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Parameter selection: data augmentation, dropout and temperature Data augmentation, the practice of artificially increasing the volume of training data to improve model performance, was implemented by altering the starting position of the marker, allowing the model to learn from any point within the SMILES encoding. Comparative analysis showed that quintupling the data augmentation in the last five training cycles yielded the best effectiveness and novelty in the generated compounds (Fig. ).
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Dropout, a technique to combat overfitting by deactivating a subset of neurons during training, slows down the training rate as the dropout value increases. After altering the dropout value, the overall model showed no significant difference in molecular generation outcomes, leading to the selection of an intermediate value of 0.3 (Fig. ).
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The model, trained in this study, employed temperature sampling for SMILES encoding. At lower temperature values, token generation is primarily based on estimated probabilities. However, as the temperature value increases, token generation tends towards uniform probability selection. The effectiveness of generating new molecules decreases with higher temperature values due to the increased randomness of token generation, leading to errors in the SMILES strings, such as missing or mismatched parentheses or ring closures. Nonetheless, higher temperature values exhibited superior performance in terms of the novelty and effectiveness of generated molecules. This is attributed to the increased randomness of token generation, which enhances molecular diversity and expands the explorable chemical space. In this experiment, the model demonstrated optimal uniqueness and novelty in generated molecules at a temperature value of 1.1 (Fig. ).
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In this section we compare the properties of the molecules generated by the pre-trained and finetuned models, as well as the properties of the molecules in the pre-trained and fine-tuned datasets. We randomly select 100 molecules from each molecule source to analyse (if the number of molecules from a source is less than 100, all molecules are used) and compare the properties of these molecules separately. In Fig. , the molecules in the ChemBridge-MPO dataset have the highest average MPO scores, while the molecules generated by the pre-trained model have the next highest MPO scores. This indicates that CNSMolGen as a molecule generation model has a strong learning capability to effectively master the rules of molecular SMILES representation and accurately capture the features of CNS molecules. In addition, the average MPO scores of the model-generated molecules decreased after transfer learning, which may be related to the lower average MPO scores of the molecules in the transfer learning dataset. Nevertheless, the MPO scores of the molecules generated after transfer learning were still high and met the MPO criteria for CNS drugs, indicating that they are potential CNS drug candidates. It is important to note that of all the parameters affecting CNS scores, the molecules generated by deep learning had lower scores for LogP and LogD, suggesting future improvement of molecule generation models.
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To investigate how the selection of pre-trained datasets affects the molecular design capability of CNSMolGen, two additional datasets were selected for analysis, the ChemBL-MPO dataset and the ChemBL-ACT dataset. A detailed description of the ChemBL-MPO dataset and the ChemBL-ACT dataset collection methods can be found in the Supporting Information. We trained these two datasets using the same training procedure and default parameter settings and compared the results of the molecules generated. The results show that CNSMolGen based on the ChemBridge-MPO dataset performs best.
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In this study, we used different pre-training datasets as well as a unified transfer learning dataset to train the CNSMolGen model and compared the results for the compounds generated (Table ). The results showed that the model generated the highest number of new compounds when using the ChemBridge-MPO dataset, followed by the use of the ChemBL-smiles dataset, while the lowest number of new compounds was generated when using the ChemBL-MPO dataset. This phenomenon may be related to the number and diversity of compounds in the datasets. The SAScore of the three datasets were further analyzed, and it was found that the average SA scores of the compounds when using the ChemBridge-MPO, ChemBL-MPO and ChemBL-smiles datasets were 2.77, 2.69 and 2.63, respectively, which were relatively close and with low mean values, suggesting that different training datasets have a synthetic approachability is limited. Subsequently, we compared the CNS scores of the three datasets and found that the average CNS scores corresponding to the ChemBridge-MPO, ChemBL-MPO and ChemBL-smiles datasets were 4.15, 4.19 and 4.35, respectively, which suggests that differences in the training datasets do not affect the chemical properties of compounds generated by the model. This suggests that the change in the pre-trained dataset does not have an impact on the final properties of molecule generation, but it is worth noting that the largest number of molecules were generated after transfer learning when ChemBridge-MPO was selected as the pre-trained dataset, followed by ChemBL-MPO. We analyzed this to be due to the fact that ChemBridge-MPO contains more data, while the molecules in ChemBL-MPO are more consistent with the results of transfer learning. This result suggests that the size of the original dataset will have a more direct impact on the final generated results during the transfer learning process. The selection of suitable similar datasets will also have a good impact on the generation of molecules. In order to entirely evaluate the promising application of the CNSMolGen in the field of CNS drug design, the 215 candidate molecules generated from the fine-tuned model were submitted for a comparative analysis of their binding modes and binding affinities to target protein SERT . Notably, four approved drugs that cocrystalized with SERT were used as controls. They are escitalopram-SERT (PDB ID: 5I71) , sertraline-SERT (PDB ID: 6AWO) , fluvoxamine-SERT (PDB ID: 6AWP) , and paroxetine (PDB ID: 6W2C) , respectively. Here, all of the 215 molecules were first docked into the ibogaine binding pocket of SERT by considering the pocket flexibility. And the ibogaine binding site was selected because of the relatively large volume of the pocket , which were more suitable for IFD study of molecules with different scaffolds. As a result, the redocking scores of escitalopram, sertraline, fluvoxamine, and paroxetine were -9.771 kcal/mol, -9.403 kcal/mol, -8.448 kcal/mol, and -8.467 kcal/mol, respectively (Fig. ). For all of the 215 generated molecules, using the docking score of fluvoxamine (-8.448 kcal/mol) and escitalopram (-9.771 kcal/mol) as a reference, the number of generated molecules that have potential higher binding affinities were 129 (60.00%) and 89 (41.40%), respectively. Thus, compared to the known SSRI molecules, the generated molecules (e.g., compounds 1 (-10.435 kcal/mol) and 2 (-10.453 kcal/mol)) may have comparable or even better binding affinities. The detailed binding mode of the compounds 1 and 2 in SERT were shown in Fig. and 8B. Among them, the ligand-receptor interaction of compound 1 is mainly due to the hydrogen bond interaction formed by amino acid residues Y95, A96, S336 with the ligand; compound 2 is mainly due to the hydrogen bond interaction of D98, F335 with the ligand. In addition, it was found that although the generated molecules have different structures from the approved drugs, they share similar binding conformations at the pocket (Fig. and). Despite the inherent limitations of molecular docking techniques, the results of this study suggest that the CNSMolGen opens up new possibilities for drug design targeting SERT. However, the actual biological effects of the generated molecules on SERT need to be further verified by subsequent experimental studies.
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In this study, we introduce CNSMolGen -a novel molecular generation model designed to design central nervous system (CNS) drugs from scratch. The model combines pre-training and transfer learning to generate new compounds with CNS activity by learning the SMILES strings of the molecules and shows superior performance on small datasets, opening up new avenues for drug design. Further, we investigated the effect of using different pre-training datasets on the model performance and found that pre-training on large datasets helps to improve the performance of the generated molecules, while pre-training on CNS-specific datasets is more favorable for generating molecules with CNS properties. The application of CNSMolGen in the actual generation of CNS drug molecules was validated using SSRI as an example. The model generated a total of 215 molecules, 129 of which showed good binding affinity in molecular docking. In conclusion, the CNSMolGen model demonstrated significant effectiveness in generating CNS drugs, especially in handling small datasets, and also demonstrated its potential to provide valuable support for future drug design and discovery. With the increasing role of AI tools in drug design and optimization, experimental validation of their results remains indispensable.
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Benzalkonium chlorides (BACs) have been of environmental concern because of their widespread use and potential harm to ecological and human health. Since the registration of the first product containing BACs in the US in 1947, the BACs production has risen for a broad range of applications, including biocides, antiseptics, disinfectants, personal care products, cosmetics, pharmaceuticals, and medical/building materials. Particularly, the ban of triclosan and triclocarban in antibacterial soaps by the US Food and Drug Administration (FDA) in 2016 and the global pandemic of COVID-19 beginning in 2020 have further promoted the use of BACs. BACs are one of the most common groups of cationic surfactants, characterized by a positively charged quaternary ammonium nitrogen atom bonded with a benzyl group and an alkyl chain (C6-C18). Their amphiphilic properties enable them to adhere to solid phases that are predominantly negatively charged such as sediment, soil, sewage sludge, and laboratory glassware. Literature studies have extensively reported the detection of BACs in the aquatic environment, which are primarily composed of BAC homologs with alkyl chain lengths of 12-18 carbons. Surface water concentrations of BACs were typically in the µg/L range; e.g., Taiwanese rivers from 2.5 to 65 µg/L 9 , U.S. stream water from 1.22 to 3.28 µg/L 10 , river water in Spain > 0.1 µg/L 11 and Polish surface water from 72.8 to 331 µg/L. Because of the strong sorption properties, sediment and sewage sludge concentrations can be high, reportedly up to 21 and 191 mg/kg, respectively. Previous studies have documented the toxicity of BACs to aquatic organisms such as fish, crustaceans, 8, 17-19 algae, and bacteria. Despite the findings raising concerns about the potential threat of BACs to the ecological system, the existing database on the toxicity of BACs to aquatic organisms remains unsatisfactory.
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The most common experimental approach in aquatic toxicity testing is to spike the exposure medium directly with the pure substance for sufficiently water-soluble organic compounds, or with a biocompatible and water-soluble solvent as an intermediate for poorly water-soluble organic compounds. However, defining and controlling their bioavailable, freely dissolved concentrations (Cfree) is a challenge for strongly sorptive compounds, including cationic surfactants. Cfree, which is usually not measured in toxicity tests, may be lower than the nominal concentration (Cnom) because of sorption of the chemical to dissolved organic matter, glass surfaces, and test organisms or degradation during the testing time, resulting in low test accuracy. Therefore, such toxicity data of the chemicals might not be reliable and useful for environmental risk assessments, and there is an urgent need for new approaches to overcome these challenges in existing test protocols.
