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65acde689138d231616726ba | 15 | In this technique, a Mach-Zehnder type of interferometer was used for the measurement ofthe fringes using ESPI. A coherent light beam of wavelength λ, which travels along with a distance (d) at time t1, was used. This beam then interfered with the reference beam. The process was then repeated at another time t2. Both the images which were obtained are subtracted from each other. Bright fringes were obtained when fringe order relationships were satisfied, leading to constructive interference . |
65acde689138d231616726ba | 16 | BS: beam splitters; CL: collimating lenses ; DC: diffusion cell; FG&C: frame grabber and computer; L: laser; M: mirrors; NDF: neutral density filter; OL: object lens; OS: opal screen;SF: spatial filters. To evaluate the diffusion coefficient, one does not need to know the wavelength, length of the cell, and initial concentration. The sensitivity is proportional to d, proportionality constantk, and inverse of wavelength. |
65acde689138d231616726ba | 17 | There are two methods of operation described in the literature . In one, the fringe orders were used, and in the other one, the separation distances of the maximas were used of the profile. A helium-neon laser was used and was passed through a density filter to avoid the phenomena of saturation of the CCD camera. The beam was first split using a beam splitter, and one of the beams passed through the diffusion cell. Both the beams were then recombined using a second beam splitter. A lens was used to project the image of the cell on a screen on which the camera was focused. Interference images of both methods have been provided below. The images obtained were digitally subtracted from each other using image processing software, and the diffusion coefficient was related using Fick's laws . |
65acde689138d231616726ba | 18 | The major advantage of using this technique is that it has high sampling rates and very short exposure times (40 microseconds) . Hence, this is not sensitive to external instabilities. This process is faster and simpler than conventional holographic techniques. The subtraction that is involved ensures a significant reduction in the noise. The process can be made fully automatic as it involves digital elements. It has an accuracy between 1-2%. . |
65acde689138d231616726ba | 19 | A 10 mW helium-neon laser was used as the light source. The beam that was generated wasthen split using a spatial filtering assembly. The light was then passed through the diffusioncell. The light then proceeded to meet the multiple beam interferometer. After multiple reflections from the interferometer, it was observed that the beam interfered at the screen S to produce interferograms. Every five minutes, an interferogram picture was captured by a CCD camera aimed at the screen and saved in the PC for processing . Since the refractive index is different for different planes in the cell, the light passing through them will have different path lengths. The extremum points will reflect as humps on the fringe pattern. As diffusion proceeds, we will see that the extremum points will shift outwards. Here,to calculate the diffusion coefficient, we need to measure the distance d (between the two extreme points in the interferogram at times t1 and t2. |
65acde689138d231616726ba | 20 | The major advantage of employing this method is that one need not maintain stringent optical conditions that are required in the other methods. The diffusion coefficient is obtained from the extremum points, and interferograms so obtained are easy to process. This technique is suitable for implementation in the industrial setup and is cost-effective asone can use low power lasers for diffusivity determination. |
65acde689138d231616726ba | 21 | A-frame grabber charged coupled device (CCD) camera was connected to a computer for measurement. The light from a LASER source fell on a spatial filter (SF) assembly and then went on to a beam splitter (BS). The light that got split and fell on the corresponding mirrorsM1 and M2, giving rise to the transmitted and reflected arm of light. The experimental solutions in the glass cell (G) were placed in the reflected arm. After reflections from the mirrors, the light passed through the glass cell, and the beams interfered. |
65acde689138d231616726ba | 22 | Care was taken so that convection currents were avoided. It was noted that there would be a change in the refractive index of a particular plane perpendicular to the direction of diffusion with time. The change of refractive index of a given plane at two different times can be related to the error function solution of Fick's second law. The separation of the two extremes of the change in refractive index can be linked to Fick's second law, and the diffusivity can be evaluated . |
65acde689138d231616726ba | 23 | It was noted that the refractive index changed with time at a particular plane. Due to this, the fringes also shifted with time going outwards, giving rise to separation distance (d). Thereby diffusivity can be evaluated by determining the separation distance from a generated Computer Trace Image generated by a charge-coupled device (CCD) camera. |
65acde689138d231616726ba | 24 | The major advantage that this technique has is that it does not need a complex recording assembly as well as a recording medium. The shift in the interferogram is identified and usedfor subsequent calculation. This shift is way simpler to calculate. The diffusivity is evaluatedbased on the distance between the two interference patterns that are generated due to the ongoing diffusion of two solutions. |
65acde689138d231616726ba | 25 | The only limitation is that the technique is more suited for transparent solutions and the requirement of stringent optical conditions that have to be maintained for successful implementation. Techniques like multiple-beam interferometry have come up, but they also have the limitation of the determination of extreme points in the interferogram . |
65acde689138d231616726ba | 26 | In this paper, we have discussed various mass diffusivity determination techniques using interferometry. Since interferometry is an optical phenomenon, all of these methods are more suited for the case where the medium is either fully or partially transparent. Initially, the basic fundamental which forms the basis of diffusivity determination was discussed. It was followed by specific diffusivity determination techniques like phase-shifting interferometry, common path shearing interferometry, holographic interferometry, electronic speckle pattern interferometry, multiple-beam interferometry and Michaelson interferometry were discussed. |
67c9c98881d2151a02592803 | 0 | In the field of molecular dynamics (MD) simulations, much work has contributed to improving molecular mechanics force fields (MMFF) to achieve higher accuracy in reproducing experimental metrics. Efforts include extending general small molecule force fields, 1,2 developing new protein force fields, and creating force fields for other biomolecules, such as DNA and lipids. Classical force fields aim to reproduce quantum mechanics (QM) results, however, it remains a challenge to accurately matching these QM results, especially when chemical reactions are involved. To overcome the challenge, a feasible solution is to combine the computational efficient MMFF method with the accurate QM methods. In the 1970s, Warshel Arieh and Levitt Michael proposed quantum mechanics/molecular mechanics (QM/MM) molecular dynamics, which applies a QM model which includes density functional theory (DFT) to describe the essential part of the system (such as atoms involved in a chemical reaction), and MMFF to describe the rest of the system. This multi-scale simulation technology make the investigation of electronic structures and chemical reactions in a large system come true. |
67c9c98881d2151a02592803 | 1 | For instance, electrostatic embedding approach was proposed to accurately calculate the electrostatic interaction, and polarizable force fields have been introduced to account for interatomic polarization effects. Additionally, improvements in long-range interaction processing have enhanced the accuracy of simulations. Most of the above measures focus on improving simulation accuracy. However, the primary limitation to the broad application of multi-scale simulation techniques remains the simulation performance. That's to say the true bottleneck in QM/MM MD is the QM calculation, which is difficult to be accelerated significantly. |
67c9c98881d2151a02592803 | 2 | However, the rise of various artificial intelligence (AI) techniques has sparked a wave of developing machine learning interatomic potentials (MLIPs). MLIPs are trained using machine learning algorithms to reproduce ab initio quantities, such as potential energy and atomic forces. For example, ANI-2x, which was trained on data from ωB97x-D/6-31G(d) calculations, achieves near-DFT levels of accuracy while maintaining computational efficiency comparable to molecular mechanics. Given by their accuracy and performance, MLIPs could potentially serve the role of ab initio models in simulating biomolecular systems with QM/MM. Incorporation of MLIPs into a molecular dynamics engine to develop a brand-new multi-scale simulation technique is appealing given their near-QM level of accuracy and near-MM level of efficiency. Thus, machine learning/molecular mechanics molecular dynamics (ML/MM MD), represents a promising opportunity for biomolecular simulations. Many MLIP models represented by the ANI series and MACE series have demonstrated robustness, transferability, and high performance. Therefore, they are ideal candidates for incorporation into MD simulation platforms. |
67c9c98881d2151a02592803 | 3 | Most of the time, free energy calculations are performed using molecular mechanics (MM) which is based upon the applied MMFFs. However, MM-based free energy methods sometimes cannot produce accurate energy values due to a lack of adequate description of some subparts of the simulation system with MMFFs, for which a QM-level description is often necessary. It is appealing to apply ML/MM MD approach to free energy calculations, given the advantage of ML over QM. In this framework, critical regions of a system, such as those being involved in chemical reactions and ligand and protein binding, are modeled with MLIPs, while the surrounding environment is modeled by MM. This approach enables high-quality free energy calculations as it strikes a balance between computational accuracy and efficiency. |
