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64ee4a7479853bbd78b21dc7 | 16 | ORDerly-forward is a benchmark created from USPTO data in ORD for retrosynthesis prediction consisting of reactions with up to two products and three reactants, solvents, and agents. A random 80/10/10 train/val/test split was applied to the benchmark. An additional test set called non-USPTO-forward was created by using all non-USPTO data in ORD (as of August 2023) and cleaning it with the same parameters as those used for ORDerly-forward. No frequency filtering was applied. |
64ee4a7479853bbd78b21dc7 | 17 | ORDerly-retro is a benchmark created from USPTO data in ORD for retrosynthesis prediction consisting of reactions with one product and up to two reactants. A random 80/10/10 train/val/test split was applied to the benchmark. An additional test set called non-USPTO-retro was created by using all non-USPTO data in ORD (as of August 2023) and cleaning it with the same parameters as those used for ORDerly-retro. No frequency filtering was applied. |
64ee4a7479853bbd78b21dc7 | 18 | ORDerly-condition is a benchmark dataset created from USPTO data in ORD for reaction condition prediction, and is, to the best of our knowledge, the first reaction condition benchmark. Each reaction in ORDerly-condition contains one product and up to two reactants, two solvents, and three agents. A minimum frequency of 100 for the spectator molecules was applied. |
64ee4a7479853bbd78b21dc7 | 19 | Experimental evaluation of the ORDerly-forward and ORDerly-retro benchmarks was performed using the Molecular Transformer architecture built by Schwaller et al. . To switch from forward prediction to retrosynthesis prediction no changes to the transformer architecture were necessary, only the data was changed. The ORDerly-condition benchmark was evaluated together with the impact of different approaches to reaction role assignment and frequency filtering using the neural network architecture built by Gao et al. . |
64ee4a7479853bbd78b21dc7 | 20 | On the forward prediction tasks the accuracies achieved are similar (albeit slightly lower) to the accuracies reported by by Schwaller et al. (88-90% top-1 accuracy when trained on the USPTO_MIT dataset), though the accuracies are not directly comparable since different subsets of USPTO were used. As expected the performance with separated agents is higher than mixed, since it is an easier task, and it is encouraging to see that the models get stereochemical information correct most of the time. Accuracy with the retrosynthesis model on the held out test set was roughly 50%, which is similar previous work on retrosynthesis . It is interesting that prediction accuracy on the non-USPTO data was similar on the forward prediction tasks, but markedly worse on the retrosynthesis task. |
64ee4a7479853bbd78b21dc7 | 21 | The reaction condition prediction model used in this work predicts five categorical variables: two solvents and three agents. These five molecules form a set (order invariant), though the loss function in the model used to predict the molecules considers them sequentially (with order) since this was found to work better in practice . The metric used to evaluate the accuracy of the model should be order invariant, since the problem is order invariant, and for this reason the accuracy metrics used are top-1 (see appendix C) and top-3 (see Table ) exact match combination accuracy for each type of component (i.e., solvent, agent). Beam search was used to identify the top-3 highest probability sets of reaction conditions. The top-3 accuracy was compared to the baseline predictive accuracy of simply predicting on the test set the most common molecules found in the train set. |
64ee4a7479853bbd78b21dc7 | 22 | Table shows the predictive performance on the test set using four different flavours of the ORDerly-condition benchmark. All models show an improvement over the frequency informed baseline. The performance of the labeling datasets at first appears to be better than those that use our custom logic to extract reaction components from the reaction string. However, as shown in Figure , many of the reactions in datasets where we trust the labeling in ORD have more than three reactants, while most reactions in organic chemistry only have two reactants. Upon manual inspection, we found that many agents were mislabeled as reactants and, therefore, the prediction problem was made significantly easier by only requiring a single catalyst to be predicted (see Appendix E). In contrast, our custom cleaning pipeline that defines components using the reaction string avoided contamination of the desired prediction targets (i.e., the agents) in the inputs, and therefore, better represents the downstream application of reaction condition prediction models. This insight is confirmed in Table ; there are fewer unique solvents and agents and a higher density of null components when using the ORD labeling instead of the reaction string indicating that many components might be mislabeled as reactants. This discrepancy demonstrates that naive creation of datasets based on ORD can lead to inflated performance metrics. |
64ee4a7479853bbd78b21dc7 | 23 | For the datasets that extract the components from the reaction string, overall top-3 accuracy is less than 25% across solvents and agents. While not directly comparable, our overall accuracy is lower than what Gao et al. achieved with 50.1% top-3 accuracy across catalysts, solvents and agents. However, Gao et al. trained on approximately ten million reactions, while we train on less than four percent of that (⇠350k). As shown in Figure , we see consistent increases in AIB (%) with the number of data points for the dataset which uses reaction strings and deletes rare reactions, and this scaling performance indicates that as ORD grows, better performance could be achieved, even with potentially fewer data points than used in the paper by Gao et al. |
64ee4a7479853bbd78b21dc7 | 24 | Finally, the approach to dealing with rare values is investigated. The reaction string datasets would have more than 10,000 unique agents (see Table ) with no frequency based filtering, which would create a sparse OHE. We initially hypothesized that the rare ! "other" strategy would allow for better generalisation, since the edge case reactions would be kept in a way that also keeps the OHE at a reasonable size. However, in practice, the rare ! delete rxn strategy had better performance across train set sizes, as seen in Figure . |
64ee4a7479853bbd78b21dc7 | 25 | There are two ways of assigning reaction roles to molecules found in ORD files, either relying on the labeling, or identifying reaction roles by considering the atom mapping of a reaction SMILES string. We found that relying on the labeling in ORD mislabels many spectator molecules as reactants, which explains the difference in reactant count distribution seen in Figure . Identifying the role of molecules in a reaction provides crucial context to machine learning models, adding domain knowledge to the data thereby improving performance. Atom mapping the reactions with the newest The role that a molecule plays in a reaction may more easily identified when only considering one reaction class at , since this allows the mechanistic details of the reaction class to be considered. Handling large and diverse datasets inevitably requires generalizations that may result in contradictions upon a more fine-grained inspection. In this work, solvents were separated from the other spectator molecules, because these can somewhat reliably be identified. Catalysts were not separated into their own category, since identifying catalysts is more subtle (especially with organocatalysis), and few reactions in the reaction string datasets contained transition metals. |
64ee4a7479853bbd78b21dc7 | 26 | Although order of addition may play a role in wet lab chemistry, reaction prediction tasks are often cast as order invariant, where the goal is to predict a set of molecules. However, both of the architectures used for experimental validation of the ORDerly datasets are not agnostic to the ordering of the targets, since the neural networks used predict one molecule at a time in the OHE, and the transformers used predict one token at a time. Incorporating order invariance (and canonicalization) of the molecules into the loss calculation during training may allow for better generalisability of the predictive models, and is an exciting area for further study. It is worth noting that the evaluation metrics used throughout are order invariant. |
64ee4a7479853bbd78b21dc7 | 27 | In this work, we presented ORDerly, an open-source framework for preparing chemical reaction data stored in the Open Reaction Database (ORD) for machine learning applications. ORDerly was used to generate benchmark datasets for forward prediction (ORDerly-forward), retrosynthesis (ORDerly-retro), and condition prediction (ORDerly-condition) based on US patent data. Transformer models were trained on the forward prediction and retrosynthesis datasets, and they were found to only generate invalid SMILES strings very infrequently, while also achieving similar test accuracy to that found in the literature on a held-out set of US patents. ORDerly was also used to generate test sets from all non-patent data from ORD, which could serve as a better indication of model generalisation. Accuracy for the forward prediction task was comparable on the non-USPTO test set, while accuracy on the retrosynthesis task was somewhat lower. The condition prediction task was used to investigate different strategies for assigning reaction roles and frequency filtering of the spectator molecules. When building datasets for condition prediction using the labeling in ORD we found contamination of the inputs (reactants) with the outputs (agents), resulting in a problem that was unrealistically easy. We therefore chose to use chemically informed logic to better assign reaction roles for the ORDerly-condition benchmark. |
64ee4a7479853bbd78b21dc7 | 28 | All benchmarks and datasets experimented with in this work, as well as the code used to generate them, are freely available online, and we hope the benchmarks will make reaction prediction tasks more accessible to ML practitioners with limited domain knowledge. ORDerly presents a fully open-source pipeline to go from raw ORD data to a fully trained condition prediction model, allowing for an avenue to leverage the growing contributions to open source chemistry. |
