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62838fef43d1f07da52f2d56
| 33 |
Figure : Quality of the V MM (λ) correction potential as a function of the order of the polynomial fit to ∂V /∂λ λ for Asp. Panel A shows the fitting error, as a function of fitting order (black line). The gray dashed line shows the average error of calculated ∂V MM /∂λ. In the panel B, the distributions of λ-coordinates for the 3 rd and 7 th order polynomial fits to ∂V /∂λ λ are shown. While with the lower order fit the distribution is significantly rugged, it is nearly flat and yields a uniform distribution for on the [0, 1] interval of the λ-coordinate, when using 7 th order.
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| 34 |
A change in the protonation state affects the total charge of the simulated system, which can lead to artifacts when Ewald summation is used to treat the electrostatic interactions. In our implementation of constant pH MD we avoid this problem by introducing titratable buffers into the simulation box that compensate for the charge fluctuations of the titratable residues. In the original implementation of constant pH MD in GROMACS, 10 the buffers were hydronium molecules that compensated the overall charge fluctuations by changing their charge between 0 and +1 e. To prevent sampling charges beyond this interval, a biasing potential with steep edges at λ = 0 and λ = 1 was introduced to restrict the sampling of λ.
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Figure : Parameterization of the buffer. Panel A shows the AWH friction metric as a function of buffer charge. Since the higher the friction metric is, the slower the sampling, the buffers should ideally be forced into a low charge region. Panel B shows the density distribution of buffers in a membrane system. Optimized buffers do not penetrate into the lipid bilayer, while uncharged sodium ions do. Panel C shows the radial distribution function between buffers. When standard sodium ion parameters are used as buffers, the tendency to form clusters is high. Optimization of buffer parameters prevents clustering. Panel D shows the radial distribution functions of buffers to protein. The original sodium parameters again led to a much higher tendency of buffer to bind to the protein than that observed with optimized parameters.
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| 36 |
Because changing the charge of a buffer particle in solution induces local rearrangements of the hydrogen bonding network that in turn could affect the proton affinity of a nearby titratable group, we want to minimize the impact of charging the buffer particles. To determine the charge range in which the buffers do not cause significant hydrogen bond network rearrangement, we ran AWH simulations with two ions, the charges of which are changed simultaneously in opposite directions (BUF 2 system). From the friction metric available in the AWH method, we estimated the local diffusion coefficient, which is related to the efficiency of sampling: The higher the friction, the slower the dynamics, and the more sampling is required to reach convergence. We calculated the friction coefficient (Figure ) for the coordinate associated with changing the charge on the buffer. For charges higher than 0.5 e the friction was more than 50% higher than for zero charges, reflecting longer correlation times and hence slower dynamics. We, therefore, conclude that the optimal range for the buffer charge is between -0.5 e and 0.5 e.
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| 37 |
The collective λ-coordinate of the buffer particles is not restricted to a fixed interval by a wall-like potential. To avoid that the buffer charge exceeds the restricted interval, multiple buffer particles are needed in the simulation box. The optimal number of buffers can be calculated based on the analysis of charge fluctuations performed by Donnini et al. With a small charge, a buffer particle is apolar. To prevent clustering of such apolar particles in water, permeation into hydrophobic areas, such as membrane interiors, or interactions with the protein, the Lennard-Jones parameters of the buffers were chosen such that the buffers have only repulsive interactions with all other atoms, except water. After experimenting with parameters for the buffer particles, we settled on a σ of 0.25 nm and an of 4 kJ mol -1 . This choice leads to decreased clustering of buffers, low buffer concentrations in the proximity of titratable sites, and reduced penetration into hydrophobic regions (Fig. ). The resulting free energies of neutral buffer insertion into water and hydrophobic region of membrane are -2.09 ± 0.07 kJ mol -1 and 1.2 ± 0.6 kJ mol -1 , compared to 8.45 ± 0.05 kJ mol -1 and 7.8 ± 0.3 kJ mol -1 for the insertion of an uncharged sodium ion into these regions.
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| 38 |
While the primary goal of introducing buffers is to avoid the artifacts associated with a non-neutral periodic simulation box, there can be other artifacts as well. In particular, the undersolvation caused by solvent orientational constraints due to periodic conditions could lead to finite-size effects especially for small boxes. To understand if such finite-size effects affect the results of constant pH simulations, we investigated how the distribution of the λ-coordinates depends on the system size. We, therefore, performed constant pH MD simulations for three different box sizes and at various ionic strengths. All simulations were performed at pH=pK a and without a barrier in the biasing potential. The uniformity of the distributions in these simulations, shown in Figure ), suggests that for the box sizes tested, the finite-size effects are negligible.
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| 39 |
To demonstrate that with the modifications of the torsional barriers, a correction potential obtained by fitting at least a 7 th order polynomial to the ∂V /∂λ λ of reference simula-Figure : Titration of cardiotoxin V. Panels A and B show the results of titrations of 1CVO 1 system performed with original and modified force fields, respectively. Gray lines show the fitted Henderson-Hasselbalch curves to the data. Red lines are Henderson-Hasselbalch curves computed for the experimental pK a value of the corresponding residue. For ASP59 the exact pK a is not known. Black dots show the deprotonation ratio for the individual replica. For each curve, the standard deviation between the calculated and fitted deprotonation ratio, averaged over all pH values and replicas, is shown. tions, and buffer particles with optimized parameters, it is possible to perform accurate constant pH MD simulations, we calculated the pK a values of all four cardiotoxin V titratable residues. We performed the pH titration simulations with both the original and modified CHARMM36m force fields. In Figure we show the titration curves obtained in the simulations and compare them to the experiment. Because there is no exact experimental estimate for the pK a of ASP59, we only compare the pK a 's obtained for the other residues.
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| 40 |
The comparison suggests that the force field corrections improve the pK a estimates, but more importantly, the lower deviation between the individual replicas (from 0.12 to 0.07 for ASP42, from 0.16 to 0.05 for ASP59, from 0.1 to 0.03 for GLU17, from 0.19 to 0.18 for HIS4, Figure ) suggests that the sampling is improved when the modified force field is used.
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| 41 |
Whereas for Asp and Glu the individual titration replicas are consistent when the modified force field is used, the replicas for HIS4 are not converged. As shown in Figure , HIS4 interacts with TYR12 and PHE10. At pH=5.5, close to the experimental pK a of HIS4, we find three dominant conformations of HIS4-TYR12 pair in both normal and constant pH MD trajectories: A close contact (around 5 Å), a medium-range contact (around 6 Å), and a long-range contact (larger than 7 Å, Figure ). The distributions of these distances are not the same in all replicas (Figure ), and neither are the distributions of the λ-coordinates associated with the doubly-protonated state of HIS4 (Figure ). These differences suggest a lack of convergence of the conformational dynamics of the protein in constant pH MD. To test if the protonation state of HIS-4 correlates with the distance distribution, we performed standard MD of cardiotoxin V with HIS-4 in the three different protonation states (Figure . S16). Because there is no clear correlation between the protonation state and the HIS4-TYR12 distance distributions, we cannot conclude that the protonation states are coupled to the conformation of the pair, at least not directly. Instead, the differences between the replicas suggest a lack of sampling of these conformations. Because the local environment differs between the states, we speculate that this lack of conformational sampling also affects the λ-distributions. Thus, we can only conclude that the sampling of these distances would require more than 100 ns to converge. Thus, even if the corrections to the torsion potentials overcome the convergence issues associated with sampling the intrinsic dihedral degrees of freedom in single amino acids, reaching converged sampling of the protonation states in proteins may still require longer timescales if the inherent conformational dynamics is too slow.
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| 42 |
Nevertheless, we observe that compared to normal MD, constant pH MD can increase the sampling of the local conformational space of the protein. In Figure and S17 we show that the HIS4 samples configurations more efficiently in constant PH simulations. Specifically, the hydrogen bond between PHE10 and the HIS4 δ hydrogen is much more stable in normal MD with a fixed protonation of δ-nitrogen (Figure ), whereas in constant pH MD, the HIS4 also samples configurations in which the H-bond is broken (Figure ), in particular around pH=pK a , as evidenced by the distribution of the N-C α -C β -C γ dihedral angle in
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| 43 |
It is now finally possible to run accurate constant pH molecular dynamics simulations on timescales of normal simulations, for example with the new implementation in the GRO-MACS package presented in the accompanying paper. 15 However, running accurate constant pH simulations on longer timescales can reveal issues with both force fields and the parametrization procedures of constant pH parameters.
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Here we demonstrated, on the basis of CHARMM36m, that molecular force fields are not optimized for constant pH simulations, and suggest a possible solution based on the reduction of torsional barriers. In standard MD such modifications do not cause any noticeable drawbacks but allow the λ-dependent side chain conformational sampling to converge in constant pH simulations. Combined with the optimal fitting of V MM , the force field modifications constitute an essential preparation step for any constant pH simulations. In this paper, we also shared an extensive use case, showing how slow torsions can influence the titration behavior of proteins. Our modification of CHARMM36m force field and optimal parameters for Asp, Glu, His, Lys, and C-and N-terminus can be obtained from (constantph). There we will also collect parameters and other force field modifications as long as we create and test them. We ask the researchers interested in constant pH simulations to share the parameters they have developed for new titratable groups or force fields with us, The other important aspect of constant pH simulations is preserving the charge neutrality of the simulation system. In our implementation, we achieved this by the addition of buffer particles, which retain the box neutrality upon protonation events. Here we discussed issues associated with the introduction of such buffers into the simulation system (e.g. disruption of hydrogen bond network, clustering, binding to protein, penetration into the hydrophobic region), and how to overcome those issues. The optimal parameters of buffers might slightly differ for different water models and force fields used, but the parameterization strategy described here provides a comprehensive guide to obtaining the best buffer parameters.
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| 0 |
Macrocycles occupy a unique segment of drug-relevant chemical space, yet they are relatively underexplored compared to acyclic small molecules. They represent a privileged class of molecules for the modulation of protein-protein interactions, and interest in macrocyclic peptides as a class has been growing in both academic and industrial circles. Natural compounds have been the main source of macrocycles with relevance for therapeutic purposes.
