Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data.

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Advancing mathematics by guiding human intuition with AI.

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning-demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

Neural algorithmic reasoning.

We present neural algorithmic reasoning-the art of building neural networks that are able to execute algorithmic computation-and provide our opinion on its transformative potential for running classical algorithms on inputs previously considered inaccessible to them.

Targeted free energy estimation via learned mappings.

Free energy perturbation (FEP) was proposed by Zwanzig [J. Chem. Phys. 22, 1420 (1954)] more than six decades ago as a method to estimate free energy differences and has since inspired a huge body of related methods that use it as an integral building block. Being an importance sampling based estimator, however, FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted FEP, uses a high-dimensional mapping in configuration space to increase the overlap of the underlying distributions. Despite its potential, this method has attracted only limited attention due to the formidable challenge of formulating a tractable mapping. Here, we cast Targeted FEP as a machine learning problem in which the mapping is parameterized as a neural network that is optimized so as to increase the overlap. We develop a new model architecture that respects permutational and periodic symmetries often encountered in atomistic simulations and test our method on a fully periodic solvation system. We demonstrate that our method leads to a substantial variance reduction in free energy estimates when compared against baselines, without requiring any additional data.

Conformations in Solution and in Solid-State Polymorphs: Correlating Experimental and Calculated Nuclear Magnetic Resonance Chemical Shifts for Tolfenamic Acid.

A new approach for quantitively assessing putative crystal structures with applications in crystal structure prediction (CSP) is introduced that is based upon experimental solution- and magic-angle spinning (MAS) solid-state NMR data and density functional theory (DFT) calculation. For the specific case of tolfenamic acid (TFA), we consider experimental solution-state NMR for a range of solvents, experimental MAS NMR of polymorphs I and II, and DFT calculations for four polymorphs. The change in NMR chemical shift observed in passing from the solution state to the solid state (ΔδExperimental) is calculated as the difference between 1H and 13C experimental solid-state chemical shifts for each polymorphic form (δSolid expt) and the corresponding solution-state NMR chemical shifts (δSolution expt). Separately, we use the gauge-included projector augmented wave (GIPAW) method to calculate the NMR chemical shifts for each form (δSolid calc) and for TFA in solution (δSolution calc) using the dynamic 3D solution conformational ensemble determined from NMR spectroscopy. The calculated change in passing from the solution state to the solid state (ΔδCalculated) is then calculated as the difference of δSolid calc and δSolution calc. Regression analysis for ΔδCalculated against ΔδExperimental followed by a t-test for statistical significance provides a robust quantitative assessment. We show that this assessment clearly identifies the correct polymorph, i.e., when comparing ΔδExperimental based on the experimental MAS NMR chemical shifts of form I or II with ΔδCalculated based on calculated chemical shifts for polymorphs I, II, III, and IV. Complementarity to the established approach of comparing δSolid expt to δSolid calc is explored. We further show that our approach is applicable if there are no solid-state crystal structure data. Specifically, δSolid calc in ΔδCalculated is replaced by the chemical shift for an isolated molecule with a specific conformation. Sampling conformations at specific 15° angle values and comparing them against experimental 13C chemical shift data for forms I and II identifies matching narrow ranges of conformations, successfully predicting the conformation of tolfenamic acid in each form. This methodology can therefore be used in crystal structure prediction to both reduce the initial conformational search space and also quantitatively assess subsequent putative structures to reliably and unambiguously identify the correct structure.

Crystal structures of tolfenamic acid polymorphic forms I and II with precise hydrogen-atom positions for nuclear magnetic resonance studies.

The structures of tolfenamic acid [TFA; 2-(3-chloro-2-methyl-anilino)benzoic acid, C14H12ClNO2] polymorph forms I and II have been redetermined [compare Andersen et al. (1989 ▸). J. Chem. Soc., Perkin Trans. 2, pp. 1443-1447] with improved precision using high-resolution X-ray diffraction data and Hirshfield atom refinement in order to better define both hydrogen-atom locations and their associated bond lengths. Covalent bond lengths to hydrogen were found to be significantly longer throughout both structures, especially for the anilino H atom, which is involved in an important intra-molecular N-H⋯O hydrogen bond to the carb-oxy-lic acid group. This hydrogen bond is shown to clearly perturb the electron density around both oxygen atoms in the latter group. The extended structures of both polymorphs feature carb-oxy-lic acid inversion dimers. These structures provide an improved foundation for nuclear magnetic resonance studies in both solution and the solid state.

Confidence modulates exploration and exploitation in value-based learning.

