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Box 1 Description of the QM/MM approach

From: Alleviating the unwanted effects of oxidative stress on Aβ clearance: a review of related concepts and strategies for the development of computational modelling

QM/MM principle: The QM/MM approach has been applied to molecular dynamic (MD) simulation to simulate and investigate chemical reactions at a molecular level and an atomic level. Two regions of this approach are the QM (inner) and the MM (outer) regions. In catalytic reactions, residues in the substrate are included in the QM region; the remaining system is considered the MM region. QM/MM can be divided into two calculation schemes: the subtractive scheme and the additive scheme

QM/MM schemes: There are three steps in the subtractive scheme. The first part of the calculation determines the total amount of force-field energy in the system (EMM), in both the MM region and the QM region. The energy of the QM region is calculated at the level of quantum mechanics (EQM) using Khon-Sham Hamiltonian’s density function theory. Finally, the QM region’s energy is calculated at the level of molecular mechanics (EMM) using the force-field calculation. The subtractive scheme equation is provided below:

\(E_{QMMM} = E_{MM} \left( {MM_{region} + QM_{region} } \right) + E_{QM} \left( {QM_{region} } \right) - E_{MM} \left( {QM_{region} } \right)\)

One of the advantages associated with the subtractive scheme is that no communication is required between the two regions (the QM region and the MM region). However, the polarisation between the QM electron and the MM environment is not considered in the calculation. Furthermore, the subtractive scheme is not flexible and cannot consider chemical change. Unlike the subtractive scheme, calculation of the additive scheme requires coupling between the MM region and the QM region (EQMMM(MMregion + QMregion)) instead of (EMM(QMregion)). The additive scheme is calculated in the following manner:

\(EQ_{MMM} = E_{MM} \left( {MM_{region} + QM_{region} } \right) + E_{QM} \left( {QM_{region} } \right) + E_{QMMM} \left( {MM_{region} + QM_{region} } \right)\)

Basically, the coupling considers both the force field and the electrostatic potential energies between the QM region and the MM region. The coupling is comprised of bonded and non-bonded energies as shown in the following equation:

\(E_{QMMM} \left( {MM_{region} + QM_{region} } \right) = E_{QMMM\;bonded} + E_{QMMM\;non\_bonded}\)

The EQMMMbonded is calculated using classical force field theory. The EQMMMnon_bonded comprises of steric energy (EQMMMsteric), also calculated using the classical force field theory, and electrostatic potential energy (EQMMMelectrostatic) and focuses on interaction charges between the

MM region and the QM region. This is calculated using the Schrodinger wave equation:

\(E_{QMMM\;non\_bonded} = E_{QMMM\;steric} + E_{QMMM\;electrostatic}\)

There are three EQMMMelectrostatic schemes: mechanical embedding, electrostatic embedding, and polarized embedding. Mechanical embedding calculates the electrostatic charge based on the QM region, without the charge from the MM region. In some methodologies, the electrostatic charge is zero. Electrostatic embedding calculates the electrostatic interaction between the QM and MM regions using the Schrodinger wave function. Finally, polarized embedding considers the polarization between the QM and the MM regions. However, researchers are still working on improving the calculation of the polarized embedding due to the simulations’ ineffective results

QM/MM Applications: Due to differences in the expected results and the number of molecules of interest, speed and accuracy are crucial issues when deciding what QM/MM schemes to use. Semi-empirical (such as AM1, MP3) methods have been used to calculate energy at a high level. These calculations require parameters from empirical data. Ab initio (such as HF, MP2, CCSD), is a method used to calculate energy at a low level. While it is more accurate due to its use of Schrodinger’s equation (instead of parameters from empirical data), it has a high computational cost. This limitation means that the ab initio method may not be suitable for computing an entire system of catalytic reactions. The density functional theory (DFT) method was developed to lower computational costs: it reduces the dimensionality of the calculation problem. The figure below provides a comparison of these methods based on their accuracy and speed

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