Probing the range of applicability of structure- and energy-adjusted QM/MM link bonds

Tutorial Review on the Set-Up and Running of Quantum Mechanical Cluster Models for Enzymatic Reaction Mechanisms

Enzymes turnover substrates into products with amazing efficiency and selectivity and as such have great potential for use in biotechnology and pharmaceutical applications. However, details of their catalytic cycles and the origins surrounding the regio- and chemoselectivity of enzymatic reaction processes remain unknown, which makes the engineering of enzymes and their use in biotechnology challenging. Computational modelling can assist experimental work in the field and establish the factors that influence the reaction rates and the product distributions. A popular approach in modelling is the use of quantum mechanical cluster models of enzymes that take the first- and second coordination sphere of the enzyme active site into consideration. These QM cluster models are widely applied but often the results obtained are dependent on model choice and model selection. Herein, we show that QM cluster models can give highly accurate results that reproduce experimental product distributions and free energies of activation within several kcal mol-1, regarded that large cluster models with >300 atoms are used that include key hydrogen bonding interactions and charged residues. In this tutorial review, we give general guidelines on the set-up and applications of the QM cluster method and discuss its accuracy and reproducibility. Finally, several representative QM cluster model examples on metal-containing enzymes are presented, which highlight the strength of the approach.

Probing the range of applicability of structure- and energy-adjusted QM/MM link bonds III: QM/MM MD simulations of solid-state systems at the example of layered carbon structures

The previously introduced workflow to achieve an energetically and structurally optimized description of frontier bonds in quantum mechanical/molecular mechanics (QM/MM)-type applications was extended into the regime of computational material sciences at the example of a layered carbon model systems. Optimized QM/MM link bond parameters at HSEsol/6-311G(d,p) and self-consistent density functional tight binding (SCC-DFTB) were derived for graphitic systems, enabling detailed investigation of specific structure motifs occurring in graphene-derived structures v i a quantum-chemical calculations. Exemplary molecular dynamics (MD) simulations in the isochoric-isothermic (NVT) ensemble were carried out to study the intercalation of lithium and the properties of the Stone-Thrower-Wales defect. The diffusivity of lithium as well as hydrogen and proton adsorption on a defective graphene surface served as additional example. The results of the QM/MM MD simulations provide detailed insight into the applicability of the employed link-bond strategy when studying intercalation and adsorption properties of graphitic materials.

PyDFT-QMMM: A modular, extensible software framework for DFT-based QM/MM molecular dynamics

PyDFT-QMMM is a Python-based package for performing hybrid quantum mechanics/molecular mechanics (QM/MM) simulations at the density functional level of theory. The program is designed to treat short-range and long-range interactions through user-specified combinations of electrostatic and mechanical embedding procedures within periodic simulation domains, providing necessary interfaces to external quantum chemistry and molecular dynamics software. To enable direct embedding of long-range electrostatics in periodic systems, we have derived and implemented force terms for our previously described QM/MM/PME approach [Pederson and McDaniel, J. Chem. Phys. 156, 174105 (2022)]. Communication with external software packages Psi4 and OpenMM is facilitated through Python application programming interfaces (APIs). The core library contains basic utilities for running QM/MM molecular dynamics simulations, and plug-in entry-points are provided for users to implement custom energy/force calculation and integration routines, within an extensible architecture. The user interacts with PyDFT-QMMM primarily through its Python API, allowing for complex workflow development with Python scripting, for example, interfacing with PLUMED for free energy simulations. We provide benchmarks of forces and energy conservation for the QM/MM/PME and alternative QM/MM electrostatic embedding approaches. We further demonstrate a simple example use case for water solute in a water solvent system, for which radial distribution functions are computed from 100 ps QM/MM simulations; in this example, we highlight how the solvation structure is sensitive to different basis-set choices due to under- or over-polarization of the QM water molecule's electron density.

