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The Hard-Soft Acid-Base Principle in Enzymatic Catalysis: Dual Reactivity of Phosphoenolpyruvate YAN LI and JEREMY N

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The Hard-Soft Acid-Base Principle in Enzymatic Catalysis: Dual Reactivity of Phosphoenolpyruvate YAN LI and JEREMY N Proc. Natl. Acad. Sci. USA Vol. 93, pp. 4612-4616, May 1996 Biochemistry The hard-soft acid-base principle in enzymatic catalysis: Dual reactivity of phosphoenolpyruvate YAN LI AND JEREMY N. S. EVANSt Department of Biochemistry and Biophysics, Washington State University, Pullman, WA 99164-4660 Communicated by R. G. Pearson, University of California, Santa Barbara, CA, January 11, 1996 (received for review October 9, 1995) ABSTRACT In this paper, the chemical reactivity of C3 of Fukui function f(r) (9) is one such quantity that is related to phosphoenolpyruvate (PEP) has been analyzed in terms of the electronic density in the frontier molecular orbitals and density functional theory quantified through quantum chem- thus determines the chemical selectivity (10). For a chemical istry calculations. PEP is involved in a number of important reaction, a Taylor series expansion can be performed up to enzymatic reactions, in which its C3 atom behaves like a base. second order by energy perturbation methods within the In three different enzymatic reactions analyzed here, C3 framework of density functional theory (11). The energy sometimes behaves like a soft base and sometimes behaves like change for a molecule will be, to second order in the changes a hard base in terms ofthe hard-soft acid-base principle. This AN and Av(r): dual nature of C3 of PEP was found to be related to the conformational change of the molecule. This leads to a ( aE\- aE testable hypothesis: that PEP adopts particular conforma- AE = AN + tions in the enzyme-substrate complexes of different PEP- aN\ vN,(r) a v (r) N Av (r)dr using enzymes, and that the enzymes control the reactivity through controlling the dihedral angle between the carboxy- _E - l( d2E late and the C=C double bond of PEP. + II ) ANAv(r)dr + 2kd2N) ANN2 aNav(r) 2aNv(r) The chemical reactivity of the C==C double bond in phos- phoenolpyruvate (PEP) in enzymatic reactions is somewhat of +1 2E an enigma. There are at least three enzymatic reactions in +2 tav(r)av(r') N Av(r)/Av(r')drdr' which PEP participates by providing C3 of its enolpyruvyl moiety rather than its phosphate group (Fig. 1). In the reaction catalyzed by EPSP synthase (1, 2) (Fig. 1, path I), C3 of PEP = ,AN + hAN2 + fp(r)Av(r)dr + ANJf(r)Av(r)dr is protonated during initiation of the reaction, which implies, in terms of the hard-soft acid-base (HSAB) theory, that this carbon is a hard base (because a proton is believed to be a hard acid). On the other hand, in the reaction catalyzed by KD08P 2J av(r') A (r) v (r')drdr' [1] synthase (3, 4) (Fig. 1, path II), this same carbon acts as a soft v A base and is used to attack an aldehyde carbon, which is believed to be a soft base, of the cosubstrate of the enzyme. This dual where r and r' are independent variables of position, r1 is the reactivity of C3 of PEP has nothing to do with entropy; nor can global hardness, and s(r) is the local softness that is related to it be explained in terms of other current theories of enzymatic the Fukui function by s(r) = f(r)/iq. After some mathematical catalysis in a straightforward way. For example, although the manipulations, Eq. 1 can be rewritten as: enzyme active site can determine the relative orientation of the two bound cosubstrates with respect to one another, the AE = + relative binding geometry is unlikely to be sufficient to explain puAN -qAN2 + f p(r)Av(r)dr + ANJf(r)Av(r)dr the dual reactivity of PEP. However, it can be understood in terms of HSAB theory. This paper addresses this issue by using the methods of density functional theory quantified by quan- + a (r)dr) s(r)(Av(r))2dr [2] tum chemistry calculations. 