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Passive dosing is an alternative approach based on the equilibrium partitioning concept introduced in toxicity testing and could solve the challenges mentioned above. The method typically uses a polymer sorbent phase that is biocompatible, does not react with the test chemical, and acts as a chemical partitioning source to the exposure medium. The passive dosing method is expected to have several advantages when applied in ecotoxicity testing. For instance, Cfree can be defined and controlled based on the partitioning equilibrium between the passive dosing phase and exposure medium (i.e., with a partition coefficient between the sorbent and water phases, Ksorbent/water). Moreover, there is no oversaturation/precipitation issue, and spiking solvent can be avoided. Cfree can remain constant throughout the test if the sorbent material has a large enough sorption capacity for the test chemical (i.e., high mass or volume and high Ksorbent/water), even if some chemical loss occurs, e.g., due to degradation. Cfree is measured directly in the medium sample or, if not possible, can be estimated from Csorbent and known Ksorbent/water, improving the reliability of toxicity data. Passive dosing methods have been successfully applied in toxicity testing for nonpolar hydrophobic organic compounds such as polycyclic aromatic hydrocarbons. However, sorption mechanisms of ionic compounds are different from those of nonpolar hydrophobic compounds and a passive dosing method for ionic compounds has not been established yet. Although passive sampling methods have recently been applied in ecotoxicity tests to obtain Cfree forBACs, 8, 40 , to the best of our knowledge, there is no prior research on a passive dosing method for cationic chemicals, including cationic surfactants with a long alkyl chain (i.e., #C ≥14), for which a tool to control the aqueous exposure concentration is urgently required.
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membranes (Fumasep FKE and FKS membranes), C18 solid phase microextraction LC (C18 SPME) fiber, and styrene-divinylbenzene (XAD2) resin. These sorbents were considered candidates because of their relatively high surface area (meshes, porous materials), known high sorption properties for ionic chemicals (C18), and/or cation exchange properties. Additional information on the chemicals, materials and cleaning procedure can be found in the Supporting Information (SI, Section S1, Table and). Solvents were purchased from Fujifilm Wako Chemicals (Osaka, Japan) and were of GC or LC/MS grade. Formic acid, ammonium formate, both of LC-MS grade, were purchased from Fujifilm Wako Pure Chemical Corporation (Osaka, Japan). Ultrapure water of LC/MS grade (Fujifilm Wako Chemicals) or reverseosmosis-treated tap water further purified with an Ultrapure Water System (RFU665DA, Advantec, Tokyo, Japan) was used in the loading experiment. For the ecotoxicity tests, tap water dechlorinated with activated charcoal was employed as exposure medium. All glass materials used in this study were baked at 450 °C for 4 h.
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Comparing sorption capacity of sorbent materials. Batch sorption experiments were carried out to screen the sorbents for their sorption capacity as a potential passive dosing reservoir. The detailed procedure is presented in Section S2, SI. Briefly, in a 20 mL amber glass vial, sorbent was immersed in 10 mL of 100 µg/L of C12-BAC in 5 mM CaCl2 solution (except a HPTLC piece, which was placed in a 50 mL glass beaker covered tightly with aluminum foil). After shaking for 24 h (i.e., for PES membrane, HPTLC plate, C18 fiber, SDB RSP membrane, C18 membrane, FKS, FKE and XAD2) or 72 h (i.e., for PE mesh, Nylon mesh, PET mesh, PPS mesh), water samples were taken and quantified by liquid chromatography-tandem mass spectrometry (LC-MS/MS) as described in Section S6, SI. The concentration in the sorbents was obtained based on the mass balance calculation. The experiment was performed in duplicate.
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Loading of BACs on PES membrane. Due to the cost and the large number of PES pieces required for the acute toxicity test, a roll of PES membrane (300 mm × 3 m, 0.1 μm pore size) purchased from GVS (Bologna, Italy), which has similar mechanical properties and the same pore size as the PES membranes used for the sorption experiments, was cut into pieces and used as passive dosing reservoirs for the following tests. For loading of BACs onto the membranes, six cleaned PES pieces of 3.5 × 3.5 cm 2 each were immersed in a 20% (v/v) methanol/water mixture with defined concentrations of a single chemical in a glass beaker at 25°C. After 24 h of shaking, water was added to each beaker to enhance the loading efficiency, yielding a total loading volume of 10 mL and a final fraction of methanol in the solution of 13.33% (v/v). The loading beakers were shaken horizontally at 150 rpm for 4 days. After loading, the PES membranes were rinsed in excess water to remove adhered loading solution and then dried in the fume hood for at least 4 h to ensure that all methanol evaporated before transfer to the clean glass beakers for the desorption and ecotoxicity tests described below. PES membrane extraction was conducted for checking the loading efficiency of C14-, C16-and C18-BACs (further details in Section S3, SI).
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Desorption kinetics and equilibrium. The desorption behavior of BACs from the PES membrane was examined to determine the pre-equilibration time. Dechlorinated tap water (hardness: ~80 mg-CaCO3/L) was selected as the exposure medium. Note that use of Elendt M4 synthetic medium resulted in lowering of the aqueous phase concentration of C14-BAC, likely due to degradation, and thus this medium was not used. In this desorption experiment, a loaded PES piece was placed in a 50 mL glass beaker, which received 50 mL of dechlorinated water and was shaken at 135 rpm, 25°C for 5 days (C14-BAC) and 7 days (C16-BAC). Note also that a piece of polyacrylate (PA) microfiber was put in the beaker for passive sampling but the results of this will be reported elsewhere. At desired time intervals, 0.5 mL water sample was taken with a glass pipette after five times aspirating and dispensing for pre-wetting of the pipette and was further diluted with 0.5 mL of acetonitrile (ACN) containing internal standard (100 µg/L) to measure the water concentration (Cw) of BACs. After the desorption test, the PES membranes were extracted two times with 0.1% formic acid/ACN at 150 rpm and 25°C for 24 h each. Then, all the dechlorinated water was replaced by 5 mL of 0.1% formic acid/ACN mixture to extract the wall of the glass beaker (2-3 h, 25°C, 150 rpm).
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The PES and glass beaker extracts were diluted with ACN/internal standard before subjected to LC-MS/MS analysis (Section S6, SI). The acute ecotoxicity test with D. magna was performed following OECD Test Guideline 202. Neonates less than 24 h old were exposed to a single BAC homolog at five concentrations and a control (with or without methanol), with 5 newborns in each of four replicate beakers. Test solutions were prepared by dissolving pure solid in water (C6-BAC), by diluting methanol stock solutions with water in a 300 mL flask before transferring to test beakers (C8-, C10-BACs), or by directly adding methanol stocks to water in test beakers (C12-C18-BACs), considering that longer chain BACs are more susceptible to losses during solution preparation. For all BACs except C6, the final methanol concentration in water was 0.01% (v/v).
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The test solutions were shaken at 150 rpm, 25°C for 24 h to dissolve the BAC in water. The preparation of the test solutions is described in more detail in Section S4, SI. The test system was set up with 50 mL dechlorinated tap water (pH: ~8) under light-dark cycles of 16:8 h at 21°C, following the culture conditions. Food and aeration were not provided throughout the acute ecotoxicity test. The test solutions were not changed during the exposure. The acute toxicity test was performed for 48 h without shaking. After 24 and 48 h, immobilization of the daphnids was determined by gently shaking the water and checking their movement for 15 s. Cw of the BAC were measured just before adding D. magna and at the end of the 48 h acute toxicity test. In some toxicity tests, dissolved organic carbon (DOC) was measured before adding daphnids and at the end of the ecotoxicity test (further details in Section S5, SI). Water quality was measured before and after the acute toxicity test (see Table ). EC50 values were obtained based on the 2-parameter log-logistic model in the drm() function of the R-package drc (version R 4.2.2, R Core Team, 2022). For each exposure level, the arithmetic mean of the measured Cw at the start and end was used for the EC50 estimation.
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Acute ecotoxicity tests with passive dosing method. The ecotoxicity test was conducted for C14-, C16-and C18-BACs using the passive dosing approach because these long alkyl chain BACs were expected to be more susceptible to chemical loss processes such as sorption onto the glass vessels and formation of micelles in exposure solution than shorter analogs. 8, The loaded PES membranes were prepared following the procedure described in the Loading experiment section. Each test beaker received a loaded PES membrane and 5 daphnids in 50 mL (C14-BAC) or 30 mL (C16-and C18-BACs) of dechlorinated water.
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The acute toxicity test was performed for 48 h without shaking after a 24 or 48 h pre-equilibrium period to allow the passive dosing system to reach equilibrium. Water was sampled every 24 h starting from just before adding daphnids to the end of the exposure experiment to observe the stability of Cw throughout the test period. A beaker containing a PES membrane that experienced the same loading procedure but without the test chemical was prepared as a control sample. The loaded PES membranes were either immediately extracted before the toxicity test or used for the toxicity test, retrieved from the beaker after 48 h exposure, and extracted to check for loss of BACs from the PES membranes to the exposure system. Beaker wall extraction was also conducted for C14-, C16-and C18-BACs after the acute ecotoxicity test, following the procedure described above.
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Sorbent selection. To be applied in the acute toxicity test, the passive dosing format should satisfy several prior requirements (i.e., inert, biocompatible, high sorption capacity for the test chemicals). As shown in Figure , the partitioning of C12-BAC from water to XAD2 resin, cation exchange membranes (FKS, FKE), C18 fiber, and all polymer meshes exhibited low log Ksorbent/water (<3). Empore disks (SDB-RPS, C18) and HPTLC sorbed C12-BAC relatively well, but the small particles detached from these materials and suspended in the aqueous phase during the experiment, which would lead to undefined exposure conditions.
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Loading of PES membrane. Efficient and uniform loading of the chemical on polymer material is a prerequisite step for the passive dosing approach. Because passive dosing would be particularly advantageous for long-chain BACs, the target substances were changed from C12-BAC to C14-, C16-and C18-BACs at this point. The actual mass of C14-, C16-and C18-BACs loaded on the PES membrane ranged from 70 to 148 % of the mass added initially to the loading solution (Figure ). Some BACs (1-30 %) remained in the loading solution, particularly when the BAC concentrations in the loading solution were high. The distribution between PES membrane and the loading solution followed the nonlinear Freundlich isotherm model (Figure ) with a Freundlich exponent of 0.23-0.43, indicating relatively weak sorption at high loading levels. C14-and C16-BACs on the glass beakers were less than 2 % of the added mass in the loading experiment (Figure ). In a preliminary loading experiment for two different exposure concentrations, the masses of C14-BAC in replicated loaded PES membranes were similar (Figure ), indicating uniform distribution to the PES membrane pieces in the loading step.
