,, a model must apply in which the only important term in N is a simple product of equilibrium constants. The necessary model may be identified as follows. The expression for N may be written as t&K, . . . I?-, + R& . . . ICeI + . . - + K,-, + 1 = M, + M2 + . . * + il4-, + M,-,. Each M term corresponds to a situation in which the equilibria in N are biased so that ES, is a dominant state of the complex. If all the equilibria arebiased in the back direction SO that each (Ki + 1) = Ki, the ES, is dominant and N = Ml = P, whereas if all are biased forward so that each (Ki + 1) = 1 then ES,-, is dominant and N = M,-, = 1. Each of the other M terms similarly corresponds to a dominant state situation; thus, in the QE-DS model, r-1

N is replaced by M = II1 Izli and log P - log N by log P/M

= log & Xi. The partial

derivatives with respect’to a given substituent parameter may then be written as in Eqs. 131~151. In the restricted model discussed by Hansch et al. (4), there is only one enzyme-substrate complex, ES, prior to the

HAVIR

rate-limiting step k+z. The above analysis suggested the alternative restricted model in which one or more explanatory variables influence k,, K1, or both, but none of the intermediate steps. With respect to k,, this could arise when only the rate-limiting step involves chemical catalysis. As log N would then be a constant, its complexity would be irrelevant and the states of the enzyme-substrate complex would be in a fixed ratio to each other. This has been referred to above as the quasi-equilibrium fixed-ratio model (the QE-FR model). The results of linear regression analysis are not interpretable if a general steadystate model for enzyme catalysis applies. The expressions for kcat, K,, and k,,,/K, all contain summations of products of rate and equilibrium constants (26) so that the same difficulty with respect to partial differentiation arises as for N above. ACKNOWLEDGMENTS The investigation was supported, in part, by Grant No. GB 29021-X from the National Science Foundation. We wish to thank Drs. Yves Parlange and Judith Klinman for helpful discussions and Katherine A. Clark for skillful technical assistance. REFERENCES 1. CHAPMAN, N. B., AND SHORTER, J. (eds.) (1972) Advances in Linear Free Energy Relationships, Plenum Press, London/New York. 2. LEFFLER, J. E., AND GRUNWALD, E. (1963) Rates and Equilibria of Organic Reactions, Wiley, New York/London. 3. SHORTER, J. (1973) Correlation Analysis in Organic Chemistry, Claredon Press, Oxford. 4. HANSCH, C., DEUTSCH, E. W., AND SMITH, R. N. (1965) J. Amer. Chem. Sot., 87, 2738-2742. 5. HANSCH, C., SCHAEFFER, J., AND KERLEY, R. (1972) J. Biol. Chem. 247, 4703-4710. 6. KIRSCH, J. F. (1972) in Advances in Linear Free Energy Relationships (Chapman, N. B., and Shorter, J., eds.), pp. 369-400, Plenum Press, New York. 7. KLINMAN, J. P. (1972) J. Biol. Chem. 247, 79777987. 8. KLINMAN, J. P. (1976) Biochemistry 15, 201% 2026. 9. CAMMARATA, A., AND ROGERS, K. S. (1972) in Advances in Linear Free Energy Relationships (Chapman, N. B., and Shorter, J., eds.), pp. 401-444, Plenum Press, New York.

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FREE-ENERGY

10. HANSCH, C., AND FUJITA, T. (1963) J. Amer. Chem. Sot. 86, 1616-1626. 11. VAN VALKENBURG, W. (1972) Biological Correlationsthe Hansch Approach, Advances in Chemistry, Series 114, American Chemical Society, Washington. 12. HANSON, K. R., AND HAVIR, E. A. (1972) in The Enzymes (Bayer, P., ed.), 3rd ed., Vol. 7, pp. 75-166, Academic Press, New York. 13. HAVIR, E. A., AND HANSON, K. R. (1975) Biochemistry 14, 1620-1626. 14. DIXON, N. E., GAZZOLA, C., BLAKELEY, R. L., AND ZERNER, B. (1976) Science 191, 1144-1150. 15. LEA, P. J., AND NORRIS, R. D. (1976)Phytochenistry 15, 585-595. 16. KRYGOWSKI, T. M., AND FAWCETT, W. R. (1975) Canad. J. Chem. 53, 3622-3633. 17. LEO, A., HANSCH, C., AND ELKINS, C. (1971) Chem. Rev. 71, 525-616. 18. CHARTON, M. (1969) J. Amer. Chem. Sot. 91, 615-618. 19. HANSCH, C. (197O)J. Org. Chem. 35, 620-621. 20. HAVIR, E. A., AND HANSON, K. R. (1968) Biochemistry 7, 1904-1914. 21. NARI, J., MOUTTET, C., FOUCHIER, F., AND RICARD, J. (1974) Eur. J. Biochem. 41, 499-515. 22. RICHARD, J., MOUTTET, C., AND NARI, J. (1974) Eur. J. Biochem. 41, 479-497.

RELATIONSHIPS

113

23. KOSHLAND, D. E., JR., N~METHY, G., AND FILMER, D. (1966) Biochemistry 5, 365-385. 24. FONES, W. S., AND LEE, M. (1953) J. Biol. Chem. 201, 847-856. 25. HAVIR, E. A., REID, P. D., AND MARSH, H. V., JR. (1971) Plant Physiol. 48, 130-136. 26. BLOOMFIELD, V., AND ALBERTY, R. A. (1963) J. Biol. Chem. 238, 2811-2816. 27. PARKHURST, J. R., AND HODGINS, D. S. (1972) Arch. Biochem. Biophys. 152, 597-605. 28. KLEE, C. B., KIRK, K. L., COHEN, L. A., AND MCPHIE, P. (1975) J. Biol. Chem. 250, 50335040. 29. HEGEMAN, G. D., ROSENBERG, E. Y., AND KENYON, G. L. (1970) Biochemistry 9,4029-4036. 30. WIGHTMAN, R. H., STAUNTON, J., BATTERSBY, A. R., AND HANSON, K. R. (1972) J. Chem. Sot. Perkin I, 2355-2364. 31. MORE O’FERRALL, R. A. (1970) J. Chem. Sot. B, 274-277. 32. SCHMID, P., AND BOURNS, A. N. (1975) Canad. J. Chem. 53, 3513-3525. 33. WINEY, D. A., AND THORNTON, E. R. (1975) J. Amer. Chem. Sot. 97, 3102-3108. 34. SNOW, M. L., LAUINGER, C., AND RESSLER, C. (1968) J. Org. Chem. 33, 1774-1780. 35. MILDVAN, A. S. (1971) Aduan. Chem. Ser. 100, 390-400.