2-(s(r)Av 2 THEORETICAL where a is a positive constant. For a bimolecular reaction of BACKGROUND molecules i andj, the energy perturbations of the whole system The HSAB principle was proposed more than 30 years ago by is AEi + AEj and can be rewritten as: Pearson (5, 6) to predict the stability and reactivity of a generalized acid-base reaction. According to the HSAB prin- AEtotal = AEi + AEj ciple, acids (and bases) can be classified into two kinds: soft and hard. The HSAB principle states that a hard acid likes to react with a hard base and a soft acid likes to react with a soft = (gi - gj)AN + (hqi + -1j)AN2 + f[pi(r)Avi(r) base. Parr et al. (7, 8) have used density functional theory to provide a theoretical basis for the HSAB principle and a method to quantify it. + pj(r)Avj(r)]dr + ANJWVi(r)Avi(r) To study chemical reactivity and selectivity, it is desirable to investigate quantities that characterize local properties. The Abbreviations: DAHP, 3-deoxy-D-arabinoheptulosonate-7-phosphate; EPSP, 5-enolpyruvyl-shikimate-3-phosphate; HOMO, highest occu- The publication costs of this article were defrayed in part by page charge pied molecular orbital; HSAB, hard-soft acid-base; KD08P, 3-deoxy- payment. This article must therefore be hereby marked "advertisement" in D-manno-2-octulosonate-8-phosphate; PEP, phosphoenolpyruvate. accordance with 18 U.S.C. §1734 solely to indicate this fact. tTo whom reprint requests should be addressed. 4612 Downloaded by guest on September 26, 2021 Biochemistry: Li and Evans Proc. Natl. Acad. Sci. USA 93 (1996) 4613 According to Eq. 7, for a given B, the larger local softnesses ia - fj(r)Avj(r)]dr + si(r)Avi(r)dr are, the lower the reaction energy will be; in other words, soft likes soft. Therefore, chemical selectivity and reactivity are controlled by the HSAB principle (6, 8). According to Eq. 5, for a protonation reaction, a minimal s(r) site is favored (11). + lj (f sj (r)A vj (r)dr) - af [si(r)(A vi(r))2 Thus, the match of the Fukui function is important for a chemical reaction to occur via a lower activation energy pathway. + sj(r)(Avj(r))2]dr [3] COMPUTATIONAL METHODS with All the calculations were carried out using the ab initio quantum chemistry program, GAMESS (12). The Fukui function AN = ANi = 2 0 [4] -ANj is approximated by the highest occupied molecular (HOMO) where Avi(r) is the external field that molecule i experiences density divided by two (13). The geometry of the molecules because of molecule j [we ignore the Avi(r) caused by the were optimized at the self-consistent field/6-31** level. To control the conformation of the molecule, the FREEZE change in geometry of molecule i]. Similarly, Avj(r) is the external field that molecule experiences command was used in GAMESS. The dihedral angle between the j because of molecule carboxylate group and the C-C double bond was fixed during i. In Eq. 3, qi is the global hardness of molecule i and rj is the the optimization procedure of the calculation. All calculations global hardness of molecule j. To understand the meaning of were carried out on the Maui High-Performance Computer Eq. 3, one can write: Center IBM model SP2 high-performance parallel computer. All the calculations converged and the equilibrium geometry was checked and shown to have one constraint. /E2otal2 Jsi(r) vi(r)dr! RESULTS AND DISCUSSION The Conformational Modulation of the Reactivity of PEP. + + A PEP has both C=C and C=O double bonds; the relative 2j(f s(r)Avi(r)dr) [5] orientation of the two planes of these bonds may be used by an enzyme to modulate the reactivity of PEP. This is loosely where analogous to pyridoxal phosphate-dependent enzymes (14), in which the relative orientation of the oa bond and the XT plane of the conjugated system is believed to be the determinant for A = (gi - tj)A N + (rji + qj)AN2 + f[pi(r)Avi(r) the chemical course of the reaction. Thus, the C-H bond, C- C bond, or C-N bond can be cleaved depending on its orientation to the ir system, and is the only example of enzymatic reaction mechanisms in which rotameric conforma- + pj(r)Avj(r)]dr + ANJ [fi(r)Avi(r) tions can be controlled by a particular enzyme to influence the outcome of the reaction. To explore the possibility that a similar mechanism controls PEP reactivity, the energy, the a )2 charge, and the Fukui function of PEP of differing conforma- -fA (r)A vj(r)]dr 2f[si(r)(A vi(r))2 tions were examined by quantum chemistry methods. The results are listed in Table 1. Thirty conformations at three + sj (r)(Av1 (r))2]dr [6] different ionization states were studied in which the dihedral angle between the carboxylate plane and the enol plane was IfA is small when compared with the first two terms of Eq. 5, varied from 00 to 90°. In Fig. 2, the energy of PEP at different then the reaction energy is lowered if the local softness of conformations and different ionization states are plotted. For molecular i and j are minimized. In other words, hard likes each ionization state, the energy at 900 is used as the reference hard. Similarly, one can have Eq. 6: for that particular ionization state and the energy reported in the plot is relative to that. The energy needed to change the conformation of PEP is highest for the monoionization state, a t2 A Ettal= - J [si(r)(Avi(r))2 about 6.5 kcal/mol.
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