Correlations in liquid water for the TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP models

Free Energy Density of a Fluid and Its Role in Solvation and Binding

The concept that a fluid has a position-dependent free energy density appears in the literature but has not been fully developed or accepted. We set this concept on an unambiguous theoretical footing via the following strategy. First, we set forth four desiderata that should be satisfied by any definition of the position-dependent free energy density, f(R), in a system comprising only a fluid and a rigid solute: its volume integral, plus the fixed internal energy of the solute, should be the system free energy; it deviates from its bulk value, fbulk, near a solute but should asymptotically approach fbulk with increasing distance from the solute; it should go to zero where the solvent density goes to zero; and it should be well-defined in the most general case of a fluid made up of flexible molecules with an arbitrary interaction potential. Second, we use statistical thermodynamics to formulate a definition of the free energy density that satisfies these desiderata. Third, we show how any free energy density satisfying the desiderata may be used to analyze molecular processes in solution. In particular, because the spatial integral of f(R) equals the free energy of the system, it can be used to compute free energy changes that result from the rearrangement of solutes as well as the forces exerted on the solutes by the solvent. This enables the use of a thermodynamic analysis of water in protein binding sites to inform ligand design. Finally, we discuss related literature and address published concerns regarding the thermodynamic plausibility of a position-dependent free energy density. The theory presented here has applications in theoretical and computational chemistry and may be further generalizable beyond fluids, such as to solids and macromolecules.

A molecular simulation study of the clinical G409V mutant in PINK1 associated with early-onset Parkinson's disease

The serine/threonine kinase PINK1 is responsible for phosphorylating a ubiquitin (Ub)-like domain in an E3 Ub ligase Parkin protein and a Parkin-bound Ub. PINK1 works as a mitochondrial quality control by phosphorylating and activating the E3 ubiquitin ligase Parkin. Recent medicinal study has reported that mutations of Parkin and PINK1 cause defects in mitophagy and induce early-onset Parkinson's disease (EOPD). In this study, we conducted molecular dynamics simulations to investigate the structural discrepancy caused by a clinical G409V mutation in PINK1 kinase domain's A-loop. The Ub phosphorylation begins with PINK1 D362 deprotonating the hydroxyl group of the substrate Ub's S65' and PINK1's A-loop is responsible for coordinating S65'. On contrary to G409 offering structural plasticity, the replaced, bulky V409 interferes with the alignment of D362-S65', seriously hampering Ub phosphorylation, leading to the accumulation of damaged mitochondria, and ultimately EOPD. In this study, we predicted the hPINK1WT-UbWT binding mode and detected the structural impact brought by G409V replacement. It is expected the concluded remarks to be beneficial for developing cures to alleviate structural interference and restore PINK1 function.

Coarse-Graining Waters: Unveiling The Effective Hydrophilicity/Hydrophobicity of Individual Protein Atoms and The Roles of Waters' Hydrogens

There have been many coarse-graining methods developed that aim to reduce the sizes of simulated systems and their computational costs. In this work, we develop a new coarse-graining method, called coarse-graining-delta (or δ-CG in short), that reduces the degrees of freedom of the potential energy surface by coarse-graining relative locations of atoms from their unit centers. Our method extends and generalizes the methods used in the coarse-grained normal mode analysis and enables us to study the roles of the individual removed atoms in a system, which have been difficult to study in molecular dynamics simulations. By applying δ-CG to coarse-grain three-point water molecules into single-point solvent particles, we successfully identify the effective hydrophilicity and hydrophobicity of all the individual protein atom types, which collectively correlate well with the known hydrophilic, hydrophobic, and amphipathic characteristics of amino acids. Moreover, our investigation shows that water's hydrogens have two roles in interacting with protein atoms. First, water molecules adjust their poses around different amino acids and their atoms, and the statistical preferences of the hydrogen poses near the atoms determine the effective hydrophilicity and hydrophobicity of the atoms, which have not been successfully addressed before. Second, the collective dynamics of the hydrogens assist the water molecules in escaping from the potential energy wells of the hydrophilic atoms. Our method also shows that coarse-graining a system mathematically leads to breaking antisymmetry of the nonbonded interactions; as a result, two interacting coarse-grained units exert different forces on each other. Our study indicates that the accuracy of coarse-grained force fields, such as the MARTINI force field and the UNRES force field, can be improved in two ways: (i) refining their potential energy functions and coefficients by analyzing the coarse-grained potential energy surface using δ-CG, and (ii) introducing non-antisymmetric interactions.

