The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10⁹ unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations

Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Determination of Hydrophobic Lengths of Membrane Proteins with the HDGB Implicit Membrane Model

A protocol for predicting the hydrophobic length of membrane proteins using the heterogeneous dielectric generalized Born (HDGB) implicit membrane model is presented. The method involves optimal positioning in the membrane and identification of lipid-facing and inward-facing residues, followed by energy optimization of the implicit membrane model to obtain the hydrophobic length from the optimal membrane width. The latest HDGB version 3 (HDGBv3) and HDGB van der Waals (HDGBvdW) models were applied to a test set containing 15 proteins (seven β-barrel and eight α-helical proteins), for which matching membrane widths are available from experiment, and an additional set contains ten α-helical and ten β-barrel proteins without any experimental data. The results with the HDGB model compare favorably with predictions from methods used in the Orientations of Proteins in Membranes (OPM) and Protein Data Bank of Transmembrane Proteins (PDB-TM) databases.

Electrokinetic Lattice Boltzmann Solver Coupled to Molecular Dynamics: Application to Polymer Translocation

We have developed a theoretical and computational approach to deal with systems that involve a disparate range of spatiotemporal scales, such as those composed of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multicomponent Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multicomponent description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. Lastly, we discuss the advantages and complexities of the approach.

Inhibition of nonenzymatic depurination of nucleic acids by polycations

DNA base depurination is one of the most common forms of DNA damage in vivo and in vitro, and the suppression of depurination is very important for versatile applications of DNA in biotechnology and medicine. In this work, it was shown that the polycations chitosan (Cho) and spermine (Spm) strongly inhibit DNA depurination through the formation of polyion complexes with DNA molecules. The intramolecular electrostatic interaction of positively charged polycations with DNA efficiently suppresses the protonation of purine groups, which is the key step of depurination. Importantly, the optimal pH for Cho's inhibition of depurination is significantly different from that of Spm. Cho is very effective in the inhibition of depurination in highly acidic media (pH: 1.5–3), whereas Spm is found to suppress the chemical reaction near neutral pH, as well as in acidic solutions. This remarkable pH specificity of the two biorelevant polycations is attributed to the difference in the pK_a values of the amino groups. The relevance of our results with the biological roles of biogenic polycations is also discussed.

Self-Assembly of Human Serum Albumin: A Simplex Phenomenon

Spontaneous self-assemblies of biomolecules can generate geometrical patterns. Our findings provide an insight into the mechanism of self-assembled ring pattern generation by human serum albumin (HSA). The self-assembly is a process guided by kinetic and thermodynamic parameters. The generated protein ring patterns display a behavior which is geometrically related to a n-simplex model and is explained through thermodynamics and chemical kinetics.

Multiparticle Brownian dynamics simulation of experimental kinetics of cytochrome bf oxidation and photosystem I reduction by plastocyanin

A model of electron transport from cytochrome f to photosystem I mediated by plastocyanin was designed on the basis of the multiparticle Brownian dynamics method. The model combines events which occur over a wide time range, including protein diffusion along the thylakoid membrane, long-distance interactions between proteins, formation of a multiprotein complex, electron transfer within a complex and complex dissociation. Results of the modeling were compared with the experimental kinetics measured in chloroplast thylakoids. Computer simulation demonstrated that the complex interior of the photosynthetic membrane, electrostatic interactions and Brownian diffusion provide physical conditions for the directed electron flow along the photosynthetic electron transport chain.

Water Dynamics in the Hydration Shells of Biomolecules

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water.

Caveat on the Boltzmann distribution function use in biology

Sigmoid semilogarithmic functions with shape of Boltzmann equations, have become extremely popular to describe diverse biological situations. Part of the popularity is due to the easy availability of software which fits Boltzmann functions to data, without much knowledge of the fitting procedure or the statistical properties of the parameters derived from the procedure. The purpose of this paper is to explore the plasticity of the Boltzmann function to fit data, some aspects of the optimization procedure to fit the function to data and how to use this plastic function to differentiate the effect of treatment on data and to attest the statistical significance of treatment effect on the data.