66f4241e51558a15ef144cfa | 0 | The fourth mechanism involves instances where small crystals come together and fuse in a specific, orientation-dependent manner to form a larger crystal (Extended Data Movie 4). This process differs from the more common random aggregation leading to polycrystalline structures; here, the particles align according to their crystallographic axes before merging, thereby maintaining a common crystallographic orientation across the newly formed, larger crystal. During these oriented attachment events, we frequently observe the melting and subsequent re-crystallization of the contact region between the two crystals. This process, which facilitates the proper alignment of the crystals, results in a flawless area, completely eliminating the seam that initially separated the two structures (Fig. ). |
66f4241e51558a15ef144cfa | 1 | We therefore employ our previously developed computational model to confirm that these mechanisms emerge naturally from our proposed interaction potential. We perform simulations of 210 nm and 170 nm particles interacting via a pair potential that accounts for the combination of surface charge and polymer brush coating on the particles used in the experiment (details in Methods). As described throughout the rest of this article, these simulations recapitulate crystallization via a two-step process and subsequent crystal growth through Ostwald ripening and blob absorption, both on surfaces and in bulk, depending on the particle concentration and solution salt concentration. |
66f4241e51558a15ef144cfa | 2 | A representative example of the formation of CsCl-like crystals can be seen in Extended Data Movie 1. Here, nucleation occurs from within these blobs, often starting from the surface where interfacial fluctuations more easily allow for transient changes in density. For lower interaction strengths, particles can rearrange resulting in blobs that are spherical to minimize surface tension, but for higher interaction strengths we also observe more dendridic gel structures, which then crystallize through nucleation within the dense phase, followed by propagation as in Fig. . Absorption of neighboring blobs is common, especially at higher density where many small blobs nucleate initially. For some of these cases, we tracked the particles in the blob being absorbed and found that the vast majority of those in the final crystal arrived via direct flow rather than through evaporation from the blob then subsequent deposition. |
66f4241e51558a15ef144cfa | 3 | To assess the generality of this two-step crystallization process, we conducted crystallization experiments varying the size ratio (β) between positive and negative particles. As shown in Extended Data Figure , we observed no substantial differences in the crystallization mechanism, although the resulting crystal structures varied as expected. Specifically, we examined systems with β = 0.36, 0.43, 0.50, 0.74, and 0.81, leading to the formation of Cs 6 C 60 -, NaCl-, K 4 C 60 -, Th 3 P 4 -, and CsCl-like structures, respectively. |
66f4241e51558a15ef144cfa | 4 | We hypothesized that the strength and range of particle interactions plays a crucial role in modulating the crystal formation pathways we observed, a phenomenon also noted in various other colloidal and molecular systems. To explore this, we concentrated on designing experiments that allowed us to gradually, and in a controlled fashion, scan different particle interaction strengths over time. Because the interaction strength is highly sensitive to salt concentration, we modified our experimental setup to allow for gradual and continuous variation of the salt concentration. These experiments begin with a high salt concentration (short Debye length), maintaining the particles in a stable gas-like state. We subsequently reduce the salt concentration by connecting the observation cell to a deionized water reservoir (Extended Data Fig. ). As salt diffuses out of the sample into the reservoir, the Debye length (λ D ) and interaction strength between the particles increase, eventually initiating crystallization (Fig. ). This design provides spatiotemporal control over the salt concentration because we can predict how the profile of ions should look given the initial inside and outside concentrations and the geometry of the capillary (Fig. , Methods), and allows us to monitor and capture images of the crystallization front (Fig. and Extended Data Movie 5). The gradual decrease of salt concentration enables us to pinpoint the relatively small window of interaction strengths where the formation of amorphous blobs is completely suppressed and where instead classical crystallization takes place. We observed similar qualitative trends conducted at fixed λ D in both experiments using sealed capillaries and simulations (Extended Data Fig. ), where at short λ D our simulation remained gaseous, but with increasing λ D we first observe a small window of values where classical crystallization takes place, then two-step crystallization, and finally random aggregation in that order. |
66f4241e51558a15ef144cfa | 5 | Continuous dialysis allows us to create well-defined, spatially and temporally variable interaction potentials between particles, enabling the identification of optimal conditions for crystal growth in a single experiment. By assessing the size and quality of the crystals in various regions of the observation cell at the experiment's conclusion, we can infer the temporal evolution of particle interaction strength that led to the formation of those crystals. For instance, in regions where the interaction strength increases very rapidly-akin to supercooling-crystal formation is interrupted, with crystalline assemblies showing small, defective, and irregular structures, along with visible presence of disordered aggregates. In contrast, in areas of the same sample where the interaction strength increases more gradually, crystals develop with well-defined polyhedral habits (Fig. and Extended Data Fig. ). |
66f4241e51558a15ef144cfa | 6 | Continuous dialysis allows us to discover and spatially resolve crystal structures with similar nucleation energy barriers, which might be overlooked in experiments using static interaction potentials. For example, in sealed capillaries, binary mixtures with β = 0.81 primarily form CsCl-like crystals that take on macroscopic rhombic dodecahedral shapes (Fig. and Extended Data Fig. ). However, under continuous dialysis, we also observe crystals structurally similar to Thorium Phosphide (Th 3 P 4 ) exhibiting distinct triakis tetrahedral habits, and this is also observed in simulation for certain values of λ D and volume fraction (ϕ p ) (Fig. and Extended Data Fig. ). |
66f4241e51558a15ef144cfa | 7 | In addition to the Th 3 P 4 crystals, we have discovered a previously unreported crystal structure that, surprisingly, forms in the same sample from the same building blocks and exhibits a distinctive needle-like morphology (Fig. ). As shown in Figure ,b, this crystal features an unusual open structure with empty channels running through its entire length. |
66f4241e51558a15ef144cfa | 8 | By analyzing the distribution of distances between particles, we constructed the crystal's unit cell, which has a 3:4 ratio of large to small particles and a remarkably low volume fraction of 56%. Hereafter, we refer to this new crystal as L 3 S 4 . Unlike CsCl and Th 3 P 4 , L 3 S 4 seems to nucleate only heterogeneously on the charged surface of the crystallization chamber, and simulations show that for sufficiently large surface charge the nucleation of L 3 S 4 can be greatly enhanced relative to CsCl despite it less favorable bulk energy (Extended Data Fig. and Extended Data Movie 6). |
66f4241e51558a15ef144cfa | 9 | While in the middle of our dialysis setup we observe regions where each one of these structures seem to be individually dominant (Figure ), towards the sealed end of the capillary, we observe coexistance of all three of these structures and several others within a single field of view (Fig. and Extended Fig. ). Since these structures had the most time available to nucleate at low salt concentration, we infer that the barriers to nucleation for these structures must be similar. |
66f4241e51558a15ef144cfa | 10 | So far, we have described how our dialysis setup allowed us to observe formation of numerous large binary single crystals with an array of forms for a system prepared with a fixed ratio of particle size, surface charge, and number ratio. Within our setup, we are also able to observe more complex hierarchical assemblies, in particular crystals formed through heteroepitaxial growth of one structure templated by another (e.g. Fig. structures IV and V, Extended Data Movie 6). Focusing on samples of L 3 S 4 , we frequently observe formation of thin 'flag'-like protrusions from the sides of L 3 S 4 rods (Fig. ). SEM images of these flags show that they have a sharp 80 degree corner, and a surface arrangement of particles that does not belong to the structure we determined for L 3 S 4 . To inspect this behavior in more detail, we seeded MD simulations with the large L 3 S 4 crystal from Fig. in bulk, which allowed the crystal to grow in all directions. Surprisingly, after several rounds of continued addition of particles, we observed not one but two simultaneous instances of heteroepitaxial growth, one of which produced a structure commensurate with the flags observed in SEM, and one of which we identified as CsCl-like (Extended Data Movie 7). Using our full knowledge of particle positions in the MD simulation, we are able to demonstrate that the nucleation of these secondary crystals occurs due to commensurate arrangements of particles within the two different unit cells. This investigation shows that the (210) face of CsCl and (022) face of L 3 S 4 are able to interlock, and that the flag structure seen in simulation can be formed by extending a rhombic subset of particles from the L 3 S 4 unit cell (Extended Data Fig. ). The flag formed in MD simulations has a surface structure that closely matches the one observed in experiments. The compatibility of the CsCl unit cell with L 3 S 4 may also explain why they are often observed in contact within the experiments. |
