Predictive Minisci late stage functionalization with transfer learning.

Structural diversification of lead molecules is a key component of drug discovery to explore chemical space. Late-stage functionalizations (LSFs) are versatile methodologies capable of installing functional handles on richly decorated intermediates to deliver numerous diverse products in a single reaction. Predicting the regioselectivity of LSF is still an open challenge in the field. Numerous efforts from chemoinformatics and machine learning (ML) groups have made strides in this area. However, it is arduous to isolate and characterize the multitude of LSF products generated, limiting available data and hindering pure ML approaches. We report the development of an approach that combines a message passing neural network and 13C NMR-based transfer learning to predict the atom-wise probabilities of functionalization for Minisci and P450-based functionalizations. We validated our model both retrospectively and with a series of prospective experiments, showing that it accurately predicts the outcomes of Minisci-type and P450 transformations and outperforms the well-established Fukui-based reactivity indices and other machine learning reactivity-based algorithms.

Can We Quickly Learn to "Translate" Bioactive Molecules with Transformer Models?

Meaningful exploration of the chemical space of druglike molecules in drug design is a highly challenging task due to a combinatorial explosion of possible modifications of molecules. In this work, we address this problem with transformer models, a type of machine learning (ML) model originally developed for machine translation. By training transformer models on pairs of similar bioactive molecules from the public ChEMBL data set, we enable them to learn medicinal-chemistry-meaningful, context-dependent transformations of molecules, including those absent from the training set. By retrospective analysis on the performance of transformer models on ChEMBL subsets of ligands binding to COX2, DRD2, or HERG protein targets, we demonstrate that the models can generate structures identical or highly similar to most active ligands, despite the models having not seen any ligands active against the corresponding protein target during training. Our work demonstrates that human experts working on hit expansion in drug design can easily and quickly employ transformer models, originally developed to translate texts from one natural language to another, to "translate" from known molecules active against a given protein target to novel molecules active against the same target.

Intradomain Interactions in an NMDA Receptor Fragment Mediate N-Glycan Processing and Conformational Sampling.

The structural and functional roles of highly conserved asparagine-linked (N)-glycans on the extracellular ligand-binding domain (LBD) of the N-methyl-D-aspartate receptors are poorly understood. We applied solution- and computation-based methods that identified N-glycan-mediated intradomain and interglycan interactions. Nuclear magnetic resonance (NMR) spectra of the GluN1 LBD showed clear signals corresponding to each of the three N-glycans and indicated the reducing end of glycans at N440 and N771 potentially contacted nearby amino acids. Molecular dynamics simulations identified contacts between nearby amino acids and the N440- and N771-glycans that were consistent with the NMR spectra. The distal portions of the N771-glycan also contacted the core residues of the nearby N471-glycan. This result was consistent with mass spectrometry data indicating the limited N471-glycan core fucosylation and reduced branch processing of the N771-glycan could be explained by interglycan contacts. We discuss a potential role for the GluN1 LBD N-glycans in interdomain contacts formed in NMDA receptors.

Computer Simulations Predict High Structural Heterogeneity of Functional State of NMDA Receptors.