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was achieved for both C14-and C16-BACs within 24 h under gentle shaking (Figure ). Afterwards, the Cw of C14-and C16-BACs remained stable, demonstrating that the chemical supply from PES membrane is sufficient to overcome any possible mass loss (e.g., sorption onto glass beakers). The calculated logarithmic partition coefficients of BACs between PES membrane and water (KPESw) for both chemicals are greater than 4 (Table ), confirming a high sorption affinity of PES membrane for these BACs.
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Cw were lower than Cnom for BACs with alkyl chain lengths of C12-16, particularly at low concentrations (Figure , Table ). The lower Cw compared to Cnom for C12-16-BACs is partially due to sorption of the chemicals to glass vessels. Figure shows the measured recoveries for BACs from water and the glass beaker in the spiking toxicity test. Losses from 7% to 60% of the total mass due to sorption to the glass beaker were observed for C12-16-BACs. The sorption affinity for the glass beaker increases with increasing alkyl chain length of BACs, which agrees well with previous studies on sorption of BACs to glass/plastic surface. The greater loss to the glass surface at lower concentrations suggests limited sorption sites on the glass surface, which may be saturated at relatively high concentrations. At low concentrations of C12-16-BACs, 20-40% of the added mass was not recovered from either the water or glass wall, indicating the presence of another loss process. It is possible that the loss was due to the glass pipette during water sampling, even after five times aspirating and dispensing in order to equilibrate the pipette surface. Furthermore, up to 140% recoveries (water + beaker wall) of C16-and C18-BACs at high concentrations were observed for an unknown reason.
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Interestingly, the agreement between the measured and nominal concentrations was better for C18-BAC than C16-BAC. Moreover, the chemical loss of C18-BAC was not particularly high at low concentrations, in contrast to C12-16-BACs. We speculate that C18-BAC was not completely dissolved into its free form and that colloidal association might have occurred with C18-BAC in water in the presence of methanol (0.01% v/v). Thus, the measured Cw may include a fraction of C18-BAC that was not available for sorption. Note however that the critical micelle concentration (CMC) of C18-BAC in deionized distilled
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All in all, there remain several challenges to define the exposure concentration in the solvent spiking toxicity testing of BACs with a long alkyl chain. Using Cnom to calculate the effect concentrations of BACs with a long alkyl chain (#C ≥ 14) in solvent spiking tests may not provide reliable data to assess their toxicity, and even measured Cw may not represent the true bioavailable exposure concentration for C18-BAC.
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In the passive dosing tests, measured Cw values remained constant during the test period, notably, even after the addition of daphnids (Figure ). DOC concentrations in the solvent spiking test (15-24 mg/L) were higher than those in the passive dosing method (0.8-4.3 mg/L) (Table ). The presence of methanol (0.01 %, v/v) in the exposure medium caused an increase in DOC in the spiking test, whereas the exposure water in the passive dosing test contained a low concentration of DOC. Therefore, the binding of C14-18
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BACs to dissolved organic components in the test medium is considered negligible and the measured Cw is regarded as Cfree in this study. Desorption equilibrium was reached within the 24 h pre-equilibration time for C14-and C16-BACs and 48 h for C18-BAC (Figure ). Sorption to the glass beaker ranged from 0.1 to 6 % of the total measured mass (i.e., the sum of masses from water, PES membrane, and glass beaker) and increased with alkyl chain length (Figure ). The PES membrane retained >91% of the loaded BACs, indicating that the PES membrane served as a partitioning source. The calculated mean log KPESw for C14-, C16-, and C18-BACs within the tested concentration range were 4.61-4.80, 4.45-5.41 and 4.14-5.33, respectively (Table ). Sorption isotherms of C14-C18-BACs on PES membrane (Figure ) indicate that BACs with longer alkyl chain lengths have higher Freundlich coefficients and lower Freundlich exponents,
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showing their strong nonlinear sorption to PES membrane. Notably, concentration-dependent sorption of C18-BAC on PES membrane is slightly stronger than C16-BAC (Figure ). Thus, the obtained KPESw values in the investigated concentration range for C18 are not higher than those for C16, although there are two more CH2 groups in the hydrocarbon chain.
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acute toxicity test on D. magna using the solvent spiking and passive dosing approaches of BACs are compared in Figure . Neither mortality nor immobilization of D. magna was observed in the blank controls, solvent controls or controls with clean PES membrane. The experimental median effective concentration (EC50) values, which were calculated using the arithmetic mean of measured Cw at adding daphnids and at the end of the experiment for each beaker, of the studied BACs are listed in Table . Notably, there was no significant difference between the arithmetic mean and the geometric mean here. D. magna 48 h-EC50
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values have been reported for only C12-and C14-BACs in the literature, and they agree with the EC50 values obtained in this study within a factor of 2-4. 8, 19 EC50 values from the solvent spiking and passive dosing methods from this study agree well for C14-BAC (Figure ). However, the EC50 values from the passive dosing method for C16-BAC and C18-BAC are lower than those from the solvent spiking method.
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Thus, according to the solvent-spiking tests, the toxicity of BACs increases with increasing alkyl chain length up to 14 carbon atoms, beyond which the trend apparently decreases. In contrast, the EC50 values are similar with the alkyl chain length ≥ 14 carbon atoms in the passive dosing tests (Figure ). It is commonly known that toxicity of chemicals increases with increasing hydrophobicity. However, a "cutoff effect" has often been observed in toxicity of amphiphile homologous series, including cationic surfactants; that is, toxicity increases with alkyl chain length up to a certain point, above which toxicity remains more or less constant or even decreases. 20, Sorption losses to glass beakers do not explain the cutoff in this study, because we used the measured Cw to calculate the EC50. There are several possible explanations for this behavior. For long-chain cationic surfactants in the spiking tests (e.g., C18-BAC), there may be difference between the freely dissolved and total concentrations due to association with dissolved organic components or formation of micelles, resulting in low bioavailability. As mentioned, this difference is considered negligible in passive dosing methods, thereby mitigating a cutoff effect. Another possible explanation for the cutoff point could be that the time required to reach organism/water equilibrium is longer for BACs with a long chain compared to those with a short chain, and the former do not reach equilibrium within the experimental time. . This could also explain why a slight cutoff effect was observed for C14-18-BACs in the 48 h toxicity test even using the passive dosing method.
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A new passive dosing method with PES membrane was developed for the acute toxicity test on D. magna of BACs. PES membrane showed its sufficient sorption strength and fast desorption of BACs to maintain a consistent exposure concentration. This passive dosing format with PES does not need frequent exchange of exposure media and is inexpensive, biocompatible, and adaptable to a large number of samples.
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Retrosynthesis, the iterative process of breaking down a molecule into simpler precursors, has traditionally been the domain of expert organic chemists. However, even for experienced chemists, this approach presents challenges due to the vast chemical space of potential transformations and the incomplete understanding of reaction mechanisms and their dependence on reaction conditions. To overcome these challenges, efforts have persisted since the 1970s to integrate computation into synthetic planning by developing Computer-Aided Synthesis Planning (CASP) tools, with one of the earliest examples being the Logic and Heuristics Applied to Synthetic Analysis (LHASA) by Pensak et al. Despite numerous attempts, CASP tools had limited success until recently. Significant progress in CASP tools has occurred in the last decade, driven by advances in machine learning (ML) methodologies and the availability of chemical datasets, such as Lowe's US Patents Office (USPTO) reaction extracts. Following the seminal work by Segler et al. on the use of neural networks and search algorithms in the 3N-MCTS CASP tool, there has been a proliferation of new ML models for retrosynthesis prediction. These models can be broadly classified into two categories: template-based and template-free methods. Templatebased methods rely on predefined reaction rules extracted from datasets, where algorithms match a target molecule with predefined templates. CASP tools utilising such models include ASKCOS, AiZynthFinder, and Retro*. In contrast, template-free methods, such as graph-based or sequence-to-sequence (seq2seq) approaches, bypass the use of an external template database by directly training on raw reaction data. While early seq2seq models were based on long-short term memory networks (LSTMs), the breakthrough in seq2seq reaction prediction came when Schwaller et al. applied the transformer model commonly used in Natural Language Processing (NLP) for forward reaction prediction, creating the Molecular Transformer. In this case, reaction prediction is treated as a translation problem using Simplified Molecular Input Line Entry System (SMILES) strings to represent the chemical transformation. Since then, seq2seq retrosynthesis prediction models have shown high accuracies on public benchmarking test sets, with the Augumented Transformer 11 achieving 46.2% top-1 reactant accuracy on the USPTO-full dataset. The recent developments have led to transformers emerging as a premier architecture for retrosynthesis planning utilised in platforms such as IBM RXN. Despite the high efficacy of CASP tools on general reaction datasets, predicting retrosynthetic disconnections for specific, less prevalent areas of chemistry remains a significant challenge due to dataset bias. Heterocycle formation reactions are an example of underrepresented reaction classes, accounting for only 5% of reported chemical reactions in the USPTO dataset. However, heterocycles are key motifs in drug design, with 85% of the top 200 best-selling small molecule drugs of 2022 featuring heterocyclic rings, where they act as bioisosteric replacements improving pharmacokinetic and toxicological properties of drug targets. Although numerous virtual libraries document theoretically synthesisable heterocyclic scaffolds, synthetic pathways towards novel heterocycles remain underexplored, with the focus in medicinal chemistry being on ring derivatisation rather than ring formation. Enhancing the prediction capacity of CASP tools for reactions forming these crucial chemical motifs could stimulate the exploration of novel heterocyclic molecules, potentially fuelling new therapeutic breakthroughs. This work aims to enhance the performance of CASP tools for heterocycle retrosynthesis by combining seq2seq models and transfer learning, where knowledge learned from one task is used to boost the performance on a related task (Figure ). Two transfer learning approaches, fine-tuning and multi-task learning, have been previously successfully applied for the forward reaction prediction of carbohydrate reactions and Heck reactions, as well as forward and retrosynthesis prediction of enzymatic reactions (Figure ). However, both of those approaches come with limitations. For example, in the reported examples, fine-tuning has shown a quick training time and increased accuracy for reactions of interest but exhibited a large drop in performance for other, more common reaction types. Conversely, multi-task learning maintained good performance on all reaction types but required longer training time, making it less suitable for frequent retraining as new reaction data becomes available. To address these limitations, here we evaluate mixed fine-tuning 31 and ensemble decoding, which have previously proven effective in language translation tasks but have not been used in retrosynthesis prediction (Figure ). We compare those methods to the template-based approach reported by Thakkar et al. specifically for ring-forming reaction prediction in the 'Ring Breaker'. We use two datasets to train these models: a large dataset of all reaction types based on USPTO ("General ") and a smaller dataset of just heterocycle formations ("Ring"). We show that the mixed fine-tuned model is the best for use in multi-step retrosynthesis, with 10% increase in accuracy over the baseline for heterocycle formations and only a marginal decrease in performance for other reactions. We then further demonstrate its applicability by predicting retrosynthetic routes towards two recently published heterocycle-containing drug-like targets. Finally, we test the mixed-fine tuned model on recently developed heterocycle formations and demonstrate how it can be further fine-tuned to improve its accuracy on this new data.
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In this study, we utilised the USPTO dataset pre-processed by Pesciullesi et al., which is henceforth referred to as the General dataset. Additionally, we curated a dataset of 165,216 ring formation reactions, referred here to as the Ring dataset, comprising about 80k reactions extracted from academic journals (CJHIF dataset ) and 80k reactions from additional patent data (Pistachio dataset). The creation of the Ring dataset is described in more detail in SI §S4. A visualisation of the chemical space of the datasets is included in the SI (Figure ), showing that ring-breaking reactions occupy distinct areas of the chemical space.
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The Ring dataset was split into train, validation, and test sets with 90:5:5 ratio based on the Tanimoto similarity of reaction products using DeepChem. The General dataset splitting was retained from the work of Pesciullesi et al. Additionally, we performed a random split of the Ring dataset and trained the mixed fine-tuned model on the randomly split dataset to assess the effect of dataset splitting (SI §S8).
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We trained the single-step retrosynthesis prediction models based on the seq2seq Transformer architecture using the OpenNMT-py package. All hyperparameters used here are provided in the SI §S1 and are based on the work of Pesciullesi et al. We trained the baseline model on only the General dataset. As fine-tuning and multi-task learning have been previously used for reaction prediction, we adopted the parameters previously reported for these models. For the multi-task model, we used a dataset weight ratio of 9 (General ):1 (Ring). For the fine-tuned model, the number of fine-tuning steps was set to 6,000. For mixed fine-tuning, a 1:1 dataset weight ratio and 6,000 fine-tuning steps were chosen after a benchmark (SI §S7). Ensemble decoding was performed with in-built OpenNMT-py functionality using the fine-tuned model and the baseline model.
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Furthermore, we trained a single-step template-based retrosynthesis prediction model on only ring-forming reactions based on the approach used by Thakkar et al. in 'Ring Breaker'. Our dataset comprised reactions from the Ring dataset and ring formations extracted from the General (USPTO 5 ) dataset. Atom-mapping of reaction data was conducted using RXNMapper, and reaction templates were subsequently extracted using RDKit 39 and RDChiral. We used TensorFlow 41 to construct the multilabel classification neural network for prediction. The selected hyperparameters are provided in the SI §S2.
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The single-step retrosynthesis prediction models were evaluated on both the General and Ring test sets using metrics based on top-N accuracy and round-trip accuracy. For the Ring test set, we calculate reactant-only accuracy, where the prediction is considered accurate if all the ground truth reactants are present. For the General test set, due to the lack of separation between reactants and reagents, we calculate top-N accuracy by directly comparing the set of predicted precursors to the ground truth. We also consider the round-trip accuracy 10 of the suggested disconnections, which represent the "chemical validity" of predictions, i.e. what proportion of predicted reactant sets are expected to produce the desired product.
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Additionally, we introduce a new metric: the ring-breaking round-trip accuracy, calculated only for the "Ring" dataset. A disconnection is considered to be ring-breaking round-trip accurate when it is round-trip accurate and the number of rings in the product is higher than in predicted reactants. In this way, we consider not only whether the prediction is chemically valid but also whether it involves a ring disconnection, i.e. the reaction type we're aiming to improve the model's performance for.
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We extracted a set of 1,475 heterocycle formations from 47 scientific publications from 2022 reporting new methodologies for heterocycle synthesis(SI §S11). This dataset (referred to as the Recent dataset) was split randomly into a train, validation and test sets with a ratio of 80:10:10. Further fine-tuning was carried out using the mixed fine-tuning approach, starting from the mixed fine-tuned model and training it for 6,000 steps on the General , Ring and Recent datasets with a 4:4:1 dataset weight ratio.
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We commenced our study by comparing the performance of different transfer learning approaches, focusing on methods previously used for chemical reaction prediction (i.e., multitask learning and fine-tuning) and methods employed in the NLP domain (mixed fine-tuning and ensemble decoding) (Figure ). The comparison is conducted on the Ring test set to assess their performance in predicting ring-breaking reactions compared to a baseline model trained only on the General dataset (Figure ). In addition to the commonly used reactantaccuracy, we also consider whether the prediction was chemically valid and corresponded to a ring-breaking reaction. This identifies predictions that differ from the ground truth disconnection present in the test set but still disconnect the ring.
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The three other approaches also show improvement over the baseline model with top-1 reactant-accuracies of around 36% and 62% valid ring-breaking top-1 predictions. While the observed improvement over baseline isn't as high as reported in previous studies (13.6% increase in accuracy for fine-tuned model here vs 27.0% for carbohydrate reactions and 28.6% for Heck reactions), there are two key aspects to note. Firstly, the mentioned studies used transfer learning for forward reaction prediction, not retrosynthesis, which is considered to be a much easier task, only having one "correct" answer. Moreover, heterocycle formations are a much larger and more diverse class of reactions than Heck reactions or even carbohydrate reactions, making it more difficult for the model to learn all the different reactivity. Interestingly, even though each of our approaches increases the proportion of top-1 valid ring-breaking predictions by at least 7% when compared to the baseline model, the same trend is not observed when considering just the top-1 round-trip accuracy of the predictions (SI §S9). For example, for the mixed fine-tuned model, the ring-breaking round-trip accuracy increases by over 10%, while the round-trip accuracy decreases by 1%. The same trend can be observed for all other approaches apart from the multi-task model, where the round-trip accurcay increases but not as much as the ring-breaking round-trip accuracy (SIS9). This indicates that the main improvement between the various models trained using transfer learning and the baseline model is in the type of disconnection suggested, i.e. ring-breaking versus more common reaction types, and not in turning chemically invalid disconnections into valid ones. It also suggests that while the molecules in the Ring test set were synthesized using ring formation reactions, there are other chemically viable disconnections available. Indeed, comparing the predictions of the baseline and mixed fine-tuned model revealed that the former often suggested more common reaction types, such as functional group interconversions (FGIs) or protection/deprotections, instead of the ground-truth heterocycle formation predicted by the mixed fine-tuned (Figure ). For instance, in example 4A. the mixed fine-tuned model correctly identifies a click reaction to generate the triazole from two fragments of similar complexity. In contrast, the baseline model only suggests a more trivial N-alkylation reaction. Similarly, for 4B. the mixed fine-tuned model suggests a condensation reaction to form the central benzimidazole ring, while the baseline model suggests a functional group interconversion, which would be more suitable earlier in the synthetic route. In 4C. and 4D. the baseline model predicts simple halogenation reactions rather than ring disconnections.
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Interestingly, although the mixed fine-tuned model's prediction is accurate for 4D., it was not counted as round-trip accurate due to the forward model predicting a condensation reaction with both the carboxylic acid and the nitro group instead of just a single condensation with the former. This highlights a limitation of metrics based on round-trip accuracy, where the model's prediction is only assessed by another model that is not 100% accurate instead of comparing the prediction to those reported in the literature or assessed by skilled organic chemists. Finally, in 4E. the mixed fine-tuned model correctly predicts the disconnection of indazole, while the baseline model suggests a Boc protection of the nitrogen without simplifying the molecule. While the ability of the model to suggest protection reactions is notable, as they are crucial parts of synthetic routes, this specific protection is unnecessary and might lead the model to predict a cycle of protection/deprotection reactions, preventing further disconnections of the molecule.
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When tested on the General test set, the models exhibit almost the opposite trend (Figure ). Performance of the fine-tuned model drastically decreases compared to the baseline model, with the top-1 accuracy dropping from 14.5% to 2.7% and top-1 round-trip accuracy from 87.4% to 52.6%. Meanwhile, the metrics for the mixed fine-tuned and multi-task model only change marginally, dropping by at most 2%. Ensemble decoding falls in between, with a top-1 accuracy of 9.3% and round-trip accuracy of 77.9%. The drop in performance observed with the fine-tuned model can most likely be attributed to catastrophic forgetting, the tendency of NNs to forget previously learned information when trained on new data. This drop can be disregarded if the model is only intended for one-step ring disconnection. However, it becomes problematic for multi-step retrosynthesis as the fine-tuned model will not be able to disconnect the linear intermediates obtained after disconnecting the ring. In that case, either the mixed fine-tuned or multi-task model would be more suitable.
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Considering time and resources, mixed fine-tuning appears preferable due to its 40 times shorter training time and comparable performance to multi-task learning, especially if planning to frequently retrain the model as new data becomes available. Ensemble decoding employs two models to make the prediction, and therefore, it takes longer at inference than the other three methods.
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Overall, both multi-task learning and mixed fine-tuning show improved performance for ring-breaking disconnections while retaining the ability to predict other reaction classes, with mixed fine-tuning being preferable due to shorter training time. While the fine-tuned model performs best for heterocycle disconnections, it is not suitable for multi-step retrosynthesis due to catastrophic forgetting. Ensemble decoding ranks in the middle, not being as good at ring disconnections as the fine-tuned model, but also performing worse for other reaction classes than the mixed fine-tuned model. Due to this, we perform all further experiments and comparisons with the mixed fine-tuned model, as the most versatile and best performing one.
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The mixed fine-tuned model was further benchmarked against 'Ring Breaker', the templatebased model trained specifically for heterocycle retrosynthesis. To allow for fair comparison, we re-trained 'Ring Breaker' with our additionally extracted ring formation data, using the whole Ring dataset and ring formation reactions from the General dataset. We compared the performance of the mixed fine-tuned model to this ring-breaking specific template-based model.