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| 1 |
While there are over 100 marketed macrocyclic drugs derived from natural sources, they are for the vast majority either the actual natural compounds, or their modifications. Between 2014 and 2021, nineteen of the FDA approved drugs are macrocycles, which represents roughly 1 in 20 FDA approvals. Macrolide antibiotics such as actinomycin and polyene antifungal compounds are among the most prominent classes of compounds. However, in the past decade there has been an increasing interest in de novo designed macrocycles, often starting from small molecule templates. The cyclization process is a very effective way to improve physio-chemical properties of molecules, improving pharmacological properties while retaining relatively low molecular weights. For example, cyclization of peptides has been used by synthetic chemists, and in natural systems through post-translational modification and non-ribosomal peptide synthesis, to confer metabolic stability as well as to restrict the conformational space to improve affinity and cell permeability. In particular, the cyclization can be used to reduce the entropic cost of binding by reducing conformational degrees of freedom, and ultimately shift the thermodynamics of binding favoring the formation of a complex. Cyclization can also be used to increase cell permeability by exploiting the switching between solvent-dependent conformational states. Modeling of macrocycles presents a number of challenges for docking algorithms due to the complexity of their constrained molecular structures. On one hand, many of the internal degrees of freedom are partially restrained by the cyclic structure, which limits the amplitude of bond torsional variability. On the other hand, the remaining intra-cyclic degrees of freedom are hard to sample because of their correlated and concerted motions. Therefore, several methods have been proposed to describe and sample these constrained degrees of freedom during molecular docking. These methods can be categorized into two main approaches. The first is a two-step process consisting in the enumeration of a possibly large number of macrocycle conformers followed by rigid docking of each conformer. The second, which is the topic of the present work, is flexible docking of the cyclic structures is simpler because it consists of a single step and allows for the sampling of cyclic conformations during docking, while taking into account the target structure. Both approaches were used successfully by participants of the D3R Grand Challenge 4, which included the prediction of the binding mode of nineteen macrocycles. In 2007 we reported the first AutoDock method for docking macrocycles flexibly. Macrocycles are challenging because AutoDock samples bond rotations independently from each other, but cyclic molecules introduce a dependence between multiple rotatable bonds to preserve their cyclic structure. The method reported in 2007 consisted in breaking the cyclic structures by removing one bond, to allow independent sampling of each rotatable bond, and use of a modified Lennard-Jones-like potential between two previously bonded atoms (which we refer to as "glue" atoms) to restore the cyclic structure. The original closure potential was isotropic because it did not depend on the relative orientation of the glue atoms. Consequently, this potential is inappropriate for chiral carbons, and can produce non-physical valence angles.
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In 2019 we reported on an improved variation of the closure potential that uses pseudo-atoms to preserve the valence angles and chirality of the input molecule. Thus, the attraction between the previously bonded atoms can now be described as anisotropic, resulting in more accurate geometries. We employed this method in the D3R Grand Challenge 4, using AutoDock-GPU, achieving RMSDs below 2 Å for all of the 19 macrocycles using visual inspection to select the best pose. The improved method was based on the Smallest Set of Smallest Rings (SSSR) perception algorithm available in OpenBabel.
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| 3 |
In the present work we describe the formalization of the closure potential reported in 2019, in which the molecule is represented by RDKit instead of OpenBabel, and rings are perceived with the Hanser-Jauffret-Kaufmann (HJK) ring perception algorithm. HJK returns the complete set of rings, instead of a SSSR, giving us more flexibility in the choice of rings to break and the bonds to remove. This change is part of our ongoing development of an interface between RDKit and AutoDock (Meeko), which enables the user to use RDKit molecules as the input and output for AutoDock calculations, facilitating the integration of docking with other modeling software.
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Here, we characterize the performance of this improved flexible macrocycle leveraging the accelerated performance of AutoDock-GPU, using a large and diverse set of ligands from the PDB, spanning rings of multiple sizes, and including large and complex multicyclic molecules, such as vancomycin. Furthermore, this work validates our implemented algorithms for ring perception (HJK) and bond removal.
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| 5 |
The method consists of three main steps represented in Figure : 1) identification of cycles in the molecular graph that are suitable for breaking (ring perception); 2) identification of the optimal set of bonds to remove to obtain the optimal linear molecular graph (ring breaking); 3) docking of the acyclic molecular graph using an energy potential to induce ring closure (docking and ring closure).
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| 6 |
The ring perception step identifies cycles (i.e. rings) in the molecular graph using the Hanser-Jauffret-Kaufmann (HJK) ring perception algorithm, which returns the complete and exhaustive set of rings. Since the complete set often has redundant ring information for our purposes, we remove "chorded rings" and "equivalent rings". Rings are chorded if there is a shortcut between any two atoms containing fewer bonds than the path of the ring itself (e.g.: rings A and A', Fig. ).
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| 7 |
Equivalent rings are rings of identical size that share at least one bond with a common neighbor ring, and for which all the bonds not contained in the common neighbor ring are the same (e.g.: rings A and A', and B and B', Fig. ). Then, rings between 7-membered and 33-membered are selected for breaking. Rings smaller than 7-membered rings have a small and well-defined set of stable conformations (e.g., boats and chairs) that do not require this method to be sampled. Rings larger than 33-membered rings are theoretically compatible with the method, but were arbitrarily excluded because the torsional complexity of their open forms would exceed the current search capabilities of our docking engines.
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| 8 |
In the following ring breaking step, we search for a set of bonds to remove such that each of the macrocycles identified in step 1 has exactly one bond removed. All bonds between non-aromatic carbon atoms that are not shared with non-breakable rings (i.e., 6-membered or smaller rings) are candidates for removal. We then perform an exhaustive search to find a set of bonds that when removed minimizes the depth of the deepest branch of rotatable bonds in the resulting acyclic molecular graph in order to minimize the search complexity during the docking. In fact, deeper branches of rotatable bonds (with respect to the central group of atoms in the graph, i.e. "root") have potentially larger conformational variation upon torsional perturbations during the search, even for small angle steps. For most molecules, the number of removed bonds is equal to the number of macrocycles, but when bonds are shared between macrocycles, it is possible that there are fewer removed bonds than macrocycles. Each of the atoms previously bonded by a removed bond (e.g., a1, a2) is first assigned a special atom type CG (CGn), and then attached to a G pseudo atom at the position of the complementary G atom (Gn).
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| 9 |
In the last step, docking and ring closure, a distance-dependent penalty potential of 50 kcal/mol/Å is defined between each CGn/Gn pairs to favoring the restoration of the broken bond, then standard docking simulations are performed on the acyclic structures. While the potential between CG atoms and G pseudoatoms is isotropic (because it depends only on their distance), the bond restoration will be driven by their complementarity, hence resulting in anisotropic bond constraint which encodes and restores the original correct geometry and chirality (unlike the original implementation) . This is the same potential used in our previous work.
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| 10 |
The ligand dictionary for the PDB was downloaded in a SMILES format from the RCSB website. RDKit was used to parse the strings and detect ring sizes, as well as removing metals and inorganic species. Boettcher scores were used to provide a metric for molecular complexity, and calculated using previously reported code. Representative ligands were sampled for each ring size, and the PDB was queried for their complexes with proteins. From that, we curated a small representative set of macrocyclic complexes matching the following criteria: deposited Xray crystal structure agreed with the chemical structure of the reported ligand; resolution <= 3.5 Å; and no cofactors in the binding site. The final set contains 90 ligands.
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| 11 |
Ligand structures were manually inspected and extracted from the crystal structure using PyMol v2.5.2. Meeko v0.3.2 was used to assign atom types, check protonation, merge non-polar hydrogens, and define rotatable bonds. Additionally, Meeko was used to handle the breaking of the macrocyclic structure and the generation of pseudoatoms, as described above. Additionally, the rotation of conjugated bonds was disabled (using the options "-r C=C-C=A -b 2 3").
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| 12 |
Receptor structure protonation states were assigned using pdb4amber [REF]. Crystallographic waters and any other non-protein components, including metals and other cofactors, were manually removed using PyMol v2.5.2. The prepare_receptor4 script available in AutoDockTools was used to assign charges to the receptor and generate the PDBQT file. AutoGrid v4.2.6 [REF] was used to generate the maps and associated files. Grid boxes were centered on and sized around the crystallographic ligand with an 8 Å padding on all sides.
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| 13 |
AutoDock-GPU v1.5.3 was run with standard options, other than the calculation of input structure energies (--rlige 1). Briefly, for each complex 20 independent genetic algorithm runs were performed, with the resulting conformations clustered using a soft RMSD tolerance of 2 Å. The number of evaluations were estimated for each complex, using a built in heuristic based on the number of rotatable bonds, and capped with an asymptotic limit at 12M evaluations.
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| 14 |
Convergence was automatically assessed by the AutoStop criterion based on the standard deviation of the energy evaluations. Default settings for AutoStop of a 5 generation test rate and an energy standard deviation of 0.15 kcal/mol were used. These settings were used for all complexes, except for the extended runs to address convergence issues, and in the peptide case studies, where the search heuristics and AutoStop criteria were turned off and the docking run was performed with 100M evaluations. The best score pose for each docking was selected as the final pose for the analysis.
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| 15 |
The dictionary of all ligands currently deposited in the PDB (N=37023) was downloaded and filtered to remove complexes containing metals (N=406), or lacking carbon atoms (N=170), and SMILES with incorrect valances (N=513). The remaining complexes (N=35934) were filtered for ligands with at least one non-aromatic ring of size 7 or larger (N=1557, Figure ), retaining 4% of the total ligands. These molecules have an increased molecular complexity relative to the overall list of deposited ligands (Figure ). Representative examples of high resolution crystal structures of complexes containing randomly selected macrocyclic ligands, and not containing any other cofactors in the site, were selected to approximately reproduce the distribution of ring sizes found in the PDB (N=90, Figure ). Details on the complexes used in this set are available in Table .
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| 16 |
Importantly, this curated set also approximates the complexity profile of the overall set of macrocycles, implying it is representative of the complexity of challenges associated with macrocycles, both in terms of ring size and from an information theory perspective. During this process each deposited crystal structure was also checked for agreement with the deposited ligand chemical structure, ensuring that the stereochemistry and hybridization reported in the ligand dictionary agreed with the geometry of the deposited ligand (for example, removing cases where the deposited SMILES indicated a sp2-sp2 bonds, but the crystal structures contained nonplanar carbons).
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Peptide ligands tend to be larger than typical organic macrocyclic structures, resulting in a very large number of active torsions. Specialized software with ad-hoc protocols such as AutoDock CrankPep 38 may be better suited to this task. However, given the relevance of cyclized peptides to drug design, several clinically relevant conformationally constrained peptides are presented Updated 04/14/2022 here as case studies, discussing the performance when docking such extra challenging structures. Details on the PDB structures used are available in Table .