67c9c98881d2151a02592803 | 4 | In this work, we incorporated MLIPs into the AMBER simulation platform. We then used the modified code to validate conservation laws within the ML/MM approach, thereby ensuring a thermodynamically consistent system. Next, we advanced the theory of free energy calculations using the thermodynamic integration (TI) method with the core part being described by MLIPs. We tested the new technique by preforming hydration free energy calculations via multi-scale ML/MM molecular dynamics simulations. To further explore potential applications of ML/MM MD to macromolecular systems, we applied the ML/MM MD engine to sample conformations and MM-PBSA method to predict binding free energy for a set of protein-ligand complexes. Finally, we performed performance tests on our code. By leveraging advancements in MLIPs and integrating them with multi-scale simulation techniques, we expect that our ML/MM approach can help address many current challenges in molecular simulation. |
67c9c98881d2151a02592803 | 5 | For the ML-MM interaction, although several methods have been proposed to improve the accuracy of electrostatic and van der Waals 43 interactions, we use the most widely used functional forms. This involves using Coulomb's law and employing Lennard-Jones (LJ) potentials to describe the interactions. The atomic partial charges and atomic LJ parameters for the ML region are also obtained from the employed MMFF. |
67c9c98881d2151a02592803 | 6 | While for the atom in ML region, its force consists of ML force (F i ML ) itself and the part due to its interaction with the MM region (F i ML-MM ). The latter (F j ML-MM ) can be calculated analytically, while the former is derived from a complicated neural network. But owing to an auto-gradient technique, which makes it possible for us to estimate the gradient of energy using the energy from eq.2 . |
67c9c98881d2151a02592803 | 7 | When calculating solvation free energy using TI, it is necessary to determine the free energy in the solvent phase ( ∂V ∂λ solvent ) and the gas phase ( ∂V ∂λ gas ) separately. Considering the bonded and non-bonded terms in ML are not separable, we need to develop a new protocol to enable TI calculations using ML/MM approach. In our protocol, we assumed the contributions from solute itself in the gas and solvent phases are the same. Under this assumption, we only need to do TI calculations in the solvent phase and the values ∂V ∂λ are calculated without considering the intramolecular energy of the solute. We then estimate the reorganization energy, which accounts for the free energy difference associated with the different conformational ensembles in the gas and solvent phases. We expect that the reorganization energy can mitigate the prediction error due to the above assumption. |
67c9c98881d2151a02592803 | 8 | Notably, most MLIPs are trained and used within the PyTorch framework, which is based on Python. In contrast, SANDER is primarily written in Fortran. Directly calling MLIPs by SANDER could result in high latency due to the frequent initialization of MLIPs in each MD step. Furthermore, Being a high-level language, Python makes direct memory manipulation challenging. To address these issues, we implemented the MLIPs in a built-in manner (see Scheme 1), meaning that the MLIPs are initialized alongside SANDER and the memory is retained until the MD simulation finishes. This approach avoids frequent memory allocation by storing the ML model in system cache for rapid access. We implemented the MLIP model in C++ to enable both inference and auto-gradient, which are essential for atomic force calculations. To integrate SANDER and MLIPs, we developed a Fortran/C++ interface, allowing MLIPs to communicate with SANDER directly through memory addresses, thereby reducing communication latency. Scheme 1: The implementation details of ML/MM module in SANDER MD engine in Amber. This module is initialized alongside SANDER. Once the MD loop begins, the ML model is invoked through an intrinsic Fortran/C++ interface, facilitating direct communication between the ML algorithms and the core MD routines. The outputs generated by the ML model are then meticulously processed, then they are incorporated into the SANDER mainstream. |
67c9c98881d2151a02592803 | 9 | To further enhance performance, we adapted the code for both the standard SANDER and the Message Passing Interface (MPI) enabled SANDER.MPI. In this configuration, SANDER manages conventional MD (cMD) calculations, accelerated through MPI, while the ML/MM module is responsible for the MLIP inference. The MLIP inference is conducted separately on graphics processing units (GPU), which significantly accelerates overall processing. During SANDER's calls to the ML/MM interface, inference jobs are dispatched to the GPU, allowing asynchronous computing: cMD calculations occur on CPU cores, while MLIP inference takes place on GPU (see Scheme 1). |
67c9c98881d2151a02592803 | 10 | Currently, we have integrated the ANI series (ANI-1x, ANI-1ccx, and ANI-2x ) and the MACE series 29 (MACE-OFF23(S), MACE-OFF23(M), MACE-OFF23(L)) MLIPs into SANDER. Our ML/MM implementation mirrors the mechanical embedding approach used in QM/MM frameworks. Users specify the atomic ML region, with the remaining atoms being in the MM region. This integrated approach enables the ML/MM module to augment traditional MD simulations with machine learning capabilities while maintaining compatibility with the Amber 2023 SANDER framework. |
67c9c98881d2151a02592803 | 11 | Leveraging this technology enables researchers to investigate the mechanisms underlying biological processes. For example, MD can be used to unravel biocatalysts behavior and understand protein-drug interactions. However, the accurate reproduction of real molecular behaviors in MD simulations relies on the MD engine can strick adherence to fundamental physical laws, such as Newton's equations of motion. By following these laws, we can assess whether our ML/MM approach upholds the two most fundamental conservation laws-energy and momentum-thereby ensuring the reliability of our simulation results. |
67c9c98881d2151a02592803 | 12 | In this study, we tested the MD system by simulating erlotinib, an EGFR inhibitor, in water under the microcanonical ensemble (NVE, i.e. constant number of particles, volume and total energy of the system). The system contains 151 atoms (Figure ), with 52 belonging to erlotinib, defined as the ML region, while the remaining 99 atoms belonging to 33 water molecules. In this configuration, the ML region constitutes approximately 34.4% of the system's atoms, allowing us to observe its influence on the total energy contribution as fully as possible. |
67c9c98881d2151a02592803 | 13 | We employed ANI-2x, which showed its accurate reproduction of DFT results and high reliability, as the MLIP model in the ML/MM MD approach and used cMD as a reference to conduct a 1 nanosecond (ns) simulation with a timestep of 0.1 femtosecond (fs). For the ML/MM simulation, the average energy was -255.28 kcal/mol (Figure ), with a standard deviation of 0.03 kcal/mol, while the cMD simulation showed an average energy of -153.75 kcal/mol (Figure ), with a standard deviation of 0.12 kcal/mol. The difference in the absolute values of the total energy arose because, in the ML/MM approach, the atoms in the ML region are calculated using the MLIP rather than molecular mechanics. Notably, the ML/MM approach demonstrates a lower deviation in energy throughout the simulation, indicating MLIP can reduce the fluctuation of potential energy. By describing a portion of these atoms with MLIP, the computational error from the MM region is minimized. Specifically, in the ML region, the ANI-2x model's potential surface is smooth and nearly consistent, resulting in a balanced net force that helps the ML/MM simulation adhere strictly to the conservation of energy law. Regarding momentum conservation, two simulations were initiated from the same minimized structure, with the initial momentum being set to zero. Throughout the simulations, the velocity of the center of mass remained close to zero: 0.02 for ML/MM (Figure ) and 0.01 for cMD (Figure ), respectively. Neither system was subjected to any external forces, as evidenced by the small fluctuations observed. To further support this observation, we also calculated the translational and rotational energies of both systems. The translational energy remained below 0.15 kcal/mol for both systems (Figure ), while the rotational energy was much lower, at 0.02 kcal/mol for ML/MM and 0.07 kcal/mol for cMD. These findings indicate that the ML/MM approach can consistenly simulate the thermodynamics of a system and produce molecular behaviors without obeying laws of thermodynamics. |
67c9c98881d2151a02592803 | 14 | TI is a useful technique in which a perturbation is applied to facilitate the system's transition from V 0 to V 1 , allowing for an estimation of the resulting free energy difference. This method is widely used in solvation energy prediction and binding free energy between a ligand and a receptor. In this study, we develop a ML/MM-based TI calculation protocol for hydration free energy calculation. |
