Anders S. Christensen

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure.

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics.

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts - sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (ru200a=u200a0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond (h3 JNC) spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.

Interface of the polarizable continuum model of solvation with semi-empirical methods in the GAMESS program

An interface between semi-empirical methods and the polarized continuum model (PCM) of solvation successfully implemented into GAMESS following the approach by Chudinov et al (Chem. Phys. 1992, 160, 41). The interface includes energy gradients and is parallelized. For large molecules such as ubiquitin a reasonable speedup (up to a factor of six) is observed for up to 16 cores. The SCF convergence is greatly improved by PCM for proteins compared to the gas phase.

Alchemical and structural distribution based representation for universal quantum machine learning

We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML models learning curve, and, through interpolation across the periodic table, even enable alchemical extrapolation to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (H2O)40-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.

Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method.

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

Bayesian Inference of Protein Structure from Chemical Shift Data

Protein chemical shifts are routinely used to augment molecular mechanics force fields in protein structure simulations, with weights of the chemical shift restraints determined empirically. These weights, however, might not be an optimal descriptor of a given protein structure and predictive model, and a bias is introduced which might result in incorrect structures. In the inferential structure determination framework, both the unknown structure and the disagreement between experimental and back-calculated data are formulated as a joint probability distribution, thus utilizing the full information content of the data. Here, we present the formulation of such a probability distribution where the error in chemical shift prediction is described by either a Gaussian or Cauchy distribution. The methodology is demonstrated and compared to a set of empirically weighted potentials through Markov chain Monte Carlo simulations of three small proteins (ENHD, Protein G and the SMN Tudor Domain) using the PROFASI force field and the chemical shift predictor CamShift. Using a clustering-criterion for identifying the best structure, together with the addition of a solvent exposure scoring term, the simulations suggests that sampling both the structure and the uncertainties in chemical shift prediction leads more accurate structures compared to conventional methods using empirical determined weights. The Cauchy distribution, using either sampled uncertainties or predetermined weights, did, however, result in overall better convergence to the native fold, suggesting that both types of distribution might be useful in different aspects of the protein structure prediction.

Random versus Systematic Errors in Reaction Enthalpies Computed Using Semiempirical and Minimal Basis Set Methods

The connectivity-based hierarchy (CBH) protocol for computing accurate reaction enthalpies developed by Sengupta and Raghavachari is tested for fast ab initio methods (PBEh-3c, HF-3c, and HF/STO-3G), tight-binding density functional theory (DFT) methods (GFN-xTB, DFTB, and DFTB-D3), and neglect-of-diatomic-differential-overlap (NDDO)-based semiempirical methods (AM1, PM3, PM6, PM6-DH+, PM6-D2, PM6-D3H+, PM6-D3H4X, PM7, and OM2) using the same set of 25 reactions as in the original study. For the CBH-2 scheme, which reflects the change in the immediate chemical environment of all of the heavy atoms, the respective mean unsigned error relative to G4 for PBEh-3c, HF-3c, HF/STO-3G, GFN-xTB, DFTB-D3, DFTB, PM3, AM1, PM6, PM6-DH+, PM6-D3, PM6-D3H+, PM6-D3H4X, PM7, and OM2 are 1.9, 2.4, 3.0, 3.9, 3.7, 4.5, 4.8, 5.5, 5.4, 5.3, 5,4, 6.5, 5.3, 5.2, and 5.9 kcal/mol, with a single outlier removed for HF-3c, PM6, PM6-DH+, PM6-D3, PM6-D3H4X, and PM7. The increase in accuracy for the NDDO-based methods is relatively modest due to the random errors in predicted heats for formation.

FragBuilder: an efficient Python library to setup quantum chemistry calculations on peptides models

We present a powerful Python library to quickly and efficiently generate realistic peptide model structures. The library makes it possible to quickly set up quantum mechanical calculations on model peptide structures. It is possible to manually specify a specific conformation of the peptide. Additionally the library also offers sampling of backbone conformations and side chain rotamer conformations from continuous distributions. The generated peptides can then be geometry optimized by the MMFF94 molecular mechanics force field via convenient functions inside the library. Finally, it is possible to output the resulting structures directly to files in a variety of useful formats, such as XYZ or PDB formats, or directly as input files for a quantum chemistry program. FragBuilder is freely available at https://github.com/jensengroup/fragbuilder/ under the terms of the BSD open source license.