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Energy Considerations Show That Low-Barrier Hydrogen Bonds Do Not

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Energy Considerations Show That Low-Barrier Hydrogen Bonds Do Not Proc. Natl. Acad. Sci. USA Vol. 93, pp. 13665–13670, November 1996 Biochemistry Energy considerations show that low-barrier hydrogen bonds do not offer a catalytic advantage over ordinary hydrogen bonds (enzymesytransition stateysubtilisinyelectrostaticsyevolution) ARIEH WARSHEL† AND ARNO PAPAZYAN Department of Chemistry, University of Southern California, Los Angeles, CA 90089-1062 Communicated by George A. Olah, University of Southern California, Los Angeles, CA, August 26, 1996 (received for review June 3, 1996) ABSTRACT Low-barrier hydrogen bonds have recently do not add any new physics to the regular HB description—i.e., been proposed as a major factor in enzyme catalysis. Here we they cannot define a new kind of HB. As we describe below, evaluate the feasibility of transition state (TS) stabilization by the only relevant and novel concept introduced by LBHBs is low-barrier hydrogen bonds in enzymes. Our analysis focuses a more covalent character, accompanied by a more disperse on the facts that (i) a low-barrier hydrogen bond is less stable charge distribution. Only to the extent that this distribution is than a regular hydrogen bond in water, (ii) TSs are more significantly different than an OHB and has different ener- stable in the enzyme active sites than in water, and (iii)a getics, especially in response to its environment, that we can nonpolar active site would destabilize the TS relative to its make sure that we are considering a distinct class of HB. energy in water. Combining these points and other experi- When a hydrogen atom is between two electronegative mental and theoretical facts in a physically consistent frame- atoms, an attractive interaction develops. This attraction is work shows that a low-barrier hydrogen bond cannot stabilize stronger than a van der Waals interaction, and is called a the TS more than an ordinary hydrogen bond. The reason for ‘‘hydrogen bond’’ (16). Hydrogen bonding can simplistically be the large catalytic effect of active site hydrogen bonds is that explained as the electrostatic attraction between the partial their formation entails a lower reorganization energy than charges on the atoms involved. For example, the dipole formed their solution counterparts, due to the preorganized enzyme by X2d 2 H1d would have a fairly strong interaction with the environment. charge on Y2D. Since a restricted electrostatic description would use the unperturbed charge distribution of the isolated The origin of the enormous catalytic power of enzymes is a fragments (i.e., X2d 2 H1d and Y2D), it would be unable to problem of great fundamental and practical importance. It is account for the distortions in those distributions when the HB becoming increasingly clear that this catalytic power is mainly donor and acceptor approach each other. However, that due to transition state (TS) stabilization, but there is yet to be process can be partly represented by polarizability and handled a consensus on how the stabilization is provided. The uncata- by the methods of classical electrostatics (17). The remaining lyzed versions of reactions that are catalyzed by enzymes often factors are strictly quantum mechanical effects, such as charge proceed extremely slowly in aqueous solution. Associating the transfer between proton donor and acceptor. The exact nature polarity of water with this slowness, a nonpolar environment of such ‘‘partitioning’’ of the hydrogen bonding and the size of has often been thought to be necessary for accelerating those the individual contributions depend on personal perspective reactions (1, 2). This has lead to proposals of enzymatic and the quantum mechanical methodology employed (18, 19). reaction mechanisms that are viable only in nonpolar media, Our choice for describing hydrogen bonding is based on a VB whereas enzyme active sites are usually polar. One such formalism and is motivated by the ease with which the envi- proposal suggests that the enzyme forms a partial covalent ronmental effects and the degree of covalent interaction can bond with the ionic TS through a low-barrier hydrogen bond be incorporated into the empirical VB (EVB) formulation (17). (LBHB) that is stabilized by quantum resonance interactions The starting point of this approach is a VB model of a HB (3–5). Hydrogen bonds (HBs) do contribute substantially to in vacuum. The corresponding Hamiltonian is based on the enzyme catalysis. This fact has been gaining increasingly wider three-orbital four-electron model of Coulson and Danielsson recognition, due, in part, to mutation experiments (6, 7) that (20) which involves three VB states as follows (17): confirmed earlier theoretical estimates of the catalytic HBs 2 and the prediction that ‘‘preorganized local dipoles’’ (e.g., HBs c1 5 XOHY and carbonyls) are very important in TS stabilization (8–10). c5X2HOY However, the physical reasons for the importance