PDB_Hydro: incorporating dipolar solvents with variable density in the Poisson-Boltzmann treatment of macromolecule electrostatics

Structure-function analysis of nucleotide housekeeping protein HAM1 from human malaria parasite Plasmodium falciparum

Non-canonical nucleotides, generated as oxidative metabolic by-products, significantly threaten the genome integrity of Plasmodium falciparum and thereby, their survival, owing to their mutagenic effects. PfHAM1, an evolutionarily conserved inosine/xanthosine triphosphate pyrophosphohydrolase, maintains nucleotide homeostasis in the malaria parasite by removing non-canonical nucleotides, although structure-function intricacies are hitherto poorly reported. Here, we report the X-ray crystal structure of PfHAM1, which revealed a homodimeric structure, additionally validated by size-exclusion chromatography-multi-angle light scattering analysis. The two monomeric units in the dimer were aligned in a parallel fashion, and critical residues associated with substrate and metal binding were identified, wherein a notable structural difference was observed in the β-sheet main frame compared to human inosine triphosphate pyrophosphatase. PfHAM1 exhibited Mg++-dependent pyrophosphohydrolase activity and the highest binding affinity to dITP compared to other non-canonical nucleotides as measured by isothermal titration calorimetry. Modifying the pfham1 genomic locus followed by live-cell imaging of expressed mNeonGreen-tagged PfHAM1 demonstrated its ubiquitous presence in the cytoplasm across erythrocytic stages with greater expression in trophozoites and schizonts. Interestingly, CRISPR-Cas9/DiCre recombinase-guided pfham1-null P. falciparum survived in culture under standard growth conditions, indicating its assistive role in non-canonical nucleotide clearance during intra-erythrocytic stages. This is the first comprehensive structural and functional report of PfHAM1, an atypical nucleotide-cleansing enzyme in P. falciparum.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Catalytic Mechanism of ATP Hydrolysis in the ATPase Domain of Human DNA Topoisomerase IIα

Human DNA topoisomerase IIα is a biological nanomachine that regulates the topological changes of the DNA molecule and is considered a prime target for anticancer drugs. Despite intensive research, many atomic details about its mechanism of action remain unknown. We investigated the ATPase domain, a segment of the human DNA topoisomerase IIα, using all-atom molecular simulations, multiscale quantum mechanics/molecular mechanics (QM/MM) calculations, and a point mutation study. The results suggested that the binding of ATP affects the overall dynamics of the ATPase dimer. Reaction modeling revealed that ATP hydrolysis favors the dissociative substrate-assisted reaction mechanism with the catalytic Glu87 serving to properly position and polarize the lytic water molecule. The point mutation study complemented our computational results, demonstrating that Lys378, part of the important QTK loop, acts as a stabilizing residue. The work aims to pave the way to a deeper understanding of these important molecular motors and to advance the development of new therapeutics.

Simultaneous Identification of Multiple Binding Sites in Proteins: A Statistical Mechanics Approach

We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility; i.e., all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson-Boltzmann Langevin (HDPBL) model, leads to a system of two equations whose solutions give the water dipole, salt, and hydrophobic molecule densities, all of them in the presence of the others in a self-consistent way. We use those to study the organization of the ions, cosolvent, and solvent molecules around proteins. In particular, peaks of densities are expected to reveal, simultaneously, the presence of compatible binding sites of different kinds on a protein. We have tested and validated the ability of HDPBL to detect pockets in proteins that bind to hydrophobic ligands, polar ligands, and charged small probes as well as to characterize the binding sites of lipids for membrane proteins.

Strategic Development of a Next-Generation Multi-Epitope Vaccine To Prevent Nipah Virus Zoonotic Infection

Nipah virus (NiV) is an emerging zoonotic pathogen, reported for the recent severe outbreaks of encephalitis and respiratory illness in humans and animals, respectively. Many antiviral drugs have been discovered to inhibit this pathogen, but none of them were that much efficient. To overcome the complications associated with this severe pathogenic virus, we have designed a multi-epitope subunit vaccine using computational immunology strategies. Identification of structural and nonstructural proteins of Nipah virus assisted in the vaccine designing. The selected proteins are known to be involved in the survival of the virus. The antigenic binders (B-cell, HTL, and CTL) from the selected proteins were prognosticated. These antigenic binders will be able to generate the humoral as well as cell-mediated immunity. All the epitopes were united with the help of suitable linkers and with an adjuvant at the N-terminal of the vaccine, for the enhancement of immunogenicity. The physiological characterization, along with antigenicity and allergenicity of the designed vaccine candidates, was estimated. The 3D structure prediction and its validation were performed. The validated vaccine model was then docked and simulated with the TLR-3 receptor to check the stability of the docked complex. This next-generation approach will provide a new vision for the development of a high immunogenic vaccine against the NiV.