66f4241e51558a15ef144cfa | 11 | A particularly promising outcome of this work is the potential to control the formation of specific structures or polymorphs by creating charged patterns on the substrate. 9 Low-density (ρ = 1.05 g/cm 3 ) polystyrene (PS) and low-refractive-index (n = 1.39) pentafluoropropyl methacrylate (PFPMA) colloids were synthesized via surfactant-free emulsion polymerization for bright-field microscopy and laser scanning confocal microscopy experiments, respectively. For the synthesis of 200 nm diameter positively charged PS particles, a mixture of 550 mL deionized water and 3 mL styrene monomer (≥ 99% from MilliporeSigma) was stirred at 330 rpm in a 1 L three-neck round-bottom flask. After purging with nitrogen for 1 hour, 0.5 g of 2,2'-azobis(2-methylpropionamidine) dihydrochloride (AIBA) (97% from MilliporeSigma), dissolved in 10 mL deionized water, was injected into the mixture. The components were then heated to 60 • C and stirred at 330 rpm under nitrogen overnight. The particles were stabilized by adding 5 mL of 5 wt% Pluronic F108 solution and washed via repeated sedimentation and resuspension cycles. Finally, the particle suspensions were dialyzed against deionized water for one week using 50 kD Spectra/Por dialysis tubing, with daily water changes to ensure complete removal of salt. Negatively charged PS particles were synthesized similarly, replacing AIBA with an equivalent weight of potassium persulfate (KPS) (≥ 99% from MilliporeSigma). |
66f4241e51558a15ef144cfa | 12 | The surface potential of each particle system was measured using a Malvern Zetasizer Nano ZS with DTS1070 folded capillary cells. Measurements were performed on highly dilute samples equilibrated in 10 mM NaCl. Zeta potentials were calculated using the Smoluchowski approximation (Henry's function f (κa) = 1.5), with refractive indices of 1.39 for PFPMA particles and 1.59 for PS particles. |
66f4241e51558a15ef144cfa | 13 | Oppositely charged PS particles were separately equilibrated with 0.1 wt% Pluronic F108 and 2-5 mM NaCl for 30 minutes. They were then mixed together while vortexing. The resulting mixture was promptly transferred into hydrophobized borosilicate glass capillaries (VitroCom, model 3520), which were then sealed on both ends with wax (Hampton Research) or epoxy resin (Norland 81). Capillaries were pre-cleaned in a Jelight Model 18 ultraviolet ozone (UVO) cleaner for 20 minutes. Subsequently, they were exposed to methyltrichlorosilane (99%, MilliporeSigma) vapor inside a moisture-free sealed chamber for 1 hour to hydrophobize the surface. After this treatment, the capillaries were washed with water and ethanol for three cycles and finally dried in an oven. This hydrophobization pre-treatment facilitates the formation of a polymer brush on the glass surface when in contact with a Pluronic F108 solution. |
66f4241e51558a15ef144cfa | 14 | CsCl-like crystals (space group P m3m, No. 221) were formed using particle size ratios ranging from 0.8 to 1.0 and a number ratio of 1:1. The Wulff shape of these crystals is a rhombic dodecahedron, bound by {110} planes, reflecting their equilibrium shape as determined by surface energy minimization (Extended Data Fig. ). |
66f4241e51558a15ef144cfa | 15 | NaCl-like crystals (space group F m3m, No. 225) were formed using 300 nm (+) PS and 130 nm (-) PS particles (β = 0.43) at a 1:1 number ratio. A precise size ratio of approximately √ 2 -1 is required to form NaCl crystals; otherwise, K 4 C 60 is typically observed. The Wulff shape of these crystals is a cube, bound by {100} planes (Extended Data Fig. ). |
66f4241e51558a15ef144cfa | 16 | K 4 C 60 -like crystals (space group I4/mmm, No. 139) were formed using 350 nm (+) PS and 160 nm (-) PS particles (β = 0.46) at a 1:4 number ratio, as well as 200 nm (+) PS and 400 nm (-) PS particles (β = 0.50) at the same number ratio. The larger particles are positioned at the body-centered cubic (bcc) lattice sites. The small particles filled all the tetrahedral interstitial sites of the (001) plane and only half of the (100) and (010) planes. |
66f4241e51558a15ef144cfa | 17 | To perform experiments at variable interaction potentials, mixtures of oppositely charged PS particles with 4.5 mM NaCl and 0.1 wt% F108 were introduced into 50-mm-long glass capillaries (inner dimensions: 2.0 mm × 0.2 mm, VitroCom) and sealed at one end. The capillaries were then immersed in 100 mm diameter Petri dishes filled with deionized water (Extended Data Fig. ). During crystallization, each capillary was imaged using a Luxonis OAK-D S2 camera, recording a time-lapse with a 10-minute delay between frames (Extended Data Movie 5). The position of the crystallization front was tracked over time using Im-ageJ, by identifying and tracking the boundary between the opaque area of the capillary (gas phase) and the transparent area (crystalline phase). Simultaneously, we tracked the crystallization front by taking microscopy images at regular intervals using a bright-field microscope equipped with a 10X air objective. |
66f4241e51558a15ef144cfa | 18 | Bright-field images and movies were acquired using a Leica DMI3000 inverted microscope equipped with differential interference contrast optics and high-resolution cameras: a grayscale Jenoptik Gryphax Rigel and a color FLIR Grasshopper3. Crystal nucleation was observed within hours using a 100X oil immersion objective. For continuous imaging of crystal growth over several days, sealed capillary samples were glued to a 100 mm Petri dish (FisherScientific), immersed in water at room temperature, and monitored using a 10X air objective with minimal light intensity to reduce heating. |
66f4241e51558a15ef144cfa | 19 | Time-lapse z-stacks of scanning fluorescent images were acquired using a Leica SP8 confocal microscope equipped with a 100X oil objective, recording the crystallization process of positively charged 375 nm and negatively charged 440 nm PFPMA particles in 40% DMSO at 30-minute intervals. The two BODIPY dyes were excited at 500 nm and 580 nm, with emission signals collected at 510-520 nm and 590-600 nm, respectively. The z-step size was set to 0.07 µm, allowing for 5 scans per particle to achieve precise tracking. To prevent dye bleaching during extended scanning, the lowest possible laser power (typically around 5% of the maximum) was used. The coordinates of oppositely charged particles were estimated from grayscale images of separated channels in the z-stack data using the TrackPy Python package. These coordinates were imported into Blender, where sizes based on scanning electron microscopy were assigned to recreate the structure in 3D. X-ray diffraction (XRD) patterns shown in Extended Data Fig. were subsequently generated using Mercury software from the particle coordinates. |
66f4241e51558a15ef144cfa | 20 | Electron Microscopy imaging was performed on fixed samples. Crystals formed in sealed capillaries were fixed by immersing the capillaries in a deionized water bath and carefully removing the sealant (wax or epoxy). The capillaries were then left undisturbed in the deionized water to allow the salt to diffuse into the water bath. After a few days, ion exchange resin (AmberLite MB from MilliporeSigma) was added to the samples to remove all remaining ions from the system. This ion removal process lasted for another 3-4 days, during which the water bath was changed daily. To recover the fixed crystals, the capillaries were scored with a glass cutter and carefully broken underwater. The broken capillaries were taped onto SEM stubs (Ted Pella) using conductive carbon adhesive tabs (Electron Microscopy Science), airdried, and coated with 3-5 nm of iridium using a Cressington 208HR high-resolution sputter coater. The samples were then imaged using a MERLIN field emission scanning electron microscope (Carl Zeiss). |
66f4241e51558a15ef144cfa | 21 | where J j is the flux of salt, D is the diffusion coefficient of salt (1.61 × 10 -9 m 2 /s), and c j is the concentration of component j. The initial NaCl concentration throughout the capillary was 4.5 mM, with boundary conditions applied such that the interface at one end was fixed at 0 mM, and there was no flux across any other interfaces. The numerical solutions were calculated for 96 hours at 15-minute intervals. Energies in Fig. were computed by converting the salt concentration at a given position and time to a λ D in meters using the formula, |
66f4241e51558a15ef144cfa | 22 | where ϵ is the dielectric constant taken to be 80.1, ϵ 0 is the vacuum permittivity, R is the ideal gas constant, F is Faraday's constant, T is the temperature and C is the salt concentration in units of mol/L. The attractive interaction strength is then found by finding the minimum of the attractive potential between negative and positive particles given in the next section. |
66f4241e51558a15ef144cfa | 23 | To model the assembly of charged colloids, we performed Langevin dynamics simulations of binary mixtures of colloidal particles using the HOOMD-Blue software, 37 as previously implemented. † A total 6750 number of charged particles were placed in the simulation boxes in a simple cubic arrangement in a 1:1 ratio at varying ϕ p . Unless otherwise indicated, the radii of the positive-and negatively charged particles were taken to be 85 nm and 105 nm, respectively. The temperature was maintained by a Langevin thermostat at 1 k B T. The drag coefficient, γ was set to 0.001. The screened Coulombic interaction between two particles is computed by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, expressed as |
66f4241e51558a15ef144cfa | 24 | Here, ϵ is the solvent permittivity which was set to 80, ψ i and ψ j are the surface potentials for the two particles which unless otherwise indicated were set to +50 mV and -50 mV for positive and negative particles, respectively, and λ D is the Debye length. h ij is the distance between the surfaces of the particles. a ij is the ionic radius coming from the Derjaguin approximation which is expressed as |
66f4241e51558a15ef144cfa | 25 | The repulsion radius, a R ij , present in the pre-factor is given by a R ij = (r i + r j )/2. L, the polymer brush length, is set to 10 nm for all simulations. 41 σ is the polymer brush density which is equal to 0.09 nm -2 . The simulations were performed at six different values of ϕ p , and for each, unless otherwise mentioned, λ D was varied from 5.1 to 5.3 nm. We performed 6 simulations in each condition. Repulsive walls, which interact with the particles by a shifted Lennard-Jones potential, were used to produce a simulation box, which is convenient for analysis but is not expected to effect results given we are studying assembly from a dilute gas phase. Simulations were carried out for 4 x 10 9 number of steps using a dimensionless time step of 0.005 unless otherwise specified. nm. All other settings were the same as described above. |