Celastrol attenuates hepatitis C virus translation and inflammatory response in mice by suppressing heat shock protein 90β

Hepatitis C virus (HCV) infection is one of the major factors to trigger a sustained hepatic inflammatory response and hence hepatocellular carcinoma (HCC), but direct-acting-antiviral (DAAs) was not efficient to suppress HCC development. Heat shock protein 90 kDa (HSP90) is highly abundant in different types of cancers, and especially controls protein translation, endoplasmic reticulum stress, and viral replication. In this study we investigated the correlation between the expression levels of HSP90 isoforms and inflammatory response marker NLRP3 in different types of HCC patients as well as the effect of a natural product celastrol in suppression of HCV translation and associated inflammatory response in vivo. We identified that the expression level of HSP90β isoform was correlated with that of NLRP3 in the liver tissues of HCV positive HCC patients (R² = 0.3867, P < 0.0101), but not in hepatitis B virus-associated HCC or cirrhosis patients. We demonstrated that celastrol (3, 10, 30 μM) dose-dependently suppressed the ATPase activity of both HSP90α and HSP90β, while its anti-HCV activity was dependent on the Ala47 residue in the ATPase pocket of HSP90β. Celastrol (200 nM) halted HCV internal ribosomal entry site (IRES)-mediated translation at the initial step by disrupting the association between HSP90β and 4EBP1. The inhibitory activity of celastrol on HCV RNA-dependent RNA polymerase (RdRp)-triggered inflammatory response also depended on the Ala47 residue of HSP90β. Intravenous injection of adenovirus expressing HCV NS5B (pAde-NS5B) in mice induced severe hepatic inflammatory response characterized by significantly increased infiltration of immune cells and hepatic expression level of Nlrp3, which was dose-dependently ameliorated by pretreatment with celastrol (0.2, 0.5 mg/kg, i.p.). This study reveals a fundamental role of HSP90β in governing HCV IRES-mediated translation as well as hepatic inflammation, and celastrol as a novel inhibitor of HCV translation and associated inflammation by specifically targeting HSP90β, which could be developed as a lead for the treatment of HSP90β positive HCV-associated HCC.

Exploration of the Product Specificity of chitosanase CsnMY002 and Mutants Using Molecular Dynamics Simulations

Chitosanase CsnMY002 is a new type of enzyme isolated from Bacillus subtilis that is used to prepare chitosan oligosaccharide. Although mutants G21R and G21K could increase Chitosan yield and thus increase the commercial value of the final product, the mechanism by which this happens is not known. Herein, we used molecular dynamics simulations to explore the conformational changes in CsnMY002 wild type and mutants when they bind substrates. The binding of substrate changed the conformation of protein, stretching and deforming the active and catalytic region. Additionally, the mutants caused different binding modes and catalysis, resulting in different degrees of polymerization of the final Chitooligosaccharide degradation product. Finally, Arg37, Ile145 ~ Gly148 and Trp204 are important catalytic residues of CsnMY002. Our study provides a basis for the engineering of chitosanases.

Free energy calculations and unbiased molecular dynamics targeting the liquid-liquid transition in water no man's land

The existence of a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) form of supercooled water has been a central and highly debated issue of physics and chemistry for the last three decades. We present a computational study that allows us to determine the free-energy landscapes of supercooled water over a wide range of pressure and temperature conditions using the TIP4P/2005 force field. Our approach combines topology-based structural transformation coordinates, state-of-the-art free-energy calculation methods, and extensive unbiased molecular dynamics. All our diverse simulations cannot detect any barrier within the investigated timescales and system size, for a discontinuous transition between the LDL and HDL forms throughout the so-called "no man's land," until the onset of the solid, non-diffusive amorphous forms.

Interfacial interaction-driven rheological properties of quartz nanofluids from molecular dynamics simulations and density functional theory calculations

Correlations of the shear viscosity of quartz nanofluids with particle concentration, particle size, and temperature were investigated with molecular dynamics simulations and density functional theory (DFT) calculations. A new understanding to the experimentally concluded correlations was addressed in terms of microscopic particle-water interfacial interaction in three aspects. First, the viscosity of quartz nanofluids at different particle concentrations, particle sizes, and temperatures were simulated using the equilibrium molecular dynamics simulations method to reproduce the experimental observations. At the same particle size, the nanofluid viscosity decreases significantly with temperature and increases with nanoparticle volume concentration, and at the same volume concentration, the nanofluid viscosity increases with the decrease of particle size. Second, DFT calculations confirm a stronger particle-water interaction than that among water molecules. The important role of particle-water interaction in the viscosity determination of nanofluids was revealed. Finally, a correlation was proposed to fit the simulated results and compared with earlier two-parameter correlations. One parameter in the correlation is indeed a constant, while the other is a function of SiO₂-water interaction energy. Our study proposes a physical basis for the experimentally concluded correlations on the viscosity of nanofluids.

