The free energy of binding between avidin and seven biotin analogues has been calculated with the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) method. We have studied how the force field and the method to generate geometries affect the calculated binding free energies. Four different force fields were compared, but we saw no significant difference in the results. However, mixing the force fields used for the geometry generation and energy calculations is not recommended. In the molecular dynamics simulations, explicit water molecules must be used, but the size of the simulated system and the boundary conditions are less important. In fact, nonperiodic simulations with a fixed protein outside a relatively small simulated system (18 A) seem to be a proper approach. The mean absolute error was 9-19 kJ/mol, with a standard error of 5-15 kJ/mol, which arises mainly from the entropy term.

We have studied the convergence of QM/MM calculations with respect to the size of the QM system. We study a proton transfer between a first-sphere cysteine ligand and a secondsphere histidine group in [Ni,Fe] hydrogenase and use a 446-atom model of the protein, treated purely with QM methods as reference. We have tested 12 different ways to redistribute charges close to the junctions (to avoid overpolarisation of the QM system), but once the junctions are moved away from the active site, there is little need to redistribute the charges. We have tested 13 different variants of QM/MM approaches, including two schemes to correct errors caused by the truncation of the QM system. However, we see little gain from such correction schemes; on the contrary they are sensitive to the charge-redistribution scheme and may cause large errors if charges are close to the junctions. In fact, the best results were obtained with a mechanical embedding approach that does not employ any correction scheme and ignores polarisation. It gives a mean unsigned error for 40 QM systems of different sizes of 7 kJ/mol with a maximum error of 28 kJ/mol. The errors can be significantly decreased if bonds between the QM and MM system (junctions) are moved one residue away from all active-site residues. Then, most QM/MM variants give mean unsigned errors of 5-9 kJ/mol, maximum errors of 16-35 kJ/mol, and only 5-7 residues give an error of over 5 kJ/mol. In general, QM/MM calculations converge faster with system size than pure QM calculations.

One of the largest challenges of computational chemistry is calculation of accurate free energies for the binding of a small molecule to a biological macromolecule, which has immense implications in drug development. It is well-known that standard molecular-mechanics force fields used in most such calculations have a limited accuracy. Therefore, there has been a great interest in improving the estimates using quantum-mechanical (QM) methods. We review here approaches involving explicit QM energies to calculate binding affinities, with an emphasis on the methods, rather than on specific applications. Many different QM methods have been employed, ranging from semiempirical QM calculations, via density-functional theory, to strict coupled-cluster calculations. Dispersion and other empirical corrections are mandatory for the approximate methods, as well as large basis sets for the stricter methods. QM has been used for the ligand, for a few crucial groups around the ligand, for all the closest atoms (200-1000 atoms), or for the full receptor-ligand complex, but it is likely that with a proper embedding it might be enough to include all groups within ∼6 Å of the ligand. Approaches involving minimized structures, simulations of the end states of the binding reaction, or full free-energy simulations have been tested.

Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid hostguest binding energies. Link to publication Citation for published version (APA): Mikulskis, P., Cioloboc, D., Andrejić, M., Khare, S., Brorsson, J., Genheden, S., ... Ryde, U. (2014). Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host-guest binding energies. Journal of Computer-Aided Molecular Design, 28(4), 375-400. DOI: 10.1007/s10822-014-9739-x General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal AbstractWe have estimated free energies for the binding of nine cyclic carboxylate guest molecules to the octa-acid host in the SAMPL4 blind-test challenge with four different approaches. First, we used standard free-energy perturbation calculations of relative binding affinities, performed at the molecular-mechanics (MM) level with TIP3P waters, the GAFF force field, and two different sets of charges for the host and the guest, obtained either with the restrained electrostatic potential or AM1-BCC methods. Both charge sets give good and nearly identical results, with a mean absolute deviation (MAD) of 4 kJ/mol and a correlation coefficient (R 2 ) of 0.8 compared to experimental results. Second, we tried to improve these predictions with 28 800 density-functional theory (DFT) calculations for selected snapshots and the non-Boltzmann Bennett acceptance-ratio method, but this led to much worse results, probably because of a too large difference between the MM and DFT potential-energy functions. Third, we tried to calculate absolute affinities using minimised DFT structures. This gave intermediate-quality results with MADs of 5-9 kJ/mol and R 2 = 0.6-0.8, depending on how the structures were obtained. Finally, we tried to improve these results using local coupled-cluster calculations with single and double excitations, and non-iterative perturbative treatment of triple excitations (LCCSD(T0)), employing the polarisable multipole interactions with supermolecular pairs approach. Unfortunately, this only degraded the predictions, probably because a mismatch between the solvation energies obtained at the DFT and LCCSD(T0) levels.Key Words: binding affinities, host-guest, free-energies perturbation, density-functional calculations, CCSD(T), polarisable multipole interactions. 2 IntroductionOne of the largest challenges of computational chemistry is to predict the binding affinity of a small ligand to a larger receptor molecule, e.g. a drug candidate to its receptor prot...