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In terms of reactant-accuracy, both the mixed fine-tuned and the template-based model have similar top-1 reactant-accuracies (Figure ), with the template-based model's reactantaccuracy being slightly higher. However, the mixed fine-tuned model has significantly higher top-1 round-trip accuracy. These trends remain consistent across top-3 and top-5 predictions (SI §S9). Moreover, the round-trip accuracies for the template-based model decrease rapidly from top-1 to top-5, from 53.4% to 31.8%, while the mixed fine-tuned model maintains high round-trip accuracy from top-1 (74.6%) to top-5 (71.8%) (Table ). The mixed fine-tuned model also suggests a higher overall proportion of chemically valid ring-breaking disconnections (defined in Methods), with 59.9% for the mixed fine-tuned model compared to 30.8% for the template-based model in the first 5 predictions (SI §S9). Additionally, the mixed fine-tuned model maintains considerable accuracy on the General test set, while the template-based model achieves a low top-1 accuracy of 0.5%. Furthermore, we observe that the template-based model generates a larger proportion of non-admissible predictions of 'None', with 48.8% of top-5 predictions being inadmissible, Overall, our results demonstrate that the mixed fine-tuned model significantly outperforms the template-based model in round-trip accuracy, suggesting more diverse disconnections for both general and ring-breaking disconnections, making it the preferred choice for multi-step retrosynthesis as discussed in the following section. However, it is important to note that the forward reaction prediction model used for calculating round-trip accuracy is of the same architecture as the mixed fine-tuned model and is trained on the same reaction data (but with reversed labels). This could be biasing the metric towards the mixed fine-tuned model and mean that the difference in round-trip accuracy between the mixed fine-tuned model and the template-based model is not as significant as it seems. A more objective way of calculating metrics such as round-trip accuracy could be to use a different model to predict reaction viability instead of the forward reaction prediction model, however we were not able to train such a model for this work due to lack of negative reaction data.
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To assess the practical use of the mixed fine-tuned model in synthesis planning for drug-like targets, we constructed a multi-step retrosynthesis prediction tool using neural-guided A* Search, based on the algorithm used in Retro*. The two drug-like targets included CZS-035 and ADD (Figure ), for which syntheses were reported in 2023. The exact reactions employed in these synthesis are therefore absent in our training set, which contains reactions from patents and literature up to 2022. For comparison, we also built an analogous multi-step retrosynthesis tool employing the baseline single-step model, maintaining identical search settings.
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The first case study, CZS-035, is a ligand for polo-like kinase 4 (PLK4) and a warhead component used to synthesise a therapeutic PROTAC for breast cancer treatment, discovered by Sun et al. (Figure ). Both the baseline and mixed fine-tuned multi-step models successfully identify retrosynthetic routes for CZS-035 from purchasable precursors in our stock molecule database. Both models accurately reproduce the protection of nitrogen with Boc (A1) as seen in the literature synthesis. Both models also correctly identify the two S N Ar disconnections used in the literature to reproduce B1 and B2. However, the mixed fine-tuned model uniquely identifies the final ring disconnection of pyrazole in B1 to C1 and C2, which aligns with the literature approach. In contrast, the baseline model suggests the more complex and more expensive pyrazolopyrimidine C3 as the final purchasable precursor.
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This result showcases the enhanced performance of the mixed fine-tuned model for predicting key ring disconnections for multi-step routes, overcoming catastrophic forgetting and correctly identifying all non-ring breaking disconnections of CZS-035. We note that the ability of seq2seq models over template-based models to simultaneously suggest protections and S N Ar disconnections in different sites as in A1 is a unique advantage.
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The second case study was ADD (compound 15d in ref ), a merged human butyrylcholinesterase (hBChE) inhibitor/cannabinoid receptor 2 (hCB2R) ligand and a therapeutic target for preventing learning impairments in Alzheimer's disease (Figure ). The baseline multi-step model failed to identify a synthetic route, while the mixed fine-tuned model predicts retrosynthetic disconnections similar to the literature route (Figure ). Reagents were omitted from the literature route to focus on the core synthons. While the mixed fine-tuned model deviated by not reproducing the carbamate disconnection of ADD to benzyl-protected phenol D1, instead using the pre-synthesised phenyl carbamate E2, it proposed subsequent disconnections featuring the same cyclisation, reduction, and S N Ar as the literature route to mutually predicted reactants E1, F1, G1, and G2. This further reaffirms the improved ring-breaking performance in multi-step retrosynthesis of the mixed fine-tuned model, where the baseline model failed for the benzoimidazole scaffold in ADD.
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To evaluate whether the mixed fine-tuned model could extrapolate to unknown systems, we extracted 1.5k heterocycle ring-forming reactions from 47 papers published in 2022 (here referred to as Recent dataset). While the model was, unsurprisingly, unable to predict the exact reported reactions, it provided chemically valid ring-breaking predictions for 30.4% of the molecules. This indicates that while the reported reactions are new, potentially more efficient or greener routes than those reported already, many of the heterocycles formed were already synthetically accessible (Figure ). Interestingly, the routes suggested by our model often resembled the ground truth (6Ai.-iii.). For example, both the mixed fine-tuned model and literature suggested the same Friedländer synthesis for quinoline (Figure .).
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In the literature synthesis, there is an additional oxime intermediate; however, the mixed fine-tuned model's prediction follows the direct approach previously taken for trifluoromethanesubstituted quinolines by Jiang et al. ). This illustrates that the model can be fine-tuned to incorporate new reaction data without significantly compromising performance on previously learned tasks. While we used a small dataset of heterocycle formations here, this approach could be applied to a larger dataset or reaction data for different reaction classes of interest.
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In this work we compared four different transfer learning approaches: fine-tuning, multi-task learning, mixed fine-tuning and ensemble decoding. Our aim was to improve the performance of seq2seq retrosynthesis prediction models for ring-breaking disconnections. We have found that mixed fine-tuning performs best overall, with short training time, top-1 reactant-accuracy We then showcased the practical utility of the mixed fine-tuned model by using it for multi-step retrosynthesis of two newly-discovered, complex drug-like compounds containing heterocycles. This illustrates how the model can be used to assist synthetic and medicinal chemists, aiding them in designing synthetic routes towards novel heterocycle-containing therapeutics.
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Finally, we have introduced a method for further fine-tuning the model on additional reaction data. By using this further mixed fine-tuning we have substantially improved the model's top-1 reactant-accuracy on ring formation reactions published in 2022 from 0% to 89.9% without significantly compromising performance for older ring formation reactions or other reaction classes. While this approach has been applied to a small dataset of less than 1.5k heterocycle formations, it has the potential to be scaled up for a larger dataset or a different reaction class.
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Functionalization of commercial polymers via copolymerization leads to a variety of polymers with interesting properties. Halogen ring-substituted ethyl 2-cyano-3-phenyl-2propenoates (HECP) offer a convenient way to introduce a variety of functional groups in polyvinyl acetate backbone. 2-Bromo HECP is reported in preparation of highly loaded MWCNT-polyamine hybrids and their application in catalysis , as well as in synthesis of thiazacridine derivatives as anticancer agents against breast and hematopoietic neoplastic cells . 3-Bromo HECP is involved in synthesis of novel selenophenes from activated acetylenes, ethyl 2-cyano-3-arylacrylate and potassium selenocyanate , also in straightforward preparation of highly loaded MWCNT-polyamine hybrids and their application in catalysis . The report on design, synthesis, anti-proliferative evaluation and cell cycle analysis of hybrid 2-quinolones cites 2-chloro HECP . Novel synthesis of 3cyano-2-pyridones derivatives catalyzed by Au-Co/TiO2 involves 3-chloro HECP . This HECP also was involved in the study of selenotungstates incorporating organophosphonate ligands and metal ions describing synthesis, characterization, magnetism and catalytic efficiency in the Knoevenagel condensation reaction . 4-Chloro HECP was reported in the study new hybrid organic-inorganic multifunctional materials based on polydopaminelike chemistry . 2-Fluoro HECP was mentioned in study of optimized monofluoromethylsulfonium reagents for fluoromethylene-transfer chemistry . Discovery, stereospecific characterization and peripheral modification of 1-(pyrrolidin-1ylmethyl)-2-[(6-chloro-3-oxo-indan)-formyl]-1,2,3,4-tetrahydroisoquinolines as novel selective κ opioid receptor agonists involves 3-fluoro HECP . 4-Fluoro HECP was mentioned in study of aerobic oxidative cleavage of C=C bond to carbonyl compound .
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2,3-Dichloro HECP was reported in synthesis of thiazacridine derivatives as anticancer agents against breast and hematopoietic neoplastic cells , whereas 2,4-dichloro HECP was in synthesis of some new dihydropyrimidine derivatives by cyclization of polarized unsaturated systems . Synthesis of multifunctional polymer containing Ni-Pd NPs via thiol-ene reaction for one-pot cascade reactions mentioned 2,6-dichloro HECP . 3,4dichloro HECP was reported in a highly efficient protocol for the regio-and stereo-selective synthesis of spiro pyrrolidine and pyrrolizidine derivatives by multicomponent reaction .
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Copolymerization (Sch. 1) of VAC and the halogen ring-substituted HECP resulted in formation of copolymers (Table ) with weight-average molecular masses 5.2 to 9.2 kD. According to the nitrogen elemental analysis, between 45.2 and 49.4 mol% of TSE monomer is present in the copolymers prepared at VAC/HECP = 3 (mol), which is indicative of relatively high reactivity of the monomers towards VAC.
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The structure of VAC-HECP copolymers was characterized by IR and NMR spectroscopy. A comparison of the spectra of the monomers, copolymers, and polyvinyl acetate with the spectra of ring-unsubstituted ethyl 2-cyano-3-phenyl-2-propenoate -VAC shows, that the reaction between the HECP monomers and VAC is a copolymerization. . Relatively high Tg of the copolymers (95-115 ºC) in comparison with that of polyvinyl acetate, Tg = 28-31ºC indicates decrease of chain mobility of the copolymer due to the high dipolar character of the HECP structural units. Information on the degradation of the copolymers was obtained from thermogravimetric analysis. Decomposition of the copolymers in nitrogen occurred in two steps, apparently due to acetic acid elimination in 160-340ºC range followed by more slow decomposition of formed residue (15.1-1.5 wt%), which then decomposed in the 500-650ºC range.
