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). Note that while the use of a coarser level typically decreases the computational effort, removing degrees of freedom involves per se a loss of information [1].
[1] Riniker et al., Phys. Chem. Chem. Phys., 14, 12423 (2012).
A promising approach to reduced the computational cost while keep a higher level of accuracy in the region of interest is to combine multiple levels of resolution in a single system. The multiscale approach with a QM solute and an atomistic (or molecular mechanics, MM) environment called QM/MM was already proposed in the 1970s by Warshel, Levitt, and Karplus. The same scheme can also be applied to mix AT and CG levels. More recently, the replacement of the QM Hamiltonian by machine-learning interatomic potentials (MLIPs) in a ML/MM set-up has gained a lot of interest as it reduces the computational cost dramatically compared to QM/MM [2].
From QM/MM to ML/MM
Five methodological aspects need 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 in the past decades, QM/MM with DFT methods is still too expensive for long MD simulations of biologically relevant systems. Although generally less accurate than DFT, semi-empirical methods in QM/MM can already provide a physially more correct description than classical force fields [3].
[3] external page Pregeljc and Riniker, J. Chem. Phys. (2026), 164, 124108.
To reduce the computational cost of QM/MM simulation with DFT accuracy, we have developed a ∆-learning scheme with high-dimensional neural network potentials (HDNNP) and a semi-empirical baseline method to replace the QM part [4]. 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 [5].
[4] external page Böselt et al., J. Chem. Theory Comput. (2021), 17, 2641.
[5] external page Hofstetter et al., Phys. Chem. Chem. Phys. (2022), 24, 22497.
The prediction accuracy of graph-convolutional neural networks can be
significantly improved when anisotropic message passing (AMP) is introduced [6]. With AMP, ∆-learning is no longer required and the necessary accuracy for the direct prediction of energies and forces can be achieved. The second version of the AMP architecture was applied to study the dissociation free energy of two types of systems in solution: ligation states of nickel phosphine complexes, and dissociation free energies of charged pyridine and quinoline dimers [7]. In both cases, we found that the ML/MM simulations in explicit solvent reproduce the experimental data better than static QM calculations with implicit solvation. AMP is shown to be highly efficient in terms of both data and computational costs and scales well with the size of the ML zone.
[6] external page Thürlemann et al., ICLR (2023).
[7] external page Pultar et al., J. Am. Chem. Soc. (2025),147,6835.
Encouraged by the results, we improved the AMP architecture further (version 3) and devised a broad training set of 1.5 QM/MM reference calculations (BMS25 dataset) [8] to train a global (or foundation) AMP model: the AMPv3-BMS25 model [9]. With this model, we simulated four proteins of different composition of secondary-structure motifs for 100 ns and demonstrated a stable fold (comparable to classical force fields). In addition, first results of two enzymatic reactions showed correct geometries along the reaction coordinate and the expected reduction of the activitation barrier when going from water to the enzyme pocket.
[8] external page Thürlemann et al., ChemRxiv (2025).
[9] external page Thürlemann et al., J. Am. Chem. Soc., online (2026).
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 [10]. 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 [11]. 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 [12]. The best performance was obtained when small atomistic water spheres were retained around charged residues.
[10] Riniker et al., Eur. Biophys. J., 41, 647 (2012).
[11] Renevey, Riniker, J. Chem. Phys., 146, 124131 (2017).
[12] external page Renevey, Riniker, J. Phys. Chem. B, 123, 3033 (2019).