Probing IgG1 FC-Multimodal Nanoparticle Interactions: A Combined Nuclear Magnetic Resonance and Molecular Dynamics Simulations Approach

In this study, NMR and molecular dynamics simulations were employed to study IgG1 F_C binding to multimodal surfaces. Gold nanoparticles functionalized with two multimodal cation-exchange ligands (Capto and Nuvia) were synthesized and employed to carry out solution-phase NMR experiments with the F_C. Experiments with perdeuterated ¹⁵N-labeled F_C and the multimodal surfaces revealed micromolar residue-level binding affinities as compared to millimolar binding affinities with these ligands in free solution, likely due to cooperativity and avidity effects. The binding of F_C with the Capto ligand nanoparticles was concentrated near an aliphatic cluster in the C_H2/C_H3 interface, which corresponded to a focused hydrophobic region. In contrast, binding with the Nuvia ligand nanoparticles was more diffuse and corresponded to a large contiguous positive electrostatic potential region on the side face of the F_C. Results with lower-ligand-density nanoparticles indicated a decrease in binding affinity for both systems. For the Capto ligand system, several aliphatic residues on the F_C that were important for binding to the higher-density surface did not interact with the lower-density nanoparticles. In contrast, no significant difference was observed in the interacting residues on the F_C to the high- and low-ligand density Nuvia surfaces. The binding affinities of F_C to both multimodal-functionalized nanoparticles decreased in the presence of salt due to the screening of multiple weak interactions of polar and positively charged residues. For the Capto ligand nanoparticle system, this resulted in an even more focused hydrophobic binding region in the interface of the C_H2 and C_H3 domains. Interestingly, for the Nuvia ligand nanoparticles, the presence of salt resulted in a large transition from a diffuse binding region to the same focused binding region determined for Capto nanoparticles at 150 mM salt. Molecular dynamics simulations corroborated the NMR results and provided important insights into the molecular basis of F_C binding to these different multimodal systems containing clustered (observed at high-ligand densities) and nonclustered ligand surfaces. This combined biophysical and simulation approach provided significant insights into the interactions of F_C with multimodal surfaces and sets the stage for future analyses with even more complex biotherapeutics.

Kinetic pathways of water exchange in the first hydration shell of magnesium: Influence of water model and ionic force field

Water exchange between the first and second hydration shell is essential for the role of Mg²⁺ in biochemical processes. In order to provide microscopic insights into the exchange mechanism, we resolve the exchange pathways by all-atom molecular dynamics simulations and transition path sampling. Since the exchange kinetics relies on the choice of the water model and the ionic force field, we systematically investigate the influence of seven different polarizable and non-polarizable water and three different Mg²⁺ models. In all cases, water exchange can occur either via an indirect or direct mechanism (exchanging molecules occupy different/same position on the water octahedron). In addition, the results reveal a crossover from an interchange dissociative (I_d) to an associative (I_a) reaction mechanism dependent on the range of the Mg²⁺-water interaction potential of the respective force field. Standard non-polarizable force fields follow the I_d mechanism in agreement with experimental results. By contrast, polarizable and long-ranged non-polarizable force fields follow the I_a mechanism. Our results provide a comprehensive view on the influence of the water model and the ionic force field on the exchange dynamics and the foundation to assess the choice of the force field in biomolecular simulations.

Molecular dynamics simulation for membrane separation and porous materials: A current state of art review

Computational frameworks have been under specific attention within the last two decades. Molecular Dynamics (MD) simulations, identical to the other computational approaches, try to address the unknown question, lighten the dark areas of unanswered questions, to achieve probable explanations and solutions. Owing to their complex microporous structure on one side and the intricate biochemical nature of various materials used in the structure, separative membrane materials possess peculiar degrees of complications. More notably, as nanocomposite materials are often integrated into separative membranes, thin-film nanocomposites and porous separative nanocomposite materials could possess an additional level of complexity with regard to the nanoscale interactions brought to the structure. This critical review intends to cover the recent methods used to assess membranes and membrane materials. Incorporation of MD in membrane technology-related fields such as desalination, fuel cell-based energy production, blood purification through hemodialysis, etc., were briefly covered. Accordingly, this review could be used to understand the current extent of MD applications for separative membranes. The review could also be used as a guideline to use the proper MD implementation within the related fields.

