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658065c9e9ebbb4db933af2c | 48 | When there is no dissolved oxygen present in the feedstock, the fouling growth rate is extremely slow, with a film thickness of micrometers to millimeters for most trays in 1 year, consistent with our finding in the base case study. However, even a concentration as low as parts per million (ppm) of dissolved oxygen can significantly accelerate film growth to centimeters in 1 year. The impacts of dissolved oxygen in the feedstock center on the colder section of the debutanizer. This suggests that the boiling point of the antioxidant is a key design parameter to maximize the contact of the antioxidant and locations most affected by the molecular oxygen contamination, and that one may improve the effectiveness of antioxidant-type additives by introducing them from the condenser. This study presented a comprehensive extension of the multiphase detailed chemical kinetic modeling approach to incorporate the effects of dissolved oxygen in the context of polymer fouling within a distillation column. The fouling model specifically focused on the debutanizer and considered the presence of dissolved oxygen in the feedstock as the primary oxygen source. By explicitly accounting for 4 phases in each tray -tray overhead vapor, tray bulk liquid, liquid absorbed in the fouling film, and the solid in the fouling film on the tray surface -we constructed a detailed representation of the fouling process on the surface of a tray for 40 trays in a distillation column. The oxygen-perturbed polymerization occurring in the tray liquid was modeled using a detailed chemical mechanism. To manage the large number of distinct chemical species involved in the real fouling system, the molecular weight distribution of the oligomers formed in the bulk liquid was represented using the Anderson-Schulz-Flory (ASF) distribution to recover associated film growth contribution. Additionally, a fragment-based modeling approach was employed to describe the film growth chemistry, where the fragment-based reaction templates were modified to incorporate oxygen-perturbed film growth pathways. |
658065c9e9ebbb4db933af2c | 49 | Analyses on ASF distribution showed that heavy tails of oligomers can be formed via radical polymerization at the colder section of the column with the presence of oxygen, due to the larger elongation probability of the peroxyl propagation chain. We analyzed the simulation using rate of production analyses, and found that oxygen chemistry predominantly impacts liquid-phase radical polymerization and film growth in the colder section of the column. This is because the O 2 rises in the column and has a very low concentration in the hotter trays. We also found that the dominating film growth pathways can change at early and later fouling stages because thick films limit diffusion. These results suggest different antifouling additives are needed in different trays and perhaps at different times. |
658065c9e9ebbb4db933af2c | 50 | Perturbations applied to the dissolved oxygen concentration in the feedstock demonstrated that even at parts-per-million (ppm) levels, dissolved oxygen had a substantial accelerat-ing effect on film growth. These findings highlight the importance of considering oxygen chemistry in the modeling of polymer fouling within distillation columns. The developed fouling model provides insights into the role of oxygen in the fouling process and its impact on film growth, contributing to a better understanding of fouling phenomena in industrial distillation operations. |
65cf36f59138d2316140f19e | 0 | Nonlinear optical (NLO) materials are crucial for the development of contemporary technologies, including communications, signal processing, and data storage. Materials possessing optical limiting (OL) qualities have the ability to effectively absorb significant amounts of high-energy lasers, hence reducing the output energy plays an important role in safeguarding human eyes and optical systems against laser-induced harm. The demand for designing of new NLO materials has significantly increased in the field of optoelectronics and photonics in recent years. The captivating photo-physical properties exhibited by NLO materials under intense laser irradiation account for their extensive range of practical uses. Organic compounds are highly sought after for designing novel NLO materials, owing to their capability to achieve rapid response rates, increased photo-electric quantum efficiency, low dielectric constants. Organic molecules also possess greater design freedom in comparison to inorganic substances, rendering them more economically efficient, compared to their inorganic counterparts. In order for a molecule to demonstrate NLO characteristics, it must contain a significant initial hyperpolarizability and non-Centrosymmetric geometry. Organic chromophores that display strong absorption and emission in the nearinfrared (NIR) region are useful for several technological applications, including, solar cells, heat absorbers and NIR-emitting diodes. BODIPY molecules possess notable absorption properties and demonstrate highly efficient fluorescence emission in this range of NIR wavelength. The absorption and emission characteristics of these molecules can be readily altered by changing the substitution pattern of the BODIPY framework, leading to an increase in their fluorescence in the NIR spectrum. These dyes are well-known for their remarkable resistance to heat and light-induced chemical reactions, and their capacity to produce fluorescent sensors. PPAB (see Figure ) was shown to possess a wide absorption spectrum in the visible and near-infrared ranges, which can be attributed to its extensive conjugate structure. In biological assays and screening procedures, dyes that have NIR absorption and emission properties are favoured because they experience less interference from auto fluorescence and have a greater ability to penetrate deeper into the sample. Of late, intramolecular charge transfer (ICT)-based molecules with electron-donating and electron-accepting components, connected either alone or via π-linkers are popular for designing chromophores for NLO materials.. Incorporating suitable electronic donor (D) and acceptor (A) components on opposing sides of the π-linker, for example, molecules with D-A, D-π-A, D-A-D, and A-D-A architectures, can lead to a high second-order NLO response. Recently, Wang et al reported a series of molecules with donor-acceptor-donor (D-π-A-π-D) framework with the Pyrrolopyrrole aza-BODIPYs as the acceptor moiety with Triphenylamine (TPA) or Diphenylamine (DPA) as donors, with thienyl or phenylene linker. They studied the singlet emission properties of these molecules, which was observed at NIR region. In this study, we investigated the absorption and NLO response properties of aforesaid molecules with (D-π-A-π-D) structure, which led us to design molecules with D-π-A architecture for obtaining chromophores for higher NLO response. |
65cf36f59138d2316140f19e | 1 | The PPAB core present in all three compounds (Figure ), and these molecules demonstrate a high level of resistance to degradation caused by light which is a phenomenon usually exhibited by inorganic framework containing NLO molecules. The π-conjugation bridge, which is in this case a thienyl or phenylene linker, promotes ICT. A π-conjugated linker is employed to establish a connection between both the electron-donating and electronwithdrawing groups in a molecule. This process leads to an improvement in the NLO properties of the molecules. Varying the nature of the donor groups and the π-conjugated bridge by means of chemical design is the most common strategy for tuning of the first hyperpolarizability (βtot). We also studied the second-order NLO properties of the PPAB molecules which form the basis for the designing of the NLO switching, among others. |
65cf36f59138d2316140f19e | 2 | Imaging using two-photon absorption (2PA) produced photoluminescence is reported to be more advantageous than one-photon induced photoluminescence due to its ability to provide three-dimensional resolution. Additionally, when excitation is conducted in the NIR range, it enables greater penetration depth. The PPAB cored molecules exhibit strong performance in the NIR range, with 2PA cross sections of approximately 3000 GM at the telecommunication window at a wavelength of around 1500-1700 nm. 29 |
65cf36f59138d2316140f19e | 3 | Where IP and εH are the ionization potential and HOMO energy of a given molecule, respectively, and N is the total number of electrons in the molecule. Absorption spectra are obtained by implementation of time-dependent DFT (TDDFT) methods. All the computational calculations were done using the Gaussian 16 program. The absorption and NLO response of the molecules are studied in three solvents with varying polarity namely, Acetonitrile, Chloroform and Toluene. The highly polar solvent acetonitrile is selected to study the dynamic NLO properties of the studied molecules. The polarizable continuum model (PCM) in the framework of the self-consistent reaction field (SCRF) has been used to mimic the presence of solvent. |
65cf36f59138d2316140f19e | 4 | In the above equation, x, y and z denote the direction and the 𝜇 , 𝜇 , 𝜇 are the dipole moment components of the molecule. The frontier molecular orbital (FMO) images, including, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are analyzed to estimate the band gap in the molecules and also to obtain global reactivity indices. Visual molecular dynamics (VMD) is used to analyze and visualize the FMOs. The percentage of CT and local excitation (LE) in a transition between the lowest excited singlet and triplet state are calculated via inter fragment charge transfer method using Multiwfn code. The 2PA calculations were done using B3LYP functional and 6-31G* basis set for the ω*B97XD optimized coordinates using DALTON software. 3 RESULTS AND DISCUSSION |
65cf36f59138d2316140f19e | 5 | As molecules with emission properties in the NIR region are highly intriguing, we examined the NLO response of molecules (1-3) with D-π-A-π-D architecture (Figure ). The ground state geometry of these molecules were optimized, followed by computation of their first hyperpolarizability. Before computing their NLO response properties, the one-photon absorption of these molecules were studied using time-dependent density functional theory (TDDFT)to find out the best basis set/functional combination. Several functional including B3LYP, PBE1PBE, CAM-B3LYP, ωB97XD, and ω*B97XD, with a 6-31G(d) basis set were used to study the absorption of the aforesaid molecules (Table and). Our analysis revealed that the tuned functional exhibited minimal divergence from the experimental absorption values. As the NLO properties of quadrupolar molecules with D-π-A π-D framework were not much satisfying (see Table and), presumably due to their Centrosymmetric nature, basic molecular structure modifications to D-π-A were made, which helped us to greatly enhance the NLO response of the molecules. The ICT is an important factor which affects the NLO properties of organic molecules. |
65cf36f59138d2316140f19e | 6 | Among the PPAB chromophores, PPAB-2 show higher percentage of CT character which results in higher βtot values, owing to the Thienyl group which is a typical electron-rich substituent. Therefore, the introduction of thienyl as bridge between the A-D is beneficial to enhance the ICT which provides a large transition dipole moment, which can strongly affect the polarizability of the molecule. The tendency to engage in ICT from TPA or DPA to PPAB and moieties, facilitated by suitable π-linkers, is a significant factor in understanding the structure-function relation for designing of NLO materials. It is known that a strong electron 'push-pull' effect has a positive influence on the NLO performance of molecules, and a high electron-donating capacity in a molecule with D-π-A architecture benefits the ICT. Consequently, the electron donating group of PPAB-2 has a greater capacity to donate electrons compared to PPAB-1. This results in a higher ICT (intramolecular charge transfer) |
65cf36f59138d2316140f19e | 7 | The calculation of the one photon absorption energies, oscillator strength (f) and the fluorescence emission of PPAB (1-3) molecules are performed using the TDDFT method. As the change in solvent polarity is likely to result in a substantial alteration of the optical characteristics of ICT-based molecules , we go beyond gas-phase calculations to investigate the impact of a continuum dielectric on the electronic structure and properties, such as, dipole 2.0 (f=0.88) |