66f4241e51558a15ef144cfa | 26 | To study the effect of a charged substrate on the crystallization, we included a negatively charged wall at position Z min in the simulation box. The charged wall is formed of a hexagonal arrangement of spherical particles of radius 30 nm. The interaction between the charged wall and a colloid particle was modeled using the same combined DLVO+brush potential as between the two primary species. The surface potential of the wall particles was varied from -45 mV to -50 mV. |
66f4241e51558a15ef144cfa | 27 | In addition to simulating the size ratio of 0.81, we performed simulations with size ratio of 0.45 (r P = 176.5 nm and r N = 80 nm) and number ratio (positive to negative particles) of 1:2 to produce K 4 C 60 crystals (see Extended Fig. ). Simulations using experimentally realistic surface potentials of positive and negative particle, +30 mV and -50 mV, formed crystals on a surface with wall particles having a charge of -50 mV. Those shown in Extended Fig. formed with λ D =5.9 nm and volume fraction 0.0345. Bulk crystallization in Extended Fig. was observed for λ D =5.3 nm with surface charges of +/-50 mV at volume fraction 0.005. All other parameters were same as described above. |
61d837ab5015eb393fb14e74 | 0 | Since the introduction of the QM/MM approach by Warshel and Levitt in 1976 it has evolved to a broadly used tool in computational chemistry. Dividing a large biomolecular system into two subsystems, one smaller subsystem treated quantum-mechanically (QM) and one larger subsystem treated with molecular mechanics (MM), allows one to investigate the mechanisms and energetics of enzymatic reactions in an efficient way. Consequently, the application of the QM/MM approach to large biomolecules such as enzymes has become a common practice in the last two decades. However, in practice setting up QM/MM calculations is far from trivial and requires many manual choices by the simulation scientist. Besides the selection of a suitable QM method and an MM force field, the most important decision is the choice of the QM region. |
61d837ab5015eb393fb14e74 | 1 | The convergence of QM/MM results with the choice and particularly the size of the QM region has been investigated in several studies, which underline that it generally has a large effect on the quality of the final results, and that often rather large QM regions are required for reaching converged results. To alleviate this problem, schemes for the systematic construction of QM regions have been proposed, usually with the aim of obtaining medium-sized QM regions that provide reliable QM/MM reaction energies. Examples of such schemes include free energy perturbation analysis, 17 charge deletion analysis, charge shift analysis (CSA), and Fukui shift analysis (FSA). For their recently developed selfparametrizing system-focused atomistic models (SFAM), Brunken and Reiher proposed an automatic scheme for the construction of hybrid QM/SFAM models, including a systematic determination of the QM region based on the energy gradient. For a given QM region, there are different possible choices of the embedding method, of a suitable coupling scheme, and for the treatment of the boundary region if covalent bonds cross the border between the subsystems. For the commonly used electrostatic embedding scheme, the choice of the MM point charges will influence the resulting QM and QM/MM energies, and further parameters need to be chosen in advanced polarizable embedding or flexible embedding schemes. Different coupling schemes are available such as IMOMM, ONIOM, or the AddRemove 30 model. The most common approach for treating covalent bonds across the QM-MM boundary is saturating the QM region with capping atoms. Here, the position and the type of these atoms is crucial for the calculations. An alternative are frozen orbitals, 31 e.g., in the Localized SCF (LSCF) or the Generalized Hybrid Orbital (GHO) approach. The uncertainties introduced by all these different choices and the corresponding parameters are interconnected and will again depend on the choice of the QM region. |
61d837ab5015eb393fb14e74 | 2 | Consequently, there is a need for rigorous uncertainty quantification for QM/MM calculations, i.e., to systematically assess the sensitivity of the QM/MM energy with respect to these technical choices and empirical parameters and to ultimately provide rigorous error bounds on the results of QM/MM calculations (compared to a full QM treatment). Mathematical and computational tools for quantifying uncertainties in computer simulations have been developed intensively in the past decades (for textbooks, see, e.g. Refs. 34,35) and are employed in many areas of simulation science, but their application is just starting to emerge in computational chemistry. Recently, we have applied such tools for analyzing the sensitivity of calculated spectra with respect to distortions of the molecular structure. Here, we aim at taking a first step towards uncertainty quantification for QM/MM methods by analyzing the sensitivity of QM/MM reaction energies with respect to variations of the MM point charges. While there are other relevant empirical parameters entering in QM/MM calculations, most importantly those related to the treatment of the QM-MM boundary (e.g., to the placement of the link atoms), we expect the MM charges to be a key factor influencing the final QM/MM results. |
61d837ab5015eb393fb14e74 | 3 | The ability to quantify the sensitivity of QM/MM calculations with respect to parameters of the MM environment provides a natural starting point for guiding the systematic choice of the QM region. With increasing size of the QM region and approaching a full QM calculation, one can expect this sensitivity to decrease. Therefore, choosing the QM region such that the uncertainty is reduced implies that the QM/MM calculation approach those of a full QM calculation. Here, we exploit this idea by proposing a simple and efficient scheme for the systematic construction of the QM region that is guided by uncertainty quantification. This work is organized as follows. In Section 2 we recall the necessary theoretical background of QM/MM approaches (Sect. 2.1, introduce our point charge variation analysis (PCVA) for analyzing the sensitivity of QM/MM energies (Sect. 2.2, and give the computational details (Section 2.3). In Section 3, we introduce the model system used in this work and discuss the convergence of ligand charges and reaction energies for QM regions of increasing size. The sensitivity of these quantities with respect to global point charge variations is analyzed in Section 4. This is followed in by the evaluation of the energy sensitivity for single amino acids in Section 5, which are used to devise a scheme for the systematic construction of QM regions based on a PCVA. The QM regions obtained with this PCVAbased scheme are assessed for QM regions of increasing size and for atom-economical QM regions in Sections 6 and 7, respectively. Finally, conclusions and an outlook can be found in Section 8. |
61d837ab5015eb393fb14e74 | 4 | 2.1 QM/MM energy partitioning QM/MM is based on the partitioning of the full target system into a QM region (A) including the interesting part of the system, such as the active center of an enzyme, and an MM region (B) containing all other atoms, i.e., the active center's environment. The total energy can be expressed as the sum of the QM energy of subsystem A, E QM (A), the MM energy of subsystem B, E MM (B), and an interaction energy between the two subsystems, E int (A, B), |
61d837ab5015eb393fb14e74 | 5 | The energy of the QM region, E QM (A), is obtained from a quantum-chemical calculation of the corresponding subsystem A. To allow for covalent bonds to cross the boundary between the QM and MM regions, the QM subsystem is usually saturated using capping atoms. The energy of the MM region, E MM (B), is calculated using a classical force field and contains the usual bonding and non-bonding force-field energy contributions. Finally, the interaction energy E int (A, B) contains both electrostatic interactions [E int,el (A)] and non-electrostatic interactions [E int,ne (A, B)] between the two subsystems. |
61d837ab5015eb393fb14e74 | 6 | In the electrostatic embedding scheme, which is commonly used when applying QM/MM to enzymatic reactions, the electron density of subsystem A is polarized by the MM point charges of subsystem B. The MM point charges are included in the QM Hamiltonian 4 to compute the interaction between the electron density ρ A (r) of subsystem A and the electrostatic potential V B (r) derived from the point charges of subsystem B, |
61d837ab5015eb393fb14e74 | 7 | The reaction energy calculated within a QM/MM model is subject to numerous sources of uncertainty (see Introduction). One important element of uncertainty quantification is the analysis of the sensitivity of the simulation results with respect to its input parameters. Here, we consider the QM/MM reaction energy ∆E reaction QM/MM as our quantity of interest (QoI) and analyze how sensitively it depends on parameters of the QM/MM model. |
61d837ab5015eb393fb14e74 | 8 | We consider the MM point charges q MM as one of the most important sources of uncertainty and want to systematically analyze the effect of variations in the MM point charges on our QoI, i.e., the reaction energy ∆E reaction QM/MM (q MM ). To this end, we follow our earlier work on the sensitivity of calculated spectra with respect to distortions of the molecular structure and consider a collective variation of the MM point charges, i.e., |
61d837ab5015eb393fb14e74 | 9 | where q MM is a vector of size N B containing all MM point charges, q 0 MM is the vector of the undistorted MM point charges as provided by the employed force field, and ∆q MM is a collective variation of these point charges, which depends on a parameter ∆q that controls the size of the variation. We chose the collective variations of the MM point charges such that I ∆q MM,I = 0, i.e., the sum of the MM point charges is preserved. |
61d837ab5015eb393fb14e74 | 10 | where N aa,i is the number of atoms in the i-th amino acid. The first will provide an estimate of the overall sensitivity of the QM/MM reaction energy to variations of the MM point charges, while the second will allow us to assess the effect of the individual single amino acids. |
61d837ab5015eb393fb14e74 | 11 | Molecular dynamics calculations were performed using GROMACS 2019.3 with the AMBER99SB-ILDN force field. The already equilibrated initial structure provided by Ku-lik et al. in the Supporting Information of Ref. 15 was solvated in TIP3P water molecules in a cubic simulation box with 1 nm distance between the borders and the enzyme. The system was neutralized by adding six sodium cations. The positions of the solvent molecules and ions were minimized using the force field, while the enzyme structure was held fixed. |
