QM/MM calculations

At the other extreme is a trend toward the increasing use of orbital-based techniques, particularly QM/MM calculations (Chapter 23). These orbital-based techniques are needed to accurately model the actual process of chemical bond breaking and formation. 

A second approach is based on the methodology first explored in the seminal work by Warshel and Levitt as early as 1976 [21], and is the use of hybrid quantum mechanics/molecular mechanics (QM/MM) calculations whereby a subsection of the system is treated by QM methods, the remainder (environment) is treated by standard molecular mechanics (MM) methods, and a coupling potential is used to connect the two regions [22], This methodology will then be exemplified with work developed in this group in recent years [23-26],... 

The second approach described here for inclusion of environment effects is the use of hybrid quantum mechanics/molecular mechanics methods (QM/MM). In a QM/MM calculation [21,22], the system is partitioned in two regions A QM region, typically consisting of a relatively small number of atoms relevant for the specific process being studied, and a MM region with all the remaining atoms. 

Scheme 1-2. Quantum zone used for QM.MM calculations of the reaction catalized by /ra/w-sialidase. The relevant coordinates are shown in red...

Figure 1-7. Free energy surface for the first step of the frans-sialidase mechanism as obtained from QM/MM calculations with SCC-DFTB...

When comparing different computational approaches to enzyme systems, several different factors have to be considered, e.g., differences in high-level (QM) method, QM/MM implementation, optimization method, model selection etc. This makes it very difficult to compare different QM/MM calculations on the same system. Even comparisons with an active-site model are not straightforward. It can be argued that adding a larger part of the system into calculaton always should make the calculation more accurate. At the same time, introducing more variables to the calculation also increases the risk of artificial effects. 

Although experimental studies provide significant amounts of information regarding the structure and the catalytic activity of these enzymes, several issues concerning the structure (presence of water in the active site) and the catalytic mechanism remained unresolved. Based on the complete X-ray structure of human plasma GPx (2.9 A resolution) [64], we performed active-site and ONIOM QM MM calculations of structure and reaction mechanism [27, 28, 65],... 

Some of the above mentioned studies also use two-layer ONIOM QM MM approaches to include the full protein in an MM description. Other examples of QM MM calculations of metal enzymes include heme oxygenase [89], nitrate reductase [90] and peptide deformylase [91]. Finally, we note that the ONIOM (I IF Amber) potential energy surface has been directly used in a molecular dynamics study (ONIOM/MD) of cytidine deaminase [92],... 

Abstract Reaction paths on potential energy surfaces obtained from QM/MM calculations of en-... 

The path optimizations are carried out by an iterative optimization procedure [25]. In the case of enzyme systems, because of the large number of degrees of freedom, we partition them into a core set and an environmental set. The core set is small and contains all the degrees of freedom that are involved with the chemical steps of the reaction, while all the remaining degrees of freedom are included in the environmental set. In all the QM/MM calculations presented below, the core set is defined by the QM subsystem and the environmental set by the MM subsystem. 

Gooding SR, Winn PJ, Maurer RI, Ferenczy GG, Miller JR, Harris JE, Griffiths DV, Reynolds CA (2000) Fully polarizable QM/MM calculations an application to die nonbonded iodine-oxygen interaction in dimethyl-2-iodobenzoylphosphonate. J Comput Chem 21(6) 478 t82... 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

Fig. 2 Plots of QM-MM calculated versus experimental fluorescence maximum wavelengths for 19 Trps in 16 proteins and for 3-methylindole in water. Charges on the Trp ring are multiplied by 0.80 and the calculated values are averages over the 2,400 values calculated during the last 24 ps of 30-ps QM-MM trajectories...

These QM/MM calculations are in contrast to a standard evaluation of chemical shielding for gas phase water clusters where the classical point charge environment is omitted entirely. The same solvation shell criterion as before was applied, and the system was treated purely quantum mechanically. 

Figure 1.4 shows a significant deviation between the isolated cluster calculations and the full calculation. The situation is, however, considerably improved by the presence of the classical point charges in the QM/MM calculation. Here the whole bandwidth of chemical shielding constants is present, and correlation with the reference values is excellent. 

Before starting the calculations, it is important to chose an appropriate initial structure for the protein. The X-ray structure is not a good starting point, because it corresponds to an average among the many different instantaneous protein conformations. It is physically more meaningful to take snapshots of previous MD simulations using the same force field as in the QM/MM calculations. 

When a biomolecular system is separated into QM and MM regions one must usually cut amino acid side chains or the protein backbone at covalent bonds (Fig. 5.2 a). The construction of the covalent boundary between the QM and MM parts is key to accurate results from QM/MM calculations. Because there is no unique way to treat the covalent boundary, several different approaches have been described. In the first applications of coupled QM/MM simulations link atoms were used to create the covalent QM/MM boundary (Fig. 5.2b). Link atoms are atoms added to the QM part to fill the broken valences of the boundary QM atoms. These atoms are placed along the broken QM/MM bond at a distance appropriate for the QM bond added. The link atoms have usually been hydrogen atoms but methyl groups and pseudohalogen atoms have also been used [35]. 

In this chapter, we will review some basic features of embedding methods, with a particular emphasis on some QM/MM techniques. We will discuss the basic theory, and some practical aspects of how to perform QM/MM calculations on biological... 

The partitioning of the system in a QM/MM calculation is simpler if it is possible to avoid separating covalently bonded atoms at the border between the QM and the MM regions. An example is the enzyme chorismate mutase [39] for which the QM region could include only the substrate, because the enzyme does not chemically catalyze this pericyclic reaction. In studies of enzyme mechanisms, however, this situation is exceptional, and usually it will be essential, or desirable, to include parts of the protein (for example catalytic residues) in the QM region of a QM/MM calculation, i.e. the boundary between the QM and MM regions will separate covalently bonded atoms (Fig. 6.1). 

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