65cf36f59138d2316140f19e | 8 | To understand the nature of the studied chromophores, we have analysed the parameters including, the HOMO-LUMO energy gap and percentage of CT and LE characters of the excited state. The assessment of the FMO, including, the HOMO-LUMO energy gap is crucial for understanding the structure-function relationships of molecules with ICT nature. |
65cf36f59138d2316140f19e | 9 | To explore the distribution patterns of molecular orbitals of HOMO and LUMO, we examined the FMO of the PPAB molecules in Acetonitrile solvent using the polarizable continuum model, as illustrated in Figure . It is clear based on the FMO analysis that the HOMO densities of all PPAB molecules exhibit similarity as they are distributed over the donor moiety, indicating a π-bonding nature and the LUMO densities are dependent upon the electron-withdrawing moieties, exhibiting a π-antibonding nature. The chemical stability, electrical, and optical characteristics of molecules are also reportedly correlated well using FMO analysis. Compounds with a lower HOMO-LUMO energy gap have higher chemical reactivity, and these compounds are highly polarizable, showing excellent NLO properties because of higher possibility of ICT. The FMO analysis is done in three solvents with different polarity as well to study the effect of polar solvent on the HOMO-LUMO energy gap. Furthermore, energy gaps (ΔEHL) of the HOMO to the LUMO are shown in Table . |
65cf36f59138d2316140f19e | 10 | The study of the electrostatic potential (ESP) provides a perceptive understanding of the distribution of charges within the molecule (see Figure ). The ESP of aza-BODIPY molecules containing DPA and TPA groups exhibit significant differences. The region with a more negative potential, is denoted by red regions, is predominantly situated on the F atoms of the aza-BODIPY group. However, the DPA and TPA group exhibits a net positive potential, indicated by blue regions. This observation suggests that the aza-BODIPY group acts as the electron-acceptor group, while the DPA and TPA group serves as the electrondonor group which results in ICT which play a major role in NLO properties of the molecule. A model molecule that has gained a lot of attention from both experimentalists and theorists. The NLO properties of p-nitroaniline is also calculated using ω*B97XD/6-31G* functional and basis set to compare its results with PPAB-D-π-A structures (see Table ). |
65cf36f59138d2316140f19e | 11 | Among the molecules studies, PPAB-2 showed the highest βtot value, while PPAB-1 showed the lowest βtot value. The higher βtot of PPAB-3 than the PPAB-1 could be assigned to the unidirectional charge transfer in the former, as indicated by the ratio of βtot to βvec close to unity. The βtot of the three molecules are investigated in different solvents in which the results clearly indicate that the inclusion of the solvation effect leads to a substantial increase in the βtot values of the compounds under investigation. As the extend of ICT is known to enhance with increasing solvent polarity, we can infer that the ICT plays a significant role in shaping the NLO response of the PPAB (1-3). The βtot value of the molecules in acetonitrile solvent is much higher compared to the values observed in the less polar solvents. This finding suggests that the presence of a polarizable environment can effectively modulate the NLO response. The increase in β by modifying the dielectric environment around the chromophore is a potential method to greatly improve the performance of nonlinear optical systems. The components of the μ as well as that of β are provided in Table . The results indicate that unlike PPAB-1, the hyperpolarizability of PPAB-3 dominated by only one component (βy), indicating unidirectional charge transfer in the later. Therefore, these results indicate that the β values of the PPAB molecules can be tuned using suitable donor and acceptor groups that facilitates unidirectional charge transfer. |
65cf36f59138d2316140f19e | 12 | Hyper-Rayleigh scattering (HRS) or the second harmonic Rayleigh scattering(SHLS) is a phenomenon in which light is scattered at harmonic frequencies of the incident light. It is an incoherent nonlinear optical process. It is important to take into account the effects of frequency dispersion correction in theoretical calculations because the hyperpolarizability obtained experimentally is under dynamic settings. To make our results useful for the experimentalists and theoreticians alike, frequency dependent NLO response in terms of the βHRS β (-2ω,ω,ω) is calculated. The βHRS is an alternative to electric-field-induced second harmonic generation (EFISHG) for directly measuring the β value of all molecules, regardless of their symmetry or charge. The efficiency of SHG for a molecule is primarily determined by the molecular second-order nonlinear polarizability, or first hyperpolarizability, β. Castet et al. devised a method to assess the HRS response βHRS (-2ω; ω; ω) effectively. The dynamic values used in this study were derived using an incident infrared wavelength (λ) of 1064 nm, which is typical of Nd: YAG laser. Second-harmonic hyperpolarizability β(-2ω,ω,ω) can be measured in solution using hyper-Rayleigh scattering where ω is the frequency of the light field. The βHRS hyperpolrizabilities of the molecules is calculated in Acetonitrile. The second-order NLO susceptibility Xlmn is a third-rank tensor and the presence of inversion symmetry of the molecule will make Xlmn= 0. In this context, molecules with inversion symmetry are not SHG active. The β (-2ω, ω, ω) can be described by the equation 10. The computed dynamic βHRS (au) values at the ω*B97XD/6-31g* level using 1064 nm incident wavelength in Acetonitrile are reported in Table . |
65cf36f59138d2316140f19e | 13 | 2PA is a third-order nonlinear process, the simultaneous absorption of two photons of similar energy is called as two photon absorption. The increase in the percentage of the CT nature in a molecule has also reported to increase the 2PA cross-section. The 2PA cross-section is typically determined using the Goppert Mayer (GM) unit. The relationship between the GM and atomic unit is determined by the following equation 13. 𝛿 = δ |
65cf36f59138d2316140f19e | 14 | The variables in the Equation 13 are defined as follows: α represents the fine structure constant, 𝑎 represents the Bohr radius; c represents the speed of light in a vacuum. The 2PA cross sections obtained for these molecules are large which suggests that the investigated chromophores are promising as new organic materials for NLO. The 2PA cross section obtained for PPAB-2 (δ TP = 6354 a.u. at 1771 nm) is five times higher than PPAB-3 (δ TP = 1136 a.u. at 1560 nm, see Table ). The two molecules consist of very similar molecular structure but two different lateral donor groups: TPA vs. DPA. Our results indicate that due to the π linker in PPAB-2 is Thienyl whereas in PPAB-3 it is phenylene linker leading to enhanced ICT and consequently larger two-photon absorption in PPAB-2. The 2PA cross-section can also be significantly enhanced through careful modification of the donor and the linker substituents. These results indicate that the present study could serve as basis for studies of second and third-order NLO properties of ICT-based chromophores consisting of PPAB electronic acceptor with suitable electronic donor and π-linkers with Dπ-A framework for future technological applications. |
65cf36f59138d2316140f19e | 15 | The supplementary material contains absorption data comparison using different functionals with the experimental provided data for : D-π-A-π-D framework containing molecules along with values of μ, αav, βtotal and βvec, obtained using the ω*B97XD tuned functional and 6-31g* basis set, HOMO-LUMO energies of the PPAB molecules in different solvents with varying polarity and the electron density images of the molecules. (PDF) |
60c7428e9abda23ec0f8c02e | 0 | Accurate estimation of protein-ligand interactions and the energetic basis of ligand binding are of great importance for successful structure-based drug discovery projects. Much effort has been devoted to develop computational methods for evaluating the binding of a ligand to a protein of interest and the strength of that binding, including docking and scoring approaches , virtual screening , and physics-based free energy methods . |
60c7428e9abda23ec0f8c02e | 1 | Blind community wide-challenges such as the Drug Design Data Resource (D3R) Grand Challenge and the Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) () provide an excellent platform for developers to test and validate their computer-aided drug design methodologies against experimental datasets. Moreover, the unbiased setting of these challenges allows the participants to compare the performance of their workflows and techniques to other computational methods in the field, thus highlighting potential areas of enhancement. |
60c7428e9abda23ec0f8c02e | 2 | Every year, the D3R Grand Challenge organizers release pharmaceutically relevant datasets of protein-ligand complexes for the evaluation of ligand pose prediction and binding affinity protocols. This year, we decided to bring together our expertise in pose prediction and binding free energy calculations to participate in the D3R Grand Challenge 4 (GC4) to rank a set of ligands based on their predicted affinities towards the β -Amyloid Cleaving Enzyme 1 (BACE-1) involved in Alzheimer s disease . |
60c7428e9abda23ec0f8c02e | 3 | In Stage 1a of D3R GC4, the participants were asked to predict the binding affinities of 154 BACE-1 compounds using any available PDB structure data or binding data. At the end of Stage 1, co-crystal structures of additional 20 ligands were released by the D3R organizers, allowing the participants to use these structures to refine the affinity predictions. In the present work, we describe our participation in Stage 2, where we predicted the binding affinities of the 154 ligands. |
60c7428e9abda23ec0f8c02e | 4 | Many previous studies have evaluated the ability of molecular mechanics combined with the Poisson-Boltzmann surface area (MM-PBSA) and molecular mechanics combined with generalized Born surface area (MM-GBSA) methods to predict ligand binding poses and binding affinities, and compared the accuracy of these predictions to that of docking scores . Kaus et al. have reported that MM-GBSA method performs better than standard scoring functions in ranking binding poses. Similarly, Rastelli et al. have shown that both MM-GBSA and MM-PBSA rescoring methodologies improve the affinity ranking estimated by AutoDock scoring function. |
60c7428e9abda23ec0f8c02e | 5 | On the other hand, participants in past D3R Grand Challenges have reported poor correlations between their estimated MM-GBSA binding scores and experimental affini-ties . In fact, MM-GBSA and MM-PBSA are not always accurate methods for drug design projects because the quality of the results appears to depend on the protein-ligand system, the ligand sets, and details used in the method, such as the interior dielectric constant, the continuum-solvation method, the charges, and the entropies . |
60c7428e9abda23ec0f8c02e | 6 | The ambition of this collaborative report was to evaluate only the binding affinity prediction accuracy of MM-GBSA scores relative to AutoDock4 scores. Therefore, starting with the same binding poses generated using AutoDock-GPU, we compared our predicted affinities with the experimental affinities for the two scoring approaches -AutoDock4 scores and MM-GBSA scores. Based on the correlation statistics and performance metrics obtained for both submissions, we found that re-scoring the affinities using MM-GBSA free energy estimates did not improve the correlation with experimental values. During post-analysis, we found that MM-GBSA scores depend on the initial protein conformation, the protonation states of the BACE-1 active site, and the charge of the ligands, and we were able to improve our MM-GBSAbased correlation metrics retrospectively. |
60c7428e9abda23ec0f8c02e | 7 | The AutoDock4 scoring function can be described as a classical (additive) force field supplemented with an implicit solvation model and a ligand entropy term. The force field consists of three terms: a 12-6 Lennard-Jones potential, a Coloumb potential with a distance-dependent dielectric constant, and a 12-10 potential for hydrogen bonds. The implicit solvation model is an additive pairwise potential in which the solvent accessibility of each atom is estimated based on the proximity of surrounding atoms . It is an empirical model that depends both on atom type parameters and the partial charges . It accounts for (de)solvation of both the ligand and the receptor. The ligand entropy term accounts for the loss of conformational freedom of the ligand upon binding, adding a penalty that is linearly dependent on the number of rotatable bonds. |