Uncertainty is ubiquitous in cognitive processing. In this study, we aim to investigate the ability agents possess to track and report the noise inherent in their mental operations, often in the form of confidence judgments. Here, we argue that humans can use uncertainty inherent in their representations of value beliefs to arbitrate between exploration and exploitation. Such uncertainty is reflected in explicit confidence judgments. Using a novel variant of a multi-armed bandit paradigm, we studied how beliefs were formed and how uncertainty in the encoding of these value beliefs (belief confidence) evolved over time. We found that people used uncertainty to arbitrate between exploration and exploitation, reflected in a higher tendency toward exploration when their confidence in their value representations was low. We furthermore found that value uncertainty can be linked to frameworks of metacognition in decision making in two ways. First, belief confidence drives decision confidence, i.e. people's evaluation of their own choices. Second, individuals with higher metacognitive insight into their choices were also better at tracing the uncertainty in their environment. Together, these findings argue that such uncertainty representations play a key role in the context of cognitive control.

Reinforcement Learning, Fast and Slow.

Deep reinforcement learning (RL) methods have driven impressive advances in artificial intelligence in recent years, exceeding human performance in domains ranging from Atari to Go to no-limit poker. This progress has drawn the attention of cognitive scientists interested in understanding human learning. However, the concern has been raised that deep RL may be too sample-inefficient - that is, it may simply be too slow - to provide a plausible model of how humans learn. In the present review, we counter this critique by describing recently developed techniques that allow deep RL to operate more nimbly, solving problems much more quickly than previous methods. Although these techniques were developed in an AI context, we propose that they may have rich implications for psychology and neuroscience. A key insight, arising from these AI methods, concerns the fundamental connection between fast RL and slower, more incremental forms of learning.

Vector-based navigation using grid-like representations in artificial agents.

Deep neural networks have achieved impressive successes in fields ranging from object recognition to complex games such as Go1,2. Navigation, however, remains a substantial challenge for artificial agents, with deep neural networks trained by reinforcement learning3-5 failing to rival the proficiency of mammalian spatial behaviour, which is underpinned by grid cells in the entorhinal cortex 6 . Grid cells are thought to provide a multi-scale periodic representation that functions as a metric for coding space7,8 and is critical for integrating self-motion (path integration)6,7,9 and planning direct trajectories to goals (vector-based navigation)7,10,11. Here we set out to leverage the computational functions of grid cells to develop a deep reinforcement learning agent with mammal-like navigational abilities. We first trained a recurrent network to perform path integration, leading to the emergence of representations resembling grid cells, as well as other entorhinal cell types 12 . We then showed that this representation provided an effective basis for an agent to locate goals in challenging, unfamiliar, and changeable environments-optimizing the primary objective of navigation through deep reinforcement learning. The performance of agents endowed with grid-like representations surpassed that of an expert human and comparison agents, with the metric quantities necessary for vector-based navigation derived from grid-like units within the network. Furthermore, grid-like representations enabled agents to conduct shortcut behaviours reminiscent of those performed by mammals. Our findings show that emergent grid-like representations furnish agents with a Euclidean spatial metric and associated vector operations, providing a foundation for proficient navigation. As such, our results support neuroscientific theories that see grid cells as critical for vector-based navigation7,10,11, demonstrating that the latter can be combined with path-based strategies to support navigation in challenging environments.

Pushing the Limits of Molecular Crystal Structure Determination From Powder Diffraction Data in High-Throughput Chemical Environments.

Crystal structure determination from powder diffraction data (SDPD) using the DASH software package is evaluated for data recorded using transmission capillary, transmission flat plate, and reflection flat plate geometries on a selection of pharmaceutical compounds. We show that transmission capillary geometry remains the best option when crystal structure determination is the primary consideration and, as expected, reflection flat plate geometry is not recommended for SDPD because of preferred orientation effects. However, the quality of crystal structures obtained from transmission plate instruments can be excellent, and the convenience factor for sample preparation, throughput, and retrieval is higher than that of transmission capillary instruments. Indeed, it is possible to solve crystal structures within an hour of a polycrystalline sample arriving in the laboratory, which has clear implications for making small-molecule crystal structures more routinely available to the practicing laboratory medicinal chemist. With appropriate modifications to crystal structure determination software, it can be imagined that SDPD could become a rapid turn-around walk-up analytical service in high-throughput chemical environments.

Accurate measurement of long range proton-carbon scalar coupling constants.

The accuracy and practicality of measuring heteronuclear scalar coupling constants, nJCH, from modern NMR experimental methods is examined, based on F1 or F2 evolution of nJCH in HSQMBC (including EXSIDE) and HMBC experiments. The results from these methods are compared to both robust experimental data (derived from coupled 13C spectra), computed (Density Functional Theory) and literature values where available. We report on the accuracy, ease of use and time efficiency of these multi-dimensional methods and highlight their extent and limitations.

