Jan H. Jensen

General atomic and molecular electronic structure system

A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines.

Very fast empirical prediction and rationalization of protein pKa values

A very fast empirical method is presented for structure‐based protein pKa prediction and rationalization. The desolvation effects and intra‐protein interactions, which cause variations in pKa values of protein ionizable groups, are empirically related to the positions and chemical nature of the groups proximate to the pKa sites. A computer program is written to automatically predict pKa values based on these empirical relationships within a couple of seconds. Unusual pKa values at buried active sites, which are among the most interesting protein pKa values, are predicted very well with the empirical method. A test on 233 carboxyl, 12 cysteine, 45 histidine, and 24 lysine pKa values in various proteins shows a root‐mean‐square deviation (RMSD) of 0.89 from experimental values. Removal of the 29 pKa values that are upper or lower limits results in an RMSD = 0.79 for the remaining 285 pKa values. Proteins 2005.

PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions

In this study, we have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better physical description of the desolvation and dielectric response for the protein. We have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with experiment than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the number of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.

PDB2PQR: Expanding and upgrading automated preparation of biomolecular structures for molecular simulations

Real-world observable physical and chemical characteristics are increasingly being calculated from the 3D structures of biomolecules. Methods for calculating pKa values, binding constants of ligands, and changes in protein stability are readily available, but often the limiting step in computational biology is the conversion of PDB structures into formats ready for use with biomolecular simulation software. The continued sophistication and integration of biomolecular simulation methods for systems- and genome-wide studies requires a fast, robust, physically realistic and standardized protocol for preparing macromolecular structures for biophysical algorithms. As described previously, the PDB2PQR web server addresses this need for electrostatic field calculations (Dolinsky et al., Nucleic Acids Research, 32, W665–W667, 2004). Here we report the significantly expanded PDB2PQR that includes the following features: robust standalone command line support, improved pKa estimation via the PROPKA framework, ligand parameterization via PEOE_PB charge methodology, expanded set of force fields and easily incorporated user-defined parameters via XML input files, and improvement of atom addition and optimization code. These features are available through a new web interface (http://pdb2pqr.sourceforge.net/), which offers users a wide range of options for PDB file conversion, modification and parameterization.

Very fast prediction and rationalization of pKa values for protein-ligand complexes.

The PROPKA method for the prediction of the pKa values of ionizable residues in proteins is extended to include the effect of non‐proteinaceous ligands on protein pKa values as well as predict the change in pKa values of ionizable groups on the ligand itself. This new version of PROPKA (PROPKA 2.0) is, as much as possible, developed by adapting the empirical rules underlying PROPKA 1.0 to ligand functional groups. Thus, the speed of PROPKA is retained, so that the pKa values of all ionizable groups are computed in a matter of seconds for most proteins. This adaptation is validated by comparing PROPKA 2.0 predictions to experimental data for 26 protein–ligand complexes including trypsin, thrombin, three pepsins, HIV‐1 protease, chymotrypsin, xylanase, hydroxynitrile lyase, and dihydrofolate reductase. For trypsin and thrombin, large protonation state changes (|n| > 0.5) have been observed experimentally for 4 out of 14 ligand complexes. PROPKA 2.0 and Klebes PEOE approach (Czodrowski P et al. J Mol Biol 2007;367:1347–1356) both identify three of the four large protonation state changes. The protonation state changes due to plasmepsin II, cathepsin D and endothiapepsin binding to pepstatin are predicted to within 0.4 proton units at pH 6.5 and 7.0, respectively. The PROPKA 2.0 results indicate that structural changes due to ligand binding contribute significantly to the proton uptake/release, as do residues far away from the binding site, primarily due to the change in the local environment of a particular residue and hence the change in the local hydrogen bonding network. Overall the results suggest that PROPKA 2.0 provides a good description of the protein–ligand interactions that have an important effect on the pKa values of titratable groups, thereby permitting fast and accurate determination of the protonation states of key residues and ligand functional groups within the binding or active site of a protein. Proteins 2008.

