van der Waals Dispersion Interactions in Biomolecular Systems: Quantum-Mechanical Insights and Methodological Advances

Intermolecular interactions are paramount for the stability, dynamics and response of systems
across chemistry, biology and materials science. In biomolecules they govern secondary structure
formation, assembly, docking, regulation and functionality. van der Waals (vdW) dispersion
contributes a crucial part to those interactions. As part of the long-range electron correlation,
vdW interactions arise from Coulomb-coupled quantum-mechanical fluctuations in the instan-
taneous electronic charge distribution and are thus inherently many-body in nature. Common
approaches to describe biomolecular systems (i.e., classical molecular mechanics) fail to capture
the full complexity of vdW dispersion by adapting a phenomenological, atom-pairwise formalism.
This thesis explores beyond-pairwise vdW forces and the collectivity of intrinsic electronic behav-
iors in biomolecular systems and discusses their role in the context of biomolecular processes
and function. To this end, the many-body dispersion (MBD) formalism parameterized from
density-functional tight-binding (DFTB) calculations is used.
The investigation of simple molecular solvents with particular focus on water gives insights into
the vdW energetics and electronic response properties in liquids and solvation as well as emergent
behavior for coarse-grained models. A detailed study of intra-protein and protein–water vdW
interactions highlights the role of many-body forces during protein folding and provides a funda-
mental explanation for the previously observed “unbalanced” description and over-compaction
of disordered protein states. Further analysis of the intrinsic electronic behaviors in explicitly
solvated proteins indicates a long-range persistence of electron correlation through the aque-
ous environment, which is discussed in the context of protein–protein interactions, long-range
coordination and biomolecular regulation and allostery. Based on the example of a restriction
enzyme, the potential role of many-body vdW forces and collective electronic behavior for the
long-range coordination of enzymatic activity is discussed. Introducing electrodynamic quantum
fluctuations into the classical picture of allostery opens up the path to a more holistic view on
biomolecular regulation beyond the traditional focus on merely local structural modifications.
Building on top of the MBD framework, which describes vdW dispersion within the interatomic
dipole-limit, a practical extension to higher-order terms is presented. The resulting Dipole-
Correlated Coulomb Singles account for multipolar as well as dispersion-polarization-like contri-
butions beyond the random phase approximation by means of first-order perturbation theory
over the dipole-coupled MBD state. It is shown that Dipole-Correlated Coulomb Singles become
particularly relevant for relatively larger systems and can alter qualitative trends in the long-range
interaction under (nano-)confinement. Bearing in mind the frequent presence of confinement in
biomolecular systems due to cellular crowding, in ion channels or for interfacial water, this so-far
neglected contribution is expected to have broad implications for systems of biological relevance.
Ultimately, this thesis introduces a hybrid approach of DFTB and machine learning for the accu-
rate description of large-scale systems on a robust, albeit approximate, quantum-mechanical
level. The developed DFTB-NN rep approach combines the semi-empirical DFTB Hamiltonian
with a deep tensor neural network model for localized many-body repulsive potentials. DFTB-
NN rep provides an accurate description of energetic, structural and vibrational properties of a
wide range of small organic molecules much superior to standard DFTB or machine learning.
Overall, this thesis aims to extend the current view of complex (bio)molecular systems being
governed by local, (semi-)classical interactions and develops methodological steps towards an
advanced description and understanding including non-local interaction mechanisms enabled
by quantum-mechanical phenomena such as long-range correlation forces arising from collective
electronic fluctuations.