Computations Underlying Social Hierarchy Learning: Distinct Neural Mechanisms for Updating and Representing Self-Relevant Information.

Knowledge about social hierarchies organizes human behavior, yet we understand little about the underlying computations. Here we show that a Bayesian inference scheme, which tracks the power of individuals, better captures behavioral and neural data compared with a reinforcement learning model inspired by rating systems used in games such as chess. We provide evidence that the medial prefrontal cortex (MPFC) selectively mediates the updating of knowledge about one's own hierarchy, as opposed to that of another individual, a process that underpinned successful performance and involved functional interactions with the amygdala and hippocampus. In contrast, we observed domain-general coding of rank in the amygdala and hippocampus, even when the task did not require it. Our findings reveal the computations underlying a core aspect of social cognition and provide new evidence that self-relevant information may indeed be afforded a unique representational status in the brain.

GPR103 antagonists demonstrating anorexigenic activity in vivo: design and development of pyrrolo[2,3-c]pyridines that mimic the C-terminal Arg-Phe motif of QRFP26.

GPR103, a G-protein coupled receptor, has been reported to have orexigenic properties through activation by the endogenous neuropeptide ligands QRFP26 and QRFP43. Recognizing that central administration of QRFP26 and QRFP43 increases high fat food intake in rats, we decided to investigate if antagonists of GPR103 could play a role in managing feeding behaviors. Here we present the development of a new series of pyrrolo[2,3-c]pyridines as GPR103 small molecule antagonists with GPR103 affinity, drug metabolism and pharmacokinetics and safety parameters suitable for drug development. In a preclinical obesity model measuring food intake, the anorexigenic effect of a pyrrolo[2,3-c]pyridine GPR103 antagonist was demonstrated. In addition, the dynamic 3D solution structure of the C-terminal heptapeptide of the endogenous agonist QRFP26(20-26) was determined using NMR. The synthetic pyrrolo[2,3-c]pyridine antagonists were compared to this experimental structure, which displayed a possible overlay of pharmacophore features supportive for further design of GPR103 antagonists.

A refined model for the TSG-6 link module in complex with hyaluronan: use of defined oligosaccharides to probe structure and function.

Tumor necrosis factor-stimulated gene-6 (TSG-6) is an inflammation-associated hyaluronan (HA)-binding protein that contributes to remodeling of HA-rich extracellular matrices during inflammatory processes and ovulation. The HA-binding domain of TSG-6 consists solely of a Link module, making it a prototypical member of the superfamily of proteins that interacts with this high molecular weight polysaccharide composed of repeating disaccharides of D-glucuronic acid and N-acetyl-D-glucosamine (GlcNAc). Previously we modeled a complex of the TSG-6 Link module in association with an HA octasaccharide based on the structure of the domain in its HA-bound conformation. Here we have generated a refined model for a HA/Link module complex using novel restraints identified from NMR spectroscopy of the protein in the presence of 10 distinct HA oligosaccharides (from 4- to 8-mers); the model was then tested using unique sugar reagents, i.e. chondroitin/HA hybrid oligomers and an octasaccharide in which a single sugar ring was (13)C-labeled. The HA chain was found to make more extensive contacts with the TSG-6 surface than thought previously, such that a D-glucuronic acid ring makes stacking and ionic interactions with a histidine and lysine, respectively. Importantly, this causes the HA to bend around two faces of the Link module (resembling the way that HA binds to CD44), potentially providing a mechanism for how TSG-6 can reorganize HA during inflammation. However, the HA-binding site defined here may not play a role in TSG-6-mediated transfer of heavy chains from inter-α-inhibitor onto HA, a process known to be essential for ovulation.

Quantification of free ligand conformational preferences by NMR and their relationship to the bioactive conformation.

Accurate unbound solution 3D-structures of ligands provide unique opportunities for medicinal chemistry and, in particular, a context to understand binding thermodynamics and kinetics. Previous methods of deriving these 3D-structures have had neither the accuracy nor resolution needed for drug design and have not yet realized their potential. Here, we describe and apply a NMR methodology to the aminoglycoside streptomycin that can accurately quantify accessible 3D-space and rank the occupancy of observed conformers to a resolution that enables medicinal chemistry understanding and design. Importantly, it is based upon conventional small molecule NMR techniques and can be performed in physiologically-relevant solvents. The methodology uses multiple datasets, an order of magnitude more experimental data than previous NMR approaches and a dynamic model during refinement, is independent of computational chemistry and avoids the problem of virtual conformations. The refined set of solution 3D-shapes for streptomycin can be grouped into two major families, of which the most populated is almost identical to the 30S ribosomal subunit bioactive shape. We therefore propose that accurate unbound ligand solution conformations may, in some cases, provide a subsidiary route to bioactive shape without crystallography. This experimental technique opens up new opportunities for drug design and more so when complemented with protein co-crystal structures, SAR data and pharmacophore modeling.