of catalytic 2 HBs are apparently still subject to debate (3–5, 11–15). c5X2H1Y2. [1] Using a valence bond (VB) description of hydrogen bonding 3 and analyzing energetic requirements, we conclude that LB- The effective VB Hamiltonian involves diagonal (diabatic) HBs do not offer extra TS stabilization over regular HBs. This energies of the three states (Fig. 1) and off-diagonal terms that conclusion is independent of specific computational or exper- represent the resonance interaction between those states. The imental methodologies, although they are used to provide ground state-energy (Eg) of the system is obtained from the examples, hopefully making the arguments clearer. effective VB Hamiltonian (17). The free energy corresponding to Eg is denoted by g#. An effective Hamiltonian can be obtained Hydrogen Bonding by fitting a three-state model to the results of gas phase ab initio (AI) calculations as is done in the EVB approach (21, 22). The Below we define ordinary HB (OHB) and LBHB in a way that three VB states can usefully be projected onto an effective will hopefully make the analysis amenable to a clear discussion. two-state model (Fig. 1) that simplifies the analysis and Note that terms such as ‘‘short’’ or ‘‘low-barrier’’ by themselves Abbreviations: TS, transition state; HB, hydrogen bond; LBHB, The publication costs of this article were defrayed in part by page charge low-barrier HB; OHB, ordinary HB; VB, valence bond; EVB, empir- payment. This article must therefore be hereby marked ‘‘advertisement’’ in ical VB; AI, ab initio. accordance with 18 U.S.C. §1734 solely to indicate this fact. †To whom reprint requests should be addressed. 13665 Downloaded by guest on October 2, 2021 13666 Biochemistry: Warshel and Papazyan Proc. Natl. Acad. Sci. USA 93 (1996) according to whether Dg#9 is larger or smaller than zero. For this purpose, it is convenient to define a parameter u by: 2 u 5 H12/@Dg9dia 1 H12/~l 1 DGPT!#. [5] Using the equality Dg#95H12(1 2 u)yu, a straightforward definition of LBHB corresponds to u $ 1 (i.e., Dg#9 # 0). Similarly, we can define an OHB as one with u , 1. Thus the existence of an LBHB is defined in terms of the competition between Dg#9dia and the resonance mixing term H12. This is also related to the competition between solvation and H12, since solvation effects increase Dgdia. FIG. 1. A three-state VB system with E1, E2, and E3 and the The existence of LBHB can also be formulated in terms of corresponding diabatic free energies g1, g2, and g3 can be projected onto a two-state VB representation. The resulting surfaces E9 and E9 a charge distribution. For example, a conventional HB with a 1 2 2 and free energies g91 and g92 no longer represent pure resonance negatively charged acceptor can be represented as X 2 HzzzY structures, but their mixing results in the same ground-state potential (or, more precisely, X2d1 2 H1d2zzzY211d12d2), where the charge surface Eg (with a corresponding free energy surface g#). When the is concentrated around one atom. This basically corresponds to donor and the acceptor are held at a distance R, the stabilization the resonance structure c1 (in the effective two-state model). resulting from the mixing of the two unpure states is given by H12(R,r), In contrast, the charge is spread out in an LBHB and its value at the barrier (r 5 r9) is denoted simply by H12. The 21y2XzzzHzzzY21y2 (or, more precisely, 21y22gXzzzHzzzY21y21g), be- coordinate r corresponds to proton movement at fixed R. cause of a ‘‘charge transfer’’ effect. In other words, when H12 discussion of HB systems. Thus the ‘‘quantum’’ or ‘‘resonance’’ at the minimum of g# is larger than the corresponding difference 2 between g2 and g1, the resonance structures [X HOY] and contribution is condensed into a mixing term between the two 2 ‘‘unpure’’ VB structures. The deformation in the charge [XOHY] contribute equally. Since the resonance mixing in distribution of the interacting species as they approach each the LBHB case is accompanied by significant charge rear- rangement, its extent is solvation-dependent. A polar environ- other is captured by the mixing term H12 and the polarizability (which is a property of the individual fragments and can be ment will favor either of the pure resonance structures because treated classically once its value is known) of each species. a concentrated charge is solvated better, whereas a nonpolar Most importantly for our discussion, the VB model provides a environment would compensate for reduced solvation by simple way for examining the effect of the environment. The increasing covalent mixing. The balance between these two ground-state free energy in a given environment can be effects determines whether or not we have an LBHB in a given expressed as (17, 22, 23): environment. (See Fig. 2 and the discussion below). 1 Free Energy Surfaces of Ionic HBs in g 5 ~g0 1 g0 1 Dg~1! 1 Dg~2!! Different Environments 2 F 1 2 sol sol 1/2 To clarify the effect of the environment on an ionic HB, we 0 0 ~2! ~1! 2 2 study HO2 HOH system in vacuum and in water.
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