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Table . Selected current quantum computers. The selection aims to demonstrate the diversity in technologies. Quantum computers based on different technologies are not directly comparable. The performance of the quantum computer cannot be measured solely by the qubit count as it depends on the interconnectivity of the qubits, the reliability of the qubits, and the reliability of the operations performed on the qubits.
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Technology companies aim to develop large-scale quantum computers that outperform classical computers in real-world problems. Quantum companies raised $2.35 billion only last year alone, according to McKinsey 2 . It is important to point out that quantum computers are not universally superior to classical computers, and the use of hybrid computation benefiting from a collaboration of classical and quantum computers may be appropriate for solving practical problems in protein science. The specialized frameworks for the combined use of classical and quantum processors, like CUDA-Q by NVIDIA, provide an excellent bridging technology for the seamless integration of classical and quantum computing.
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Quantum advantage, or quantum supremacy, refers to the ability of a quantum computer to outperform a classical computer on a specific computational task. The key idea is that quantum computers can leverage quantum mechanical phenomena, such as superposition and entanglement, to perform computations much more efficiently than classical computers. In the 1980s, Richard Feynman proposed that a quantum computer would be an effective tool to solve challenging problems in physics and chemistry, given that it is exponentially costly to simulate large quantum systems with classical computers. The impact of quantum computers on chemistry and material science alone would be revolutionary, as these fields have historically driven major advancements in human civilisation. The Stone Age, Bronze Age, Iron Age, and Silicon Age are all named after materials, and innovations in these areas are estimated to affect 96% of all manufactured goods.
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We believe it is important to distinguish quantum advantage demonstrated for solving (i) theoretical computational tasks, and (ii) practical problems. In 2019, Google announced that it achieved quantum supremacy with its Sycamore processor, performing a calculation in seconds that would take a classical supercomputer 10,000 years . Subsequent studies have however introduced better-optimised classical algorithms, correcting Google's overestimation of the computational costs for a classical computer and ultimately disproving the quantum supremacy claims. In another experiment, physicists in China could find solutions to the boson-sampling problem in 200 seconds using the photonic quantum computer, which would take 2.5 billion years to calculate on the TaihuLight supercomputer 4 -a quantum supremacy of around 10 14 . Nonetheless, the circuit Jiuzhang is not programmable and can not solve practical problems. In the rest of this article, we will focus on quantum advantage linked to solving practical problems in biocatalysis.
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Benefits of Quantum Computing. Among the main advantages is speedup, enabling quantum computers to solve certain problems faster, in some cases exponentially, than classical computers. This is particularly useful for such tasks as factoring large numbers, simulating complex quantum systems, database search, and optimizing complex problems. Arguably the most famous example of an exponential speedup by a quantum algorithm over a classical algorithm is provided by the Harrow-Hassidim-Lloyd algorithm for solving a system of linear equations. It is expected that quantum computing will lead to the development of entirely new technologies and applications that are impossible with classical computers. Risks of Quantum Computing. Building quantum computers is challenging due to the delicate nature of quantum states. Maintaining quantum states long enough for meaningful computation is a significant technical challenge. Quantum systems are susceptible to their environment, leading to issues like decoherence, where qubits lose their quantum state. Error correction requires additional qubits, which complicates building scalable quantum systems. The development of quantum computers requires advanced materials, extremely low temperatures, and sophisticated technology for qubit control and error correction. Energy consumption is an essential factor to consider when selecting classical versus quantum computing for specific computational tasks.
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Selected examples illustrating the practical application of quantum computing in protein science have been published in the scientific literature (Table ) and covered by three excellent recent reviews . Several categories of problems have already been tackled by quantum algorithms. For instance, Variational Quantum Eigensolver Algorithms have been applied to find low-energy states of biomolecular systems -albeit for relatively small systems -which is a crucial step for molecular simulations, protein folding, or simulations of enzymatic reactions . Protein folding and molecular docking can also be formulated as a quadratic unconstrained binary optimisation (QUBO) problem on a lattice, solvable using Quantum Approximate Optimization Algorithm . Similarly, sequence similarity calculations can be reformulated as a QUBO problem using conflict graphs , showing great promise for future quantum-based BLAST-like algorithms. Graph-based approaches have also shown potential in molecular docking, for which Gaussian Boson Sampling can produce stable docking configurations .
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Biological sequence optimization has been recast as using Hamiltonian whose solution can then be found using a Quantum Annealer Algorithm . Other notable approaches in protein design include algorithms based on Grover's algorithm , Quantum Markov Chain Monte Carlo , Quantum Phase Estimation , and simulations of Quantum Dynamics . Moreover, Grover's algorithm has recently been suggested to find the best subset of antibodyderived tags . Finally, quantum machine learning has been explored in such tasks as protein and peptide classification or drug design . It is important to emphasize here that classical computers could have also been used to conduct these studies and, therefore, none of the cases represents a quantum advantage.
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Based on three decades of developing software tools for the scientific community, we identified several key areas in biocatalysis where quantum computing could be applied (Figure ). Our suite of fifteen software tools () currently handles 55,000 jobs annually via web servers. The increasing complexity of workflows and the expanding user base make incorporating methods like quantum mechanics or molecular dynamics challenging. For example, a new version of Caver Web will analyze access tunnels in multiple protein structures obtained by molecular dynamic simulations , but we will simulate only 20 nanosecond trajectories. Large protein conformational changes occur on micro-or millisecond timescales, requiring a million-fold speedup to capture functionally relevant conformations.
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Applications can target (i) highthroughput mining of novel enzymes in genomic and metagenomic databases, and (ii) in silico computational enzyme evolution. Rational protein design can focus on (iii) the reconstruction of robust ancestral enzymes, (iv) the engineering of highly enantioselective enzymes, and (v) the engineering of highly active enzymes. The enzymes before optimization are shown in brown, while the enzymes mined or engineered using quantum computing are shown in blue. The demonstration of quantum speedup is achievable in each of these domains of biocatalysis and will depend on available computing power.
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Mining of novel enzymes. Nature provided us with an incredible repertoire of catalytically efficient enzymes. Thanks to advances in sequencing technologies, we can access vast repositories of protein sequences, potentially coding for the biocatalysts of interest. Automated systems like EFI-EST and EnzymeMiner 31 are based on searches of homologous sequences, multiple sequence alignments and extensive annotations. Searches can be complemented by an assessment of essential properties, like solubility or aggregation . A critical comparison of catalytic properties of mined and engineered haloalkane dehalogenases over three decades revealed that mining was a more successful strategy than engineering for this class of enzymes . The constant growth of genomic and metagenomic databases will require new technologies to correctly identify hits within a reasonable time frame, motivating quantum search algorithms. Moreover, with the advent of accurate protein structure prediction using AlphaFold , we wish to start using structural bioinformatics for all-againstall docking and calculation of chemical reactions using quantum mechanics. Quantum simulations will provide a framework for an efficient search of protein/ligand databases and combinatorial execution of quantum calculations 36 with multiple protein structures and multiple ligands, which is impossible using current classical computers. Systematic analysis of multiple enzyme-substrate complexes will provide information on catalytic efficiency as well as substrate specificity.
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Ancestral sequence reconstruction is one of the most reliable techniques for designing robust biocatalysts. It requires the identification of evolutionarily related sequences, constructing accurate multiple-sequence alignment, and inference of non-existing ancestral sequences. Fully automated workflows for non-experts are available, e.g., FireProt or GRASP . For computational reasons, only up to 150 sequences are often used for the reconstruction, and quantum computing will provide tools for the efficient use of much larger phylogenetic trees . Positioning of insertions and deletions is the most critical step of the entire workflow, determining foldability and expressibility of designs. Quantum parallelism will provide means for more systematic mining of genomic and metagenomic databases , processing much larger sets of sequences, re-running inference and most importantly in silico evaluation of designs with variable locations of insertions and deletions. Solving the Achilles Heel of ancestral reconstruction by more reliable positioning of insertions and deletions will dramatically improve the success of designs.
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Catalytically efficient enzymes bind substrates with high affinity, stabilize the transition state and swiftly release reaction products. The active site must be complementary to the transition state, further stabilized by an electrostatically pre-organized protein environment and hydrogen bonds. Catalytic residues are often highly rigid. Access tunnels connecting the active site cavities with the protein surface, which transfers ligands and waters, are frequently lined by flexible loops. These loops undergo intrinsic or ligand-induced conformational changes, assisting the entry of substrates and releasing products after the reaction. Both physical and chemical steps can be limiting. Optimization of the active site geometry can be achieved by quantum mechanics or diffusion models like RF Diffusion . The geometry of tunnels can be studied by programs like Caver 41 , while ligand transport can be simulated by accelerated molecular dynamics or approximated by methods like CaverDock 42 . The clustering of tunnels in multiple snapshots is demanding, hitting the limits of current classical computers, and quantum clustering holds the potential to break those limits . Moreover, current machine-learning models work for static structures, while predicting dynamic structures is an unsolved problem, partially due to lacking training data. Quantum computers will provide access to highly standardized molecular dynamics simulations to train machine-learning models. Moreover, long simulations will allow the study of ligand transport in real time to design mutations far from the active site. Multiple quantum simulations 45 may help us rationalize and resolve possible substrate and product inhibitions, which are rarely discussed, but critical for the practical use of engineered biocatalysts.
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Engineering of highly enantioselective enzymes. The computational design of enantioselective biocatalysts is challenging, and the development of enantioselective enzymes often relies on focused directed evolution. Why is it difficult? Enantioselectivity is driven by the ratio of binding or Rand S-enantiomer and the ratio of their respective catalytic rates. Accessing enantioselectivity requires accurate modelling of two enzyme-substrate complexes and precise calculation of binding energies. Moreover, two reaction coordinates and transition states must be evaluated using high-level quantum mechanics. Accurate calculation of enantioselectivities using high-level quantum mechanics is possible , but it requires high skills and nontrivial computing power, preventing combinatorial searches of the effects of mutations on enantioselectivity. We can explain experimentally observed enantioselectivities, but we can not design them rationally. Quantum parallelism will allow simultaneous exploration of multiple reaction coordinates of mutants starting from enzymesubstrate configurations obtained by molecular docking or diffusion models . Moreover, calculations of electron dynamics using quantum simulations can provide higher accuracy . In our opinion, reproducible in silico design of enantioselective biocatalysts would be a clear demonstration of quantum advantage.
