High‐Accuracy Computation of Reaction Barriers in Enzymes

Abstract

The accurate prediction of enzyme kinetics from first principles is one of the central goals of theoretical biochemistry. Currently there is considerable debate [1][2][3] about the applicability of transition state theory (TST) to compute rate constants of enzyme-catalyzed reactions. Classical TST is known to be insufficient in some cases, but corrections for dynamical recrossing and quantum mechanical tunneling can be included. [1,2,4] Many effects that go beyond the framework of TST have been proposed, particularly focusing on the possible role of protein dynamics and conformational effects on the enzyme activity. Unfortunately, the overall importance of these effects for the effective reaction rate is difficult (if not impossible) to determine experimentally. However, if one could compute the quasi-thermodynamical free energy of activation with chemical accuracy (i.e. 1 kcal mol À1 ), comparison with the effective measured free energy of activation would directly show the importance of other effects.Combined quantum mechanical/molecular mechanical (QM/MM) methods have become an important tool for computational modeling of enzyme-catalyzed reactions. Only the substrate(s) and relevant residues in the active site are treated quantum mechanically, the rest of the protein is described at the empirical MM level. This lowers the computational expense, making it possible to treat large enzyme systems and the surrounding solvent, and to sample phase space. Nevertheless, the number of QM atoms is still relatively large, and until now only low levels of QM theory, such as semiempirical methods or density functional theory (DFT), have been feasible. Semiempirical methods, though applicable to large systems, are generally not accurate enough because computed free energies of activation may have an error of ten or more kcal mol À1 . DFT (especially with the B3LYP functional [5] ) offers improved accuracy but still lacks key physical interactions (e.g., dispersion). Often, DFT underestimates barrier heights by several kcal mol À1 , which cannot be systematically improved. Thus, when theoretical barriers do not agree with those from experiment, it is not clear whether the discrepancy arises from deficiencies in the electronic structure theory and the sampling, in the experimental observations, or in the underlying theoretical framework of QM/MM and TST.Consequently, there is a need for high-level electronic structure calculations for reliable predictions of enzyme reactivity. The ab initio electron correlation methods MP2 (Møller-Plesset second-order perturbation theory), CCSD (coupled-cluster theory with single and double excitations), and CCSD(T) (CCSD with a perturbative treatment of triple excitations) provide a well-established hierarchy that converge reliably to give high accuracy, and rate constants of gasphase reactions involving only a few atoms can be predicted with error bars comparable to those found experimentally. [6,7] However, the computational expense of these methods increases very rapidly with the number o...

Comparison of DFT and ab initio QM/MM methods for modelling reaction in chorismate synthase

“…LCCSD(T)/aVDZ/CHARMM27//B3LYP/6-31G(d)/CHARMM27 single point energy calculations predict a barrier of 16.7 kcal/mol for the proton transfer step in excellent agreement with the 16.9 kcal/mol barrier at the SCS-MP2 level of theory. Coupled cluster theory can predict energies to within chemical accuracy [5] and this result and those reported for other enzymes [6] shows that the SCS-MP2 method gives results very close to this 'gold standard' ab initio method. SCS-MP2 calculations give better results than B3LYP calculations when compared to more accurate coupled cluster methods [36].…”

“…QoMMMa [28], an in-house interface between QM packages such Jaguar The B3LYP method has several well-known limitations, including the lack of dispersion, and it often (but not always) underestimates reaction barriers [5]. To further investigate the energetic of the reaction further (and to test the performance of B3LYP for this system), single point energy calculations on the structures generated by B3LYP/6-31G(d)/CHARMM27 were carried out at the MP2/aVDZ and SCS-MP2/aVDZ levels (i.e.…”

“…The accuracy of the QM method employed is also another important factor in the assessment of QM/MM methods. It is now possible to approach chemical accuracy with QM/MM calculations using coupled cluster methods for the QM region [5,6], but these methods remain expensive particularly for large QM regions. Density functional theory (DFT) provides a good compromise between accuracy and computational expense and is widely used for the QM region in QM/MM calculations.…”

An efficient local coupled cluster method for accurate thermochemistry of large systems

“…II C. For example, this is important when bonds are elongated at transition states. 76,77 This is also the preferred way to avoid basis set superposition errors (BSSE) in local correlation calculations on intermolecular complexes and clusters. 7,78,79 Unless otherwise noted, we will use connectivity criteria in the current paper, and these will be defined in Sec.…”

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

“…21 and 22)), have revolutionized the applicability of reliable correlation methods to large molecular systems. 23 The key criticism of the Pulay-Saebø approach and Werner-Schütz implementations is dependence on a large number of parameters, required to determine the level of theory applied to each occupied-orbital pair, and to determine the domains of PAOs. It has also been noted that without care potentials obtained by these local methods can display discontinuities.…”