Self-assembled α-Tocopherol Transfer Protein Nanoparticles Promote Vitamin E Delivery Across an Endothelial Barrier

Vitamin E is one of the most important natural antioxidants, protecting polyunsaturated fatty acids in the membranes of cells. Among different chemical isoforms assimilated from dietary regimes, RRR-α-tocopherol is the only one retained in higher animals. This is possible thanks to α-Tocopherol Transfer Protein (α-TTP), which extracts α-tocopherol from endosomal compartments in liver cells, facilitating its distribution into the body. Here we show that, upon binding to its substrate, α-TTP acquires tendency to aggregation into thermodynamically stable high molecular weight oligomers. Determination of the structure of such aggregates by X-ray crystallography revealed a spheroidal particle formed by 24 protein monomers. Oligomerization is triggered by refolding of the N-terminus. Experiments with cultured cell monolayers demonstrate that the same oligomers are efficiently transported through an endothelial barrier (HUVEC) and not through an epithelial one (Caco-2). Discovery of a human endogenous transport protein with intrinsic capability of crossing endothelial tissues opens to new ways of drug delivery into the brain or other tissues protected by endothelial barriers.

Experimental charge density from electron microscopic maps

The charge density (CD) distribution of an atom is the difference per unit volume between the positive charge of its nucleus and the distribution of the negative charges carried by the electrons that are associated with it. The CDs of the atoms in macromolecules are responsible for their electrostatic potential (ESP) distributions, which can now be visualized using cryo-electron microscopy at high resolution. CD maps can be recovered from experimental ESP density maps using the negative Laplacian operation. CD maps are easier to interpret than ESP maps because they are less sensitive to long-range electrostatic effects. An ESP-to-CD conversion involves multiplication of amplitudes of structure factors as Fourier transforms of these maps in reciprocal space by 1/d² , where d is the resolution of reflections. In principle, it should be possible to determine the charges carried by the individual atoms in macromolecules by comparing experimental CD maps with experimental ESP maps.

[Prediction of protein thermostability from their primary structure: the current state and development factors]

The construction of proteins and peptides with desired properties, including resistance to high temperatures, as well as optimization of their amino acid composition, is an important and complex task, which attracts much attention in various branches of the basic sciences, and also in biomedicine and biotechnology. This raises the question: what method is more relevant for the at the pilot stage of research in order to estimate the influence of the planned amino acid substitutions on the thermostability of the resultant protein construct? In this brief review we have classified existing basic practical and theoretical approaches used in studies and predicting the thermal stability of native and recombinant polypeptides. Particular attention has been paid to the predictive potential of statistical methods for studying the thermodynamic parameters of the primary protein structure and prospects of their use.

Designing the Sniper: Improving Targeted Human Cytolytic Fusion Proteins for Anti-Cancer Therapy via Molecular Simulation

Targeted human cytolytic fusion proteins (hCFPs) are humanized immunotoxins for selective treatment of different diseases including cancer. They are composed of a ligand specifically binding to target cells genetically linked to a human apoptosis-inducing enzyme. hCFPs target cancer cells via an antibody or derivative (scFv) specifically binding to e.g., tumor associated antigens (TAAs). After internalization and translocation of the enzyme from endocytosed endosomes, the human enzymes introduced into the cytosol are efficiently inducing apoptosis. Under in vivo conditions such enzymes are subject to tight regulation by native inhibitors in order to prevent inappropriate induction of cell death in healthy cells. Tumor cells are known to upregulate these inhibitors as a survival mechanism resulting in escape of malignant cells from elimination by immune effector cells. Cytosolic inhibitors of Granzyme B and Angiogenin (Serpin P9 and RNH1, respectively), reduce the efficacy of hCFPs with these enzymes as effector domains, requiring detrimentally high doses in order to saturate inhibitor binding and rescue cytolytic activity. Variants of Granzyme B and Angiogenin might feature reduced affinity for their respective inhibitors, while retaining or even enhancing their catalytic activity. A powerful tool to design hCFPs mutants with improved potency is given by in silico methods. These include molecular dynamics (MD) simulations and enhanced sampling methods (ESM). MD and ESM allow predicting the enzyme-protein inhibitor binding stability and the associated conformational changes, provided that structural information is available. Such "high-resolution" detailed description enables the elucidation of interaction domains and the identification of sites where particular point mutations may modify those interactions. This review discusses recent advances in the use of MD and ESM for hCFP development from the viewpoints of scientists involved in both fields.

