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Considering individual ligands and the corresponding model predictions illustrates cases of model versatility and failure. A naïve approach to determining the number of coordinating atoms may involve simply counting the number of heteroatoms in the ligand, although this would lead to highly inaccurate results (SI Appendix, Table ). A manually curated set of diverse ligands and their associated predicted number of coordinating atoms illustrates the shortcomings of this approach, as there are numerous ligands with far more heteroatoms than coordinating atoms (Figure ). We observe that the trained model is able to effectively distinguish between the underlying chemistry of heteroatoms and coordinating atoms in the dataset, as it correctly classifies the true monodentate ligand and identifies cases of carbon (i.e., a non-heteroatom) being a coordinating atom in the true six-coordinate structure. The reported instance of a true twocoordinate ligand being incorrectly classified as one-coordinate involves a case of a ligand coordinating to the metal with both oxygen atoms in a carboxylate group (Figure ). While this bonding interaction as represented in the crystal structure involves both oxygens, carboxylate groups are also frequently observed in the dataset to coordinate with only one oxygen, suggesting the monodentate ligand coordination predicted by the model is also physically realistic.
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For ligand coordinating atoms, we again observe that the model effectively distinguishes between non-coordinating heteroatoms and coordinating atoms, with the true one-, two-, four-, and five-coordinate cases serving as examples of ligands with more heteroatoms than coordinating atoms on which the model classified every atom correctly (Figure ). Furthermore, the case with six coordinating atoms is an example of a correctly classified ligand with a benzene substructure, a common coordinating motif in TMCs. We note that while there are three distinguishable six-
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To better analyze model performance and develop more accurate methods for classifying ligands and automating TMC structure generation, we require a measure of uncertainty that reliably indicates confidence in a model's prediction. We define confidence thresholds for each model in terms of a raw prediction's difference from a true negative (0) or true positive (1) label and use these thresholds as a means of quantifying prediction uncertainty (i.e., a threshold of 0.3 would include predictions less than 0.3 and greater than 0.7). As anticipated, we observe increased accuracy in both models at more restrictive thresholds, with the coordinating atoms count model reaching 97.4% overall accuracy and the coordinating atoms identification model reaching 97.1% molecular accuracy at the tightest threshold of 0.05 (SI Appendix, Figures and). Although such a threshold may seem stringent, for 68.4% of test set molecules, coordinating atom count predictions are within the threshold of 0.05 (SI Appendix, Figure ). We observe a lower level of confidence for coordinating atom identity predictions, with 51.9% of ligands in the test set having every atom prediction fall within this threshold (SI Appendix, Figure ). This difference between dataset percentages included by each model is preserved across various thresholds, suggesting that the model for predicting total number of coordinating atoms had slightly more confident predictions for than the model for predicting coordinating atom identities, which is consistent with the expectation of increased complexity of predicting coordinating atom identities.
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Through this analysis we demonstrate that our threshold metric is a reliable indicator of model ). In the case of greater uncertainty in coordinating atom identity, only the atoms most confidently predicted as coordinating are returned until the predicted total number of coordinating atoms is met. This increases the molecular accuracy for the synergistic model on the whole test set from 84.8% to 86.9% (SI Appendix, Figure and Table ). This strategy for identifying instances of high uncertainty in each model and leveraging the two models to update predictions synergistically is valuable for increasing prediction accuracy on unseen ligands.
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We next aimed to analyze the learned molecular representations of our trained models to gain further insight into model performance and the underlying chemistry governing ligand coordination. The D-MPNN phase of the model architecture uses message-passing operations between graph edges (i.e., bonds) to update node (i.e., atomic) embeddings based on the local graph (i.e., molecular) environment. The learned atomic embeddings are then aggregated into a single molecular embedding that represents the full ligand. We extracted the molecular representations of the test set ligands learned by the trained models, reducing the dimensionality via the t-distributed stochastic neighbor embedding (t-SNE) method. In the case of the multiclass coordinating atom count model, analysis of these representations shows distinct regions in latent space corresponding to the different classes of true number of coordinating atoms (Figure ). The separation between the learned representations of one-, two-, and three-coordinate ligands is most evident. This is to be expected since these classes are the most well-represented in the dataset and are the classes on which the trained model is the most accurate. In the case of the higher-denticity ligands with four, five, and six coordinating atoms, the distinction between classes in latent space is less well-defined, with significant overlap occurring in learned representations (Figure ). This is consistent with the observed decrease in model accuracy on these less frequent classes and is indicative of the model's difficulty in distinguishing between these chemically similar ligands with high numbers of coordinating atoms. Visualizing the learned representations by the average atomic number of coordinating atoms in each ligand from 6 (i.e., all C) to 16 (i.e., all S), we observe that the majority of ligands of all classes have low average atomic numbers of coordinating atoms (Figure ). The few distinct groups with higher coordinating atom atomic numbers are all observed in regions corresponding to lower denticities, primarily monodentate and bidentate ligands (Figure ). This observed trend of higher-denticity ligands primarily coordinating with 2p atoms and only lower-denticity ligands observed coordinating with both 2p and 3p atoms in large numbers suggests higher-denticity ligands coordinating with 3p atoms are less abundant in the CSD, which may indicate their being relatively under-sampled.
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Rather than a single large region in latent space corresponding to ligands with a particular total number of coordinating atoms, ligands of the same number of coordinating atoms are grouped into smaller aggregates. This suggests that the model relies on a more nuanced molecular description to classify ligands beyond the number of coordinating atoms, which is consistent with our chemical understanding that denticity and hapticity alone are not sufficient to identify a ligand's coordinating atoms. The resulting learned representations are more distinct and correspond to ligands that are chemically similar ligand rather than only those with identical denticities or hapticities. This observation is confirmed when analyzing the model's learned representations in terms of average atomic numbers of coordinating atoms (Figure ). We find that ligands grouped together in distinct regions of latent space typically have the same coordinating atoms, indicating that the model is learning to represent ligands in terms of their coordinating motifs and generates a similar learned embedding for ligands with similar coordinating atom environments. The distinct learned representations of the coordinating atoms model provide insight into the model's accurate understanding of coordination chemistry and reveal underlying trends of chemical interest.
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Next, we demonstrate the utility of our trained models for predicting metal-ligand coordination in high-throughput screening campaigns of novel TMCs. This involves both the evaluation of our models on a final held-out set of ligands as well as integrating our models with structure generation tools. Towards this end, we develop a Python-based package called pydentate to first read ligand SMILES strings and use the trained models to generate predictions of coordinating atoms (Figure ). The ligand SMILES and its predicted coordinating atoms from pydentate are passed to molSimplify, and bonds are added to connect every coordinating atom to a user-specified transition metal center. The code supports addition of multiple unique ligands of different denticities or hapticities to a single complex in geometries determined by the user. The resulting complex is optimized by the Universal force field (UFF) , and the atomic coordinates are provided to the user for use in property evaluation (e.g., with semiempirical methods or DFT). To determine the suitability of the machine learning models in a structure generation workflow, we use the held-out set of ligands so far unseen by the machine learning models.
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Evaluated on this set with the synergistic model use strategy outlined previously, the trained model for predicting the number of coordinating atoms reaches 89.6% accuracy, while the coordinating atoms identification model reaches 87.4% molecular accuracy (97.1% balanced accuracy), both of which are comparable to the test set accuracy (SI Appendix, Table ). This comparable performance is indicative of the ability of our trained models to generalize well across chemical space to unseen ligands. Furthermore, given ligands with correctly predicted coordinating atoms, we validate the capability of pydentate to accurately recreate 3D structures of metal-ligand combinations observed in the CSD, with an average root mean squared deviation in atomic coordinates of 1.50 Å between structures observed in the CSD and recreated with pydentate (SI Appendix, Table , Figure ). By integrating good predictive coordinating atom assignment in pydentate with existing structure generation tools, this approach is expected to be suitable for constructing combinations of ligands needed for high-throughput virtual screening campaigns of novel TMCs.
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In order to validate our workflow more rigorously, it is necessary to demonstrate not just ligand coordination atom assignment but the successful generation and evaluation of DFT properties of realistic TMCs. We sought to identify a subset of TMCs with previously unseen (i.e., in the CSD) combinations of ligands with a transition metal. We selected Ti(IV) as our metal center, motivated in part by the fact that transition metal complexes based on Ti(IV) have applications in catalysis, with their performance as chiral and polymerization catalysts being particularly well-documented in the literature, along with more recent applications that indicate their promise as anticancer agents. To choose a coordination symmetry that would result in novel complexes, we considered a previous analysis of the theoretical space of possible TMCs. This analysis distinguished TMCs by the symmetry of the placement of unique ligands around a metal center in an octahedral geometry. Enumeration of these unique symmetry classes and analysis of their relative abundance in the CSD identified equatorial asymmetric (EA) and mer asymmetric trans (MAT) symmetries as under-sampled in experimental, structurally characterized TMCs (SI Appendix, Figure ). We selected these EA and MAT symmetry classes for use in testing our integrated coordination prediction and structure generation workflow, specifically generating complexes with novel metal-ligand coordination never observed in the CSD as an opportunity for generating structures with new combinations of metals and ligands (SI Appendix, Tables S16-S17). these are the only ligands from which EA and MAT structures may be generated. We separate the set of all predicted monodentate, bidentate, and tridentate ligands into combinations of ligands that will yield overall neutral complexes in combination with the EA and MAT symmetries (i.e., 0 to -1 charge for monodentate, 0 to -2 charge for bidentate, and -1 to -2 charge for tridentate, SI Appendix, Tables ). Using these seven subsets, we enumerated all possible combinations of ligand charge and denticity to produce in a net neutral overall complex charged when coordinated to Ti(IV) and randomly select five ligands from each subset to provide a sufficiently large space of possible structures, resulting in 1,175 unique structures (SI Appendix, Tables ). From these 35 total ligands, our models predict the coordination atoms of 32 cases correctly, which corresponds to a molecular accuracy of 91.4% that is 4.5% above our model's baseline performance on the set-aside test set. Examining the cases where the model performs incorrectly, we note two instances of true bidentate ligands with one oxygen and one nitrogen coordinating atom being incorrectly predicted as tridentate. In both cases, our models correctly identify the two true coordinating atoms and incorrectly predict a nearby nitrogen atom as coordinating, resulting in the overall classification as tridentate. In the third case of an incorrect model prediction, a true monodentate ligand with a sulfur coordinating atom is correctly identified as monodentate but with an incorrectly predicted carbon coordinating atom. Inspection of the raw prediction probabilities generated by the model reveal higher probabilities for the carbon atoms in the ligand's benzene substructure, suggesting the model was initially predicting this ligand to have a haptic coordination mode along the conjugated π system along the carbon ring (SI Appendix, Table ). Because the coordinating atoms count prediction model was more confident in the monodentate classification than the coordinating atoms identification model, only the single highest probability coordinating atom was returned, resulting in the incorrect prediction of a single carbon coordinating atom.
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Interestingly, the deprotonated form of this ligand also appears in the randomly selected subset used for structure generation and was correctly predicted by both the coordinating atom count (uncertainty 4.8E-6) and identification (uncertainty 1.2E-3) models, suggesting the absence of the single hydrogen atom made the identity of the sulfur coordinating atom more clear (SI Appendix, Table ). A fourth ligand prediction was initially flagged as incorrect but is relabeled as correct due to equivalence of the true and predicted coordinating atoms by resonance (SI Appendix, Table and Text S1).
