Polarization effects in protein-ligand calculations extend farther than the actual induction energy

The various roles that polarizabilities play in the calculation of protein-ligand interaction energies with a polarizable force field are investigated, and the importance and distance dependence of some common approximations is determined for each of these roles separately, using quantum-mechanical calculations as the reference. It is found that the pure induction energy, if defined as the energetic gain from the charge redistribution upon interaction between the protein and ligand, is a rather short-ranged effect that becomes independent of the exact implementation at distances above ∼4Å. On the other hand, the polarization between the protein residues in the assembly of a protein from separately computed fragments (as is routinely done in force field development) has a significant effect on the computed interaction energies, even for residues as far as 15Å from the ligand. Finally, polarization improves the transferability of partial charges, but the simple polarization model used in, for example, the Amber force field explains only 14-19% of the conformational variation of the charges. In all cases, more advanced polarization models, especially involving anisotropic polarizabilities, seem to give significantly better descriptions of these effects. The study suggests that an accurate treatment of polarization can be important even in systems where the actual induction energy is small in magnitud

Teaming over time : team and team leadership development through different interventions

Organizing work in groups or teams is becoming almost the norm in contemporary organizations (West, 2012; Wheelan, 2005). This has implications on leadership, team membership and the way organization are designed to favor teamwork. Organizational change and team building do not come effortlessly, but often out of necessity, a driver being the distribution of knowledge through digitalization. In 2016-2017 researchers at the consultancy firm Deloitte interviewed some 7.000 leaders worldwide on the most pressing corporate issues for the immediate future: adaptability to global competition and digitalization. The leaders stressed the necessity to move away from hierarchical organizational structures toward work in teams (Bersin et al., 2017). The team structure is preferable, since information is no longer hierarchically distributed. With knowledge comes responsibility. The new challenges consist of creating an engaged team environment, and organizations where the learning from the different teams is communicated and made use of. Few workplaces have an abundance of resources, thus people at a workplace need to learn how to best manage scarce resources. In so doing, Elinor Ostrom (1990), concluded that people easily get caught in the Prisoners’ dilemma (individually rational strategies lead to collectively irrational outcomes) unless they cooperate, and that learning how to cooperate can override the Prisoners’ dilemma and create a base for collective action that benefits all. The aim of this thesis was to contribute with knowledge regarding the mechanisms influencing and resulting in team and team leadership development lasting over time, induced through interventions. The interventions were either on the individual level, trying to increase levels of team leadership skills for the individual manager. Or on the collective level including the whole team. This latter approach seems somewhat more unusual (Jackson & Parry 2011). The individual approach was to, for the first time, evaluate and compare the outcomes of two established Swedish leadership development programs: Developmental Leadership (UL) and Understanding group and leader (UGL). The DL- program with a strong focus on developmental leadership (Larsson et al., 2003), and the UGL-program with focus both on developmental leadership and on group development (Wheelan, 2005). The collective level approach was through a program developed for a specific context; academic leadership in a Medical University, including whole management teams. The findings point toward some crucial factors for team development to happen. Communication was vital; how to, where, what and when to communicate. The interventions included both theory, and practice, the latter probably the most important. The intervention, which included the whole team had an advantage in that the team practiced communicating their real communal problems. This could also start the process of co-creating leadership. Including the whole team bridges the gap between intervention and work-life, something lone participants in leadership interventions struggled with, especially since few organizations followed up on their learning. If course participants were met with skepticism or enthusiasm had impact on their maintenance of new learning. Here the factor if the participants had gained an increase in their confidence in their role as leader, on the course or not had a large impact. Confidence could also be a factor in whether the participants claimed an opportunity to perform their new learnings or not, back at the work place. This thesis has an explorative approach, since its focus is on lesser researched problems. The word ‘problems’ is used consciously. Using ‘research gaps’ would imply exact knowledge of where these are and in the field of team and leadership development that is not obvious, this is in line with Alvesson and Sandberg (2011). Little research has been done specifically on leadership teams in a medical academic setting, as was also the case with the longitudinal studies on UGL and DL courses

