Real-space quantum-based refinement for cryo-EM: Q|R#3.

Electron cryo-microscopy (cryo-EM) is rapidly becoming a major competitor to X-ray crystallography, especially for large structures that are difficult or impossible to crystallize. While recent spectacular technological improvements have led to significantly higher resolution three-dimensional reconstructions, the average quality of cryo-EM maps is still at the low-resolution end of the range compared with crystallography. A long-standing challenge for atomic model refinement has been the production of stereochemically meaningful models for this resolution regime. Here, it is demonstrated that including accurate model geometry restraints derived from ab initio quantum-chemical calculations (HF-D3/6-31G) can improve the refinement of an example structure (chain A of PDB entry 3j63). The robustness of the procedure is tested for additional structures with up to 7000 atoms (PDB entry 3a5x and chain C of PDB entry 5fn5) using the less expensive semi-empirical (GFN1-xTB) model. The necessary algorithms enabling real-space quantum refinement have been implemented in the latest version of qr.refine and are described here.

Including crystallographic symmetry in quantum-based refinement: Q|R#2.

Three-dimensional structure models refined using low-resolution data from crystallographic or electron cryo-microscopy experiments can benefit from high-quality restraints derived from quantum-chemical methods. However, nonperiodic atom-centered quantum-chemistry codes do not inherently account for nearest-neighbor interactions of crystallographic symmetry-related copies in a satisfactory way. Here, these nearest-neighbor effects have been included in the model by expanding to a super-cell and then truncating the super-cell to only include residues from neighboring cells that are interacting with the asymmetric unit. In this way, the fragmentation approach can adequately and efficiently include nearest-neighbor effects. It has previously been shown that a moderately sized X-ray structure can be treated using quantum methods if a fragmentation approach is applied. In this study, a target protein (PDB entry 4gif) was partitioned into a number of large fragments. The use of large fragments (typically hundreds of atoms) is tractable when a GPU-based package such as TeraChem is employed or cheaper (semi-empirical) methods are used. The QM calculations were run at the HF-D3/6-31G level. The models refined using a recently developed semi-empirical method (GFN2-xTB) were compared and contrasted. To validate the refinement procedure for a non-P1 structure, a standard set of crystallographic metrics were used. The robustness of the implementation is shown by refining 13 additional protein models across multiple space groups and a summary of the refinement metrics is presented.

A Probabilistic Framework for Constructing Temporal Relations in Replica Exchange Molecular Trajectories.

Knowledge of the structure and dynamics of biomolecules is essential for elucidating the underlying mechanisms of biological processes. Given the stochastic nature of many biological processes, like protein unfolding, it is almost impossible that two independent simulations will generate the exact same sequence of events, which makes direct analysis of simulations difficult. Statistical models like Markov chains, transition networks, etc. help in shedding some light on the mechanistic nature of such processes by predicting long-time dynamics of these systems from short simulations. However, such methods fall short in analyzing trajectories with partial or no temporal information, for example, replica exchange molecular dynamics or Monte Carlo simulations. In this work, we propose a probabilistic algorithm, borrowing concepts from graph theory and machine learning, to extract reactive pathways from molecular trajectories in the absence of temporal data. A suitable vector representation was chosen to represent each frame in the macromolecular trajectory (as a series of interaction and conformational energies), and dimensionality reduction was performed using principal component analysis (PCA). The trajectory was then clustered using a density-based clustering algorithm, where each cluster represents a metastable state on the potential energy surface (PES) of the biomolecule under study. A graph was created with these clusters as nodes with the edges learned using an iterative expectation maximization algorithm. The most reactive path is conceived as the widest path along this graph. We have tested our method on RNA hairpin unfolding trajectory in aqueous urea solution. Our method makes the understanding of the mechanism of unfolding in the RNA hairpin molecule more tractable. As this method does not rely on temporal data, it can be used to analyze trajectories from Monte Carlo sampling techniques and replica exchange molecular dynamics (REMD).

Planning chemical syntheses with deep neural networks and symbolic AI.

To plan the syntheses of small organic molecules, chemists use retrosynthesis, a problem-solving technique in which target molecules are recursively transformed into increasingly simpler precursors. Computer-aided retrosynthesis would be a valuable tool but at present it is slow and provides results of unsatisfactory quality. Here we use Monte Carlo tree search and symbolic artificial intelligence (AI) to discover retrosynthetic routes. We combined Monte Carlo tree search with an expansion policy network that guides the search, and a filter network to pre-select the most promising retrosynthetic steps. These deep neural networks were trained on essentially all reactions ever published in organic chemistry. Our system solves for almost twice as many molecules, thirty times faster than the traditional computer-aided search method, which is based on extracted rules and hand-designed heuristics. In a double-blind AB test, chemists on average considered our computer-generated routes to be equivalent to reported literature routes.

