An Efficient Method to Evaluate Intermolecular Interaction Energies in Large Systems Using Overlapping Multicenter ONIOM and the Fragment Molecular Orbital Method

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

Computational Methods for Biochemical Simulations Implemented in GAMESS

Computational methods for modeling biochemical processes implemented in GAMESS package are reviewed; in particular, quantum mechanics combined with molecular mechanics (QM/MM), semi-empirical, and fragmentation approaches. A detailed summary of capabilities is provided for the QM/MM implementation in QuanPol program and the fragment molecular orbital (FMO) method. Molecular modeling and visualization packages useful for biochemical simulations with GAMESS are described. GAMESS capabilities with corresponding references are tabulated for reader's convenience.

Analyzing Interactions with the Fragment Molecular Orbital Method

Basic concepts in the analysis of binding using the fragment molecular orbital method are discussed at length: polarization, desolvation, and interaction. The components in the pair interaction energy decomposition analysis are introduced, and the analysis is illustrated for a water dimer and a protein-ligand complex.

Accurate Quantum Mechanical/Molecular Mechanical Calculations of Reduction Potentials in Azurin Variants

Understanding the regulation mechanism and molecular determinants of the reduction potential of metalloprotein is a major challenge. An ab initio quantum mechanical/molecular mechanical (QM/MM) method combining the minimum free energy path (MFEP) and fractional number of electron (FNE) approaches has been developed in our group to simulate the redox processes of large systems. The FNE scheme provides an efficient unique description for the redox process, while the MFEP method provides improved conformational sampling on complex environments such as protein in the QM/MM calculations. The reduction potentials of wild-type and seven mutants of azurin, a type 1 copper metalloprotein, were simulated with the QM/MM-MFEP+FNE approach in this paper. A range of 350 mV for the variations of the reduction potentials of these azurin proteins was reproduced faithfully with relative errors around 20 mV. The correlation between structural interactions and reduction potentials observed in simulations provides in-depth insight into the regulation of reduction potentials, which potentially can also be very useful to the engineering of metalloprotein-based electrocatalysts in artificial photosynthesis. The excellent accuracy and efficiency of the QM/MM-MFEP+FNE approach demonstrate the potential for simulations of many electron transfer processes in condensed phases and biochemical systems.

A two-layer ONIOM study of thiophene cracking catalyzed by proton- and cation-exchanged FAU zeolite

A two-layer ONIOM study on the hydrodesulfurization mechanism of thiophene in H-FAU and M-FAU (M = Li(+), Na(+), and K(+)) has been carried out. The calculated results reveal that in H-FAU, for a unimolecular mechanism, the rate-determining step is hydrogenation of alkoxide intermediate. The assistance of H2O and H2S molecules does not reduce the difficulty of the C-S bond cracking step more effectively. A bimolecular hydrodesulfurization mechanism is more favorable due to the lower activation barriers. The rate-determining step is the formation of 2-methylthiophene, not the C-S bond cracking of thiophene. Moreover, the ring opening of thiophene is much easier to occur than the desulfurization step. A careful analysis of energetics indicates that H2S, propene, and methyl thiophene are the major products for the hydrodesulfurization process of thiophene over H-FAU zeolite, in good agreement with experimental findings. In M-FAU zeolites, both unimolecular and bimolecular cracking processes are difficult to occur because of the high energy barriers. Compared to the case on H-FAU, the metal cations on M-FAU increase the difficulty of occurrence of bimolecular polymerization and subsequent C-S bond cracking steps. Graphical abstract Hydrodesulfurization process of thiophene can take place in H-FAU zeolite. Two different mechanisms, unimolecular and bimolecular ones, have been proposed and evaluated in detail. The bimolecular mechanism is more favorable due to lower activation barrier as described in the picture above. Our calculated data indicate that H2S, propene, and methylthiophene are the major products, in good agreement with experimental observations. The effect of metal cations on the reaction mechanism is also investigated in this work.

Multiple active zones in hybrid QM/MM molecular dynamics simulations for large biomolecular systems

A new QM/MM molecular dynamics approach that can deal with the dynamics of large real systems involving several simultaneous active zones is presented.

The use of many-body expansions and geometry optimizations in fragment-based methods

Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures.

A double-QM/MM method for investigating donor–acceptor electron-transfer reactions in solution

A double-QM/MM method can explore the distant-dependent phenomena of outer-sphere electron transfer processes. This method allows easy control of donor–acceptor spin-charge densities within the full-reaction scheme.

Mapping enzymatic catalysis using the effective fragment molecular orbital method: towards all ab initio biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be kcal mol⁻¹ for MP2/cc-pVDZ and for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.