Electrostatic component of binding energy: Interpreting predictions from poisson-boltzmann equation and modeling protocols

Long-range charge transfer mechanism of the III2IV2 mycobacterial supercomplex

Aerobic life is powered by membrane-bound redox enzymes that shuttle electrons to oxygen and transfer protons across a biological membrane. Structural studies suggest that these energy-transducing enzymes operate as higher-order supercomplexes, but their functional role remains poorly understood and highly debated. Here we resolve the functional dynamics of the 0.7 MDa III2IV2 obligate supercomplex from Mycobacterium smegmatis, a close relative of M. tuberculosis, the causative agent of tuberculosis. By combining computational, biochemical, and high-resolution (2.3 Å) cryo-electron microscopy experiments, we show how the mycobacterial supercomplex catalyses long-range charge transport from its menaquinol oxidation site to the binuclear active site for oxygen reduction. Our data reveal proton and electron pathways responsible for the charge transfer reactions, mechanistic principles of the quinone catalysis, and how unique molecular adaptations, water molecules, and lipid interactions enable the proton-coupled electron transfer (PCET) reactions. Our combined findings provide a mechanistic blueprint of mycobacterial supercomplexes and a basis for developing drugs against pathogenic bacteria.

Electrostatic complementarity at the interface drives transient protein-protein interactions

Understanding the mechanisms driving bio-molecules binding and determining the resulting complexes' stability is fundamental for the prediction of binding regions, which is the starting point for drug-ability and design. Characteristics like the preferentially hydrophobic composition of the binding interfaces, the role of van der Waals interactions, and the consequent shape complementarity between the interacting molecular surfaces are well established. However, no consensus has yet been reached on the role of electrostatic. Here, we perform extensive analyses on a large dataset of protein complexes for which both experimental binding affinity and pH data were available. Probing the amino acid composition, the disposition of the charges, and the electrostatic potential they generated on the protein molecular surfaces, we found that (i) although different classes of dimers do not present marked differences in the amino acid composition and charges disposition in the binding region, (ii) homodimers with identical binding region show higher electrostatic compatibility with respect to both homodimers with non-identical binding region and heterodimers. Interestingly, (iii) shape and electrostatic complementarity, for patches defined on short-range interactions, behave oppositely when one stratifies the complexes by their binding affinity: complexes with higher binding affinity present high values of shape complementarity (the role of the Lennard-Jones potential predominates) while electrostatic tends to be randomly distributed. Conversely, complexes with low values of binding affinity exploit Coulombic complementarity to acquire specificity, suggesting that electrostatic complementarity may play a greater role in transient (or less stable) complexes. In light of these results, (iv) we provide a novel, fast, and efficient method, based on the 2D Zernike polynomial formalism, to measure electrostatic complementarity without the need of knowing the complex structure. Expanding the electrostatic potential on a basis of 2D orthogonal polynomials, we can discriminate between transient and permanent protein complexes with an AUC of the ROC of [Formula: see text] 0.8. Ultimately, our work helps shedding light on the non-trivial relationship between the hydrophobic and electrostatic contributions in the binding interfaces, thus favoring the development of new predictive methods for binding affinity characterization.

Assessing the Performance of Screening MM/PBSA in Protein-Ligand Interactions

Accurate calculation of the binding free energies between a protein and a ligand is the primary objective of structure-based drug design, but it still remains a challenging problem. In this work, we apply the screening molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) method to calculate the binding affinity of protein-ligand interactions. Our results show that the performance of the screening MM/PBSA is better than that of the standard MM/PBSA, especially in a charged-ligand system. In addition, we also investigate the effect of the solute dielectric constant on the results, and find that the optimal solute dielectric constants are different between the neutral-ligand system and the charged-ligand system. Moreover, we also evaluate the effect of the atomic-charge methods on the performance of the screening MM/PBSA. The present study demonstrates that the screening MM/PBSA should be a reliable method for calculating binding energy of biosystems.

Computational Design of PDZ-Peptide Binding

This chapter describes two computational methods for PDZ-peptide binding: high-throughput computational protein design (CPD) and a medium-throughput approach combining molecular dynamics for conformational sampling with a Poisson-Boltzmann (PB) Linear Interaction Energy for scoring. A new CPD method is outlined, which uses adaptive Monte Carlo simulations to efficiently sample peptide variants that tightly bind a PDZ domain, and provides at the same time precise estimates of their relative binding free energies. A detailed protocol is described based on the Proteus CPD software. The medium-throughput approach can be performed with standard MD and PB software, such as NAMD and Charmm. For 40 complexes between Tiam1 and peptide ligands, it gave high a2ccuracy, with mean errors of around 0.5 kcal/mol for relative binding free energies and no large errors. It requires a moderate amount of parameter fitting before it can be applied, and its transferability to other protein families is still untested.

The urokinase plasminogen activator binding to its receptor: a quantum biochemistry description within an in/homogeneous dielectric function framework with application to uPA–uPAR peptide inhibitors

DFT calculations using the MFCC fragment-based model considering a spatial-dependent dielectric function based on the Poisson–Boltzmann approximation were performed to describe the uPA–uPAR interactions.

Modeling Electrostatic Force in Protein-Protein Recognition

Electrostatic interactions are important for understanding molecular interactions, since they are long-range interactions and can guide binding partners to their correct binding positions. To investigate the role of electrostatic forces in molecular recognition, we calculated electrostatic forces between binding partners separated at various distances. The investigation was done on a large set of 275 protein complexes using recently developed DelPhiForce tool and in parallel, evaluating the total electrostatic force via electrostatic association energy. To accomplish the goal, we developed a method to find an appropriate direction to move one chain of protein complex away from its bound position and then calculate the corresponding electrostatic force as a function of separation distance. It is demonstrated that at large distances between the partners, the electrostatic force (magnitude and direction) is consistent among the protocols used and the main factors contributing to it are the net charge of the partners and their interfaces. However, at short distances, where partners form specific pair-wise interactions or de-solvation penalty becomes significant, the outcome depends on the precise balance of these factors. Based on the electrostatic force profile (force as a function of distance), we group the cases into four distinctive categories, among which the most intriguing is the case termed "soft landing." In this case, the electrostatic force at large distances is favorable assisting the partners to come together, while at short distance it opposes binding, and thus slows down the approach of the partners toward their physical binding.

What Are We Missing by Not Measuring the Net Charge of Proteins?

The net electrostatic charge (Z) of a folded protein in solution represents a bird's eye view of its surface potentials-including contributions from tightly bound metal, solvent, buffer, and cosolvent ions-and remains one of its most enigmatic properties. Few tools are available to the average biochemist to rapidly and accurately measure Z at pH≠pI. Tools that have been developed more recently seem to go unnoticed. Most scientists are content with this void and estimate the net charge of a protein from its amino acid sequence, using textbook values of pK_a . Thus, Z remains unmeasured for nearly all folded proteins at pH≠pI. When marveling at all that has been learned from accurately measuring the other fundamental property of a protein-its mass-one wonders: what are we missing by not measuring the net charge of folded, solvated proteins? A few big questions immediately emerge in bioinorganic chemistry. When a single electron is transferred to a metalloprotein, does the net charge of the protein change by approximately one elementary unit of charge or does charge regulation dominate, that is, do the pK_a values of most ionizable residues (or just a few residues) adjust in response to (or in concert with) electron transfer? Would the free energy of charge regulation (ΔΔG_z ) account for most of the outer sphere reorganization energy associated with electron transfer? Or would ΔΔG_z contribute more to the redox potential? And what about metal binding itself? When an apo-metalloprotein, bearing minimal net negative charge (e.g., Z=-2.0) binds one or more metal cations, is the net charge abolished or inverted to positive? Or do metalloproteins regulate net charge when coordinating metal ions? The author's group has recently dusted off a relatively obscure tool-the "protein charge ladder"-and used it to begin to answer these basic questions.

Can Combined Electrostatic and Polarization Effects Alone Explain the F···F Negative-Negative Bonding in Simple Fluoro-Substituted Benzene Derivatives? A First-Principles Perspective

The divergence of fluorine-based systems and significance of their nascent non-covalent chemistry in molecular assemblies are presented in a brief review of the field. Emphasis has been placed to show that type-I and -II halogen-centered F···F long-ranged intermolecular distances viable between the entirely negative fluorine atoms in some fluoro-substituted dimers of C6H6 can be regarded as the consequence of significant non-covalent attractive interactions. Such attractive interactions observed in the solid-state structures of C6F6 and other similar fluorine-substituted aromatic compounds have frequently been underappreciated. While these are often ascribed to crystal packing effects, we show using first-principles level calculations that these are much more fundamental in nature. The stability and reliability of these interactions are supported by their negative binding energies that emerge from a supermolecular procedure using MP2 (second-order Møller-Plesset perturbation theory), and from the Symmetry Adapted Perturbation Theory, in which the latter does not determine the interaction energy by computing the total energy of the monomers or dimer. Quantum Theory of Atoms in Molecules and Reduced Density Gradient Non-Covalent Index charge-density-based approaches confirm the F···F contacts are a consequence of attraction by their unified bond path (and bond critical point) and isosurface charge density topologies, respectively. These interactions can be explained neither by the so-called molecular electrostatic surface potential (MESP) model approach that often demonstrates attraction between sites of opposite electrostatic surface potential by means of Coulomb’s law of electrostatics, nor purely by the effect of electrostatic polarization. We provide evidence against the standalone use of this approach and the overlooking of other approaches, as the former does not allow for the calculation of the electrostatic potential on the surfaces of the overlapping atoms on the monomers as in the equilibrium geometry of a complex. This study thus provides unequivocal evidence of the limitation of the MESP approach for its use in gaining insight into the nature of reactivity of overlapped interacting atoms and the intermolecular interactions involved.

Combining the polarizable Drude force field with a continuum electrostatic Poisson-Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson-Boltzmann/solvent-accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self-consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well-experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas-phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute-solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non-polar solvation effects. © 2018 Wiley Periodicals, Inc.

Assessment of a Single Decoupling Alchemical Approach for the Calculation of the Absolute Binding Free Energies of Protein-Peptide Complexes

The computational modeling of peptide inhibitors to target protein-protein binding interfaces is growing in interest as these are often too large, too shallow, and too feature-less for conventional small molecule compounds. Here, we present a rare successful application of an alchemical binding free energy method for the calculation of converged absolute binding free energies of a series of protein-peptide complexes. Specifically, we report the binding free energies of a series of cyclic peptides derived from the LEDGF/p75 protein to the integrase receptor of the HIV1 virus. The simulations recapitulate the effect of mutations relative to the wild-type binding motif of LEDGF/p75, providing structural, energetic and dynamical interpretations of the observed trends. The equilibration and convergence of the calculations are carefully analyzed. Convergence is aided by the adoption of a single-decoupling alchemical approach with implicit solvation, which circumvents the convergence difficulties of conventional double-decoupling protocols. We hereby present the single-decoupling methodology and critically evaluate its advantages and limitations. We also discuss some of the challenges and potential pitfalls of binding free energy calculations for complex molecular systems which have generally limited their applicability to the quantitative study of protein-peptide binding equilibria.

Reproducing the Ensemble Average Polar Solvation Energy of a Protein from a Single Structure: Gaussian-Based Smooth Dielectric Function for Macromolecular Modeling

Typically, the ensemble average polar component of solvation energy (ΔG_polar^solv) of a macromolecule is computed using molecular dynamics (MD) or Monte Carlo (MC) simulations to generate conformational ensemble and then single/rigid conformation solvation energy calculation is performed on each snapshot. The primary objective of this work is to demonstrate that Poisson-Boltzmann (PB)-based approach using a Gaussian-based smooth dielectric function for macromolecular modeling previously developed by us (Li et al. J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) can reproduce that ensemble average (ΔG_polar^solv) of a protein from a single structure. We show that the Gaussian-based dielectric model reproduces the ensemble average ΔG_polar^solv(⟨ΔG_polar^solv⟩) from an energy-minimized structure of a protein regardless of the minimization environment (structure minimized in vacuo, implicit or explicit waters, or crystal structure); the best case, however, is when it is paired with an in vacuo-minimized structure. In other minimization environments (implicit or explicit waters or crystal structure), the traditional two-dielectric model can still be selected with which the model produces correct solvation energies. Our observations from this work reflect how the ability to appropriately mimic the motion of residues, especially the salt bridge residues, influences a dielectric model's ability to reproduce the ensemble average value of polar solvation free energy from a single in vacuo-minimized structure.

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is underdetermined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parametrization problems, including those beyond continuum solvation calculations. The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

A Simple PB/LIE Free Energy Function Accurately Predicts the Peptide Binding Specificity of the Tiam1 PDZ Domain

PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB) continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or “PB/LIE” free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α₂ helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo. The overall performance of the model should allow its use in the design of new PDZ ligands in the future.

DelPhiForce, a tool for electrostatic force calculations: Applications to macromolecular binding

Long-range electrostatic forces play an important role in molecular biology, particularly in macromolecular interactions. However, calculating the electrostatic forces for irregularly shaped molecules immersed in water is a difficult task. Here, we report a new tool, DelPhiForce, which is a tool in the DelPhi package that calculates and visualizes the electrostatic forces in biomolecular systems. In parallel, the DelPhi algorithm for modeling electrostatic potential at user-defined positions has been enhanced to include triquadratic and tricubic interpolation methods. The tricubic interpolation method has been tested against analytical solutions and it has been demonstrated that the corresponding errors are negligibly small at resolution 4 grids/Å. The DelPhiForce is further applied in the study of forces acting between partners of three protein-protein complexes. It has been demonstrated that electrostatic forces play a dual role by steering binding partners (so that the partners recognize their native interfaces) and exerting an electrostatic torque (if the mutual orientations of the partners are not native-like). The output of DelPhiForce is in a format that VMD can read and visualize, and provides additional options for analysis of protein-protein binding. DelPhiForce is available for download from the DelPhi webpage at http://compbio.clemson.edu/downloadDir/delphiforce.tar.gz © 2017 Wiley Periodicals, Inc.

Accurate estimation of electrostatic binding energy with Poisson-Boltzmann equation solver DelPhi program

Poisson–Boltzmann (PB) model is a widely used implicit solvent approximation in biophysical modeling because of its ability to provide accurate and reliable PB electrostatic salvation free energies ([Formula: see text] as well as electrostatic binding free energy ([Formula: see text] estimations. However, a recent study has warned that the 0.5[Formula: see text]Å grid spacing which is normally adopted can produce unacceptable errors in [Formula: see text] estimation with the solvent excluded surface (SES) (Harris RC, Boschitsch AH and Fenley MO, Influence of grid spacing in Poisson–Boltzmann equation binding energy estimation, J Chem Theory Comput 19: 3677–3685, 2013). In this work, we investigate the grid dependence of the widely used PB solver DelPhi v6.2 with molecular surface (MS) for estimating both electrostatic solvation free energies and electrostatic binding free energies. Our results indicate that, for the molecular complex and components the absolute errors of [Formula: see text] are smaller than that of [Formula: see text], and grid spacing of 0.8[Formula: see text]Å with DelPhi program ensures the accuracy and reliability of [Formula: see text]; however, the accuracy of [Formula: see text] largely relies on the order of magnitude of [Formula: see text] itself rather than that of [Formula: see text] or [Formula: see text]. Our findings suggest that grid spacing of 0.5[Formula: see text]Å is enough to produce accurate [Formula: see text] for molecules whose [Formula: see text] are large, but finer grids are needed when [Formula: see text] is very small.