Formation of Ligand Clusters on Multimodal Chromatographic Surfaces

Multimodal chromatography is a powerful tool which uses multiple modes of interaction, such as charge and hydrophobicity, to purify protein-based therapeutics. In this work, we performed molecular dynamics simulations of a series of multimodal cation-exchange ligands immobilized on a hydrophilic self-assembled monolayer surface at the commercially relevant surface density (1 ligand/nm²). We found that ligands that were flexible and terminated in a hydrophobic group had a propensity to aggregate on the surface, while less flexible ligands containing a hydrophobic group closer to the surface did not aggregate. For aggregating ligands, this resulted in the formation of a surface pattern that contained relatively large patches of hydrophobicity and charge whose sizes exceeded the length scale of the individual ligands. On the other hand, lowering the surface density to 1 ligand/3 nm² reduced or eliminated this aggregation behavior. In addition, the introduction of a flexible linker (corresponding to the commercially available ligand) enhanced cluster formation and allowed aggregation to occur at lower surface densities. Further, the use of flexible linkers enabled hydrophobic groups to collapse to the surface, reducing their accessibility. Finally, we developed an approach for quantifying differences in the observed surface patterns by calculating distributions of the patch size and patch length. This clustering phenomenon is likely to play a key role in governing protein-surface interactions in multimodal chromatography. This new understanding of multimodal surfaces has important implications for developing improved predictive models and designing new classes of multimodal separation materials.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Multi-resolution dimer models in heat baths with short-range and long-range interactions

This work investigates multi-resolution methodologies for simulating dimer models. The solvent particles which make up the heat bath interact with the monomers of the dimer either through direct collisions (short-range) or through harmonic springs (long-range). Two types of multi-resolution methodologies are considered in detail: (a) describing parts of the solvent far away from the dimer by a coarser approach; (b) describing each monomer of the dimer by using a model with different level of resolution. These methodologies are then used to investigate the effect of a shared heat bath versus two uncoupled heat baths, one for each monomer. Furthermore, the validity of the multi-resolution methods is discussed by comparison to dynamics of macroscopic Langevin equations.

Assimilating Radial Distribution Functions To Build Water Models with Improved Structural Properties

The structural properties of three- and four-site water models are improved by extending the ForceBalance parametrization code to include a new methodology allowing for the targeting of any radial distribution function (RDF) during the parametrization of a force field. The mean squared difference (MSD) between the experimental and simulated RDFs contributes to an objective function, allowing for the systematic optimization of force field parameters to reach closer overall agreement with experiment. RDF fitting is applied to develop modified versions of the TIP3P and TIP4P/2005 water models in which the Lennard-Jones potential is replaced by a Buckingham potential. The optimized TIP3P-Buckingham and TIP4P-Buckingham potentials feature 93 and 98% lower MSDs in the OO RDF compared to the TIP3P and TIP4P/2005 models respectively, with marked decreases in the height of the first peak. Additionally, these Buckingham models predict the entropy of water more accurately, reducing the error in the entropy of TIP3P from 11 to 3% and the error in the entropy of TIP4P/2005 from 11 to 2%. These new Buckingham models have improved predictive power for many nonfitted properties particularly in the case of TIP3P. Our work directly demonstrates how the Buckingham potential can improve the description of water's structural properties beyond the Lennard-Jones potential. Moreover, adding a Buckingham potential is a favorable alternative to adding interaction sites in terms of computational speed on modern GPU hardware.

Determination of the μ-Conotoxin PIIIA Specificity Against Voltage-Gated Sodium Channels from Binding Energy Calculations

Voltage-gated sodium (NaV) channels generate and propagate action potentials in excitable cells, and several NaV subtypes have become important targets for pain management. The μ-conotoxins inhibit subtypes of the NaV with varied specificity but often lack of specificity to interested subtypes. Engineering the selectivity of the μ-conotoxins presents considerable complexity and challenge, as it involves the optimization of their binding affinities to multiple highly conserved NaV subtypes. In this study, a model of NaV1.4 bound with μ-conotoxin PIIIA complex was constructed using homology modeling, docking, molecular dynamic simulations and binding energy calculations. The accuracy of this model was confirmed based on the experimental mutagenesis data. The complex models of PIIIA bound with varied subtypes of NaV1.x (x = 1, 2, 3, 5, 6, 7, 8, or 9) were built using NaV1.4/PIIIA complex as a template, and refined using molecular dynamic simulations. The binding affinities of PIIIA to varied subtypes of NaV1.x (x = 1 to 9) were calculated using the Molecular Mechanics Generalized Born/Surface Area (MMGB/SA) and umbrella sampling, and were compared with the experimental values. The binding affinities calculated using MMGB/SA and umbrella sampling are correlated with the experimental values, with the former and the latter giving correlation coefficient of 0.41 (R²) and 0.68 (R²), respectively. Binding energy decomposition suggests that conserved and nonconserved residues among varied NaV subtypes have a synergistic effect on the selectivity of PIIIA.

