Quantum mechanical modeling: a tool for the understanding of enzyme reactions

Abstract

Most enzyme reactions involve formation and cleavage of covalent bonds, while electrostatic effects, as well as dynamics of the active site and surrounding protein regions, may also be crucial. Accordingly, special computational methods are needed to provide an adequate description, which combine quantum mechanics for the reactive region with molecular mechanics and molecular dynamics describing the environment and dynamic effects, respectively. In this review we intend to give an overview to non-specialists on various enzyme models as well as established computational methods and describe applications to some specific cases. For the treatment of various enzyme mechanisms, special approaches are often needed to obtain results, which adequately refer to experimental data. As a result of the spectacular progress in the last two decades, most enzyme reactions can be quite precisely treated by various computational methods.

Figure 1

Hierarchical composition of a full enzyme system. Active site or quantum mechanical region (A); protein core or molecular mechanical region (P); bulk or dielectric continuum shell (B) (figure drawn on the basis of the crystal structure of human aromatase, 3EQM).

Figure 2

Reaction steps during serine protease catalyzed cleavage of the peptide bond (left). The acyl-enzyme intermediate hydrolyses via the reverse route (right).

Figure 3

The oxyanion hole stabilizing the tetrahedral intermediate in α-chymotrypsin. Backbone amide NH groups of Gly193 and Ser195 form hydrogen bonds with the amide oxygen atom of the substrate.

Figure 4

Reaction energy profile of the chymotrypsin-catalyzed cleavage of a model substrate (after Hudáky and Perczel [53]). Note that the tetrahedral intermediates as well as the acyl enzyme represent local minima.

Figure 5

Reaction paths for phosphoryl transfer reactions. (a) Dissociative (top), (b) associative (middle), (c) S_N2-type (bottom) mechanism. Square brackets represent the transition state.

Figure 6

Quantum mechanically calculated reaction profile for the phosphoryl transfer reaction catalyzed by HIV integrase (figure drawn on the basis of Ref. 56).

Figure 7

Molecular graphics model of the transition state in the reaction catalyzed by phoshoenol-pyruvate (PEP) mutase (on the basis of Figure 3 by Xu and Guo [70]). Note the planar metaphosphate intermediate stabilized by hydrogen bonds to amino-acid residues of the active site.

Figure 8

Two possible reaction routes for the hydrolysis of ribonuclease H. Top: schematic structure of the active site, bottom: blue line: attack by a water molecule, red line: attack by a hydroxyl group (figure drawn on the basis of Figure 3 of Ref. 72).

Scheme 1

Reaction mechanism of heme peroxidases. P is the porphyrin group of the enzyme whose heme iron is indicated, S is the substrate.

Figure 9

Schematic active-site models of cytochrome c peroxidase (CCP) (left) and ascorbate peroxidase (APX) (right). Top: distal position, bottom: proximal position, a separated red dot represents a water molecule (figure drawn on the basis of the crystal structures 1ZBZ and 2XI6).

Figure 10

Catalytic mechanism of the formation of Compound I. The distal His assists in removing a proton from the incoming peroxide and delivering it to the peroxide O₂ atom.

Figure 11

Singly occupied molecular orbitals of Compound I.

Figure 12

Thermodynamic cycle showing the relationship between ΔE₁, ΔE₂, (Fe-O bond enthalpy) and ΔE₃.

Figure 13

Quantum mechanical/molecular mechanical (QM/MM) optimized snapshot of Compound I with residues hydrogen-bonded to the axial cysteinate in P450 2D6.

Figure 14

Metabolic routes of dextromethorphan in man as indicated by arrows.

Figure 15

(a) QM region used in the calculations (b) Barriers of O-demethylation and aromatic carbon oxidation obtained from quantum mechanical and QM/MM calculations.

Figure 16

Active site of P450 2D6 with dextromethorphan. The movement of dextromethorphan in the active site is hindered by its salt bridge to Glu216 and by the steric hindrance of the bulky amino acid side-chains.

Scheme 2

Conversion reaction catalyzed by P450_nor.

Figure 17

The position of the NADH ligand in the docked structure (structure A) and in the crystal structure (structure B).

Figure 18

Energy profiles for closed-shell and open-shell singlet pathways for hydride transfer in the P450_nor and the schematic structure of the transition state.

Figure 19

Catalytic mechanism of xylose isomerase. Top: ring opening, middle: substrate deprotonation, bottom: hydride shift.

Figure 20

Initial, transition and final structures in the proton transfer steps of the ring opening reaction (relative energies are given in kJ/mol).