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| 18 |
In order to assess the docking performance of the method in modeling full ring flexibility, ligands were docked both by modeling the full macrocycle flexibility (flexible), and while keeping rigid only the macrocycle conformation found in the crystallographic model (rigid). This allowed us to identify complexes in which other factors (e.g., scoring function limitations, water-mediated interactions, etc.) prevented reproducing the correct conformation, as well as assess the impact of the increased search complexity induced by the ring opening, In the case of rigid redocking the best pose of the most populous cluster found was within 2 Å of the crystallographic pose in 76% (68/90) cases (Figure ). In the flexible redocking task, the success rate dropped to 53% (48/90) cases. In the rigid redocking the macrocycle conformation is known from the crystal structure, making it an inherently simpler task that not representative of the challenge of prospective dockings, when only the chemical structure is known and not its conformation. The difference in success rate between rigid and flexible redocking reflects this increased difficulty but is more representative of the task faced in docking and screening. The flexible success rate substantially improves when considering only smaller ring sizes (<15 atoms), becoming comparable to the rigid redocking success rate (59% vs 69%, n=54). This is an important aspect because these ring sizes are much more abundant in crystallographic structures, constituting more than 70% of all structures, and more relevant for drug discovery programs. The results also indicate this method comes at virtually no cost to the success rate while not requiring prior knowledge of ring conformations in most relevant situations. Selected successful flexible redocking results are shown in Figure . ). If unphysical bond geometries were produced during ring closing, these would likely lead to larger RMSDs. However, we observe no evidence of this being the case, because larger RMSD are not associated with better scores from the flexible docking. This suggests that the ring closing method does not introduce scoring aberrations.
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| 19 |
To validate this and address the increased search complexity, cases were identified where results did not converge to well-defined clusters. We found 23 complexes where the most populous cluster contained three or fewer poses out of 20 generated/runs. This suggests that the automatic search termination criteria somehow hindered the docking performance by triggering an early energy convergence auto stopping and preventing from sampling sufficiently the ring conformational space. This convergence issue was addressed by disabling the auto stopping criteria and heuristic for limiting evaluations, and instead running a docking for 100M evaluations, which far exceeds the usual number of evaluations. Of the 23 complexes treated this way, only 3 had RMSDs values that improved to be within the success criteria, while none got worse (5ta4, 5eqi, and 1nm6; Figure and). The success rate for this subset of challenging systems increased from 17% to 29%.
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| 20 |
Macrocyclic peptides feature in several therapeutically relevant contexts. To provide a proof-ofprinciple of the application of this method to these challenging systems, we selected a small adhoc set of 6 conformationally restrained peptides which were not included in the main dataset (Figures 9 and 10, Table ): 3 inhibitors of HIV-1 protease (PDB: 1b6j, 1b6p, 4cpw); 3 antibiotics: arylomycin C (PDB: 3s04), darobactin (PDB: 7nrf), and vancomycin (PDB: 1rrv). Due to the high number of torsions present in these compounds, they were docked by disabling the AutoStop and search heuristic, and using 100M evaluations. For the complexes in PDBs 1b6j and 1b6p, the top pose was within 2 Å of the crystallographically determined ligand. For 1b6p, this involved two cyclic systems, a 15-membered ring and a 16-membered ring. Interestingly, in the latter, two of the carbons were not resolved in the crystal structure. While these atoms were excluded from the RMSD calculation, the docking was performed with the goal of assessing the application of this method to help refine incomplete structural data and infer the positions of the unresolved atoms in the macrocycle. The re-docking of the 4cpw complex is the only example of this set in which the top pose did not match the crystal structure. The best pose for the third ranked cluster was accurate to within 1 Å and was scored within 1 kcal/mol of the best cluster, showing that while AutoDock-GPU failed to properly rank the poses, the search algorithm showed to be capable of properly sampling the correct pose. For arylomycin C (PDB: 3s04), darobactin (PDB: 7nrf), and vancomycin (PDB: 1rrv) <2 Å RMSD poses were identified as the top result. These antibiotic peptides represent a series of increasing complexity challenges, with a progressively increasing number of torsions and flexible ring systems from arylomycin (24 torsions, 1 macrocyclic ring), to darobactin (32 torsions, 2 macrocyclic rings), to vancomycin (39 torsions, 3 macrocyclic rings). In both arylomycin and vancomycin, the accuracy of the macrocyclic portion is higher than for the linear chains attached to it, likely due to the more specific and constrained interactions established by the former versus the latter. In particular, for vancomycin the higher accuracy portions of the docked pose are near to the intersections of rings, and in regions with more contact with the protein, compared to distal portions of the molecule.
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| 21 |
In this work, we formalize and validate the flexible treatment of macrocyclic rings in AutoDock-GPU on a large set of diverse macrocyclic molecules from the PDB. The method leverages an improved preparation protocol for the ligands for flexible docking of macrocyclic structures, which is now enabled by default in Meeko, our recently developed interface between AutoDock and RDKit. Meeko streamlines the ligand preparation workflow, enabling users to use RDKit molecule objects to manage the AutoDock input and output data. Given the popularity and wide use of RDKit, this interface enables users to more easily integrate AutoDock with other software that supports the RDKit library. For docking methods requiring pseudo atoms, such as the macrocycle flexibility described herein, having streamlined input and output in a well-established molecular representation (as opposed to running scripts to add and remove pseudo-atoms from AutoDockspecific file formats) reduces the burden on the user and makes it easy to use docked poses as input for other modeling tools, such as molecular dynamics simulations. Docking macrocycles flexibly greatly increases the number of conformations that are scored during the search. In comparison to rigid docking, there is a greater chance of finding wrong conformers with good scores, which would be detrimental to docking performance. However, we found no evidence of this being the case (Figure ), which we attribute to the fact that the anisotropic closure potential used here retains bonding information and prevents deformations in bonding geometry from erroneously being scored favorably. Thus, our data suggests that the method does not introduce scoring functions issues.
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| 22 |
A flexible system has a greater number of active torsions than does a rigid system. This increases the difficulty of searching the torsional space for the appropriate binding mode, decreasing the rate of convergence. We show that removing the heuristic for estimating the number of evaluations needed for a system and turning off the auto stopping criteria (both of which designed to reduce the time taken to dock small molecules) can improve performance on some of the larger systems that do not converge. Importantly, this difference in number of torsions is intrinsically dependent on the ring size for the broken macrocycle, and this is reflected in the fact that this method performs better for smaller rings (up to 15-membered rings). As shown in Fig. , these rings represent the majority of deposited complexes, and are more commonly accessible through medicinal chemistry approaches. Some of these inaccuracies in the scoring and ranking of the correct results could be also mitigated in the context of a focused drug discovery effort by using knowledge-based post-processing steps, such as the presence of known interactions, (e.g., the key hydrogen bonding with the catalytic aspartates in the context of the HIV-1 protease inhibitors).
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With respect to cyclic peptides, which are possibly the most studied class of macrocycles, a systematic treatment would be challenging because of the large number of active torsions. Nevertheless, our work shows that select clinically relevant cyclic peptides, with relatively few torsions, can be handled by this method. We obtained very satisfactory results for vancomycin, which contains 39 torsions. While it would be helpful to address such molecules with specialized representations and energy models, from the perspective of the docking software and scoring function, there is fundamentally no difference between molecules with amino acid constituents and any other chemical matter. Therefore, the success in this space suggests that improvements in the search function will be able to extend this method to larger and more torsionally complex peptides.
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We have presented here the validation of our flexible ring docking method. The method has been implemented and validated in AutoDock-GPU, extending the original approach implemented for AutoDock3 and AutoDock 4.2. Using an anisotropic ring closure potential provides a robust approach to dock cyclic molecules containing one or more flexible rings consisting of 7 or more atoms, and addresses most of the limitations of the first implementation. The results show the performance of the method is related to the complexity of the search, while the anisotropic potential does not alter the scoring function value of converged systems. This is further reinforced by the responsiveness of these systems to increased numbers of evaluations, which are shown to improve performance. This additionally means the method performs very well on the smaller ring systems most prevalent in druglike molecules. Finally, we show this method is capable of handling challenging multicyclic systems of clinical relevance. The method is compatible with all the other protocols available in the AutoDock Suite, therefore we recommend, and internally use, this method as a standard part of our docking pipeline. The automated preparation and simulation steps make this method suitable for high-throughput applications.
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Over Visible-light photocatalysis has become a widely used technique in synthetic organic chemistry. Photocatalysis functions by harnessing the electronic excited state of a photocatalyst (PC*), generated via the absorption of a photon, to interact with an organic substrate through either electron or energy transfer. Photocatalytic photoinduced single electron transfer (PET), commonly known as photoredox catalysis, proceeds either via a reductive or an oxidative quenching mechanism, dependent on whether the PC* gains or loses an electron, respectively, during the initial PET. Alternatively, photoinduced energy transfer (PEnT) implicates the transfer of energy from the PC* to the substrate through either a Dexter or Förster energy transfer mechanism, regenerating the ground state photocatalyst (PC). Organometallic complexes based on Ru(II) and Ir(III) are the most widely used PCs (Figure ). They possess an attractive suite of properties including suitably long-lived stable excited states, absorption that extends into the visible region where most organic substrates are transparent, plus (especially for Ir(III) complexes), the capacity to modulate both the ground and excited state redox properties through ligand variation. However, the scarcity, toxicity and cost of the noble metals employed has spurred intense efforts to find alternative PCs. There are now many established examples of Earth-abundant metal complexes and metal-free organic photocatalysts, and numerous examples where these perform comparably to the noble metal PCs. While organic photocatalysts, such as xanthene dyes, phenothiazines, and acridinium-based compounds are commonplace (Figure ), their ground and excited state redox potentials are difficult to tune. Donor-acceptor (D-A) thermally activated delayed fluorescent (TADF) PCs, most widely exemplified by the compound 4CzIPN, have rapidly been adopted in the field as their properties are readily tunable through substituent variation (Figure ). 9,10 4CzIPN, initially developed as an emitter for organic light-emitting diodes a decade ago, luminesces via a TADF mechanism. As a result, 4CzIPN possesses microsecond-long emission lifetimes that, coupled with similar redox properties to that of the widely used [Ir(dF(CF3)ppy)2(dtbbpy)]PF6, endows it with similar photochemical reactivity. 4CzIPN was first used as a photocatalyst by Luo and Zhang to achieve a dual catalysed (C)sp 3 -(C)sp 2 cross-coupling reaction. 12 Subsequent work by Speckmeier et al. demonstrated the versatility of this class of D-A TADF photocatalyst and the tunability of their redox potentials by varying the nature and number of electron-donating and electron-accepting groups. A growing number of structurally related D-A PCs have since been reported. TADF operates when the energy gap between the lowest energy singlet and triplet excited states, ΔEST, is sufficiently small such that there is an endothermic upconversion of triplet excitons into singlets by reverse intersystem crossing (RISC). This is possible when the exchange integral between the frontier orbitals involved in the emissive excited state is sufficiently small, which occurs in D-A compounds where the donor and acceptor groups are poorly conjugated such as when they adopt a highly twisted conformation, Ground state redox potentials of DiKTa and Mes3DiKTa in MeCN. Excited state redox properties of DiKTa and Mes3DiKTa calculated from the experimentally determined Eox/Ered and E0,0 values in MeCN, using Eox(PC •+ /PC*) = Eox -E0,0 and Ered(PC*/PC •-) = Ered + E0,0. 16 as is the case for 4CzIPN and its derivatives. An alternative molecular design strategy to reduce the exchange integral is based on the exploitation of opposing resonance effects of p-and n-dopants in nanographenes that is embodied in multi-resonance TADF (MR-TADF) emitters. Herein we present the use of two MR-TADF compounds as photocatalysts for the first time, using DiKTa and Mes3DiKTa, previously reported by us as emitters in OLEDs, as typical examples (Figure ).
