Multi-Resolution Methods

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). QM calculations allow the study of bond breaking and forming in chemical and enzymatic reactions, however, the high computational cost of these method limits the application to systems with a comparatively small number of atoms. 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, but 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 have 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. However, benchmarking of the approach on a diverse set of 23 proteins showed that the size mismatch between the CG water beads and the atoms still caused a small preference for intramolecular hydrogen bonds by charged residues [4]. The best performance was obtained when small atomistic water spheres were retained around charged residues.

[2] Riniker et al., Eur. Biophys. J., 41, 647 (2012).
[3] Renevey, Riniker, J. Chem. Phys., 146, 124131 (2017).
[4] external pageRenevey, Riniker, J. Phys. Chem. B, 123, 3033 (2019).

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.

Although the computer power has increased dramatically in the past decades, QM/MM with DFT methods is still too expensive for long MD simulations of biologically relevant systems. To reduce the computational cost, we have developed a ∆-learning scheme with high-dimensional neural network potentials (HDNNP) and a semi-empirical baseline method to replace the QM part [5]. Electrostatic embedding was enabled by integrating the MM particles directly as an additional element type in the ML model. Usage of ∆-learning simplifies the learning task, which means that the size of the training can be smaller and the robustness of the approach is increased. This was demonstrated by performing prospective MD simulations with (QM)ML/MM approach of solutes in water. Instead of HDNNP, graph-convolutional networks can be used, resulting in a similar performance [6]. The prediction accuracy of graph-convolutional neural networks can be significantly improved when anisotropic message passing is introduced [7].

[5] external pageBöselt et al., J. Chem. Theory Comput. (2021), 17, 2641.
[6] external pageHofstetter et al., Phys. Chem. Chem. Phys. (2022), 24, 22497.
[7] external pageThürlemann et al., ICLR (2023).