61d837ab5015eb393fb14e74 | 12 | All QM/MM calculations were performed using the Amsterdam Modeling Suite (AMS Version 2020.203). The Amsterdam Density Functional (ADF) engine was used for the QM part applying density functional theory (DFT) with the PBE exchange-correlation functional employing a DZ and a TZP Slater-type orbital basis set 49 for all geometry optimizations and single point calculations, respectively. For the MM region the ForceField engine of AMS was used with the AMBER95 force field, which was extended by parameters for SAM and catecholate using Antechamber 51,52 and acpype. Electrostatic embedding as implemented in AMS was applied for the interaction be- All QM/MM geometry optimizations were performed using the FIRE minimization algorithm with all solvent molecules fixed to their initial coordinates. All charges evaluated for charge convergence tests are calculated from the Voronoi deformation density (VDD) of the reactant structure only. |
61d837ab5015eb393fb14e74 | 13 | were achieved using Python. Plots were generated with Matplotlib 58,59 and structures were visualized using Vmd. A data set containing PDB files of the reactant and product starting structures, a modified AMBER95 force field file, AMS fragment files for the ligands and ions, and the AMS input files for all geometry optimizations and single point calculations is available at Ref. All QM calculations were performed using the GGA exchange-correlation functional PBE. In contrast to Ref. 15, we did not encounter a closing of the HUMO-LUMO gap with increasing size of the QM region. Instead, the HOMO-LUMO gap remained constant at about 1 eV for the larger QM regions (see Supporting Information, Fig. ). Note that the results presented in Ref. 15 that will be discussed in the following, have been obtained with the range-separated hybrid functional ωPBEh, which also avoids a spurious closing of the HOMO-LUMO gap. |
61d837ab5015eb393fb14e74 | 14 | To test the overall QM region size convergence we first evaluated the distances between SAM methyl and the catecholate oxygen atom in the reactant structures (see Supporting Information, Fig. ). The SAM to catechol distance in the initial MM-equilibrated structure before QM/MM optimization is 3.11 Å which is similar to the most likely distance in the underlying distance distribution. With increasing QM region size the distance significantly decreases for regions 2 and 3 from about 3.05 Å to 2.7 Å and 2.8 Å, respectively. With a distance of 2.97 Å for region 4 and 5 the SAM-CAT distance starts converging for region 6 and larger to between 2.8 and 2.9 Å. Given the differences in the QM treatment, this behavior is in reasonable agreement with the results of Ref. 15, particularly for the larger QM regions. The absence of only one of these three residues causes the charge of +0.55. |
61d837ab5015eb393fb14e74 | 15 | Overall, it can be stated that small QM regions are not sufficient for reproducing the ligand charges found for large QM regions because important residues coordinating the ligands might be missing. When using a distance-based construction of the QM region, rather larger QM regions need to be reached before all relevant residues are included in the QM region. |
61d837ab5015eb393fb14e74 | 16 | For small QM regions, the reaction energy shows large oscillations, while starting from QM Overall, our results confirm the slow convergence of the reaction energy with increasing size of the QM region found in earlier studies and emphasize the need for systematic protocols for the construction and selection of the QM region. We note that Jindal and Warshel 14 |
61d837ab5015eb393fb14e74 | 17 | found that in COMT, the activation barrier shows a much smaller sensitivity with respect to the choice of the QM region than the reaction energy. Therefore, we will not consider activation barriers and focus on the reaction energies in the present work. In addition to the VDD charges obtained with the undistorted MM charges for the different QM regions considered above, Fig. includes the VDD charges obtained with collective point-charge variations ∆q tot MM with ∆q between +0.005 and -0.005. The corresponding sensitivities (defined in analogy to Eq. ( ) for the VDD charges and evaluated numerically using a symmetric two-point finite difference formula [Eq. ( )] with ∆q = 0.005) are plotted in Fig. . |
61d837ab5015eb393fb14e74 | 18 | Significant deviations from the unvaried curve are visible for ∆q = ±0.005. Overall, the variations do not affect the charge convergence behavior, but lead to different ligand-dependent observations concerning the sensitivity. For CAT and Mg 2+ , the VDD charge sensitivity decreases with increasing QM region size (with the exception of region 1 for CAT) and converges for region 4 and larger. For the largest QM regions 8 and 9, the sensitivity of the Mg 2+ charge is reduced to almost zero. |
61d837ab5015eb393fb14e74 | 19 | For SAM, in contrast to CAT and Mg 2+ , the VDD charge sensitivity is initially increasing until a QM region size of about 300 atoms is reached (region 4), before the sensitivity starts to slightly decrease when further enlarging the QM region. This different behavior arises because SAM is a much larger molecule than CAT and thus offers numerous possibilities for charge redistribution and more contact sites to adjacent residues. For the small QM regions, the possibilities of charge redistribution to adjacent QM residues are reduced, which results in a smaller VDD charge sensitivity in these cases. In region 4, five residues (GLY65, TYR67, TYR70, SER71 and ILE90) which are part of the SAM coordination sphere are added to the QM region. This enables a wide variability for the SAM charge to be redistributed, resulting in an increase in sensitivity for this QM model. In larger QM regions, the SAM charge sensitivity is then gradually decreasing because only single residues being part of the SAM coordination sphere are added, such as MET39 in region 5 or TRP142 in region 6. |
61d837ab5015eb393fb14e74 | 20 | The plot of the QM/MM reaction energies for the different QM regions in Fig. also includes the reaction energies obtained for collective point-charge variations ∆q tot MM , whereas Fig. shows the corresponding sensitivities δ∆E reaction QM/MM . The point charge variation leads to significant changes in the reaction energy especially for a variation of ∆q = ±0.005, for which changes of up to 8 kcal/mol could be observed for small QM regions. The convergence behavior of the energy itself is not affected by the point charge variation. The sensitivity starts decreasing strongly with region 4 while the reaction energy converges towards the one found for the largest QM region 9. An exception is found for QM region 8, for which the reaction energy does not follow this trend. This can be attributed to the inclusion of four rather critical charged residues in region 8, namely the negatively charged GLU5, GLU63, and ASP168 as well as the positively charged LYS45. Remarkably, for this outlier the sensitivity is also strongly increased. |
61d837ab5015eb393fb14e74 | 21 | Overall, these first point charge variation tests show that small changes in the MM point charges have an impact on the QM region. While VDD charges and the reaction energy slowly converge for larger QM regions, the corresponding sensitivities to global point-charge variations decrease, whereas outliers are accompanied by an increased sensitivity. Generally, sensitivities are smaller for reaction energies closer to our best estimate (i.e., the reaction energy obtained for the largest QM region). This indicates that the sensitivity to global point-charge variations might indeed be useful as an indicator for the reliability of QM/MM calculations, and that systematically reducing this sensitivity could be a promising strategy for the systematic construction of the QM region. |
61d837ab5015eb393fb14e74 | 22 | Motivated by the results of a global point charge variation analysis presented in the previous section, we set out to develop a protocol of the systematic construction of the QM region that aims at minimizing the sensitivity of the QM/MM reaction energy. To this end, we consider the sensitivity of the QM/MM reaction energy with respect to variations of the point charges in single amino acids, i.e., we perform a single amino acid PCVA. The resulting protocol for systematic QM region construction is summarized in Fig. and will be described in the following. |
61d837ab5015eb393fb14e74 | 23 | As starting point, we consider the minimal QM/MM model with QM region 1, i.e., for our COMT test case only the ligands and the catalytically active magnesium ion are included in the QM region. For single-point energy calculations of the geometry-optimized reactant and product structures, we calculate the sensitivity of the QM/MM energy with respect to variations of a single amino acid ∆q aa,i MM,I [cf. Eq. ( )]. Here, we use ∆q = -0.5, i.e., the total charge of the considered amino acid is decreased by 0.5 while an equal charge of opposite sign is distributed over all other MM atoms. |
61d837ab5015eb393fb14e74 | 24 | To reduce the computational effort for the evaluations of this sensitivity for each amino acid, we assessed several possible simplifications compared to the global PCVA in the previous section. The different levels of simplification are referred to as PCVA-A to PCVA-E, and the sensitivities obtained in these different approximations are shown in Fig. . First, instead of the full QM/MM reaction energy (PCVA-A) we use only the QM contribution (PCVA-B), i.e., the approximation of Eq. ( ) is employed. This is justified as the effect on the QM energy is the main focus of the analysis and possible undesired MM-only effects will be excluded. Furthermore, no significant differences in the calculated sensitivities are observed comparing the full and QM energy approach. Second, instead of the reaction energy we could use the sensitivity of the product (PCVA-C) or reactant (PCVA-D) energy instead. |
61d837ab5015eb393fb14e74 | 25 | While this does change the values of the sensitivities, it leads to overall similar trends (cf. Fig. ). Using the product or reactant energy sensitivities could also be advantageous for avoiding error cancelation that might be present when considering the sensitivity of the reaction energy only. Consequently, we choose to use only the reactant energies, which reduces the number of calculations to be performed by half. The impact for this approximation on the selection of the QM region will be discussed below. Finally, instead of using a symmetric two-point formula for the numerical differentiation, it turns out to be sufficient to use a forward finite-difference formula (PCVA-E), which again reduces the number of QM calculation by another factor of two. |