60c7428e9abda23ec0f8c02e | 8 | Several approximations are employed in AutoDock, in order to make the calculations suitable for rapidly docking large libraries of compounds. Scores are single point evaluations of the scoring function, thus neglecting the majority of entropic contributions. Bond lengths and bond angles are treated as rigid and non-polar hydrogens are omitted. Rotatable bonds are allowed to rotate freely, neglecting rotamer preferences. Partial charges are based on the empirical method from Gasteiger and Marsili , and can be considered "lower quality" in comparison to charge assignment methods based on some form of electronic structure calculation, even via semi-empirical methods such as AM1-BCC . |
60c7428e9abda23ec0f8c02e | 9 | MM-GBSA calculations are usually performed on an set of protein-ligand binding conformations generated using a short MD simulation, which can either be in implicit or explicit solvent. MM-GBSA energy values, which provide an estimate of the free energy of binding (∆ G bind ), are then calculated using end-point estimates given in the equation below: |
60c7428e9abda23ec0f8c02e | 10 | where E MM is the molecular mechanical energy in the gasphase consisting of contributions for electrostatic, van der Waals and internal energies, E GB is the polar solvation free energy based on the Generalized-Born implicit solvent model, E SASA is the non-polar solvation term calculated using the solvent accessible surface area (SASA) and T S solute is the product of the absolute temperature T and the solute entropy S solute . The solute entropy term can either be ignored (often done for congeneric series) or approximated. The quasiharmonic approximation and normal mode analysis of the vibration frequencies are most commonly used for estimating the solute entropy term. |
60c7428e9abda23ec0f8c02e | 11 | Here, MM-GBSA scores are reported in units of kcal/mol and are based on end-point free energy estimates. However, they should not be confused with true binding free energy calculations , as they involve several additional approximations. Partly as a result, calculated MM-GBSA values are typically much lower (more negative) than experimental binding free energies. The differences arise from the different approximations used to account for the solvation and configurational entropy of the protein and the ligand. Also, water molecules or cavities in the binding pocket are modeled using bulk (continuum) water, which cannot capture the finer details of water-mediated interactions present in explicit water simulations, and in some cases can produce artifactual water placements. Hence in this work, we will be referring the MM-GBSA values as MM-GBSA scores and not MM-GBSA free energies. |
60c7428e9abda23ec0f8c02e | 12 | Docking was performed using AutoDock-GPU, an OpenCL implementation of AutoDock4. The search procedure utilizes three types of ligand motion: translation, rotation (of the entire ligand as a rigid body) and rotation of atoms affected by each rotatable bond. The search algorithm is a genetic algorithm (GA) hybridized with ADADELTA , a gradient-based optimizer. In every GA generation, all individuals (i.e. poses) are subjected to 500 ADADELTA iterations. The number of GA runs was 100, and each GA performed 10 million score evaluations, totaling 10 9 score evaluations per docking. |
60c7428e9abda23ec0f8c02e | 13 | Each ligand was docked to 10 different protein conformations, corresponding to the following PDB IDs (chain): 2B8V (A), 2F3F (C), 2P4J (D), 2WF3 (A), 3L59 (B), 3MSJ (C), 3MSK (A), 4EWO (A), 4FS4 (A) and 4RCF (A). These structures were the selected representatives of different binding pocket conformations. REDUCE added hydrogen atoms assuming pH 7, while allowing Asn, Gln and His side chains to flip. Then, the standard protocol was used to assign AutoDock4 atom types, partial charges, and determine which bonds are rotatable. After all dockings were performed, the binding pose with the best score, as well as the protein structure it was docked into, constituted the starting structure for the MD simulation and subsequent MM-GBSA calculation. |
60c7428e9abda23ec0f8c02e | 14 | Macrocycle conformations were explored during the docking by artificially breaking one of the chemical bonds within each macrocycle, generating the corresponding open linear structure which can be modeled as fully flexible during docking. To restore the original bond, and consequently the cyclic structure, a potential is applied to attract the atoms formally bonded to their covalent bond distance. This allows the macrocycle conformation to be fully sampled flexibly during docking. |
60c7428e9abda23ec0f8c02e | 15 | Nearly all BACE-1 ligands of GC4 share a common substructure that is also found in several PDB structures. This substructure consists of a hydroxyl group attached to a short two-carbon aliphatic chain, followed by an amide. Based on publicly available BACE-1 structures, this substructure has a conserved binding mode, making several hydrogen bonds with the binding pocket. To exploit this information during the docking, we used the ligand in the PDB 4DPF as a template for the position of the common substructure of GC4 ligands. A biasing penalty was applied to three atoms: the hydroxyl oxygen, one of the carbons in the aliphatic chain and the nitrogen in the amide. This penalty increases linearly with the distance from the corresponding atom of the template structure. If this distance is below 1.2 Å, the biasing penalty is zero, and the output score corresponds to the original, unaltered AutoDock4.2 scoring function. |
60c7428e9abda23ec0f8c02e | 16 | To take advantage of further similarities with BACE-1 ligands in the PDB, we used pose filters to discard docked poses that differ from the binding modes observed in 2F3F, 4DPF and 4K8S. These pose filters act on specific chemical motifs that occur both in GC4 ligands and in these reference structures. The chemical motifs were identified manually by visual inspection, and the filtering process was automated using Python scripts and OpenBabel . |
60c7428e9abda23ec0f8c02e | 17 | This docking protocol, including the biasing penalty and pose filters, was used to predict the binding poses of the 20 BACE-1 ligands in Stages 1a and 1b of GC4. We describe the performance of variations of this protocol, as well as further details about the methodology in a separate publication . |
60c7428e9abda23ec0f8c02e | 18 | We generated a 14ns long MD trajectory for each of the protein-ligand complexes in explicit solvent and then reevaluated the binding scores using end-point MM-GBSA calculations. The MD simulations were performed using the pmemd.cuda module of Amber18 simulation package . We added partial charges to the ligand atoms using the Antechamber program (from Amber 16 package ) and AM1-BCC charge model . The simulated system was prepared using tleap (also available in Amber16 package) and used Amberff99sb , GAFF version 1.8 and TIP3P water for the protein, ligand and water force field respectively. The protein-ligand complex was placed in a cubic simulation box with 10 Å of water surrounding the complex. We next added Na+ and Cl-ions to neutralize the system and to ensure a salt concentration of 0.1M. The protein heavy atom-hydrogen bonds were constrained using SHAKE. The simulation used a time step of 2 fs. Particle mesh Ewald method was used to evaluate long-range electrostatic interactions with 9.0 Å cutoff for the real space electrostatics and van der Waals forces. |
60c7428e9abda23ec0f8c02e | 19 | We first minimized the ligand, water, and the ions for 1000 steps with 25 kcal/mol-Å2 positional restraints on the protein, followed by another 1000 steps of minimization with the protein restraints reduced to 10 kcal/mol-Å2 . Next, the system was heated from 10 K to 300 K in NVT ensemble for 140 ps with 10 kcal/mol-Å2 restraints on the protein-ligand complex. We then successively decreased the restraints on the protein-ligand complex for 20 ps to first 5 and then to 2 kcal/mol-Å2 , followed by 2 kcal/mol-Å2 restraint only on the ligand. We used Langevin thermostat with a collision frequency of 2 ps -1 to maintain the temperature of the system. We simulated the system for 14 ns in NPT ensemble for the production run. Isotropic pressure scaling was used to regulate the pressure with a relaxation time of 2 ps. The first four ns was discarded as equilibration. |
60c7428e9abda23ec0f8c02e | 20 | We saved the positions of the atoms every 100 ps during MD. The final trajectory used for the MM-GBSA calculations consisted of 100 frames that correspond to the last 10 ns of the production trajectory. MM-GBSA scores were calculated using the MMPBSA.py program in Amber16 at a salt concentration of 0.1 nM and using the GBneck2 model . Quasi-harmonic approximation was used to approximate the solute entropy. |
60c7428e9abda23ec0f8c02e | 21 | Our main goal in this work was to see whether re-scoring docked poses with MM-GBSA scores can improve the correlation of predicted binding affinities with experimental values. We used AutoDock4.2 scores and MM-GBSA scores to rank the binding affinities of BACE-1 ligands in Stage 2 in D3R GC4. Our workflow consists of a series of entirely automated steps, starting with a SMILES representation of the ligands up to the MM-GBSA score. For this reason, the results reported herein are representative of automated approaches. The performance of docking and MM-GBSA scores in predicting the affinities of the 154 ligands is assessed by the Kendall's τ and Spearman's ρ rank correlation coefficients. We also report Pearson's r and R 2 . We have compiled all these metrics for our predictions in Table . Since all metrics lead to the same conclusions, we base our discussion on Kendall's τ values, which is the first metric reported in the D3R evaluation page. Re-scoring docked poses with MM-GBSA did not improve correlation with experimental values. The Kendall's τ between experimental pK d and AutoDock4.2 scores (submission cq7ug) is 0.19 ± 0.06, and that of MM-GBSA scores (submission utgv6) is 0.20 ± 0.06. Thus, the predictive performance of these methods is statistically identical and both of them correlate poorly with the experimental values. Nevertheless, our predictions are statistically better than a random prediction which has an average Kendall tau of zero. In the context of all submissions to Stage 2 of GC4, our predictions ranked in the top third (Fig. ). |
60c7428e9abda23ec0f8c02e | 22 | MM-GBSA calculations have more detailed representation of the underlying physics at play than docking scores and literature work from other groups suggested they would be more accurate . So it was perhaps surprising that there was not any improvement in the affinity estimation with the MM-GBSA rescoring. We also saw that there was no correlation between the AutoDock4 scores and MM-GBSA scores (Kendall's τ equal to -0.06 ± 0.05). These findings prompted us to investigate more about our protocol to check whether any change in the simulation conditions could improve the results. |
60c7428e9abda23ec0f8c02e | 23 | With the goal of identifying aspects of the MM-GBSA approach that could be improved, we searched for features that are associated with particularly good predictions. Our ligand dataset consisted of both positive and neutral ligands. Previous work by Rastelli et al. has shown that there is a decrease in correlation between predicted and experimental affinities for ligands with different formal charges, which led us to separately analyze ligands with different formal charges (Table ). |
60c7428e9abda23ec0f8c02e | 24 | We found that the predicted affinities of ligands modeled in a neutral state (n=18) exhibited better rank correlation (Kendall's τ of 0.44 ± 0.15) with experiment than those for ligands modeled with a +1 charge (Kendall's τ of 0.19 ± 0.07). This suggests that neutral ligands are more amenable to MM-GBSA calculations. Sun et al. have reported ligand binding affinity prediction accuracy degrading with net charge of the ligand. Their Pearson's r degraded from 0.608 ± 0.003 for ligands with net charge zero to 0.564 ± 0.003 for those with net charge one. It is to be noted here, that in our study the sample size for neutral ligands is small (only 18 ligands). |