AMMOS2: a web server for protein-ligand-water complexes refinement via molecular mechanics

AMMOS2 is an interactive web server for efficient computational refinement of protein-small organic molecule complexes. The AMMOS2 protocol employs atomic-level energy minimization of a large number of experimental or modeled protein-ligand complexes. The web server is based on the previously developed standalone software AMMOS (Automatic Molecular Mechanics Optimization for in silico Screening). AMMOS utilizes the physics-based force field AMMP sp4 and performs optimization of protein-ligand interactions at five levels of flexibility of the protein receptor. The new version 2 of AMMOS implemented in the AMMOS2 web server allows the users to include explicit water molecules and individual metal ions in the protein-ligand complexes during minimization. The web server provides comprehensive analysis of computed energies and interactive visualization of refined protein-ligand complexes. The ligands are ranked by the minimized binding energies allowing the users to perform additional analysis for drug discovery or chemical biology projects. The web server has been extensively tested on 21 diverse protein-ligand complexes. AMMOS2 minimization shows consistent improvement over the initial complex structures in terms of minimized protein-ligand binding energies and water positions optimization. The AMMOS2 web server is freely available without any registration requirement at the URL: http://drugmod.rpbs.univ-paris-diderot.fr/ammosHome.php.

The role of C-terminal extensions in controlling ECF σ factor activity in the widely conserved groups ECF41 and ECF42

The activity of extracytoplasmic function σ-factors (ECFs) is typically regulated by anti-σ factors. In a number of highly abundant ECF groups, including ECF41 and ECF42, σ-factors contain fused C-terminal protein domains, which provide the necessary regulatory function instead. Here, we identified the contact interface between the C-terminal extension and the core σ-factor regions required for controlling ECF activity. We applied direct coupling analysis (DCA) to infer evolutionary covariation between contacting amino acid residues for groups ECF41 and ECF42. Mapping the predicted interactions to a recently solved ECF41 structure demonstrated that DCA faithfully identified an important contact interface between the SnoaL-like extension and the linker between the σ₂ and σ₄ domains. Systematic alanine substitutions of contacting residues support this model and suggest that this interface stabilizes a compact conformation of ECF41 with low transcriptional activity. For group ECF42, DCA supports a structural homology model for their C-terminal tetratricopeptide repeat (TPR) domains and predicts an intimate contact between the first TPR-helix and the σ₄ domain. Mutational analyses demonstrate the essentiality of the predicted interactions for ECF42 activity. These results indicate that C-terminal extensions indeed bind and regulate the core ECF regions, illustrating the potential of DCA for discovering regulatory motifs in the ECF subfamily.

Structural evidence for an in trans base selection mechanism involving Loop1 in polymerase μ at an NHEJ double-strand break junction

Eukaryotic DNA polymerase (Pol) X family members such as Pol μ and terminal deoxynucleotidyl transferase (TdT) are important components for the nonhomologous DNA end-joining (NHEJ) pathway. TdT participates in a specialized version of NHEJ, V(D)J recombination. It has primarily nontemplated polymerase activity but can take instructions across strands from the downstream dsDNA, and both activities are highly dependent on a structural element called Loop1. However, it is unclear whether Pol μ follows the same mechanism, because the structure of its Loop1 is disordered in available structures. Here, we used a chimeric TdT harboring Loop1 of Pol μ that recapitulated the functional properties of Pol μ in ligation experiments. We solved three crystal structures of this TdT chimera bound to several DNA substrates at 1.96-2.55 Å resolutions, including a full DNA double-strand break (DSB) synapsis. We then modeled the full Pol μ sequence in the context of one these complexes. The atomic structure of an NHEJ junction with a Pol X construct that mimics Pol μ in a reconstituted system explained the distinctive properties of Pol μ compared with TdT. The structure suggested a mechanism of base selection relying on Loop1 and taking instructions via the in trans templating base independently of the primer strand. We conclude that our atomic-level structural observations represent a paradigm shift for the mechanism of base selection in the Pol X family of DNA polymerases.