Heterogeneous dielectric generalized Born model with a van der Waals term provides improved association energetics of membrane-embedded transmembrane helices

The heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is extended by the addition of a van der Waals dispersion term to better describe the nonpolar components of the free energy of solvation. The new model, termed HDGBvdW, improves the energy estimates in the hydrophobic interior of the membrane, where polar and charged species are rarely found and nonpolar interactions become significant. The implicit van der Waals term for the membrane environment extends the model from Gallicchio et al. (J. Comput. Chem. 2004, 25, 479) by combining separate contributions from each of the membrane components. The HDGBvdW model is validated with a series of test cases ranging from membrane insertion and pair association profiles of amino acid side chain analogs and transmembrane helices. Overall, the HDGBvdW model leads to increased agreement with explicit membrane simulation results and experimental data. © 2016 Wiley Periodicals, Inc.

ESES: Software for Eulerian solvent excluded surface

Solvent excluded surface (SES) is one of the most popular surface definitions in biophysics and molecular biology. In addition to its usage in biomolecular visualization, it has been widely used in implicit solvent models, in which SES is usually immersed in a Cartesian mesh. Therefore, it is important to construct SESs in the Eulerian representation for biophysical modeling and computation. This work describes a software package called Eulerian solvent excluded surface (ESES) for the generation of accurate SESs in Cartesian grids. ESES offers the description of the solvent and solute domains by specifying all the intersection points between the SES and the Cartesian grid lines. Additionally, the interface normal at each intersection point is evaluated. Furthermore, for a given biomolecule, the ESES software not only provides the whole surface area, but also partitions the surface area according to atomic types. Homology theory is utilized to detect topological features, such as loops and cavities, on the complex formed by the SES. The sizes of loops and cavities are measured based on persistent homology with an evolutionary partial differential equation-based filtration. ESES is extensively validated by surface visualization, electrostatic solvation free energy computation, surface area and volume calculations, and loop and cavity detection and their size estimation. We used the Amber PBSA test set in our electrostatic solvation energy, area, and volume validations. Our results are either calibrated by analytical values or compared with those from the MSMS software. © 2017 Wiley Periodicals, Inc.

Phosphoramidate hydrolysis catalyzed by human histidine triad nucleotide binding protein 1 (hHint1): a cluster-model DFT computational study

The histidine triad of hHint1 serves as a proton shuttle in the DFT proposed mechanism of the hydrolysis of phosphoramidate.

Development of the modern theory of polymeric complex coacervation

Oppositely charged polymers can undergo the process of complex coacervation, which refers to a liquid-liquid phase separation driven by electrostatic attraction. These materials have demonstrated considerable promise as the basis for complex, self-assembled materials. In this review, we provide a broad overview of the theoretical tools used to understand the physical properties of polymeric coacervates. In particular, we discuss historic theories (Voorn-Overbeek, Random Phase Approximation), and then describe recent developments in the field (Field Theoretic, Counterion Release, Molecular Simulation, and Polymer Reference Interaction Site Model methods). We provide context for these methods, and map out the patchwork of theoretical models that are used to describe a diverse array of coacervate systems. We use this review of the literature to clarify a number of important theoretical challenges remaining in our physical understanding of complex coacervation.

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.