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Owing to their rigid structure, MR-TADF compounds typically show much narrower emission profiles and smaller Stokes shifts while also exhibiting larger molar absorptivities for the low-energy short-range charge transfer (SRCT) absorption band (see Figure ). The emissive excited state also shows SRCT character, which is identifiable due to the modest positive solvatochromism, in contrast to the large positive solvatochromism observed for D-A TADF compounds (see Figures ). Enhanced molar absorptivity and reduced positive solvatochromism are expected to have positive implications for photocatalysis reactivity. The higher molar absorptivity of the band that is being targeted for photoexcitation could translate to faster reaction rates and lower required photocatalyst loadings. The attenuated positive solvatochromism of MR-TADF compounds implies that less energy is lost due to stabilization of the excited state by solvent, potentially leading to greater reactivity of the PC, particularly in commonly used polar aprotic solvents such as MeCN and DMF. DiKTa and its mesitylated analogue Mes3DiKTa were chosen for investigation as photocatalysts because of their similar redox potentials to those of 4CzIPN (Figure ). An additional benefit is that the raw material cost per mmol is significantly lower for DiKTa (£0.94/mmol) than for 4CzIPN (£3.26/mmol, see SI). These PCs were assessed across a diverse range of transformations including reductive quenching reactions, oxidative quenching reactions, energy transfer reactions, nickel dual catalysis and hydrogen atom transfer (HAT) dual catalysis. The result of this assessment shows that DiKTa and Mes3DiKTa are attractive alternatives to the widely used 4CzIPN.
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Reductive Quench. Our investigations began with a decarboxylative photo-Giese reaction. This process has previously been reported by Ji et al. for their comparison of the effectiveness of different acridinium photocatalysts and also by Speckmeier et al. for their comparison of the suitability of alternative D-A photocatalysts. In the latter study Speckmeier et al. found that when 4CzIPN was used, a superior isolated yield of 80% is achieved compared to the previously reported best acridinium photocatalyst, which produced an isolated yield of 73%. Using N-Cbz protected proline 1a as the carboxylic acid substrate and diethyl maleate 2 as the electron deficient alkene, both DiKTa and Mes3DiKTa gave comparable NMR yields to that of 4CzIPN (Table , therefore, the more challenging iso-butyric acid, 1b, and propanoic acid, 1c, were also investigated in order to differentiate the photooxidation ability of the PCs. With iso-butyric acid both DiKTa and Mes3DiKTa showed improved NMR yields of 78% and 79%, respectively (Table , entries 4 and 5), relative to the 64% achieved using 4CzIPN (Table , entry 6). Changing to the primary radical formed when using propanoic acid resulted in lower yields for all three PCs (Table , entries 7-9). This is likely due to the decreased nucleophilicity of primary radicals relative to secondary radicals, leading to alternative and undesired reaction pathways becoming competitive. Notwithstanding the lower yields, both DiKTa and Mes3DiKTa still outperformed 4CzIPN (Table , entries 7-9).
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Entry Acid PC Yield / % PC loading was next investigated as a discriminating parameter. The reaction using N-Cbz-proline 1a as starting material was therefore repeated at 1 mol%, 0.5 mol%, 0.25 mol% and 0.1 mol% (Table ). Yields remained largely the same for all three PCs down to 0.5 mol% (Table , entries 1-6). Contrastingly, differences in NMR yield were observed at 0.25 mol%, with 4CzIPN only achieving an average yield of 28% (Table , entry 7), while DiKTa and Mes3DiKTa maintained an average yield of 80% (Table , entries 8 and 9). When using 0.1 mol% PC loading, the use of both 4CzIPN and DiKTa produced poor average yields of 9% and 18%, respectively (Table , entries 10 and 11), while Mes3DiKTa achieved a significantly higher yield of 59% (Table , entry 12). The evidence suggests that DiKTa and Mes3DiKTa perform better than 4CzIPN at lower catalyst loadings, which is consistent with the higher molar absorptivity of DiKTa and Mes3DiKTa relative to 4CzIPN at the excitation wavelength used. Oxidative Quench. Subsequent studies assessed these PCs in an oxidative quenching process based upon the atom transfer radical addition (ATRA) reaction developed by Pirtsch et al. Using perfluorobutyl iodide 4a (Ep red = -1.42 V vs SCE in MeCN) and tert-butyl-N-allyl carbamate 5 as the substrates, 4CzIPN produced the desired ATRA product 6a in 83% yield (Table , entry 1). Interestingly, when using DiKTa and Mes3DiKTa, near quantitative yields of 97% and 93%, respectively, could be achieved ( and is commonly used in the literature; however, this value is erroneous and occurs only as a result of electrochemical degradation (Figure ). Indeed, a previous report by Bahamonde et al. found that the peak reduction potential is significantly more negative Ep red = -1.39 vs SCE in MeCN, and our own measurements have found it to be Ep
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Dual Photoredox Catalysis. Metallaphotoredox catalysis is a fast growing area of research as it often offers a mild alternative to existing transition metal catalytic reactions and give access to different redox couples of the co-catalyst, resulting in new reactivity. Nickel in particular has been paired with photocatalysts for a wide range of different coupling reactions with Luo and Zhang 12 reporting the first use of 4CzIPN as a photocatalyst in a dual-mode catalyzed (C)sp 3 -(C)sp 2 cross-coupling. Employing a modified version of this reaction to assess the performance of DiKTa and Mes3DiKTa, using 4CzIPN, the coupling reaction between 1a and aryl bromide 9 gave the desired product 10 in 78% yield (Table , entry 1). Both DiKTa and Mes3DiKTa gave similar results of 78% and 72%, respectively (Table , entries 2 and 3), providing further evidence of the versatility of these two PCs. Hydrogen atom transfer (HAT) catalysts are also commonly partnered with photocatalysts and have been used for dehalogenation reactions. A recent example, reported by Constantin et al., used the alkyl radicals generated after the reductive quenching between PC* and triethylamine to abstract iodine atoms from alkyl iodides 11 to generate alkyl radicals that typically would require a far more potent reductant (Ered(R-I) < -2 V). These alkyl radicals can then be trapped by a thiol HAT catalyst to generate the dehalogenation products 12 (Table ). Under the literature conditions using 4CzIPN, an 85% yield of 12 was obtained (Table , entry 1). Both DiKTa and Mes3DiKTa were able to achieve comparable average yields of 88% and 86%, respectively (Table , entries 2 and 3). Reaction Profile and Rates Analysis. Reactions in the previous sections have used the yield of the reaction after a given time to compare the efficiency of the PCs. While useful, this provides an incomplete picture of these reaction processes as it does not allow comparison of relative rates of product formation. This prompted an investigation into the reaction kinetics of the PCs for a model transformation, with the ATRA reaction between 4a and 5 shown in Table chosen. Inspired by Yi et al. in situ NMR was used to monitor the generation of product employing each of the PCs (Figure ).
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Notably, using this experimental set-up, the reaction reached completion for all three PCs in less than 3 hours, significantly faster than using a photoreactor, presumably due to more efficient irradiation within the in situ NMR set-up. Furthermore, when catalysed by Mes3DiKTa or DiKTa the rate of product formation is significantly enhanced than with 4CzIPN. To quantify these differences, initial rates of the reaction with each photocatalyst were calculated and compared, with the use of DiKTa giving a slightly larger initial rate (5 x 10 -4 M s -1 ) than Mes3DiKTa (3.7 x 10 -4 M s -1 ), but with both an order of magnitude larger than that of 4CzIPN (0.6 x 10 -4 M s -1 ) (Table ).
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tetrads are formed by the self-association of four guanine residues in a square-planar arrangement, stabilized by Hoogsteen hydrogen bonding and coordination to a central metal cation. The folding of the oligonucleotide strand causes the stacking of these tetrads to form the G4 architecture (Figure ). The presence of G4 forming sequences in the human genome is well-documented and their transient formation in vivo has been linked to essential genomic functions, such as transcription, replication, repair, and telomere maintenance. For instance, G4s are overrepresented in the promoter regions of oncogenes (e.g. c-myc, BCL2 and c-kit ) and it has been proposed that targeting of the folded G4 with small molecules can inhibit the binding of transcription factors leading to downstream silencing of oncogene expression. More recently, putative G4-forming sequences in the genomes of the protazoan parasites Trypanosoma brucei and Leishmania major have been reported, and bacteria (Escherichia coli, Pseudomonas aeruginosa and Mycobacterium bovis). G4s are also found in viral genomes such as the human papilloma virus (HPV), herpes simplex virus-1 (HSV-1), Epstein-Barr virus (EBV) human and the immunodeficiency virus 1 (HIV-1). The selective targeting of G4s with small molecule ligands has revealed a variety of promising therapeutic effects, both in cellular models and in whole organisms. During the course of our studies of G-quadruplex binding ligands, we became interested in the potential of G-quadruplex DNA as a target for photoresponsive molecules, the structure of which may switched, either irreversibly or reversibly, by irradiation with light, thus providing a non-invasive means to modulate the DNA binding properties and downstream function of the molecule with an external trigger in a biological or materials chemistry context. Indeed, the reversible photoregulation of oligonucleotide structure and function offers exciting opportunities for the control of biological function and for the development of novel tools for chemical biology, nanotechnology, material sciences, pharmacology and medicine applications. The use of light as an external stimuli offers significant advantages over alternative chemical methods, since it can be delivered with high spatiotemporal precision allowing localized control of the therapeutic activity, minimizing potential off-target effects. Importantly, control of the DNA architecture through the use of a photoresponsive supramolecular guest species obviates the need to engineer the photoresponsive functionality into the biomolecule itself, which presents several synthetic and practical challenges towards the potential applications. Whilst several studies have already investigated the potential of photoresponsive molecules to control DNA structure, these generally focus on classical duplex DNA helices. Very significant progress has been made in this research area, and photoresponsive DNA binders based on a variety of scaffolds including azobenzene, stilbene and diarylethene derivatives have been reported. However, despite the unique opportunities afforded by targeting G4 structures specifically, given their unique polymorphic nature, and their relevance in biological systems and materials chemistry, the development of photoresponsive G4 binding molecules has received little attention until recently. Figure . Regulation of G4 structures using photoresponsive ligands Towards the development of such photoresponsive G4 ligands, Wang and co-workers disclosed an azobenzene derivative that was able to reversible regulate G4 formation and dissociation in buffered aqueous conditions in the absence of metal cations (Figure ). However, the system proved ineffective in physiological conditions of high ionic strength.
