Matthew J. L. Mills

Polarisable multipolar electrostatics from the machine learning method Kriging: an application to alanine

We present a polarisable multipolar interatomic electrostatic potential energy function for force fields and describe its application to the pilot molecule MeNH-Ala-COMe (AlaD). The total electrostatic energy associated with 1, 4 and higher interactions is partitioned into atomic contributions by application of quantum chemical topology (QCT). The exact atom–atom interaction is expressed in terms of atomic multipole moments. The machine learning method Kriging is used to model the dependence of these multipole moments on the conformation of the entire molecule. The resulting models are able to predict the QCT-partitioned multipole moments for arbitrary chemically relevant molecular geometries. The interaction energies between atoms are predicted for these geometries and compared to their true values. The computational expense of the procedure is compared to that of the point charge formalism.

Computer aided enzyme design and catalytic concepts

Gaining a deeper understanding of enzyme catalysis is of great practical and fundamental importance. Over the years it has become clear that despite advances made in experimental mutational studies, a quantitative understanding of enzyme catalysis will not be possible without the use of computer modeling approaches. While we believe that electrostatic preorganization is by far the most important catalytic factor, convincing the wider scientific community of this may require the demonstration of effective rational enzyme design. Here we make the point that the main current advances in enzyme design are basically advances in directed evolution and that computer aided enzyme design must involve approaches that can reproduce catalysis in well-defined test cases. Such an approach is provided by the empirical valence bond method.

The dynamic behavior of a liquid ethanol–water mixture: a perspective from quantum chemical topology

Quantum Chemical Topology (QCT) is used to reveal the dynamics of atom-atom interactions in a liquid. A molecular dynamics simulation was carried out on an ethanol-water liquid mixture at its azeotropic concentration (X(ethanol)=0.899), using high-rank multipolar electrostatics. A thousand (ethanol)(9)-water heterodecamers, respecting the water-ethanol ratio of the azeotropic mixture, were extracted from the simulation. Ab initio electron densities were computed at the B3LYP/6-31+G(d) level for these molecular clusters. A video shows the dynamical behavior of a pattern of bond critical points and atomic interaction lines, fluctuating over 1 ns. A bond critical point distribution revealed the fluctuating behavior of water and ethanol molecules in terms of O-H···O, C-H···O and H···H interactions. Interestingly, the water molecule formed one to six C-H···O and one to four O-H···O interactions as a proton acceptor. We found that the more localized a dynamical bond critical point distribution, the higher the average electron density at its bond critical points. The formation of multiple C-H···O interactions affected the shape of the oxygen basin of the water molecule, which is shown in three dimensions. The hydrogen atoms of water strongly preferred to form H···H interactions with ethanols alkyl hydrogen atoms over its hydroxyl hydrogen.

Multipolar electrostatics for proteins: Atom–atom electrostatic energies in crambin

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom‐atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom‐atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ℓA+ ℓB + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom‐atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug‐cc‐pVTZ and MP2/aug‐cc‐pVTZ levels are only slightly larger than those calculated at HF/6‐31G(d,p) level. This convergence behavior is transferable to the well‐known amyloid beta polypeptide Aβ1–42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance.

The entropic contributions in vitamin B12 enzymes still reflect the electrostatic paradigm

Significance The origin of the catalytic power of B12 enzymes has been a major puzzle despite our previous finding that this effect is due to electrostatic stabilization of the leaving group. Recent findings of very large entropic contributions to catalysis were presented as an alternative to the electrostatic idea. Here, we use our ability to evaluate entropic contributions by the restraint release (RR) approach to reexamine the nature of the catalytic effect. The RR approach reproduces the observed entropic contributions to the activation barrier and demonstrates that the entropic effect is due to the previously identified electrostatic factors. Thus, we have further substantiated our paradigm for the origin of the catalytic power of B12 enzymes. The catalytic power of enzymes containing coenzyme B12 has been, in some respects, the “last bastion” for the strain hypothesis. Our previous study of this system established by a careful sampling that the major part of the catalytic effect is due to the electrostatic interaction between the ribose of the ado group and the protein and that the strain contribution is very small. This finding has not been sufficiently appreciated due to misunderstandings of the power of the empirical valence bond (EVB) calculations and the need of sufficient sampling. Furthermore, some interesting new experiments point toward entropic effects as the source of the catalytic power, casting doubt on the validity of the electrostatic idea, at least, in the case of B12 enzymes. Here, we focus on the observation of the entropic effects and on analyzing their origin. We clarify that our EVB approach evaluates free energies rather than enthalpies and demonstrate by using the restraint release (RR) approach that the observed entropic contribution to the activation barrier is of electrostatic origin. Our study illustrates the power of the RR approach by evaluating the entropic contributions to catalysis and provides further support to our paradigm for the origin of the catalytic power of B12 enzymes. Overall, our study provides major support to our electrostatic preorganization idea and also highlights the basic requirements from ab initio quantum mechanics/molecular mechanics calculations of activation free energies of enzymatic reactions.

On the Challenge of Exploring the Evolutionary Trajectory from Phosphotriesterase to Arylesterase Using Computer Simulations

The ability to design effective enzymes presents a fundamental challenge in biotechnology and also in biochemistry. Unfortunately, most of the progress on this field has been accomplished by bringing the reactants to a reasonable orientation relative to each other, rather than by rational optimization of the polar preorganization of the environment, which is the most important catalytic factor. True computer based enzyme design would require the ability to evaluate the catalytic power of designed active sites. This work considers the evolution from a phosphotriesterase (with the paraoxon substrate) to arylesterase (with the 2-naphthylhexanoate (2NH) substrate) catalysis. Both the original and the evolved enzymes involve two zinc ions and their ligands, making it hard to obtain a reliable quantum mechanical description and then to obtain an effective free energy sampling. Furthermore, the options for the reaction path are quite complicated. To progress in this direction we started with DFT calculations of the energetics of different mechanistic options of cluster models and then used the results to calibrate empirical valence bond (EVB) models and to generate properly sampled free energy surfaces for different mechanisms in the enzyme. Interestingly, it is found that the catalytic effect depends on the Zn-Zn distance making the mechanistic analysis somewhat complicated. Comparing the activation barriers of paraoxon and the 2NH ester at the beginning and end of the evolutionary path reproduced the observed evolutionary trend. However, although our findings provide an advance in exploring the nature of promiscuous enzymes, they also indicate that modeling the reaction mechanism in the case of enzymes with a binuclear zinc center is far from trivial and presents a challenge for computer-aided enzyme design.

Electrostatic Forces: Formulas for the First Derivatives of a Polarizable, Anisotropic Electrostatic Potential Energy Function Based on Machine Learning

Explicit formulas are derived analytically for the first derivatives of a (i) polarizable, (ii) high-rank multipolar electrostatic potential energy function for (iii) flexible molecules. The potential energy function uses a machine learning method called Kriging to predict the local-frame multipole moments of atoms defined via the Quantum Chemical Topology (QCT) approach. These atomic multipole moments then interact via an interaction tensor based on spherical harmonics. Atom-centered local coordinate frames are used, constructed from the internal geometry of the molecular system. The forces involve derivatives of both this geometric dependence and of the trained kriging models. In the near future, these analytical forces will enable molecular dynamics and geometry optimization calculations as part of the QCT force field.

Structure of aryl O-demethylase offers molecular insight into a catalytic tyrosine-dependent mechanism.