The long-range convergence of the energetic properties of the water monomer in bulk water at room temperature

The Interacting Quantum Atoms (IQA) energy partitioning scheme has been applied to a set of liquid water largely spherical clusters (henceforth called spheres) of up to 9 Å radius, with a maximum cluster size of 113 molecules. This constitutes half of the commonly used 216 molecules in a typical simulation box of a liquid water box, and to our knowledge is the largest analysis of this kind ever undertaken. As well as demonstrating the topological analysis of large systems, which has only recently become computationally feasible, important long range properties of liquid water are obtained. The full topological partitioning of each sphere into atomic basins is used to consider the long-range convergence of the energetic and multipolar properties of the water molecule at the centre of each sphere. It is found that the total molecular energy converges to its 9 Å value after 7 Å, which corresponds to approximately the first three solvation shells, while the molecular dipole and quadrupole moments approximately converge after 5.5 Å, which corresponds to approximately the first two solvation shells. The effect of water molecule flexibility is also considered.

Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics

Molecular dynamics (MD) simulations of ions (K+, Na+, Ca2+ and Cl-) in aqueous solutions are investigated. Water is described using the SPC/E model. A stochastic coarse-grained description for ion behaviour is presented and parametrized using MD simulations. It is given as a system of coupled stochastic and ordinary differential equations, describing the ion position, velocity and acceleration. The stochastic coarse-grained model provides an intermediate description between all-atom MD simulations and Brownian dynamics (BD) models. It is used to develop a multiscale method which uses all-atom MD simulations in parts of the computational domain and (less detailed) BD simulations in the remainder of the domain.

The structure of liquid water beyond the first hydration shell

Distance dependent excess entropy calculations reveal that water is tetrahedrally structured up to long distances.

On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility

The increase in solubility for indole in methanol water solutions relative to pure water is a result methanol −OH–π interactions. In addition, excess entropy calculations suggest that this process is enthalpically rather than entropically driven.

Estimation of Solvation Entropy and Enthalpy via Analysis of Water Oxygen-Hydrogen Correlations

A statistical-mechanical framework for estimation of solvation entropies and enthalpies is proposed, which is based on the analysis of water as a mixture of correlated water oxygens and water hydrogens. Entropic contributions of increasing order are cast in terms of a Mutual Information Expansion that is evaluated to pairwise interactions. In turn, the enthalpy is computed directly from a distance-based hydrogen bonding energy algorithm. The resulting expressions are employed for grid-based analyses of Molecular Dynamics simulations. In this first assessment of the methodology, we obtained global estimates of the excess entropy and enthalpy of water that are in good agreement with experiment and examined the method's ability to enable detailed elucidation of solvation thermodynamic structures, which can provide valuable knowledge toward molecular design.

Structure and dynamics of TIP3P, TIP4P, and TIP5P water near smooth and atomistic walls of different hydroaffinity

We perform molecular dynamics simulations to observe the structure and dynamics of water using different water models (TIP3P, TIP4P, TIP5P) at ambient conditions, constrained by planar walls, which are either modeled by smooth potentials or regular atomic lattices, imitating the honeycomb-structure of graphene. We implement walls of different hydroaffinity, different lattice constant, and different types of interaction with the water molecules. We find that in the hydrophobic regime the smooth wall generally represents a good abstraction of the atomically rough walls, while in the hydrophilic regime there are noticeable differences in structure and dynamics between all stages of wall roughness. For a small lattice constant however the smooth and the atomically rough wall still share a number of structural and dynamical similarities. Out of the three water models, TIP5P water shows the largest degree of tetrahedral ordering and is often the one that is least perturbed by the presence of the wall.

Direct Mixing of Atomistic Solutes and Coarse-Grained Water

We present a new dual-resolution approach for coupling atomistic and coarse-grained models in molecular dynamics simulations of hydrated systems. In particular, a coarse-grained point dipolar water model is used to solvate molecules represented with standard all-atom force fields. A unique characteristic of our methodology is that the mixing of resolutions is direct, meaning that no additional or ad hoc scaling factors, intermediate regions, or extra sites are required. To validate the methodology, we compute the hydration free energy of 14 atomistic small molecules (analogs of amino acid side chains) solvated by the coarse-grained water. Remarkably, our predictions reproduce the experimental data as accurately as the predictions from state-of-the-art fully atomistic simulations. We also show that the hydration free energy of the coarse-grained water itself is in comparable or better agreement with the experimental value than the predictions from all but one of the most common multisite atomistic models. The coarse-grained water is then applied to solvate a typical atomistic protein containing both α-helix and β-strand elements. Moreover, parallel tempering simulations are performed to investigate the folding free energy landscape of a representative α helical and a β hairpin structure. For the simulations considered in this work, our dual-resolution method is found to be 3 to 6 times more computationally efficient than corresponding fully atomistic approaches.

From molecular dynamics to Brownian dynamics

Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analysing multi-scale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.