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To establish the value of our integrated prediction and structure generation on a problem of chemical and industrial interest, we generated these 1,175 TMCs with ligands from the holdout set, using the predicted coordination in all cases, even in cases where it was incorrect. We performed DFT geometry optimizations calculations on the 1,175 resulting structures and investigate trends in calculated molecular properties over this de novo set. Of all calculations performed, the majority (75% or 876 of 1,175) yielded a "successful" optimization of a structure after optimization that preserved the initial correctly predicted connectivity of the generated structure, among other criteria (SI Appendix, Table ). The success rates of the complexes for which the model predicted at least one incorrect coordination geometry were 25% in comparison to 88% for the ones where the model predicted the correct coordination, although whether these ligands coordinate to Ti(IV) experimentally remains unknown. While true coordinating atom identities will be unknown for predictions generated on novel ligands not in the training, validation, test, or holdout sets, the high degree of overlap of 95% between structures with successful optimization (920) and those with successful optimization and correct coordinating atom predictions (876) suggests that, given a structure for which geometry optimization converged, the coordinating atom predictions are likely correct (SI Appendix, Table ). This correlation between prediction accuracy and successful geometry optimization is a promising result for deploying the developed workflow on novel ligands, validating the use of our models and workflow for screening TMCs with de novo metal-ligand connectivity for target molecular properties.
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To characterize these successfully geometry optimized de novo complexes, we computed their HOMO-LUMO gap with DFT (see Methods). Intuitively, we might expect to see a strong system size dependence of the HOMO-LUMO gap. The range in number of atoms (molecular weights) in our studied systems is from 32 to 132 (511 to 1032 amu), with an average size of 80 atoms (Figure , SI Appendix, Figure ). While the mean HOMO-LUMO gap is 2.83 eV, the range is large from 1.12 to 4.44 eV (279 to 1108 nm, Figure ). Comparing MAT and EA complexes, we observe that MAT has the higher average HOMO-LUMO gap (2.97 vs. 2.78 eV), potentially due to the greater compatibility of tridentate ligand combinations with the MAT symmetry group (Figure , SI Appendix, Figure and Table ). Nevertheless, even for a fixed size and the same neutral charge, we observe a wide variation in HOMO-LUMO gaps, regardless of symmetry (Figure ). For example, our set includes one EA and one MAT complex with 4 ligands each and are 63 and 64 atoms in size and both have gaps of over 4.32 eV (Figure ). Conversely, we observe EA and MAT complexes with a gap as low as 1.95 eV (Figure ). The cluster of seven EA complexes with HOMO-LUMO gaps less than 2.00 eV and between 100 and 125 atoms all contain the same bidentate 2-(4,5-Dimethyl-1,3-dithiol-2-ylidene)-1,3-dithiole-4,5dithiolate ligand and monodentate di-tert-butylhydroxyphosphine ligand, along with various combinations of other ligands with group 16 coordinating atoms (i.e., O or S, Figure ). The lack of significant trend for HOMO-LUMO gaps with the size of the molecule highlights the potential for discovering complexes with novel structure-property relationships through use of our de novo generation approach (Figure ). Overall, the high 75% success rate of executed calculations combined with the diversity of properties of the studied complexes suggests that the model should be useful in de novo transition metal complex discovery. One possible route to further improvements is to explicitly require higher confidence in coordination atom assignment or to compute multiple potential binding modes when model predictions of coordinating atoms are uncertain.
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In summary, we developed a data-driven strategy to predict metal-ligand coordination preferences. To do so, we first curated a diverse dataset of 70,069 unique, synthetically accessible ligands of known metal-ligand connectivity in transition metal complexes from the CSD. Analysis of this dataset revealed trends in common coordinating atom counts and identities well-represented in experimental investigations, such as the fact that bidentate ligands are the most common in the dataset and that ruthenium is the most frequently coordinating metal, which we rationalize in terms of the stabilizing chelate effect for bidentate ligands and the catalytic and pharmacological relevance of ruthenium TMCs. Nevertheless, we also observed deviations from expectations for particular transition metals, notably the high frequency of five-coordinate ligands bonding to iron and four-coordinate ligands coordinating to nickel, which could be expected from the abundance of ferrocene and bis(cyclooctadiene) nickel derivatives in the CSD.
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We then trained individual graph neural network models to predict the total number and identity of coordinating atoms of ligands from their SMILES representations with high accuracy (88.5% for denticity, 98.8% for coordinating atoms) and precision (0.82 for denticity, 0.97 for coordinating atoms). The trained model for coordinating atoms identification also performed well even in terms of the strictly defined molecular accuracy metric (84.8%). We developed a strategy to use the two trained models synergistically to further improve predictions by leveraging information from the more confident model in cases of conflicting predictions, increasing accuracy in test set predictions of coordinating atom count from 88.5% to 90.0% and molecular accuracy in coordinating atom identity from 84.8% to 86.9%. Analyzing the learned representations of the trained model to predict coordinating atom count revealed distinct regions of latent space corresponding to each class of total numbers of coordinating atoms, while no such trends were apparent in the latent space of the coordinating atoms identification model. These findings revealed that denticity and hapticity alone are not sufficient to identify coordinating atoms, and that 3p coordinating atoms are highly under-sampled for ligands with higher total numbers of coordinating atoms.
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We demonstrated the value of our models by integrating them into a structure generation workflow for transition metal complexes. We developed a Python-based package, pydentate, that takes as input a SMILES string of a ligand, predicts coordinating atom counts and identities, and adds bonds between the predicted coordinating atoms and a user-specified transition metal. We ). The metal atom was then converted to a dummy atom, and the structures and molecular graphs of each ligand were stored in both the coordinated (i.e., with the dummy atom present) and uncoordinated (i.e., without) states. Weisfeiler-Lehman graph hashing, filter was applied to all ligands used in any learning task. Only ligands with metal-coordinating atoms corresponding to C, N, O, Si, P, and S were retained (SI Appendix, Table ). For the remainder of the ligand, an element filter was applied that allowed these elements (i.e., C, N, O, Si, P, S) as well as other well-represented elements (i.e., H, B, F, Cl, Br, and I), removing ligands containing any other elements (SI Appendix, Table and Figure ). Additionally, ligands with more than six coordinating atoms or consisting of only a single atom (e.g., Cl) were also removed (SI Appendix, Table ). We employ Chemprop for model training (see next) on SMILES strings.
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We canonicalized the SMILES strings from molSimplify because Chemprop operates on SMILES interpreted by RDKit, which could be different, to ensure that the correct connecting atom indices were preserved in the RDKit SMILES. A small number of instances of failed canonicalization and atom matching were removed and are available in the Zenodo repository 104
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Due to the difficulty in identifying confident labels for hemilability, the positive and negative labels identified by semi-supervised learning in previous work are used to train models for identifying hemilabile ligands (SI Appendix, Table ). and). Hyperparameter tuning was performed with the training and validation data for 100 epochs using either 25 (coordinating atom models) or 50 (hemilability models) combinations of the number of message-passing steps, dropout, number of FFN layers, and hidden layer size using Chemprop's implementation of hyperopt (version 0.2.7) (SI Appendix, Table and Table ). All models were trained for 100 epochs using the cross-entropy loss function, rectified linear unit (ReLU) activation function, and identified optimal hyperparameters. The validation data was used for early stopping to prevent overfitting, while the test data was used for evaluating model performance. Additional ML-predicted QM descriptors are predicted using the qmdesc package (version 1.0.5) (SI Appendix, Table ). The source codes of Chemprop and qmdesc were modified slightly to increase their functionality in atom-level prediction tasks (SI Appendix, Text S2).
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A workflow for building novel transition metal complexes was developed and implemented hartree/bohr) and energy difference between optimization steps (10 -6 hartree) and a maximum of 1,000 optimization steps. All calculations used level shifting with shift values of 0.25 hartree for both the virtual and beta-spin orbitals and the hybrid DIIS/A-DIIS scheme for SCF convergence.
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Prussian blue (PB) is an important porous metal-cyanide framework structure (A x Fe 3+ [Fe II (CN) 6 ] y .nH 2 O) with exchangeable A cations. Along with its analogs, it shows promise for a range of important applications including as cathodes in secondary ion batteries. Indeed, PB cathodes have potential in widespread, low-cost energy storage applications, using abundant and affordable Na + or K + based aqueous electrolytes. In particular, K + ions can be readily accommodated by the open structure of PB, which allows for reversable intercalation processes that are challenging in layered transition metal oxide cathodes.
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Despite the identified potential, unexpected complexities within the PB structure have made fundamental understanding of intercalation processes difficult. The PB structural framework is highly flexible, forming a cubic structure that can accommodate up to 25% [Fe II (CN) 6 ] 4- defects, with the subsequent under-coordinated Fe 3+ ions being bound to water, forming (H 2 O) 6 clusters (Scheme 1). In addition, the structure can accommodate significant amounts of uncoordinated occluded water. These structural variations influence the location of A site alkali cations within PB, which has ramifications in understanding the balance of charges during redox processes. In an ideal structure (Scheme 1a), reduction of Fe 3+/III sites is balanced by the intercalation of K + within the vacant channels of the structure, with the fully reduced Fe 2+ Fe II structure, known as Prussian white (PW) having a 1:1 K:Fe ratio. In the fully oxidized Fe 3+ Fe III structure, commonly referred to as Berlin Green (BG), K + is fully deintercalated. However, the influence of (H 2 O) 6 clusters, which are prevalent within the defective structure, has been debated, with some work concluding that these sites can inhibit ion insertion into the channels, while others deducing that K + sits within the (H 2 O) 6 cluster itself (Scheme 1b). The complications in understanding K + ion location have resulted in ambiguity when assigning the charge-balancing species during framework redox processes, with suggestions that in aqueous electrolytes H 3 O + or K + can act as counterions. Indeed, similar uncertainty is also observed for other cations that can be incorporated into the structure, such as Mg . Another challenge in utilizing PB for energy storage applications is its varied stability over repeated cycling. Highly crystalline materials, considered to have a limited number of defects, are reported to favor superior cycle-life and rate capability. The importance of [Fe(CN) 6 ] 4- defects in contributing to structural collapse is stated to be due to their inhibition of ion insertion and decrease in electronic conductivity. However, understanding the loss of capacity is again complicated by the differing process mechanisms that are suggested for charge balancing and K + intercalation.
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Importantly, current understanding of the location of K + in PB is deduced from general long range structural information such as diffraction data, or via theoretical simulation. Herein, we show that operando potassium K-edge X-ray absorption near edge structure (XANES) can successfully be employed to understand, with the aid of theoretical simulations, the local structure of K + in PB cathodes. While XANES has previously been employed to follow sulfur species (at the S K-edge) in batteries during operation, there have been few attempts to monitor group 1 or 2 species in battery cathodes. Villevieille and co-workers have identified different Na K-edge spectra of ex-situ isolated charged and discharged Na x MnO 2 cathodes, while Weatherup and co-workers showed that ex-situ Mg K-edge XANES could be used to identify changes at the solid electrolyte interface of a Mg anode. Yet neither of these studies are performed during battery operation. We show that such XANES studies can be employed simultaneously with electrochemical testing in an operando experiment. Two samples of varying crystallinity and electrochemical stability are studied, and the evolution of K + within the structure monitored over repeated cyclic voltammograms.
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Prior to analysis of the local structure of K + within the samples, electrochemical properties and ex-situ structural analysis was performed to identify any informative structure-function properties that may enhance our analysis of the potassium K-edge XANES. The PB samples of high crystallinity (HC-PB) and low crystallinity (LC-PB) can both be assigned by XRD to crystalize with a face-centered Fm3 � m PB structure, with varying average crystallite sizes of 103 ±3 nm and 14 ± 2 nm, respectively (Figure and Table ). IR spectroscopy further confirmed the formation of PB through the presence of a single ν(C≡N) mode at 2086 cm -1 (HC-PB) and 2081 cm -1 (LC-PB), as shown in Figure . The morphology of the two samples is notably different when imaged with scanning electron microscopy (SEM) (Figure ), with HC-PB comprised of 140 ± 30 nm faceted crystalline particles, and LC-PB of ill-defined <18±4 nm particles that agglomerate into >10 µm aggregates. Notably, the large aggregates of LC-PB proved harder to disperse amongst the conductive carbon black during electrode preparation (Figure ).