Beyond Antibodies: Development of a Novel Protein Scaffold Based on Human Chaperonin 10

Human Chaperonin 10 (hCpn10) was utilised as a novel scaffold for presenting peptides of therapeutic and diagnostic significance. Molecular dynamic simulations and protein sizing analyses identified a peptide linker (P1) optimal for the formation of the quarternary hCpn10 heptamer structure. hCpn10 scaffold displaying peptides targeting Factor VIIa (CE76_-P1) and CD44 (CP7) were expressed in E. coli. Functional studies of CE76_-P1 indicated nanomolar affinity for Factor VIIa (3 nM) similar to the E-76 peptide (6 nM), with undetectable binding to Factor X. CE76_-P1 was a potent inhibitor of FX activity (via inhibition of Factor VIIa) and prolonged clot formation 4 times longer than achieved by E-76 peptide as determined by prothrombin time (PT) assays. This improvement in clotting function by CE76_-P1, highlights the advantages of a heptamer-based scaffold for improving avidity by multiple peptide presentation. In another example of hCPn10 utility as a scaffold, CP7 bound to native CD44 overexpressed on cancer cells and bound rCD44 with high affinity (K_D 9.6 nM). The ability to present various peptides through substitution of the hCpn10 mobile loop demonstrates its utility as a novel protein scaffold.

High-Frequency Nanocapacitor Arrays: Concept, Recent Developments, and Outlook

We have developed a measurement platform for performing high-frequency AC detection at nanoelectrodes. The system consists of 65 536 electrodes (diameter 180 nm) arranged in a sub-micrometer rectangular array. The electrodes are actuated at frequencies up to 50 MHz, and the resulting AC current response at each separately addressable electrode is measured in real time. These capabilities are made possible by fabricating the electrodes on a complementary metal-oxide-semiconductor (CMOS) chip together with the associated control and readout electronics, thus minimizing parasitic capacitance and maximizing the signal-to-noise ratio. This combination of features offers several advantages for a broad range of experiments. First, in contrast to alternative CMOS-based electrical systems based on field-effect detection, high-frequency operation is sensitive beyond the electrical double layer and can probe entities at a range of micrometers in electrolytes with high ionic strength such as water at physiological salt concentrations. Far from being limited to single- or few-channel recordings like conventional electrochemical impedance spectroscopy, the massively parallel design of the array permits electrically imaging micrometer-scale entities with each electrode serving as a separate pixel. This allows observation of complex kinetics in heterogeneous environments, for example, the motion of living cells on the surface of the array. This imaging aspect is further strengthened by the ability to distinguish between analyte species based on the sign and magnitude of their AC response. Finally, we show here that sensitivity down to the attofarad level combined with the small electrode size permits detection of individual 28 nm diameter particles as they land on the sensor surface. Interestingly, using finite-element methods, it is also possible to calculate accurately the full three-dimensional electric field and current distributions during operation at the level of the Poisson-Nernst-Planck formalism. This makes it possible to validate the interpretation of measurements and to optimize the design of future experiments. Indeed, the complex frequency and spatial dependence of the data suggests that experiments to date have only scratched the surface of the method's capabilities. Future iterations of the hardware will take advantage of the higher frequencies, higher electrode packing densities and smaller electrode sizes made available by continuing advances in CMOS manufacturing. Combined with targeted immobilization of targets at the electrodes, we anticipate that it will soon be possible to realize complex biosensors based on spatial- and time-resolved nanoscale impedance detection.

Effect of allosteric molecules on structure and drug affinity of HIV-1 protease by molecular dynamics simulations

Recent experiments show that small molecules can bind onto the allosteric sites of HIV-1 protease (PR), which provides a starting point for developing allosteric inhibitors. However, the knowledge of the effect of such binding on the structural dynamics and binding free energy of the active site inhibitor and PR is still lacking. Here, we report 200ns long molecular dynamics simulation results to gain insight into the influences of two allosteric molecules (1H-indole-6-carboxylic acid, 1F1 and 2-methylcyclohexano, 4D9). The simulations demonstrate that both allosteric molecules change the PR conformation and stabilize the structures of PR and the inhibitor; the residues of the flaps are sensitive to the allosteric molecules and the flexibility of the residues is pronouncedly suppressed; the additions of the small molecules to the allosteric sites strengthen the binding affinities of 3TL-PR by about 12-15kal/mol in the binding free energy, which mainly arises from electrostatic term. Interestingly, it is found that the action mechanisms of 1F1 and 4D9 are different, the former behaviors like a doorman that keeps the inhibitor from escape and makes the flaps (door) partially open; the latter is like a wedge that expands the allosteric space and meanwhile closes the flaps. Our data provide a theoretical support for designing the allosteric inhibitor.