The fuzzy oil drop model, based on hydrophobicity density distribution, generalizes the influence of water environment on protein structure and function

In this paper we show that the fuzzy oil drop model represents a general framework for describing the generation of hydrophobic cores in proteins and thus provides insight into the influence of the water environment upon protein structure and stability. The model has been successfully applied in the study of a wide range of proteins, however this paper focuses specifically on domains representing immunoglobulin-like folds. Here we provide evidence that immunoglobulin-like domains, despite being structurally similar, differ with respect to their participation in the generation of hydrophobic core. It is shown that β-structural fragments in β-barrels participate in hydrophobic core formation in a highly differentiated manner. Quantitatively measured participation in core formation helps explain the variable stability of proteins and is shown to be related to their biological properties. This also includes the known tendency of immunoglobulin domains to form amyloids, as shown using transthyretin to reveal the clear relation between amyloidogenic properties and structural characteristics based on the fuzzy oil drop model.

Structural elucidation of SrtA enzyme in Enterococcus faecalis: an emphasis on screening of potential inhibitors against the biofilm formation

Enterococcus faecalis is a pathogenic Gram-positive bacterium, which mainly infects humans through urinary tract infections. SrtA is an essential enzyme for survival of E. faecalis, and inhibition of this particular enzyme will reduce the virulence of biofilm formation. It is proved to be associated with the microbial surface protein embedded signal transduction mechanism and promising as a suitable anti-microbial drug target for E. faecalis. The present work gives an inclusive description of SrtA isolated from E. faecalis through computational and experimental methodologies. For exploring the mechanism of SrtA and to screen potential leads against E. faecalis, we have generated three-dimensional models through homology modeling. The 3D model showed conformational stability over time, confirming the quality of the starting 3D model. Large scale 100 ns molecular dynamics simulations show the intramolecular changes occurring in SrtA, and multiple conformations of structure based screening elucidate potential leads against this pathogen. Experimental results showed that the screened compounds are active showing anti-microbial and anti-biofilm activity, as SrtA is known to play an important role in E. faecalis biofilm formation. Experimental results also suggest that SrtA specific screened compounds have better anti-biofilm activity than the available inhibitors. Therefore, we believe that development of these compounds would be an impetus to design the novel chief SrtA inhibitors against E. faecalis.

Comparing distance metrics for rotation using the k-nearest neighbors algorithm for entropy estimation

Distance metrics facilitate a number of methods for statistical analysis. For statistical mechanical applications, it is useful to be able to compute the distance between two different orientations of a molecule. However, a number of distance metrics for rotation have been employed, and in this study, we consider different distance metrics and their utility in entropy estimation using the k-nearest neighbors (KNN) algorithm. This approach shows a number of advantages over entropy estimation using a histogram method, and the different approaches are assessed using uniform randomly generated data, biased randomly generated data, and data from a molecular dynamics (MD) simulation of bulk water. The results identify quaternion metrics as superior to a metric based on the Euler angles. However, it is demonstrated that samples from MD simulation must be independent for effective use of the KNN algorithm and this finding impacts any application to time series data.

Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory

An efficient methodology has been developed to quantify water energetics by analysis of explicit solvent molecular simulations of organic and biomolecular systems. The approach, grid cell theory (GCT), relies on a discretization of the cell theory methodology on a three-dimensional grid to spatially resolve the density, enthalpy, and entropy of water molecules in the vicinity of solute(s) of interest. Entropies of hydration are found to converge more efficiently than enthalpies of hydration. GCT predictions of free energies of hydration on a data set of small molecules are strongly correlated with thermodynamic integration predictions. Agreement with the experiment is comparable for both approaches. A key advantage of GCT is its ability to provide from a single simulation insightful graphical analyses of spatially resolved components of the enthalpies and entropies of hydration.

Combining solvent thermodynamic profiles with functionality maps of the Hsp90 binding site to predict the displacement of water molecules

Intermolecular interactions in the aqueous phase must compete with the interactions between the two binding partners and their solvating water molecules. In biological systems, water molecules in protein binding sites cluster at well-defined hydration sites and can form strong hydrogen-bonding interactions with backbone and side-chain atoms. Displacement of such water molecules is only favorable when the ligand can form strong compensating hydrogen bonds. Conversely, water molecules in hydrophobic regions of protein binding sites make only weak interactions, and the requirements for favorable displacement are less stringent. The propensity of water molecules for displacement can be identified using inhomogeneous fluid solvation theory (IFST), a statistical mechanical method that decomposes the solvation free energy of a solute into the contributions from different spatial regions and identifies potential binding hotspots. In this study, we employed IFST to study the displacement of water molecules from the ATP binding site of Hsp90, using a test set of 103 ligands. The predicted contribution of a hydration site to the hydration free energy was found to correlate well with the observed displacement. Additionally, we investigated if this correlation could be improved by using the energetic scores of favorable probe groups binding at the location of hydration sites, derived from a multiple copy simultaneous search (MCSS) method. The probe binding scores were not highly predictive of the observed displacement and did not improve the predictivity when used in combination with IFST-based hydration free energies. The results show that IFST alone can be used to reliably predict the observed displacement of water molecules in Hsp90. However, MCSS can augment IFST calculations by suggesting which functional groups should be used to replace highly displaceable water molecules. Such an approach could be very useful in improving the hit-to-lead process for new drug targets.