60c7428e9abda23ec0f8c02e | 25 | A total of ten protein conformations were considered for docking the ligands. The MM-GBSA calculations were performed using the protein conformation that produced the ligand pose with the best docking score, according to the AutoDock4.2 scoring function. The majority of ligands were simulated in the protein conformations associated with PDBs 4EWO (n=75) and 2WF3 (n=69). |
60c7428e9abda23ec0f8c02e | 26 | The subset of ligands simulated in 4EWO exhibited poorer rank correlation with experiment (Kendall's τ of 0.15 ± 0.09) for the MM-GBSA scores compared to the other protein structures used -2WF3, 2B8V, 2P4J (Kendall's τ of 0.36 ± 0.07). For AutoDock4 scores, we see similar rank correlation coefficients for different protein conformations. Hence in the succeeding work, we looked into the protein structure 4EWO to see whether we modeled it correctly. |
60c7428e9abda23ec0f8c02e | 27 | We noticed while doing post-analysis of our results that the catalytic aspartyl dyad (Asp32, Asp228) of BACE-1 in the prepared protein structure for 4EWO had both aspartates in the protonated form (i.e., Asp32 H , Asp228 H ). This is a possible source of error, because in the apo state, Asp32 is protonated and Asp228 is de-protonated in the active pH range (3.5-5.5) of BACE-1 . Although the protonation state of the aspartyl dyad changes in the presence of inhibitors , it is a safer choice to model the aspartyl dyad as Asp32 protonated, and Asp228 de-protonated (Asp32 H , Asp228 -). |
60c7428e9abda23ec0f8c02e | 28 | The correlation statistics of the 4EWO simulations with the Asp32 H , Asp228 -protonation state are reported in Table 3 and the plot of predicted versus experimental affinities is depicted in Fig. . Also, Fig. shows the distribution of the MM-GBSA scores for the two protonation states. Overall, the MM-GBSA scores were lower for the single protonated aspartyl dyad compared to the double protonated, indicating that the binding pose is more stable for the single protonation state. The Kendall τ improved by about one standard deviation, confirming that the Asp32 H , Asp228 - form is more adequate than modeling both Asp as protonated. |
60c7428e9abda23ec0f8c02e | 29 | Moreover, we computed the RMSD of the ligands between the initial docked poses and the final states at the end of the MD simulations for the two protonation states of 4EWO: i) Asp32 H , Asp228 H and ii) Asp32 H , Asp228 -. We used Chimera to align the active site of each initial BACE-1-ligand complex to the last frame of the corresponding MD trajectory. The alignment of the active site was done within 5 Å of the ligand. Then, we computed the RMSD values with Chimera. Out of 75 ligands, 54 had lower RMSD values when docked and simulated in BACE-1 with the single protonated aspartyl dyad (Asp32 H , Asp228 -). The RMSD values are reported in the Supplementary Information available on MMGBSA/blob/master/RMSD.csv. This result shows that the binding mode of BACE-1 ligands depends on the protonation states of aspartates 32 and 228 and confirms that it is better to model the protonation state of BACE-1 as Asp32 H , Asp228 -for the given ligand dataset. Overall, these findings suggest that in large-scale binding affinity calculations, it is better to use the protonation state of the apo form of the protein. |
60c7428e9abda23ec0f8c02e | 30 | Since the correlation between predicted and experimental affinities was better for the subset of ligands modeled in the structure 2WF3 than in 4EWO (Table ), we recalculated the docking and MM-GBSA scores for the ligands modeled in 4EWO using the 2WF3 structure instead. Then, the correlation coefficients on the entire set were computed using the updated scores (Table ). The performance of MM-GBSA improved, displaying a Kendall τ equal to 0.30 ± 0.05, while the performance of docking remained constant (Kendall τ equal to 0.21 ± 0.06). This shows that MM-GBSA is potentially better than docking, in agreement with the more accurate physical description, but the results are sensitive to modeling choices, such as protein conformation and protonation state, making it difficult to achieve optimal predictive performance in a prospective context. |
60c7428e9abda23ec0f8c02e | 31 | The largest difference between 2WF3 and 4EWO is in the 'flap' region (Fig. ), which interacts extensively with BACE-1 ligands. Interestingly, docking scores are generally lower when docking to 4EWO (Fig. ), while MM-GBSA scores are lower when simulated in 2WF3 (Fig. and). The exact reasons behind this opposite trend are unknown, but we speculate that none of the 10 protein conformations used for docking was "good enough" to accommodate the 75 ligands that displayed lower (i.e. better) docking scores in 4EWO. Arguably, the docking score was better in 4EWO because the flap is slightly more open, thereby accommodating ligands that could not fit as well in 2WF3. On the other hand, we argue that 2WF3 is more representative of the actual protein-ligand complex, resulting in lower (i.e. better) MM-GBSA scores on average. |
60c7428e9abda23ec0f8c02e | 32 | Overall, these arguments highlight the sensitivity of docking to receptor conformation, and motivate the inclusion of flexibility into the receptor , not only for the improvement of docking methodology by itself, but also for providing better docked poses for free energy calculations. In this study, we looked at two different parameters for the MM-GBSA calculations, namely protonation state and protein conformation during our retrospective analysis. Both of these parameters turned out to have non-trivial impact on the calculated binding affinities. However, they are many more MM-GBSA calculation parameters which can possibly affect the binding affinities which were not explored in the current work. |
60c7428e9abda23ec0f8c02e | 33 | We performed the MM-GBSA calculations using the GB-neck2 model in this work, which has not, to our knowledge, been benchmarked against older GBSA models (GB-HCT, GB-OBC1 and GB-OBC2 ) for affinity prediction. Protein targets are sensitive to GBSA models , hence using older GBSA models might improve the binding affinities. Another option is to perform MM-PBSA calculations instead, which are physically more accurate and computationally more expensive. |
60c7428e9abda23ec0f8c02e | 34 | We used the popular 'single trajectory protocol' in this work, which involves simulating only the protein-ligand complex and re-purposing the bound conformations of the protein and ligand for the unbound calculations. It is assumed that the protein and the ligand sample similar conformations in the bound and unbound states which might not be always valid. We do not expect to see a big difference in predicted affinities when using the alternative 'multiple trajectory protocol'. However, it may be worth trying this in the future for the macrocycles in the current dataset since the macrocycles do not have much flexibility in the binding pocket due to their size, and might possibly sample other conformations when simulated in pure solvent. |
60c7428e9abda23ec0f8c02e | 35 | Other parameters which could be investigated in this context are different entropic approximations, ligand charge models and the solute or interior dielectric constant . Lastly, another avenue worth exploring from a cost-cutting point of view is to use single-point minimized structures for the MM-GBSA calculations, similar to single-point docking score calculations. There are studies present in the literature which have shown similar correlations between MM-GBSA scores obtained using single-point structures and those using ensembles of MD generated structures. However, recently published literature suggests that most studies still use multiple conformational snapshots from MD for the MM-GBSA calculations . |
60c7428e9abda23ec0f8c02e | 36 | There are two components in structure-based affinity prediction challenges -pose prediction and binding score evaluation. Both of these contribute to the accuracy of predicted binding affinities. In order to evaluate only the affinity prediction capability of different scoring methods, the starting protein-ligand binding poses need to be the same, which is rarely the case in D3R Grand Challenges where each participating group has its own pose prediction and binding score evaluation methodology. |
60c7428e9abda23ec0f8c02e | 37 | To better separate pose prediction from scoring, our two groups decided to collaborate and combine our different areas of expertise in this study -docking and free energy calculations and participate in the structure-based binding affinity prediction challenge for the target BACE-1 in D3R GC4. We used AutoDock-GPU for docking the ligands, employing the AutoDock4 scoring function, and then calculated MM-GBSA binding affinities. MM-GBSA binding energy calculations did not improve the predictive performance with respect to AutoDock4 scores. In a retrospective analysis, we identified two modeling aspects that were detrimental to the quality of MM-GBSA scores, namely the choice of protein conformation and the protonation state of residues in the binding pocket. While it is clear that MM-GBSA can make better predictions than docking scores, making the optimal modeling choices is a non-trivial task that requires knowledge of the system under study and thus is likely difficult in a prospective setting. Thus, our assessment of MM-GBSA performance roughly agrees with that of several previous research groups which participated in previous D3R Grand Challenges specifically, we find that MM-GBSA does not perform par-ticularly well at binding affinity estimation. These resultsnot just our own -highlight the importance of blind challenges for the community to evaluate method performance, particularly for drug design projects. |
63b82a16055be759d9c3ddd5 | 0 | Quantum interference (QI) is a phenomenon that can be harnessed to increase or decrease the electronic conductance of single-molecules. Originally reported for benzene in the context of electron transfer, 1 destructive quantum interference effects in molecules were first explored theoretically before the suppressed conductance was experimentally observed in mono-layers and single molecules . |
63b82a16055be759d9c3ddd5 | 1 | Due to its utility in controlling electron transport, there has been a significant focus on developing rules to predict when quantum interference effects will dominate, for example the graphical rules , curly arrow rules and molecular orbital rules . While these rules allow us to readily determine whether a molecule is likely to exhibit suppressed conductance due to destructive interference, they do not provide more insight into "what is interfering with what" in these systems. |
63b82a16055be759d9c3ddd5 | 2 | The archetypal example of QI is Young's double-slit a) Electronic mail: [email protected] b) Electronic mail: [email protected] interference experiment, where light passes through slits in two barriers. The first barrier has a single slit and the second has two slits. On the wall behind the second barrier, an interference pattern is observed. This experiment is illustrated in Figure (a). Wave-particle duality means that the light displays characteristics of both classically defined waves and particles. In the double-slit experiment, the interference pattern is due to the phase difference of the waves caused by the differing lengths of the optical paths as light passes through the two slits in the second barrier. Similarly, wave-particle duality also governs the behavior of electrons. When the size of the device is comparable to the electronic phase coherence length, QI effects can manifest. This QI can change the electronic transport through molecular sized devices dramatically, as illustrated in Figure . The QI can be destructive or constructive depending on whether the phase difference between interfering paths are π or 0. We use the language of "paths" to draw an analogue with the two-slit experiment, although no such paths in physical space are evident through the molecule. While there are mathematical arguments to support the idea that the cyclic structure of a benzene ring can represent the two paths , destructive QI is also present in acyclic molecules, challenging this interpretation. Instead, QI in molecules can be understood in terms of interfering contributions between pairs of molecular orbitals 22 (MOs). While the MOs of the isolated molecule are perturbed by the coupling to the electrodes, the coupling to the electrodes is typically small. This means that the molecular conductance orbitals (MCOs) which are the eigenbasis of the molecular Hamiltonian including the self-energies of electrodes are similar to the MOs or eigenbasis of the isolated molecules. Therefore, a distinction is generally not made between MOs and MCOs in practice. When describing the MOs of organic molecules, it is useful to distinguish between the σ-and π-orbitals. Destructive QI in the π-system of conjugated molecules is frequently observed in calculations as a sharp transmission dip and has been reported in many systems, such as graphene-like molecules , π-stacked molecules and cross-conjugated molecules . The molecular orbital analysis by Gunasekaran, et al. provides a method to visualize the constructive and destructive QI between pairs of π-MOs. Typically the σ-orbitals are not considered in the methods for predicting QI in conjugated molecules as σ-orbital contribution drops off extremely rapidly with length and is only signficant in certain limited situations. Recently, destructive QI has also been identified in the σ-systems of molecules, such as saturated silanes , the Bicyclo[2.2.2]octane class of molecules and cyclo-alkanes . The QI in σ-systems has been utilized to engineer short molecules with comprehensive suppression of the electronic transmission. Given the differences in the orbital character of the π-orbitals of conjugated molecules and the σ-orbitals of saturated systems, a natural question to ask is: is the orbital picture of destructive QI in σ-systems similar to that seen in π-systems or do we expect differences? |
