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# Multi-Resolution Methods

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Processes in biological systems typically span a broad range of temporal and spatial scales, which makes the accurate simulation of the dynamics of these processes by computational means extremely challenging. In chemistry, three broad levels of resolution are distinguished [1]: (i) electronic, quantum-mechanical (QM), (ii) atomistic (AT), and (iii) supra-atomic or supra-molecular coarse-grained (CG).

The behavior of electrons in molecules is governed by the laws of quantum mechanics. QM calculations allow the study of bond breaking and forming in chemical and enzymatic reactions. However, the high computational cost of QM calculations limits the application to systems with a comparatively small number of atoms (i.e. often only the molecule of interest in vacuum or in a drastically reduced environment). Solvent effects and - in the case of enzymatic reactions - the protein environment can play, however, an important role, and neglecting them affects the accuracy of the results of the calculations.

The interactions of systems at the AT and CG levels are governed by classical statistical mechanics, and can be simulated using classical molecular dynamics (MD). The use of CG models tends to decrease the computational time by one or multiple orders of magnitude, making them very attractive to study large biomolecular systems. However, coarse-graining involves per se a loss of information [1], which can affect the accuracy of the results.

Many interesting chemical and biological questions require the inclusion of quantum effects, but also require the presence of the protein which in turn should be sufficiently solvated. A promising approach is therefore to combine multiple levels of resolution in a single simulation to benefit from the strengths and circumvent the limitations of the individual methods. Thus, the region of interest is modelled at a high level of accuracy with the surrounding environment being treated at lower resolution.

[1] Riniker et al., Phys. Chem. Chem. Phys., 14, 12423 (2012).

## Hybrid AT/CG Approach

In hybrid AT/CG simulations, the region of interest which is treated atomistically typically consists of the solute (e.g. a protein and/or ligand), whereas the solvent (and membrane) is at the coarse-grained level. The major challenge of hybrid AT/CG approaches is the description of the interactions between AT and CG particles.

Our hybrid AT/CG approach is based on the previously developed CG water model, and has been successfully applied to study atomistic proteins in CG water [2]. In this model, a CG bead subsumes five water molecules, and consists of two particles connected by a half-harmonic spring, representing a polarisable dipole.

Recently, we reparametrised the AT-CG interactions to reproduce better the solvation free energies of atomistic side-chain analogues in CG water [3]. Through this the structural and energetic properties of the proteins were better preserved.

[2] Riniker et al., Eur. Biophys. J., 41, 647 (2012).

[3] Renevey, Riniker, J. Chem. Phys., 146, 124131 (2017).

## QM/MM

The concept of QM/MM was first introduced by Warshel and Levitt in 1976, while widespread application of the approach started only with the report of Field, Bash and Karplus in 1990. There are five methodological aspects that have to be considered in QM/MM simulations: (i) choice of the QM Hamiltonian, (ii) choice of the classical force field for the MM region, (iii) size of the QM region, (iv) boundary and coupling between the QM and MM regions, and (v) boundary condition for the MM region. Three main approaches were developed for modelling the electronic structure of molecules with varying accuracy and computational demand: quantum-chemical *ab initio* methods, density functional theory (DFT) and semi-empirical methods. Traditionally, semi-empirical QM methods were used in QM/MM, but many current applications rely on DFT for the QM Hamiltonian due to a favorable ratio between accuracy and computational cost. The boundary treatment and coupling between the QM and MM part of the system is one of the major challenges of QM/MM simulations.

We are particularly interested in the application of QM/MD to address biomolecular questions, and our research focus is thus on the development of strategies to reduce the computational effort of QM/MM simulations.