67c9c98881d2151a02592803 | 15 | Mobley and Guthrie reported hundreds of molecules with experimental hydration free energy data. Notably, for these molecules, the energy estimated using the MMFF method with the traditional TI protocol demonstrated a deviation of ±1.5 kcal/mol. We randomly selected 20 compounds containing the elements C, H, O, N, F, and Cl from this dataset, applied our newly-proposed protocol to predict hydration free energies using ANI-2x in combination with GAFF2. We used ABCG2 charge model 61 to calculate the electrostatic interactions, considering it outperforms AM1-BCC in many molecular property calculations. Figure illustrates the prediction accuracy of different models. Note that the results for CGenFF 1 and GAFF 2 were directly obtained from previous publications. In summary, the overall data distributions of ANI-2x and GAFF2 are relatively similar, with nearly the same mean absolute error (MAE) of 0.47 kcal/mol and 0.41 kcal/mol (Figure ), respectively, which are significantly lower than those obtained using either CGenFF (0.84 kcal/mol) or GAFF (0.57 kcal/mol). We suspect that the slightly lower accuracy of ANI-2x compared to GAFF2 is due to some cooperation or consistency issue between them. After all, ANI-2x was trained to reproduce high-accuracy DFT energetics and forces (ωB97x-D/6-31G(d)), whereas GAFF 2 and TIP3P water were developed to reproduce both quantum mechanics and experimental data. This difference might account for the observed discrepancy. However, the quartile line distribution and mean squared error (MSE) indicate that the hydration free energies estimated by ANI-2x are closer to the experimental data. All these results indicate that our postulated theory regarding ML/MM demonstrates its comparability to the traditional TI approach in a novel way. Traditional TI, however, employs a gradual scaling-down method to reduce intramolecular interactions, which may also affect interactions between water and the molecule. This creates a highly coupled system; while our approach aims to reasonably decouple these interactions, further efforts are needed to estimate the coupling effects in TI calculations, thereby enhancing the accuracy of ML/MM TI calculations. |
67c9c98881d2151a02592803 | 16 | We selected six well-studied protein-ligand complexes as candidates for our analysis and then conducted ML/MM MD simulations. Figures and illustrate that these proteins exhibit small fluctuations (less than 1 Å) during the 5 ns simulations. The ligands described by MLIPs also exhibit small fluctuations of less than 2 Å (Figures and). |
67c9c98881d2151a02592803 | 17 | Among the structures, the Myeloid cell leukemia 1 protein (PDB ID: 4HW3) showed the lowest correlation coefficient of 0.18. However, the dynamics of the protein may be still reasonable due to the following reason. The original protein from the PDB entry is a multimer, but only the biological unit of the protein, which is a monomer, was chosen to do the simulations. (Figure ). In this altered environment, transitioning from protein-protein interactions to a solvent-based context, the protein's dynamic behavior may be altered. |
67c9c98881d2151a02592803 | 18 | Simulation performance is the main factor that limits the broad applications of QM/MM MD, whereas ML/MM MD provides a promising alternative. Therefore, for further ML/MM MD development, performance is a primary concern. We collected data from protein-ligand systems to evaluate the effectiveness of our built-in methods and parallel processing approaches in accelerating computations. All computation results were obtained using the NVIDIA L40s and the Intel Xeon Platinum 8462Y+. Figures and illustrate the performance of the ANI-2x and MACE-OFF23(S) models within the ML/MM framework. In most cases using ANI-2x, simulations achieve over 2 ns/day, while MACE operates at approximately 1.5 ns/day. Notably, all simulations used a timestep of 1 fs. When bonds involving hydrogen were constrained using the SHAKE algorithm, the timestep can be extended to 2 fs. This approach is suitable for large systems where detailed hydrogen behavior is not the focus, effectively doubling the simulation performance. |
67c9c98881d2151a02592803 | 19 | Our implementation is designed to perform MD simulations on CPU and ML inference on GPU, with these two processes running in parallel. To achieve optimal performance, we need to carefully balance the workloads on CPU and GPU. For testing, we selected a protein-ligand complex with nearly 42,000 atoms (Figure ). We found that as the number of CPU cores increased up to 16 CPU cores, the simulation performance of both ML models improved. |
67c9c98881d2151a02592803 | 20 | Especially, ANI-2x shows a steeper increase than MACE, indicating the more CPUs are desirable for ANI-2x than MACE. Before the simulation speed reaching the plateau of the curves, the bottleneck of ML/MM MD is the limited number of CPU cores, however, the bottleneck becomes the inference itself when the simulation speed reaches the plateau. |
67c9c98881d2151a02592803 | 21 | As shown in Figure , the ANI-2x model consistently outperforms MACE-OFF23(S) in terms of speed. Compared to ANI-2x, MACE is a larger model, capable of processing additional inputs such as environmental forces and cell size, and predicting properties like dipole moments and stress. Even though these features are not utilized in our current study, they do impact computational performance. Conversely, the ANI-2x model is designed for efficiency, focusing on the rapid prediction of molecular energies and atomic forces. Although MACE currently runs slower than ANI-2x, various methods, such as reducing model parameters and implementing the JAX MD framework, have been proposed to enhance its speed. Overall, compared to traditional QM/MM MD simulations, ML/MM enables nanosecond-timescale simulations with near-DFT level of accuracy. |
67c9c98881d2151a02592803 | 22 | In this study, we implemented the ML/MM approach within the Amber software suite and used it to validate the conservation of energy and momentum. This demonstrates that the ML region and MM region can exchange energy harmoniously, underscoring the robustness of our implementation. Notably, we proposed a new thermodynamic integration protocol for applying ML/MM mixed potentials in alchemical free energy calculations. This development offers new insights in biomolecular systems via high accurate and efficient free energy simulations enabled by multi-scale ML/MM potentials. Additionally, the high quality samplings by mutli-scale ML/MM MD is achieved as the crystal structure properties can bve very well predicted. Combining ML/MM MD sampling with the MM-PBSA endpoint free energy method, we are able to very well predict the binding free energies of a series of compounds binding to a receptor. Thus our approach can integrate seamlessly with other advanced methodologies to expand its functionality. Last, performance testing indicates that the ML/MM approach is a promising method for simulating molecular systems which can achieve a nanosecond per day sampling speed for a typical biological system in drug design. |
67c9c98881d2151a02592803 | 23 | In summary, ML/MM represents a promising direction for the future of molecular simulations. By leveraging the Amber platform, we anticipate that ML/MM can be extended beyond its current capabilities, and be easily combined with other advanced simulation technologies. We envision our future work will focus on integrating more MLIPs, further expanding the method's functionality, and enabling ML/MM to handle increasingly complex scenarios. |
61cd11b61e13ebdf8b0a2f91 | 0 | Metal phosphido compounds are important synthetic intermediates in organophosphorus chemistry . Most copper phosphido compounds characterized by X-ray crystallography have oligomeric structures with a few notable exceptions . We have been studying these types of compounds as intermediates in copper catalyzed hydrophosphination . During our study, we isolated the novel bridging phosphido copper cluster, Cu4(μ-PPh2)4(P t Bu3)2 and were able to determine its molecular structure using X-ray diffraction (Figure ). We also demonstrate that 1 is an active hydrophosphination pre-catalyst. |
61cd11b61e13ebdf8b0a2f91 | 1 | Treatment of a THF solution of copper(I) chloride with potassium diphenylphosphide in the presence of tri-tert-butylphosphine at -30 °C results in the formation of compound 1 (eq. 1) as determined by single crystal X-ray diffraction, 1 H, 31 P, 13 C NMR, and 31 P HMBC NMR spectroscopy. Compound 1 can also be synthesized by treatment of mesitylcopper(I) with diphenylphosphine in the presence of tri-tert-butylphosphine (eq. |
61cd11b61e13ebdf8b0a2f91 | 2 | 2) or by treatment of Cu(acac)2 with three equivalents of diphenylphosphine in the presence of tri-tert-butylphosphine (eq. 3). The 1 H and 31 P NMR spectra of products from these three methods are equivalent. Compound 1 prepared via eq. 1 forms as yellow prismatic crystals that vary in length from plates to columns from a mixture of greater than 99 : 1 pentane : THF when stored at -30 °C. Two co-crystalized THF molecules per asymmetric unit could be localized with 1. |
61cd11b61e13ebdf8b0a2f91 | 3 | The molecular core of 1 consists of an eight-membered Cu4P4 ring that is capped by a P t Bu3 (P5 and P6) on Cu1 and Cu3 (Figure ). Formally, 1 has 2-fold symmetry but does not crystalize with symmetry intact. Instead, 1 adopts a chair-like configuration (Figure ) in which the greatest deviations from a least-squares plane of best fit of the eight atoms in the Cu4P4 core is -1.0453 (0.0007) and 0.9814 (0.0007) Å, for P3 and P4 respectively. The greatest distance from a plane of best fit consisting of the four copper atoms is -1.2939 Eq. 1 |
61cd11b61e13ebdf8b0a2f91 | 4 | The structure of 1 resembles Cu4(μ-PPh2)4(PHPh2)4 (2) described by Fenske . However, in compound 2, Cu1 and Cu3 adopt tetrahedral geometry resulting from the coordination of two Ph2PH molecules per copper. The increased steric bulk of the P t Bu3 versus that of Ph2PH provides a rationale for the observed three coordinate trigonal planar geometry as only one P t Bu3 can coordinate to copper. The closest Cu-Cu distance in 2 is 3.17 Å which is larger than the corresponding distance in 1. This may be a result of 2 having a closer to linear structure than 1 with no deviations greater than 0.2 Å from the best fit plane of the Cu4P4 ring. Compound 1 also resembles Cu4(μ-PPh2)4(dppm)2 (3) (dppm = bis(diphenylphosphino)methane) that has a Cu4P4 core but is not capped at Cu1 and Cu3 but is instead supported by two dppm bridges between Cu1-Cu2 and Cu3-Cu4. Sulfide cluster (CuStBu)4(Ph3P)2 (4) is also related, consisting of a Cu4S4 core that is capped by PPh3 on Cu1 and Cu3. Similar to 1, both 3 and 4 adopt a chair-like conformation with maximum deviations of 1.52 and 1.55 Å respectively, from a plane of best fit consisting of the four copper atoms. |
61cd11b61e13ebdf8b0a2f91 | 5 | Compound 1 displays evidence for dynamic behavior in solution by 1 Compound 1 was found to be an active hydrophosphination catalyst. Treatment of a benzene-d6 solution of styrene, diphenylphosphine, and 6 mol% of 1 under 360 nm irradiation resulted in a 94% NMR conversion to the hydrophosphination product, diphenyl(2-phenylethyl)-phosphine (5), after 24 h (eq. 4). We did not purse further hydrophosphination reactivity given this derivative compound showed no improvement in reactivity compared to Cu(acac)2 . |