Differential binding of latrunculins to G-actin: a molecular dynamics study

Latrunculins are unique macrolides containing a thiazolidinone moiety. Latrunculin A (1), latrunculin B (2), 16-epi-latrunculin B (3), and latrunculin T (4) were isolated from the Red Sea sponge Negombata magnifica. In the present study, after testing compounds 2-4 for cytotoxic activity, they were docked into the crystal structure of G-actin and subjected to binding energy calculation and a 20 ns MD simulation. The modeling study shows that latrunculins binding depends on both hydrophobic interaction of the macrocycle as well as H bonding of the thiazolidinone ring with Asp157 and Thr186. It was noticed that epimerization at C16 of latrunculin B was well tolerated as it could form an alternative H bonding network. However, opening of the macrocyclic ring deteriorates the actin binding due to reduced hydrophobicity. MD simulation showed that latrunculin B (2) possesses a more significant stabilizing effect on G-actin than latrunculin T (4) and could efficiently hinder the flattening transition of G-actin into F-actin. These findings could explain, at the molecular level, the impact of epimerization and macrolide ring-opening on latrunculins activity, an issue that has not been addressed before. Also, the study gives insights into the mechanism of cytotoxicity of diverse latrunculins and provides direction for future lead optimization studies.

Polarizable water models from mixed computational and empirical optimization

Here we suggest a mixed computational and empirical approach serving to optimize the parameters of complex and polarizable molecular mechanics (PMM) models for complicated liquids. The computational part of the parameter optimization relies on hybrid calculations combining density functional theory (DFT) for a solute molecule with a PMM treatment of its solvent environment at well-defined thermodynamic conditions. As an application we have developed PMM models for water featuring ν = 3, 4, and 5 points of force action, a Gaussian inducible dipole and a Buckingham potential at the oxygen, the experimental liquid phase geometry, the experimental gas phase polarizability α(exp)(g) = 1.47 ų, and, for ν = 4 and 5, the gas phase value μ(exp)(g) = 1.855 D for the static dipole moment. The widths of the Gaussian dipoles and, for ν = 4 and 5, also the electrostatic geometries of these so-called TLνP models are derived from self-consistent DFT/PMM calculations, and the parameters of the Buckingham potentials (and the static TL3P dipole moment) are estimated from molecular dynamics (MD) simulations. The high quality of the resulting models is demonstrated for the observables targeted during optimization (potential energy per molecule, pressure, radial distribution functions) and a series of predicted properties (quadrupole moments, density at constant pressure, dielectric constant, diffusivity, viscosity, compressibility, heat capacity) at certain standard conditions. Remaining deficiencies and possible ways for their removal are discussed.

Correlation of structural order, anomalous density, and hydrogen bonding network of liquid water

We use extensive molecular dynamics simulations employing different state-of-the-art force fields to find a common framework for comparing structural orders and density anomalies as obtained from different water models. It is found that the average number of hydrogen bonds correlates well with various order parameters as well as the temperature of maximum densities across the different models, unifying apparently disparate results from different models and emphasizing the importance of hydrogen bonding in determining anomalous properties and the structure of water. A deeper insight into the hydrogen bond network of water reveals that the solvation shell of a water molecule can be defined by considering only those neighbors that are hydrogen-bonded to it. On the basis of this view, the origin of the appearance of a non-tetrahedral peak at a higher temperature in the distribution of tetrahedral order parameters has been explained. It is found that a neighbor that is hydrogen-bonded to the central molecule is tetrahedrally coordinated even at higher temperatures. The non-tetrahedral peak at a higher temperature arises due to the strained orientation of the neighbors that are non-hydrogen-bonded to the central molecule. With the new definition of the solvation shell, liquid water can be viewed as an instantaneously changing random hydrogen-bonded network consisting of differently coordinated hydrogen-bonded molecules with their distinct solvation shells. The variation of the composition of these hydrogen-bonded molecules against temperature accounts for the density anomaly without introducing the concept of large-scale structural polyamorphism in water.