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Elemental analysis and TGA (Figure and Table ) result in structural formulae of K 0.55 Fe[Fe(CN) 6 ] 0.92 •3.3H 2 O and K 1.04 Fe[Fe(CN) 6 ] 0.94 •4.1H 2 O for HC-PB and LC-PB, respectively. Given that values of <1 were observed for [Fe(CN) 6 ] 4-, defect sites are concluded to be present in both samples. Fe K-edge EXAFS analysis of the samples is indicative of the PB structure (Figures and), with features associated with the Fe-C/N 1 st and 2 nd shells and the Fe-Fe 1 st shell. The intensity of Fourier Transform magnitude features is similar between samples, indicating that the short-range order was comparable. Room temperature 57 Fe Mossbauer spectra of the two samples (Figure and Tables &) also show limited differences, with similar average quadrupole splittings and the ratio of Area Fe(III) : Area Fe(II) is equal to 1. The high spin Fe 3+ component of the spectra required fitting with two doublets that are associated with the ideal Fe(NC) 6 site and another with partial water coordination, demonstrating comparable defects exist in both samples. The results are in contrast to the impactful assumption that small crystallite size equated to a more defective structure, which was applied in previous studies of PB electrochemical stability. In the present study, both high and low crystallinity samples contain a notable, but comparable, number of defects, despite their very different crystallite size.
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A cyclic voltammogram (CV) of HC-PB within the operando XAS cell, in 0.1 M KNO 3 (aq) electrolyte, is shown in Figure . The reduction and oxidation peaks at 0.034 V and 0.22 V are due to the transition of PB to PW (and vice versa). The reduction peak suggests intercalation of K + ion into the HC-PB lattice although, as noted previously, contributions from H + or OH -cannot be excluded (see Scheme 1). The observation of an oxidation peak at 0.22 V, with an identical area and height to the reduction peak, indicates the deintercalation of K + ion as well as the quasi-reversibility of the process. The 186 mV peak separation suggests that the rate of intercalation and deintercalation of the hydrated K + ion in and out of the HC-PB lattice is slow and Nernstian concentration is not maintained throughout these processes. The peaks corresponding to the transition of BG to PB (and vice versa) are at 0.88 V and 0.73 V, respectively, and appear to be quasi-reversible with peak-to-peak separation of 150 mV.
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While the same oxidation and reduction features are observed in LC-PB, the electrochemical behavior is somewhat different (Figure ). The redox processes show a significantly greater peak separation of 460 mV (transition of BG to PB) vs 150mV seen for HC-PB versa), illustrating a quasi-reversible process with much slower kinetics than HC-PB. This could be due to slower charge transfer or alternatively greater particle and contact resistance seen with LC-PB. Unwin and co-workers clearly illustrated that increased electrical resistance increased CV peak separation in scanning electrochemical cell microscopy measurements of LiMn 2 O 4 at fast scan rates of 1 V s -1 . Although the impact of resistance on peak separation is anticipated to be reduced by the slow scan rate of 0.77 mV s -1 used in our study, the impact of the relatively poor conductivity of PB (ca 1x 10 -7 S cm -1 ) should not be discounted. In particular the large aggregates of LC-PB seen by SEM (Figure ) with relatively poor dispersion, when compared to HC-PB, in the conductive carbon of the assembled matrix could well account for substantial resistance within the LC-PB cathode.
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The varying stability of HC-PB and LC-PB was further investigated over repeated CV cycles, with calculated discharge capacities given in Figure (Specific changes in CVs are discussed in Section 2.4 with XANES analysis). HC-PB capacity was mostly retained with a 35% reduction over 13 cycles, while LC-PB showed significant instability with 80% loss of capacity over 9 cycles.
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Ex-situ analysis of electrodes after cycling showed a loss of structural order in both cathodes, but to a significantly greater extent in LC-PB (Figure ). Specifically, Fe K-edge EXAFS showed reductions in 2 nd shell Fe-C/N and Fe-Fe path intensities, indicating a loss of short-range order in both samples, although to a far greater extent for LC-PB. There is a clear correlation from EXAFS between the loss in intensity of 2 nd shell Fe-C/N and the loss of capacity of the PB samples on cycling. No change in phasing was observed in the EXAFS of HC-PB, indicating no bulk formation of a new structure. In contrast, an increased contribution of a Fe-O path, as indicated by a shift in the 1 st feature of the FT towards 1.5 Å, is seen in LC-PB after cycling, attributable to the presence of a new additional oxidic phase. Fe Mössbauer analysis (Figure and Tables &) shows no degradation to HC-PB after cycling, while significant changes were seen for LC-PB. For the spectrum of the LC-PB material, the conventional fitting with 2 Fe (III) doublets was not valid and a further 3rd Fe component with a larger quadrupole splitting was needed to satisfactorily fit the data. The resultant ratio of Area Fe(III) : Area Fe(II) for LC-PB after cycling changed from 1:1 to 3:1, which is far beyond the reasonable limit for PB and implies the presence of an additional Fe phase. A further fit of the LC-PB after cycling spectrum using the original PB components revealed hyperfine parameters of two doublets, which is consistent with the poorly crystalline phase, ferrihydrite (Figure ). The presence of ferrihydrite within the sample is further evidenced when comparing Fe-K edge XANES and EXAFS of the LC-PB used electrode and a ferrihydrite standard (Figures &). There was no change in microstructure, formation of cracks, or exfoliation from the current collector observed in the used samples by SEM (Figure ).
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The combination of techniques provides an overall picture a relatively stable HC-cathode with a small but notable loss of long-range order over cycling, and a LC-PB cathode that undergoes rapid degradation through loss of PB short-range order and formation of non-conductive ferrihydrite. The analysis provides an understanding of differences in framework electrochemical properties and associated bulk structural changes, though further work is necessary to provide information on the K + charge carrier speciation and evolution during charge/discharge cycling.
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Potassium K-edge XANES of HC-PB were recorded at voltages of 0.41 V during charging, and 0.9 V and -0.1 V during discharge (indicated on the CV in Figure , with spectra shown in Figure ). At 0.41 V, the spectrum was comparable with that recorded for PB prior to the addition of electrolyte (Fig S9 ) with notable features at 3610.1 eV (pre-edge), 3612.3 eV (white line shoulder), 3614.3 eV (white line), 3617.7 eV and 3619.8 eV (small doublet peaks after white line), and extended features beyond 3625 eV. Significantly, the XANES spectra of the KNO 3(aq) electrolyte alone is clearly distinguishable, through a more intense pre-edge feature, and a broad single structure centered at 3616.7 eV. The observations show the potential of operando K-edge potassium XANES, as the spectrum of K + within the cathode and electrolyte can be easily differentiated. At 0.9 V (discharge), the spectrum of the cathode is comparable to the electrolyte with residual features associated with PB, showing that almost all K + has been deintercalated from the now oxidized BG structure. The result suggests that K + is acting as a charge carrier under the conditions monitored and can be fully deintercalated from the structure. Lastly, holding at -0.1V resulted in a 3 rd XANES spectrum, which is associated with the fully reduced Fe 2+ Fe II PW structure, with full K + intercalation. The features of the XANES spectrum for the postulated PW structure differ from that of PB, with an enhanced pre-edge feature, a change in intensity ratios of the split main feature, and emergence of another strong shoulder at 3616.3 eV.
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By comparison, LC-PB analyzed prior to addition of electrolyte, or an applied voltage, shows subtle difference in K + speciation (Figure ). Linear combination fitting (LCF) allows assignment of 68% K + within a comparable environment to HC-PB, and 32% adsorbed K + in a solvated environment. Subsequently, the structural formula determined by elemental analysis can be revised to K 0.71 Fe[Fe(CN) 6 ] 0.94 .4.1H 2 O + 0.33K + (ads) . Introduction of electrolyte results in the XANES spectrum of LC-PB changing to that seen for HC-PB, which shows the removal of adsorbed K + from the PB surface. At the same voltages of -0.1 V, 0.4 V, and 0.9 V that were applied to HC-PB, potassium XANES of LC-PB gives comparable pre-edge positions, main feature splitting, and extended structural features for K + in PB, PW and electrolyte environments, as seen for HC-PB (Figure ). Interestingly, these results show that the local environment of K + is comparable in both samples after residual K + (ads) is washed from the surface by the aqueous solvent. This observation correlates to information from the framework perspective, as provided by Fe K-edge XAS and 57 Fe Mössbauer, which showed similar structural order and defect formation in both samples.
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To rationalize the observed spectra, several theoretical structures were validated by density functional theory (DFT) simulation before being used to simulate the potassium K-edge XANES. The electronic and structural properties of K + inclusion within the ideal PB structure verified that the ion sits in half of the center of the primitive cubic structural cavities (8c sites), in an ordered tetrahedral pattern (as shown in Scheme 1a). Analysis of the electronic density of states (DOS) is consistent with the expected changes in Fe oxidation and spin states on removing all K + (BG), or when fully oxidizing the system by filling all 8c sites (PW) (Figure ). Next, the inclusion of H 2 O was considered in competition with K + for the 8c site, which would increase the distance between intercalated K + , as it is pushed towards the corners of the primitive cell into the 32f' position (Figures &). Increasing the water content from 4 to 16 H 2 O molecules per unit cell pushes the K + further away from the central 8c site, with the inclusion of 8 H 2 O calculated as the most thermodynamically viable. Finally, the influence of the Fe II (CN) 6 defects was considered by the removal of the central Fe II (CN) 6 octahedra and addition of a (H 2 O) 6 cluster. In this scenario K + has been considered in two locations (Figure ). When K + was considered within the cavities, it was pushed away from the 8c site towards the 32f' position, relative to the ideal water free PB structure. The enthalpy of formation (ΔH form ) of this intercalated structure is higher with the inclusion of the defect, supporting notions that structural defects would inhibit K + intercalation. Alternatively, K + was considered within the central (H 2 O) 6 cluster (equivalent to Scheme 1b), with ΔH form at comparable K + loading less favorable than for the defective system with K + within the channel. Therefore, K + is unlikely to be located within this defect site.
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Simulation of the XANES spectrum of the ideal PB structure, with K + on the 8c site, is compared in Figure with the experimental spectra of HC-PB. The pre-edge (Feature A), white line shoulder (Features B & C) and white line (Feature D) were successfully simulated. These features are attributed from the projected DOS (Figures and) to low lying K p-states overlapped with Fe orbitals (A), hybridized K pstates with CN anti-bonding π orbitals (B & C), and isolated K p-states (D), respectively. While most features are well represented, the intensity of feature C is significantly underestimated in the original simulation. Given that K + at the 8c site is a significant distance from CN π anti-bonding orbitals, a lack of overlap between K p-states and these π orbitals can account for the low intensity of feature C and dominance of D. As noted, when performing the DFT simulations, the inclusion of water molecules or defects pushes K + towards the Fe 3+ -N corners of the primitive cube (32f' position), which would increase orbital overlap of states associated with feature C. XANES simulation of K + within this 32f' position (Figure ) did indeed show an increased contribution to the XANES from feature C and brought the XANES simulation into closer agreement with experiment. The greater ΔH form calculated by DFT suggests that that K + does not reside within the defect (Fig. ); with the evidence is more compelling for K + being forced into the corners of the channels by these defect sites or occluded water within the structure.
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The XANES spectrum calculated for the PW structure (Figure ) replicated the experimental features seen at -0.1 V, including the additional feature at 3616.3 eV (Feature E) that is not observed for PB. The results validate the assignment of the experimental XANES spectrum to a fully intercalated PW structure, where the sample is fully reduced. Using simulation to validate the spectrum is particularly important given that PW readily oxidized under ambient conditions to PB, making validation via the use of a synthesized material analyzed ex-situ unsuitable. As seen with the simulated spectra of PB with K + within the 8c site, the shoulder of the white line is mispresented in the simulated spectrum of PW, showing that K + continues to be off center from the 8c site within the fully intercalated structure.
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Unnormalized operando spectra, obtained throughout a CV of HC-PB, are shown in Figure , alongside the determined compositions of potassium within PB, PW, and electrolyte environments (Figure ). The compositions are determined from the potassium K-edge step values and associated fractions of each K + species determined by LCF analysis (Figure ). Visual inspection of the unnormalized spectra in Figure shows a clear evolution of speciation through the voltage sweep, and a change in edge step height. As K + speciation evolves through the different environments of PB and residual electrolyte, the edge step decreases as K + is removed from the cathode. The edge step then increases as the sample is oxidized to PB and then PW. Consequently, comprehensive analysis of both K + speciation and its relative concentration within the PB cathode, with respect to applied potential and current response, can be made during charge/discharge cycling.