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Imagine drawing the chemical reaction of interest, converting it into chemical structures, and screening millions of predicted protein structures for potential binders . Next, we will conduct highly parallel quantum-mechanical calculations of the reaction coordinates for thousands of selected enzyme-substrate complexes to identify enzymes with low activity . Machine learning models will filter hits based on protein stability, low aggregation, and high expression in the preferred host organism . Massively parallel molecular dynamics will explore significant conformational changes during substrate binding and product release, identifying bottlenecks and potential substrate and product inhibitions. By integrating data from quantum mechanics, molecular dynamics, and machine learning, we will be able to (i) predict enzyme-ligand complexes with atomic accuracy, (ii) quantitatively assess protein fitness, (iii) identify rate-limiting steps, and (iv) select "hotspot" regions for in silico mutagenesis. Combinatorial substitutions and indels will be introduced to these hotspot regions, followed by iterative cycles of calculations to gradually fix beneficial mutations and improve protein fitness. While we have the majority of algorithms and models available, we lack the computing power for in silico protein evolution. Computationally evolving highly efficient, enantioselective, and expressible biocatalysts would be a clear demonstration of quantum supremacy in the biocatalysis domain.
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Quantum computing represents a disruptive technology that will open new horizons in various areas of science. Considering its current advantages and limitations (Table ), we see a clear niche for implementing this technology in biocatalyst discovery and design. The very first examples illustrating the applications of quantum computing in protein science have already appeared in the scientific literature (Table ), and we foresee more tasks to be addressed with quantum computing in the future.
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With ongoing hardware improvement (Table ), a more significant number of qubits, but also higher stability and hopefully lower energy consumption will accelerate quantum computing applications in biocatalysis. Academy-industry collaborations among large technology companies, spin-offs, and academic labs are being established to push technology forward. Quantum computers are being gradually installed in various companies and research institutions, making the technology more widely accessible and, at the same time cautioning us to keep watching its impact on the environment.
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Decisions must be made regarding which parts of the computational workflows for enzyme engineering are amenable to quantum computing (Figure ) and which are more suitable for classical computers. We envision that a hybrid setup, where quantum computers are connected to classical computers, will provide a more efficient framework than operating isolated quantum computers. Current quantum computers providing tens of qubits (Table ) are not sufficient for solving practical problems in biocatalysis. It has been estimated that the models accessing the electronic structure of the enzyme cytochrome P450 could be simulated in 73 h of quantum computer time using 4.6 million qubits, with an error rate of 0.1%; or only 25 h using 0.5 million qubits, anticipating the error rate reduction to 0.001% .
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Software engineering is a critical next step in using these computers regularly. The first specialized software packages for chemistry applications are appearing, e.g., PennyLane, TEQUILA, PySCF, Qiskit Chemistry, Quantum Inspire, Quantum Package, and QuEST. The developers benefit from software development kits like Cirq, Forest, Ocean, ProjectQ, Qiskit, Quil, and QuTiP. Maintaining an open-source policy is crucial, especially as technology giants Google, Microsoft, IBM, and NVIDIA are spearheading development and potentially limiting access, as evidenced by the community's experience with AlphaFold3 or AlphaProteo. Training events, hands-on courses, hackathons, and the sharing of reusable computer code via public repositories will be beneficial.
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We have outlined enzyme discovery and design problems that cannot be carried out by current classical computers (Figure ). Quantum acceleration will be needed to address the lack of computing power for well-defined tasks. In looking for an early practical quantum advantage, it is best to consider the simulation of quantum-mechanical systems. This is the most natural application of quantum computers, where we aim to use a quantum computer to mimic the rules that describe physical microscopic quantum systems. These problems are computationally challenging for the same underpinning reason that quantum computers can be powerful . Once the milestone of quantum advantage in biocatalysis is met, we expect a rapid transformation of the entire domain, similar to what we recently experienced with machine learning for protein structure prediction.
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As quantum computers grow in capabilities, we will encounter entirely new applications beyond our imagination. The Holy Grail could be the identification of "optimal" natural catalysts purely in silico or the design of selective, highly efficient, and expressible enzymes from scratch. Equally exciting will be the integration of classical-quantum computational workflows with single-molecule techniques , microfluidics , self-driving robotic laboratories 51 , brain biocomputers , and AI scientists .
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In order to address this gap in the field, our lab recently described a catalytic process involving the reductive coupling of aliphatic aldehydes with alkyl bromides in a pathway proposed to proceed through the intermediacy of a-silyloxyalkylnickel intermediates derived from aldehydes, silyl chlorides, and low-valent nickel (Figure ). In order to address limitations of that protocol, including substrate access, scope, and yield, we have now explored the utility of more broadly available substrate classes in catalytic couplings with aliphatic aldehydes (Figure ). The main focus of this study is the coupling of aliphatic aldehydes with redox-active esters, providing access to numerous product types derived from simple carboxylic acid precursors. Additionally, preliminary examples of reductive couplings between aldehydes and alkyl tosylates or epoxides are described. This combination of procedures provides strategies where alkyl fragments are derived from carboxylic acids, alcohols, or alkenes, thus greatly expanding the range of precursors available for aldehyde functionalization processes. Our initial investigation geared towards developing the catalytic reductive coupling of aldehydes 1a with the N-hydroxyphthalimide (NHPI) ester 2a (Table ). Systematic investigation of the reaction parameters showed that the desired product 3a was isolated in good yield (91%) with a combination of Ni(cod)2 and bioxazoline (BiOx). Control experiments indicated that a nickel catalyst was necessary for the reaction to proceed, and other nickel sources only led to moderate yield (entries 2, 11 and 12). The ligand (BiOx), reductant (nanopower Zn), 1,5-hexadiene and LiCl also A. Grignard, Barbier, and Nozaki-Hiyama-Kishi couplings
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C. This work -Unactivated sp 3 -sp 3 cross couplings with aliphatic aldehydes played a crucial role in successful transformation (entries 3-6). A ligand screen revealed that BiOx is uniquely effective when compared with other common ligands (entries 13-15). Of note, olefin additives can dramatically improve the efficiency, with 1,5-hexadiene proving the most effective (entries 5, 8-10). Furthermore, the particle size of Zn is critical, with the use of nanopowder Zn (40-60 nm) enhancing the yield (entry 7). With optimal conditions in hand, we sought to define the reaction scope (Table ). Various 1º and 2º carboxylic acids were converted to the corresponding NHPI-esters and coupled efficiently with aldehyde 1a. A range of functional groups were well tolerated including ketones (3h, 3i, 3ab), esters (3j, 3x), N-Boc (3y), N-tosyl (3z), and alkenes (3g, 3v, 3ac, 3ad). A simple methyl group can also be added effectively using the RAE 3c derived from acetic acid. Notably, some potentially reactive functional groups, including alkyl chloride 3k and aryl bromide 3l were left intact under current conditions, offering opportunities for subsequent cross-coupling. Protected alcohols (3f, 3ac) and ethers (3m, 3t, 3u) were also competent coupling partners, allowing for the construction of polyol motifs. Moreover, heterocycles including pyridine (3o), and indole (3p) were also readily accommodated as were a series of secondary redox-active esters (3q-3z). The protocol was scalable to 5 mmol, obtaining the desired product 3a in 81% isolated yield.
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After defining the scope of RAEs, attention then turned to the scope of the aliphatic aldehyde ). Sterically encumbered aldehydes with b-branching, such as isovaleraldehyde (3af) and citronellal (3ag) were competent coupling partners. a-Branched aldehydes (3as-3au) also delivered the desired products without diminished efficiency. Benzyl ethers (3ah), silyl ethers (3ai), acetals (3aj), alkynes (3ak), and phthalimide groups (3ar) were also tolerated. Substrates with functional groups known to engage in transition-metal-catalyzed transformations such as aryl chlorides (3al), aryl bromides (3am) and aryl boronate esters (3an), delivered the desired product smoothly without competing reactivity. Notably, heterocycle substrates, such as indole (3aq), was likewise suitable for this chemistry. The scope and chemoselectivity of this method in activating aldehydes in the presence of a wide array of reactive functional groups including ketones is thus quite broad, addressing an important limitation of classical methods for carbonyl additions. While this method demonstrates considerable scope with carboxylic acid-derived RAEs, we considered that utilizing alkyl precursors derived from simple alcohols and alkenes would further extend the utility and scope of the strategy (Table ). To enable the use of alcohol precursors, we explored the use of alkyl tosylates as the coupling partner. With simple modification of the reaction conditions (see SI), our catalytic system can activate the C-O bond of tosylates, delivering the desired product in good yield (Table ) with attractive functional group compatibility including esters (5b), ethers (5c), and furans (5d).
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With an eye towards utilizing alkene feedstocks, we then considered the use of epoxides as the alkyl precursor (Table ). After extensive investigation of reaction parameters (see SI), an effective method was realized, obtaining the desired silyl-protected 1,3-diols in good yield, tolerating a range of functional groups, such as furans (7c), ethers (7d), aryl bromides (7e), and alkynes (7f). This approach further diversifies the range of product types accessible by this method, with 1,3-diols being obtained in the epoxide-based procedure. A cyclopropane-containing RAE 8 afforded a 92:8 ratio of ring-opened product 3g and compound 9 with the cyclopropane ring intact (Figure ). Additionally, in an experiment involving hexenyl transfer, a direct linear dependence of the ratio of 11/12 on the catalyst loading was observed (Figure ). These experiments are consistent with a mechanism involving free-radical intermediates, in analogy to prior studies on nickel-catalyzed processes with both alkyl halides or
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NiCl redox-active esters. 14v,20 Similarly, ring opening was observed in couplings of cyclopropanecarboxaldehyde (13) leading to product 14 exclusively as the Z-isomer (Figure ). In this case, we attribute ring-opening of the cyclopropane unit to a nickel-catalyzed process involving the intermediacy of 15, potentially involving the initial oxidative addition of a low-valent nickel species to the aldehyde, promoted by Et3SiCl. An experiment employing stoichiometric Ni(cod)2 but lacking the zinc reductant resulted in the formation of product 3a in high yield, suggesting that key organonickel intermediates involved in product formation do not require reduction at the nickel center, but rather that the zinc reductant is involved in catalyst regeneration (Figure ).
