Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

Modeling the Opening SARS-CoV-2 Spike: an Investigation of its Dynamic Electro-Geometric Properties

The recent COVID-19 pandemic has brought about a surge of crowd-sourced initiatives aimed at simulating the proteins of the SARS-CoV-2 virus. A bottleneck currently exists in translating these simulations into tangible predictions that can be leveraged for pharmacological studies. Here we report on extensive electrostatic calculations done on an exascale simulation of the opening of the SARS-CoV-2 spike protein, performed by the Folding@home initiative. We compute the electric potential as the solution of the non-linear Poisson-Boltzmann equation using a parallel sharp numerical solver. The inherent multiple length scales present in the geometry and solution are reproduced using highly adaptive Octree grids. We analyze our results focusing on the electro-geometric properties of the receptor-binding domain and its vicinity. This work paves the way for a new class of hybrid computational and data-enabled approaches, where molecular dynamics simulations are combined with continuum modeling to produce high-fidelity computational measurements serving as a basis for protein bio-mechanism investigations.

On tungstates of divalent cations (III) – Pb5O2[WO6]

Abstract${\text{Pb}}_{5}{\text{O}}_{2}\left[{\text{WO}}_{6}\right]$ was discovered as a frequently observed side phase during our investigation on lead tungstates. Its crystal structure was solved by single-crystal X-ray diffraction ($P{2}_{1}/n$, $a=7.4379\left(2\right)$ Å, $b=12.1115\left(4\right)$ Å, $c=10.6171\left(3\right)$ Å, $\beta =90.6847\left(8\right)$°, $Z=4$, ${R}_{\text{int}}=0.038$, ${R}_{1}=0.020$, $\omega {R}_{2}=0.029$, 4188 data, 128 param.) and is isotypic with ${\text{Pb}}_{5}{\text{O}}_{2}\left[{\text{Te}}_{6}\right]$. ${\text{Pb}}_{5}{\text{O}}_{2}\left[{\text{WO}}_{6}\right]$ comprises a layered structure built up by non-condensed [WO6]${}^{6-}$ octahedra and ${\left[{\text{O}}_{4}{\text{Pb}}_{10}\right]}^{12+}$ oligomers. The compound was characterised by spectroscopic measurements (Infrared (IR), Raman and Ultraviolet–visible (UV/Vis) spectra) as well as quantum chemical and electrostatic calculations (density functional theory (DFT), MAPLE) yielding a band gap of 2.9 eV fitting well with the optical one of 2.8 eV. An estimation of the refractive index based on the Gladstone-Dale relationship yielded $n\approx 2.31$. Furthermore first results of the thermal analysis are presented.

The properties of buried ion pairs are governed by the propensity of proteins to reorganize

Charges are incompatible with the hydrophobic interior of proteins, yet proteins use buried charges, often in pairs or networks, to drive energy transduction processes, catalysis, pH-sensing, and ion transport. The structural adaptations necessary to accommodate interacting charges in the protein interior are not well understood. According to continuum electrostatic calculations, the Coulomb interaction between two buried charges cannot offset the highly unfavorable penalty of dehydrating two charges. This was investigated experimentally with two variants of staphylococcal nuclease (SNase) with Glu:Lys or Lys:Glu pairs introduce at internal i, i+4 positions on an α-helix. Contrary to expectations from previous theoretical and experimental studies, the proteins tolerated the charged ion pairs in both orientations. Crystal structures and NMR spectroscopy studies showed that in both variants, side chains or backbone are reorganized. This leads to the exposure of at least one of the two buried groups to water. Comparison of these ion pairs with a highly stable buried ion pair in SNase shows that the location and the amplitude of structural reorganization can vary dramatically between ion pairs buried in the same general region of the protein. The propensity of the protein to populate alternative conformation states in which internal charges can contact water appears to be the factor that governs the magnitude of electrostatic effects in hydrophobic environments. The net effect of structural reorganization is to weaken the Coulomb interactions between charge pairs; however, the reorganized protein no longer has to pay the energetic penalty for burying charges. These results provide the framework necessary to understand the interplay between the dehydration of charges, Coulomb interactions and protein reorganization that tunes the functional properties of proteins.

Variable van der Waals Radii Derived From a Hybrid Gaussian Charge Distribution Model for Continuum-Solvent Electrostatic Calculations

We introduce a hybrid Gaussian charge distribution model (HGM) that partitions the molecular electron density into overlapping spherical atomic domains. The semi-empirical HGM consists of atom-centered spherical Gaussian functions and discrete point charges, which are optimized to reproduce the electrostatic potential on the molecular surface as well as the number of electrons in atom-centered and certain off-atom-centered spherical regions as closely as possible. In contrast, our previous Gaussian charge distribution model [J. Chem. Phys.

Molecular recognition enrichment rules in crystals and protein/ligand complexes

To analyze the propensity of chemical species to interact with each other, we have developed the concept of enrichment ratios. The ratios are derived from the decomposition of the contact surface between pairs of interacting chemical species. The actual contacts are compared with those computed as if all types of contacts had the same probability to form. As expected, several polar contacts, which can be hydrogen bonds and show electrostatic complementarity, show enrichment values larger than unity. Among other results, O···O and N···N contacts are impoverished while H···H interactions appear very slightly disfavored. We have also investigated the directionality and stereochemistry of hydrogen bonds with an oxygen acceptor including in the Cambridge Structural Database [1]. The results obtained through this survey are correlated with the charge density of these different chemical groups. The electron density of these different oxygen atoms types show striking dissimilarities in the electron lone pairs configuration. As previously observed, the directional attraction of hydrogen bond donors towards the lone pairs is much more pronounced for strong H-bonds. Van der Waals and solvent accessible surfaces are widely used representations in protein modelling and drug design. We propose in the software MoproViewer [2] a revisited definition of the molecular surface based on flattened atoms when strong hydrogen bonding is possible. These stereochemical relationships found in molecular recognition within crystal structures of small compounds have implications in drug design and were investigated in some protein/ligand cases. Finally protein/ligand electrostatic calculations are compared using two different charge density models: multipoles vs spherical dummy charges on bonds and lone pairs[3].

DelEnsembleElec: Computing Ensemble-Averaged Electrostatics Using DelPhi

A new VMD plugin that interfaces with DelPhi to provide ensemble-averaged electrostatic calculations using the Poisson-Boltzmann equation is presented. The general theory and context of this approach are discussed, and examples of the plugin interface and calculations are presented. This new tool is applied to systems of current biological interest, obtaining the ensemble-averaged electrostatic properties of the two major influenza virus glycoproteins, hemagglutinin and neuraminidase, from explicitly solvated all-atom molecular dynamics trajectories. The differences between the ensemble-averaged electrostatics and those obtained from a single structure are examined in detail for these examples, revealing how the plugin can be a powerful tool in facilitating the modeling of electrostatic interactions in biological systems.

DelPhi Web Server: A Comprehensive Online Suite for Electrostatic Calculations of Biological Macromolecules and Their Complexes

Here we report a web server, the DelPhi web server, which utilizes DelPhi program to calculate electrostatic energies and the corresponding electrostatic potential and ionic distributions, and dielectric map. The server provides extra services to fix structural defects, as missing atoms in the structural file and allows for generation of missing hydrogen atoms. The hydrogen placement and the corresponding DelPhi calculations can be done with user selected force field parameters being either Charmm22, Amber98 or OPLS. Upon completion of the calculations, the user is given option to download fixed and protonated structural file, together with the parameter and Delphi output files for further analysis. Utilizing Jmol viewer, the user can see the corresponding structural file, to manipulate it and to change the presentation. In addition, if the potential map is requested to be calculated, the potential can be mapped onto the molecule surface. The DelPhi web server is available from http://compbio.clemson.edu/delphi_webserver.