63b82a16055be759d9c3ddd5 | 3 | In this work, we first outline the expectations for benzene (a π system) with different substitution patterns to illustrate how QI maps visualize QI. We then apply this method to butane whose transport properties are calculated using the ladder C model to analyze QI in σ-systems. Finally, we compare the QI between the πsystem and σ-system. We see that the orbital contributions to QI in π-systems and σ-systems are quite different, with the QI in π-systems caused by phase alteration and in σ-systems caused by the change in the width and position of the individual MO transmission peaks. |
63b82a16055be759d9c3ddd5 | 4 | To investigate how QI in σ-systems might differ from that in π-systems, we study a model for butane as shown in the Figure (a) as an example. The transport properties of a σ-system can be calculated using the ladder C model. While this model is parameterised for a permethylated silane chain, we use the parameters to represent a generic saturated system that we will refer to butane for simplicity. With this model, the Hamiltonian for butane is written as, |
63b82a16055be759d9c3ddd5 | 5 | Here, ϵ = 0eV are the on-site energies, with the primary integrals τ prim = -3.5eV, the geminal integrals τ gem = -1.1eV, and the vicinal integrals τ vic = 0.11 -0.7 cos θ where θ is the dihedral angle. For θ = 180 • , butane is in an all-trans configuration and for θ = 0 • it is in a cis-configuration. Using the model Hamiltonian of Equation 1, the transmission can be calculated as |
63b82a16055be759d9c3ddd5 | 6 | In the following, the method to decompose and calculate the transmission will be introduced in a way to enable easy visualization of whether there is constructive or destructive interference between any two MOs. For a more detailed description, we refer to Gunasekaran, Greenwald, and Venkataraman. In the MO basis, the transmission can be expressed as the contributions from all the individual MOs, which can be further split into a sum over the non-interfering parts, T i , and a sum over the interfering parts, T ij , |
63b82a16055be759d9c3ddd5 | 7 | By means of the above methods, we will show how QI can be better understood using both QI maps and the phase of individual MOs. First, we revisit the case of benzene, to outline the expectations from conjugated molecules and for comparison with the butane study below. We consider two kinds of connections with the electrodes as shown in Figure . For benzene, we use the Hückel model with nearest neighbour coupling and the value of β is set to be -1. Benzene has six π orbitals with two degenerate pairs of orbitals as the frontier orbitals. Here, we will refer to the frontier orbitals as the HOMO and HOMO ′ and LUMO and LUMO ′ to highlight their degenerate nature and distinguish the non-degenerate HOMO-1 and LUMO+1 orbitals (that in the usual numbering would be the HOMO-2 and LUMO+2). The connection to the electrodes results in a small splitting between the degenerate pairs and influences the energetic ordering of the MOs. For para-substituted benzene, the HOMO and LUMO are the frontier MOs, whereas for meta-substituted benzene, HOMO ′ and LUMO ′ are the frontier MOs. The difference in the electrode positions results in a significant change in the transmission as shown in Figure . More specifically, benzene with meta connection exhibits a sharp dip at E F , whereas that with para connection exhibits a flat curve around E F . |
63b82a16055be759d9c3ddd5 | 8 | The decompositions of the transmission into interfering and non-interfering contributions are displayed in Figure (d) and Figure . This QI map provides a diagramatic visualization of the Q matrix calculated using Equation . The squares along the main diagonal (highlighted with bold lines) represent the noninterfering transmission terms. As these terms are always positive, they will either be red or change gradually to white when decreasing close to zero. The off-diagonal squares illustrate the QI between different MOs. They may either be red, denoting constructive QI, or be blue, denoting destructive QI. The shade of the color indicates the magnitude of the term. White squares indicate that the magnitude of these items are close or equal to zero. In the case of para-substituted benzene constructive QI dominates the contribution to the transmission, while for meta-substituted benzene, the destructive QI cancels exactly with the non-interfering terms. In both cases, the maps are dominated by interactions between the two frontier orbitals, with lesser contributions from all other orbitals. This result reproduces the earlier work of Gunasekaran et al. on this system. The electronic transmission for butane calculated using the ladder C model is shown in Figure . The transmission varies significantly with the change in the dihedral angle. At a dihedral angle of 180 • there are no anti-resonances whereas two anti-resonances are present at ±2.23eV for a dihedral angle of 0 • . When the dihedral angle is increased from 0 • to 49 • , the anti-resonances move closer to the Fermi energy while the transmission decreases and vanish altogether at a dihedral angle of 50 • . With the further increase in the dihedral angle, the transmission increases again and becomes a broad valley. |
63b82a16055be759d9c3ddd5 | 9 | To understand the anti-resonances of butane, QI maps are used to analyze the electronic transmission, as shown in Figure . Specifically, the QI maps for the cases with dihedral angles of 0 • and 180 • are presented at three different energies: E F (with E = 0eV) and the energies of the two antiresonances for 0 • (E = ±2.23eV). In our model, the σ-system of butane has 6 σ orbitals, the QI map is a 6 × 6 block matrix. |
63b82a16055be759d9c3ddd5 | 10 | We first focus on the θ = 0 • case. At E = 0eV, the contributions from the lowest unoccupied MO +1 (LUMO+1) and highest occupied MO-1 (HOMO-1) contribute the most to the electronic transmission. These contributions are seen as four dark-red squares in the QI map: two non-interfering terms and two constructively interfering terms. Other destructively interfering terms are much smaller, primarily between the HOMO and LUMO and these two dominant orbitals. At E = -2.23eV, the non-interfering contributions from the HOMO and the HOMO-1 increase while the contributions from the LUMOs decrease nearly to zero. On the contrary, at E = 2.23eV, the tendency is opposite, where the non-interfering contributions from the LUMOs are dominant. The destructive interference between HOMO and HOMO-1 for -2.23eV and that between LUMO and LUMO+1 for 2.23eV are very strong (see the blue blocks), reminiscent of the two orbital interference picture observed for meta-substituted benzene. |
63b82a16055be759d9c3ddd5 | 11 | There are two differences between the interference effects observed at ±2.23eV in butane and the interference feature at 0eV in meta-substituted benzene. Firstly, the non-interfering contributions from the two orbitals in butane are unequal, whereas they are equal in metasubstituted benzene. Secondly, the interference feature in meta-substituted benzene is midway between the occupied and virtual orbitals, that is, midway between the orbitals that interfere destructively, whereas for butane the interference feature appears at an energy above/below the pairs of occupied/virtual orbitals that are dominant. |
63b82a16055be759d9c3ddd5 | 12 | The QI maps of θ = 180 • are both similar to and different from those of θ = 0 • . The similarity is in the color structure, red terms remain red in both cases and similarly blue terms remain blue, the differences come from the relative magnitudes of the terms (here represented by the darkness of the color) and this gives a visual appearance of a significant difference. At E = 0eV, the HOMO and LUMO constructively interfere as seen by the dark red squares in Figure . There are destructive interference terms between these frontier orbitals and the HOMO-1 and LUMO+1, however, the constructive QI terms between the HOMO and the LUMO, and the noninterfering terms do not cancel with the destructive interference terms. Thus, the transmission at E = 0eV does not go to zero. For the QI maps calculated at E = ±2.23eV, the transport is dominated by a single orbital with a single non-interfering term from either the HOMO or LUMO (the energetically proximate orbital in each case. Interestingly, this is the closest approximation we see to the single-orbital/single-level tunnelling model that has sometimes been invoked to explain the differences in transport properties between different molecules. |
63b82a16055be759d9c3ddd5 | 13 | While θ = 180 • and θ = 0 • , are clearly distinct limits for butane, it is also interesting to examine the behavior at θ = 49 • and θ = 50 • . As seen in Figure , at these dihedral angles a very small angular change results in qualitatively different transmission, with the two sharp dips present at θ = 49 • disappearing at θ = 50 • with only a single 'V' shaped dip remaining. We note here that in terms of experimental observables (eg. current and conductance) this change is not significant as the transmission is extremely low in both cases. The significance in this qualitative change in the transmission is in how sure one can be in labelling the low transmission as coming from destructive interference if we consider transmission alone, as these sharp dips are a definitive feature. We also note here that there other situations where we are confident that low transmission results from destructive interference, despite the absence of a sharp dip, for example if transport through the σ system masks destructive interference in the π transport or if we see ring current reversal in a local current picture . |
63b82a16055be759d9c3ddd5 | 14 | In Figure we illustrate the QI maps for θ = 49 • and θ = 50 • at E = ±0.38eV (the energies of the interference features for θ = 49 • ) and at E = 0eV. The most striking feature of all these maps is how similar they are. In both cases, the map at E = 0eV is more symmetric in terms of the contributions from occupied and virtual orbitals, while the maps at E = ±0.38eV show some asymmetry, however this asymmetry is not very pronounced. While there are undoubtedly quantitative differences between the two dihedral angles, it is not possible to see this from the plots. In all cases, the similar color structure that was seen for θ = 180 • and θ = 0 • is retained, and the similarity is more readily apparent as the quantitative differences are reduced. Figure and Figure paint a different orbital picture of destructive interference in butane from what was seen in benzene. Firstly, in butane more orbitals are involved (4) compared with benzene (2) despite the significantly larger HOMO-LUMO gap (over 4eV for butane versus 2eV for benzene). Secondly, the change from a system with clear destructive interference effects(θ = 0 -49 • ) to a system with suppressed transmission(θ = 50 -180 • ) results from a change in the magnitude of the various orbital contributions rather than any contributions changing sign. Together, these two differences mean that the QI maps are not as simple to interpret for saturated systems. This is not an indication of any failure of the QI map, but simply an indication that the interference effects in saturated systems are more subtle as the system can vary from continuously from being dominated by constructive to destructive interference without any dramatic change in the orbital character. |