Generating Focused Molecule Libraries for Drug Discovery with Recurrent Neural Networks.

In de novo drug design, computational strategies are used to generate novel molecules with good affinity to the desired biological target. In this work, we show that recurrent neural networks can be trained as generative models for molecular structures, similar to statistical language models in natural language processing. We demonstrate that the properties of the generated molecules correlate very well with the properties of the molecules used to train the model. In order to enrich libraries with molecules active toward a given biological target, we propose to fine-tune the model with small sets of molecules, which are known to be active against that target. Against Staphylococcus aureus, the model reproduced 14% of 6051 hold-out test molecules that medicinal chemists designed, whereas against Plasmodium falciparum (Malaria), it reproduced 28% of 1240 test molecules. When coupled with a scoring function, our model can perform the complete de novo drug design cycle to generate large sets of novel molecules for drug discovery.

Yoink: An interaction-based partitioning API.

Herein, we describe the implementation details of our interaction-based partitioning API (application programming interface) called Yoink for QM/MM modeling and fragment-based quantum chemistry studies. Interactions are detected by computing density descriptors such as reduced density gradient, density overlap regions indicator, and single exponential decay detector. Only molecules having an interaction with a user-definable QM core are added to the QM region of a hybrid QM/MM calculation. Moreover, a set of molecule pairs having density-based interactions within a molecular system can be computed in Yoink, and an interaction graph can then be constructed. Standard graph clustering methods can then be applied to construct fragments for further quantum chemical calculations. The Yoink API is licensed under Apache 2.0 and can be accessed via yoink.wallerlab.org. © 2018 Wiley Periodicals, Inc.

Rational Density Functional Selection Using Game Theory.

Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.

Solving the scalability issue in quantum-based refinement: Q|R#1.

Accurately refining biomacromolecules using a quantum-chemical method is challenging because the cost of a quantum-chemical calculation scales approximately as nm, where n is the number of atoms and m (≥3) is based on the quantum method of choice. This fundamental problem means that quantum-chemical calculations become intractable when the size of the system requires more computational resources than are available. In the development of the software package called Q|R, this issue is referred to as Q|R#1. A divide-and-conquer approach has been developed that fragments the atomic model into small manageable pieces in order to solve Q|R#1. Firstly, the atomic model of a crystal structure is analyzed to detect noncovalent interactions between residues, and the results of the analysis are represented as an interaction graph. Secondly, a graph-clustering algorithm is used to partition the interaction graph into a set of clusters in such a way as to minimize disruption to the noncovalent interaction network. Thirdly, the environment surrounding each individual cluster is analyzed and any residue that is interacting with a particular cluster is assigned to the buffer region of that particular cluster. A fragment is defined as a cluster plus its buffer region. The gradients for all atoms from each of the fragments are computed, and only the gradients from each cluster are combined to create the total gradients. A quantum-based refinement is carried out using the total gradients as chemical restraints. In order to validate this interaction graph-based fragmentation approach in Q|R, the entire atomic model of an amyloid cross-ß spine crystal structure (PDB entry 2oNA) was refined.

ChemPreview: an augmented reality-based molecular interface.

Human computer interfaces make computational science more comprehensible and impactful. Complex 3D structures such as proteins or DNA are magnified by digital representations and displayed on two-dimensional monitors. Augmented reality has recently opened another door to access the virtual three-dimensional world. Herein, we present an augmented reality application called ChemPreview with the potential to manipulate bio-molecular structures at an atomistic level. ChemPreview is available at https://github.com/wallerlab/chem-preview/releases, and is built on top of the Meta 1 platform https://www.metavision.com/. ChemPreview can be used to interact with a protein in an intuitive way using natural hand gestures, thereby making it appealing to computational chemists or structural biologists. The ability to manipulate atoms in real world could eventually provide new and more efficient ways of extracting structural knowledge, or designing new molecules in silico.

Neural-Symbolic Machine Learning for Retrosynthesis and Reaction Prediction.

