| 51. |
- Söderhjelm, Pär, et al.
(author)
-
Conformational dependence of charges in protein simulations
- 2009
-
In: Journal of Computational Chemistry. - : Wiley. - 1096-987X .- 0192-8651. ; 30:5, s. 750-760
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Journal article (peer-reviewed)abstract
- We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges. (c) 2008 Wiley Periodicals, Inc. J Comput Chem 2008.
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| 52. |
- Söderhjelm, Pär, et al.
(author)
-
Conformational Dependence of Isotropic Polarizabilities
- 2011
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In: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 7:5, s. 1404-1414
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Journal article (peer-reviewed)abstract
- We perform a statistical and energetic analysis of atomic polarizabilities obtained with the LoProp approach for all atoms in the avidin tetramer for 70 snapshots from molecular dynamics simulations with seven different biotin analogues, and from the crystal structure of the photosynthetic reaction center (in total 560 698 individual polarizabilities). Dynamic effects give a variation of the polarizabilities of 0.09 angstrom(3) on average. Atoms at different positions in the sequence show a variation of 0.14 angstrom(3) on average, caused by the conformational dependence of the polarizabilities. This variation gives errors of 2 and 1 kJ/mol for relative conformational and ligand-binding induction energies. Averaged elementwise or atom type polarizabilities give larger errors, e.g., 9 and 7 kJ/mol, respectively, for the relative conformational energies. Therefore, we recommend that polarizabilities should be assigned atomwise (i.e., individual polarizabilities for each atom in all residues), in the same way as for charges. We provide such a set of extensively averaged polarizabilities (xAvPol) for all atoms in avidin and the photosynthetic reaction center, applicable at the B3LYP/aug-cc-pVTZ level, which is converged with respect to the basis-set limit.
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| 53. |
- Söderhjelm, Pär, et al.
(author)
-
Estimates of ligand-binding affinities supported by quantum mechanical methods.
- 2010
-
In: Interdisciplinary sciences, computational life sciences. - : Springer Science and Business Media LLC. - 1913-2751 .- 1867-1462. ; 2:1, s. 21-37
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Journal article (peer-reviewed)abstract
- In this paper, we review our efforts to use quantum mechanical (QM) methods to improve free-energy estimates of the binding of drug candidates to their receptor proteins. First, we have tested the influence of various implicit solvation models on predictions of the ligand-binding affinity. The accuracy of implicit solvation models strongly depend on the parameterisation, but also on the magnitude of the solvation energy (i.e. their accuracy should be discussed in relative terms). However, if only relative solvation energies within a series of similar drug molecules with the same net charge are considered, nearly all methods tested give a comparable accuracy of 2-5 kJ/mol. Second, we have studied the conformational dependence of QM charges and their influence on ligand-binding affinities. The conformational dependence is significant, but it is to a large extent cancelled by solvation energies. Third, we have estimated the effect and range of electrostatic interactions beyond a point-charge model. The results show that multipoles up to octupoles and anisotropic polarisabilities have a significant influence on energies for residues up to 10-15 A from the ligand and that different sets of point-charge models may give strongly varying results. However, if only relative energies are considered, the effect is to a large extent cancelled. Fourth, we have tried to develop an accurate QM-based molecular mechanics potential, in which not only the electrostatic terms are improved, but also the dispersion and repulsion. However, even with quite sophisticated expressions, it seems difficult to reduce the average error below 2-3 kJ/mol per interaction (e.g. a hydrogen bond), compared to the full QM treatment. Finally, we have developed a new method, PMISP (polarised multipole interaction with supermolecular pairs), for the calculation of accurate interaction energies. It employs an accurate force field for electrostatics and induction, including multipoles up to octupoles and anisotropic polarisabilities calculated by QM methods on amino-acid fragments of the protein in each conformation observed in snapshots from a molecular dynamics simulation, whereas short-range interactions are estimated by high-level QM calculations for all pairs of the ligand with near-by residues. We show that this approach allows us to go far beyond the current accuracy of molecular mechanics methods, down to an error of 5-10 kJ/mol for a full protein-ligand complex. It can be combined with estimates of solvation, entropy, and dynamic effects to give estimates of binding affinities. However, several problems remain to be solved before any significant improvement in the accuracy can be seen.
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| 54. |
- Söderhjelm, Pär, et al.
(author)
-
How Accurate Can a Force Field Become? A Polarizable Multipole Model Combined with Fragment-wise Quantum-Mechanical Calculations
- 2009
-
In: Journal of physical chemistry. A. - : American Chemical Society (ACS). - 1520-5215 .- 1089-5639. ; 113:3, s. 617-627
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Journal article (peer-reviewed)abstract
- A new method to accurately estimate the interaction energy between a large molecule and a smaller ligand is presented. The method approximates the electrostatic and induction contributions classically by multipole and polarizability expansions, but uses explicit quantum-mechanical fragment calculations for the remaining (nonclassical) contributions, mainly dispersion and exchange repulsion. Thus, it represents a limit of how accurate a force field can ever become for interaction energies if pairwise additivity of the nonclassical term is assumed (e.g., all general-purpose force fields). The accuracy is tested by considering protein-ligand model systems for which the true MP2/6-31G* interaction energies can be computed. The method is shown to be more accurate than related fragmentation approaches. The remaining error (2-5 and ∼10 kJ/mol for neutral and charged ligands, respectively) can be decreased by including the polarizing effect from surrounding fragments in the quantum-mechanical calculations.
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| 55. |
- Söderhjelm, Pär, et al.
(author)
-
Ligand affinities estimated by quantum chemical calculations
- 2010
-
In: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 6:5, s. 1726-1737
-
Journal article (peer-reviewed)abstract
- We present quantum chemical estimates of ligand-binding affinities performed, for the first time, at a level of theory for which there is a hope that dispersion and polarization effects are properly accounted for (MP2/cc-pVTZ) and at the same time effects of solvation, entropy, and sampling are included. We have studied the binding of seven biotin analogues to the avidin tetramer. The calculations have been performed by the recently developed PMISP approach (polarizable multipole interactions with supermolecular pairs), which treats electrostatic interactions by multipoles up to quadrupoles, induction by anisotropic polarizabilities, and nonclassical interactions (dispersion, exchange repulsion, etc.) by explicit quantum chemical calculations, using a fragmentation approach, except for long-range interactions that are treated by standard molecular-mechanics Lennard-Jones terms. In order to include effects of sampling, 10 snapshots from a molecular dynamics simulation are studied for each biotin analogue. Solvation energies are estimated by the polarized continuum model (PCM), coupled to the multipole-polarizability model. Entropy effects are estimated from vibrational frequencies, calculated at the molecular mechanics level. We encounter several problems, not previously discussed, illustrating that we are first to apply such a method. For example, the PCM model is, in the present implementation, questionable for large molecules, owing to the use of a surface definition that gives numerous small cavities in a protein.
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| 56. |
- Söderhjelm, Pär, et al.
(author)
-
On the coupling of intermolecular polarization and repulsion through pseudo-potentials
- 2009
-
In: Chemical Physics Letters. - : Elsevier BV. - 0009-2614. ; 468:1-3, s. 94-99
-
Journal article (peer-reviewed)abstract
- To improve the accuracy and transferability of molecular mechanics force fields, one needs a simple physical description of intermolecular polarization based on quantum chemistry. Ideally, in the quantum-chemical description, each molecule is treated separately and the interactions with other molecules are included as a perturbation. We propose a simple formulation of this perturbation, viz. to model the electrostatic part of the interactions exactly and the repulsive counterpart by a two-parameter pseudo-potential. Tests on three dimers at the Hartree–Fock and MP2 levels show that the interaction energies and the polarized charge densities are well reproduced.
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| 57. |
- Söderhjelm, Pär, et al.
(author)
-
Protein Influence on Electronic Spectra Modeled by Multipoles and Polarizabilities
- 2009
-
In: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 5:3, s. 649-658
-
Journal article (peer-reviewed)abstract
- We have developed automatic methods to calculate multipoles and anisotropic polarizabilities for all atoms and bond centers in a protein and to include such a model in the calculation of electronic properties at any level of quantum mechanical theory. This approach is applied for the calculation of the electronic spectra of retinal in rhodopsin at the CASPT2//CASSCF level (second-order multiconfigurational perturbation theory) for the wild-type protein, as well as two mutants and isorhodopsin in QM/MM structures based on two crystal structures. We also perform a detailed investigation of the importance and distance dependence of the multipoles and the polarizabilities for both the absolute and the relative absorption energies. It is shown that the model of the surrounding protein strongly influences the spectrum and that different models give widely different results. For example, the Amber 1994 and 2003 force fields give excitation energies that differ by up to 16 kJ/mol. For accurate excitation energies, multipoles up to quadrupoles and anisotropic polarizabilities are needed. However, interactions with residues more than 10 A from the chromophore can be treated with a standard polarizable force field without any dipoles or quadrupoles.
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| 58. |
- Söderhjelm, Pär, et al.
(author)
-
Quantum mechanics in structure-based ligand design
- 2012
-
In: Protein-ligand interactions. - Weinheim, Germany : Wiley-VCH Verlag GmbH & Co. KGaA. - 9783527329663 - 9783527645947 ; 53, s. 121-143
-
Book chapter (peer-reviewed)
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| 59. |
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| 60. |
- Söderhjelm, Staffan, et al.
(author)
-
Binary Statistics from Hipparcos
- 2001
-
In: The influence of binaries on stellar population studies ( Astrophysics and space science library ; Vol. 264). - 0792371046
-
Book chapter (other academic/artistic)abstract
- Book abstract: The book reviews recent observations of non-evolved and evolved binary populations in clusters and the field with special emphasis on statistical biases, incompleteness and distribution functions. Different binary types are considered: cataclysmic variables, super-soft X-ray sources, double degenerate binaries, Algol-type binaries, Be binaries, X-ray binaries, and Wolf-Rayet binaries. The observational part ends with a discussion on stellar winds in massive stars, on new results of massive starbursts and on the characteristics and the rates of the different types of supernovae. Population synthesis relies on stellar evolution. Recent results on single star and binary evolution are presented. We then compare theoretical models of population synthesis to observations. Much attention is given at population dynamics, spectral synthesis of starbursts, number synthesis of the binaries and supernova rates discussed in the first part of this book. Finally, the book highlights the possible effects of binaries on galactic chemical evolution.
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