Improved Treatment of Ligands and Coupling Effects in Empirical Calculation and Rationalization of pKa Values.

The new empirical rules for protein pKa predictions implemented in the PROPKA3.0 software package (Olsson et al. J. Chem. Theory Comput.2010, 7, 525-537) have been extended to the prediction of pKa shifts of active site residues and ionizable ligand groups in protein-ligand complexes. We present new algorithms that allow pKa shifts due to inductive (i.e., covalently coupled) intraligand interactions, as well as noncovalently coupled interligand interactions in multiligand complexes, to be included in the prediction. The number of different ligand chemical groups that are automatically recognized has been increased to 18, and the general implementation has been changed so that new functional groups can be added easily by the user, aided by a new and more general protonation scheme. Except for a few cases, the new algorithms in PROPKA3.1 are found to yield results similar to or better than those obtained with PROPKA2.0 (Bas et al. Proteins: Struct., Funct., Bioinf.2008, 73, 765-783). Finally, we present a novel algorithm that identifies noncovalently coupled ionizable groups, where pKa prediction may be especially difficult. This is a general improvement to PROPKA and is applied to proteins with and without ligands.

An Effective Fragment Method for Modeling Solvent Effects in Quantum Mechanical Calculations

An effective fragment model is developed to treat solvent effects on chemical properties and reactions. The solvent, which might consist of discrete water molecules, protein, or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water‐formamide are in good agreement with fully ab initio calculations.

Chapter 10 The Effective Fragment Potential: A General Method for Predicting Intermolecular Interactions

Publisher Summary The interactions between molecules and molecular systems play key roles in many important phenomena in chemistry, biological sciences, materials science and engineering, and chemical and mechanical engineering. An approach for studying intermolecular interactions is to employ a model potential. Such potentials, broadly referred to as “molecular mechanics” (MM), can generally not account for bond breaking but can, in principle, account for a range of intermolecular interactions. The effective fragment potential (EFP) is an accurate method for treating the broad range of intermolecular interactions, at a small fraction of the cost of ab initio calculations that produce comparable accuracy. Because no empirically fitted parameters are required, an EFP can easily be generated automatically for any closed shell species simply by running the appropriate GAMESS calculation on the isolated molecule.

Evaluation of Charge Penetration between Distributed Multipolar Expansions

A formula to calculate the charge penetration energy that results when two charge densities overlap has been derived for molecules described by an effective fragment potential (EFP). The method has been compared with the ab initio charge penetration, taken to be the difference between the electrostatic energy from a Morokuma analysis and Stone’s Distributed Multipole Analysis. The average absolute difference between the EFP method and the ab initio charge penetration for dimers of methanol, acetonitrile, acetone, DMSO, and dichloromethane at their respective equilibrium geometries is 0.32 kcal mol−1.

The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO)

The polarizable continuum model (PCM) for the description of solvent effects is combined with the fragment molecular orbital (FMO) method at several levels of theory, using a many‐body expansion of the electron density and the corresponding electrostatic potential, thereby determining solute (FMO)–solvent (PCM) interactions. The resulting method, denoted FMO/PCM, is applied to a set of model systems, including α‐helices and β‐strands of alanine consisting of 10, 20, and 40 residues and their mutants to charged arginine and glutamate residues. The FMO/PCM error in reproducing the PCM solvation energy for a full system is found to be below 1 kcal/mol in all cases if a two‐body expansion of the electron density is used in the PCM potential calculation and two residues are assigned to each fragment. The scaling of the FMO/PCM method is demonstrated to be nearly linear at all levels for polyalanine systems. A study of the relative stabilities of α‐helices and β‐strands is performed, and the magnitude of the contributing factors is determined. The method is applied to three proteins consisting of 20, 129, and 245 residues, and the solvation energy and computational efficiency are discussed.