| 1. |
- Caldararu, Octav, et al.
(författare)
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Are crystallographic : B-factors suitable for calculating protein conformational entropy?
- 2019
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Ingår i: Physical Chemistry Chemical Physics. - : Royal Society of Chemistry (RSC). - 1463-9076 .- 1463-9084. ; 21:33, s. 18149-18160
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Tidskriftsartikel (refereegranskat)abstract
- Conformational entropies are of great interest when studying the binding of small ligands to proteins or the interaction of proteins. Unfortunately, there are no experimental methods available to measure conformational entropies of all groups in a protein. Instead, they are normally estimated from molecular dynamics (MD) simulations, although such methods show problems with convergence and correlation of motions, and depend on the accuracy of the underlying potential-energy function. Crystallographic atomic displacement parameters (also known as B-factors) are available in all crystal structures and contain information about the atomic fluctuations, which can be converted to entropies. We have studied whether B-factors can be employed to extract conformational entropies for proteins by comparing such entropies to those measured by NMR relaxation experiments or obtained from MD simulations in solution or in the crystal. Unfortunately, our results show that B-factor entropies are unreliable, because they include the movement and rotation of the entire protein, they exclude correlation of the movements and they include contributions other than the fluctuations, e.g. static disorder, as well as errors in the model and the scattering factors. We have tried to reduce the first problem by employing translation-libration-screw refinement, the second by employing a description of the correlated movement from MD simulations, and the third by studying only the change in entropy when a pair of ligands binds to the same protein, thoroughly re-refining the structures in exactly the same way and using the same set of alternative conformations. However, the experimental B-factors seem to be incompatible with fluctuations from MD simulations and the precision is too poor to give any reliable entropies.
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| 2. |
- Caldararu, Octav, et al.
(författare)
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Binding free energies in the SAMPL5 octa-acid host–guest challenge calculated with DFT-D3 and CCSD(T)
- 2017
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 0920-654X .- 1573-4951. ; 31:1, s. 87-106
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Tidskriftsartikel (refereegranskat)abstract
- We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO–CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11–16 kJ/mol. DLPNO–CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum–mechanical methods.
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| 3. |
- Caldararu, Octav, et al.
(författare)
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Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods
- 2018
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 0920-654X .- 1573-4951. ; 32:10, s. 1027-1046
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Tidskriftsartikel (refereegranskat)abstract
- We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10–20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4–5.2 kJ/mol and a correlation coefficient (R2) of 0.77–0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD = 3–8 kJ/mol and R2 = 0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.
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| 4. |
- Caldararu, Octav
(författare)
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Bridging the gap between computational chemistry and macromolecular crystallography
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Knowledge of the atomic structure of biomolecules, such as proteins, is paramount to understanding their function and interactions in the human body. For example, knowledge of the atomic structure of a target protein is crucial for developing drugs that bind strongly to it and thus help cure diverse diseases.Macromolecular crystallography is the forefront method for determining the atomic structure of proteins, especially through X-ray diffraction experiments. However, the data obtained from these experiments are not the atomic structure but need to be processed and interpreted before arriving at the individual positions of atoms in a protein. This intepretation is done through computational techniques that share some of the algorithms and problems with computational chemistry.In this thesis, we use several methods that combine computational chemistry and macromolecular crystallography for the study of multiple important proteins. Crystallographic refinement combined with quantum mechanical calculations (quantum refinement) is used to improve the X-ray structures of three metalloenzymes. Furthermore, a quantum refinement procedure for neutron structures is developed and applied to two important enzymes. We also investigate how to use and improve the existing information on dynamics from crystallography experiments. To this end, we test whether conformational entropy can be calculated directly from B-factors. Additionally, ensemble refinement is used to explore ligand dynamics in the binding site of galectin-3 and reveals hidden conformations that were not apparent in traditional crystallographic refinement methods. Finally, we study the modeling of water molecules in protein X-ray and neutron crystal structures. We show that molecular dynamics simulations can reproduce crystal water molecules, if protein movements are correctly taken into account. Moreover, we have developed a method to automatically improve the orientation of water molecules in neutron structures.
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| 5. |
- Caldararu, Octav, et al.
(författare)
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Exploring ligand dynamics in protein crystal structures with ensemble refinement
- 2021
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Ingår i: Acta Crystallographica Section D: Structural Biology. - 2059-7983. ; 77, s. 1099-1115
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Tidskriftsartikel (refereegranskat)abstract
- Understanding the dynamics of ligands bound to proteins is an important task in medicinal chemistry and drug design. However, the dominant technique for determining protein-ligand structures, X-ray crystallography, does not fully account for dynamics and cannot accurately describe the movements of ligands in protein binding sites. In this article, an alternative method, ensemble refinement, is used on six protein-ligand complexes with the aim of understanding the conformational diversity of ligands in protein crystal structures. The results show that ensemble refinement sometimes indicates that the flexibility of parts of the ligand and some protein side chains is larger than that which can be described by a single conformation and atomic displacement parameters. However, since the electron-density maps are comparable and R free values are slightly increased, the original crystal structure is still a better model from a statistical point of view. On the other hand, it is shown that molecular-dynamics simulations and automatic generation of alternative conformations in crystallographic refinement confirm that the flexibility of these groups is larger than is observed in standard refinement. Moreover, the flexible groups in ensemble refinement coincide with groups that give high atomic displacement parameters or non-unity occupancy if optimized in standard refinement. Therefore, the conformational diversity indicated by ensemble refinement seems to be qualitatively correct, indicating that ensemble refinement can be an important complement to standard crystallographic refinement as a tool to discover which parts of crystal structures may show extensive flexibility and therefore are poorly described by a single conformation. However, the diversity of the ensembles is often exaggerated (probably partly owing to the rather poor force field employed) and the ensembles should not be trusted in detail.
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| 6. |
- Caldararu, Octav, et al.
(författare)
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Mechanism of hydrogen peroxide formation by lytic polysaccharide monooxygenase
- 2019
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Ingår i: Chemical Science. - : Royal Society of Chemistry (RSC). - 2041-6520 .- 2041-6539. ; 10:2, s. 576-586
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Tidskriftsartikel (refereegranskat)abstract
- Lytic polysaccharide monooxygenases (LPMOs) are copper-containing metalloenzymes that can cleave the glycosidic link in polysaccharides. This could become crucial for production of energy-efficient biofuels from recalcitrant polysaccharides. Although LPMOs are considered oxygenases, recent investigations have shown that H2O2 can also act as a co-substrate for LPMOs. Intriguingly, LPMOs generate H2O2 in the absence of a polysaccharide substrate. Here, we elucidate a new mechanism for H2O2 generation starting from an AA10-LPMO crystal structure with an oxygen species bound, using QM/MM calculations. The reduction level and protonation state of this oxygen-bound intermediate has been unclear. However, this information is crucial to the mechanism. We therefore investigate the oxygen-bound intermediate with quantum refinement (crystallographic refinement enhanced with QM calculations), against both X-ray and neutron data. Quantum refinement calculations suggest a Cu(ii)-O-2 system in the active site of the AA10-LPMO and a neutral protonated -NH2 state for the terminal nitrogen atom, the latter in contrast to the original interpretation. Our QM/MM calculations show that H2O2 generation is possible only from a Cu(i) center and that the most favourable reaction pathway is to involve a nearby glutamate residue, adding two electrons and two protons to the Cu(ii)-O-2 system, followed by dissociation of H2O2.
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| 7. |
- Caldararu, Octav, et al.
(författare)
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QM/MM study of the reaction mechanism of sulfite oxidase
- 2018
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 8:1
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Tidskriftsartikel (refereegranskat)abstract
- Sulfite oxidase is a mononuclear molybdenum enzyme that oxidises sulfite to sulfate in many organisms, including man. Three different reaction mechanisms have been suggested, based on experimental and computational studies. Here, we study all three with combined quantum mechanical (QM) and molecular mechanical (QM/MM) methods, including calculations with large basis sets, very large QM regions (803 atoms) and QM/MM free-energy perturbations. Our results show that the enzyme is set up to follow a mechanism in which the sulfur atom of the sulfite substrate reacts directly with the equatorial oxo ligand of the Mo ion, forming a Mo-bound sulfate product, which dissociates in the second step. The first step is rate limiting, with a barrier of 39-49 kJ/mol. The low barrier is obtained by an intricate hydrogen-bond network around the substrate, which is preserved during the reaction. This network favours the deprotonated substrate and disfavours the other two reaction mechanisms. We have studied the reaction with both an oxidised and a reduced form of the molybdopterin ligand and quantum-refinement calculations indicate that it is in the normal reduced tetrahydro form in this protein.
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| 8. |
- Caldararu, Octav, et al.