Eclipsing binary statistics - theory and observation

The expected distributions of eclipse-depth versus period for eclipsing binaries of different luminosities are derived from large-scale population synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code, we have evolved several hundred million binaries, starting from various simple input distributions of masses and orbit-sizes. Eclipse probabilities and predicted distributions over period and eclipse-depth (P/dm) are given in a number of main-sequence intervals, from O-stars to brown dwarfs. The comparison between theory and Hipparcos observations shows that a standard (Duquennoy & Mayor) input distribution of orbit-sizes (a) gives reasonable numbers and P/dm-distributions, as long as the mass-ratio distribution is also close to the observed flat ones. A random pairing model, where the primary and secondary are drawn independently from the same IMF, gives more than an order of magnitude too few eclipsing binaries on the upper main sequence. For a set of eclipsing OB-systems in the LMC, the observed period-distribution is different from the theoretical one, and the input orbit distributions and/or the evolutionary environment in LMC has to be different compared with the Galaxy. A natural application of these methods are estimates of the numbers and properties of eclipsing binaries observed by large-scale surveys like Gaia.Comment: 11 pages, 16 figures, accepted for publication in A&

Accurate reaction energies in proteins obtained by combining QM/MM and large QM calculations

We here suggest and test a new method to obtain stable energies in proteins for charge-neutral reactions by running large quantum mechanical (QM) calculations on structures obtained by combined QM and molecular mechanics (QM/MM) geometry optimisation on several snapshots from molecular dynamics simulations. As a test case, we use a proton transfer between a metal-bound cysteine residue and a second-sphere histidine residue in the active site of [Ni,Fe] hydrogenase, which has been shown to be very sensitive to the surroundings. We include in the QM calculations all residues within 4.5 Å of the active site, two capped residues on each side of the active-site residues, as well as all charged groups that are buried inside the protein, which for this enzyme includes three iron–sulphur clusters, in total 930 atoms. These calculations are performed at the BP86/def2-SV(P) level, but the energies are then extrapolated to the B3LYP/def2-TZVP level with a smaller QM system and zero-point energy, entropy, and thermal effects are added. We test three approaches to model the remaining atoms of the protein solvent, viz. by standard QM/MM approaches using either mechanical or electrostatic embedding, or by using a continuum solvation model for the large QM systems. Quite encouragingly, the three approaches give the same results within 13 kJ/mol and variations in the size of the QM system do not change the energies by more than 8 kJ/mol, provided that the QM/MM junctions are not moved closer to the QM system. The statistical precision for the average over ten snapshots is 1–3 kJ/mol

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model.

The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc

Conformational Dependence of Isotropic Polarizabilities

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

Ligand affinities estimated by quantum chemical calculations

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

Effect of geometry optimisations on QM-cluster and QM/MM studies of reaction energies in proteins

We have examined the effect of geometry optimisation on energies calculated with the quantum-mechanical (QM) cluster, the combined QM and molecular-mechanics (QM/MM), the big-QM approaches (very large single-point QM calculations taken from QM/MM-optimised structures, including all atoms within 4.5 Å of the minimal active site, all buried charged groups in the protein, and truncations moved at least three residues away from the active site). We study a simple proton-transfer reaction between His-79 and Cys-546 in the active site of [Ni,Fe] hydrogenase and optimise QM systems of 50 different sizes (56–362 atoms). Geometries optimised with QM/MM are stable and reliable, whereas QM-cluster optimisations give larger changes in the structures and sometimes lead to large distortions in the active site if some hydrogen-bond partners to the metal ligands are omitted. Keeping 2–3 atoms for each truncated residue (rather than one) fixed in the optimisation improves the results, but does not solve all problems for the QM-cluster optimisations. QM-cluster energies in vacuum and a continuum solvent are insensitive to the geometry optimisations with a mean absolute change upon the optimisations of only 4–7 kJ/mol. This shows that geometry optimisations do not decrease the dependence of QM-cluster energies on how the QM system is selected – there is still a ~60 kJ/mol difference between calculations in which groups have been added to the QM system according to their distance to the active site or based on QM/MM free-energy components. QM/MM energies do not show such a difference, but they converge rather slowly with respect to the size of the QM system, although the convergence is improved by moving truncations away from the active site. The big-QM energies are stable over the 50 different optimised structures, 57±1 kJ/mol, although some smaller trends can be discerned. This shows that both QM-cluster geometries and energies should be interpreted with caution. Instead, we recommend QM/MM for geometry optimisations and energies calculated by the big-QM approach

Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions