Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction‐Field Method for the Solvation Free Energies of Amino Acid Side‐Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model’s accuracy in predicting conformational free‐energy differences. The solvation free energies of neutral and polar amino acid side‐chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol^?1. The new parameters were evaluated for charged side‐chain analogs. The HADES results were compared with explicit‐solvent, generalized Born, Poisson–Boltzmann, and QM‐based methods. The potentials of mean force (PMFs) between pairs of side‐chain analogs obtained by using HADES and explicit‐solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.     

Calculation of absolute ligand binding free energy to a ribosome-targeting protein as a function of solvent model

A comparative analysis is provided of the effect of different solvent models on the calculation of a potential of mean force (PMF) for determining the absolute binding affinity of the small molecule inhibitor pteroic acid bound to ricin toxin A-chain (RTA). Solvent models include the distance-dependent dielectric constant, several different generalized Born (GB) approximations, and a hybrid explicit/GB-based implicit solvent model. We found that the simpler approximation of dielectric screening and a GB model, with Born radii fitted to a switching-window dielectric-boundary surface Poisson solvent model, severely overpredicted the binding affinity as compared to the experimental value, estimated to range from -4.4 to -6.0 kcal/mol. In contrast, GB models that are parametrized to fit the Lee-Richards molecular surface performed much better, predicting binding free energy within 1-3 kcal/mol of experimental estimates. However, the predicted free-energy profiles of these GB models displayed alternative binding modes not observed in the crystal structure. Finally, the most rigorous and computationally costly approach in this work, which used a hybrid explicit/implicit solvent model, correctly determined a binding funnel in the PMF near the crystallographic bound state and predicted an absolute binding affinity that was 2 kcal/mol more favorable than the estimated experimental binding affinity.     

Potential of mean force of hydrophobic association: dependence on solute size

The potentials of mean force (PMFs) were determined for systems involving formation of nonpolar dimers composed of methane, ethane, propane, isobutane, and neopentane, respectively, in water, using the TIP3P water model, and in vacuo. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field was carried out for each pair in either water or in vacuo. The PMFs were calculated by using the weighted histogram analysis method (WHAM). The shape of the PMFs for dimers of all five nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule, that is, for larger molecules they shift toward larger distances. The PMF of the neopentane dimer is similar to those of other small nonpolar molecules studied in this work, and hence the neopentane dimer is too small to be treated as a nanoscale hydrophobic object. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from the PMF in explicit solvent. The molecular surface area model correctly describes the solvent contribution to the PMF together with the changes of the height and positions of the desolvation barrier for all dimers investigated. The water molecules in the first solvation sphere of the dimer are more ordered compared to bulk water, with their dipole moments pointing away from the surface of the dimer. The average number of hydrogen bonds per water molecule in this first hydration shell is smaller compared to that in bulk water, which can be explained by coordination of water molecules to the hydrocarbon surface. In the second hydration shell, the average number of hydrogen bonds is greater compared to bulk water, which can be explained by increased ordering of water from the first hydration shell; the net effect is more efficient hydrogen bonding between the water molecules in the first and second hydration shells.     

Theoretical calculations of homoconjugation equilibrium constants in systems modeling acid-base interactions in side chains of biomolecules using the potential of mean force

The potentials of mean force (PMFs) were determined for systems forming cationic and anionic homocomplexes composed of acetic acid, phenol, isopropylamine, n-butylamine, imidazole, and 4(5)-methylimidazole, and their conjugated bases or acids, respectively, in three solvents with different polarity and hydrogen-bonding propensity: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water (H(2)O). For each pair and each solvent a series of umbrella-sampling molecular dynamics simulations with the AMBER force field, explicit solvent, and counterions added to maintain a zero net charge of a system were carried out and the PMF was calculated by using the Weighted Histogram Analysis Method (WHAM). Subsequently, homoconjugation-equilibrium constants were calculated by numerical integration of the respective PMF profiles. In all cases but imidazole stable homocomplexes were found to form in solution, which was manifested as the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated homoconjugation constants were found to be greater for complexes with the OHO bridge (acetic acid and phenol) than with the NHN bridge and they were found to decrease with increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H(2)O), both facts being in agreement with the available experimental data. It was also found that interactions with counterions are manifested as the broadening of the contact minimum or appearance of additional minima in the PMF profiles of the acetic acid-acetate, phenol/phenolate system in acetonitrile, and the 4(5)-methylimidazole/4(5)-methylimidzole cation conjugated base system in dimethyl sulfoxide.     

Synergistic Effects of External Electric Field and Solvent Vapor Annealing with Different Polarities to Enhance β-Phase and Carrier Mobility of the Poly(9,9-dioctylfluorene) Films

In this work, the synergistic effects of external electric field(EEF) and solvent vapor annealing to enhance β-phase and carrier mobility of poly(9,9-dioctylfluorene)(PFO) films were investigated. It is found that EEF can promote the PFO β-phase conformation transition and orientate the PFO chains along the EEF direction with the assistance of polar solvent vapor annealing. PFO chain orderness is closely related to the solvent polarity. In particular, the β-phase content in the annealed film of strong polar chloroform vapor increases from 18.7% to 34.9% after EEF treatment. Meanwhile a characteristic needle-like crystal is formed in the film, as a result, the hole mobility is enhanced by an order of magnitude. The mechanism can be attributed to the fast polarization of solvent dipole under the action of EEF, thus forming a driving force that greatly facilitates the orientation of PFO dipole unit. Research also reveals that EEF driving of the PFO chains does not occur with an insoluble solvent vapor since the solvent molecules cannot swell the film, thus there is insufficient free volume for PFO chains to adjust their conformation. This research enriches the understanding of the relationship between solvent vapor annealing and EEF in orientation polymers, and this method is simple and controlled, and capable of integrating into large-area thin film process, which provides new insights to manufacture low-cost and highly ordered polymer films, and is of great significance to enhance carrier mobility and efficiency of photoelectric devices based on polymer condensed matter physics.     

Protegrin‐1 orientation and physicochemical properties in membrane bilayers studied by potential of mean force calculations

Protegrin‐1 (PG‐1) belongs to the family of antimicrobial peptides. It interacts specifically with the membrane of a pathogen and kills the pathogen by releasing its cellular contents. To fully understand the energetics governing the orientation of PG‐1 in different membrane environments and its effects on the physicochemical properties of the peptide and membrane bilayers, we have performed the potential of mean force (PMF) calculations as a function of its tilt angle at four distinct rotation angles in explicit membranes composed of either DLPC (1,2‐dilauroylphosphatidylcholine) or POPC (1‐palmitoyl‐2‐oleoylphosphatidylcholine) lipid molecules. The resulting PMFs in explicit lipid bilayers were then used to search for the optimal hydrophobic thickness of the EEF1/IMM1 implicit membrane model in which a two‐dimensional PMF in the tilt and rotation space was calculated. The PMFs in explicit membrane systems clearly reveal that the energetically favorable tilt angle is affected by both the membrane hydrophobic thickness and the PG‐1 rotation angle. Local thinning of the membrane around PG‐1 is observed upon PG‐1 tilting. The thinning is caused by both hydrophobic mismatch and arginine‐lipid head group interactions. The two‐dimensional PMF in the implicit membrane is in good accordance with those from the explicit membrane simulations. The ensemble‐averaged Val16 ¹⁵N and ¹³CO chemical shifts weighted by the two‐dimensional PMF agree fairly well with the experimental values, suggesting the importance of peptide dynamics in calculating such ensemble properties for direct comparison with experimental observables. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Mapping electron paramagnetic resonance spin label conformations by the simulated scaling method

In order to efficiently simulate spin label behavior when attached to the protein backbone we developed a novel approach that enhances local conformational sampling. The simulated scaling (SS) approach (Li, H., et al. J. Chem. Phys. 2007, 126, 24106) couples the random walk of a potential scaling parameter and molecular dynamics in the framework of hybrid Monte Carlo. This approach allows efficient barrier crossings between conformations. The method retains the thermodynamic detailed balance allowing for determination of relative free energies between various conformations. The accuracy of our method was validated by comparison with the recently resolved X-ray crystal structure of a spin labeled T4 lysozyme in which the spin label was in the interior of the protein. Consistent potentials of mean force (PMF) are obtained for the spin label torsion angles to illustrate their behavior in various protein environments: surface, semiburied, and buried. These PMFs reflect the experimentally observed trends and provide the rationale for the spin label dynamics. We have used this method to compare an implicit and explicit solvent model in spin label modeling. The implicit model, which is computationally faster, was found to be in excellent agreement with the explicit solvent treatment. Based on this collection of results, we believe that the presented approach has great potential in the general strategy of describing the behavior of the spin label using molecular modeling and using this information in the interpretation of EPR measurements in terms of protein conformation and dynamics.     

Validated reversed phase LC method for quantitative analysis of polymethoxyflavones in citrus peel extracts

Polymethoxyflavones (PMFs), which exist exclusively in the citrus genus, have biological activities including anti-inflammatory, anticarcinogenic, and antiatherogenic properties. A validated RPLC method was developed for quantitative analysis of six major PMFs, namely nobiletin, tangeretin, sinensetin, 5,6,7,4'-tetramethoxyflavone, 3,5,6,7,3',4'-hexamethoxyflavone, and 3,5,6,7,8,3',4'-heptamethoxyflavone. The polar embedded LC stationary phase was able to fully resolve the six analogues. The developed method was fully validated in terms of linearity, accuracy, precision, sensitivity, and system suitability. The LOD of the method was calculated as 0.15 microg/mL and the recovery rate was between 97.0 and 105.1%. This analytical method was successfully applied to quantify the individual PMFs in four commercially available citrus peel extracts (CPEs). Each extract shows significant difference in the PMF composition and concentration. This method may provide a simple, rapid, and reliable tool to help reveal the correlation between the bioactivity of the PMF extracts and the individual PMF content.     

Solvent effect on intramolecular electron transfer rates of mixed-valence biferrocene monocation derivatives

Intramolecular electron transfer (ET) rates in various solvents of mixed-valence biferrocene monocation (Fe(II), Fe(III)) and the 1',1' '-diiodo and 1',1' '-diethyl derivatives (respectively abbreviated as BFC(+), I(2)BFC(+), and Et(2)BFC(+)) were determined by means of the spin-lattice relaxation times of the protons, taking into account the local magnetic field fluctuation caused by the electron hopping between the two ferrocene units. We also determined the ET rates of a mixed-valence diferrocenylacetylene monocation (DFA(+)) in order to examine the effect of the insertion of an acetylene bridge between the two ferrocene units. The insertion of the bridge decreased the ET rate, while the effect of substitution on the cyclopentadienyl rings on the rate was minor. The observed rates for each mixed-valence monocation in various solvents did not correlate with the reorganization energies, but we did find a significant contribution of the solvent dynamics. The observed rates were considerably higher than those expected on the basis of the Sumi-Marcus-Nalder model in which the solvents were regarded as dielectric continua. The slope of the logarithm plot of the pre-exponential factors in various solvents for each mixed-valence monocation versus the inverse of the longitudinal dielectric relaxation times of the solvents was significantly smaller than unity, and the slope for DFA(+) was larger than those for BFC(+), I(2)BFC(+), and Et(2)BFC(+). These results were ascribed to a partial contribution of the dielectric friction to the dynamics along the solvent coordinate; the extent of the contribution decreased with a reduction in the ET distance. For the dynamics along the solvent coordinate of the ET reactions in methanol, the observed rates indicated an important contribution by the minor dielectric relaxation components with faster relaxation times, rather than the major component with an extraordinarily long relaxation time.     

Association constants and distribution functions for ion pairs in binary solvent mixtures: application to a cyanine dye system

The computations of the association constants K(ass) were performed at the microscopic level for the ion pair Cy(+)I(-) composed of the complex cyanine dye cation Cy(+) coupled to the negative iodine counterion. The wide array of K(ass) values is arranged by a variation of the composition of the binary solvent mixtures toluene/dimethylsulfoxide with the accompanying change of the solvent polarity. The potentials of mean force (PMFs) are calculated for a set of interionic separations R in the Cy(+)I(-) by a methodology which combines the quantum-chemical techniques for the treatment of the electronic structure of the Cy(+)I(-) system with the recent dielectric continuum approach which accounts for the solvation effects. For a given solute/solvent system the probability function P(R), which describes the distribution of interionic separations, is constructed in terms of the PMFs and implemented for the evaluation of the K(ass).     

Enthalpy-entropy compensation in the effects of urea on hydrophobic interactions

By comparison of neopentane pair potentials of mean force (PMFs) in room temperature water and 6.9 molar aqueous urea, it was recently shown that urea molecules affect the PMF minima in an unexpected way (Lee, M.-E.; van der Vegt, N. F. A. J. Am. Chem. Soc. 2006, 128, 4948). While the first PMF minimum in urea solution has an identical shape and depth to those of the corresponding minimum in water, the second minimum in urea solution is broader, deeper, and shifted out to a slightly larger distance. Here, we present a study of the enthalpic and entropic contributions to these PMFs. Its significance for understanding the driving forces responsible for thermodynamically favorable neopentane contact and solvent-separated distances in urea solution is discussed. We propose that the solute-solvent entropy and solute-solvent enthalpy changes should be analyzed for obtaining an unambiguous molecular-scale picture. In urea solution, enthalpy-entropy compensation effects associated with structural solvent reorganization processes are large, causing changes of the system's enthalpy and entropy with hydrophobic pair separation to be very different from the solute-solvent enthalpy and entropy changes. The entropies are discussed in terms of the molecular-scale solvent reorganization processes.     

Halide anion capture and recognition by a tetrahedral tetraammonium receptor in water: a molecular dynamics investigation

We report molecular dynamics potential of mean force (PMF) simulations on the capture of halide anions X(-) (F(-), Cl(-), Br(-)) by a tetrahedral receptor L(4+) built from four quaternary ammonium sites connected by six (CH(2))(n) chains, leading to the formation of inclusion complexes X(-) subset L(4+). Simulations performed with a reaction field correction of the electrostatics and with PME-Ewald summation gave very similar energy profiles. In aqueous solution, an energy barrier of 12-17 kcal mol(-1) was found for the three anions, mainly due to their dehydration when they enter through the largest triangular face of L(4+). In the inclusion complexes, the anion is anchored near the center of the cavity due to the electrostatic field of the four positively charged ammonium sites, shielded from the surrounding water molecules. It was predicted that L(4+) is selective for Cl(-) over Br(-) which both form stable inclusion complexes, while the F(-) complex should dissociate. The comparison of PMFs in aqueous solution and in the gas phase and the energy component analysis demonstrates the importance of solvent on the nature of these complexes and on the complexation energy profiles. The Cl(-)/Br(-) selectivity obtained from the dissociation pathways in water was in good agreement with the results of free energy perturbation simulations based on the "alchemical route" of a thermodynamic cycle, and consistent with experimental observations.     

Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models

Ionizable residues play important roles in protein structure and activity, and proton binding is a valuable reporter of electrostatic interactions in these systems. We use molecular dynamics free energy simulations (MDFE) to compute proton pKa shifts, relative to a model compound in solution, for three aspartate side chains in two proteins. Simulations with explicit solvent and with an implicit, dielectric continuum solvent are reported. The implicit solvent simulations use the generalized Born (GB) model, which provides an approximate, analytical solution to Poisson's equation. With explicit solvent, the direction of the pKa shifts is correct in all three cases with one force field (AMBER) and in two out of three cases with another (CHARMM). For two aspartates, the dielectric response to ionization is found to be linear, even though the separate protein and solvent responses can be nonlinear. For thioredoxin Asp26, nonlinearity arises from the presence of two substates that correspond to the two possible orientations of the protonated carboxylate. For this side chain, which is partly buried and has a large pKa upshift, very long simulations are needed to correctly sample several slow degrees of freedom that reorganize in response to the ionization. Thus, nearby Lys57 rotates to form a salt bridge and becomes buried, while three waters intercalate along the opposite edge of Asp26. Such strong and anisotropic reorganization is very difficult to predict with Poisson-Boltzmann methods that only consider electrostatic interactions and employ a single protein structure. In contrast, MDFE with a GB dielectric continuum solvent, used for the first time for pKa calculations, can describe protein reorganization accurately and gives encouraging agreement with experiment and with the explicit solvent simulations.     

Comparing pairwise‐additive and many‐body generalized Born models for acid/base calculations and protein design

Generalized Born (GB) solvent models are common in acid/base calculations and protein design. With GB, the interaction between a pair of solute atoms depends on the shape of the protein/solvent boundary and, therefore, the positions of all solute atoms, so that GB is a many‐body potential. For compute‐intensive applications, the model is often simplified further, by introducing a mean, native‐like protein/solvent boundary, which removes the many‐body property. We investigate a method for both acid/base calculations and protein design that uses Monte Carlo simulations in which side chains can explore rotamers, bind/release protons, or mutate. The fluctuating protein/solvent dielectric boundary is treated in a way that is numerically exact (within the GB framework), in contrast to a mean boundary. Its originality is that it captures the many‐body character while retaining the residue‐pairwise complexity given by a fixed boundary. The method is implemented in the Proteus protein design software. It yields a slight but systematic improvement for acid/base constants in nine proteins and a significant improvement for the computational design of three PDZ domains. It eliminates a source of model uncertainty, which will facilitate the analysis of other model limitations. © 2017 Wiley Periodicals, Inc.     

Dynamic information for cardiotoxin protein desorption from a methyl-terminated self-assembled monolayer using steered molecular dynamics simulation

Dynamic information, such as force, structural change, interaction energy, and potential of mean force (PMF), about the desorption of a single cardiotoxin (CTX) protein from a methyl-terminated self-assembled monolayer (SAM) surface was investigated by means of steered molecular dynamics (SMD) simulations. The simulation results indicated that Loop I is the first loop to depart from the SAM surface, which is in good agreement with the results of the nuclear magnetic resonance spectroscopy experiment. The free energy landscape and the thermodynamic force of the CTX desorption process was represented by the PMF and by the derivative of PMF with respect to distance, respectively. By applying Jarzynski's equality, the PMF can be reconstructed from the SMD simulation. The PMFs, calculated by different estimators based upon Jarzynski's equality, were compared with the conventional umbrella sampling method. The best estimation was obtained by using the fluctuation-dissipation estimator with a pulling velocity of v = 0.25 nm/ns for the present study.     

Defect structures and three-body potential of the mean force for nanoparticles in a nematic host

We have investigated the defect structures and potential of mean force (PMF) of three colloidal spheres immersed in a nematic liquid crystal (for linear and equilateral-triangular configurations), using a coarse-grained theory for the tensor order parameter. At large separations, each sphere is surrounded by an equatorial Saturn ring defect; at short separations, the theory predicts a drastic reorganization of the disclination lines: additional disclination rings are observed in planes perpendicular to the original ones. For both types of configurations, the PMF is attractive and always greater than a pairwise sum of binary PMFs. Comparing the PMFs of linear and equilateral-triangular configurations, we have found the triangular configuration to be more stable than the linear configuration. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1033-1040, 2005     