N-methyl-D-aspartate receptors (NMDARs)-i.e., transmembrane proteins expressed in neurons-play a central role in the molecular mechanisms of learning and memory formation. It is unclear how the known atomic structures of NMDARs determined by x-ray crystallography and electron cryomicroscopy (18 published Protein Data Bank entries) relate to the functional states of NMDARs inferred from electrophysiological recordings (multiple closed, open, preopen, etc. states). We address this problem by using molecular dynamics simulations at atomic resolution, a method successfully applied in the past to much smaller biomolecules. Our simulations predict that several conformations of NMDARs with experimentally determined geometries, including four "nonactive" electron cryomicroscopy structures, rapidly interconvert on submicrosecond timescales and therefore may correspond to the same functional state of the receptor (specifically, one of the closed states). This conclusion is not trivial because these conformational transitions involve changes in certain interatomic distances as large as tens of Å. The simulations also predict differences in the conformational dynamics of the apo and holo (i.e., agonist and coagonist bound) forms of the receptor on the microsecond timescale. To our knowledge, five new conformations of NMDARs, with geometries joining various features from different known experimental structures, are also predicted by the model. The main limitation of this work stems from its limited sampling (30 µs of aggregate length of molecular dynamics trajectories). Though this level significantly exceeds the sampling in previous simulations of parts of NMDARs, it is still much lower than the sampling recently achieved for smaller biomolecules (up to a few milliseconds), thus precluding, in particular, the observation of transitions between different functional states of NMDARs. Despite this limitation, such computational predictions may guide further experimental studies on the structure, dynamics, and function of NMDARs, for example by suggesting optimal locations of spectroscopic probes. Overall, atomic resolution simulations provide, to our knowledge, a novel perspective on the structure and dynamics of NMDARs, complementing information obtained by experimental methods.

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics.

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit time scale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule has never been formally proved. In this work, we present analytical results for the slowest time scale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit time scale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit time scale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit time scale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest time scales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.

Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM).

Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.

Simulated Dynamics of Glycans on Ligand-Binding Domain of NMDA Receptors Reveals Strong Dynamic Coupling between Glycans and Protein Core.

N-Methyl-d-aspartate (NMDA) receptors, key neuronal receptors playing the central role in learning and memory, are heavily glycosylated in vivo. Astonishingly little is known about the structure, dynamics, and physiological relevance of glycans attached to them. We recently demonstrated that certain glycans on the ligand binding domain (LBD) of NMDA receptors (NMDARs) can serve as intramolecular potentiators, changing EC50 of NMDAR coagonists. In this work, we use molecular dynamics trajectories, in aggregate 86.5 µs long, of the glycosylated LBD of the GluN1 subunit of the NMDAR to investigate the behavior of glycans on NMDARs. Though all glycans in our simulations were structurally the same (Man5), the dynamics of glycans at different locations on NMDARs was surprisingly different. The slowest-time scale motions that we detected in various glycans in some cases corresponded to a flipping of parts of glycans relative to each other, while in other cases they reduced to a head-to-tail bending of a glycan. We predict that time scales of conformational changes in glycans on the GluN1 LBD of NMDARs range from nanoseconds to at least hundreds of microseconds. Some of the conformational changes in the glycans correlate with the physiologically important clamshell-like opening and closing of the GluN1 LBD domain. Thus, glycans are an integral part of NMDARs, and computational models of NMDARs should include glycans to faithfully represent the structure and the dynamics of these receptors.

Computationally Discovered Potentiating Role of Glycans on NMDA Receptors.

N-methyl-D-aspartate receptors (NMDARs) are glycoproteins in the brain central to learning and memory. The effects of glycosylation on the structure and dynamics of NMDARs are largely unknown. In this work, we use extensive molecular dynamics simulations of GluN1 and GluN2B ligand binding domains (LBDs) of NMDARs to investigate these effects. Our simulations predict that intra-domain interactions involving the glycan attached to residue GluN1-N440 stabilize closed-clamshell conformations of the GluN1 LBD. The glycan on GluN2B-N688 shows a similar, though weaker, effect. Based on these results, and assuming the transferability of the results of LBD simulations to the full receptor, we predict that glycans at GluN1-N440 might play a potentiator role in NMDARs. To validate this prediction, we perform electrophysiological analysis of full-length NMDARs with a glycosylation-preventing GluN1-N440Q mutation, and demonstrate an increase in the glycine EC50 value. Overall, our results suggest an intramolecular potentiating role of glycans on NMDA receptors.

Highly Coarse-Grained Representations of Transmembrane Proteins.