The self-association and thermal denaturation of caprine and bovine β-lactoglobulin

Milk components, such as proteins and lipids, have different physicochemical properties depending upon the mammalian species from which they come. Understanding the different responses of these milks to digestion, processing, and differences in their immunogenicity requires detailed knowledge of these physicochemical properties. Here we report on the oligomeric state of β-lactoglobulin from caprine milk, the most abundant protein present in the whey fraction. At pH 2.5 caprine β-lactoglobulin is predominantly monomeric, whereas bovine β-lactoglobulin exists in a monomer-dimer equilibrium at the same protein concentrations. This behaviour was also observed in molecular dynamics simulations and can be rationalised in terms of the amino acid substitutions present between caprine and bovine β-lactoglobulin that result in a greater positive charge on each subunit of caprine β-lactoglobulin at low pH. The denaturation of β-lactoglobulin when milk is heat-treated contributes to the fouling of heat-exchange surfaces, reducing yields and increasing cleaning costs. The bovine and caprine orthologues of β-lactoglobulin display different responses to thermal treatment, with caprine β-lactoglobulin precipitating at higher pH values than bovine β-lactoglobulin (pH 7.1 compared to pH 5.6) that are closer to the natural pH of these milks (pH 6.7). This property of caprine β-lactoglobulin likely contributes to the reduced heat stability of caprine milk compared to bovine milk at its natural pH.

Incorporation of ion and solvent structure into mean-field modeling of the electric double layer

An electric double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the electric double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded volume effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations.

TMPL: a database of experimental and theoretical transmembrane protein models positioned in the lipid bilayer

Knowing the position of protein structures within the membrane is crucial for fundamental and applied research in the field of molecular biology. Only few web resources propose coordinate files of oriented transmembrane proteins, and these exclude predicted structures, although they represent the largest part of the available models. In this article, we present TMPL (http://www.dsimb.inserm.fr/TMPL/), a database of transmembrane protein structures (α-helical and β-sheet) positioned in the lipid bilayer. It is the first database to include theoretical models of transmembrane protein structures, making it a large repository with more than 11 000 entries. The TMPL database also contains experimentally solved protein structures, which are available as either atomistic or coarse-grained models. A unique feature of TMPL is the possibility for users to update the database by uploading, through an intuitive web interface, the membrane assignments they can obtain with our recent OREMPRO web server.

Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory

Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent-a dipolar Coulomb fluid-including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations.

Binding interaction of a gamma-aminobutyric acid derivative with serum albumin: an insight by fluorescence and molecular modeling analysis

gamma-Aminobutyric acid (GABA) is a naturally occurring inhibitory neurotransmitter and some of its derivatives showed potential to act as neuroprotective agents. With the aim of developing potential leads for anti-Alzheimer’s drugs, in this study we synthesized a novel GABA derivative, methyl 4-(4-((2-(tert-butoxy)-2-oxoethyl)(4-methoxyphenyl)amino)benzamido)butanoate by a unique method of Buchwald–Hartwig cross coupling synthesis; with some modification the yield was significant (97 %) and spectroscopic analysis confirmed that the compound was highly pure (98.8 % by HPLC). The druglikeness properties such as logP, logS, and polar surface area were 3.87, −4.86 and 94.17 Ų respectively and it satisfied the Lipinski’s rule of five. We examined the binding behavior of the molecule to human serum albumin (HSA) and bovine serum albumin (BSA) which are known as universal drug carrier proteins. The molecule binds to the proteins with low micromolar efficiency and the calculated binding constants were 3.85 and 2.75 micromolar for BSA and HSA, respectively. Temperature dependent study using van’t Hoff equation established that the binding was thermodynamically favorable and the changes in the Gibb’s free energy, ΔG for the binding process was negative. However, the binding of the molecule to HSA was enthalpy driven and the change of enthalpy (ΔH) was −10.63 kJ/mol, whereas, the binding to BSA was entropy driven and the change in entropy ΔS was 222 J/mol. The molecular docking analysis showed that the binding sites of the molecule lie in the groove between domain I and domain III of BSA, whereas it is within the domain I in case of HSA, which also supported the different thermodynamic nature of binding with HSA and BSA. Molecular dynamics analysis suggested that the binding was stable with time and provided further details of the binding interaction. Molecular dynamics study also highlighted the effect of this ligand binding on the serum albumin structure.

Molecular density functional theory of water including density-polarization coupling

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Identification of modes of interactions between 9-aminoacridine hydrochloride hydrate and serum proteins by low and high resolution spectroscopy and molecular modeling

Photophysical studies on binding interactions of 9-aminoacridine hydrochloride hydrate (9AA-HCl) with serum proteins using low and high resolution spectroscopic techniques in conjunction with molecular modeling.