61cd11b61e13ebdf8b0a2f91 | 6 | All manipulations were performed under a nitrogen atmosphere with dry, oxygenfree solvents using an M. Braun glovebox or standard Schlenk techniques. Tetrahydrofuran was dried over sodium/benzophenone and vacuum transferred. Benzene-d6 was purchased and then degassed and dried over 3 and 4 Å molecular sieves. Diphenylphosphine , copper(I)chloride , and mesitylcopper(I) , were synthesized according to literature procedures and stored under an inert atmosphere of N2. Potassium diphenylphosphine was made by a modified literature procedure in which Ph2PH was deprotonated by KH in THF and then filtered through celite, and concentrated to dryness by vacuum. All other reagents were acquired from commercial sources and dried by conventional means, as necessary. 1 H, 13 C, 31 P and 31 P HMBC NMR spectra were recorded with a Bruker AXR 500 MHz spectrometer. All 1-D 31 P NMR spectra were 1 H decoupled. Resonances in 1 H NMR spectra are referenced to the residual solvent resonance (C6D6 = δ 7.16). |
61cd11b61e13ebdf8b0a2f91 | 7 | Method A: In an N2 filled glovebox, P( t Bu)3 (51 mg, 0.25 mmol), Cu(I)Cl (25 mg, 0.25 mmol) and 5 mL of cold THF (stored at -30 °C and removed immediately before use) were stirred in a scintillation vial. After 30 seconds, a KPPh2 (56 mg, 0.25 mmol) solution in 5 mL of cold THF was added dropwise resulting in a color change to yellow. The solution was stirred for 30 min at ambient temperature, then concentrated to a yellow residue under reduced pressure. The crude product was redissolved pentane and filtered through a bed of Celite. The filtrate was immediately pipetted into a scintillation vial and placed in a freezer at -30 °C. Crystals suitable for X-ray crystallography precipitated overnight. To isolate the product for NMR the mother liquor was decanted from the precipitate, and the precipitate was washed with 2 mL of cold pentane and dried in vacuo. Yield 57 mg (65%). |
61cd11b61e13ebdf8b0a2f91 | 8 | In an N2 filled glovebox, P( t Bu)3 (166 mg, 0.824 mmol) and mesitylcopper(I) (150 mg, 0.824 mmol) were dissolved in 2-3 mL of cold THF (-30 °C). Neat Ph2PH (153 mg, 143 μl, 0.824 mmol) was added dropwise. The resulting yellow solution was stirred for 24 h. (Note: subsequent trials with less concentrated solutions monitored by 31 P NMR indicate that full conversion is reached after 4 h). The solution was then layered with ~8 mL of pentane and placed in a freezer at -30 °C. After decanting the mother liquor, 107 mg (37 % yield) of 2 was recovered upon washing the precipitate with cold pentane and drying. |
61cd11b61e13ebdf8b0a2f91 | 9 | Method C: In an N2 filled glovebox, 31.5 mg Ph2PH (29.5 μl, 0.170 mmol) was added dropwise at -30 °C to a scintillation vial containing a toluene solution of 15 mg (0.057 mmol) Cu(acac)2 and 11.5 mg (0.057 mmol) of P( t Bu)3. The solution allowed to warm to ambient temperature and stirred for 24 h. Then the solvent was removed under reduced pressure, the residue was taken up in pentane, filtered through a bed of Celite, and placed in a freezer at -30 °C. The resultant precipitate was dissolved in a minimum amount of THF ~ 1 mL and layered with three mL of pentane and placed in the freezer again. The 10.6 mg (53% yield) of solid was isolated by decanting the mother liquor, washing with cold pentane, and drying. The 1 H and 31 P NMR spectra of the compound obtained by this method matched methods A and B. |
61cd11b61e13ebdf8b0a2f91 | 10 | In an N2 filled dry box, 8 mg (.023 mmol, 6 mol %) of 1, 70.7 mg (66 μl, 0.38 mmol) diphenylphosphine and 39.5 mg (43.5 μl, 0.38 mmol) of styrene was measured and mixed in 0.6 mL benzene-d6. This solution was transferred to an NMR tube. Initial 1 H and 31 P NMR spectra were obtained before placing the tube in a photoreactor containing a Rexim G23 UV-A (9W) lamp at ambient temperature. The temperature of the 360 nm photoreactor was measured to be 25-30 °C, depending on how long it had been in use. |
61cd11b61e13ebdf8b0a2f91 | 11 | X-ray diffraction data were collected on a Bruker APEX 2 CCD platform diffractometer (Mo Kα (λ = 0.71073 Å)) at 150(2) K. A suitable yellow prismatic plate crystal of Cu4(μ-PPh2)4(P t Bu3)2, was mounted on a MiTeGen Micromount with Paratone-N cryoprotectant oil. The structure was solved using direct methods and standard difference map techniques and was refined by full-matrix least-squares procedures on F2 with using the Bruker SHELXTL Software Package . All non-hydrogen atoms were refined anisotropically. Hydrogen atoms on carbon were included in calculated positions and were refined using a riding model. |
6642c357418a5379b02fd6d2 | 0 | General force fields offer a computationally efficient alternative to quantum mechanical (QM) calculations, in particular for pharmaceutical and biomolecular applications. Parametrizing general force fields or training machine learning (ML) potentials, for molecular mechanics (MM), requires extensive quantum chemistry datasets, with molecules covering a large chemical space, that inform the bonded parameters, typically bonds, angles, and torsions as well as nonbonded terms. The datasets include optimized chemical structures of different conformers of molecules and associated properties such as charges, bond orders, dipole moments, Hessian matrices, and torsion energy profiles for rotatable bonds, dimer interaction energies, among other data. A quantum mechanical method is needed that is globally accurate for different chemistries and properties, is computationally cost effective, and can converge with a predefined set of hyperparameters (or a template with minimal changes) without too much human intervention, thus enabling automated generation of larger datasets essential for this effort. There are hundreds of density functionals, post Hartree-Fock methods, and basis sets to choose from, and it is cumbersome to pick one without a proper benchmark study. |
6642c357418a5379b02fd6d2 | 1 | Recent benchmark studies address the issue of how accurate a quantum mechanical method is with respect to a highly accurate gold standard such as coupled cluster with singles, doubles and perturbative triples in the complete basis set limit (CCSD(T)/CBS). Some studies are from the viewpoint of quantum chemistry method developers, where one would be concerned by a difference of even 0.1 kcal/mol in mean accuracy of absolute energies, with respect to the reference level of theory. However, from the perspective of practitioners engaged in force field development and general biochemical simulations, where relative energies such as conformer energetics and torsional profiles are of primary concern (as emphasized in Sellers et al. ), it is crucial that the quantum mechanical (QM) methods used to generate reference data for force field parametrization can reproduce torsion energy profiles with deviations of approximately 0.5 to 1.0 kcal/mol or smaller. This level of accuracy, as demonstrated in high-level QM calculations, is vital for ensuring the accuracy of trained force fields, and boosts the reliability of property predictions like protein-ligand binding affinities. By achieving accuracy within this specified range for the QM reference data employed in force field parametrization, and assuming the trained force field mimics the QM training data quite well, we can effectively capture the essential conformational behavior and energetic trends exhibited by the molecules under investigation. Our focus here is precisely in this area, conformational energetics, and not on modeling long-range electrostatic interactions, which may involve different considerations. Our primary focus is on accurately modeling small molecule organic compounds within pharmaceutically relevant regions of chemical space using force fields. As a result, we do not concern ourselves with evaluating the performance of quantum mechanical (QM) methods for compounds involving transition elements, lanthanides, noble gases, and other elements not directly implicated in the fundamental molecular interactions governing the binding and recognition of small molecule drugs. At the Open Force Field (OpenFF) Initiative, our attention lies on achieving performance benchmarks for organic molecules within the chemical space that is pertinent to small molecule drugs and that our force fields are currently capable of modeling. This chemical space encompasses C, H, O, N, P, S, F, Cl, Br, and I, as well as the monoatomic ions Li + , Na + , K + , Rb + , F -, Cl -, Br -, and I -. |
6642c357418a5379b02fd6d2 | 2 | For example, B3LYP does not have the meta-GGA term, but M06 does. Hybrid and doublehybrid functionals are distinguished by including a percentage of HF exchange, and a percentage of MP2 correlation, respectively. Therefore double hybrid functionals are at least the cost of a MP2 calculation. Range separated functionals (RSF) are another very important development in DFT methods. In RSFs, such as ωB97 family, the percentage of HF exchange depends on the distance between the electrons. This accounts for the electron self-interaction error, and has become incorporated into several of the most modern functionals (i.e. the ones starting with LC or ω). DFT methods with dispersion corrections, which can be either ab initio, or empirical in nature, are notably more accurate than their standard forms as they improve the description of the non-covalent interactions. Grimme's DFT-D3, along with Becke-Johnson (BJ) damping, is one of the most prominent dispersion corrections widely used in the field. On the other hand, wave function based methods (WFT) include Hartree-Fock, post-Hartree-Fock methods viz., Møller-Plesset perturbation theory of different orders (MP2, MP3, MP4), configuration interaction (CI), coupled cluster (CC), and multi-reference methods such as complete active space self-consistent field (CASSCF), in increasing order of complexity in describing electron correlation, and approaching higher accuracy. |
6642c357418a5379b02fd6d2 | 3 | Based on earlier benchmark studies, the OpenFF initiative initially chose B3LYP-D3(BJ) /DZVP as the method for generating QM training data to train OpenFF force fields, with the expectation that this choice might need to be revisited at a later date. Such a 'revisit' is our focus here. The prior benchmarks 2 included assessing accuracy of conformer energetics on the MPCONF196 set, 46 which is a dataset of conformers of smaller peptides and mediumsized macrocycles, that were all neutral, and of relative energies of torsional profiles on a curated set of 15 one-dimensional torsion scans. A good compromise between accuracy and cost on MPCONF196 and the smaller set of torsion scans led to the choice of the B3LYP-D3(BJ) functional along with Salahub's double-zeta split-valence + polarization (DZVP) basis set for building OpenFF force fields. |