61d837ab5015eb393fb14e74 | 26 | Naively, it could be expected that residues closer to the active site show higher sensitivities to point charge variations than distant ones. However, there are also several high-sensitivity amino acids at medium distances to the active site and low-sensitivity residues very close to the substrates. This observation confirms that an exclusively distance-based approach to include residues into the QM region is not able to detect all important amino acids and furthermore includes residues which are probably not necessary to obtain consistent QM regions. To find a compromise between including amino acids that show a high sensitivity and those that are close to the active site, we define an empirical QM region indicator Θ i for each amino acid by dividing the sensitivity by the COM distance between the amino acid and the active site, i.e., |
61d837ab5015eb393fb14e74 | 27 | The resulting indicator is plotted in Fig. . A comparison of the indicators for the schemes PCVA-A to PCVA-D is shown in the Supporting Information (Fig. ), and an additional Table lists the 16 amino acid residues with the highest QM region indicators for the schemes PCVA-A to PCVA-E (see also Section 7). When using the QM-only instead of the full QM/MM reaction energy (i.e., comparing PCVA-A and PCVA-B), the only change among the highest-ranked amino acids is that ILE88 is replaced by CYS68. Similarly, only two changes among the 16 amino acids with the highest indicators are found when using the reactant instead of the product energies (i.e., comparing PCVA-C and PCVA-D). Here, LEU64 and TRP142 are replaced by VAL41 and CYS172. All these amino acids show very similar sensitivities and indicators in the different schemes. Larger differences are found going form the reaction energies (PCVA-B) to using the reactant energies (PCVA-D), where six differences appear among the top-16 amino acids. However, these changes mostly occur for amino acids with very close values of the QM region indicator. Furthermore, the use of the reactant or product energies avoids error cancelation that might be present when using the reaction energy. Finally, only two differences (VAL41 and TYR67 instead of LEU64 and TYR146) are found among the 16 highest-ranked amino acids when going to a simplified numerical differentiation formula (i.e., from PCVA-D to PCVA-E). Overall, this confirms that the PCVA-E approximation seems to be a reasonable choice. |
61d837ab5015eb393fb14e74 | 28 | Ideally, by using PCVA for a systematic construction of QM regions, the convergence towards the results obtained with very large QM regions should be accelerated compared to an exclusively distance-based construction of the QM region. To this end, we construct QM regions consisting of just as many residues as in the distance-based approach (see Section 4) |
61d837ab5015eb393fb14e74 | 29 | and label these regions as 2', 3' etc. (e.g., QM regions 3 and 3' both contain seven amino acid residues). Fig. and Tab. S4 in the Supporting Information show which residues are included for each QM region. Again, geometry optimizations of the reactant and product structures were performed for each of these QM regions. |
61d837ab5015eb393fb14e74 | 30 | Fig. shows the convergence of the VDD charges and the QM/MM reaction energy as well as the corresponding sensitivities to global point charge variations (cf. Fig. for the same plot PCVA-constructed QM regions deliver overall lower sensitivities regarding VDD ligand charges (see Fig. ), which marks an expected behavior because high-sensitivity residues are included in the QM region by PCVA. The convergence of the charge sensitivities is similar to the analysis for distance-based QM regions (cf. Fig. ) with a fast convergence for Mg 2+ , a constant behavior for CAT, and jumps for SAM with a slightly decreasing trend. |
61d837ab5015eb393fb14e74 | 31 | The reaction energy (see Fig. ) decreases for the smallest QM regions, starts to stabilize for QM regions 4', and oscillates around our best estimate of about -11 kcal/mol for larger QM regions. However, these oscillations are smaller than for the distance-based construction of the QM regions. Note that compared to Fig. , we updated our best estimate to correspond to QM region 9' in Fig. . |
61d837ab5015eb393fb14e74 | 32 | In contrast to the distance-based case, a slightly increasing trend is observed for the reaction energy sensitivity (Fig. ). For QM region 8', at which the reaction energy is further from our best estimate, the sensitivity also shows a marked increase. Except for the smallest QM regions, the global PCVA sensitivity can thus be used to judge the accuracy of the calculated QM/MM reaction energy. The overall larger sensitivity for the PCVAbased QM regions compared to the distance-based construction could be an effect of a larger contact area between the MM and QM regions because in the PCVA case, MM residues close to the active site with low sensitivities remain in the MM part and can affect adjacent QM residues. (e.g., VAL41, GLU89, or ASP140). Moreover, also more distant residues are included that would not be considered in a 16-residue QM region in the distance-based case (e.g., MET39, LYS45, ALA66, or ASP168). This indicates the ability of PCVA to even detect high-impact residues located relatively distant from the active site COM. Nevertheless, there are several residues included by CSA and/or FSA that are not under the 16 highest-ranked residues when applying the PCVA approach. However, most of these residues are assigned a PCVA rank close to 16 such as ASN40, GLU63, or ILE90. |
61d837ab5015eb393fb14e74 | 33 | An extreme case with a very low PCVA rank (178) compared to CSA (10) and FSA (10-11) is SER71. This residue is located very close to the active site and thus potentially important for ligand binding, but it shows a very low electrostatic effect on the substrates and is thus not detected by PCVA. Another case is SER118, which is ranked about 30 places lower in PCVA than in CSA and FSA. Both these cases concern serine residues, which might show only a small electrostatic effect. |
61d837ab5015eb393fb14e74 | 34 | PCVA also detects residues that are much lower ranked in CSA and FSA. PHE138 and LEU139 are both part of the ligand binding site and obviously have a high electrostatic impact on the substrates. Consequently, PCVA ranks them very high at 12 and 13, respectively, in contrast to FSA (156-163) while CSA also assigns quite high ranks to these residues (24-36). Similar results are observed for TRP142 and LYS143, which also seem to play a role in ligand binding and are ranked on 10 and 11 in PCVA, whereas FSA assigns much lower ranks (17 and 18-155) than CSA (37+). |
61d837ab5015eb393fb14e74 | 35 | In Fig. , we compare the VDD charges of SAM, CAT, and the catalytically-active Mg 2+ cation as well as the QM/MM reaction energy obtained for the atom-economical QM regions constructed using CSA, FSA, and PCVA to those obtained for PCVA-constructed QM regions of increasing size discussed in Section 6. Note that the size of the atom-economical QM regions of 16 amino acids is in between those of QM regions 4' (13 amino acids) and 5' |
61d837ab5015eb393fb14e74 | 36 | Regarding VDD charges (see Fig. ), PCVA performs as well as CSA and FSA. The change in the Mg 2+ charge to about 0.3 with the distance-based region 8 (34 residues) and larger is achieved already in the QM regions containing 16 residues. For SAM, all three atom-economical QM regions also provide the converged charge. In the SAM case, none of the methods is able to detect the charge change to 0.25 for region 7 and larger. This is a fundamental limitation of QM regions of a given size and can probably only be rectified by using larger QM regions. |
61d837ab5015eb393fb14e74 | 37 | As a first step towards systematically quantifying the uncertainties of QM/MM calculations, we have presented a point charge variation analysis for assessing the sensitivity of QM/MM reaction energies to changes of the MM point charges. To this end, we considered the derivative of the QM/MM reaction energy with respect to selected distortions of the MM charges. |
61d837ab5015eb393fb14e74 | 38 | This derivative can be calculated numerically by performing QM/MM calculations with varied MM point charges, and different efficient approximations can be employed. Generally, the most simple approximation (PCVA-E), in which a forward finite difference is used and only the reactant structure is considered, turns out to be sufficient for a qualitative assessment of uncertainties. |
61d837ab5015eb393fb14e74 | 39 | A global PCVA, in which all protein point charges are varied simultaneously, can be used as a simple indicator of the accuracy of the resulting QM/MM reaction energy as well as other properties of the active site, such as ligand charges. For the considered test cases we found that when comparing different QM regions, the sensitivity in a global PCVA is smaller for those QM regions that yield results closer to the best estimate obtained for the largest QM regions, i.e., the sensitivity generally decreases when approaching the limit of a full QM calculation. However, this only holds once the QM regions have reached a reasonable size and the correlation between the sensitivity in a global PCVA and the deviation from the best estimate is not always clear. |
61d837ab5015eb393fb14e74 | 40 | Nevertheless, our results demonstrate that the analysis of the sensitivity with respect to the MM point charges is a good starting point for the investigation of uncertainties in QM/MM calculations. We are planning to extent this work in the future by considering not only selected distortions of the MM point charges, but performing a full sensitivity analysis that allows one to identify the collective point charge variations that have the largest influence on QM/MM reaction energies, following our earlier work on structural distortions in theoretical spectroscopy. While the reliability of considering only one global distortion of the MM point charges is limited, such a more comprehensive assessment of the sensitivity can be expected to overcome the limitations of our present approach. |