Membrane positioning for high- and low-resolution protein structures through a binary classification approach

The critical importance of algorithms for orienting proteins in the lipid bilayer stems from the extreme difficulty in obtaining experimental data about the membrane boundaries. Here, we present a computational method for positioning protein structures in the membrane, based on the sole alpha carbon coordinates and, therefore, compatible with both high and low structural resolutions. Our algorithm follows a new and simple approach, by treating the membrane assignment problem as a binary classification. Compared with the state-of-the-art algorithms, our method achieves similar accuracy, while being faster. Finally, our open-source software is also capable of processing coarse-grained models of protein structures.

4,6-Substituted-1,3,5-triazin-2(1H)-ones as monocyclic catalytic inhibitors of human DNA topoisomerase IIα targeting the ATP binding site

Human DNA topoisomerase IIα (htIIα) is a validated target for the development of novel anticancer agents. Starting from our discovered 4-amino-1,3,5-triazine inhibitors of htIIα, we investigated a library of 2,4,6-trisubstituted-1,3,5-triazines for novel inhibitors that bind to the htIIα ATP binding site using a combination of structure-based and ligand-based pharmacophore models and molecular docking. 4,6-substituted-1,3,5-triazin-2(1H)-ones 8, 9 and 14 were identified as novel inhibitors with activity comparable to the established drug etoposide (1). Compound 8 inhibits the htIIα decatenation in a superior fashion to etoposide. Cleavage assays demonstrated that selected compounds 8 and 14 do not act as poisons and antagonize the poison effect of etoposide. Microscale thermophoresis (MST) confirmed binding of compound 8 to the htIIα ATPase domain and compound 14 effectively inhibits the htIIα mediated ATP hydrolysis. The molecular dynamics simulation study provides further insight into the molecular recognition. The 4,6-disubstituted-1,3,5-triazin-2(1H)-ones represent the first validated monocyclic class of catalytic inhibitors that bind to the to the htIIα ATPase domain.

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

Understanding nucleic acid-ion interactions

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Solvation of complex surfaces via molecular density functional theory

We show that classical molecular density functional theory, here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a fully molecular level, the solvation of complex surfaces and interfaces by polar solvents. This implicit solvent method allows for the determination of structural, orientational, and energetic solvation properties that are on a par with all-atom molecular simulations performed for the same system, while reducing the computer time by two orders of magnitude. This is illustrated by the study of an atomistically-resolved clay surface composed of over a thousand atoms wetted by a molecular dipolar solvent. The high numerical efficiency of the method is exploited to carry a systematic analysis of the electrostatic and non-electrostatic components of the surface-solvent interaction within the popular Clay Force Field (CLAYFF). Solvent energetics and structure are found to depend weakly upon the atomic charges distribution of the clay surface, even for a rather polar solvent. We conclude on the consequences of such findings for force-field development.

Molecular Density Functional Theory of Water

Three-dimensional implementations of liquid-state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short-range. The approach is shown to provide the correct 3-D microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two to three orders of magnitude lower than with explicit simulations.

Ion solvation in liquid mixtures: effects of solvent reorganization

Using field-theoretic techniques, we study the solvation of salt ions in liquid mixtures, accounting for the permanent and induced dipole moments, as well as the molecular volume of the species. With no adjustable parameters, we predict solvation energies in both single-component liquids and binary liquid mixtures that are in excellent agreement with experimental data. Our study shows that the solvation energy of an ion is largely determined by the local response of the permanent and induced dipoles, as well as the local solvent composition in the case of mixtures, and does not simply correlate with the bulk dielectric constant. In particular, we show that, in a binary mixture, it is possible for the component with the lower bulk dielectric constant but larger molecular polarizability to be enriched near the ion.

Differential geometry based solvation model. III. Quantum formulation

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model.

Differential geometry based solvation model II: Lagrangian formulation

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.

Differential geometry based solvation model II: Lagrangian formulation

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.

AquaSAXS: a web server for computation and fitting of SAXS profiles with non-uniformally hydrated atomic models

Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server (http://lorentz.dynstr.pasteur.fr/aquasaxs.php).

Differential geometry based solvation model I: Eulerian formulation

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Conferring a template-dependent polymerase activity to terminal deoxynucleotidyltransferase by mutations in the Loop1 region

Terminal deoxynucleotidyltransferase (Tdt) and DNA polymerase mu (pol mu) are two eukaryotic highly similar proteins involved in DNA processing and repair. Despite their high sequence identity, they differ widely in their activity: pol mu has a templated polymerase activity, whereas Tdt has a non-templated one. Loop1, first described when the Tdt structure was solved, has been invoked as the major structural determinant of this difference. Here we describe attempts to transform Tdt into pol mu with the minimal number of mutations in and around Loop1. First we describe the effect of mutations on six different positions chosen to destabilize Tdt Loop1 structure, either by alanine substitution or by deletion; they result at most in a reduction of Tdt activity, but adding Co(++) restores most of this Tdt activity. However, a deletion of the entire Loop1 as in pol lambda does confer a limited template-dependent polymerase behavior to Tdt while a chimera bearing an extended pol mu Loop1 reproduces pol mu behavior. Finally, 16 additional substitutions are reported, targeted at the two so-called 'sequence determinant' regions located just after Loop1 or underneath. Among them, the single-point mutant F401A displays a sequence-specific replicative polymerase phenotype that is stable upon Co(++) addition. These results are discussed in light of the available crystal structures.