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The changes in K + for the 1 st full CV, starting from PW, are shown in Figure . Deintercalation of K + , as evidenced by the decrease in the step edge, clearly occurs in two stages and at the same potentials of 0.22V and 0.88V as seen from the current responses in the voltammogram. When observing the evolution of individual K + species, the stages that occur are the deintercalation of K + from within PW due to its oxidation to PB, and then further deintercalation from oxidation to BG. The evolution of specific K + environments associated with these framework structures can be directly correlated to redox features within a CV. Each deintercalation event is followed by further small and gradual losses in K + signal (i.e., poorly defined plateaus of K + concentration), which occur within the voltage windows of 0.4-0.8 V and 1.0 V charging cycle to 1.0 V discharge cycle. Analysis of the individual XANES components shows that this gradual loss of K + concentration between oxidation events is due to deintercalation of kinetically hindered K + from within PW and PB environments respectively. Furthermore, the sluggish deintercalation of K + from residual PB sites within the cathode is particularly apparent from the LCF of the normalized spectra (Figure ). Zampardi et al. noted that the deintercalation of K + from PB to BG can be sluggish in composite electrodes, corresponding to the slow K + evolution seen in the XANES. Interestingly, this kinetically hindered K + was hypothesized not to be an intrinsic property of PB but of the assembled electrode and associated electrostatic effects, as supported by the resent multiscale measurements by Unwin and co-workers using scanning electrochemical microscopy on LiMn 2 O 4 . The corresponding two step intercalation of K + during reduction of BG to PB, and then to PW, can also be directly observed from the increases in K + concentration and the evolution of K + environment. In contrast to oxidation, a clear plateau in K + concentration, and PB speciation, is observed between the two reduction events. The result suggests that the reduction process is more facile, with no residual intercalation being observed. Given that the total edge step intensity does not return to its initial value the apparent improvement in kinetics could be the consequence of poorly conductive intercalation sites seen during reduction not participating in the subsequent oxidation. Evidently, throughout the entire redox process of PB, K + acts as the predominant charge-balancing species through intercalation processes, with no clear discrepancies seen between this process and the recorded current response during cycling. It is important to note that the apparent loss of solvated K + associated with electrolyte when the sample is fully reduced to PW is likely an artifact of the analysis, as the PW standard XANES spectrum used in LCF analysis itself contained an electrolyte component.
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Operando XANES of LC-PB (Figure & Figure ) revealed significantly different behavior to HC-PB. Starting from -0.2 V of the 2 nd CV cycle, a very low current response is seen when sweeping the potential between 0.1 to 0.5 V. The lack of current response suggests minimal oxidation of species, either due to minimal PW being formed from the preceding PB reduction or a lack of oxidation of PW. Interestingly, XANES analysis of K + speciation shows that ca. 20% of K + was already within a PB environment at -0.2 V, partially explaining the low current response. However, the remaining ca. 80% of K + was present within a PW environment and the deintercalation of the K + from the PW environment is clearly observed during the oxidative potential sweep. The rate of deintercalation from PW was incredibly sluggish, with considerable K + being retained in LC-PB up to 0.8 V (i.e., within PW) and no clear plateau of K + concentration exists. Surprisingly, the deintercalation process shows minimal current response, suggesting a non-faradaic chemical process is responsible for a significant proportion of the PW deintercalation.
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Further oxidation of PB to BG was facile, with rapid K + deintercalation and a strong simultaneous current response. Given that little difference in defect structure has been demonstrated for HC-PB and LC-PB, these differences are attributed to variation in composite film microstructure seen by SEM (Figure ), as reported by Zampardi et al. From the XANES analysis, it is evident that K + is almost completely deintercalated from PB, with the remaining K + that is seen after the current response attributed with the electrolyte. Therefore, while the high spin redox process appears to be incomplete (i.e., K + is not completely converted from a PB environment to a PW one), the K + removal during low spin PB to BG is far more favorable and goes to completion. The subsequent intercalation of K + from BG to PB also appears facile, although observation of the total edge step shows that significantly less K + is present within the sample after the low spin redox process, in agreement with the reduced current response (i.e., K + signal at the two relevant current response plateaus). Finally, unlike during oxidation, the intercalation of K + during PB reduction to PW corresponds to a clearly observable current response, indicating that this process is faradaic in nature.
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Operando XANES was used to follow changes in K + speciation within HC-PB between CV cycles 3 and 10 (Figure ), over which time a 15% loss in capacity was observed. While minor shifts in the CV peak positions occurred during HC-PB cycling, the electrochemical properties of the sample remained relatively consistent. Based on the edge step of the unnormalized XANES (Figure ), clear repeatable cycles of K + concentration can be observed. Notably, the plateaus and maxima of K + concentration reduce slightly, by 30%, while the minima remain constant. LCF of the potassium XANES across the repeated cycles is shown in Figure , with the cycling of the three K + environments being relatively consistent as expected. Therefore, it can be concluded that the intercalation sites present, while dropping slightly in absolute number, continuing to effectively cycle between the K + species discussed over the 8 CV cycles investigated. The modest loss of structural order and intercalation sites on cycling of HC-PB, as determined by Fe K-edge EXAFS analysis (Section 2.1), explains the decrease in K + intercalation seen from edge step analysis. Nevertheless, the effective cycling of the remaining K + species shows that sufficient framework order is retained to maintain conductivity and electrochemical efficiency.
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In contrast, LC-PB showed clear instability over the 8 cycles when studied by operando XANES, with 62.5% loss of capacity. (CV scans shown in Figure ). Changes to the CVs consist of a shift in peak potential by 0.08 V for PB → BG oxidation and a reduction in peak current magnitude. A shift to lower V for the BG reduction is also observed for the 1 st cycle, and then the peak position stabilized at 0.6 V but with a reduction in peak magnitude with increasing cycles. A minimal shift in peak potential was observed for the high spin redox couple, with a dramatic decrease in the magnitude of the features, which was particularly prominent for the current response associated with PW reduction to PB. Evidently a series of complex changes occur during cycling, which the operando XANES can help rationalize.
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In accordance with the dramatic capacity loss seen for LC-PB, the Δ edge step, which corresponds to the change in un normalized potassium K-edge XANES edge step during charge/discharge, decreases by 54% over 7 cycles (Figure ). In LC-PB, the edge step values show a different trend to that observed for HC-PB on repeat cycling, with the maximum and minimum K + concentrations both converging on a relatively stable PB plateau. By contrast K + signal only decreased in respect to a loss of fully intercalated PW sites on cycling. LCF analysis (Figure ) of the LC-PB data shows a dramatic loss of K + signal variation associated with either electrolyte or PW as CV cycling progresses, with complementary increase of a signal associated with K + trapped within the PB structure. The entrapment of K + within an PB environment throughout the potential sweeps showed that LC-PB becomes electrochemically inactive. A loss of conductivity due to the collapse of the short-range order within PB and ferrihydrite formation (Section 2.1) explains the observed trapping of charge carriers in the remaining PB sites within the cathode.
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Potassium K-edge XANES has been used to understand the location of K + within the Prussian blue structure. Differentiated K + species were clearly observed, associated with the fully intercalated Prussian white structure, partial intercalation within Prussian blue, and within the aqueous KNO 3 electrolyte. Theoretical simulations of Prussian blue, and associated XANES simulations, show that K + resides within the cavities of the structure, but located away from the center of the primitive cubic cavities (8c site) and towards the corners of the cavities (32f' position), due to structural defects or occluded water.
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Operando spectroscopy has been applied during electrochemical redox reactions of Prussian blue within an aqueous KNO 3 electrolyte, and definitively shows that K + is the predominant species that balances structural charge during the relevant redox reaction. Within a highly crystalline Prussian blue sample, the intercalation process was reproducible over repeated charge/discharge cycles, although full deintercalation of K + was kinetically hindered. with residual evolution of K + species being observed by XANES at potentials beyond that of the observed current response.
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Significant degradation in electrochemical performance of a low crystalline Prussian Blue, with almost complete loss of capacity over 10 voltammetry cycles, was identified as being caused by K + becoming trapped within the partially intercalated Prussian blue structure. The degradation is caused by an increase in structural disorder on cycling, which can be observed from the perspectives of framework Fe and also the K + species. Specifically, non-conductive ferrihydrite forms on repeated cycling, which results in a loss of electrochemical activity, and K + becomes trapped within the remaining thermodynamically stable Prussian blue within the cathode. Potentially this process is exacerbated by the poor electrical conductivity of these small crystallite containing samples that aggregate together when forming composite electrodes.
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The study shows that operando potassium K-edge XANES can be successfully employed to effectively study the evolution of charge carrier species during an electrochemical process. The potential of XANES to monitor the speciation of alkaline charge carriers, in a host of different battery and other electrochemical processes, has exciting future potential in characterization and development of new materials. EXPERIMENTAL SECTION Material Synthesis. LC-PB preparation is based on wet chemical precipitation method. Equimolar concentrations of Fe(NO 3 ) 3 and K 4 Fe(CN) 6 solutions (5 mmol in 15 mL in DI water) were mixed together through dropwise addition. The solution was heated to 60 °C and kept under vigorous stirring for 2 hours. The resulting blue precipitate was separated via centrifugation at 10,000 rpm for 5 minutes and washed 5 times with acetone and DI water. The resulting precipitate was dried in a vacuum oven at 80 °C for 3 hours.
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HC-PB preparation is based on a previously described method with modifications. An equimolar ratio of K 3 (Fe(CN) 6 and K 4 Fe(CN) 6 (10 mmol) was dissolved in a 150 mL 0.6 M HCl solution. The solution was heated to 80 o C and stirred for 20 hours. The resulting precipitate was filtered under vacuum and washed with DI water several times. The powder collected was dried in a vacuum oven at 80 o C for 3 hours.
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Material Characterisation. The thermogravimetric analyses were collected on a TA Q600 SDT system, the samples were heated to 900 o C under air with a 2 °C/min ramp rate. X-ray diffraction (XRD) patterns were collected on a Brucker D8 Discover diffractometer using Co Kα (λ = 1.79 Å) operating at 35 kV and 40 mA with a PSD Braun detector. CHN elemental analysis was performed on a Perkin Elmer 2400. Before measurements, the samples were degassed overnight at 90 °C. ICP-AES experiments were performed on reaction filtrates using an Agilient 4210 MP-AES fitted with a SPS4 autosampler. SEM images were taken using the lower electron detector in a JEOL 7100F REGSEM. Infrared measurements were taken using a Schimadzu IT Affinity-1 spectrometer, using an attenuated total reflection crystal sampling technique. The investigated spectral range was from 4000 to 400 cm -1 with a resolution of 4 cm -1 . The signal was obtained by averaging 16 scans. Fe Mössbauer spectra were recorded at room temperature in the transmission mode using a constant acceleration spectrometer and a 57 Co(Rh) source. The velocity scale was calibrated using a 6 μm thick α-Fe foil. All the spectra were computer-fitted and the isomer shifts referred to the centroid of the spectrum of α-Fe at room temperature. ELECTROCHEMCIAL EVALUATION. Electrochemical performances were performed in an operando cell (Figure ). To compensate for the low energy of potassium XANES, 60 µm glassy carbon windows were used as both the current collector and X-ray window of the cell. The electrodes consisted of 80 % active material, 10 % C65 carbon black, and 10 % polyvinylidene fluoride (PVDF) binder, which were ground together into a paste and spread on the substrate with a K-Bar at ca. 100 μm thickness. The electrochemical performance of active material was evaluated using cyclic voltammetry (CV) at ambient temperature. The measurements were performed using an Ivium OctoStat30 potentiostat. Measurements were performed in a three-electrode cell. A Pt wire acted as the counter electrode, and a Ag/AgCl (3M NaCl) filled capillary tube as the reference electrode. The electrolyte comprised of flowing 0.1 M KNO 3 (aq). XANES MEASUREMNTS. XANES measurements was performed at B18 Beamline at Diamond Light Source, Didcot, UK. XANES were set-up with a fast-scanning silicon (111) double-crystal monochromator. Operando measurements were taken in fluorescence mode. For ex-situ measurements, sample preparation consisted of spreading a thin layer of material on carbon tape and taken in total electron yield (TEY). XANES data was processed using Athena software of the Demeter package. Linear Combination Fitting of operando XANES on normalised datasets was caried out in the energy window of 3593-3643 eV. Standards for PB and electrolyte were recorded within the operando cell environment to mitigate for self-absorption effect. The PW standard was taken at a fixed -0.1 V potential after the current response stabilised.