Challenges in Protein QM/MM Simulations with Intra-Backbone Link Atoms

Hybrid quantum mechanical/molecular mechanical (QM/MM) simulations fuel discoveries in many fields of science including computational biochemistry and enzymology. Development of more convenient tools leads to an increase in the number of works in which mechanical insights into enzymes' mode of operation are obtained. Most commonly, these tools feature hydrogen-capping (link atom) approach to provide coupling between QM and MM subsystems across a covalent bond. Extensive studies were conducted to provide a solid foundation for the correctness of such an approach when a bond to a nonpolar MM atom is considered. However, not every task may be accomplished this way. Certain scenarios of using QM/MM in computational enzymology encourage or even necessitate the incorporation of backbone atoms into the QM region. Two out of three backbone atoms are polar, and in QM/MM with electrostatic embedding, a neighboring link atom will be hyperpolarized. Several schemes to mitigate this effect were previously proposed alongside a rigorous assessment of quantitative effects on model systems. However, it was not clear whether they may translate into qualitatively different results and how link atom hyperpolarization may manifest itself in a real-life enzymological scenario. Here, we show that the consequences of such an artifact may be severe and may completely overturn the conclusions drawn from the simulations. Our case advocates for the use of charge redistribution schemes whenever intra-backbone QM/MM boundaries are considered. Moreover, we addressed how different boundary types and charge redistribution schemes influence backbone dynamics. We showed that the results are heavily dependent on which boundary MM terms are retained, with charge alteration being of secondary importance. In the worst case, only three intra-backbone boundaries may be used with relative confidence in the adequacy of resulting simulations, irrespective of the hyperpolarization mitigation scheme. Thus, advances in the field are certainly needed to fuel new discoveries. As of now, we believe that issues raised in this work might encourage authors in the field to report what boundaries, boundary MM terms, and charge redistribution schemes they are using, so their results may be correctly interpreted.

Cu2+ in liquid ammonia-The impact of solvent flexibility and electron correlation in ab initio quantum mechanical charge field molecular dynamics

The impact of solvent flexibility and electron correlation on the simulation results of Cu²⁺ in liquid ammonia has been investigated via an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach. To achieve this, three different simulation systems were considered in this study, namely Cu²⁺ in rigid and flexible ammonia at Hartree-Fock (HF) level of theory, as well as resolution of identity second order Møller-Plesset (MP2) perturbation theory in the rigid body case. In all cases, a stable octahedral [Cu(NH₃ )₆ ]²⁺ complex subject to dynamic Jahn-Teller distortions without the occurrence of ligand exchange was observed. The Cu²⁺  - NH₃ distance in the first shell agrees well with the experimental and other theoretical data. In all three cases, the structural data shows that the rigid-body ammonia model in conjunction with the HF level of theory provides accurate data for the first solvation shell, while at the same time, the computational demand and thus the achievable simulation time are much more beneficial. The vibrational analysis of the Cu²⁺  - NH₃ interaction yields similar force constants in the three investigated systems indicating that there is no distinct difference on the dynamical properties of the first solvation shell. In addition to the QMCF MD simulations, a number of natural bond orbital (NBO) analyses were carried out, confirming the strong electrostatic character of the Cu²⁺  - NH₃ interaction.

The Jahn-Teller effect in mixed aqueous solution: the solvation of Cu2+ in 18.6% aqueous ammonia obtained from ab initio quantum mechanical charge field molecular dynamics

The solvation structure and dynamics of Cu2+ in 18.6 % aqueous ammonia have been investigated using an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach at the Hartree–Fock (HF) level of theory applying the LANL2DZ ECP and Dunning DZP basis sets for Cu2+, ammonia and water, respectively. During a simulation time of 20 ps, only NH3 molecules are observed within the first solvation shell of Cu2+, resulting in the formation of an octahedral [Cu(NH3)6]2+ complex. While no exchange of these ligands with the second solvation shell are observed along the simulation, the monitoring of the associated N-Ntrans distances highlight the dynamics of the associated Jahn-Teller distortions, showing on average 2 elongated axial (2.19 Å) and 4 equatorial Cu–N bonds (2.39 Å). The observed structural properties are found in excellent agreement with experimental studies. In addition, an NBO analysis was carried out, confirming the strong electrostatic character of the Cu2+–NH3 interaction.