(författare)
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Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data
- 2019
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Ingår i: Acta Crystallographica Section D: Structural Biology. - 2059-7983. ; 75, s. 368-380
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Tidskriftsartikel (refereegranskat)abstract
- Neutron crystallography is a powerful method to determine the positions of H atoms in macromolecular structures. However, it is sometimes hard to judge what would constitute a chemically reasonable model, and the geometry of H atoms depends more on the surroundings (for example the formation of hydrogen bonds) than heavy atoms, so that the empirical geometry information for the H atoms used to supplement the experimental data is often less accurate. These problems may be reduced by using quantum-mechanical calculations. A method has therefore been developed to combine quantum-mechanical calculations with joint crystallographic refinement against X-ray and neutron data. A first validation of this method is provided by re-refining the structure of the galectin-3 carbohydrate-recognition domain in complex with lactose. The geometry is improved, in particular for water molecules, for which the method leads to better-resolved hydrogen-bonding interactions. The method has also been applied to the active copper site of lytic polysaccharide monooxygenase and shows that the protonation state of the amino-terminal histidine residue can be determined.
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| 9. |
- Caldararu, Octav, et al.
(författare)
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Water structure in solution and crystal molecular dynamics simulations compared to protein crystal structures
- 2020
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Ingår i: RSC Advances. - : Royal Society of Chemistry (RSC). - 2046-2069. ; 10, s. 8435-8443
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Tidskriftsartikel (refereegranskat)abstract
- The function of proteins is influenced not only by the atomic structure but also by the detailed structure of the solvent surrounding it. Computational studies of protein structure also critically depend on the water structure around the protein. Herein we compare the water structure obtained from molecular dynamics (MD) simulations of galectin-3 in complex with two ligands to crystallographic water molecules observed in the corresponding crystal structures. We computed MD trajectories both in a water box, which mimics a protein in solution, and in a crystallographic unit cell, which mimics a protein in a crystal. The calculations were compared to crystal structures obtained at both cryogenic and room temperature. Two types of analyses of the MD simulations were performed. First, the positions of the crystallographic water molecules were compared to peaks in the MD density after alignment of the protein in each snapshot. The results of this analysis indicate that all simulations reproduce the crystallographic water structure rather poorly. However, if we define the crystallographic water sites based on their distances to nearby protein atoms and follow these sites throughout the simulations, the MD simulations reproduce the crystallographic water sites much better. This shows that the failure of MD simulations to reproduce the water structure around proteins in crystal structures observed both in this and previous studies is caused by the problem of identifying water sites for a flexible and dynamic protein (traditionally done by overlaying the structures). Our local clustering approach solves the problem and shows that the MD simulations reasonably reproduce the water structure observed in crystals. Furthermore, analysis of the crystal MD simulations indicates a few water molecules that are close to unmodeled electron density peaks in the crystal structures, suggesting that crystal MD could be used as a complementary tool for identifying and modelling water in protein crystallography.
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| 10. |
- Cao, Lili, et al.
(författare)
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Does the crystal structure of vanadium nitrogenase contain a reaction intermediate? Evidence from quantum refinement
- 2020
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Ingår i: Journal of Biological Inorganic Chemistry. - : Springer Science and Business Media LLC. - 0949-8257 .- 1432-1327. ; 25:6, s. 847-861
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Tidskriftsartikel (refereegranskat)abstract
- Abstract: Recently, a crystal structure of V-nitrogenase was presented, showing that one of the µ2 sulphide ions in the active site (S2B) is replaced by a lighter atom, suggested to be NH or NH2, i.e. representing a reaction intermediate. Moreover, a sulphur atom is found 7 Å from the S2B site, suggested to represent a storage site for this ion when it is displaced. We have re-evaluated this structure with quantum refinement, i.e. standard crystallographic refinement in which the empirical restraints (employed to ensure that the final structure makes chemical sense) are replaced by more accurate quantum–mechanical calculations. This allows us to test various interpretations of the structure, employing quantum–mechanical calculations to predict the ideal structure and to use crystallographic measures like the real-space Z-score and electron-density difference maps to decide which structure fits the crystallographic raw data best. We show that the structure contains an OH−-bound state, rather than an N2-derived reaction intermediate. Moreover, the structure shows dual conformations in the active site with ~ 14% undissociated S2B ligand, but the storage site seems to be fully occupied, weakening the suggestion that it represents a storage site for the dissociated ligand. Graphic abstract: [Figure not available: see fulltext.]
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