Reaction prediction and retrosynthesis are the cornerstones of organic chemistry. Rule-based expert systems have been the most widespread approach to computationally solve these two related challenges to date. However, reaction rules often fail because they ignore the molecular context, which leads to reactivity conflicts. Herein, we report that deep neural networks can learn to resolve reactivity conflicts and to prioritize the most suitable transformation rules. We show that by training our model on 3.5 million reactions taken from the collective published knowledge of the entire discipline of chemistry, our model exhibits a top10-accuracy of 95 % in retrosynthesis and 97 % for reaction prediction on a validation set of almost 1 million reactions.

Q|R: quantum-based refinement.

Quantum-based refinement utilizes chemical restraints derived from quantum-chemical methods instead of the standard parameterized library-based restraints used in refinement packages. The motivation is twofold: firstly, the restraints have the potential to be more accurate, and secondly, the restraints can be more easily applied to new molecules such as drugs or novel cofactors. Here, a new project called Q|R aimed at developing quantum-based refinement of biomacromolecules is under active development by researchers at Shanghai University together with PHENIX developers. The central focus of this long-term project is to develop software that is built on top of open-source components. A development version of Q|R was used to compare quantum-based refinements with standard refinement using a small model system.

Modelling Chemical Reasoning to Predict and Invent Reactions.

The ability to reason beyond established knowledge allows organic chemists to solve synthetic problems and invent novel transformations. Herein, we propose a model that mimics chemical reasoning, and formalises reaction prediction as finding missing links in a knowledge graph. We have constructed a knowledge graph containing 14.4 million molecules and 8.2 million binary reactions, which represents the bulk of all chemical reactions ever published in the scientific literature. Our model outperforms a rule-based expert system in the reaction prediction task for 180 000 randomly selected binary reactions. The data-driven model generalises even beyond known reaction types, and is thus capable of effectively (re-)discovering novel transformations (even including transition metal-catalysed reactions). Our model enables computers to infer hypotheses about reactivity and reactions by only considering the intrinsic local structure of the graph and because each single reaction prediction is typically achieved in a sub-second time frame, the model can be used as a high-throughput generator of reaction hypotheses for reaction discovery.

Sequence-Dependent Duplex Stabilization upon Formation of a Metal-Mediated Base Pair.

An artificial nucleoside surrogate with 1H-imidazo[4,5-f][1,10]phenanthroline (P) acting as an aglycone has been introduced into DNA oligonucleotide duplexes. This nucleoside surrogate can act as a bidentate ligand, and so is useful in the context of metal-mediated base pairs. Several duplexes involving a hetero base pair with an imidazole nucleoside have been investigated. The stability of DNA duplexes incorporating the respective Ag(I) -mediated base pairs strongly depends on the sequence context. Quantum mechanical/molecular mechanical (QM/MM) calculations have been performed in order to gain insight into the factors determining this sequence dependence. The results indicated that, in addition to the stabilizing effect that results from the formation of coordinative bonds, destabilizing effects may occur when the artificial base pair does not fit optimally into the surrounding B-DNA duplex.

Cooperativity in bimetallic glutathione complexes.

Glutathione interacting with Au(+), Ag(+), and [HgMe](+) metal ions is investigated using density functional theory. An extensive conformational search shows that the sulfhydryl group of cysteine is the predominant binding motif for Au(+), Ag(+), and [HgMe](+). The order of binding affinities and binding free energies for the metal:ligand complexes are calculated at the B3LYP-D3(BJ)/def2-TZVP level of theory. Analysis of the gas-phase optimized structures has shown that the increase in the number of metal ions (1:1 → 2:1) during the complex formation with a single glutathione leads to a strong cooperative behavior. Conversely, anti-cooperativity is demonstrated in implicit solvation corrections as well as in explicit solvent corrections to the energies in the explicitly solvated-phase structures optimized using a density-based adaptive QM/MM methodology.

pH response and molecular recognition in a low molecular weight peptide hydrogel.

In this article we report the preparation and characterization of a peptide-based hydrogel, which possesses characteristic rheological properties, is pH responsive and can be functionalized at its thiol function. The tripeptide N-(fluorenyl-9-methoxycarbonyl)-L-Cys(acetamidomethyl)-L-His-L-Cys-OH 1 forms stable supramolecular aggregates in water leading to hydrogels above 1.5 wt%. Rheological analysis of the hydrogel revealed visco-elastic and shear thinning properties of samples containing 1.5 wt% of peptide 1. The hydrogel reversibly responds to pH changes. Below and above pH 6, electrostatic repulsion of the peptide results in a weakening of the three-dimensional gel network. Based on atomic force microscopy, small angle X-ray scattering and molecular dynamics simulations, it is proposed that the peptide assembles into nanostructures that tend to entangle at higher concentrations in water. The development of functional materials based on the peptide assemblies was possible via thiol-ene-click chemistry of the free thiol function at the C-terminal cysteine unit. As a proof of concept, the functionalization with adamantyl units to give 1-Ad was shown by molecular recognition of ß-cyclodextrin vesicles. These vesicles were used as supramolecular cross-linkers of the assemblies of peptide 1 mixed with peptide 1-Ad leading to gel networks at a reduced peptide concentration.

A density-based adaptive quantum mechanical/molecular mechanical method.

We present a density-based adaptive quantum mechanical/molecular mechanical (DBA-QM/MM) method, whereby molecules can switch layers from the QM to the MM region and vice versa. The adaptive partitioning of the molecular system ensures that the layer assignment can change during the optimization procedure, that is, on the fly. The switch from a QM molecule to a MM molecule is determined if there is an absence of noncovalent interactions to any atom of the QM core region. The presence/absence of noncovalent interactions is determined by analysis of the reduced density gradient. Therefore, the location of the QM/MM boundary is based on physical arguments, and this neatly removes some empiricism inherent in previous adaptive QM/MM partitioning schemes. The DBA-QM/MM method is validated by using a water-in-water setup and an explicitly solvated L-alanyl-L-alanine dipeptide.

Peptide-based carbohydrate receptors.

A broad spectrum of physiological processes is mediated by highly specific noncovalent interactions of carbohydrates and proteins. In a recent communication we identified several cyclic hexapeptides in a dynamic combinatorial library that interact selectively with carbohydrates with high binding constants in water. Herein, we report a detailed investigation of the noncovalent interaction of two cyclic hexapeptides (Cys-His-Cys (which we call HisHis) and Cys-Tyr-Cys (which we call TyrTyr)) with a selection of monosaccharides and disaccharides in aqueous solution. The parallel and antiparallel isomers of HisHis or TyrTyr were synthesized separately, and their interaction with monosaccharides and disaccharides in aqueous solution was studied by isothermal titration calorimetry, NMR spectroscopic titrations, and circular dichroism spectroscopy. From these measurements, we identified particularly stable complexes (Ka> 1000 M(-1)) of the parallel isomer of HisHis with N-acetylneuraminic acid and with methyl-a-d-galactopyranoside as well as of both isomers of TyrTyr with trehalose. To gain further insight into the structure of the peptide­carbohydrate complexes, structure prediction was performed using quantum chemical methods. The calculations confirm the selectivity observed in the experiments and indicate the formation of multiple intermolecular hydrogen bonds in the most stable complexes.

JACOB: an enterprise framework for computational chemistry.

Here, we present just a collection of beans (JACOB): an integrated batch-based framework designed for the rapid development of computational chemistry applications. The framework expedites developer productivity by handling the generic infrastructure tier, and can be easily extended by user-specific scientific code. Paradigms from enterprise software engineering were rigorously applied to create a scalable, testable, secure, and robust framework. A centralized web application is used to configure and control the operation of the framework. The application-programming interface provides a set of generic tools for processing large-scale noninteractive jobs (e.g., systematic studies), or for coordinating systems integration (e.g., complex workflows). The code for the JACOB framework is open sourced and is available at: www.wallerlab.org/jacob.

A QM/MM refinement of an experimental DNA structure with metal-mediated base pairs.

A series of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations was performed on models of a DNA duplex with artificial silver(I)-mediated imidazole base pairs. The optimized structures were compared to the original experimental NMR structure (Nat. Chem. 2 (2010) 229-234). The metal⋯metal distances are significantly shorter (~0.5Å) in the QM/MM model than in the original NMR structure. As a result, argentophilic interactions are feasible between the silver(I) ions of neighboring metal-mediated base pairs. Using the computationally determined metal⋯metal distances, a re-refined NMR solution structure of the DNA duplex was obtained. In this new NMR structure, all experimental constraints remain fulfilled. The new NMR structure shows less deviation from the regular B-type conformation than the original one. This investigation shows that the application of QM/MM models to generate additional constraints to be used during NMR structural refinements represents an elegant approach to obtaining high-resolution NMR structures.