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DFT simulations. Ab initio DFT calculations were performed using the numeric atomic orbital (NAO) package, FHI-aims, which is an allelectron, full-potential electronic structure code. The generalised gradient approximation (GGA) of Perdew-Burke-Ernzerhof, reparametrized for solids (PBEsol), was used as the exchange-correlation (XC) functional during geometry optimisations, with the XC functional of Heyd, Scuseria and Ernzerhof (HSE06) and a screening parameter, w, of 0.11 bohr -1 used for subsequent single point energy calculations on the optimised structures. Dispersion interactions were accounted for using the Tkatchenko-Scheffler method, which is a pair-wise additive approach to include van der Waals interactions within the system. Calculations were performed using a 'light' basis set of the 2010 FHI-aims release, with SCF convergence assumed when the change in density was 10
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XANES simulation. Simulations of X-ray absorption have been performed using the plane-wave pseudopotential DFT method available within the code CASTEP, with the generalized-gradient approximation taken for the XC functional, in the form of Perdew-Burke-Ernzerhof, reparametrized for solids (PBEsol). . All ground-state simulations were converged with respect to the basis set and cutoff energy for all explored materials, resulting in the use of 750 eV cutoff energy and a 9x9x9 integration grid. Self-consistent calculations were performed to a total energy convergence value of 10 -7 eV. Spectra have been generated via the inclusion of a core-hole potential on the ground-state electronic structure, as implemented in the code.
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Supporting Information. XRD, FT-IR, elemental analysis, electron microscopy, XANES, EXAFS, 57 Fe Mössbauer, and DFT simulations are presented in the Supporting Information. This material is available free of charge via the Internet at . All computational structures associated with the presented work are available from the NOMAD repository (upload ID: pM_C4vbtTFqbg-uwrMe1Qg). All XANES data and meta-data presented is available from the Loughborough University repository (TBC).
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depicted here are average values for all of 1972 -2022 at each unique geographic coordinate (gray dots; sites for ZNO3, 5 n = 8,508; sites for ZPO4, n = 9,033). The thresholds for defining these nutricline depths were 3 µmol kg -1 and 3/16 µmol kg -1 for nitrate and phosphate respectively. The dashed line is the contour of 50 m depth; we determined trends from nutriclines deeper than 50 m. (C) The difference of average nitracline and phosphacline depths (sites for ZNO3 -ZPO4, n = 8,284). These maps show values that were spatially interpolated using DIVA in Ocean Data View.
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To test our hypothesis of a deepening nutricline, we estimated the temporal trends for the annually averaged nitracline and phosphacline depths using two separate linear regressions (Fig. ). The nitracline regression shows no significant change over time (p = 0.07). However, the phosphacline 5 significantly deepened (p = 9 x 10 -7 ) by 23 m over the past 5 decades (TPO4 slope = 0.47 m yr -1 , slope SE = 0.10 m yr -1 ) (Fig. ,B and Table ). To put this rate into perspective, the average phosphacline depth in southern oligotrophic waters (45°S to 1°S) is only 62 m, and the average difference between the nitracline and phosphacline depths (ZNO3 -ZPO4) is only 31 m throughout the global oligotrophic ocean (45°S to 45°N) (Table ). To account for seasonality in sampling, we corrected observed nutricline depths by subtracting their respective monthly climatological value. Again, only the phosphacline exhibits a deepening trend, whereas the nitracline displays no temporal trend (Fig. ). However, using different global data sets or threshold concentrations does sometimes indicate nitracline deepening, although this deepening rate never exceeds the rate for phosphacline depths (Table ). Also, nitracline and phosphacline slopes were not significantly 15 different for the lowest threshold concentrations, likely due to poorly resolved phosphacline depths at these low concentrations. Nonetheless, these global regressions consistently show that the phosphacline is deepening faster than the nitracline.
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We next quantified site-specific trends for the nitracline (TNO3) and phosphacline (TPO4) depths 20 (Fig. and Table ). This was done to eliminate the possibility that the spatiotemporal variability in sampling induced a spurious trend by over-representing locations with particularly deep nutriclines at later years. The median TNO3 was negative (-0.11 m yr -1 , CI95% = [-0.22, -0.02]) indicating a possible shoaling. In contrast, the median TPO4 shows a greater inclination for phosphacline deepening (0.35 m yr -1 , CI95% = [0.20, 0.49]). Similar with the global regression, this suggests a general deepening of the phosphacline at a rate of 18 m over the past 50 years. Thus, the site-specific trends show that only the phosphacline is deepening, whereas the nitracline is stable or could even be shoaling. = 1 μmol kg -1 and [PO4 3-] = 1/16 μmol kg -1 ) and higher ([NO3 -] = 5 μmol kg -1 and [PO4 3-] = 5/16 μmol kg -1 ) threshold concentrations. Additionally, the global density trends of nutricline depths. See Table for detailed statistics of these observed trends. (C) Regional medians of TNO3 and TPO4. See Table for detailed descriptions of these regions and their respective statistics.
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We also observed extensive variability among site-specific trends (Fig. ), including both deepening and shoaling nutriclines across smaller ocean regions. Multiple mechanisms, including seasonality, likely contribute to the observed variation among sites. However, we will next show that none of the tested mechanisms can account for the long-term deepening in the phosphacline, but not nitracline. Simulating the actual sampling dates onto a fixed monthly climatology (WOA18 5 with no long-term change) resulted in interquartile ranges of TNO3 and TPO4 that are about 50% of the observed variances. This suggests that monthly variability in nutrient concentrations is an important source of variation in site-specific trends (Fig. and Fig. ). Next, we constructed 10,000 random populations of the fixed monthly climatology to robustly quantify the effect of seasonal variance without any long-term changes (Fig. ). The median trends in nutricline 10 depths are indistinguishable from zero, showing that monthly variability does not lead to an overall bias in median trends. We then introduced an artificial fixed long-term trend at all sites in the random populations. This resulted in the same variance with different locations showing a mix of deepening or shoaling trends in agreement to what we found in the actual observations. However, the median shifted to match the fixed imposed trend (Fig. ). We interpret these analyses as 15 the observed median capturing the actual underlying tendency in trends, whereas the variance in site-specific trends is mostly attributed to seasonality. To match both the observed median trends and overall variance in depths, each nitracline trend had to be sampled from a normal distribution with a shoaling tendency (mean = -0.63 m yr -1 , SD = 1.5 m yr -1 ), and each phosphacline trend came from one with a deepening tendency (mean = 0.20 m yr -1 , SD = 1.0 m yr -1 ) (Fig. ). This 20 demonstrates that the median trend robustly captures the underlying tendency of the site-specific trends despite their high variability. In summary, these analyses show that sampling timing contributes to the observed variability in trends between sites, but any overall shift in the median must come from a long-term change in nutricline depths.
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Outside of seasonality, variability in the site-specific trends could also arise from measurement error or interannual climate forcings. When we simulated measurement uncertainty to the observed nutrient concentrations, we found that the interquartile range of TNO3 only increased about 5% (Fig. ). In contrast, the interquartile range of TPO4 increased about 40% due to the low threshold 5 concentration (Fig. ). This suggests that measurement error is a considerable factor for the variability of TPO4 but not TNO3, despite both having nearly equal total variance. However, accounting for sampling error to nutrient concentrations still yielded a median TNO3 indicative of shoaling, and a median TPO4 indicative of deepening (median TNO3 = -0.18 m yr -1 , CI95% = [-0.27, -0.03]; median TPO4 = 0.26 m yr -1 , CI95% = [0.09, 0.43]). Part of the total variance could also be 10 attributed to ENSO or other climate modes, which can affect upper ocean nutrient profiles on interannual timescales . We found that during some El Niño years, the global median nitracline and phosphacline depths were relatively deeper (Fig. ). Thus, the combination of seasonal and interannual changes in nutrient concentrations together with measurement uncertainty explain most of the observed variance in nutricline trends.
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Despite a large variability, the median values of TNO3 and TPO4 are both significantly different from zero and from each other. To confirm this, we scrambled the sampling time to construct 10,000 randomized conglomerate data sets and found the median trends for each of these random populations (MToRP). This showed that the probabilities of the observed medians in TNO3 and 20 TPO4 being zero are less than 2 x 10 -2 and 1 x 10 -5 respectively when compared to 10,000 randomized data sets (Table ). Moreover, sign and Kruskal-Wallis tests also supported that both median trends are significantly different from zero and each other (Table ). Thus, there is some support for a shoaling of the nitracline, and strong support for a deepening of the phosphacline.
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The median trends are also consistent across different observational products and choice of threshold concentrations (Fig. and Table ). WOD hosts nearly an order of magnitude more nutrient observations than GO-SHIP, but these observations were collected with a diversity of protocols. Nonetheless, WOD similarly shows overall shoaling and deepening trends of the 5 nitracline and phosphacline, respectively (Table ). The GLODAPv2.2022 adjusted product also shows that any measurement bias with time has little influence on the median trends (Table ).
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We finally explored the robustness of the median trends with a variety of additional tests. First, we found a negative median trend for the paired residual ZNO3 -ZPO4, which also suggests a faster deepening of the phosphacline relative to the nitracline (Fig. ). Second, there was no indication 15 of a bias due to changing measurement methods during the observation period. After subtracting mean climatological concentrations, we saw no negative trend at depths well below the nutricline where concentrations presumably should be stable (Fig. ). Third, the water density at the depth of the nitracline and phosphacline show decreasing and increasing trends respectively (median TNO3 = -5 x 10 -3 kg m -3 yr -1 , CI95% = [-7 x 10 -3 , -4 x 10 -3 ]; median TPO4 = 3 x 10 -3 kg m -3 yr -1 , CI95% 20 = [8 x 10 -4 , 5 x 10 -3 ]; Fig. ). This indicates that the nutricline depths are shifting independently of density layers, suggesting that biological processes may control the nutricline depth trends.
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Based on the combination of these tests and analyses, we conclude that there is strong support for a general deepening of the phosphacline. It is less certain if the nitracline is stable or possibly shoaling, but it is clearly not deepening as fast as the phosphacline. Thus, our analysis points to differential shifts in nutricline depths for these two nutrients, revealing a contemporary depletion of upper ocean phosphate relative to nitrate.
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There are multiple possible biogeochemical drivers for shifting nutricline depths, including changes in phytoplankton resource demands, external nutrient inputs (riverine or atmospheric), or biological nitrogen fixation. First, it is commonly proposed that phytoplankton have an increasing N:P demand in a warming ocean due to a reduction of P-rich ribosomes needed for protein synthesis (25). We find that this biochemical mechanism is unlikely to explain our results as it implies a faster deepening of the nitracline relative to the phosphacline. Second, changes in riverine inputs and atmospheric deposition of predominantly nitrogenous material can increase the demand for phosphorus relative to nitrogen. This mechanism is also unlikely to explain our results, as increasing nitrogenous input is primarily occurring in the northern hemisphere , 5 whereas a deepening phosphacline is mostly observed in the southern hemisphere (Fig. and Table ). Hence, neither changes in phytoplankton demands nor external inputs can explain the observed nutricline trends.
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A third possibility is that changes in biological nitrogen fixation compensate for a declining supply 10 of nitrate from stratification, but not for phosphate (22). Marine nitrogen fixation is often limited by iron (28 -30), and for many reasons, this iron stress may be decreasing . found that Trichodesmium cells use iron more efficiently at elevated temperature (32). Moreover, increasing stratification results in an increase in the Fe:N supply ratio by moderating the relative importance of vertical vs. aeolian nutrient supply . Deposition of soluble iron from combustion 15 sources, including wildfire and fossil fuel burning, has been increasing in recent decades , and significantly impacting marine biogeochemistry . Considering these findings, diazotrophs are more commonly limited by iron in the southern and phosphorus in the northern hemisphere (36). Decreasing iron stress would therefore mostly stimulate nitrogen fixation and phosphate drawdown in the southern hemisphere. Hence, we hypothesize that the regulation of nitrogen 20 fixation is important for the observed decline in phosphate-to-nitrate availability and can explain the hemispherical difference in depth trends.
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To test this hypothesis, we compared trends in nitracline and phosphacline depths in the CMIP6 Earth System Models across historical and future emission scenarios (i.e., less and more stratified scenarios, respectively) (Fig. ). In the historical scenario, all models predicted nutricline trends notably smaller than the observed trends. In some models, equivalent trends for the 5 nitracline and phosphacline depths at Redfield proportions (i.e., TPO4 = TNO3) were seen. For other models, the phosphacline showed a faster deepening trend compared to the nitracline, whereas the opposite was never seen. These findings generally held true under future emission scenarios, although most models predicted faster deepening of both nitracline and phosphacline depths in the future. In conclusion, greater stratification generally led to a faster nutricline deepening in CMIP6, 10 but some models included biogeochemical processes causing a faster deepening of the phosphacline relative to the nitracline.
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The faster deepening of the phosphacline relative to the nitracline was correlated with ocean nitrogen fixation rates across Earth System Models (Fig. ). A differential deepening (i.e., residual TPO4) was quantified as the orthogonal distance from the TPO4 = TNO3 line. Across all three model scenarios, we found significant positive relationships between ocean nitrogen fixation rates and the residual TPO4 (Table ). The correlation coefficients and regression slopes also increased 5 with stronger emissions. This shows that the relationship between nitrogen fixation and declining phosphate-to-nitrate availability is dependent on the rate ocean warming and increasing stratification. Therefore, the CMIP6 model dynamics were consistent with the hypothesis that nitrogen fixation with stratification determines the faster deepening of the phosphacline relative to the nitracline.
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Among the CMIP6 models, CESM2 had the highest ocean nitrogen fixation rates as well as the highest residual TPO4. Although higher than most, this model was consistent with the convergent estimate of ocean nitrogen fixation quantified by Wang et al. (2019) (36). Finally, CESM2 showed 15 nutricline trends that were the most consistent with observations. Hence, we next investigated different processes in CESM2 that may affect nitracline and phosphacline trends. phosphate requirement led to reduced upper ocean phosphate demand by 2100 (37). We analyzed these same experiments and found that flexible phosphate uptake also led to shallower phosphacline depths (Fig. ) (37). However, flexible phosphate uptake did not have a major effect Submitted Manuscript: Confidential Template revised November 2023 16 on nutricline trends through time (Fig. ). Therefore, flexible nutrient uptake stoichiometry impacted the initial depths of nutriclines, but was not a factor for the long-term trends.
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Decreasing iron stress may enhance the deepening of the phosphacline relative to the nitracline through stimulation of nitrogen fixation. . In CESM2, we adjusted iron stress by increasing 5 atmospheric iron deposition (DFe) rates either by hemisphere or globally (Fig. ). Increased deposition rates increased nitrogen fixation and resulted in a faster deepening of the phosphacline relative to the nitracline (Fig. ). We again found a significant relationship between the residual TPO4 and integrated nitrogen fixation (slope = 7 x 10 -4 m x [Tg Nfix] -1 , slope SE = 2 x 10 -4 m x [Tg Nfix] -1 , p = 3 x 10 -3 , n = 10). Additionally, we determined nutricline trends in regions with 10 different primary nutrient limitations (Fig. ). Increased DFe led to a faster deepening of the phosphacline relative to the nitracline no matter the location, but the strongest effect was in ironlimited regions. This suggested that as iron stress was alleviated, it was eventually replaced with increased phosphorus stress. Thus, an increase in nitrogen fixation by alleviating iron stress directly results in a faster deepening of the phosphacline relative to the nitracline.
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We presented evidence for a deepening of the phosphacline that is decoupled from any commensurate change in the nitracline. However, there are caveats to be considered. First, we restricted our global trend analysis to nutricline depths that were deeper than 50 m and from 45°S -45°N. Omitting depths shallower than 50 m did not appreciably affect the observed trends, as they remained consistent when including depths deeper than 25 m (Tables and). The applied latitudinal range removed the Arctic Ocean from our analyses, despite this region experiencing some degree of nitrogen limitation (38). However, the sampling density in the Arctic was too low to quantify trends from nutricline depths that met our criteria. Furthermore, the Arctic experiences high variability in sea-ice cover, which is a major driver of stratification absent from the rest of the oligotrophic ocean (39). Second, there were notably less cruise observations from the earliest 5 and latest years, but we still found a significantly faster deepening of the phosphacline from 1982 -2012 (Tables and). Third, ocean basins were sampled at different frequencies leading to less statistical power for some basins, most notably for the Indian Ocean. However, the nitrate and phosphate depth profiles were mostly sampled concurrently throughout time and space; thus, the sampling variability is not expected to have any effect on the differences in the trends observed 10 for the two nutrients (Fig. ). Fourth, although the global trends were robust, we recognize that variability in the phosphacline trends were more influenced by measurement error than the nitracline trends. Accounting for these caveats, we still find significant evidence for declining phosphate-to-nitrate availability over the past 5 decades .
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The cruise observations suggest that phosphacline depths deepened by approximately 20 m over the past 5 decades, a rate that is almost an order of magnitude larger than most CMIP6 predictions for the historical period (Fig. , Tables and). At the observed rate, nutrient availability throughout the southern oligotrophic gyres may soon resemble the western side of the North Pacific subtropical gyre (Fig. and Table ). This transition is possible due to the predicted 20 decrease in iron stress for nitrogen fixation in this region . In turn, nutrient availability at the western side of the North Pacific subtropical gyre may soon resemble the North Atlantic subtropical gyre with widespread phosphorus stress (Fig. and Table ). A trend towards more phosphorus stress possibly driven by nitrogen fixation has already been observed in this area (41, 42). Therefore, the current patterns and trends in nutricline depths provide a basis for predicting which regions will begin to show increasing phosphorus stress for marine productivity.
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Although phosphate has been suggested to be the ultimate control on phytoplankton production , variability in phytoplankton C:P and nitrogen fixation may buffer productivity despite increasing stratification (37, 43). In contrast, increasing nitrogen stress might have greater impacts on marine productivity, as phytoplankton have less ability to acclimate by modifying their C:N 10 ratio . Nonetheless, phosphorus limitation does select for higher C:P in phytoplankton , consequently reducing food quality throughout many marine food webs . These potential changes for marine ecosystems underscore the importance of constraining the rate of rising phosphorus stress throughout the ocean.
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Increasing stratification and atmospheric iron inputs will likely continue in the coming decades , but the decline in phosphate-to-nitrate availability is still subject to change. A declining phosphate supply would eventually start to limit nitrogen fixation rather than iron . and WOD for conglomerating and managing these cruise data sets. We thank Jennifer Martiny and François Primeau for their helpful suggestions on our initial manuscript. We thank Eun Young Kwon and Mohanan Sreeush for their assistance in providing their CESM2 nutrient uptake experiments. We acknowledge that we referred to ChatGPT 3.5 for suggesting code in data analysis and edits in the manuscript text.
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On the GO-SHIP cruises, temperature and salinity were recorded at various depths and stations using a Conductivity Temperature Depth (CTD) instrument (54). Nutrients were sampled from seawater collected by a Niskin bottle rosette fitted onto the CTD (55). Nutrient concentrations were photometrically determined from the collected seawater via continuous flow analysis. Nitrate was determined by first reducing nitrate to nitrite in a copperized cadmium column. A sulfanilamide solution and N-Napthylethylene-diamine were introduced to produce a red azo dye (55, 56). To determine phosphate, molybdic acid was introduced to form phosphomolybdic acid.
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| 20 |
Here, we analyzed each CTD cast where nitrate or phosphate was measured. Nitrate profiles inclusive of nitrite concentrations (i.e., nitrate + nitrite) were excluded from our analysis, as were any negative or outlier concentrations. We defined outlier concentrations as instances where a nutrient decreased with depth by more than 10 µmol kg -1 in the upper ocean. Nutrient concentrations were predominantly in units of μmol kg -1 , but for concentrations expressed as μmol L -1 , we converted them to μmol kg -1 by calculating seawater density. We calculated density using a UNESCO formula by incorporating temperature (℃) and salinity (psu) measurements included in each bottle file (57).
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| 21 |
For every cast with nutrient measurements at 2 or more pressures, we linearly interpolated nitrate and phosphate concentrations for every 1 dbar down to a maximum pressure of 1000 dbar. The interpolation only spanned between the lowest and highest pressures with nutrient measurements. Similarly, we interpolated temperature and salinity from the respective cruise CTD file for every 1 dbar. We then recorded the nutricline as the pressure and density where the interpolated nutrient concentrations first reached threshold concentrations. The nutricline pressure was converted to depth (m) using a UNESCO formula revised by Leroy & Parthiot (1998) (58).
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We followed a series of criteria for quantifying nutricline depths and trends to improve the accuracy of our analyses. First, we only recorded the nutricline depth of a cast if there existed interpolated concentrations above and below said depth. Second, we binned the coordinates of each nutricline depth to the nearest degree of latitude and longitude to quantify average nutricline depths per unique coordinate and year. Lastly, we quantified trends only from average nutricline depths that were deeper than 50 m and at a latitude from 45°S to 45°N. We also repeated our analysis using a depth boundary of 25 m. We selected these boundaries to target trends in regions where nutrients limit growth, and minimize effects from seasonal changes in stratification (59).
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We tested the significance of nutricline trends using two independent methods. First, we fitted linear regression models to average nutricline depths through time. These nutricline depths were annual averages for each unique geographic coordinate. Two separate regressions were fitted to nitracline and phosphaclines, and an F-test determined if each regression was significant (i.e., p < 0.05). Second, we analyzed each geographic coordinate that had average nutricline depths recorded for two or more unique years. For each coordinate, we fitted a regression to its average nutricline depths vs. years to quantify its site-specific trend. These site-specific trends were quantified separately for nitraclines and phosphaclines. The sign test determined if the global median sitespecific trend was significantly different from zero. Additionally, the Kruskal-Wallis test determined if the median trends of nitracline and phosphaclines were significantly different from each other. We also calculated 95% confidence intervals (CI95%) for the median trends by generating 10,000 bootstrap samples of the data set. Thus, with global regressions and site-specific trends, we were able to test if nitracline and phosphacline depths were generally shifting in recent decades.
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To explore potential temporal biases in the cruise observations, we analyzed nutrient concentrations from the National Oceanic and Atmospheric Administration's World Ocean Atlas data product version 2018 (WOA18). WOA18 is an objectively-analyzed global climatology of nutrient concentrations per 1° of latitude and longitude for every month (61). The vertical profiles reached down to 800 m deep with depth bin sizes ranging 5 -50 m. For every geographic coordinate, we interpolated nitrate and phosphate concentrations per 1 m and found the average nutricline depths.
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We investigated WOA18 to reveal if there was a notable bias in the months nutriclines were sampled. First, we indexed each nutricline depth based on the latitude, longitude, and month of the respective cast. We then replaced each observed nutricline depth with its respective monthly value in WOA18. Next, we proceeded to find the annually-averaged nutricline depth for each geographic coordinate of each year. Then, we determined the trends of nutricline depths with time. If there were considerable seasonal biases in cruise casts, then the global medians of these trends would deviate from zero.