Quantum Mechanics/Molecular Mechanics Studies on the Relative Reactivities of Compound I and II in Cytochrome P450 Enzymes

The cytochromes P450 are drug metabolizing enzymes in the body that typically react with substrates through a monoxygenation reaction. During the catalytic cycle two reduction and protonation steps generate a high-valent iron (IV)-oxo heme cation radical species called Compound I. However, with sufficient reduction equivalents present, the catalytic cycle should be able to continue to the reduced species of Compound I, called Compound II, rather than a reaction of Compound I with substrate. In particular, since electron transfer is usually on faster timescales than atom transfer, we considered this process feasible and decided to investigate the reaction computationally. In this work we present a computational study using density functional theory methods on active site model complexes alongside quantum mechanics/molecular mechanics calculations on full enzyme structures of cytochrome P450 enzymes. Specifically, we focus on the relative reactivity of Compound I and II with a model substrate for O⁻H bond activation. We show that generally the barrier heights for hydrogen atom abstraction are higher in energy for Compound II than Compound I for O⁻H bond activation. Nevertheless, for the activation of such bonds, Compound II should still be an active oxidant under enzymatic conditions. As such, our computational modelling predicts that under high-reduction environments the cytochromes P450 can react with substrates via Compound II but the rates will be much slower.

The Binding Mode of the Sonic Hedgehog Inhibitor Robotnikinin, a Combined Docking and QM/MM MD Study

Erroneous activation of the Hedgehog pathway has been linked to a great amount of cancerous diseases and therefore a large number of studies aiming at its inhibition have been carried out. One leverage point for novel therapeutic strategies targeting the proteins involved, is the prevention of complex formation between the extracellular signaling protein Sonic Hedgehog and the transmembrane protein Patched 1. In 2009 robotnikinin, a small molecule capable of binding to and inhibiting the activity of Sonic Hedgehog has been identified, however in the absence of X-ray structures of the Sonic Hedgehog-robotnikinin complex, the binding mode of this inhibitor remains unknown. In order to aid with the identification of novel Sonic Hedgehog inhibitors, the presented investigation elucidates the binding mode of robotnikinin by performing an extensive docking study, including subsequent molecular mechanical as well as quantum mechanical/molecular mechanical molecular dynamics simulations. The attained configurations enabled the identification of a number of key protein-ligand interactions, aiding complex formation and providing stabilizing contributions to the binding of the ligand. The predicted structure of the Sonic Hedgehog-robotnikinin complex is provided via a PDB file as Supplementary Material and can be used for further reference.

Understanding How Prolyl-4-hydroxylase Structure Steers a Ferryl Oxidant toward Scission of a Strong C-H Bond