Numerous biomolecules and biomolecular complexes, including transmembrane proteins (TMPs), are symmetric or at least have approximate symmetries. Highly coarse-grained models of such biomolecules, aiming at capturing the essential structural and dynamical properties on resolution levels coarser than the residue scale, must preserve the underlying symmetry. However, making these models obey the correct physics is in general not straightforward, especially at the highly coarse-grained resolution where multiple (∼3-30 in the current study) amino acid residues are represented by a single coarse-grained site. In this paper, we propose a simple and fast method of coarse-graining TMPs obeying this condition. The procedure involves partitioning transmembrane domains into contiguous segments of equal length along the primary sequence. For the coarsest (lowest-resolution) mappings, it turns out to be most important to satisfy the symmetry in a coarse-grained model. As the resolution is increased to capture more detail, however, it becomes gradually more important to match modular repeats in the secondary structure (such as helix-loop repeats) instead. A set of eight TMPs of various complexity, functionality, structural topology, and internal symmetry, representing different classes of TMPs (ion channels, transporters, receptors, adhesion, and invasion proteins), has been examined. The present approach can be generalized to other systems possessing exact or approximate symmetry, allowing for reliable and fast creation of multiscale, highly coarse-grained mappings of large biomolecular assemblies.

Cations Stiffen Actin Filaments by Adhering a Key Structural Element to Adjacent Subunits.

Ions regulate the assembly and mechanical properties of actin filaments. Recent work using structural bioinformatics and site-specific mutagenesis favors the existence of two discrete and specific divalent cation binding sites on actin filaments, positioned in the long axis between actin subunits. Cation binding at one site drives polymerization, while the other modulates filament stiffness and plays a role in filament severing by the regulatory protein, cofilin. Existing structural methods have not been able to resolve filament-associated cations, and so in this work we turn to molecular dynamics simulations to suggest a candidate binding pocket geometry for each site and to elucidate the mechanism by which occupancy of the "stiffness site" affects filament mechanical properties. Incorporating a magnesium ion in the "polymerization site" does not seem to require any large-scale change to an actin subunit's conformation. Binding of a magnesium ion in the "stiffness site" adheres the actin DNase-binding loop (D-loop) to its long-axis neighbor, which increases the filament torsional stiffness and bending persistence length. Our analysis shows that bound D-loops occupy a smaller region of accessible conformational space. Cation occupancy buries key conserved residues of the D-loop, restricting accessibility to regulatory proteins and enzymes that target these amino acids.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation.

The increasing interest in the modeling of complex macromolecular systems in recent years has spurred the development of numerous coarse-graining (CG) techniques. However, many of the CG models are constructed assuming that all details beneath the resolution of CG degrees of freedom are fast and average out, which sets limits on the resolution of feasible coarse-grainings and on the range of applications of the CG models. Ultra-coarse-graining (UCG) makes it possible to construct models at any desired resolution while accounting for discrete conformational or chemical changes within the CG sites that can modulate the interactions between them. Here, we discuss the UCG methodology and its numerical implementation. We pay particular attention to the numerical mechanism for including state transitions between different conformations within CG sites because this has not been discussed previously. Using a simple example of 1,2-dichloroethane, we demonstrate the ability of the UCG model to reproduce the multiconfigurational behavior of this molecular liquid, even when each molecule is modeled with only one CG site. The methodology can also be applied to other molecular liquids and macromolecular systems with time scale separation between conformational transitions and other intramolecular motions and rotations.

The Theory of Ultra-Coarse-Graining. 1. General Principles.

Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and relative entropy minimization methods, provide attractive tools for the systematic development of CG models. However, these methods have important drawbacks when used in the "ultra-coarse-grained" (UCG) regime, e.g., at a resolution level coarser or much coarser than one amino acid residue per effective CG particle in proteins. This is due to the possible existence of multiple metastable states "within" the CG sites for a given UCG model configuration. In this work, systematic variational UCG methods are presented that are specifically designed to CG entire protein domains and subdomains into single effective CG particles. This is accomplished by augmenting existing effective particle CG schemes to allow for discrete state transitions and configuration-dependent resolution. Additionally, certain conclusions of this work connect back to single-state force matching and open up new avenues for method development in that area. These results provide a formal statistical mechanical basis for UCG methods related to force matching and relative entropy CG methods and suggest practical algorithms for constructing optimal approximate UCG models from fine-grained simulation data.