The Protective Effects of Sour Orange (Citrus aurantium L.) Polymethoxyflavones on Mice Irradiation-Induced Intestinal Injury

Sour orange (Citrus aurantium L.) is one of the biological sources of polymethoxyflavones (PMFs), which are often used to deal with gastrointestinal diseases. The intestine is highly sensitive to irradiation damage. However, limited certain cures have been released for irradiation-induced gastrointestinal injury, and the potentials of sour orange PMFs as radio-resistance agents have not been fully discussed yet. The present study aims to (1) investigate the PMF components in 12 sour orange cultivars, (2) determine the protective effects of PMFs on irradiation-induced intestinal injury by treating mice that received 12 Gy abdominal irradiation with different doses of PMFs and observing the changes in organ indexes and pathological sections and (3) test cytotoxicity of PMFs by CCK-8 method. The results showed that sour orange PMFs appeared to have high intraspecies similarity. Besides, PMFs protected mice from irradiation-induced injury by alleviating body weight loss, reliving organ index changing and maintaining the intestinal structure. Finally, IC₅₀ concentrations to cell line CCD 841 CoN of PMFs and nobiletin were calculated as 42.23 μg/mL and 51.58 μg/mL, respectively. Our study uncovered PMF contents in 12 sour orange materials and determined the protective effects on irradiation-induced intestinal injuries, providing guidance for the utilization of sour orange resources.     

Balancing solvation and intramolecular interactions: toward a consistent generalized Born force field

The efficient and accurate characterization of solvent effects is a key element in the theoretical and computational study of biological problems. Implicit solvent models, particularly generalized Born (GB) continuum electrostatics, have emerged as an attractive tool to study the structure and dynamics of biomolecules in various environments. Despite recent advances in this methodology, there remain limitations in the parametrization of many of these models. In the present work, we demonstrate that it is possible to achieve a balanced implicit solvent force field by further optimizing the input atomic radii in combination with adjusting the protein backbone torsional energetics. This parameter optimization is guided by the potentials of mean force (PMFs) between amino acid polar groups, calculated from explicit solvent free energy simulations, and by conformational equilibria of short peptides, obtained from extensive folding and unfolding replica exchange molecular dynamics (REX-MD) simulations. Through the application of this protocol, the delicate balance between the competing solvation forces and intramolecular forces appears to be better captured, and correct conformational equilibria for a range of both helical and beta-hairpin peptides are obtained. The same optimized force field also successfully folds both beta-hairpin trpzip2 and mini-protein Trp-Cage, indicating that it is quite robust. Such a balanced, physics-based force field will be highly applicable to a range of biological problems including protein folding and protein structural dynamics.     

Comparison of various implicit solvent models in molecular dynamics simulations of immunoglobulin G light chain dimer

The present study tests performance of different solvation models applied to molecular dynamics simulation of a large, dimeric protein molecule. Analytical Continuum Electrostatics (ACE) with two different parameter sets, older V98 and new V01, and Effective Energy Function (EEF) are employed in molecular dynamics simulation of immunoglobulin G (IgG) light chain dimer and variable domain of IgG light chain. Results are compared with explicit solvent and distance dependent dielectric constant (DDE) calculations. The overall analysis shows that the EEF method yields results comparable to explicit solvent simulations; however, the stability of simulations is lower. On the other hand, the ACE_V98 model does not seem to achieve the accuracy or stability expected in nanosecond timescale MD simulation for the studied systems. The ACE_V01 model greatly improves stability of the calculation; nonetheless, changes in radius of gyration and solvent accessible surface of the studied systems may indicate that the parameter set still needs to be improved if the method is supposed to be used for simulations of large, polymeric proteins. Additionally, electrostatic contribution to the solvation free energy calculated in the ACE model is compared with a numerical treatment of the dielectric continuum model. Wall clock time of all simulations is compared. It shows that EEF calculation is six times faster than corresponding ACE and 50 times faster than explicit solvent simulations.