Comparative pharmacology and computational modelling yield insights into allosteric modulation of human alpha7 nicotinic acetylcholine receptors.

The human alpha7 nicotinic acetylcholine receptor (nAChR) subunit and its Caenorhabditis elegans homolog, ACR-16, can generate functional recombinant homomeric receptors when expressed in Xenopus laevis oocytes. Both nAChRs express robustly in the presence of the co-injected chaperone, RIC-3, and show striking differences in the actions of a type I positive allosteric modulator (PAM), ivermectin (IVM). Type I PAMs are characterised by an increase in amplitude only of the response to acetylcholine (ACh), whereas type II PAMs exhibit, in addition, changes in time-course/desensitization of the ACh response. The type I PAMs, ivermectin, 5-hydroxyindole (5-HI), NS-1738 and genistein and the type II PAM, PNU-120596, are all active on human alpha7 but are without PAM activity on ACR-16, where they attenuate the amplitude of the ACh response. We used the published structure of avermectin B1a to generate a model of IVM, which was then docked into the candidate transmembrane allosteric binding site on alpha7 and ACR-16 in an attempt to gain insights into the observed differences in IVM actions. The new pharmacological findings and computational approaches being developed may inform the design of novel PAM drugs targeting major neurological disorders.

Investigating the molecular basis for the virulence of Escherichia coli K5 by nuclear magnetic resonance analysis of the capsule polysaccharide.

The capsular polysaccharide of Escherichia coli K5 has been hypothesised to promote virulence through its molecular mimicry of host heparan sulphate. To test this hypothesis, we have produced pure oligosaccharides from K5 capsular polysaccharide and investigated their conformational properties with ultra-high-field nuclear magnetic resonance (NMR) (900 MHz). Ultra-high-field affords a significant resolution enhancement over previous studies and allowed a full-atomic assignment of the K5 hexasaccharide for the first time. All carbohydrate rings adopt a (4)C(1) conformation, the amide sidechains have a trans orientation and the hydroxymethyl group is freely exposed to bulk solvent. Initial models of the glycosidic linkage conformation based upon simple interpretation of NOE cross-peaks suggests that the beta1-->4 linkage adopts a 3D geometry of phi approximately 60 degrees , psi approximately 0 degrees and the alpha1-->4 linkage prefers phi approximately -30 degrees , psi approximately -30 degrees (phi and psi being defined by dihedral angles involving linkage protons). In this conformation the overall molecular geometries of K5 polysaccharide, heparan sulphate and even fully-sulphated heparin are remarkably similar. These results substantiate the hypothesis that the K5 capsular polysaccharide confers virulence to E. coli K5 by being a 3D molecular mimetic of host heparan sulphate, helping it to evade detection by the mammalian immune system.

Plasticity of the TSG-6 HA-binding loop and mobility in the TSG-6-HA complex revealed by NMR and X-ray crystallography.

Tumour necrosis factor-stimulated gene-6 (TSG-6) is a glycosaminoglycan-binding protein expressed during inflammatory and inflammation-like processes. Previously NMR structures were calculated for the Link module of TSG-6 (Link_TSG6) in its free state and when bound to an octasaccharide of hyaluronan (HA(8)). Heparin was found to compete for HA binding even though it interacts at a site that is distinct from the HA-binding surface. Here we present crystallography data on the free protein, and (15)N NMR relaxation data for the uncomplexed and HA(8)-bound forms of Link_TSG6. Although the Link module is comparatively rigid overall, the free protein shows a high degree of mobility in the beta4/beta5 loop and at the Cys47-Cys68 disulfide bond, both of which are regions involved in HA binding. When bound to HA(8), this dynamic behaviour is dampened, but not eliminated, suggesting a degree of dynamic matching between the protein and sugar that may decrease the entropic penalty of complex formation. A further highly dynamic residue is Lys54, which is distant from the HA-binding site, but was previously shown to be involved in heparin binding. When HA is bound, Lys54 becomes less mobile, providing evidence for an allosteric effect linking the HA and heparin-binding sites. A mechanism is suggested involving the beta2-strand and alpha2-helix. The crystal structure of free Link_TSG6 contains five molecules in the asymmetric unit that are highly similar to the NMR structure and support the dynamic behaviour seen near the HA-binding site: they show little or no electron density for the beta4/beta5 loop and display multiple conformations for the Cys47-Cys68 disulfide bond. The crystal structures were used in docking calculations with heparin. An extended interface between a Link_TSG6 dimer and heparin 11-mer was identified that is in excellent agreement with previous mutagenesis and calorimetric data, providing the basis for further investigation of this interaction.