61d837ab5015eb393fb14e74 | 41 | In addition to a global PCVA, we have considered a single amino acid PCVA, in which the MM charges of each amino acid residue are varied. This makes it possible to assess the contribution of each amino acid to the uncertainty in the QM/MM reaction energy, and can be used to guide the systematic construction of the QM region. By including amino acids with a high sensitivity to point charge variations in the QM region, the overall sensitivity of the QM/MM reaction energy can be reduced. Here, we devised a PCVA-based scheme for the systematic construction of the QM region. |
61d837ab5015eb393fb14e74 | 42 | For the considered test case, our scheme leads to a faster and more reliable convergence with the size of the QM region compared to distance-based QM region construction. Comparing to atom-economical QM regions of the same size provided by the other common approaches, in particular CSA and FSA, our PCVA-based approach performed well and yields similar QM regions. |
61d837ab5015eb393fb14e74 | 43 | The huge advantage of PCVA is its much lower computational cost compared to the CSA or FSA approach (see Supporting Information, Tab. S5). Our PCVA-based approach requires only a geometry optimization of the target system with a minimal QM region including substrates, which is followed by single-point calculations for the point-charge variation of each amino acid. In contrast, CSA is a very expensive approach based on large QM regions with up to 1000 atoms. For these large systems, geometry optimizations have to be performed for the holo and apo enzyme structure for several snapshots along the reaction coordinate. FSA, even though being much cheaper than CSA, still needs as many geometry optimization as there are amino acids in the system for the minimal QM region plus one additional residue in each calculation. A rather similar approach to our PCVA-based construction of the QM region, the charge deletion analysis (CDA), is mostly reported for the usage with mediumsized QM regions, which also increases the required computational effort. Of course, our PCVA-based approach can also be applied for larger QM regions, but we found that this does not improve the results substantially. |
61d837ab5015eb393fb14e74 | 44 | The PCVA-based construction of the QM region is limited to the electrostatic effect of the amino acids and thereby lacking other properties which may also play an important role in QM region determination. Therefore, it is possible that crucial residues (e.g. catalytically important) may be absent under the detected residues. Here, the biochemical and structural understanding should be considered as well when constructing QM regions. Altogether, we suppose that our fast and computationally cheap approach is a good complement to existing methods for the automatic and systematic QM region construction. We expect that future developments concerning uncertainty quantification for QM/MM calculation will also allow for the development of more sophisticated schemes for the systematic construction of QM |
6731b093f9980725cfce7488 | 0 | of mechanochemical reactions, especially for those initiated by tensile force. It is known that stereochemistry plays an important role for determining the activation force F act (i.e., cis-isomers are more reactive than trans-isomers), however, the presence of a highly-strained cyclopropane ring was thought to contribute the most to the reactivity. Recently, the Boydston group has confirmed the mechanochemical reactivity of VA-PNB (vinyl-addition polynorbornene) under sonication conditions and owed its reactivity to the strained rings. However, as shown below, the reactivity is actually caused by a specific confirmation (named "node" by us) rather than the ring strain. We first raised this idea back to 2022 when we studied the retro-Diels Alder reaction using the extended artificial force induced reaction method (EX-AFIR method). We have also noticed that Moore and co-workers have extended this concept in their recent work. Given this, we studied the reactivity of both cis-VA -PNB and trans-VA -PNB under a variety of force levels using EX-AFIR method, and the results are shown in Figure Figure . ΔG ‡ τ -F τ graph of cis-VA -PNB and trans-VA -PNB, suggesting ring strain is not the major reason for the mechanochemical reactivity observed in the sonication reaction. |
6731b093f9980725cfce7488 | 1 | A node means the dihedral is lower than 90°, and an ideal node should have a dihedral close to 0°. We found the force transduction is inhibited and meets resistance at "node", causing a severe distortion of the structure and increasing of energy, therefore making a large stress at the node, which finally leads to a bond cleavage (see Figure for more details). Conventional mechanophores either have a highly strained small ring (e.g., cyclopropane, cyclobutane) or a chemically weak bond (e.g., O-O bond, S-S bond). However, our guideline suggests these are sufficiency rather than necessity. Molecules with a "node" conformation (i.e., a small dihedral angle) should be reactive under tensile force to form mechanoradicals. To generate such a "node" conformation, a bond that cannot rotate freely is required. |
6731b093f9980725cfce7488 | 2 | A ring or even bulky groups can result in such a rigid σ bond. No significant distortion of bond angles and bond length is observed. An ideal node can have the dihedral angle close to 0°. To generate such a "node", a rigid σ bond that cannot rotate freely, is required. |
6731b093f9980725cfce7488 | 3 | Following this, camphanediol and pinanediol, which are natural products either used in the cosmetics industry or the auxiliary ligand for the synthesis of chiral boron compounds, were selected as candidate mechanophores. Both have a "node", as the bridged ring helps to fix the conformation of O-C-C-O dihedral angle. We first conducted a series of EX-AFIR calculations, aiming at providing reliable activation force (F act ) values for camphanediol, pinanediol and their analogues, transand cis-cyclohexanediol. Shown in Figure is the computed ΔG ‡ τ -F τ curves for all the compounds mentioned above, where ΔG ‡ τ is force-coupled free energy barrier of C-C bond homolysis and F τ is force level. Camphanediol was found as the most reactive species under external forces. If the timescale is set to 0.1 second, the computed F act values of camphanediol, pinanediol, ciscyclohexanediol and trans-cyclohexanediol are 1850, 2320, 2970 and 3970 pico-newton, respectively. |
6731b093f9980725cfce7488 | 4 | Therefore, camphanediol, to the best of our knowledge, which was never considered reactive under force, is indeed a mechanophore. Further inspection on the force-coupled transition state revealed that its O-C-C-O dihedral angle is only 10.55°, while it is 35.35° for pinanediol, 79.61° for ciscyclohexanediol and 165.92° for trans-cyclohexanediol, respectively (see Figure ). Different from the conventional mechanophores, which either have small rings or weak bonds, camphanediol does not possess a significantly large ring-strain (see Figure for details) or a weak covalent bond. It is the bridged rings that help to fix a preferred conformation called "node", which eventually leads to its high mechanochemical reactivity. Despite the reactivity to generate radicals under tensile force, the further utilisation of these mechanoradicals requests them to be relatively long-lived. To study what is evolving in the reaction system, a reaction path exploration was performed using the single component EX-AFIR (SC/EX-AFIR) method on the potential energy surface of the quality of UB3LYP-D3/Def2-SV(P) level, where the exploration was greatly accelerated by an iterative explo-ration framework using a DFT-xTB Δlearning scheme (see SI for details). During the exploration, a tensile force was applied between the terminal -OMe groups at all times (see computational methods in SI for more details). Shown in Scheme 1 is the computed reaction paths of camphanediol under a tensile force of 1800 pN (i.e., its activation force level at the timescale of ~ 0.1s, F act[T = 298.15 K, t = 0.1 s],calc ). The energetically accessible pathways discovered by the automated search were further optimized at UB3LYP-D3/6-311G(d,p)//UB3LYP-D3/6-311G(d,p) level of theory under the tensile force of 1800 pN. The first step is the force-promoted C-C bond homolysis, which eventually generates Cam_Int1. The intermediate Cam_Int1 is a 1,5-diradical species with a five-membered ring staying in the middle. Though fivemembered ring is commonly stable, since it is adjacent to a carbon radical, it will still undergo a radical ring-opening reaction via three possible pathways. Cam_TS2A was found to have the highest energy, and the barrier is calculated as +91.0 kJ/mol. It is because the breaking C-C bond in Cam_TS2A does not have the force directly passing through. Our previous computational studies have already revealed that, the force always chooses the shortest path between two points. The force-coupled transition state Cam_TS2B has a slightly higher energy than that of Cam_TS2C, because Cam_TS2C leads to a tertiary carbon radical. Therefore, the effective barrier of ring-opening for Cam_Int1 is +56.1 kJ/mol under 1800 pN, suggesting it has a relatively long half-life. The ring-opening results in the formation of a 1,3-diradical, which cannot further break into alkene molecules. Instead of generating an alkene and a carbene, in fact, it will form a cyclopropane derivative which possesses a three-membered ring. |
6731b093f9980725cfce7488 | 5 | Due to the force effect, the generated three-membered ring does not have a "node", and our EX-AFIR calculations suggests that the ring-opening of this three-membered ring requires a much higher activation force of 2700 pN (Figure ). Reaction path explorations regarding the degradation of pinanediol under tensile force were also performed (see SI for details). However, though pinanediol also has a relatively low F act , from which the mechanoradicals generated are very short-lived. The force-coupled ring-opening reaction has a barrier of only 31.1 kJ/mol under F τ = 2300 pN (see Figure for the comparison of stability for mechanoradicals derived from camphanediol and pinanediol) and leads to the formation of a 1,4diradical species. This 1,4-diradical species can readily go scissile decomposition to form two alkene species. Therefore, it is very unlikely that these mechanoradicals derived from pinanediol can be experimentally observed or further utilized. |