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We also constructed random populations from WOA18 to determine how variability in sitespecific trends affected their median values. First, we randomly selected a potential monthly nutricline depth for each geographic coordinate with nutricline depths observed for two or more years in the GO-SHIP collection. We then paired these to another random, potential monthly nutricline depth to simulate a 50-year trend for each geographical coordinate. We repeated this procedure until 10,000 random populations of the conglomerate data set were made. Second, we performed a similar procedure where we paired one set of monthly values to another set, but here we imposed a ubiquitous site-specific trend by changing the second set of monthly values by a rate equivalent to the median trend from observations. These two analyses determined if the median trend was controlled by monthly variability in sampling. Third, we imposed a variable site-specific trend by changing each monthly value in the second set by a rate of change randomly selected from a normal distribution of rates. We altered the mean and standard deviation of this normal distribution until the median trend and the variance of simulated nutricline depths (i.e., IQR) both matched the observations. This analysis determined if the median trend actually captured an underlying tendency of the site-specific trends despite their high variability. In summary, these analyses with WOA18 determined if variability in the site-specific trends had considerable influence on their median values.
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Improved technology may have increased the accuracy of nutrient concentrations over time. To test this, we investigated GLODAPv2.2016, another mapped climatology of nutrient concentrations for each 1° of latitude and longitude (51, 62). GLODAPv2.2016 provided nitrate and phosphate concentrations down to 5,500 m with depth bins ranging from 10 -500 m. At each geographical coordinate, we linearly interpolated nutrient concentrations for every 1 m of depth.
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We then recorded the interpolated concentrations at the depths of 100, 300, 500, 1,000, 2,000, 3,000, and 4,000 m for each coordinate. Next, we went through each cast of the GO-SHIP observations and recorded the interpolated concentrations at these same depths. For each cast, we found the difference of the observed concentrations and the mapped climatology at these specified depths. We then fitted linear regressions to the differences at each coordinate. If improved technology imposed a measurement bias, then the differences at deeper depths may show a negative trend with time.
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The Coupled Model Intercomparison Project Phase 6 (CMIP6) is a collection of global models that each predict biogeochemical cycles with time . outline some key model differences that contribute to their contrasting predictions of biogeochemistry. These models differ in their ocean-climate interactions, organic matter cycling rates, marine plankton communities, biological processes, nutrient ratios, and more .
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Here, we analyzed nutrient concentrations from CMIP6 under three emission scenarios: the historical period, middle-of-the-road (SSP2-4.5), and business-as-usual (SSP5-8.5) (Table ) . For the historical scenario, we confined the years to 1972 -2014 to better match the time span of the observations. The future emission scenarios were confined to the years 2015 -2100. Our primary variables of interest were marine concentrations of nitrate and phosphate ("no3" and "po4" respectively). We also analyzed sea temperature ("thetao") and salinity ("so") through time to convert the nutrient concentrations from mol m -3 to µmol kg -1 , and determine trends in nutricline densities. These variables came from consistent model variants in terms of realization, initialization, method, physics, and forcing; the "r1i1p1f1" variant was used when available. With these variables, we quantified nitracline and phosphacline depths with time.
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Nutricline depths in CMIP6 were quantified similar to the cruise observations. For each model grid point, we linearly interpolated nutrient concentrations for every 1 dbar of pressure up to 1000 years) for five repeated cycles (305 years in total), using a modified version of the CESM2-MARBL ecosystem (67). We ran a control run after the 305-year initialization, where historical emissions continued for another 61 years. For experimental runs, we tested how nitrogen fixation rates and nutricline depths responded to changing DFe either increasing globally, in just the northern hemisphere, or in just the southern hemisphere. We augmented DFe in these areas by either 25%, 50%, or 100%. Each experimental run started immediately after the 305-year initialization and lasted for 61 years as well. Therefore, a total of 9 experimental runs were conducted to constrain how DFe affects nitrogen fixation rates and nutricline trends in CESM2. For this analysis, nutrient concentrations were converted to µmol kg -1 and nutricline depths were quantified using the same method as the CMIP6 models.
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Organic cages are discrete molecular systems assembled through covalent bond formation and possessing internal cavities capable of binding guest species. Shape-persistent cages with a permanent accessible cavity are often referred to as porous organic cages (POCs). The ability of POCs to encapsulate guests has led to their use in a variety of applications including catalysis, gas sorption, and molecular separations. Furthermore, the synthetic tunability of organic cages has allowed a wide range of topologies to be realised and for them to be studied as materials in the solid-state, in solution, and as porous liquids. Dynamic covalent chemistry (DCC), such as imine bond formation, is often exploited for the synthesis of POCs due to the 'error correction' inherent to reversible chemical bonds, enabling access to the most thermodynamically favourable structures in high yields. The modularity of DCC also permits facile exchange of related building blocks to modulate the properties of organic cages. In 2011, for example, Cooper and co-workers reported the tuneable porosity of a 'scrambled' mixture of POCs assembled from a trialdehyde and a combination of two diamine building blocks, compared to topologically isostructural POCs formed from just a single diamine, due to increased structural disorder. Later, this group also reported the increased solubility of a similar, structurally analogous scrambled mixture of POCs due to increased structural disorder. While the dynamic nature of imine bonds makes them highly convenient for preparing POCs, they can be hydrolytically unstable, although there are exceptions, limiting the utility of the cages. To overcome this, imines can be 'fixed' by reduction to amines, providing a level of kinetic robustness, although sometimes at the expense of their permanent porosity due to structural collapse resulting from increased flexibility. 'Fixing' can also allow post-synthetic modification (PSM) of the cage scaffolds, to both modify their properties and install functional units, that might otherwise be incompatible with dynamic covalent bonds.
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There have been a number of previous reports of POCs that, rather than forming as monomeric architectures, undergo interpenetration to form mechanically interlocked molecules (MIMs). Often this interlocking significantly reduces the accessibility of the internal cavity space, limiting guest-binding potential. The incorporation of mechanically interlocked components on the periphery of the POCs could, however, be used to modify the structure and thus properties of the cages while theoretically leaving the cavity intact. Indeed, MIM architectures have previously been used to modulate the solubility, electronic and biological properties of molecular components. Although there have been reports of coordination cages functionalised with interlocked components, the introduction of MIMs onto organic cages has yet to be explored.
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In this work, we present the synthesis of organic cage[n]rotaxanes by exploiting the copper(I)-catalysed azidealkyne cycloaddition (CuAAC) active metal template (AMT) approach. Using this method, we were able to mechanically append macrocyclic components to peripherally functionalise organic cages with unoccupied cavities. Subsequent investigations into the differences in physiochemical properties between the interlocked and noninterlocked species demonstrated the potential for using the mechanical bond to modify the behaviour of these discrete systems.
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For our core structure we chose a Tri 2 Di 3 or [2+3] cage design (where for Tri x Di y or [x + y], x = number of tritopic building blocks and y = number of ditopic building blocks in the cage structure), originally reported by Delgado and co-workers. This system was formed through imine condensation between triamine 1 and dialdehyde 2a, followed by reduction to give the robust amine cage C (Fig. ). To incorporate interlocked macrocycle components via CuAAC-AMT, alkyne units were chosen to be installed on the periphery of the structure. To this end, an analogous dialdehyde, 2b, was synthesised incorporating a TIPS-protected alkyne. To allow control over the incorporation of a defined number of mechanically interlocked components, which would enable us to investigate how the extent of functionalisation affected the properties of the cage, we sought to generate POCs with one to three alkyne units on the periphery (C1 to C3, respectively). To achieve this, a scrambled library of DCC cages was generated through the reaction of triamine 1 with a mixture of dialdehydes 2a and 2b in a 3:2:1 ratio (Fig. ). An excess of triamine 1 was used as this has previously been shown to promote conversion to the targeted cages. Figure . Synthesis of alkyne-functionalised cages C1-C3 through imine condensation between triamine 1 and dialdehydes 2, followed by reduction.
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The imine cages were then reduced in situ to form a mixture of amine organic cages that could be separated by column chromatography, yielding the cages C1 TIPS and C2 TIPS in 20% and 14% isolated yield, respectively. Removal of the TIPS protecting groups furnished the terminal alkyne-functionalised cages, C1 and C2, with one and two alkyne units, respectively. The tri-alkyne cage C3 was directly synthesised using three equivalents of dialdehyde 2b and triamine 1, followed by reduction and deprotection, in 41% overall yield. The successful synthesis of each of C1-C3 was confirmed by high-resolution electrospray ionisation mass spectrometry (HR-ESI-MS) and NMR spectroscopy.
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With the alkyne-functionalised cages in-hand, the synthesis of cage[n]rotaxanes was envisaged using Goldup and co-workers' small 2,2'-bipyridine macrocycle modification of Leigh and co-workers' CuAAC-AMT method with macrocycle M and 3,5-di-tert-butylbenzyl azide, S, as a stopper (Fig. ). Molecular modelling (molecular dynamics in Macromodel, OPLS4 forcefield) of each of the prospective rotaxane structures confirmed a loss in shape-persistency of the cage core on reduction of the imines, as expected, but indicated that the cage framework should be large enough to prevent dethreading of M.
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Initially, we confirmed the viable reactivity of the alkyne units through reaction of C1-C3 with S under standard CuAAC conditions (CuSO4•5H2O, sodium ascorbate, DMF, RT). Pleasingly, each of the non-interlocked axle cages with 1-3 triazole units (A1-A3, respectively) was obtained in good isolated yield (38-64%). Subsequently, each of C1-C3 was submitted to CuAAC-AMT conditions which, following column chromatography, yielded the target [2]-, [3]-, and [4]rotaxane structures (CR1, CR2 and CR3, respectively) in quantities >100 mg. This bulk material was contaminated with small amounts of non-interlocked triazole components that could be quantified by 1 H NMR spectroscopy (Fig. ). Due to difficulties in separating the interlocked and non-interlocked components by standard chromatographic techniques, isolation of the pure rotaxanes CR1, CR2 and CR3 required reverse-phase preparative TLC, giving the interlocked structures in isolated yields of 10%, 13% and 28%, respectively. Such purification techniques, however, limited the amount of pure CR products that could be brought through (<30 mg). Successful rotaxane formation was confirmed by HR-ESI-MS and NMR spectroscopy (Fig. ). In particular, characteristic shifts in 1 H NMR spectral peaks compared to the non-interlocked axle (A1-A3) and macrocycle (M) components supported the formation of the target interlocked structures. For example, the downfield shift of the triazole resonance (He) in rotaxane CR1 compared to the non-interlocked axle A1 (Δδ = 2.31 ppm; Fig. and) was indicative of C-H•••N hydrogen bonding between the triazole and bipyridyl unit of the macrocycle, as previously observed in related systems. Cage[n]rotaxanes CR2 and CR3 (Fig. and, respectively) displayed similar resonance shifts compared to their non-interlocked components. Disappointingly, despite multiple attempts, we were not able to grow X-ray quality single crystals of any of the cages to confirm their structure in the solid-state. With the target cage[n]rotaxanes in hand, we looked to investigate how the properties of the interlocked structures differed from their non-interlocked counterparts. In this regard we investigated the thermal properties, CO2 uptake, and solubilities of the cages, axles and rotaxanes.