Optimal number of coarse-grained sites in different components of large biomolecular complexes.

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

Phenomenological model of spin crossover in molecular crystals as derived from atom-atom potentials.

The method of atom-atom potentials, previously applied to the analysis of pure molecular crystals formed by either low-spin (LS) or high-spin (HS) forms (spin isomers) of Fe(II) coordination compounds (Sinitskiy et al., Phys. Chem. Chem. Phys., 2009, 11, 10983), is used to estimate the lattice enthalpies of mixed crystals containing different fractions of the spin isomers. The crystals under study were formed by LS and HS isomers of Fe(phen)(2)(NCS)(2) (phen = 1,10-phenanthroline), Fe(btz)(2)(NCS)(2) (btz = 5,5',6,6'-tetrahydro-4H,4'H-2,2'-bi-1,3-thiazine), and Fe(bpz)(2)(bipy) (bpz = dihydrobis(1-pyrazolil)borate, and bipy = 2,2'-bipyridine). For the first time the phenomenological parameters Γ pertinent to the Slichter-Drickamer model (SDM) of several materials were independently derived from the microscopic model of the crystals with use of atom-atom potentials of intermolecular interaction. The accuracy of the SDM was checked against the numerical data on the enthalpies of mixed crystals. Fair semiquantitative agreement with the experimental dependence of the HS fraction on temperature was achieved with use of these values. Prediction of trends in Γ values as a function of chemical composition and geometry of the crystals is possible with the proposed approach, which opens a way to rational design of spin crossover materials with desired properties.

Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method.

The variational two-electron reduced-density-matrix (2-RDM) method, scaling polynomially with the size of the system, was applied to linear chains and three-dimensional clusters of atomic hydrogen as large as H(64). In the case of the 4x4x4 hydrogen lattice of 64 hydrogen atoms, a correct description of the dissociation requires about 10(18) equally weighted determinants in the wave function, which is too large for traditional multireference methods. The correct energy in the dissociation limit was obtained from the variational 2-RDM method in contrast to Hartree-Fock and single-reference methods. Analysis of the occupation numbers demonstrates that even for 1.0 A bond distances the presence of strong electron correlation requires a multireference method. Three-dimensional systems exhibit a marked increase in electron correlation from one-dimensional systems regardless of size. The metal-to-insulator transition upon expansion of the clusters was studied using the decay of the 1-RDM off-diagonal elements. The variational 2-RDM method was shown to capture the metal-to-insulator transition and dissociation behavior accurately for all systems.

Modeling molecular crystals formed by spin-active metal complexes by atom-atom potentials.

We apply the atom-atom potentials to molecular crystals of iron(II) complexes with bulky organic ligands. The crystals under study are formed by low-spin or high-spin molecules of Fe(phen)(2)(NCS)(2) (phen = 1,10-phenanthroline), Fe(btz)(2)(NCS)(2) (btz = 5,5',6,6'-tetrahydro-4H,4'H-2,2'-bi-1,3-thiazine), and Fe(bpz)(2)(bipy) (bpz = dihydrobis(1-pyrazolil)borate, and bipy = 2,2'-bipyridine). All molecular geometries are taken from the X-ray experimental data and assumed to be frozen. The unit cell dimensions and angles, positions of the centers of masses of molecules, and the orientations of molecules corresponding to the minimum energy at 1 atm and 1 GPa are calculated. The optimized crystal structures are in a good agreement with the experimental data. Sources of the residual discrepancies between the calculated and experimental structures are discussed. The intermolecular contributions to the enthalpy of the spin transitions are found to be comparable with its total experimental values. It demonstrates that the method of atom-atom potentials is very useful for modeling molecular crystals undergoing the spin transitions.