6642c357418a5379b02fd6d2 | 4 | Although very insightful, this prior benchmark study did not include charged molecules, and was limited to [C, H, N, O] chemical space. Because of these limitations, here we focused on running a new benchmark which would more adequately represent the pharmaceutically relevant chemical space that our force field needs to describe accurately. Thus, to expand the scope of the prior benchmark we selected 59 torsions from molecules in OpenFF's Roche (general, and tautomer+protomer dataset) and Coverage molecule sets. |
6642c357418a5379b02fd6d2 | 5 | The benchmark geometries were the final geometries from the torsion scan at MP2/heavyaug-cc-pVTZ level of theory. Whereas, the benchmark relative energies were obtained using coupled-cluster with single, double, and perturbative triple excitations at the complete basis set limit, CCSD(T)/CBS. For the complete basis set calculation, Helgaker's 2-point extrapolation scheme was used as implemented in Psi4. Helgaker extrapolation scheme here includes a reference total energy from Hartree-Fock, correlation correction which includes correlation effects beyond HF with the MP2 method, and a delta correction, which gives a highly accurate correlation calculation with CCSD(T), accounting for the error in MP2. |
6642c357418a5379b02fd6d2 | 6 | The difference between CCSD(T) and MP2 converges quickly with increase in basis functions and hence a smaller basis set can be used for this part of calculation. Psi4 performs these calculations in stages and the treatment follows this equation: E CBS total = F scf scheme E scf basis total,SCF + F corl scheme E corl basis corl,corl wfn + δ delta wfn delta wfn lesser (1) where, F is an energy or energy extrapolation scheme. And, in our case this translates to |
6642c357418a5379b02fd6d2 | 7 | Although heavy-aug-cc-pVDZ (or haDZ) is computationally affordable it may fall short of the gold standard reference level of theory often used in the community. It is ex-13 pected that the delta correction error with haDZ would fall somewhere in between 0.1 and 0.25 kcal/mol, the errors observed with aug-cc-pVDZ and cc-pVDZ on either end of the range. To assess how good our choice of reference theory level is we have performed energy calculations with the gold standard reference theory level for a subset of 7 molecules from the benchmark set at CCSD(T)/CBS, where for the extrapolation to CBS the correlation basis is aug-cc-pV[TQ]Z, and delta basis is aug-cc-pVTZ. The gold standard energy is calculated as, 60 |
6642c357418a5379b02fd6d2 | 8 | for delta correction when compared to a larger basis (aTZ) used in the gold standard reference. And, the RMSE in relative energies for the 7 molecule subset (7 x 24 grid points) of our reference theory with respect to the gold standard was 0.0761 0.0904 0.0609 kcal/mol (the subscript and superscript are the 95% confidence intervals). So, the difference with respect to the gold standard was one tenths of a kcal/mol for our choice of reference theory level, which was accurate enough and quite affordable for our study. |
6642c357418a5379b02fd6d2 | 9 | We have chosen a smaller pool of density functional approximations (DFA) that are cost effective from the get go and we are not looking into a comprehensive evaluation of all available DFAs. The choice of DFAs include those commonly used in developing force fields and charge models, and better performing ones from other benchmark studies. From our prior studies DZVP has been proven cost friendly and all the DFAs were tested with this basis set. And, within our current choice of DFA used in developing OpenFF force fields, B3LYP-D3BJ, we tested Ahlrichs def2 basis sets incrementing them systematically in size, |
6642c357418a5379b02fd6d2 | 10 | The energy barriers observed in torsion energy profiles are a measure of the strength of steric hindrance or strong intramolecular interactions that prevent certain conformations. Thus, accurately capturing torsion profiles is relevant for understanding molecular recognition, binding, and other interactions that occur in complex systems. Our aim here is to pick an accurate and computationally efficient QM level of theory to train the valence parameters in a general small molecule force field. For this purpose, single point energies were evaluated at different levels of theory for comparison at the benchmark geometries, and the RMSE in relative energies was tabulated. Single point energies were evaluated at the same geometry to ensure parity between the methods since performing a geometry optimization with each of the methods will result in minor differences in final geometries, and sometimes TorsionDrive may push them to a completely different minima. SI Table lists the RMSE in torsion profile energies for each of the molecules considered in this benchmark set with respect to the reference level of theory, CCSD(T)/[haTQZ; δ:haDZ]. |
6642c357418a5379b02fd6d2 | 11 | where, E' represents the absolute energies, x 0 represents the minimum energy point. And, the RMSE and MUE were evaluated with the relative energies. For calculating the RMSE of thermally relevant low-energy region (TRLR), only the relative energies below 5 kcal/mol on the reference energy surface were chosen. The cutoff of 5 kcal/mol was chosen to favor low-energy regions in state space. Table : Overall RMSE and MUE (in kcal/mol) in torsion profile energies of the molecule set with respect to the reference level CCSD(T)/[haTQZ; δ:haDZ]//MP2/heavy-aug-cc-pVTZ level of theory. The 95% confidence intervals, calculated with cinnabar, were presented on the side. Furthermore, the last column includes the RMSE within the thermally relevant low-energy region (TRLR) of energies < 5 kcal/mol, averaged over all the molecules, which serves as a metric for assessing accuracy in low-energy regions. The best performer on this set of molecules is ωB97M-D3(BJ)/DZVP, and our current choice of theory level, B3LYP-D3(BJ)/DZVP, lags behind it by only 0. The RMSEs on the whole set and the subsets of neutral and charged molecule sets were depicted in Figure and tabulated in Table . We can see from Figure (f), and from Table , that the accuracy of B3LYP-D3(BJ) functional increases for charged molecules with addition of polarization and diffuse functions from DZVP to def2-TZVP and higher. |
6642c357418a5379b02fd6d2 | 12 | And, OpenFF's default level of theory, B3LYP-D3(BJ)/DZVP, has an RMSE error 0.18 kcal/mol worse than the best method, with an overall RMSE of 0.58 kcal/mol. The difference in RMSE between charged molecules and the neutral molecules is slightly higher for B3LYP-D3(BJ)/DZVP level of theory, and addition of basis functions helped drive this error down. |
6642c357418a5379b02fd6d2 | 13 | Despite observing higher errors in certain molecules, the methodology used to construct the torsion profile target data, which prioritizes the match to low energy regions, has the potential to mitigate some of these discrepancies. During the training of OpenFF force fields we construct a torsion profile target and optimize the force field using ForceBalance, and the objective function in terms of relative energies is defined as follows: 3 |
6642c357418a5379b02fd6d2 | 14 | where x i represents the coordinates of i th conformer, the 0 th conformer is the minimum energy conformer in respective potential energy landscapes, θ is the force field parameter set at that iteration, and OptMM(x i , θ) corresponds to the MM energy obtained via constrained minimization and d E = 1 kcal/mol is a conversion factor to make the sum over deviations dimensionless. The applied weights w(E QM ) in equation 6 prioritize matching the torsion profile at energy minima since Boltzmann sampling favors low-energy regions in state space. w(E QM ) = |
6642c357418a5379b02fd6d2 | 15 | In the context of fitting OpenFF force fields, the torsion profile energy loss function defined above in equation 6 may further mitigate the differences between the methods since we applied a hard cutoff of 5 kcal/mol to exclude the higher energy regions from torsion fits for the OpenFF Parsley and Sage line of force fields. The RMSE on thermally relevant low-energy region (TRLR), only considering the energies less than 5 kcal/mol with respect to the minima on the torsion profile, were tabulated in the last column of Table . We can see that ωB97M-D3(BJ)/DZVP still holds its place as the most accurate functional with torsion target score as well, and the differences between various methods drop drastically in the low energy regions. In a sense, the modeling of low-energy, thermally relevant regions was quite accurate, while it was in the high-energy regions where the influence of stereoelectronic and steric effects became prominent, leading to discernible differences between various methods. |
6642c357418a5379b02fd6d2 | 16 | The error in the subset of neutral molecules (30 data points) is small for OpenFF's default of B3LYP-D3(BJ) and close to the best functional, ωB97M-D3(BJ). However, the error is larger for the charged subset of molecules (29 data points) with OpenFF's default, compared to the best functional, and yet remains accurate in low-energy regions. Most of the large deviations come from high energy regions which were (and usually are) excluded in fitting to torsion profile energies as they are thermally irrelevant. In this sense, our default method may remain appealing given its low computational cost and relatively low error in key regions of torsion profiles. For charged molecules, addition of more basis functions would help as seen in subplot 3, subplot (f). ). The horizontal dashed line represents 5 kcal/mol and if we truncate the energies above it we can see that the low energy regions were captured better when compared to the high energy regions. |
6642c357418a5379b02fd6d2 | 17 | Referring to SI table S1, when we examine the molecule with the largest error using OpenFF's default, B3LYP-D3(BJ)/DZVP, which exhibits an RMSE in relative energies of 1.36 kcal/mol, we observe that the majority of discrepancies arise from the high-energy region exceeding 5 kcal/mol. The torsion profile for this molecule with respect to different basis sets was shown in Figure . It is worth reiterating that we exclude this high-energy region during the training process. |