Assessing the accuracy of inhomogeneous fluid solvation theory in predicting hydration free energies of simple solutes

Accurate prediction of hydration free energies is a key objective of any free energy method that is applied to modeling and understanding interactions in the aqueous phase. Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. IFST has found wide application in understanding hydration phenomena in biological systems, but quantitative applications have not been comprehensively assessed. In this study, we report the hydration free energies of six simple solutes calculated using IFST and independently using free energy perturbation (FEP). This facilitates a validation of IFST that is independent of the accuracy of the force field. The results demonstrate that IFST shows good agreement with FEP, with an R² coefficient of determination of 0.99 and a mean unsigned difference of 0.7 kcal/mol. However, sampling is a major issue that plagues IFST calculations and the results suggest that a histogram method may require prohibitively long simulations to achieve convergence of the entropies, for bin sizes which effectively capture the underlying probability distributions. Results also highlight the sensitivity of IFST to the reference interaction energy of a water molecule in bulk, with a difference of 0.01 kcal/mol changing the predicted hydration free energies by approximately 2.4 kcal/mol for the systems studied here. One of the major advantages of IFST over perturbation methods such as FEP is that the systems are spatially decomposed to consider the contribution of specific regions to the total solvation free energies. Visualizing these contributions can yield detailed insights into solvation thermodynamics. An insight from this work is the identification and explanation of regions with unfavorable free energy density relative to bulk water. These regions contribute unfavorably to the hydration free energy. Further work is necessary before IFST can be extended to yield accurate predictions of binding free energies, but the work presented here demonstrates its potential.

Matching of additive and polarizable force fields for multiscale condensed phase simulations

Inclusion of electronic polarization effects is one of the key aspects in which the accuracy of current biomolecular force fields may be improved. The principal drawback of such approaches is the computational cost, which typically ranges from 3 - 10 times that of the equivalent additive model, and may be greater for more sophisticated treatments of polarization or other many-body effects. Here, we present a multiscale approach which may be used to enhance the sampling in simulations with polarizable models, by using the additive model as a tool to explore configuration space. We use a method based on information theory to determine the charges for an additive model that has optimal overlap with the polarizable one, and we demonstrate the feasibility of enhancing sampling via a hybrid replica exchange scheme for several model systems. An additional advantage is that, in the process, we obtain a systematic method for deriving charges for an additive model that will be the natural complement to its polarizable parent. The additive charges are found by an effective coarse-graining of the polarizable force field, rather than by ad hoc procedures.

Application of inhomogeneous fluid solvation theory to model the distribution and thermodynamics of water molecules around biomolecules

The structures of biomolecules and the strengths of association between them depend critically on interactions with water molecules. Thus, understanding these interactions is a prerequisite for understanding the structure and function of all biomolecules. Inhomogeneous fluid solvation theory provides a framework to derive thermodynamic properties of individual water molecules from a statistical mechanical analysis. In this work, two biomolecules are analysed to probe the distribution and thermodynamics of surrounding water molecules. The great majority of hydration sites are predicted to contribute favourably to the total free energy with respect to bulk water, though hydration sites close to non-polar regions of the solute do not contribute significantly. Analysis of a biomolecule with a positively and negatively charged functional group predicts that a charged species perturbs the free energy of water molecules to a distance of approximately 6.0 Å. Interestingly, short simulations are found to provide converged predictions if samples are taken with sufficient frequency, a finding that has the potential to significantly reduce the required computational cost of such analysis. In addition, the predicted thermodynamic properties of hydration sites with the potential for direct hydrogen bonding interactions are found to disagree significantly for two different water models. This study provides important information on how inhomogeneous fluid solvation theory can be employed to understand the structures and intermolecular interactions of biomolecules.

Thermodynamics of transport through the ammonium transporter Amt-1 investigated with free energy calculations

Amt-1 from Archaeoglobus fulgidus (AfAmt-1) belongs to the Amt/Rh family of ammonium/ammonia transporting membrane proteins. The transport mode and the precise microscopic permeation mechanism utilized by these proteins are intensely debated. Open questions concern the identity of the transported substrate (ammonia and/or ammonium) and whether the transport is passive or active. To address these questions, we studied the overall thermodynamics of the different transport modes as a function of the environmental conditions. Then, we investigated the thermodynamics of the underlying microscopic transport mechanisms with free energy calculations within a continuum electrostatics model. The formalism developed for this purpose is of general utility in the calculation of binding free energies for ligands with multiple protonation forms or other binding forms. The results of our calculations are compared to the available experimental and theoretical data on Amt/Rh proteins and discussed in light of the current knowledge on the physiological conditions experienced by microorganisms and plants. We found that microscopic models of electroneutral and electrogenic transport modes are in principle thermodynamically viable. However, only the electrogenic variants have a net thermodynamic driving force under the physiological conditions experienced by microorganisms and plants. Thus, the transport mechanism of AfAmt-1 is most likely electrogenic.

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P-2005 and TIP5P-Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water-water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application.