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Though the reasons were not fully elicited, we suspect that that the inherent flexibility of the azobenzene core, particularly the free rotation possible about the C-N bonds, weakened the ability of this scaffold to serve as a G4 ligand. Indeed, in a related study by Zhou and workers, similar azobenzene derivatives displayed only weak G4 binding properties in physiologicallyrelevant conditions. In general, the most successful G4 binding molecules are derived from highly rigid scaffolds that allow efficient π-π stacking interactions with the planar G-tetrads.
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Our recent efforts to develop photoresponsive G4 ligands found that a highly rigid bispyridinium stiff-stilbene E-II (Figure ), was a very efficient G-quadruplex binder in the planar E-configuration even in physiologically-relevant conditions of high ionic strength and inactive in the bent Z-configuration. Ligand E-II was able to fuel the reversible unfolding of G4 DNA under Na + -rich conditions, thus enabling a way to control G4 topology on demand using light an external stimulus. A key drawback of the system, however, was that in aqueous conditions the oxidative fragmentation of the stiff-stilbene core rendered the phototriggered process irreversible, and thus repeated additions of the ligand were required in order to fuel multiple switching cycles of DNA topology. Subsequently, we found that dithienylethene derivatives o-/c-IV display excellent photochromic properties and switchable binding modes towards G4 DNA by toggling the ligand between the open and closed forms with photoirradiation, although the change in binding mode did deliver the significant change in binding affinity that is likely necessary to realise the majority of potential applications. In light of the results of the aforementioned studies, we reasoned that the fully reversible switching of G4 ligand binding in physiological conditions required a chemotype that combined the rigidity of the stiff-stilbene scaffold with the photostability of the azobenzene chromophore. Recently, cyclic bridged azobenzene derivatives have been investigated by Zeller, Herges, Temps and co-workers, and later by Trauner and colleagues. These derivatives display excellent photophysical properties and prove to be photoswitchable over many switching cycles without photofatigue. Unlike the most commonly employed photochromic azobenzenes, which are thermodynamically more stable in their elongated transform, cyclic azobenzene photoswitches feature the diazene motif constrained within an eightmembered ring, and are thermodynamically more stable in their "bent" cis form, where the ring adopts a relaxed confirmation, rather than the unusual sterically-demanding twisted conformation observed in the trans state. Depending on the substitution pattern and electronic nature of the substituents, the thermal back-isomerization from the trans to the cis can vary from nanoseconds to days under physiological conditions. These photoswitches have recently emerged as promising motifs to be incorporated into a range of photopharmaceuticals including into oligonucleotides for the photo-regulation of DNA hybridization. However, the use of the cyclic azobenzene fragment as the basis DNAtargeting small molecules has not yet been explored. In the context of our work, we were very curious to investigate the binding of trans and cis bridged azobenzene derivatives to DNA structures, particularly G4s, for several reasons. Firstly, the high photostability of the scaffold coupled with its increased rigidity (compared to its 'free' azobenzene analogue) appeared to combine the best features of the photoresponsive G4 ligands developed to date. Moreover, the very unusual, twisted, geometry of the trans form of the scaffold represents an exceptionally unique chemotype for DNA recognition: of the hundreds of G-quadruplex ligands reported to date, to the best of our knowledge there is no example of a G4 binding fragment that possesses this type of molecular geometry.
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HIV-1 is an etiologic agent of the acquired immunodeficiency syndrome (AIDS) that belongs to the retroviridae viral family which is responsible for one the greatest human health crises of the 20 th century. The development of effective antiviral treatments is of utmost importance. In this context, the presence of several G4 motifs in the U3 promoter region of the HIV-1 long terminal repeat (LTR), in both the viral and proviral genome, have been reported and it has been hypothesized that targeting these dynamic G4 sequences with small molecules can lead to the regulation of viral transcription, which in turn will result in decreased viral production. However, despite its significance, there are relatively few examples of small molecules that can selectively target viral G4 sequences including HIV-1. 2 Results
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We began our study by synthesising cyclic azobenzene ligand (Z)-1 (Scheme 1), the design of which was informed from our previous studies of N-methylated pyridinium compounds as photoresponsive G4-binding ligands. (Z)-2, 9-dibromo-11,12dihydrodibenzo[c,g][1,2]diazocine 2 was prepared using an established procedure with minor modifications. Briefly, Suzuki coupling of 4-pyridinylboronic acid with the bis-brominated cyclic azobenzene 2 afforded compound 3 in 99% yield. Finally, alkylation with iodomethane provided the target compound (Z)-1 in excellent yield of 75%. All compounds were completely characterized by using standard spectroscopic and analytical techniques (ESI).
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With ligand (Z)-1 in hand, we initially focussed our efforts on evaluating its photophysical properties. In particular, the nature of the cationic N-methylated pyridinium groups on the photochemistry of the cyclic azobenzene was unknown, and our previous studies have demonstrated this moiety can significantly affect the photochemistry of conjugated chromophores by virtue of its strongly inductive and mesomeric electron withdrawing properties. In conditions relevant to G4 folding (namely 100 mM potassium phosphate buffer, pH 7.4), the thermodynamically-stable Z isomer exhibits a π-π* absorbance band at 394 nm (compared to 404 nm in the corresponding unsubstituted cyclic azobenzene). Upon irradiation close to this maximum (λ = 405 nm), we observed rapid spectral changes (reaching a photostationary state after approximately 4.5 minutes, Krel = (15.37 ± 0.43)x10 -3 s -1 ) namely a decrease in absorbance at 400 nm and the emergence of a red-shifted absorbance band at 480 nm, corresponding to the n-π* transition of the E isomer (Figure ).
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Next, we investigated the reversibility of the system under both photochemical and thermal (in the dark) conditions. The relative rates of isomerisation under otherwise comparable experimental conditions are summarised in Figure . The initial Z state of the molecule was recovered both under photochemical (λirr = 520 nm) and thermal conditions, although the back-isomerisation is significantly slower under thermal conditions. In fact, the half-lives followed a first-order rate decay, and were 42 s and 5.4 min under photochemical and thermal (in the dark) conditions, respectively. Finally, we examined the photostability of the system over 14 switches between Z and E, by alternately irradiating the system with blue light (λ = 405 nm) and green light (λ = 520 nm). As showing in Figure , the isosbestic points are preserved across throughout the experiment and the respective UV/Visible spectra are perfectly superimposable, indicating no photodecomposition under the reaction conditions. [Ligand] = 100 µM, 100 mM potassium phosphate buffer (pH 7.4).
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Having demonstrated the robust and reversible photoisomerization of ligand 1 under conditions relevant to G4 DNA folding, we turned our attention to a proof-of-concept experiment that would provide an initial indication of its suitability as a photoresponsive G4 ligand. In order to benchmark the new ligand against our previously reported photoresponsive derivatives, we initially studied the binding to the human telomeric G4 sequence in potassium buffer (telo23-K + ). UV/Visible titrations studies revealed an association constant (Ka) of 2.07
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x 10 5 M -1 for the E isomer, whilst the affinity of the Z isomer for the same G4 was 25-fold lower, Ka = 0.08 x 10 5 M -1 (Figure ). Whilst the affinity of the active E isomer 1 is lower than for the stiff-stilbene analogue (Ka = 25 and 0.1 x 10 5 M -1 for E and Z isomers, respectively)
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and the difference in activity between E/Z 1 (25-fold), it must be noted that in the case of the cyclic azobenzene derivatives, the ligand can be switched reversibly under the experimental conditions (by alternative irradiation with blue and green visible light) whilst the stilbene derivatives both photofragment under UV-light (λ = 405 nm) leading to an irreversible process. Thus the azobenzene scaffold represents a significant improvement over the first generation scaffold.
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Following this proof-of-concept, we extended the study to investigate a more complex G4 DNA model. Elegant structural work from Phan, Ritcher et al. reported the distinctive structural features of LTR-III, which is the major G-quadruplex conformation observed in vitro of all the G-quadruplexes formed in the HIV-1 LTR sequence. Their NMR studies of LTR-III in K + solution revealed the formation of a unique quadruplex-duplex hybrid consisting of a three-layer (3 + 1) G4 scaffold, a 12-nt diagonal loop containing a conserved duplex-stem, a 3nt lateral loop, a 1-nt propeller loop, and a V-shaped loop. The team proposed this unique quadruplex-duplex junction as potential druggable target and we considered it worthy of investigation as a potential candidate for targeting with a photoresponsive G4 ligand.
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M -1 ). This difference in DNA binding activity between two photoisomers of the same compound is, to the best of our knowledge, significantly higher than those previously reported to date. Moreover, (E)-1 showed hypochromic and bathochromic shifts upon ligand binding, suggesting end-stacking ligand binding modes, where the energy of the π-π* transition responsible for the Soret band is lowered by the interactions of the ligand chromophores with the G-tetrad. Figure . a) UV/visible titration studies of (Z)-1 (right) and (E)-1 (left) with LTR-III (K + ) and b) binding isotherms.
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Based on the superior results observed for the LTR-III G4 in the UV/Visible titration studies, we chose to investigate the binding of (E)-and (Z)-1 to this DNA sequence in greater detail using a battery of structural techniques, namely 1 H NMR spectroscopy, circular dichroism spectroscopy and enhanced molecular dynamics simulations. Previous work by our group has identified that this combination of theoretical and experimental approaches is wellsuited to understanding the different binding modes of G4 DNA targeting molecules. Moreover, unlike the UV/Visible titrations which required isomerisation of the ligand before the experiments, these additional studies also allowed us to confirm the DNA-binding properties of our ligand could be controlled reversibly with photoisomerization taking place in situ.