Prolyl-4-hydroxylase (P4H) is a non-heme iron hydroxylase that regio- and stereospecifically hydroxylates proline residues in a peptide chain into R-4-hydroxyproline, which is essential for collagen cross-linking purposes in the human body. Surprisingly, in P4H, a strong aliphatic C-H bond is activated, while thermodynamically much weaker aliphatic C-H groups, that is, at the C³ and C⁵ positions, are untouched. Little is known on the origins of the high regio- and stereoselectivity of P4H and many non-heme and heme enzymes in general, and insight into this matter may be relevant to Biotechnology as well as Drug Development. The active site of the protein contains two aromatic residues (Tyr₁₄₀ and Trp₂₄₃) that we expected to be crucial for guiding the regioselectivity of the reaction. We performed a detailed quantum mechanics/molecular mechanics (QM/MM) and molecular dynamics (MD) study on wild-type and mutant structures. The work shows that Trp₂₄₃ is involved in key protein loop-loop interactions that affect the shape and size of the substrate binding pocket and its mutation has major long-range effects. By contrast, the Tyr₁₄₀ residue is shown to guide the regio- and stereoselectivity by holding the substrate and ferryl oxidant in a specific orientation through hydrogen bonding and π-stacking interactions. Compelling evidence is found that the Tyr₁₄₀ residue is involved in expelling the product from the binding pocket after the reaction is complete. It is shown that mutations where the hydrogen bonding network that involves the Tyr₁₄₀ and Trp₂₄₃ residues is disrupted lead to major changes in folding of the protein and the size and shape of the substrate binding pocket. Specifically, the Trp₂₄₃ residue positions the amino acid side chains of Arg₁₆₁ and Glu₁₂₇ in specific orientations with substrate. As such, the P4H enzyme is a carefully designed protein with a subtle and rigid secondary structure that enables the binding of substrate, guides the regioselectivity, and expels product efficiently.

Sulfoxide Synthase versus Cysteine Dioxygenase Reactivity in a Nonheme Iron Enzyme

The sulfoxide synthase EgtB represents a unique family of nonheme iron enzymes that catalyze the formation of a C-S bond between N-α-trimethyl histidine and γ-glutamyl cysteine, which is the key step in the biosynthesis of ergothioneine, an important amino acid related to aging. A controversy has arisen regarding its catalytic mechanism related to the function of the active-site Tyr₃₇₇ residue. The biosynthesis of ergothioneine in EgtB shows structural similarities to cysteine dioxygenase which transfers two oxygen atoms to the thiolate group of cysteine. The question, therefore, is how do EgtB enzymes catalyze the C-S bond-formation reaction, while also preventing a dioxygenation of its cysteinate substrate? In this work we present a quantum mechanics/molecular mechanics study into the mechanism of sulfoxide synthase enzymes as compared to cysteine dioxygenase enzymes and present pathways for both reaction channels in EgtB. We show that EgtB contains a conserved tyrosine residue that reacts via proton-coupled electron transfer with the iron(III)-superoxo species and creates an iron(III)-hydroperoxo intermediate, thereby preventing the possible thiolate dioxygenation side reaction. The nucleophilic C-S bond-formation step happens subsequently concomitant to relay of the proton of the iron(II)-hydroperoxo back to Tyr₃₇₇. This is the rate-determining step in the reaction cycle and is followed by hydrogen-atom transfer from the CE1-H group of trimethyl histidine substrate to iron(II)-superoxo. In the final step, a quick and almost barrierless sulfoxidation leads to the sulfoxide product complexes. The work highlights a unique machinery and active-site setup of the enzyme that drives the sulfoxide synthase reaction.

The influence of metal-ion binding on the structure and surface composition of Sonic Hedgehog: a combined classical and hybrid QM/MM MD study

The interaction of metal ions with Shh binding-sites and their structural impact are assessed via classical and quantum mechanical simulations.

Quantum Mechanics/Molecular Mechanics Modeling of Enzymatic Processes: Caveats and Breakthroughs

Nature has developed large groups of enzymatic catalysts with the aim to transfer substrates into useful products, which enables biosystems to perform all their natural functions. As such, all biochemical processes in our body (we drink, we eat, we breath, we sleep, etc.) are governed by enzymes. One of the problems associated with research on biocatalysts is that they react so fast that details of their reaction mechanisms cannot be obtained with experimental work. In recent years, major advances in computational hardware and software have been made and now large (bio)chemical systems can be studied using accurate computational techniques. One such technique is the quantum mechanics/molecular mechanics (QM/MM) technique, which has gained major momentum in recent years. Unfortunately, it is not a black-box method that is easily applied, but requires careful set-up procedures. In this work we give an overview on the technical difficulties and caveats of QM/MM and discuss work-protocols developed in our groups for running successful QM/MM calculations.