63b82a16055be759d9c3ddd5 | 15 | To better understand the nature of the orbital contributions, we compute the phase and transmission through individual MOs. For benzene, the phases are presented in Figure and the MO contributions to the transmission (|t i | 2 ) are presented in Figure . We can understand the differences between meta and para substitution by considering the differences in the transmission and phase of three pairs of orbitals: the HOMO and LUMO, the HOMO ′ and LUMO ′ , and the HOMO-1 and LUMO+1. For each case, these pairs of orbitals are symmetry related (from the Coulson-Rushbrooke orbital pairing theorem ). This results in equal widths for the transmission peaks from paired orbitals as well as identical lineshapes for the phase as a function of energy (shifted in energy). |
63b82a16055be759d9c3ddd5 | 16 | In order to understand the QI maps in Figure and (e) we consider the relative phase of the orbital pairs at E = 0. In each case the para contributions are inphase and differ by 0/2π, while the meta contributions are out of phase and differ by π. The relative transmission through each orbital differs significantly for each pair of orbitals and also for the two different substitution patterns. For para-substituted benzene, only four of the six orbitals have non-zero transmission, with the HOMO and LUMO being approximately an order of magnitude more transmissive at E = 0 than the HOMO-1/LUMO+1. All six orbitals contribute for the meta-substituted system but in this case the HOMO ′ /LUMO ′ pair is approximately an order of magnitude more transmissive than the other pairs. Comparing with Figure (d) and (e), we can conclude that the color intensity is related to the magnitude of the orbital transmission, while the sign/color of the interference terms is related to the phase difference between the orbital contributions at that energy (π phase difference giving destructive/blue contributions and 0/2π giving constructive/red contributions). Indeed, if we extend our analysis beyond the three pairs of orbitals, it is clear that the phase difference between two orbitals generally predicts the color of the interference terms in the QI map, for example meta HOMO ′ is π out of phase with the HOMO and HOMO-1. |
63b82a16055be759d9c3ddd5 | 17 | In Figure the phase of the transmission of each MO for butane is shown for both the all-trans (θ = 180 • ) and the all-cis (θ = 0 • ) configuration. It is clear that the phase of the MOs of the σ-system only varies slightly when the dihedral angle changes. This minor change is in contrast with π-system where the different electrode positions have a substantial impact on the resulting phase. |
63b82a16055be759d9c3ddd5 | 18 | While the Coulson-Rushbrooke orbital pairing theorem is generally applied to the π-system of conjugated molecules, the mathematical form of the ladder C model we employ means that it also applies to butane. In this case however, it is very clear that the interference is not between the paired orbitals (shown as the rows in Figure :HOMO-2 and LUMO+2, HOMO-1 and LUMO+1, HOMO and LUMO) as the phase does not differ. Instead, from Figure , Figure and Figure it is clear that the balance between constructive and destructive interference is only shifted by the varying magnitude of the destructive interference between the pair of HOMO-1 and LUMO+1 with primarily the HOMO and LUMO (and to a lesser extent the HOMO-2 and LUMO+2). The orbital pairing theorem means that the energetic position of paired orbitals will always be symmetrical above/below 0eV as well as that the widths of the transmission peaks are identical. Together this means that when interference is between paired orbitals, the interference dip must also be at 0eV. On the other hand, when the interference is between non-paired orbitals, the details of the balance between orbital positions and weights mean that the interference features can shift in energy as well as appearing/disappearing, as seen in Figure (c). |
63b82a16055be759d9c3ddd5 | 19 | , where √ T i is the amplitude and θ i is the phase. The total transmission probability for the σ-system or the π-system is thus modulus squared of the sum of the complex transmission coefficients for all MOs, T = |t 1 + t 2 + t 3 + t 4 + t 5 + t 6 | 2 . |
63b82a16055be759d9c3ddd5 | 20 | Away from the transmission resonances, the transmission phase is 0 or ±π so t i = ± √ T i . As the transmission phase is unchanged with dihedral angle changes for butane, Equation 12 can be written in a large energy range around the Fermi level (at least in [-2.0, 2.0]eV) as, (13) where the sign in front of each term is determined by the phase indicated in Figure , '+' for 0 and '-' for ±π. With the change of the dihedral angle from 0 • to 180 • , transmission dips may appear or disappear in the energy range [-2.0, 2.0]eV but the phase of each MO is constant, consequently the transmission dips can only be caused by the change of the width and position of individual MO contributions to the transmission. Conversely, the sign of each term in Equation for the π-system benzene will change depending on the connection to the electrodes giving a different picture of the orbital contributions to interference in this case. |
63b82a16055be759d9c3ddd5 | 21 | By comparing the QI maps of a π-system (benzene) and a σ-system (butane), as well as the transmission phase of the orbital contributions, we have shown that the orbital contributions to constructive/destructive interference are quite different in these two cases. Namely, the transmission dip in the transmission for metasubstituted benzene arises due to phase differences between paired MOs. These contributions cancel exactly as the orbital pairing theorem guarantees that they are equidistant from 0eV and that the individual contributions to the transmission are of equal magnitude. In contrast, for σ-system of butane the transmission dip is due to cancelation between non-paired orbitals as the position and width of individual orbital contributions to the transmission changes with the dihedral angle changes. Together, these results provide a richer picture of interactions and contributions to destructive interference, and an indication of how orbitals might be manipulated to exert fine control of quantum interference effects in molecules. |
65eb2e449138d23161070396 | 0 | Chalcogenides of IV-VI and V2-VI3 families have attracted the attention of the scientific community for decades since some of the members of these families, recently named incipient metals , feature extraordinary properties. The property portfolio of these incipient metals includes soft and anharmonic bonds, relatively small band gaps, moderately high electrical conductivity, high Born effective charges, high dielectric constants, high thermoelectric figures of merit, and high optical absorption [1-4]. These extraordinary properties make them ideal as phase change materials (PCMs) in data storage applications, as highly efficient thermoelectric and photovoltaic materials for green technologies, and also as topological materials for quantum computation. |
65eb2e449138d23161070396 | 1 | In the last decade, a big effort has been made to understand the nature of the chemical bonding in PCMs for designing materials with enhanced properties. For many years, the chemical bonding in PCMs and related materials, such as pnictogens and chalcogens, was considered to be a rare case of covalent bonding in which occurred a resonant bonding of p-type orbitals [5-8]. In the last decade, the consensus on the chemical bonding in PCMs has been broken as shown by the papers published in 2023 [4,9-13]. Since 2018, Wuttig and coworkers have considered that PCMs feature a new and unconventional type of bond called "metavalent" bond. This bond is different from the resonant bond present in graphite and benzene and is responsible for the extraordinary properties of PCMs and also of lead halide perovskites [1-4,14 . Taking into account that electrons are fully localized in covalent bonding and fully delocalized in metallic bonding, metavalent bonding has been described as a linear or quasi-linear type of two-center one-electron (2c-1e) bonding in which resonant p-type orbitals result in a combination of electrons that are partly localized and partly delocalized; i.e. as an intermediate bonding type between covalent and metallic bonding, hence its name. Therefore, PCMs are considered to be incipient metals, but with unique properties different from those of covalent and metallic materials. On the other hand, other researchers have considered that there is no need to claim a new type of bonding since they consider that PCMs feature a hypervalent bond [20-28]; i.e. the old known electron-rich multicenter bond (ERMB), whose most known example is the three-center four-electron (3c-4e) bond. |
65eb2e449138d23161070396 | 2 | Longuet-Higgings . This bond is typically present in molecules and solids of electron-deficient elements (hydrogen and elements of groups 1, 2, and 13), such as in boranes (BxHy) and hydrogenonium ion H3 + , and is considered to be a well-established type of bond for whose understanding Lipscomb was awarded the Nobel Prize in Chemistry in 1976 [38]. On the other hand, the ERMB was modeled as a 3c-4e bond (see In relation to the multicenter bonds, it is commonly believed that EDMBs could only be formed by electron-deficient elements and ERMBs could only be formed by electron-rich elements . Since both 3c-2e EDMBs and 3c-4e ERMBs are "half" or "partial" bonds, as deduced from their longer bond lengths when compared with those of the single covalent (two-center two-electron, 2c-2e) bond, it has been also believed that both 3c-2e and 3c-4e bonds have a single electron shared between two atoms. In other words, both multicenter bonds have been considered as two different cases of two-center one-electron (2c-1e) bonds. The reason for such a belief was based on the simple molecular orbitals proposed to describe both kinds of multicenter bonds (see Fig. ). In both 3c-2e and 3c-4e bonds there are two electrons in the low-energy three-center bonding orbital, thus leading to one shared electron between each two atoms. In addition, there are two additional electrons in the case of 3c-4e bonds that are located at the three-center nonbonding orbital (note that this orbital could have a slight antibonding character, as suggested by Hoffmann and coworkers ). These two electrons are considered to be exclusively located in the external atoms of the three-atom molecule, so they are not considered up to now to be even partially shared between the two nearest atoms . |
65eb2e449138d23161070396 | 3 | In a recent work, the number of electrons shared (ES) and the normalized number of electrons transferred (ET) between two centers has been calculated for typical hypervalent molecules with 3c-4e ERMBs, such as ClF3, XeF2, and SF4 and the less than one electron shared between every bridged B-H pair in diborane (B2H6) On the other hand, Wuttig and coworkers have proposed that metavalent bonding might be seen as a kind of electron-deficient 2c-1e bond, but they have not considered the multicenter character of unconventional bonding in PCMs. This multicenter character of half bonds, which was already suggested by Rundle ("half-bonds occur in pairs") more ). Typically, the ES value of ERMBs is smaller than that of non-polar (ET= 0) covalent bonds, but higher than that of polar (ET≠ 0) single covalent bonds of comparable polarity; i.e. similar ET value. On the other hand, the ES value of EDMBs is smaller than that of single covalent bonds of comparable polarity. Unlike the supporters of the metavalent bonding model, Manjón and coworkers have shown that the term metavalent is unnecessary to describe bonds in PCMs since they are electron-deficient, such as the bridged B-H-B bonds in B2H6 and the bonds in sc-As (or sc-Sb) . Manjón and coworkers consider that metallic bonding is indeed characterized by delocalized electrons and can be qualified as an electron-deficient bond since it is the last step in the process of electron delocalization. However, it should be emphasized that the metallic bond cannot be considered as a multicenter bond because it is not a directional bond, unlike ionocovalent bonds, ERMBs, and EDMBs. In these last three bond types, the total or partial electron localization accounts for the directionality of the bonds. |