6642c357418a5379b02fd6d2 | 18 | The computation time of a single point (energy + gradient) calculation provides a rough approximation of the method's cost for a torsion scan or geometry optimization. When examining the OpenFF QM datasets of small molecules, it is observed that a geometry optimization typically requires a median of 42 gradient calculations (based on data from approximately 8000 geometry optimizations). Additionally, a 1D torsion scan with 24 grid points generally costs around 788 gradient calculations (from data on roughly 4000 torsion scans). As a rule of thumb, a geometry optimization calculation is 40x costlier than a single point energy and gradient calculation, and a 1D torsion scan is 800x costlier if executed serially, or nearly 72-fold for parallelized torsion scans (considering the median of maximum number of optimization steps taken among all grid points). So, the differences scale up pretty quickly with the type of calculation. To provide a reference point, we present timing data for a molecule containing 16 heavy atoms. The timings were normalized with the time for a B3LYP-D3(BJ)/DZVP calculation. The cost factor versus RMSE plot is shown in Figure , and the most accurate functional is almost twice the cost of a B3LYP-D3(BJ)/DZVP calculation, despite only a modest accuracy benefit. It is to be noted that Psi4, as of v1.4.1, does not yet have analytic gradients for NL and VV10 dispersion terms, and also for DSD-BLYP method, so for these methods only the costs of an energy calculation were reported and scaled with respect to the cost of a B3LYP-D3(BJ) energy calculation. |
6642c357418a5379b02fd6d2 | 19 | an increase in molecule size. Both the quadratic and linear fits of the data yielded a similar R 2 , which prompted considering the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to differentiate the models better. Higher R 2 , lower AIC, and lower BIC values indicate a better fit to the quadratic model. From Figure we can see that with an increase in number of atoms represented by an increase in number of basis functions and the scaling of computation cost for a B3LYP-D3(BJ)/DZVP single point energy plus gradient calculation. The scaling of B3LYP-D3(BJ)/DZVP single point energy plus gradient calculation with an increase in number of basis functions, which in turn represents an increase in number of atoms. The time of calculation for the dispersion correction term is not included as it is negligible, of the order of fraction of a second. The quadratic (in orange) and linear (in blue) fits to the data were shown along with the metrics R 2 , Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Quadratic scaling model seems appropriate from these metrics. |
6642c357418a5379b02fd6d2 | 20 | Creating bespoke force fields on-the-fly adds a lot of new torsion parameters, which in turn requires generation of new QM reference data for training them. Generation of new QM data is time consuming, and a possible alternative for faster parametrization, without too much loss in accuracy, can be a semiempirical method, or a couterpoise corrected method with minimal basis, or machine learning potentials. Here we checked the performance of the semiempirical method GFN2-XTB, Grimme's 3-corrected Hartree-Fock method (HF-3c), and two recent machine learning potentials, AIMNET2 and MACE-OFF23, the ML potentials which have demonstrated accuracy very close to the level of DFT that they were trained on. Only single point energies were evaluated here, as in the comparisons above. |
6642c357418a5379b02fd6d2 | 21 | Table summarizes the performance of the four methods across the whole benchmark set, and also broken down into neutral and charged subsets (see also Table ). GFN2-XTB shows reasonable accuracy, but is not competitive with the DFT methods. AIMNet2 shows very good accuracy, close to DFT, consistently across both neutral and charged species. |
6642c357418a5379b02fd6d2 | 22 | shows remarkable accuracy for the neutral subset, in fact more accurate than any of the DFT methods studied here. Note that MACE-OFF23 was not trained on charged species, and hence the error is much higher for this subset, but this will be addressed in future models. HF-3c does not perform well here. Thus, machine learning potentials such as these are a reasonable alternative to DFT, particularly for high-throughput, bespoke parametrization work. 88 |
6642c357418a5379b02fd6d2 | 23 | We conducted a benchmark of QM levels of theory that strike a balance between accuracy and computational efficiency for generating large QM datasets with diverse chemistries to train the valence parameters in a general small molecule force field. The benchmark set of molecules included charged molecules, biaryls, complex hypervalent sulfur chemistry, and complex nitrogen chemistry. This benchmark study is an extension to an earlier work 2 on benchmarking conformer energies, which suggested B3LYP-D3(BJ)/DZVP as the level of theory to generate OpenFF force field training and validation data. In the context of force field development, aside from conformer energies and optimized geometries, torsion energy profiles represent another indispensable source of molecular interaction data. Achieving accuracy in torsion profile energies relative to a highly accurate QM level of theory reflects in the trained force field. For this purpose, relative energies were compared against CCSD(T)/[haTQZ; δ:haDZ]//MP2/haTZ level of theory for different functional and basis set combinations. And, among the tested methods, ωB97M-D3(BJ) outperforms the others even within a smaller basis set of DZVP, boasting an RMSE in torsion profile energies of just 0.41 kcal/mol. This range-separated hybrid functional has consistently ranked among the top performers in various recent studies 43,44 which were done with a larger basis set. |
6642c357418a5379b02fd6d2 | 24 | OpenFF's choice of B3LYP-D3(BJ)/DZVP closely follows it with an RMSE in relative energies of 0.52 kcal/mol. And, the computational cost of B3LYP-D3(BJ)/DZVP for a single gradient is only half of the best functional, but depending on the type of dataset, geometry optimization or torsion scans, the cost would scale up with the number of steps taken during the calculation. Within a subset of neutral molecules the RMSE in relative energies with B3LYP-D3(BJ)/DZVP is comparable to the most accurate method. And, the larger errors appear to originate from molecules with charges. However, in practice, the distinctions between levels of theory become evident in the high-energy regions, which are typically excluded during force field training with torsion profiles as they are thermally irrelevant. QCFractal+QCEngine. Each entry in the calculation input being sent to the server for computation corresponds to a single molecule and an associated QM calculation schema. |
6642c357418a5379b02fd6d2 | 25 | A QM calculation schema in each dataset entry specifies the program to use, the type of calculation to perform such as torsion scan or single point energy calculation, and QM calculation details such as functional, basis set, convergence criteria, maximum number of steps, SCF properties to derive from the final wave function, etc., and each of those inputs were validated to have the correct input syntax that can be parsed by the program. This input validation ensures we can skip any calculations which would have failed due to invalid input syntax before even submitting to the compute cluster. |
6642c357418a5379b02fd6d2 | 26 | The QCFractal package is utilized to instantiate a compute manager and compute workers on a cluster, enabling the execution of a substantial number of independent calculations or jobs in parallel. A compute manager monitors the job completion status and compute workers grab any incomplete jobs from the compute manager and send back completed jobs. |
6642c357418a5379b02fd6d2 | 27 | The compute managers interface with the QCA server to update the QCA database with finished calculations. Automated error-cycling has been set up using GitHub actions, a backend tool provided by GitHub for workflow management, allowing resubmission of failed jobs and also generating high level summaries on the progress of the calculations. These automated error reports help in diagnosing whether the failures were due to early preemption of compute workers, or due to lack of resources, such as low memory for calculations with larger molecules, or redundant failures due to a systematic issue with the compute environment on the worker compute node, and other failure modes that may occur during computation. |
6642c357418a5379b02fd6d2 | 28 | Psi4 is a versatile, open source, quantum chemistry package. Psi4 is highly parallel, and has the most efficient implementation of density-fitting method. Psi4 has fast analytic gradients for many high level methods such as Møller-Plesset perturbation theory (MP2) as well as for most functional and dispersion corrections. For geometry optimizations an external optimizer, GeomeTRIC, 114 was used. GeomeTRIC uses a translation-rotation-internal coordinate (TRIC) system which significantly speeds up geometry optimizations. And for torsion scans, the TorsionDrive 57 program, which uses a wavefront propagation algorithm and multiple initial guesses in parallel, independent of the search direction, to avoid hysteresis in the atomic configurations involved in driving the torsion. The completed calculations can be conveniently accessed from the QCA server at any time, and from anywhere in the world. |
6642c357418a5379b02fd6d2 | 29 | Figure : OpenFF dataset generation workflow, qca-dataset-submission. Starting with a set of 2D or 3D representations of molecules and using openff-qcsubmit 88 a dataset submission can be prepared with the required level of theory and other hyperparameters that are necessary for a calculation. After the inputs are ready one can make a pull request on this repository, and a reviewer will then process the submission and after approval the calculations are submitted to QCArchive server, a public repository of data hosted by MolSSI. QCFractal is the backend server software that manages the calculations to be done and sends them to compute managers on HPC clusters hosted at different compute centers. Finished calculations are sent back to QCArchive. |
6642c357418a5379b02fd6d2 | 30 | Dipole moment, an electrostatic property, is an overall measure of geometry and electronic structure within a molecule and getting it right is crucial for intermolecular interactions. For all the methods tested, the deviations in the magnitude and the direction of dipole moment vectors with respect to the reference level of theory, CCSD(T)/haDZ//MP2/haTZ, are tabulated in Table . All the methods tested give overall comparable performance statistics relative to one another, with an RMSE in dipole magnitudes of around 0.6 Debye, and deviations in dipole moment vectors of around 0.1-0.2 degrees. Dipole moment is a key metric for modeling the quality of electrostatic interactions, and we refer the reader to more detailed studies that benchmarked electronic structure methods for electrostatic properties, such as polarizabilities, hyperpolarizabilities, and magnetizabilities. Table : The deviations in dipole moment magnitudes (in Debye) with respect to the reference CCSD(T)/heavy-aug-cc-pVDZ//MP2/heavy-aug-cc-pVTZ level of theory, for the whole benchmark set and the neutral and charged subsets. The 95% confidence intervals, calculated with cinnabar, were presented on the side. The deviations are minimal for all the theory levels benchmarked and the values are comparable to each other. Large deviations were seen on the charged subset of molecules. Origin (0, 0, 0) is chosen as the reference point for the dipoles. |
65ef0567e9ebbb4db972fc82 | 0 | Living cells exhibit well-organized dynamics in bio-soft matter assemblies, such as membrane deformation, cell division, and cell differentiation 1 , which are essential features that distinguish living systems from non-living matter. Recently, liquid-liquid phase separation (LLPS) droplets of bio-soft matter have been found in living cells, and their dynamic behaviors have attracted attention , such as nucleolar assembly through non-equilibrium processes of rRNA transcription , sol-gel transition , and activation/inhibition of molecular reactions . These examples show that precise temporal control of biological LLPS droplets via non-equilibrium chemical reactions realizes such dynamic behaviors. Synthetic LLPS droplets have recently been explored in bottom-up synthetic biology for constructing artificial cells , molecular robots , molecular computers , and biomedical nanodevices . Various dynamic behaviors of synthetic LLPS droplets have been reported, such as sequestration of molecules , motion , and division . More recently, non-equilibrium dynamics such as cyclic assembly/disassembly and transient shell-formation of synthetic coacervate droplets were achieved by coupling LLPS droplets with non-equilibrium chemical reactions such as phosphorylation/dephosphorylation and enzymatic synthesis of polynucleotide . However, temporal control of LLPS droplet dynamics remains difficult. Programmable temporal control methods must be developed to mimic cell dynamics. |
65ef0567e9ebbb4db972fc82 | 1 | DNA is well known for its programmable structures and reactions . DNA programmability also facilitates the temporal control of chemical reactions. For example, DNA computing reactions have been demonstrated, such as the chemical oscillation of DNA concentrations , temporal logic circuit , and timing-controlled generation of chemical signals . Moreover, the programmability of DNA has been utilized not only for controlling chemical reactions but also for controlling the physical dynamics of mechanical DNA-based nanostructures . Particularly, DNA-based coacervates (also referred to as DNA droplets) formed with branched DNA nanostructures can couple physical dynamics with chemical reactions in a programmable manner. DNA droplets divide autonomously with enzymatic and photo cleavage reactions and locomotion via enzymatic degradation . Phase separation of DNA droplets based on molecular logic computation and reaction-diffusion pattern formation coupled with RNA transcription and diffusion have also been demonstrated. However, achieving the timing-controlled physical dynamics of DNA droplets coupled with non-equilibrium chemical reactions remains challenging. |
65ef0567e9ebbb4db972fc82 | 2 | In the present study, we demonstrated the timing-controlled division dynamics of DNA droplet-based artificial cells by coupling them with non-equilibrium chemical reactions, resulting in the pathway control of artificial cell division (Figure ). We used DNA droplets constructed by mixing two Y-shaped branched DNA nanostructures (YA and YB; called binary-mixed DNA droplets), in which 6-branched DNA linkers crosslinked YA and YB (Figures and). Mixed DNA droplets are divided into YA and YB by cleaving the DNA linkers through the hybridization with division trigger DNAs. Here, we coupled the mixed DNA droplet with non-equilibrium chemical reactions; the time delay of division triggers (Figure ) realized timing and pathway control of DNA droplet division (Figures ). We used temporal control of DNA reactions based on RNA degradation with a ribonuclease H (RNase H), which has been used in many dynamic DNA reactions such as DNA oscillators , DNA bistable switch , logic computation 50 , DNA walker , and timers for DNA strand displacement reactions ; however, there is no report on temporal control of LLPS droplets with the RNase H reaction. Finally, we present a molecular computing element to compare the concentrations of microRNA (miRNA) sequences (called molecular comparators) as an application of the timing-controlled division of DNA-droplet-based artificial cells. Our results provide a method for chemically regulating the timing-controlled physical dynamics of LLPS droplets for artificial cell studies. |
65ef0567e9ebbb4db972fc82 | 3 | Figure shows the design of DNA droplets for artificial cells. Y-shaped branched DNA nanostructures self-assemble to form DNA droplets via hybridization of selfcomplementary sticky ends at their branches . Because YA and YB have noncomplementary sticky ends (Figure ; detailed sequences are in Supplemental Table ), the resultant A-and B-droplets do not fuse; however, a 6-branched DNA linker (LAB) (Figure ; Supplemental Table ) can crosslink YA and YB, forming a binary-mixed DNA droplet (A•B-droplet) (Figure ). Here, '•' (a single center dot) in 'A•B' indicates that one type of linker (LAB) crosslinks YA and YB in A•B-droplet. Figure shows confocal laser scanning microscopy (CLSM) images of the A•B-droplet. The A•B-droplet can be divided by cleaving LAB into two portions (Figure ). For LAB cleavage, we used a nucleic acid strand displacement reaction induced by single-stranded DNA (ssDNA) division triggers (TAB1 and TAB2) (Figure ). The division triggers hybridize to the toehold sequences (ToeholdAB1 and ToeholdAB2) in LAB and invade the branches of LAB via strand-displacement reactions (Figure , middle), cleaving LAB into two portions (Figure , right). Considering the reaction landscape (Figure ), the LAB cleavage reaction uses division triggers as chemical "fuels" . After adding the division triggers, the cleaved-LAB is more stable than the initial LAB because of the Gibbs free energy change (ΔGClv) induced by division trigger hybridization and strand displacement reactions. Thus, cleavage is a non-equilibrium chemical reaction that uses chemical energy. Figure shows the time-lapse images of the division of the A•B-droplet after adding the division triggers. The A•B-droplet started to divide just after adding division triggers. |
65ef0567e9ebbb4db972fc82 | 4 | We hypothesized that inhibiting "active" division triggers causes the time delay of the linker cleavage, resulting in timing control over DNA droplet division. Figure shows the design of a time-delay circuit comprising reactions (i) and (ii). (i) Active division triggers changed to inhibited division triggers by the hybridization of excess singlestranded RNAs (ssRNAs), named inhibitor RNAs. (ii) An RNase H degrades the inhibitor RNAs in the inhibited division triggers, thereby releasing active division triggers. These two reactions cause a time delay in the cleavage of the DNA linker. |
65ef0567e9ebbb4db972fc82 | 5 | To tune the time delay of the binary-mixed DNA droplet division, we introduced L † AB in addition to the original DNA linker, LAB (Figure ). We describe this binary-mixed DNA droplet as "A:B-droplet," where ':' (double dots) indicates that YA and YB are crosslinked with two DNA linkers, LAB and L † AB. A:B-droplets divide only when both LAB and L † AB are cleaved. In addition, linkers and triggers with " †" indicate those that can achieve a time delay in the presence of inhibitor RNAs and RNase H (Figure ). LAB is cleaved by the active division triggers TABi (i=1, 2), while L † AB is cleaved by active division triggers T † ABi (i=1, 2). Inhibitor RNAs R † ABi hybridize with T † ABi, and form inhibited division triggers iT † ABi, inducing the time delay of A:B-droplet division. This time-delay circuit was inspired by intracellular time-delay control via reaction suppression based on small RNA expression . For such biological meaning and applications shown later, we used natural miRNA sequences, miR-6875-5p and miR-4634 , for R † ABi sequences, respectively (Supplemental Table ); that is, if either of the miRNAs exist, the A:Bdroplet division is delayed. |
65ef0567e9ebbb4db972fc82 | 6 | The first terms in Eqs. 1 and 2 denote the spatial diffusion of T † ABi and L † AB, respectively; 𝐷(𝒙) is the diffusion coefficient depending on the position x (x = "inside" or "outside" of A:B-droplet). The term 𝑓(⋯ ) denotes the consumption of division triggers T † AB1 via hybridization with L † AB and other molecules (details in Supplemental Note S1). 𝑔(⋯ ) denotes the time delay reaction (defined by Eq.3), modulated by the concentrations of RNase H and the inhibitor RNAs; 𝐾 # and 𝑘 $%& are the Michaelis-Menten parameters for the RNase H reaction; 𝑐 ' "# is the total RNase H concentration; 𝑘 ( $% and 𝑘 ) $&! are the hybridization rates of the division triggers with linker LAB and the inhibitor RNAs, respectively. The second term of Eq.2 denotes the hybridizations of L † AB with T † ABi. We also obtained partial differential equations for the other molecules; the details of the full numerical model and numerical simulations are described in Supplemental Note S1. |