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The thermal properties of the cage[n]rotaxanes (Table ) were studied using thermogravimetric analysis (TGA) and optical differential scanning calorimetry (DSC) after activating the samples to remove solvent. The decomposition temperatures (Td) for non-interlocked A1-A3 increased with the number of triazole units from 170 °C (A1) to 220 °C (A3). In comparison, the rotaxanes CR1-CR3 all showed lower Td values, with limited variation between the different systems (150-160 °C). In contrast to the non-interlocked axles, which all decomposed prior to melting (Fig. , S113 and S126), each of the rotaxanes was observed to partially melt (Fig. , S155 and S169), with this process occurring over a broad temperature range of 10-20 °C, a feature previously observed with other reduced organic cages. The apparent degree and onset of melting increased with the number of interlocked components, suggesting the incorporation of the macrocycle, which itself melts at ~100 °C with a sharp endotherm (Fig. ), is leading to this observed behaviour. We subsequently shifted our focus to carrying out gas sorption studies (Fig. ), comparing the alkynefunctionalised cages (C1-C3), non-interlocked axles (A1-A3), and rotaxanes (CR1-CR3). Due to the difficulties in purifying large quantities of the cage[n]rotaxanes, we performed these on the bulk amorphous samples which, after removing residual azide and macrocycle from the crude material, contained quantities of non-interlocked axle and/or partially rotaxanated products (14, 7 and 31 mol% for CR1, CR2, and CR3, respectively; see Fig. ). While the rotaxanes all exhibited no porosity to N2 (77 K, 1 bar) based on their Brunauer-Emmett-Teller (BET) surface areas (4.9, 12.8 and 1.7 m 2 /g for CR1, CR2, and CR3, respectively), due to the presence of the free amines in the cage structures, we turned our attention to CO2 uptake under standard conditions (298 K, 1 bar). Interestingly, C3 displayed much higher CO2 uptake (0.35 mmol g -1 ) compared to C1 and C2 (0.12 and 0.06 mmol/g, respectively). A1-A3 showed enhanced uptake over their respective alkyne precursors, and increased adsorption values with each additional triazole unit (0.42, 0.53 and 0.68 mmol g -1 for A1, A2 and A3, respectively). As C1-C3 and A1-A3 have chemically identical cavities, they would be expected to have the same intrinsic porosity. Therefore, the observed trends in CO2 uptake are likely to be due to increased extrinsic porosity resulting from poor packing efficiency of the bulky di-tert-butylphenyl stopper units. Finally, the rotaxanes CR1-CR3 also showed enhanced uptake with an increasing number of substituents (0.17, 0.19 and 0.26 mmol g -1 , respectively); however, these values were consistently lower than their non-interlocked counterparts. We surmise that this is likely a result of the macrocyclic components occupying the void spaces created by the bulky stopper units, reducing the available extrinsic porosity. In addition, the simulated structures indicate that the macrocyclic components could limit the free space surrounding the amine groups in the cage scaffold. This would additionally frustrate the coordination of CO2 molecules with the amine sites, reducing the CO2 sorption capacity of the materials containing more macrocyclic components. As has been previously demonstrated, inter-component interactions can result in MIMs possessing drastically different solubilities compared to their individual non-interlocked components. Consequently, we sought to investigate how the mechanically appended bipyridyl macrocycles affected the solubilities of the cages (Fig. ), as this is an important factor when processing these species into mixed-matrix membranes and porous liquids. The non-interlocked cage axles (A1-A3) all displayed similar solubilities (~0.08 M) in chloroform that were greater than their precursor alkyne cages (C1-C2). A further notable enhancement was observed for the rotaxane structures (CR1-CR3), with each displaying solubilities of ~0.13 M. Thus, the presence of M (itself displaying high solubility of 0.82±0.032 M) significantly enhanced the solubility of the rotaxanes compared to the non-interlocked cages.
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| 8 |
In summary, using a component scrambling methodology following by reduction, we were able to synthesise robust, amine-based organic cages with a defined number of alkyne units on the periphery. These functional handles were able to undergo CuAAC reactions, including AMT to install mechanically interlocked macrocycle components in the formation of [2]-, [3]-and [4]rotaxanes. The presence of the macrocycle components was shown to increase the solubility in CHCl3 of the cage rotaxanes compared to their non-interlocked congeners, as well as modify the thermal properties and gas uptake capability of these materials. More generally, the ability to post-synthetically modify POCs using facile CuAAC chemistry opens the door to readily attaching a range of functional units to the cage scaffolds and prepare functionalised POCs from a common precursor. Ultimately, this will allow the precision engineering of (multi-)functional POCs with customisable properties and behaviours. Studies towards this goal are ongoing in our laboratory.
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65eeac0a66c1381729b9206e
| 0 |
Renal excretion of drugs involves glomerular filtration, tubular secretion and reabsorption processes . Compounds whose renal clearance is greater than glomerular filtration clearance will be subject to renal tubular secretion and hence can interact with transporters expressed on renal epithelial cells. Most cationic organic compounds are substrates for the organic cation transporter (OCT) 2, multidrug and toxin extrusion transporter (MATE) 1, and MATE2-K . Their renal excretion in vivo is largely mediated by OCT2, which is expressed on the apical side of renal epithelial cells, and MATE1, MATE2-K which are expressed on the basolateral side . It has been clinically reported that concomitant use of drugs which are also inhibitors of OCT2, MATE1 and MATE2-K results in drug-drug interactions (DDI) with decreased renal excretion. For example, renal clearance of metformin, which is a substrate for OCT2, MATE1, and MATE-2K, was decreased in the co-administration of cimetidine and pyrimethamine, which are inhibitors of those transporters . Regarding the mechanism of the clinical DDI between cimetidine and metformin, it has been hypothesized mechanistically that MATE1 and MATE2-K play major roles for DDIs in the kidney because of the lower Ki values for MATE1 and MATE2-K than OCT2 . This was also supported by PBPK modeling . MATE1 that is significantly more highly expressed than MATE2-K, is considered to have the similar potency of transportability with MATE2-K, and we have limited information of specific substrates in MATE2-K, suggesting that MATE1 plays a major role in the renal DDI of drugs . The current DDI guidelines (of the United States 10 , Europe 11 and Japan ) list MATE1 as a transporter to be evaluated, suggesting MATE1 is a clinically relevant transporter in terms of clinical DDI risk assessment. Consequently, a predictive method to prospectively evaluate the inhibitory potential of MATE1 in the early drug discovery stages is desirable to evaluate new molecular entities with respect to this clinically relevant endpoint.
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65eeac0a66c1381729b9206e
| 1 |
Since the ROC-AUC in 2-fold cross validation (CV) was 0.82, this model was considered to have high predictivity . However, the number of compounds was rather limited for the model to be utilized in practical drug discovery projects from the viewpoint of chemical space coverage. In 2013, a larger dataset of 910 compounds was used to predict percentage inhibition at 20 μM concentration, with 50% inhibition used as the threshold for a binary classification model 14 based on Random Forest (RF) with 21 Dragon descriptors . The ROC-AUC by multiple external datasets was 0.78, and this model hence also had high numerical predictivity. In 2015, a pharmacophore model was constructed using docked poses obtained from GLIDE . The dataset was the same as in the preceding study , and 42 inhibitors were used to construct the pharmacophore model and tested by another 42 inhibitors and 398 noninhibitors. Since the best balanced accuracy of this model was 0.59, the predictivity was numerically moderate; however, this research for the first time utilized structural information in MATE1 activity modelling . The most recent models also used structural information: In one study performed in early 2021, although there was no construction of predictive models, the authors built a homology model of hMATE1 from PDB entry 3MKT (the multidrug transport protein NorM from Vibrio cholerae) .
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65eeac0a66c1381729b9206e
| 2 |
In subsequent work performed in late 2021, Alphafold2 was used to build a MATE1 protein structure, which resulted in a pharmacophore classification model with an accuracy 0.51 . In this research the authors also built a machine learning classification model using Neural Networks (with an accuracy of 0.83) and Support Vector Machines (with an accuracy 0.75). Although the accuracies were relatively high numerically, the thresholds of active/inactive were derived from percentage inhibition values (here of less than 10% and more than 50% inhibition), which is on the one hand not a quantitative inhibition value, and performance values were likely inflated due to the range of activities in between the thresholds not considered in the model. Also, the compounds used for modeling were limited to 58 tyrosine kinase inhibitors, which would not allow for model application across wider chemical space. Based on these related works, all of them are classification models; however, in practice often two-class models are not sufficient for decision making, which also agrees with regulatory guidelines . To sum up these related works, on the one hand we can find the difficulty of the construction of regression models, assuming due to the shortage of reliable experimental data. On the other hand, the progress of utilizing structural information can be seen as a promising method for the prediction of inhibitory activity of MATE1.
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65eeac0a66c1381729b9206e
| 3 |
Based on the above related work, in this study we aimed to identify a new approach, based jointly on ligand features, and ligand-protein interaction scores. While docking scores have been used frequently in particular in high-throughput settings, correlations with quantitative activity are not always a given , which is why in this work instead of docking we used Molecular Mechanics with Generalised Born and Surface Area solvation (MM-GB/SA) scores as a more accurate scoring function of binding affinity . MM-GB/SA includes the interaction between not only ligand and receptor but also receptor and solvent (water) when calculating enthalpy (ΔH), and also entropy (ΔS) . Practically MM-GB/SA is often used in the drug discovery process where better estimates of affinity are needed, which is also why we used it in the current work.
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65eeac0a66c1381729b9206e
| 4 |
In this study considering both the importance of the exact values from IC50 or Ki data and the difficulty of the constructing of regression model, we hence built in silico models for the classification with the practical threshold of the inhibitory activity (10 μmol/L) against MATE1 using three different types of information to explore their information content, namely a MM-GB/SA model by itself, a machine learning model based on ligand chemical descriptors, and finally a machine learning model utilizing both ligand chemical descriptors and MM-GB/SA scores.
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65eeac0a66c1381729b9206e
| 5 |
The workflow in this study is shown in Figure . The compounds in the dataset were docked and the binding energies were calculated by MM-GB/SA method. Then, the fingerprints were also calculated and used for ML model. Additionally, a ML model which combines MM-GB/SA scores and fingerprints were built. The explanation of each step in detail was described below.
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65eeac0a66c1381729b9206e
| 6 |
For the MATE1 inhibitors that have showed clinically relevant DDI with metformin, most of inhibitors have the Ki value of less than 10 μmol/L for MATE1 such as cimetidine, pyrimethamine, trimethoprim, and vandetanib (isabuconazole and ranolazine have no data for Ki against metformin in this report) . IC50 can be converted to Ki using the Cheng-Prusoff equation assuming the competitive inhibition ;
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65eeac0a66c1381729b9206e
| 7 |
Therefore, collected IC50 were used assuming they equal Ki. Therefore, in this study 10 μmol/L was set as the reference criteria to judge whether the MATE1-mediated DDI risk can be negligible or not. In total the number of compounds labelled as positive (inhibitor) is 101, and as negative (non-inhibitor) is 124. We investigated the chemical space present in the dataset comparing United States Food and Drug Administration (FDA) approved drugs from DrugBank (version5.1.8) through using Uniform Manifold Approximation and Projection (UMAP) . For the input we calculated a similarity matrix with ECFP4 (1,024 bit, radius: 2) chemical descriptors 36 . ECFP4 was calculated using the corresponding RDKit (version 2020.09.01) Chem functions 37 AllChem.
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65eeac0a66c1381729b9206e
| 8 |
Since no human MATE1 protein structures solved, the AlphaFold 38 model of human MATE1 was used as a template of docking simulations. The model (AF-Q96FL8-F1-model_v4.pdb) was downloaded and processed for docking by assigning bond orders, adding hydrogen atoms and optimization of hydrogen atom positions, followed by optimization of hydrogen bond and whole complex energy minimization using the protein preparation wizard of Schrodinger Suite 2021-2 .
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65eeac0a66c1381729b9206e
| 9 |
Before docking simulation, sitemap was used for the identification of the binding site of MATE1 (Schrodinger Suite 2021-2) . The site with highest SiteScore was selected as the binding site (Figure ). We used the Glide SP 16 , using the OPLS-2005 41 force field and the following parameters: a protein van der Waals (vdW) radius scaling of 1.0, a ligand vdW radius scaling of 0.80, and a grid size (centered on the amino acid residues within 4 Å of the ligand in the cocrystallized X-ray structure) of 10 ×10× 10 Å 3 (Figure ). Regarding ligands, using the SMILES strings mentioned before, three-dimensional conformations were generated using LigPrep (pH 7 was set for protonation state calculation) , followed by multiple conformer generation using Confgen 43 . In cases of multiple possible stereoisomers, tautomer, protonation states for a single ligand, we selected the one which corresponds to the minimum energy conformation. Docking was performed without specific interaction controls with individual amino acids in GLIDE generating the one lowest energy docking pose per ligand.
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