The impact of surface area, volume, curvature, and Lennard-Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

Influence of pH and ionic strength on electrostatic properties of ferredoxin, FNR, and hydrogenase and the rate constants of their interaction

Ferredoxin (Fd) protein transfers electrons from photosystem I (PSI) to ferredoxin:NADP⁺-reductase (FNR) in the photosynthetic electron transport chain, as well as other metabolic pathways. In some photosynthetic organisms including cyanobacteria and green unicellular algae under anaerobic conditions Fd transfers electrons not only to FNR but also to hydrogenase-an enzyme which catalyzes reduction of atomic hydrogen to H₂. One of the questions posed by this competitive relationship between proteins is which characteristics of thylakoid stroma media allow switching of the electron flow between the linear path PSI-Fd-FNR-NADP⁺ and the path PSI-Fd-hydrogenase-H₂. The study was conducted using direct multiparticle simulation approach. In this method protein molecules are considered as individual objects that experience Brownian motion and electrostatic interaction with the surrounding media and each other. Using the model we studied the effects of pH and ionic strength (I) upon complex formation between ferredoxin and FNR and ferredoxin and hydrogenase. We showed that the rate constant of Fd-FNR complex formation is constant in a wide range of physiologically significant pH values. Therefore it can be argued that regulation of FNR activity doesn't involve pH changes in stroma. On the other hand, in the model rate constant of Fd-hydrogenase interaction dramatically depends upon pH: in the range 7-9 it increases threefold. It may seem that because hydrogenase reduces protons it should be more active when pH is acidic. Apparently, regulation of hydrogenase's affinity to both her reaction partners (H⁺ and Fd) is carried out by changes in its electrostatic properties. In the dark, the protein is inactive and in the light it is activated and starts to interact with both Fd and H⁺. Therefore, we can conclude that in chloroplasts the rate of hydrogen production is regulated by pH through the changes in the affinity between hydrogenase and ferredoxin.

Electrostatic Similarity Analysis of Human β-Defensin Binding in the Melanocortin System

The β-defensins are a class of small cationic proteins that serve as components of numerous systems in vertebrate biology, including the immune and melanocortin systems. Human β-defensin 3 (HBD3), which is produced in the skin, has been found to bind to melanocortin receptors 1 and 4 through complementary electrostatics, a unique mechanism of ligand-receptor interaction. This finding indicates that electrostatics alone, and not specific amino acid contact points, could be sufficient for function in this ligand-receptor system, and further suggests that other small peptide ligands could interact with these receptors in a similar fashion. Here, we conducted molecular-similarity analyses and functional studies of additional members of the human β-defensin family, examining their potential as ligands of melanocortin-1 receptor, through selection based on their electrostatic similarity to HBD3. Using Poisson-Boltzmann electrostatic calculations and molecular-similarity analysis, we identified members of the human β-defensin family that are both similar and dissimilar to HBD3 in terms of electrostatic potential. Synthesis and functional testing of a subset of these β-defensins showed that peptides with an HBD3-like electrostatic character bound to melanocortin receptors with high affinity, whereas those that were anticorrelated to HBD3 showed no binding affinity. These findings expand on the central role of electrostatics in the control of this ligand-receptor system and further demonstrate the utility of employing molecular-similarity analysis. Additionally, we identified several new potential ligands of melanocortin-1 receptor, which may have implications for our understanding of the role defensins play in melanocortin physiology.