6731b093f9980725cfce7488 | 6 | To confirm the mechano-reactivity of camphanediol and demonstrate its application for selfstrengthening materials, we covalently incorporated these molecules into a promising polymer-double network (DN) hydrogels and investigated their capacity to generate more mechanoradicals and strengthen the materials. We modified cis-cyclohexanediol, pinanediol, and camphanediol into diacrylate crosslinkers and used them to synthesize poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPS) single network (SN) hydrogels. These PAMPS networks with different crosslinkers serve as the first network in a DN hydrogel, with the second network identically consisting of polyacrylamide (PAAm) crosslinked with N,N'-methylenebis(acrylamide) (MBA) (Figure ). The resultant DN gels are denoted as DN-Cy, DN-Pin, and DN-Cam, respectively. Previous research has shown that DN systems are well-suited for studying mechanophore activation, where mechano-phore crosslinker with the lower activation force in the first network can be more efficiently and selectively activated. Figure and Figure show that the three SN gels and DN hydrogels exhibited similar swelling and mechanical properties, indicating comparable network structures. However, they displayed significant differences in generating reactive mechanoradicals. As shown in Figure and Figure , when the gels, fed with ferrous ions and xylene orange (XO), were stretched to a strain of 6 and then unloaded in air, DN-Cam exhibited a noticeable color change in the necked region, while DN-Cy and DN-Pin showed much weaker changes (see SI for a video clip). This color change occurs because the generated mechanoradicals oxidize ferrous ions to ferric ions in the presence of oxygen and water, and the ferric ions then react with xylenol orange to form a purple complex. Quantitative UV spectrum analysis revealed that DN-Cam generated approximately 130 µM mechanoradicals, over four times the amount produced by DN gels crosslinked with pinanediol and cis-cyclohexanediol, which generated around only 30 µM. We also investigated whether these mechanoradicals could trigger the polymerization of monomers and crosslinkers, endowing the gel with mechanoresponsive self-strengthening properties (Figure ). After oxygen extraction in a glove box for 2 hours, DN gels fed with 2.0 M monomer N-isopropylacrylamide (NIPAm) and 0.15 M crosslinker MBA were stretched to a strain of 6 and unloaded. After 3 minutes, DN-Cam turned white in its necked region and became stronger during a second cycle of loading-unloading test, while DN-Cy and DN-Pin did not. This suggests that a high concentration of mechanoradicals was generated in DN-Cam, facilitating the formation of a new PNIPAm network to strengthen the material. |
6731b093f9980725cfce7488 | 7 | long-lived radicals (though the later requires a high F act ). In contrast, pinanediol, despite also having a similar low Fact, cannot generate long-lived radicals suitable for application because its intermediate (Pin_Int1) is short-lived and undergo rapid scissile cleavage into the two alkenes (Pin_TS3CC, see Scheme S1). Compared to the conventional azoalkane mechanophore, camphanediol exhibits excellent thermal and UV stability. After heating at 80°C or exposing it to UV light for 10 hours, the NMR spectra of all three diols remained unchanged (see Figure ). This stability allows camphanediol mechanophore to be incorporated into the polymer materials using high-temperature or UV polymerization and endows the resultant material with superior stability, which can expand the potential applications of camphanediol mechanophore. In conclusion, a general procedure to identify or design mechano-reactive radical-type mechanophore was proposed, as what is shown in Figure . The existence of a "node" along the force transduction direction, which is literally a bond that cannot rotate freely, is believed to enhance the force effect. In fact, highly strained rings or intrinsically weak bonds is not a must for a considerably high mechanochemical reactivity. Following pre-screening guideline, those molecules with "node" were subjected to the EX-AFIR calculations to derive their F act . In our case, camphanediol and pinanediol, molecules with a bridged six-membered ring, were identified as a qualified mechanophore that can undergo reactions at a relatively low F act . These two are economical natural products, which means that they are relatively cheap, easily accessible, and no complicated synthetic processes are required. However, only mechanoradical with relatively long half-life is beneficial to the selfstrengthening materials. Here, the reaction path explorations facilitated by the EX-AFIR method were subsequently conducted for the plausible decay pathways of mechanoradicals derived from camphanediol and pinanediol. It then revealed that a 1,5-diradical intermediate, which is believed to have a longer half-life, is formed in the case of camphanediol. The relatively long-lived diradical species enables it to react with the monomers fed to the system, thus ensuring a good self-strengthening process. For pinanediol, two alkene molecules are formed rapidly following the radical decay channel. |
6731b093f9980725cfce7488 | 8 | More importantly, owing to our selection guideline which does not require strained rings or weak covalent bonds, such a camphanediol-containing DN gel shows a satisfactory thermal and UV stability, and only evolves rapidly when the force stimuli are applied. This theory-driven selection procedure would be promising for the identification of mechanophores among commercially available or easily synthesizable molecules, and would greatly contribute to the expansion of the field of polymer mechanochemistry. |
648741004f8b1884b731451d | 0 | The increased concentration of CO 2 in the atmosphere is the single most important anthropogenic cause of global warming. Decreasing the release of CO 2 into the atmosphere requires efficient CO 2 capture and separation technologies. Decades of research have been devoted to improving existing gas separation technologies, but there is still an imminent need to find new methodologies given the current course of climate change . Traditional unit operations have the ability to isolate high-purity products, but they have a high carbon footprint due to the high energy requirements. Membrane-based technologies are an attractive alternative because they provide savings in capital and energy-related operating costs, and offer advantages related to the ease of operation and compact environmental footprint . Polymer membranes have been successfully investigated for H 2 recovery, N 2 generation, but there is still a significant opportunity to improve polymer membrane technology for CO 2 separations. Although hundreds of new materials are synthesized each year, most of the commercial membranes used today are from the 1990s, and they rely on a dozen or so common polymer structures. This is largely because the two properties that are important for a membrane material -high flux (permeability) and high gas purity (selectivity) -are inversely correlated. This inverse relationship between gas selectivity and permeability was first examined by Robeson in 1991 and revisited in 2008 for pure homopolymer membranes and is famously known as the Robeson Upper Bound. Since then, there have been considerable efforts in designing polymers that are above the empirically determined upper bound for a given application . |
648741004f8b1884b731451d | 1 | Designing polymers with targeted structural and functional properties is challenging due to the practically infinite polymer chemistry design space. Trial-and-error or intuition-based strategies are not efficient, and they are likely to miss optimal solutions due to the complexity of chemical composition and morphology of polymers. Furthermore, these strategies with traditional experimental and computational routes are time and resource consuming. Machine Learning (ML) models trained on polymer data sets can mitigate this problem, as it is possible to predict a new material's properties instantaneously by interpolating within an existing dataset . There have been a number of studies in the recent literature that leveraged ML to predict the properties of polymers. For example, Alves et al. developed models to discover polymeric micelle formulations for poorly soluble drugs using micellar solubilization data . |
648741004f8b1884b731451d | 2 | Tao et al. used ML models to predict the glass transition temperature of a polymer based on its structural formulation . Later, these authors also did a benchmarking study to compare the predictive power of numerous ML models and showed the importance of structure and feature representations . Xu et al. used ML models to study swelling of polymer membranes in different solvents with chemically informed molecular representations and descriptors . |
648741004f8b1884b731451d | 3 | Wang et al. used ML models to screen polymers for pervaporation separation and developed a data-driven approach to predict the fractional free volume of polymers . There are also excellent review articles published in the last couple of years that summarize the recent developments in ML studies of polymer properties . |
648741004f8b1884b731451d | 4 | The success of applying ML models to design new polymer membranes for gas separation has been comparatively lacking, largely owing to limitations in data availability. al. used experimental gas permeability data to develop a ML model to predict gas separation in polymer membranes . They have successfully identified several polymers for improved CO 2 /CH 4 separation and synthesized two of them to experimentally validate the ML predictions. Yuan et al. used ML algorithms to predict the missing values for the permeability of different gases in the online Polymer Gas Separation Membrane Database of the Membrane Society of Australasia . Yang et al. used the same data set and leveraged ML models to predict gas permeability based on the polymer chemistry . However, a ML model that predicts polymer properties by itself does not lead to the discovery of new polymer membranes with optimal properties. In principle, one can propose many candidate polymers, possibly at random, and use ML to predict their performance. This is obviously not an efficient strategy. A ML "forward model" needs to be coupled with an inverse design/generative algorithm to efficiently explore the polymer material space. Genetic algorithms (GA) are an example of a data-driven inverse design method, which can be effectively coupled with an ML model. Srinivasan et al. |
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