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Based on these experiments and insights from prior studies, we propose a mechanistic picture consistent with the above findings (Figure ). Oxidative addition of aldehyde 1 and silyl chloride to Ni(0) generates Ni(II) silyloxyalkyl complex II. Species related to II have been previously described, and our prior studies of aldehyde -alkyl halide couplings illustrated characteristic byproducts that are best explained by the involvement of II. Addition of free radical VI to II affords Ni(III) species III, which undergoes rapid reductive elimination to form product 3 and Ni(I) species IV. Combination of IV with the RAE 2 results in V and the free radical VI that recombines with species II. The above steps are consistent with the observation that Ni(0) undergoes product formation in the absence of zinc, illustrating that reduction of intermediate II to the corresponding Ni(I) complex is not strictly required for turnover. Additionally, the above evidence (Figure ) for free radical intermediates derived from the RAE 2 are consistent with this proposed mechanistic pathway.
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The conversion of Ni(II) complex V to the Ni(II) silyloxyalkyl nickel intermediate II requires a net two-electron reduction by zinc and oxidative addition of the aldehyde and silyl chloride. The commonly invoked reduction of nickel complex V to Ni(0) complex I completes the catalytic cycle, although this possibility must be viewed within the context of recent work from Diao that illustrates that Ni(II) BiOx complexes are more resistant to reduction compared with the corresponding Ni(II) complexes of other commonly employed pyridyl-based ligands. The presence of the phthalimido substituent in V and the interaction of V with the aldehyde and silyl chloride may affect the facility of this reduction by nanopowder zinc. Given these complexities, the precise nature of the conversion of V to II will require further investigation.
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The generation of free radical VI from RAE 2 is depicted (Figure ) as involving Ni(I) species IV in analogy to studies from Baran in the coupling of anhydrides with redox-active esters. 11a The efficiency of product formation in the absence of zinc (Table ) illustrates that the nickel catalyst is competent in mediating the decomposition of redox-active esters. We observed that zinc and Et3SiCl rapidly promotes the decomposition of RAE 2, however, the presence of the nickel catalyst has a protective effect as previously described by Baran, slowing the rate of consumption of 2 compared to control experiments where the nickel catalyst is omitted (see SI). Recent studies from Rousseaux have provided evidence in reductive arylation reactions that TMSCl and Zn promote the formation of free radicals. Our studies, which potentially involve effects of the silyl chloride in several steps including aldehyde activation and/or redox-active ester decomposition, have not clearly elucidated the active agent in mediating radical formation from the redox-active ester. Finally, the role of 1,5-hexadiene is not illustrated in the mechanistic scheme since the 4-and 5coordinate complexes II and III cannot accommodate the bidentate coordination of this additive. Coordination of this additive likely prevents catalyst decomposition and/or inhibits competing side reactions that lie off the productive catalytic pathway. active esters has been developed. The procedure is broad in scope, tolerant of a wide array of functional groups, high-yielding, experimentally simply, and scalable. This process was extended to include the reductive cross-coupling of alkyl tosylates or epoxides with aliphatic aldehydes, thus providing a broad range of precursors derived from carboxylic acids, alcohols, or alkenes. Preliminary mechanistic experiments on this aldehyde -redox-active ester coupling are consistent with initial aldehyde activation to produce a-silyloxyalkylnickel species as a key intermediate that is captured by free radicals generated from the redox-active ester. Future work will include efforts to further study the mechanism of these transformation and expand the scope in increasingly complex applications.
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Isomerism, phenomena in which compounds share the same molecular formula (isomers) but are otherwise different, and isomerization, transformations between isomers, is a fundamental aspect of Chemistry. The two major forms of isomerism -constitutional isomerism (involving isomers that have different connectivity) and stereoisomerism (involving isomers with the same connectivity but different spatial arrangement) -have been treated as distinct and isolated domains of study, with separate theoretical frameworks. This division, however, has long limited a comprehensive understanding of isomerism. Herein, a unifying framework that applies common principles to both these types of isomerism is introduced, overcoming this artificial separation thus providing a unified view of molecular isomerism.
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The existing paradigm for addressing constitutional isomerism relies upon the imposition of canonical forms to molecular structure where localised bond multiplicities are assigned to each atom-atom connection, and element valence is satisfied (a "valence structure"). While this approach has proved powerful and underpins digital representations of molecular structure, the imposition of canonical form hinders a more general description that captures the making and breaking of bonds. In our approach to constitutional isomerism, we focus only on atom-connectivity regardless of bond order. This complies with the IUPAC definition for connectivity. To illustrate shortcomings of the established approach compared with an atom-connectivity one, a [1,5]-sigmatropic rearrangement is examined (Fig. ). The rearrangement where both the reactant and product are drawn using standard canonical formseach featuring formal single and double bonds (Fig. ). The transition-state structure (TS) that links the reactant and product is drawn in such a way to indicate bonds being made and broken, including changes in bond multiplicity throughout the molecule. This TS is not, and indeed cannot, be represented in canonical form and thus would not be recognised using such approaches to constitutional isomerism. In Fig. , these same three structures are each drawn where only atom connectivity is shown (red); all structuresincluding the TSnow feature distinct atom-atom connectivity patterns. Note: explicit H-atoms are necessary here to avoid confusion with the more familiar canonical form representation where H-atoms are implicit. There exists a subtle limitation in using atom connectivity rather than canonical forms. For some reaction types (e.g., cycloadditions and chelotropic reactions) the formalism, in its basic form, "under-samples" the configuration space. This is explored later.
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It is also important to note that, for our purposes, an interatomic connection is defined to exist between pairs of atoms and thus excludes those representations of bonding such as that for a three-centre bond and the "side-on bond" convention for polyhapto systems. In each case, such representations of "bonding" can be resolved into atom-connectivity pairs as shown in the Supplementary Information.
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Any process that leads to a change in atom connectivity can be described, in the broadest sense, as desmotropic. As constitutional isomerism is only concerned with differences in atom connectivity for a given set of atoms, desmotropic describes the transformation between such isomers. This general term encompasses the existing more narrowly focussed concepts, for example, of pericyclic and sigmatropic processes.
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Class refers to the system of atoms for which atomconnectivity permutations are applied; family is characterised by a combination of total connections and the set of general atomconnectivity configuration patterns; genus captures more nuanced details of the atom-connectivity configuration patterns; species represents a specific arrangement of atom connections for the set of atoms. The distinctions between family and genus are demonstrated herein through the worked examples and is based upon the mathematics notions of set partitioning, Bell numbers, and equivalence relations.
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Within constitutional isomerism, the different isomers represent different atom-connectivity patterns or permutations. In recognising that the set of possible atom-connectivity configurations also represents combinatorial structure, each configuration can be treated as an abstract polytope representable as a matrix. These abstract polytope species (henceforth simply called "species"), and their matrix representation, are equivalent to what in cheminformatics is called the adjacency matrix of a simple molecular graph. These encode which atoms in a molecule are connected. Fig. gives some simple examples for the 5-atom class.
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Within this application of the Polytope Formalism, graphs are used to describe and encode the relationships between the different atom-connectivity configurations. This graphical information describes the desmotropic transformation of one atom-connectivity configuration species into anotheror in the language of chemistrythis type of graph describes the concerted reaction pathways between the chemical species. The wider utility of using graphs arises from the suite of theorems and powerful tools that Graph Theory provides for processing graphs, determining their properties, and extracting information.
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In focusing on atom connectivity, it follows that in its most general case where there are no restrictions upon the atom connectivity, the full scope of mathematically possible atomconnection configurations for N atoms, spans everything from the unique case where all N atoms are unconnected, through to the unique case where each atom is connected to every other atom (e.g., 10 connection species in Fig. ).
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Enumeration of all unrestricted atom-connectivity configurations for N atoms is simply the sum of all possible arrangements of k atom connections for N atoms, where k runs from 0 through to the maximum number of connections. Hence, for N atoms, the number of mathematically possible atomconnectivity configurations is equal to 2 𝑁(𝑁-1) 2 ⁄ .
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The expression 2 𝑁(𝑁-1) 2 ⁄ places an upper bound on any enumeration; any imposed constraints will reduce the total number. Valence and steric considerations place obvious limitations on the maximum number of atom connections any atom in the set may form, greatly reducing the number of realistic atom-connectivity configuration combinations. Indeed, previous methods of isomer enumeration relied heavily upon the restrictions imposed by valence. Another constraint concerns minimal connectivity where existing isomer-enumeration approaches impose the requirement that the atom-connectivity configurations (the species) must constitute a single connected entity thus complying with the IUPAC definitions for constitution and constitutional isomerism.
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A key strength of the Polytope Formalism, for both stereoisomerism and constitutional isomerism, is that all possible configurations are consideredthus providing information about interconversion processes. In contrast with previous approaches, in the Polytope Formalism of constitutional isomerism, all sensible subvalent and hypervalent atom-connectivity This journal is © The Royal Society of Chemistry 20xx configurations are explicitly included to account for those configurations representing reaction intermediates.
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The interrelationships within the set of connectivity-permuted species generated by the formalism can be represented as graphs. The component species are represented as "nodes" or graph vertices. The pairwise relationships between these are represented as graph edges connecting the graph vertices; each edge represents a R de c process equivalent to the elementary reaction. The entire graph represents the full network of desmotropic processes and hence a full network of reactions. A powerful corollary of this is that, at least where steric interactions allow, such a graph maps onto its corresponding potential energy surface (PES). These reaction graphs encode the "shape" (topology) of the corresponding chemical space. The unsymmetrical dissociation of the bifluoride anion (2a) into [HF + fluoride] (1a and 1b) is depicted in Fig. . This reaction is equivalently represented as the graph in Fig. where the graph vertices are labelled by their species. The 1D PES for the reaction with locations of the species indicated is shown in Fig. . While 2a has a well-defined position on the PES, species 1a and 1b are each located at an arbitrary point where one of the H-F connections of 2a is said to be qualitatively broken.
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A related example is shown in Fig. where the desmotropic reaction is the [1,5]-sigmatropic rearrangement of 3a to 3b via 4a. Here, only the coloured bonds are permuted with all other atom connectivities remaining unchanged (recall that, under this formalism, the bond order is not recognized). In contrast to the prior example, here all three species (3a, 3b, and 4a) correspond to precise locations on their PES (Fig. ).
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