DNA-HMGB1 interaction: The nuclear aggregates of polyamine mediation

Nuclear aggregates of polyamines (NAPs) are supramolecular compounds generated by the self-assembly of protonated nuclear polyamines (spermine, spermidine and putrescine) and phosphate ions. In the presence of genomic DNA, the hierarchical process of self-structuring ultimately produces nanotube-like polymers that envelop the double helix. Because of their modular nature and their aggregation-disaggregation dynamics, NAPs confer plasticity and flexibility to DNA. Through the disposition of charges, NAPs also enable a bidirectional stream of information between the genome and interacting moieties. High mobility group (HMG) B1 is a non-histone chromosomal protein that binds to DNA and that influences multiple nuclear processes. Because genomic DNA binds to either NAPs or HMGB1 protein, we explored the ability of in vitro self-assembled NAPs (ivNAPs) to mediate the DNA-HMGB1 interaction. To this end, we structured DNA-NAPs-HMGB1 and DNA-HMGB1-NAPs ternary complexes in vitro through opportune sequential incubations. Mobility shift electrophoresis and atomic force microscopy showed that the DNA-ivNAPs-HGMB1 complex had conformational assets supposedly more suitable those of the DNA-HGMB1-ivNAPs to comply with the physiological and functional requirements of DNA. Our findings indicated that ivNAPs act as mediators of the DNA-HMGB1 interaction.

Control of the Redox Activity of PbS Quantum Dots by Tuning Electrostatic Interactions at the Quantum Dot/Solvent Interface

This paper describes the control of electron exchange between a colloidal PbS quantum dot (QD) and a negatively charged small molecule (9,10-anthraquinone-2-sulfonic acid sodium salt, AQ), through tuning of the charge density in the ligand shell of the QD, within an aqueous dispersion. The probability of electron exchange, measured through steady-state and time-resolved optical spectroscopy, is directly related to the permeability of the protective ligand shell, which is a mixed monolayer of negatively charged 6-mercaptohexanoate (MHA) and neutral 6-mercaptohexanol (MHO), to AQ. The composition of the ligand shell is quantitatively characterized by (1)H NMR. The dependence of the change in Gibbs free energy, ΔGobs, for the diffusion of AQ through the charged ligand shell and its subsequent adsorption to the QD surface is well-described with an electrostatic double-layer model for the QD/solvent interface. Fits of the optical data to this model yield an increase in the free energy for transfer of AQ from bulk solution to the surface of the QD (where it exchanges electrons with the QD) of 154 J/mol upon introduction of each additional charged MHA ligand to the ligand shell. This work expands the set of chemical parameters useful for controlling the redox activity of QDs via surface modification and suggests strategies for the use of nanoparticles for molecular and biomolecular recognition within chemically complex environments and for design of chemically stable nanoparticles for aqueous photocatalytic systems.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Refinement of Atomic Structures Against cryo-EM Maps

This review describes some of the methods for atomic structure refinement (fitting) against medium/high-resolution single-particle cryo-EM reconstructed maps. Some of the tools developed for macromolecular X-ray crystal structure analysis, especially those encapsulating prior chemical and structural information can be transferred directly for fitting into cryo-EM maps. However, despite the similarities, there are significant differences between data produced by these two techniques; therefore, different likelihood functions linking the data and model must be used in cryo-EM and crystallographic refinement. Although tools described in this review are mostly designed for medium/high-resolution maps, if maps have sufficiently good quality, then these tools can also be used at moderately low resolution, as shown in one example. In addition, the use of several popular crystallographic methods is strongly discouraged in cryo-EM refinement, such as 2Fo-Fc maps, solvent flattening, and feature-enhanced maps (FEMs) for visualization and model (re)building. Two problems in the cryo-EM field are overclaiming resolution and severe map oversharpening. Both of these should be avoided; if data of higher resolution than the signal are used, then overfitting of model parameters into the noise is unavoidable, and if maps are oversharpened, then at least parts of the maps might become very noisy and ultimately uninterpretable. Both of these may result in suboptimal and even misleading atomic models.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12).

Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions

Continuum solvation modeling based upon the Poisson-Boltzmann equation (PBE) is widely used in structural and functional analysis of biomolecules. In this work, we propose a charge-central interpretation of the full nonlinear PBE electrostatic interactions. The validity of the charge-central view or simply charge view, as formulated as a vacuum Poisson equation with effective charges, was first demonstrated by reproducing both electrostatic potentials and energies from the original solvated full nonlinear PBE. There are at least two benefits when the charge-central framework is applied. First the convergence analyses show that the use of polarization charges allows a much faster converging numerical procedure for electrostatic energy and forces calculation for the full nonlinear PBE. Second, the formulation of the solvated electrostatic interactions as effective charges in vacuum allows scalable algorithms to be deployed for large biomolecular systems. Here, we exploited the charge-view interpretation and developed a particle-particle particle-mesh (P3M) strategy for the full nonlinear PBE systems. We also studied the accuracy and convergence of solvation forces with the charge-view and the P3M methods. It is interesting to note that the convergence of both the charge-view and the P3M methods is more rapid than the original full nonlinear PBE method. Given the developments and validations documented here, we are working to adapt the P3M treatment of the full nonlinear PBE model to molecular dynamics simulations.

Internal configuration and electric potential in planar negatively charged lipid head group region in contact with ionic solution

The lipid bilayer composed of negatively charged lipid 1-palmitoyl-3-oleoyl-sn-glycero-3-phosphatidylserine (POPS) in contact with an aqueous solution of monovalent salt ions was studied theoretically by using the mean-field modified Langevin-Poisson-Boltzmann (MLPB) model. The MLPB results were tested by using molecular dynamic (MD) simulations. In the MLPB model the charge distribution of POPS head groups is theoretically described by the negatively charged surface which accounts for negatively charged phosphate groups, while the positively charged amino groups and negatively charged carboxylate groups are assumed to be fixed on the rod-like structures with rotational degree of freedom. The spatial variation of relative permittivity, which is not considered in the well-known Gouy-Chapman (GC) model or in MD simulations, is thoroughly derived within a strict statistical mechanical approach. Therefore, the spatial dependence and magnitude of electric potential within the lipid head group region and its close vicinity are considerably different in the MLPB model from the GC model. The influence of the bulk salt concentration and temperature on the number density profiles of counter-ions and co-ions in the lipid head group region and aqueous solution along with the probability density function for the lipid head group orientation angle was compared and found to be in qualitative agreement in the MLPB and MD models.

Protein side chain conformation predictions with an MMGBSA energy function

The prediction of protein side chain conformations from backbone coordinates is an important task in structural biology, with applications in structure prediction and protein design. It is a difficult problem due to its combinatorial nature. We study the performance of an "MMGBSA" energy function, implemented in our protein design program Proteus, which combines molecular mechanics terms, a Generalized Born and Surface Area (GBSA) solvent model, with approximations that make the model pairwise additive. Proteus is not a competitor to specialized side chain prediction programs due to its cost, but it allows protein design applications, where side chain prediction is an important step and MMGBSA an effective energy model. We predict the side chain conformations for 18 proteins. The side chains are first predicted individually, with the rest of the protein in its crystallographic conformation. Next, all side chains are predicted together. The contributions of individual energy terms are evaluated and various parameterizations are compared. We find that the GB and SA terms, with an appropriate choice of the dielectric constant and surface energy coefficients, are beneficial for single side chain predictions. For the prediction of all side chains, however, errors due to the pairwise additive approximation overcome the improvement brought by these terms. We also show the crucial contribution of side chain minimization to alleviate the rigid rotamer approximation. Even without GB and SA terms, we obtain accuracies comparable to SCWRL4, a specialized side chain prediction program. In particular, we obtain a better RMSD than SCWRL4 for core residues (at a higher cost), despite our simpler rotamer library. Proteins 2016; 84:803-819. © 2016 Wiley Periodicals, Inc.