65eb2e449138d23161070396 | 4 | On the other hand, unlike the supporters of the hypervalent bonding model, Manjón and coworkers have proposed that bonds in PCMs should be considered electron-deficient and not electron-rich. Moreover, they have also shown that linear bonding motifs might be formed in both ERMBs and EDMBs, so the term "hypervalent" loses its validity. |
65eb2e449138d23161070396 | 5 | Therefore, Manjón and coworkers suggest that the term hypervalent is unnecessary and it should be replaced by the word "hypercoordinated" in ERMBs and EDMBs The reason is that for defenders of the hypervalent model, the kind of bonding is not given by the number of electrons shared between two atoms (around one in PCMs) but by the electron configuration of the involved atoms. This idea is not shared by us nor by Wade (see last chapter in Ref. an additional example here on we illustrate how electron-rich elements, such as iodine, can form linear electron-rich bonds in three-center molecules (I3 -) and linear electrondeficient bonds when these bonds extend beyond three centers, as it is the case of infinite linear iodine chains. We hope this will help the supporters of the hypervalent bonding model to consider their position regarding the electron-deficient character of bonding in PCMs. |
65eb2e449138d23161070396 | 6 | To discuss about the different nature of covalent, ERMBs, and EDMBs, we show in Regarding the linear I5 -anion, with a total of 36 electrons (average of 7.2 electrons per atom), one could think at first glance that it could be considered as forming an electronrich 5c-6e bond. This would lead to a scheme of molecular levels similar to those plotted for the 3c-4e bonds in Figure It is to be remarked that we have preferred the use of the term secondary bond in the previous paragraph as it possesses a broader group-wise meaning than the term halogen bond. It is to be noticed that neither a halogen bond view nor a secondary bonding picture are here fully adequate to describe the bonding in the linear I5 -anion. On the one hand, the halogen bond is linked to a nucleophile/electrophile interaction, according to IUPAC recommendation [53], forcing one to formally tear apart a well-defined molecule and picture it as arbitrary nucleophilic or electrophilic non-factual fragments (an always possible yet needless exercise). On the other hand, weak bonds in I5 -involve valence electrons, so they cannot be considered as mere "secondary Lewis acid-base interactions", as per original secondary bonding proposition From all the mentioned studies, it can be assumed that the electronic charge for the different iodine atoms in the infinite linear chain should be small and the same for all of them. Note also that for an infinite linear chain in a solid, such as that of Te -atoms in 4a |
65eb2e449138d23161070396 | 7 | Wyckoff site in TlTe To finish this work, we want to make a comment regarding a recent paper in which the bond in a PCM, such as cubic rocksalt GeTe, has been compared to the bond in polyiodides . While there are similarities between GeTe and polyiodide bonding, the interpretation provided in Ref. cannot cover the range of possibilities encountered in polyiodides . In Scheme 1 we have already reasoned that the type of bonding in linear polyiodides depends on the length of the chain. Now in order to refute the reasoning in Ref. we also show in Scheme 2 that the type of bonding in polyiodides also depends on the geometry of the chain. In Scheme 2 we just show three types of infinite polyiodide molecules, the infinite linear chain of iodine atoms (I∞), the infinite zigzag or angular chain of iodine atoms that is bent at every atom (I∞(1 � )), and the infinite zigzag or angular chain of iodine atoms that is bent every two atoms (I∞(2 � )). A full discussion of the explanation of the different units in polyiodides is out of the scope of the present paper and will be published elsewhere. |
65eb2e449138d23161070396 | 8 | In the infinite linear chain, each iodine atom has 6 electrons forming three pairs of nonbonding LEPs, as previously commented, that are perpendicular to the linear chain and show a sp 2 geometrical configuration that minimizes the electronic repulsion between In the infinite zigzag chain I∞(1 � ), each I atom has four electrons distributed in two LEPs and the three remaining electrons should be shared between the two next-neighbor iodine atoms. In this chain, all I atoms show a sp 3 configuration to minimize the electronic of compounds featuring ERMBs and EDMBs allows us to prompt the supporters of the hypervalent bonding model in PCMs to reconsider their positions in relation to the type of bonding present not only in PCMs, such as rocksalt GeTe, but also in all other electronrich molecules and solids as it is here the case of the infinite linear iodine chain. |
65eb2e449138d23161070396 | 9 | At this point, we want to comment that the current state of ideas concerning the bonding in phase change materials reminds us of the words attributed to W.L. Bragg "The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them" . The new chemical perspective given by Manjón and coworkers opens an opportunity for reconciliation of the two previously proposed bonding models in PCMs if one considers the pros and cons of both the metavalent and hypervalent (or electron-rich multicenter) bonding models. |
65eb2e449138d23161070396 | 10 | In brief, according to Manjón and coworkers, the success of the metavalent bonding model is that bonds in PCMs are soft and directional electron-deficient bonds, while its pitfall is that it does not consider the multicenter character of the 2c-1e bond. When the multicenter character of the bond is considered, the metavalent bonding model becomes naturally the electron-deficient multicenter bonding model, in such a way that the term "metavalent" is no longer necessary since metavalent bonding is not a brand-new bonding type. On the other hand, the success of the hypervalent (electron-rich multicenter) bonding model resides in the discovery of the multicenter character of the bonds in PCMs that leads to hypercoordinated linear bonding motifs. However, Manjón and coworkers have shown that these linear motifs can be found in both electron-rich and electrondeficient molecules and solids . Therefore, the term "hypervalent" is no longer valid and should be replaced by "hypercoordinated". In any case, the main pitfall of the hypervalent bonding model resides in that it considers that the bond in PCMs is electronrich and not electron-deficient. If this consideration is discarded, the electron-rich multicenter bonding model becomes in a natural way the electron-deficient multicenter bonding model. |
65eb2e449138d23161070396 | 11 | In conclusion, we have here shown how a reconciliation of both the metavalent bonding and the hypervalent (electron-rich multicenter) bonding models for PCMs can be reached if we assume that PCMs are governed by the old known electron-deficient multicenter bonds. We want to finish by stressing that the electron-deficient multicenter bonding model not only allows one to explain the structure and properties of PCMs but also of |
669e64b75101a2ffa894951f | 0 | Amyloid assembly and disassembly have attracted great interest in recent years, with Fmoc-derived gelators having gained wide popularity. By contrast, mastering the supramolecular behavior of short peptides devoid of synthetic appendages, which are more relevant to natural processes, is still very challenging. On one hand, amyloid disassembly could be of high value in a therapeutic context, yet fibril re-assembly is unavoidable when it is the thermodynamic product. On the other hand, general rules for the design of building blocks of three or four unprotected amino acids (aa) that self-organize into macroscopicand ideally functional -hydrogels, as opposed to insoluble aggregates, are not yet fully elucidated, although integration of experiments with computational tools is enabling fast progress in the field. It is well-established that amyloids have an amphipathic nature. Hydrophobic components segregate in steric zippers that exclude water and stabilize the structure. In particular, phenylalanine (Phe)-based zippers have been reported for minimalistic peptides.[5] Yet, hydrophilic components must favorably interact with water to yield a bulk hydrogel. Gel-to-sol transition can be conveniently induced by heating, and usually the gel reforms upon cooling to rt. Reported examples of unprotected gelling peptides as short as three or four residues indeed display such thermo-reversible behavior. |
669e64b75101a2ffa894951f | 1 | For the design of self-assembling short peptides, the combination of D-and L-residues in heterochiral sequences is an attractive approach. Syndiotactic stereochemistry in cyclic peptides is well-known to permit the formation of nanotubes, with potential applications spanning from membrane transporters to hydrogels in confined droplets. We recently introduced D-aa in non-gelling, L-tripeptides as a convenient strategy to modulate self-assembly in linear sequences. Molecular dynamics (MD) simulations suggest that this approach may favor the segregation of hydrophobic and hydrophilic components on opposite faces ofstructures, thus yielding amphiphilic assemblies that favorably interact with water and gel.[6a] D-aa are advantageous for their known resistance to protease-mediated hydrolysis, and self-assembly of their derivatives has been used to develop new therapies. Besides, D-aa can interfere with amyloid fibrillation and hold therapeutic potential in related pathologies. . There is thus scope to study self-assembling peptides with D-aa. |
669e64b75101a2ffa894951f | 2 | We report here the first unprotected D,L-tetrapeptide (Figure ) that assembles into a highly stable hydrogel at physiological pH and undergoes a thermally-induced irreversible re-organization from fibrils to plates. We support experimental data with all-atom MD simulations that focus not only on peptide-peptide but also on peptide-water interactions. Interestingly, the supramolecular re-organization is not dictated by a key conformational change of the peptide, but rather by an irreversible change in its hydration, revealing water as a key player in the process. |
669e64b75101a2ffa894951f | 3 | The peptide was designed with two aliphatic D-aa at the N-terminus and the L-Phe-Phe self-assembling motif at the C-terminus, synthesized in solid phase, purified by HPLC and characterized by NMR and ESI-MS (Fig. and ESI Section S2). In particular, the design featured the elongation of the reported gelator DLeu-Phe-Phe[5b] with D-Nle, which displays a linear sidechain favoring intermolecular packing. While design rules for self-assembling D,L-tripeptides are emerging, to date there is limited understanding of the supramolecular behavior of unprotected D,L-tetrapeptides, and filling the gap answers an interesting and still open research question. It should be noted that even subtle chemical modifications of these systems can dramatically affect their supramolecular behavior. Indeed, Nacetylation of DLeu-Phe-Phe completely hindered self-assembly, and analogous results were obtained for the L-homochiral analog Nle-Leu-Phe-Phe (see ESI Section S9). These data confirmed the importance of both termini in establishing intermolecular salt bridges, as evident from the single-crystal XRD structure of a similar D,L-tripeptide, as well as heterochirality in hydrophobic short peptides to enable hydrogelation of amphipathic superstructures. MD simulations of DNle-DLeu-Phe-Phe in explicit water revealed that the most representative conformation of the zwitterion is a turn with all hydrophobic chains on the same side of the backbone (Fig. ). Such isotactic spatial arrangement was recently reported to be key for the self-assembly of hydrophobic D,L-tripeptides into stable hydrogels. In both cases, the backbone is kinked. Peptide molecules stack thanks to hydrogen bonding between amides, with a pattern similar to that characterizing β-sheets and the aromatic rings running up the stack in a helical arrangement (Fig. ). Dihedral angles of the peptide backbone were calculated for the 2nd (D-Leu) and the 3rd residue (L-Phe) and are shown in the Ramachandran plot (Fig. ). ). The presence of intramolecular H-bonds that could hold together the turn of the heterochiral tetrapeptide was verified by variable-temperature 1 H-NMR spectroscopy, firstly in DMSO as a non-aggregating solvent (Fig. ), and then in the presence of water (Fig. ). 1 H-NMR shifts of amide signals were visible and displayed a linear correlation with temperature from 298 K to 333 K, indicating no conformational loss. In particular, the NH chemical shifts of Leu and C-terminal Phe (Fig. ) displayed a temperature gradient Δδ/ΔT > -4.6 ppb/K, which is a strong indication of involvement in H-bonding. Remarkably, the presence of water did not lead to loss of amide signals (Fig. ), indicating they were not exchanging with the solvent, although only the NH of Leu maintained a temperature coefficient within the expected range for H-bonds (Fig. ). Conversely, the same experiment carried out on the homochiral analog did not lead to any indication of H-bonds (see ESI section S6). |