Computing ion solvation free energies using the dipolar Poisson model

A new continuum model is presented for computing the solvation free energies of cations in water. It combines in a single formalism based on statistical thermodynamics the Poisson model for electrostatics with the Langevin dipole model to account for nonuniform water dipole distribution around the ions. An excellent match between experimental and computed solvation free energies is obtained for 10 monovalent and divalent ions.

Beyond the Poisson-Boltzmann model: modeling biomolecule-water and water-water interactions

We present an extension to the Poisson-Boltzmann model in which the solvent is modeled as an assembly of self-orienting dipoles of variable densities. Interactions between these dipoles are included implicitly using a Yukawa potential field. This model leads to a set of equations whose solutions give the dipole densities; we use the latter to study the organization of water around biomolecules. The computed water density profiles resemble those derived from molecular dynamics simulations. We also derive an excess free energy that discriminates correct from incorrect conformations of proteins.

Incorporating dipolar solvents with variable density in Poisson-Boltzmann electrostatics

We describe a new way to calculate the electrostatic properties of macromolecules that goes beyond the classical Poisson-Boltzmann treatment with only a small extra CPU cost. The solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. The method effectively unifies both the Poisson-centric view and the Langevin Dipole model. The model results in a variable dielectric constant epsilon(r) in the solvent region and also in a variable solvent density rho(r) that depends on the nature of the closest exposed solute atoms. The model was calibrated using small molecules and ions solvation data with only two adjustable parameters, namely the size and dipolar moment of the solvent. Hydrophobicity scales derived from the solvent density profiles agree very well with independently derived hydrophobicity scales, both at the atomic or residue level. Dimerization interfaces in homodimeric proteins or lipid-binding regions in membrane proteins clearly appear as poorly solvated patches on the solute accessible surface. Comparison of the thermally averaged solvent density of this model with the one derived from molecular dynamics simulations shows qualitative agreement on a coarse-grained level. Because this calculation is much more rapid than that from molecular dynamics, applications of a density-profile-based solvation energy to the identification of the true structure among a set of decoys become computationally feasible. Various possible improvements of the model are discussed, as well as extensions of the formalism to treat mixtures of dipolar solvents of different sizes.

A repulsive field: advances in the electrostatics of the ion atmosphere

The large electrostatic repulsion arising from the negatively charged backbone of RNA molecules presents a large barrier to folding. Solution counterions assist in the folding process by screening this electrostatic repulsion. While early research interpreted the effect of these counterions in terms of an empirical ligand-binding model, theories based on physical models have supplanted them and revised our view of the roles that ions play in folding. Instead of specific ion-binding sites, most ions in solution interact inside an 'ion atmosphere'--a fluctuating cloud of nonspecifically associated ions surrounding any charged molecule. Recent advances in experiments have begun the task of characterizing the ion atmosphere, yielding valuable data that have revealed deficiencies in Poisson-Boltzmann theory, the most widely used theory of the ion atmosphere. The continued development of experiments will help guide the development of improved theories, with the ultimate goal of understanding RNA folding and function and nucleic acid/protein interactions from a quantitative perspective.

Assessing the performance of implicit solvation models at a nucleic acid surface

Implicit solvation models are popular alternatives to explicit solvent methods due to their ability to "pre-average" solvent behavior and thus reduce the need for computationally-expensive sampling. Previously, we have demonstrated that Poisson-Boltzmann models for polar solvation and integral-based models for nonpolar solvation can reproduce explicit solvation forces in a low-charge density protein system. In the present work, we examine the ability of these continuum models to describe solvation forces at the surface of a RNA hairpin. While these models do not completely describe all of the details of solvent behavior at this highly-charged biomolecular interface, they do provide a reasonable description of average solvation forces and therefore show significant promise for developing more robust implicit descriptions of solvent around nucleic acid systems for use in biomolecular simulation and modeling. Additionally, we observe fairly good transferability in the nonpolar model parameters optimized for protein systems, suggesting its robustness for modeling general nonpolar solvation phenomena in biomolecular systems.