Demian Riccardi

Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules

A robust approach for dealing with electrostatic interactions for spherical boundary conditions has been implemented in the QM/MM framework. The development was based on the generalized solvent boundary potential (GSBP) method proposed by Im et al. [J. Chem. Phys. 114, 2924 (2001)], and the specific implementation was applied to the self-consistent-charge density-functional tight-binding approach as the quantum mechanics (QM) level, although extension to other QM methods is straightforward. Compared to the popular stochastic boundary-condition scheme, the new protocol offers a balanced treatment between quantum mechanics/molecular mechanics (QM/MM) and MM/MM interactions; it also includes the effect of the bulk solvent and macromolecule atoms outside of the microscopic region at the Poisson-Boltzmann level. The new method was illustrated with application to the enzyme human carbonic anhydrase II and compared to stochastic boundary-condition simulations using different electrostatic treatments. The GSBP-based QM/MM simulations were most consistent with available experimental data, while conventional stochastic boundary simulations yielded various artifacts depending on different electrostatic models. The results highlight the importance of carefully treating electrostatics in QM/MM simulations of biomolecules and suggest that the commonly used truncation schemes should be avoided in QM/MM simulations, especially in simulations that involve extensive conformational samplings. The development of the GSBP-based QM/MM protocol has opened up the exciting possibility of studying chemical events in very complex biomolecular systems in a multiscale framework.

Importance of van der Waals interactions in QM/MM simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

Interactions of the Osmolyte Glycine Betaine with Molecular Surfaces in Water: Thermodynamics, Structural Interpretation, and Prediction of m-Values

Noncovalent self-assembly of biopolymers is driven by molecular interactions between functional groups on complementary biopolymer surfaces, replacing interactions with water. Since individually these interactions are comparable in strength to interactions with water, they have been difficult to quantify. Solutes (osmolytes, denaturants) exert often large effects on these self-assembly interactions, determined in sign and magnitude by how well the solute competes with water to interact with the relevant biopolymer surfaces. Here, an osmometric method and a water-accessible surface area (ASA) analysis are developed to quantify and interpret the interactions of the remarkable osmolyte glycine betaine (GB) with molecular surfaces in water. We find that GB, lacking hydrogen bond donors, is unable to compete with water to interact with anionic and amide oxygens; this explains its effectiveness as an osmolyte in the Escherichia coli cytoplasm. GB competes effectively with water to interact with amide and cationic nitrogens (hydrogen bonding) and especially with aromatic hydrocarbon (cation-pi). The large stabilizing effect of GB on lac repressor-lac operator binding is predicted quantitatively from ASA information and shown to result largely from dehydration of anionic DNA phosphate oxygens in the protein-DNA interface. The incorporation of these results into theoretical and computational analyses will likely improve the ability to accurately model intra- and interprotein interactions. Additionally, these results pave the way for development of solutes as kinetic/mechanistic and thermodynamic probes of conformational changes and formation/disruption of molecular interfaces that occur in the steps of biomolecular self-assembly processes.

Application of Elastic Network Models to Proteins in the Crystalline State

Normal mode analysis using elastic network models has grown popular for probing the low-frequency collective dynamics of proteins and other biomolecular assemblies. In most previous studies, these models were validated by comparing calculated atomic fluctuations for isolated proteins with experimental temperature factors determined in the crystalline state, although there were also hints that including crystal contacts in the calculations has an impact on the comparison. In this study, a set of 83 ultra-high resolution crystal structures with experimentally determined anisotropic displacement parameters is used to evaluate several C(alpha)-based elastic network models that either ignore or treat the crystal environment in different ways; the latter include using periodic boundary conditions defined with respect to the asymmetric unit or the primitive unit cell as well as using the Born-von Kármán boundary condition that accounts for lattice vibrations. For all elastic network models, treating the crystal environment leads to better agreement with experimental anisotropic displacement parameters with the Born-von Kármán boundary condition giving the best agreement. Atomic correlations over the entire protein are clearly affected by the presence of the crystal contacts and fairly sensitive to the way that the crystal environment is treated. These observations highlight the importance of properly treating the protein system in an environment consistent with experiment when either evaluating approximate protein models or using approximate dynamic models in structural refinement application types. Finally, investigation of the scaling behaviors of the cumulative density of states and the heat capacity indicates that there are still gaps between simplified elastic models and all-atom models for proteins.

Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.

Evaluating Elastic Network Models of Crystalline Biological Molecules with Temperature Factors, Correlated Motions, and Diffuse X-Ray Scattering

In this study, the variance-covariance matrix of protein motions is used to compare several elastic network models within the theoretical framework of x-ray scattering from crystals. A set of 33 ultra-high resolution structures is used to characterize the average scaling behavior of the vibrational density of states and make comparisons between experimental and theoretical temperature factors. Detailed investigations of the vibrational density of states, correlations, and predicted diffuse x-ray scatter are carried out for crystalline Staphylococcal nuclease; correlations and diffuse x-ray scatter are also compared to predictions from the translation, libration, screw model and a liquid-like dynamics model. We show that elastic network models developed to best predict temperature factors without regard for the crystal environment have relatively strong long-range interactions that yield very short-ranged atom-atom correlations. Further, we find that the low-frequency modes dominate the variance-covariance matrix only for those models with a physically reasonable vibrational density of states, and the fraction of modes required to converge the correlations is higher than that typically used for elastic network model studies. The practical implications are explored using computed diffuse x-ray scatter, which can be measured experimentally.

X-ray Structure of a Hg2+ Complex of Mercuric Reductase (MerA) and Quantum Mechanical/Molecular Mechanical Study of Hg2+ Transfer between the C-Terminal and Buried Catalytic Site Cysteine Pairs

Mercuric reductase, MerA, is a key enzyme in bacterial mercury resistance. This homodimeric enzyme captures and reduces toxic Hg2+ to Hg0, which is relatively unreactive and can exit the cell passively. Prior to reduction, the Hg2+ is transferred from a pair of cysteines (C558′ and C559′ using Tn501 numbering) at the C-terminus of one monomer to another pair of cysteines (C136 and C141) in the catalytic site of the other monomer. Here, we present the X-ray structure of the C-terminal Hg2+ complex of the C136A/C141A double mutant of the Tn501 MerA catalytic core and explore the molecular mechanism of this Hg transfer with quantum mechanical/molecular mechanical (QM/MM) calculations. The transfer is found to be nearly thermoneutral and to pass through a stable tricoordinated intermediate that is marginally less stable than the two end states. For the overall process, Hg2+ is always paired with at least two thiolates and thus is present at both the C-terminal and catalytic binding sites as a neutral complex. Prior to Hg2+ transfer, C141 is negatively charged. As Hg2+ is transferred into the catalytic site, a proton is transferred from C136 to C559′ while C558′ becomes negatively charged, resulting in the net transfer of a negative charge over a distance of ∼7.5 Å. Thus, the transport of this soft divalent cation is made energetically feasible by pairing a competition between multiple Cys thiols and/or thiolates for Hg2+ with a competition between the Hg2+ and protons for the thiolates.

HackaMol: An Object-Oriented Modern Perl Library for Molecular Hacking on Multiple Scales

HackaMol is an open source, object-oriented toolkit written in Modern Perl that organizes atoms within molecules and provides chemically intuitive attributes and methods. The library consists of two components: HackaMol, the core that contains classes for storing and manipulating molecular information, and HackaMol::X, the extensions that use the core. The core is well-tested, well-documented, and easy to install across computational platforms. The goal of the extensions is to provide a more flexible space for researchers to develop and share new methods. In this application note, we provide a description of the core classes and two extensions: HackaMol::X::Calculator, an abstract calculator that uses code references to generalize interfaces with external programs, and HackaMol::X::Vina, a structured class that provides an interface with the AutoDock Vina docking program.