Structure-Based Design of a Br Halogen Bond at the Complex Interface of the Human Placental HtrA1 PDZ Domain with Its Heptapeptide Ligand

The shock-induced serine protease HtrA1 is a potential regulator of human placenta development during pregnancy. The protein contains a functional PDZ domain that has been solved in complex with a phage display-derived heptapeptide: Asp-6 Ser-5 Arg-4 Ile-3 Trp-2 Trp-1 Val0 . In this study, a rationally designed halogen bond was introduced to the domain-peptide complex based on its NMR structure in solution. We computationally compared the stabilization energies and hindrance effects due to the presence of different halogens X (X = F, Cl, Br, or I), using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach, and found that the Br atom could considerably promote the peptide binding free energy (ΔΔG = -5.2 kcal/mol). Fluorescence assays confirmed that the peptide affinity to the HtrA1 PDZ domain was improved by approximately sevenfold upon bromination. Structural analysis identified a geometrically perfect halogen bond between the Br atom of the peptide Trp-1 residue and the carbonyl O atom of the HtrA1 Ile385 residue, with a bond length and an interaction energy of d = 3.20 Å and ΔE = -3.7 kcal/mol, respectively.

Protofold II: Enhanced Model and Implementation for Kinetostatic Protein Folding1

A reliable prediction of three-dimensional (3D) protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this paper, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU/GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels, namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.

Probing binding mechanism of interleukin-6 and olokizumab: in silico design of potential lead antibodies for autoimmune and inflammatory diseases

Computer-aided antibody engineering has been successful in the design of new biologics for disease diagnosis and therapeutic interventions. Interleukin-6 (IL-6), a well-recognized drug target for various autoimmune and inflammatory diseases such as rheumatoid arthritis, multiple sclerosis, and psoriasis, was investigated in silico to design potential lead antibodies. Here, crystal structure of IL-6 along with monoclonal antibody olokizumab was explored to predict antigen-antibody (Ag - Ab)-interacting residues using DiscoTope, Paratome, and PyMOL. Tyr56, Tyr103 in heavy chain and Gly30, Ile31 in light chain of olokizumab were mutated with residues Ser, Thr, Tyr, Trp, and Phe. A set of 899 mutant macromolecules were designed, and binding affinity of these macromolecules to IL-6 was evaluated through Ag - Ab docking (ZDOCK, ClusPro, and Rosetta server), binding free-energy calculations using Molecular Mechanics/Poisson Boltzman Surface Area (MM/PBSA) method, and interaction energy estimation. In comparison to olokizumab, eight newly designed theoretical antibodies demonstrated better result in all assessments. Therefore, these newly designed macromolecules were proposed as potential lead antibodies to serve as a therapeutics option for IL-6-mediated diseases.

The selectivity and promiscuity of brain-neuroregenerative inhibitors between ROCK1 and ROCK2 isoforms: An integration of SB-QSSR modelling, QM/MM analysis and in vitro kinase assay

The Rho-associated kinases (ROCKs) have long been recognized as an attractive therapeutic target for various neurological diseases; selective inhibition of ROCK1 and ROCK2 isoforms would result in distinct biological effects on neurogenesis, neuroplasticity and neuroregeneration after brain surgery and traumatic brain injury. However, the discovery and design of isoform-selective inhibitors remain a great challenge due to the high conservation and similarity between the kinase domains of ROCK1 and ROCK2. Here, a structure-based quantitative structure-selectivity relationship (SB-QSSR) approach was used to correlate experimentally measured selectivity with the difference in inhibitor binding to the two kinase isoforms. The resulting regression models were examined rigorously through both internal cross-validation and external blind validation; a nonlinear predictor was found to have high fitting stability and strong generalization ability, which was then employed to perform virtual screening against a structurally diverse, drug-like compound library. Consequently, five and seven hits were identified as promising candidates of 1-o-2 and 2-o-1 selective inhibitors, respectively, from which seven purchasable compounds were tested in vitro using a standard kinase assay protocol to determine their inhibitory activity against and selectivity between ROCK1 and ROCK2. The structural basis, energetic property and biological implication underlying inhibitor selectivity and promiscuity were also investigated systematically using a hybrid quantum mechanics/molecular mechanics (QM/MM) scheme.

Effects of extreme pH on ionic transport through protein nanopores: the role of ion diffusion and charge exclusion

We combine electrophysiological experiments with the structure-based Poisson–Nernst–Planck 3D calculations to investigate the transport properties of the bacterial porin OmpF under large pH gradients and particularly low salt concentrations.