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Under the experimental conditions reported by Phan and co-workers, the formation of the duplex/G4 hybrid is observed by two positive CD signals at 269 and 285 nm. Based on previous investigations, it is likely that the duplex stem contributes the signal at ~270 nm, whilst the G4 structure contributes the signal at ~290 nm. A strong negative band at 240 nm is also observed, another common spectral feature of G4 DNA secondary structures. Upon titrating the DNA structure with the inactive Z ligand, virtually no changes in the CD signal are observed, either in the DNA spectral region (λ < 320 nm) or in the ligand-only region (λ > 320 nm) where certain binding modes may be evidenced by the appearance of an induced CD in the achiral ligand upon binding to the chiral DNA structure (Figure ). n the case of the active E ligand however, a strikingly different behaviour is observed (Figure ). As the ligand concentration is increased, a hyperchromic shift in the positive CD signal of the DNA structure is clearly observed, and a strong CD signal is induced into the ligand (specifically, a negative band at λ = 330 nm and a positive band at λ = 480 nm). This provides compelling evidence for the association of the ligand with the achiral DNA and, together, the CD results observed for the Z and E isomers support the results of the UV/Visible titration studies that indicate the large difference in affinity of the two photoisomers for the DNA structure. Importantly, we found that the ligand binding and dissociation from the LTR-III G4 could be controlled reversibly by alternate irradiation with blue light (λ = 405 nm) and green light (λ = 520 nm) with no evidence of photofatigue after seven switches, and no disruption of the overall DNA structure was observed (Figure ). Moreover, in agreement with the preliminary experiments that demonstrated the back-isomerisation of E to Z, we observed the dissociation of the ligand from the DNA structure under dark conditions triggered by the reversion of the active E isomer to the inactive Z form (Figure ). These results are significant, as they demonstrate the presence of the DNA structure does not adversely affect the photochemical properties of the ligand and that its activity can be controlled in situ. ligand. However, more importantly, the E ligand, active in binding to the G4 structure, show no apparent binding to the duplex structure. Only a very modest hypochromicity in the DNA bands is observed, possibly due to non-specific binding. Moreover, in agreement with the preliminary experiments that demonstrated the thermal back-isomerisation of the ligand, we observed the dissociation of the ligand from the DNA structure under thermal conditions, demonstrating the presence of the DNA does not affect the electrostatic interactions, and no induced CD signal in the ligand region is seen, suggesting the lack of affinity of the ligand for the double-stranded structure. It should be noted that the appearance of induced CD signals is strongly dependent on the ligand binding mode to the chiral molecule and, as such, the absence of such an effect does not unequivocally rule-out the formation of a complex. Nonetheless, NMR experiments (vide infra) provided further evidence to support the ability of the E isomer to target the G4 region of the DNA structure.
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To further probe the different binding properties of E and Z isomers, we turned to 1 H NMR spectroscopy to obtain more detailed structural information about the binding interactions. Owing to the fast thermal relaxation of the active E form, it was not possible to study the binding by NMR at ambient temperature, because the ligand reverts to the inactive Z form too quickly on the timescale of the NMR experiment. Therefore, we studied the ligand binding at lower temperature (5 °C) in order to discriminate the different binding properties of the two isomers. In each case, ligand aliquots were added and the spectral changes of the G4
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ligand. This behaviour reflects slow-to-medium exchange on the NMR timescale, indicative of a strong binding event where the dissociation rate of the complex is slow in comparison to the difference in frequencies between the free and bound resonances. ligand. These results demonstrate that in the planar E form, the ligand is able to efficiently stack with the top G-tetrad, between the G4/duplex junction, whilst it does not have strong affinity for the lower G-tetrad.
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bases. Generally, and as can be seen in Figure , the G-quadruplex region remains stable in all systems except for the model2-E(1) complex. In the model2-E(1) complex, G28 underwent a structure change and moved way from G17, G21, and G25, thus disrupting the hoogsteen base pairs which lead to the increase in the RMSD observed in Figure . The RMSD profiles for the whole DNA segment are higher than the G-quadruplex region, thus highlighting the highly flexible nature of the duplex region (Figure ).
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The time evolution of the RMSD for the (E)-1 and (Z)-1 ligands was also determined to evaluate the stability of the lowest energy binding pose identified from docking (Figures and). The ligand's RMSD is a commonly used feature for comparing different ligand conformations. Although simple, this metric is an very informative way to measure the quality of a known binding pose by comparing the conformations adopted in the MD simulations with a reference binding mode (in this case, the lowest energy binding mode determined by AutoDock Vina). As can be seen in Figure , the comparison of the (E)-1 and
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(Z)-1 RMSD for all ten models clearly shows that in general the (E)-1 and (Z)-1 conformations remain relatively close to their initial binding poses. A diversity of behaviours can be observed for the different (E)-1 and (Z)-1 complexes during the simulations (Figure ). In in some cases, (Z)-1 binding to the DNA is very stable with its binding mode staying close to the initial one whereas in others, the oposite behaviour is observed with (E)-1
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Interestingly, in all models, (Z)-1 and (E)-1 remained bound to the region located above the top G-quadruplex plane (formed by G2, G15, G19 and G26). While (E)-1 was located nearer to the duplex region, (Z)-1 adjusted its position to get closer to the duplex-quadruplex junction (even embeding itselve into that junction in some of the simulations) (Figures S10 and S11). This observation may suggest that the (E)-1 binds preferentially at the junction part whereas (Z)-1 favors the duplex part, which seems to be in accordance with the NMR observations.
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We demonstrated the robust and fully reversible photoisomerization of the diazocine ligand under high cationic conditions and show a >50-fold difference between the E and Z isomers as determined by UV/Vis and CD titration studies. CD experiments further demonstrated that the ligand binding and dissociation from the LTR-III G4 can be controlled reversibly by alternate irradiation with blue light (λ = 405 nm) and green light (λ = 520 nm). Further evidence of the differential behaviour between the E-and Z-isomers was obtained by 1 H-NMR studies in combination with molecular dynamic calculations. These experiments suggest the (E)-ligand binds preferentially at the G4/duplex junction of the LTR-III sequence, whereas the (Z)-isomer favors the duplex region. Our results demonstrate that the conformational switch of the ligand by an external stimuli such as light can be used to control binding affinity and mode of binding in a fully reversible manner, without the need to pre-incorporate photoresponsive functionality in the biomolecule. Further investigations into the activity and application of these type of G4 ligands are already underway and will be reported in due course.
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The goal of this work is to open new possibilities for rationalizing charge transfer, by practically connecting the chemical potential to reinterpretations of well-established chemical and physical concepts. To do so, we describe a theory that explicitly links one set of definitions of electronegativity and chemical hardness, to the chemical potential and the Fermi energy of molecular and condensed phase systems. Detailed definitions of these concepts and other factors will be introduced gradually during the discussion.
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Since Pauling formalized the idea in 1932, electronegativity has grown into a useful tool for rationalizing trends in charge transfer, bond polarity, bond strength, reactivity, and various chemical properties. Electronegativity is a simple and intuitive concept; in that it quantifies the ability of atoms (or groups of atoms) to attract (or hold on to) electrons. Over time, many different electronegativity scales have been proposed, each attempting to tie this chemical concept to different physical properties, typically including ionization energies, electron affinities and other spectroscopical properties of valence electrons. Some electronegativity scales are based on physical properties of bonded atoms, such as the Pauling or Walsh scales, while other are defined from properties of isolated atoms, such as the Mulliken, Allred & Rochow and Allen scales. A particular challenge with electronegativity is to reconcile its many definitions with its common practice and resulting chemical predictions (and failed predictions). How electronegativity changes upon bond formation is, consequently, a long debated topic. A well-known postulate by Sanderson states that electronegativity of atoms in molecules should equal the mean of the values for the isolated atoms. In other words, the electronegativity of isolated atoms are postulated to equalizes when bonded together inside molecules or materials. Sanderson's idea was supported by Parr and coworkers, who defined electronegativity as the negative of the chemical potential, in turn a homogeneous value across any system in equilibrium. Chemical potentials determine where electrons flow. Nevertheless, alternative viewpoints on electronegativity equalization have been voiced by several. One of the critiques to Sanderson's postulate is rooted in the chemical expectation that electronegativity should reflect how the nature of atoms differs, even when they are bonded in a material. Equalization requires all atoms to adopt the same electronegativity within a molecule, regardless of the element. A related objection is that Sanderson's postulate requires electronegativity to be defined as the chemical potential. In other words, Sanderson's postulate excludes a host of electronegativity definitions, many of which are by their own right useful. Many opposing viewpoints on electronegativity have merit but it is outside our scope to weigh them. We stress that this work is not intended as a critique of related theories and methods that can provide chemical insight (e.g., Refs. 50-62). Rather, we aim to develop a complementary perspective.
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and electronegativity attributed to the average valence electron energy, 𝜒 #$% . This definition is inspired by, but not equal to, that of Allen, and has allowed for the compilation of an extensive ground state (T → 0K) scale of the electronegativity of atoms. This scale has been productively used in the literature, for example to rationalize trends in intermetallic compounds. . It has also been extended to high pressure conditions, allowing for the successful rationalization of unexpected phenomena, such as redox inversion in nitric sulfur hydrides. How to formally separate core from valence in eq. ( ) is not always obvious. However, such choices do not influence the validity of our following arguments and results. We refer to previous work for a detailed discussion on what constitutes a valence level, and for a comparison with the Allen electronegativity scale. We note that both Allen's and our preferred scale of electronegativity are related to the average local ionization energy that have been extensively studied by Politzer and coworkers. The average electron energy is also related to the theory of moments of the electronic energy distribution, useful for rationalizing structure in extended systems. Our choice for defining electronegativity allows us to connect this central chemical concept to the total energy of a system,
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| 3 |
In eq. ( ) 𝑉 )) and 𝐸 !! are the electrostatic repulsions between nuclei and electrons, respectively. Equation ( ) is exact within the Born-Oppenheimer approximation, and all its terms can be evaluated quantum-mechanically, at various levels of theory, as well as be estimated experimentally through a combination of techniques. For example, the value of 𝜒 #$% can be experimentally estimated as an average of photoionization energies of valence levels, or be approximated by averaging the energy of occupied valence orbitals. Because of the possibility of interchangeable use of both experimental and computed data, we refer to eq. ( ) as an Experimental Quantum Chemistry (EQC) energy decomposition scheme. There is no unique way to decompose energies and several other elegant methods exist to do so (e.g., see Refs. 78-101). EQC energy terms have been successfully used to, for example, classify chemical bonds in diatomic molecules and small hydroxides, 102 for distinguishing red-and blue-shifted hydrogen bonds, 103 and for estimating substituent effects in benzoic acids. In what follows, we develop upon the EQC framework to address its relationship with the chemical potential. As we do so, we will prove why, with our definition, electronegativity equilibrates within molecules rather than equalizes. We begin by exploring an expression of the chemical potential that connects to the notion of electronegativity in a new way.
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In eq. ( ), n is the number of particles, T is the temperature, p is the pressure and 7𝑅 *+ 9 are the internal coordinates that define the geometry. The subscript in eq. ( ) indicates that we consider 𝐺 as being differentiated at constant temperature, pressure and system geometry. The symbol 〈… 〉 represent ensemble averaging. The theory to be described will consider a grand canonical (𝜇𝑉𝑇) ensemble. Equilibrium in such an ensemble means that each system has reached the same chemical potential, temperature and volume. In other words, the free energy is at a minimum. Figure illustrates an example of an n-electron system surrounded by an environment that acts as an infinite electron reservoir with which the system can exchange electrons. A large collection of such open systems, all in equilibrium with a reservoir, is, by definition, a grand canonical ensemble. What is the connection between eq. ( ) and electronegativity? With the help of eq. ( ), the Gibbs free energy can be expressed within EQC as,
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Furthermore, we can assume that a system shares electrons with its environment exclusively via valence levels. The population of core levels are then a constant in the ensemble. We note that this is a chemically motivated definition of what constitutes a core level: a level that cannot, in chemical interactions, share electrons with a surrounding environment. From such a definition follows that
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, describes how the electronegativity (the average energy of valence electrons) of a system change as a function of its electronic population. The larger this derivative is, the larger impact does a change in the electron density have on the electronic potential of that system. The 8〈= *+, 〉 <〈-〉 term will be important when we return to discuss chemical hardness in the context of EQC. The third term,
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6297c4d56057b176fe8dd9dd
| 7 |
is related to the shift of core levels upon ionization of a system. Core electrons arguably have no direct role in chemical bonding. However, this third term formalizes how the movement of core levels relate to the chemical potential, which, in turn, can change over any transformation. The last term of eq. ( ),
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| 8 |
Table shows a test of eq. ( ) in which we have calculated 𝜇, and each of its components, for all atoms of the first three rows of the periodic table . In these examples, 𝜒 is approximated as the average energy of occupied Kohn-Sham (KS) orbitals, while the derivatives in eq. ( ) are evaluated through a finite-difference approximation (see the computational details section). The results of eq. ( ) agree near perfectly with the in-practice definition of the Fermi level in computational physics and chemistry: the average energy of the highest occupied and lowest unoccupied (HOMO and LUMO) orbitals. This agreement is significant because the terms of eq. ( ) are all evaluated from occupied electronic states, avoiding the use of virtual orbitals. The root mean square deviation between these two options for estimating 𝜇, or 𝜀 @ , is 0.06 eV.
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in eq. ( ) reminds us of another textbook concept in chemistry: chemical hardness. This concept was proposed by Pearson in 1963 as an integral part of his hard and soft acids and bases (HSAB) theory. Together with Parr, Pearson later gave a quantitative definition, which became part of the conceptual density functional theory (CDFT) framework. Within CDFT, chemical hardness is defined as the negative of the derivative of electronegativity with respect to electron population. Since then, HSAB theory has been proven a useful tool in several chemical applications. What is the physical interpretation of chemical hardness ? Table . Components of the chemical potential 𝜇, evaluated for atoms in the first three rows of the periodic table. Values of 𝜇 are calculated via eq. ( ). Shown for comparison is the Fermi energy 𝜀 @ , evaluated as the average of occupied and unoccupied orbital energies. In the HSAB theory and CDFT, the hardness of a system, be it an atom, a molecule or an ion, has a well-established inverse cube root relationship to polarizability. Figure demonstrates that the exact same proportionality holds true between atomic polarizability and the negative of the 8〈= *+, 〉 <〈-〉 term in eq. ( ). The correlation is remarkably strong across atoms and a selection of alkali and alkaline-earth cations and halide anions (r 2 = 0.99). The relationship shown in Figure motivates us to define chemical hardness (within the EQC framework) as:
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Because this definition of chemical hardness shows the same proportionality to polarizability as the Parr-Pearson chemical hardness, the two definitions are indistinguishable on a practical level. On a conceptual level, chemical hardness now shares a common definition in both EQC and CDFT, i.e., as the negative derivative of electronegativity. There is a close analogy in the physical meaning of the two definitions: in both cases hardness represents a resistance of the chemical potential to changes in the number of electrons. 107-109 One fundamental difference is that in CDFT hardness is also the derivative of the chemical potential. As we will show next, analogies between the two frameworks, EQC and CDFT, go beyond the concept of chemical hardness.
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where E and n are the DFT energy and number of electrons, respectively, and v is the external potential that uniquely defines the electron density of a system. The electronegativity scale defined by eq. ( ) was first proposed by Iczkowski and Margrave, and it implies Sanderson's equalization. Because the chemical potential is homogenous throughout a system at equilibrium, all atoms in such a system will, by the CDFT definition, have equal electronegativity. A well-known approximation to this electronegativity is the Mulliken scale, χ I , which can be obtained by a finite-difference approach. The Mulliken electronegativity can be expressed in DFT terms as:
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| 12 |
In eq. ( ) I, A, µ, and F are the ionization potential, electron affinity, chemical potential and the universal DFT functional, respectively. Δρ C and Δρ K represent changes in electron density when losing or gaining an electron, respectively. Higher order terms in eq. ( ), and following equations in this section, are not relevant for the discussion and will be omitted. Note that eq. ( ) expresses χ I as a function of the chemical potential. CDFT hardness also has a well-known approximation (the Parr-Pearson hardness, η T ), obtainable by finite-differences:
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Equation ( ) is an alternative expression for the CDFT chemical potential. However, we stress that χ I and η T are only approximations to the CDFT electronegativity and chemical hardness. With this consideration in mind, we can point to term-by-term analogies between our EQC-derived eq. ( ) and eq. ( ). In both equations, the first term corresponds to electronegativity and the second term relates to chemical hardness (although in eq. ( ), the second term also contains the number of valence electrons). The last term of both equations relates to changes in the electron-electron interactions: one of the principal components of the universal functional F[ρ] is the electron repulsion energy, as stated by Parr. One noticeable difference between the EQC chemical potential, eq. ( ), and the CDFT chemical potential, eq. ( ), is that the former includes a term accounting explicitly for the role of core electrons. We stress that these analogies should only be considered qualitative in nature. Because the definition of electronegativity and hardness differs between the EQC and CDFT frameworks, there is no formal correspondence between the right-hand side terms of Eq. ( ) and ( ). However, the chemical potential links the two equations, and we note that both definitions of electronegativity and hardness provide values of comparable magnitude (see Table
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| 14 |
We emphasize that our comparison with CDFT is not meant as a critique of the latter, but the contrary. By building bridges between theoretical frameworks, and highlighting commonality and complementarity of different perspectives, we become better equipped to analyzing and understanding electronic structure and chemical transformations. A notable merit of the CDFT framework is the establishment of a series of electronic structure principles connected to reactivity, such as the "|Δµ| big is good" rule 121,122 and the principle of maximum hardness. 123,124 A detailed discussion of these principles within the EQC framework is beyond the scope of this work. However, we note that any principle based on the chemical potential will remain valid within EQC, even as a given value may find a complementary interpretation through Eq. ( ) or (9). The principle of maximum hardness is likely to remain valid in EQC. We postulate this as both the EQC and CDFT definitions of chemical hardness result in strong connections to polarizability, and because the response to electronic perturbations is invariably linked to the HOMO orbital.
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Moving away from global quantities that describe a system as a whole, we next consider atomic properties. As we do so, we change our point of view to consider each atom within a molecule, crystal, or any material, as a sub-system. Atomic quantities can be defined similarly, as an ensemble of single atoms, while the rest of the system becomes part the of the environment (Right Panel).
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For each atomic sub-system, the rest of the molecule can be treated as the environment with which the atom exchanges electrons. In this perspective, each atom is represented by a grand canonical ensemble in chemical and thermal contact with the ensembles representing the other bonded atoms. Upon equilibration, the chemical potential of such atomic ensembles will be equal, which allows their combination into a larger molecular ensemble, i.e., the general case we discussed previously.
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To consider molecules as comprising of different fragments is common practice in chemistry. However, there is no unique way to quantum mechanically do so. In principle, the framework we propose herein can make use of any partitioning method, regardless if they are, for example, based on topological analysis of electron densities, or population analysis of wavefunctions. By partitioning into atoms, we can recast the Gibbs free energy expression of a molecule, eq. ( ), as a function of atomic electronegativities:
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| 18 |
In eq. ( ), n L is the electronic population of an atom A, and the subscript {n [ } [dL means that G is differentiated at constant populations for all atoms except A. Note that this atomic chemical potential has the same functional form as the macroscopic chemical potential of a component in a multi-component mixture. However, here n L is the number of electrons attributed to atom A, while in a macroscopic system n L would represent the number of particles of component A in a mixture. Following the same reasoning illustrated before for an ensemble of n-electron molecular systems (see eq. ( )), we can express the atomic chemical potential as:
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| 19 |
where δ [L is either 0 or 1 depending on whether α ≠ A or α = A, respectively. We also know that <〈e HH 〉 <〈E B 〉 = 0. Finally, for the in vacuo zero-temperature limit of µ L the terms <f IJGFK56 <〈E B 〉 and <〈Y〉e <〈E B 〉 are negligible. We can then simplify eq. ( ):
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| 20 |
Equation ( ) shows how the chemical potential of an atom A, in a molecular environment, is a function of its electronegativity. Note that the label A marks the specific atom for which the chemical potential µ L is evaluated, while the index α runs over all atoms in the molecule. At face value, eq. ( ) looks similar to eq. ( ). However, the latter describes the properties of the whole system, with no external forces influencing its chemical potential. In contrast, eq. ( ) makes explicit the connection between the electronegativity and the chemical potential of an atom within a molecular environment. Expressing chemical potentials of atoms as in eq. ( ) provides a perspective closely related to the well-known example of a junction between p-and n-type semiconductors. When two different semiconductors are put in contact, electrons flow from a higher chemical potential to a lower one. In a p-n junction, the chemical potential is homogeneous at equilibrium. However, each side of the junction is still expressed as a sum of two inhomogeneous quantities. One is a local potential, which relates to the type of the semiconductor. The second is an external electrostatic potential, which arises from inhomogeneous doping of the two semiconductors. We argue that the flow of electrons between bonded atoms can be described in similar terms, by the chemical potentials provided by eq. ( ).
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| 21 |
When bonds are formed, electron density is redistributed among atoms so to minimize the Gibbs energy, i.e., dG = 0. Equation (15) shows the Gibbs energy of a system as a function of temperature, pressure, atomic populations, and its geometry. If we consider a bonding process at constant temperature and pressure, the total differential of that energy can be expressed as:
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| 22 |
Borrowing a perspective from Marcus theory, 130 the change in populations -at fixed geometry -is the proper reaction coordinate of an electron transfer (ET) process. The first term on the right-hand side of eq. ( ) corresponds to the change in energy along this ideal ET reaction coordinate. Conversely, the last term of eq. ( ) captures the response of Gibbs free energy to changes in nuclear geometry. In DFT terminology, this last term is the energy response due to a change in the external potential. The different 2 <g <〈Z :; 〉 6 <,=,{?:} terms relate directly to Hellman-Feynman forces, i.e., the forces experienced by nuclei in a molecule. We note that Averill and Painter have studied and named similar terms "dynamic orbital forces". In a similar fashion to eq. ( ), we next outline an EQC expression of 2 <g <〈Z :; 〉 6 <,=,{?:} for any given pair of atoms: 20) where 𝛼 and 𝛽 denote a specific pair of atoms, while 𝛾 runs over all atoms. Equation (20) tells us that the forces experienced by nuclei are mainly influenced by two factors: (1) how energies of electronic levels shift because of nuclear movement, and (2) the changing balance between electrostatic repulsions (nuclear-nuclear and electron-electron).
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where 𝛼, 𝛽 and 𝛾 run over all atoms. Note how the chemical potential of each atom contains sums over all atoms when expressed in eq. (18). Summing over the chemical potential for all atoms in eq. ( ) consequently result in a double summation in eq. ( ). Similarly, the sum over all atoms in eq. ( ) results into the triple summations in eq. (21).
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Equation describes energy changes in any chemical process. For example, when integrated over a chemical reaction eq. ( ) allows the study of how individual atomic energy contributions evolve. We focus on the conceptual meaning of the first right-hand side term of eq. ( ) in what follows but remind that the second term relates to chemical hardness. The quantification of all these terms is possible through different methods (e.g., see Ref. 133) and we will return to discuss their physical rationale and implications in detail, in future work.
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When dG equals zero, eq. ( ) represents the equilibrium condition between atoms exchanging electrons within a molecule, or any other material. In such a case, the first right-hand side term of eq. ( ) corresponds to an electronegativity difference. To see why, we look at the example of a heteronuclear diatomic molecule AB. In such a molecule, the change in electron population of one atom (relative to the isolated atom) must perfectly equal that of the other atom, but with reversed sign, i.e., d〈n L 〉 = -d〈n k 〉. It then follows that ∑ 𝑞 ! 〈χ *,FGH 〉d〈n [ 〉 [ is exactly the difference in electronegativity between the two atoms in the molecule, 〈χ l,FGH 〉 -〈χ m,FGH 〉. Equation ( ) explains why differences in electronegativity between non-equivalent atoms (or fragments) are expected to persist at equilibrium. Atomic electronegativities (of the sort we investigate c.f., eqs. ( ) and ( )) can equalize only in special cases where contributions from hardness, core shifts and electrostatic repulsions cancel out. Equation (22) therefore formalizes the concept of electronegativity equilibration and explains why equalization of electronegativity is not strictly necessary.
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Independently of its precise definition, electronegativity is a powerful concept for quickly predicting the direction of charge transfer and bond polarity. But even so, we know that trends in this atomic property can disagree with a range of observables, such as trends in bond energies, reactivity or stability. For example, the dipole moments in molecules such as CO, CS and BF are inverted relative to expectations from simple electronegativity arguments (these dipole moments can be explained in other ways). We believe this work constitutes an important step towards better understanding the occasional practical shortcomings of electronegativity.
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| 27 |
Chemical potentials are what ultimately determines where electrons move. In the theory we present, the chemical potential is expressed in terms of reinterpretations of several well-known chemical concepts and physical quantities, including electronegativity, chemical hardness, changes in electronic repulsions within a molecule, and the sensitivity of core levels to changes in the electron density. One effect formalized (but not explored in this work) is the effect of pressure on the chemical potential. Conditions of high pressure are likely to significantly affect equilibration of electronegativity in chemical reactions, as also suggested elsewhere. At the zero-temperature limit, an expression of the Fermi level emerges that, we think, helps to connect several central chemical concepts to a plethora of material properties, theories and phenomena predominantly explored in condensed matter physics.
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In this work, we make clear that with a definition of electronegativity as the average energy of valence electrons (a definition related but not equal to that of Allen ) we allow for a perspective in which atoms within molecules and materials can have different electronegativities. This premise is at odds with the electronegativity equalization postulate of Sanderson, which holds true only when electronegativity is defined as the negative of the chemical potential. Our analysis is enabled by the theoretical framework EQC, which is intended to encompass and connect useful concepts within theoretical chemistry and physics. Analogies and differences between EQC and CDFT are discussed, and we stress the complementarity of these two approaches.
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One motivation for EQC is to facilitate for the interchangeable use of theoretically and experimentally derived data when analyzing electronic structure. Several terms in our partitioning of the chemical potential, eq. ( ), can, in principle, be estimated experimentally. Valence and core levels can be probed by photoemission spectroscopies, and so should their sensitivity to electronic perturbations. For atomic quantities, a strict connection between theory and experiment becomes harder. Core energies can be probed selectively by X-ray spectroscopy in many instances. However, attributing experimental estimates of average binding energies of valence electrons to atoms inside molecules is challenging. Developments of the resonant inelastic X-ray scattering (RIXS) technique are encouraging, as it may allow for the probing of valence levels with atomic selectivity. We intend for the outlined theory to stimulate constructive discussion on the driving forces responsible for chemistry, and the limits of chemical rationales in chemistry at large.
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All DFT calculations were performed at the LC-BLYP/TZP level of theory, using ADF version 2021.207. The derivatives in eq. ( ) were evaluated through a finite-difference approximation, which relies on the computation of a fractional occupation number of the HOMO. The addition and removal of non-integer numbers of electrons (± 0.01 e -in this work) is a mathematical trick allowed by DFT. This approach can be regarded as a small perturbation to the electronic structure. Alternatively, in a statistical perspective, fractional HOMO occupations approximate the ionization of a small percentage of systems within an ensemble. All experimental values of atomic polarizabilities are from the CRC Handbook of Chemistry and Physics. PDC and NSC partially funded by the Swedish Research Council through grant agreement no. 2018-05973. We thank Alvaro Lobato Fernandez, Stefano Racioppi and Hilda Sandström for valuable discussions and comments.
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| 0 |
Molecular docking is a widely used for ligand discovery, both in industry and academia . The goal of docking is to predict the binding affinity and pose of small molecules in the binding site of a target protein. The method can screen libraries of billions of molecules and, unlike ligand-based methods, often discovers novel ligands entirely unrelated to those previously known . In some cases, docking can lead to the discovery of compounds in the sub-nM range , with some of these being active in vivo . However, compared to other techniques in computational biology, such as homology modeling and sequence database searching , docking as a procedure remains labor-intensive and intimidating to new users, thereby limiting its wider adoption and hindering its application on a proteomic scale. Docking software is typically complicated and comes with a steep learning curve, making it difficult to use to its full potential. This is especially true during the model optimization stage of the docking process, which involves fine-tuning numerous parameters of the model to improve its accuracy and reliability. It does not help that, even when performed by experts, docking can still sometimes fail to accurately reproduce experimentally determined binding characteristics for some targets. These liabilities have diminished the technique's overall impact, not only by deterring researchers coming from limited computational backgrounds, but also by making it arduous even for experienced computational researchers to deploy docking models at a large scale on the order of billions of molecules.
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| 1 |
Automating the several stages of the docking process all in a single pipeline could significantly reduce the need for expert involvement, which would enhance the accessibility of docking as a technology. An ideal pipeline would simplify the preparation of the docking model for those with less experience while still allowing experts the option to adjust the model as needed. Moreover, beyond merely create a docking model, an optimal pipeline would also optimize the model's parameters to ensure that its performance is at least comparable to that of a model produced by an expert provided the same initial data. For this to be possible, the pipeline must first be capable of evaluating the quality of candidate models. Typically, this evaluation is performed using retrospective docking . This method involves assessing a model's ability to (1) accurately predict the binding characteristics of known ligand structures, such as pose, and (2) consistently assign them more favorable docking scores compared to designated decoy molecules. These decoy molecules may be property-matched to the known ligands or selected by other methods .
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| 2 |
Several attempts have been made to automate some parts of the docking process over the past 14 years , a few of which have web interfaces . While many of these computational pipelines excel at automating the routine aspects of generating docking models, they usually lack the capability to integrate the nuanced practices of evaluation and optimization that experts commonly apply in the preparation of models for large-scale screening . As both evaluation and optimization are essential for developing models that can reliably distinguish between binding and non-binding compounds , integrating them into these pipelines represents a crucial milestone toward automating the specialized skills of docking experts.
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64ff1ea1b338ec988a49fb1a
| 3 |
Our work on automating the docking process began in 2009 with the introduction of the web-based tool DOCK Blaster . Although it successfully performed retrospective docking on thousands of targets, DOCK Blaster had noteworthy limitations. Notably, it lacked a framework for evaluating results, leaving it difficult to trust the predicted binding modes of resultant models without further assessment. Consequently, it was also unable to optimize the parameters of the DOCK scoring function, which estimates the binding affinity between a candidate molecule pose and the target protein. In effect, DOCK Blaster served merely as a prototype, composed of isolated scripts that made it fragile and difficult to maintain or develop further. In short, although DOCK Blaster demonstrated potential, its shortcomings highlighted the need for a more robust automated pipeline.
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64ff1ea1b338ec988a49fb1a
| 4 |
Given the mentioned limitations of existing methods, we focused our efforts on improving our own techniques to streamline the docking process. To that end, we rewrote the command-line tool for creating docking models, Blastermaster, making it more modular and feature-rich , and standardized and published our lab's docking protocol . Despite these advancements, expert supervision remained necessary for conducting model evaluation and optimization, and the absence of a web interface curtailed the potential for wider accessibility to these improvements.
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