669e64b75101a2ffa894951f | 4 | In silico data were in qualitative agreement with experiments in solution. Detailed analyses were performed on the trajectories extracted from MD simulations of a single homo-or hetero-chiral peptide in explicit water. For each peptide, we performed a MD simulation of 1 µs in length at 298 K, followed by heating to 363 K in 20 ns, and finally an equilibrium simulation of 1 µs at this temperature. We analyzed the secondary structural content and the Ramachandran plot (reported only for the 2nd and 3rd residues of the tetrapeptide, that is those for which both angles can be calculated), the preferred conformations, the end-to-end intramolecular distances, the frequency of formation of intramolecular H-bonds, and the peptide hydration. The heterochiral peptide displayed an intrinsic propensity towards turns (Table ). Importantly, this feature seemed to be energy-driven and temperature-independent (i.e., there was no entropic gain with heating). The opposite was true for the homochiral analog, whose structural preference towards turns at rt was halved as compared to the heterochiral isomer (Table ). The Cα1-to-Cα4 distance (Fig. ) was significantly longer for the homochiral peptide (visiting extended conformations) relative to the heterochiral one (adopting turns). MD confirmed the formation of an intramolecular salt bridge between termini, and the engagement of Phe4 NH in intramolecular H-bonding, and of Phe3 and Leu NH to a lesser extent, in agreement with NMR data (Table ). |
669e64b75101a2ffa894951f | 5 | A turn conformation stabilized by the intramolecular salt bridge between the charged termini was confirmed for the heterochiral tetrapeptide by single-crystal X-ray diffraction (XRD) (Figure ). Surprisingly, the NH of Leu and Phe3 were engaged in H-bonding, albeit intermolecularly with the CO of the same residues of an adjacent tetrapeptide molecule, as a distinctive feature of the solid phase, as opposed to the intramolecular H-bond of the peptide in solution. The dihedral angles of the crystal structures are compatible with one of the visited conformations observed by MD, albeit not the most representative one (Fig. ). |
669e64b75101a2ffa894951f | 6 | The gelator was first dissolved in alkaline phosphate buffer, thanks to repulsion between negative charges in its anionic form. Subsequent pH lowering to neutral triggered amyloid fibrillation of the zwitterion in samples as diluted as 0.050 % wt. When the concentration was increased to 0.67 % wt. a self-supportive hydrogel was obtained, in contrast with the L-analog (see ESI Sections S8-S9). Interestingly, no cytotoxicity was found for the heterochiral peptide gel in live/dead assays on fibroblast cells (see ESI Section S10). Furthermore, the gel was highly resistant to protease digestion. Despite the presence of one natural peptide bond in the building block, the hydrogel was nearly unaltered after 24h of treatment with a large excess of enzyme (see ESI Section S11). Interestingly, the amyloid assembly contributed to such resistance, since the majority of the tetrapeptide in solution was digested within a few hours. We infer that the amyloid structure displays dry regions of phenylalanine zippers[5b, 15] that reduce contact with water and thus provide protection against enzymatic hydrolysis. Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM) investigations revealed bundles of fibrils spanning the microscale in length (Fig. ). Heating up to 363 K was required to disassemble the stable supramolecular arrangement. Instead of dissolution, as typically observed for short peptide gels, an irreversible transition to plates occurred (Fig. ). Differential scanning calorimetry (DSC) confirmed the stability of the sample up to an endothermic transition at Tm = 362 K (see ESI Fig. ). |
669e64b75101a2ffa894951f | 7 | All-atom MD simulations of heterochiral peptides' self-assembly revealed a general rigidification of the system after heating that persisted upon subsequent cooling to rt, with peptides sampling a significantly smaller range of conformations (see ESI Section S7). Initially (Fig. ), the supramolecular assemblies at rt gave rise to a 3D network containing water channels along three directions and compatible with the observed fibrillar hydrogel. During heating, solubility decreased, the hydrophobic peptides aggregated, and 5-to-9 water molecules per peptide molecule were released from solvation shells, leading to an increase in entropy and the formation of aggregates that are fully separated from each other along one direction (Fig. ). These aggregates could serve as seeds for the onset of plates, that is structures likely corresponding to a thermodynamic sink and thus leading to an irreversible transition. Re-assembly was driven by the entropic gain of the system due to the release of water molecules during the heating phase. Due to the temperature dependence of this term (TΔS) in the overall free energy balance of the process, this gain increases with increasing temperatures, leading the system to a deeper free energy minimum and rendering the process virtually irreversible. This picture is corroborated by several analyses including the calculation of the Solvent Accessible Surface Area (SASA), which decreases in the morphological transition, and the number of water molecules set free in the bulk phase, correlated with that reduction. The reduction in SASA (Table ), leading also to a reduction in the number of water-peptide H-bonds is, however, partly compensated by the increase in the number of such bonds involving only the peptides (Table ). Moreover, the overall number of bridging waters did not change before and after the heating/cooling steps. This is likely because virtually all the possible H-bonds of the termini and backbone were saturated in the MD simulation before the heating of the system, a picture consistent with the very minor changes in the nature of the surface exposed to the solvent (Figure ). Interestingly, the β-structure content was reduced, but no dramatic change to a different conformation was seen, as confirmed by MD simulations, FT-IR, circular dichroism (CD), and Thioflavin T fluorescence analyses (Fig. and). An increase of the temperature up to 363 K leads the peptide to sample different conformations, some corresponding to L-α-helices. However, this difference almost vanishes when simulating self-assembly of hundreds of tetrapeptides in explicit solvent (Fig. ), thus supporting the role of water thermodynamics in the process and the high stability of β-structures. Layered βstructures have been predicted to be the most stable secondary conformation for amyloid superstructures, due to the preference of backbones to engage in extended H-bonding to form sheets. Figure . Representative conformations extracted from MD simulations of heterochiral tetrapeptide assemblies at rt before (a) and after heating to 363 K and cooling to 298 K . Surfaces are colored by atom type (grey, white, blue, and red for C, H, N, and O respectively). In conclusion, we describe the first uncapped D,L-tetrapeptide self-assembly into a hydrogel that, upon heating, undergoes an irreversible morphological transition from fibrils to plates, in marked contrast with all the short peptide assemblies described thus far. This investigation reveals that the peptide undergoes only minor conformational changes, while water plays a key role in the transition, whereby water-peptide interactions are replaced with peptide-peptide interactions, and the entropic gain of the water molecules that are set free locates the system in an energetic sink. These results shed new light on the modulation of peptide assemblies and their morphology. |
669e64b75101a2ffa894951f | 8 | 2-chlorotrytil resin, O-Benzotriazole-N,N,N,N'-tetramethyl-uronium-hexafluoro-phosphate (HBTU), and Fmoc-protected amino acids were purchased from GL Biochem (Shanghai) Ltd. All solvents were purchased of analytical grade from Merck. All the other chemicals were from Sigma. High purity Milli-Qwater (MQ water) with a resistivity greater than 18 M Ω cm was obtained from an in-line Millipore RiOs/Origin system. 1H-NMR spectra were recorded at 400 MHz and 13C-NMR spectra were recorded at 101 MHz on a Varian Innova Instrument with chemical shift reported as ppm (in DMSO with tetramethylsilane as internal standard). ESI-MS spectra were recorded on an Agilent 6120 single quadrupole LC-MS system. Peptides were synthesized in solid phase using standard protocols and Fmoc protection (more details are provided in the ESI). Each peptide was dissolved by 10 min of ultrasonication and heating in sodium phosphate buffer (0.1 M pH 12.0) to a final concentration of 30 mM and then an equal volume of sodium phosphate buffer (0.1 M pH 5.8) was added to get a final pH of 7.2 ± 0.1 and a final concentration of 15 mM. All-atom MD simulations and analyses were performed with the AMBER22 and AmberTools23 software packages. The parameters for D/L N-terminal norleucine were taken from the literature, and the ff19SB AMBER force field was employed together with an OPC model for water. Simulations of single peptides in solution. First, we performed MD simulations of a single homo-(Nle-Leu-Phe-Phe) and hetero-(DNle-DLeu-Phe-Phe) chiral peptide in explicit water as follows. The initial structure of the homochiral peptide was generated using the sequence command from the xleap tool of AMBER22 and relaxing the structure. The heterochiral peptide was built from the homochiral structure using VMD1.9.3. Starting from these structures, three consecutive restrained structural optimizations (up to 25,000 steps) were performed in the presence of harmonic restraints (k=1 kcal/mol•Å) applied to: a) all non-hydrogenous atoms of the system; b) backbone atoms; c) Cα atoms. Reference structures at steps b) and c) were the final ones from the previous step. Next, up to 50,000 cycles of unrestrained optimization were performed. Each system was then heated to 298 K in 1 ns via constant-pressure-temperature (NTP) MD simulations (using the isotropic Berendsen barostat and the Langevin thermostat) followed by an equilibration phase of 10 ns. Starting from the equilibrated structure, a MD simulation in the NVT ensemble of 1 µs in length was performed using a time step of 2 fs. Next, heating to 363K in was simulated in 20 ns, followed by another equilibrium simulation of 1 µs in length at this temperature. Periodic boundary conditions were employed, and electrostatic interactions were estimated using the Particle Mesh Ewald scheme with a cutoff of 9.0 Å for the short-range evaluation in direct space and for Lennard-Jones interactions (with a continuum model correction for energy and pressure). Self-assembly. 5 independent MD simulations of the self-assembly of 512 heterochiral tetrapeptides in water solution were performed following published protocols. Briefly, the initial conformation of the assembling peptides was generated by placing their centers of mass on a 8x8x8 grid of 17.5 Å-spaced points. Initial orientations of peptides were randomized, and the systems were solvated with water molecules, for a total number of atoms around 235,000. Initial structures of the 5 independent simulations were taken from the optimized structure of the corresponding peptides (simulation 1) and from the most populated conformations extracted (simulations 2 to 5) from a cluster analysis performed on the 1 s-long MD simulation described in the previous paragraph. Hierarchical agglomerative clustering was performed, setting the number of clusters to 4 and using the average distance (average linkage keyword in cpptraj) and symmetric RMSD as metric (srmsd keyword). Each simulation was performed as described in the previous paragraph regarding the structural optimization and initial heating steps. Then, a MD simulation of 100 ns in length at 298 K (NVT ensemble) was performed, followed by: heating (in 20 ns) and equilibrium simulation (1 µs) at 363 K, cooling to 298 K in 100 ns, and finally another equilibrium simulation of 1 µs in length at this temperature. |
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