65ef0567e9ebbb4db972fc82 | 7 | Figures and show the distributions of LAB and L † AB, respectively, in an A:B-droplet at several normalized simulation time steps (the white broken-line circle indicates the surface of the A:B-droplet). In the present study, we fixed the percentages of LAB and L † AB to the total amount of linker DNA to 90% and 10%, respectively. We referred to previously reported kinetic parameters and diffusion coefficients . The results show that L † AB remains longer than LAB, although the percentage of L † AB is lower than that of LAB. This indicates that the decrease of L † AB becomes slower due to the time-delay circuit. |
65ef0567e9ebbb4db972fc82 | 8 | We performed the experiments shown in Figure for the timing-controlled division of the A:B-droplets. The droplet division reaction started by adding active triggers (TABi), inhibited triggers (iT † ABi), excess inhibitors (R † ABi), and RNase H into an A:B-droplet solution (Methods in detail). Figures and show time-lapse images of A:B-droplet division. The required time for the division was elongated with decreasing 𝑐 ' "# or increasing 𝑢 ) & $%' |
65ef0567e9ebbb4db972fc82 | 9 | . Furthermore, we quantified the division ratio rdiv of the A:B-droplet using image processing (see Supplemental Note S3) (Figures and). rdiv is 0 if the A-and B-droplets are fully mixed in the A:B-droplets, and 1 if the A:B-droplets are completely divided into A-and B-droplets. The results demonstrated that the increasing rate of rdiv became slower with decreasing 𝑐 ' "# or increasing |
65ef0567e9ebbb4db972fc82 | 10 | , which is consistent with the numerical simulation results. Thus, we concluded that the timingcontrolled division of DNA droplets was achieved using a time-delay circuit. Next, we applied the time-delay circuit to control the pathway of DNA droplet division (Figure ). We used a ternary-mixed C•A•B-droplet, comprising three types of Y-shaped branched DNA nanostructures (YC, YA, and YB) connected with two types of linkers (L † AC and L † AB) (Figure ). YA, YB, and L † AB are the same as those used in the previously described experiment; L † AC was designed to crosslink YC and YA. From the viewpoint of the reaction landscape shown in Figure ). This indicates that Pathway 1 was selected via the inhibition of T † ABi due to the presence of R † ABi (miR-6875-5p and miR-4634). Next, to achieve Pathway 2, we added active triggers T † ABi (for cleaving L † AB earlier); inhibited triggers iT † ACi, excess inhibitors R † ACi, and RNase H (for cleaving L † AC later). For R † ACi, miRNA sequences, miR-1246 and miR-1307-3p, were used (Supplemental Table ). Supplemental Movie S7 shows that the order of the division of B-and C-droplets was also controlled well. The C•A•B-droplets were first divided into B-droplets and C•Adroplets approximately 30 min after the addition (Figure ). After another 20 min, the C•A-droplets were divided into A-and C-droplets (Figure (ii)). This indicates that Pathway 2 was selected because of the presence of R † ACi (miR-1246 and miR-1307-3p). Thus, the pathway-controlled division was achieved using time-delay circuits. |
65ef0567e9ebbb4db972fc82 | 11 | ), which are for the cleavage delay of L † AB and L † AC, respectively. The comparator accepts miRNA sequences (Figure ) as inputs; i.e., the input miRNAs work as the inhibitor RNAs, R † ABi and R † ACi (Figure ). Theoretically, if 𝑐+ , > 𝑐+ . , Pathway 1 is selected; the L † AB cleavage delays longer than the L † AC because more R † ABi causes a longer time delay (Figure ). Contrarily, if 𝑐+ , < 𝑐+ . , Pathway 2 is selected; the L † AC cleavage delays longer. Thus, the observed pathway indicates the result of the comparison between 𝑐+ , and 𝑐+ . (Figure ). |
65ef0567e9ebbb4db972fc82 | 12 | Comparator experiments were performed using several RNA concentrations. Here, we define ∆𝑐̃ = 𝑐̃+ , -𝑐̃+ . and 𝑐̃& = 𝑐̃+ , + 𝑐̃+ . . We investigated five types of conditions of the initial RNA concentrations shown in Figure the C-droplet divided first, whereas under conditions (iv) and (v), the B-droplet divided first (Supplemental Figure ). Figure shows the time courses of the division ratios of B-(rdiv_B) and C-(rdiv_C) droplets quantified using the image processing method shown in Supplementary Note S3. These results showed that with higher ∆𝑐, C-droplet division was faster. Note that an increase in 𝑐& caused a delay in the overall reaction, probably because more RNA molecules induced competition in the degradation of RNA by RNase H in the condition of the same RNase H concentration. |
65ef0567e9ebbb4db972fc82 | 13 | For quantitative estimation, we calculated the time difference Δτ between the division timings of B-and C-droplets (Figures 6d): ∆𝜏 = 𝜏 /01_, -𝜏 /01_. , where 𝜏 /01_, and 𝜏 /01_. are defined as the times when rdiv_B and rdiv_C were both approximately 0.5, respectively. As shown in Figure , Δτ > 0 was observed when the RNA concentration difference ∆𝑐̃= 1.25 (i), 0.5 (ii), and -0.5 (iii), indicating that the division occurred through Pathway 1. Alternatively, Δτ < 0 was observed when ∆𝑐̃= -1.0 (iv) and -1.25 (v), indicating that Pathway 2 was selected. These results demonstrated that the division pathway changed depending on the RNA concentration differences, confirming that the concentration comparator for the miRNA sequences worked as expected. |
65ef0567e9ebbb4db972fc82 | 14 | Ideally, the sign of Δτ is expected to switch when ∆𝑐̃= 0. However, the results imply that the sign switches between ∆𝑐̃= -0.5 and -1.0 (i.e., ∆𝑐̃≠ 0). Here, we define an offset concentration of this molecular comparator, 𝜎, at which the sign of Δτ switches, where the output of the comparator switches. Regular electrical comparators generally have a non-zero offset voltage because of non-ideal circuit properties; similarly, our molecular comparator has a non-zero offset (𝜎 ≠ 0). 𝜎 ≠ 0 would be observed probably because B-droplet division took longer than that of the C-droplet for some reasons; for example, the DNA sequence difference induced the slower cleavage of L † AB than L † AC, or more linker cleavage is required for B-droplet division than C-droplet division. In future studies, 𝜎 may be tuned by sequence designing of DNAs. |
65ef0567e9ebbb4db972fc82 | 15 | To estimate the hypothesis for the mechanism of the non-zero offset, we performed numerical simulations using a reaction-diffusion model that considered differences in the cleavage rate of linker DNAs (see Supplemental Note S2). First, we changed the hybridization and the strand displacement rates for L † AB cleavage. Next, we varied the threshold parameters KAB and KAC for rdiv_B and rdiv_C (Eqs. S.90 and S.91 in Supplemental Note S2); the larger the threshold parameters, the faster the division. |
65ef0567e9ebbb4db972fc82 | 16 | We set the hybridization rate and the strand displacement rate between T † ABi and L † AB to be 10 times lower than that between T † ACi and L † AC. KAB and KAC are set to asymmetric values of 0.1, and 0.9, respectively. Figure shows the time courses of rdiv_B and rdiv_C in the simulation results. As ∆𝑐̃ increased, the C-droplets tended to divide earlier. |
65ef0567e9ebbb4db972fc82 | 17 | Additionally, as shown in Figure , the offset concentration 𝜎 was approximately -0.5, indicating that the trend is consistent with the experimental result. These results suggest that the differences in the cleavage rate between L † AB and L † AC and the required amount of linker cleavage for B-droplet and C-droplet divisions resulted in 𝜎 ≠ 0. Furthermore, numerical simulations were performed using different parameter values (Supplemental Figures ), producing different offset concentrations. These results suggest that changing DNA sequences could potentially control the offset concentration 𝜎. Note that, when more 𝑐& , the simulation results reproduce the delay in the overall reaction as observed in experiments due to the competition in the RNase H reaction. |
65ef0567e9ebbb4db972fc82 | 18 | We demonstrated the timing-controlled division dynamics of DNA droplets using a timedelay circuit. We developed the reaction-diffusion model and numerically investigated the strategy to control the division timing by controlling the cleavage rate of L † AB. Using this strategy, we experimentally demonstrated timing control of the division of an A:Bdroplet by tuning the time-delay circuit parameters. We realized the pathway control of the C•A•B-droplet division by changing the order of two types of linker DNA cleavage based on the time-delay circuit. Finally, we employed the pathway control of the C•A•Bdroplet division for molecular computation and achieved a comparator of miRNA concentrations, which may be applied to a diagnosis based on the concentration difference of expressed miRNAs. |
65ef0567e9ebbb4db972fc82 | 19 | The RNA concentration comparator had non-zero offset (𝜎 ≠ 0) (Figure ), and the simulation results suggested that 𝜎 changed depending on hybridization rates or strand displacement rates of linker DNAs (Figure and Supplemental Figures ). Because the hybridization and strand displacement rates of DNAs depend on their sequence and length , these results suggest that the non-zero offset was probably due to the sequences of the linker DNA nanostructure. Previously, Saleh et al. and Sato et al. have shown that differences in the sequences of DNA nanostructures changed the kinetic and thermodynamic properties of DNA droplets. To further control the DNA droplet dynamics, the influence of DNA sequences on the kinetic properties of DNA nanostructures must be clarified. |
65ef0567e9ebbb4db972fc82 | 20 | The present study demonstrated that non-equilibrium chemical reactions could control DNA droplet dynamics such as droplet division. In future, the control of chemical reactions via the physical dynamics of DNA droplets should be explored. Such bidirectional control over more complex dynamics can help build artificial cells with more living cell-like functions, such as biochemical reactions controlled by the condensates of transcriptional factors and cell/organelle behaviors controlled by transcripts . Moreover, enzymatic reactions regulated by synthetic protein-based coacervates 60 can be combined with our DNA-based droplet system. We believe that this technology provides a new strategy to create artificial cells and molecular robots with more sophisticated functions, such as timing-controlled self-replication, drug delivery, and diagnosis, with more accuracy and quantitative specifications. |
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