Significance Modern industrial and agricultural practices generate large quantities of aromatic pollutants; however, these waste products can be converted into fine chemicals, fuels, and plastics through biocatalytic pathways. The bacterial world can inform such utilization strategies as certain strains of soil and marine bacteria metabolize environmentally derived aromatics. Many of these metabolic pathways involve aryl intermediates that require demethylation to facilitate modification and ring opening for assimilation into the tricarboxylic acid (TCA) cycle. Aryl demethylases, which catalyze this reaction, are poorly understood, making their utilization in biotechnology difficult. We provide the structural and mechanistic characterization of a single-domain aryl demethylase, LigM, which employs a tyrosine-dependent mechanism. Insights from this work will inform synthetic biology approaches to convert underutilized aromatics into higher value compounds. Some strains of soil and marine bacteria have evolved intricate metabolic pathways for using environmentally derived aromatics as a carbon source. Many of these metabolic pathways go through intermediates such as vanillate, 3-O-methylgallate, and syringate. Demethylation of these compounds is essential for downstream aryl modification, ring opening, and subsequent assimilation of these compounds into the tricarboxylic acid (TCA) cycle, and, correspondingly, there are a variety of associated aryl demethylase systems that vary in complexity. Intriguingly, only a basic understanding of the least complex system, the tetrahydrofolate-dependent aryl demethylase LigM from Sphingomonas paucimobilis, a bacterial strain that metabolizes lignin-derived aromatics, was previously available. LigM-catalyzed demethylation enables further modification and ring opening of the single-ring aromatics vanillate and 3-O-methylgallate, which are common byproducts of biofuel production. Here, we characterize aryl O-demethylation by LigM and report its 1.81-Å crystal structure, revealing a unique demethylase fold and a canonical folate-binding domain. Structural homology and geometry optimization calculations enabled the identification of LigM’s tetrahydrofolate-binding site and protein–folate interactions. Computationally guided mutagenesis and kinetic analyses allowed the identification of the enzyme’s aryl-binding site location and determination of its unique, catalytic tyrosine-dependent reaction mechanism. This work defines LigM as a distinct demethylase, both structurally and functionally, and provides insight into demethylation and its reaction requirements. These results afford the mechanistic details required for efficient utilization of LigM as a tool for aryl O-demethylation and as a component of synthetic biology efforts to valorize previously underused aromatic compounds.

Understanding factors controlling depolymerization and polymerization in catalytic degradation of β-ether linked model lignin compounds by versatile peroxidase

Lignin is a major component of lignocellulosic biomass and is responsible for much of its recalcitrant nature. Enzymatic breakdown of lignin into valuable products potentially represents an additional revenue stream in biofuels production. Many enzymes have been characterized which perform oxidative catalysis of lignin decomposition. However, the nature of the decomposition products from a given enzyme-catalyzed reaction depends on competition between depolymerization of lignin and repolymerization of the resulting depolymerization products, resulting in either polymeric products or small, aromatic species. The latter have greater value, as aromatic monomers can be used as precursors in the production of fuels and specialty chemicals via chemical or synthetic biological routes. An understanding of the factors that control the equilibrium between depolymerization and polymerization remains elusive. In this study we investigated this equilibrium for a versatile peroxidase from B. adusta using several lignin model compounds containing β-ether bonds as substrates and characterized the effects of reaction conditions (pH, addition of H2O2 and mediators) on catalysis. In tandem, quantum chemistry calculations of free energy changes of relevant chemical reactions and of electron spin density distributions of radical species were performed. Due to the low oxidation potential of the neutral radical, this enzyme is unable to oxidize non-phenolic lignin subunits. The results indicate that for phenolic lignin dimers the versatile peroxidase first produces a neutral radical via oxidation of the 4-OH position, followed by polymerization and depolymerization reactions. Selection between polymerization and depolymerization reaction pathways was found to be dependent on the functional group at the 5 position of the guaiacyl group (G5). In the case of a hydrogen atom at the G5 position (guaiacylglycerol-β-ether), the unpaired electron is distributed between the 4-OH and G5 positions, resulting in polymerization. However, substitution of G5 with a methoxy group (S-O-4) results in roughly equal distribution of the unpaired electron at G1 and 4-OH, leading to extensive side chain cleavage. The degradation pathway of phenolic β-O-4 was identified as Cα-aryl cleavage rather than Cα–Cβ.

Rhorix: An Interface Between Quantum Chemical Topology and the 3D Graphics Program Blender

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter‐free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add‐On” named Rhorix for the state‐of‐the‐art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed.