Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

New developments in first-principles excited-state dynamics simulations: unveiling the solvent specificity of excited anionic cluster relaxation and electron solvation

Charge-transfer-to-solvent excited iodide–polar solvent molecule clusters, [I^? (Solv)_n]^*, have attracted substantial interest over the past 20 years as they can undergo intriguing relaxation processes leading ultimately to the formation of gas-phase molecular analogues of the solvated electron. In this review article, we present a comprehensive overview of the development and application of state-of-the-art first-principles molecular dynamics simulation approaches to understand and interpret the results of femtosecond photoelectron spectroscopy experiments on [I^? (Solv)_n]^* relaxation, which point to a high degree of solvent specificity in the electron solvation dynamics. The intricate molecular details of the [I^? (Solv)_n]^* relaxation process are presented, and by contrasting the relaxation mechanisms of clusters with several different solvents (water, methanol and acetonitrile), the molecular basis of the solvent specificity of electron solvation in [I^? (Solv)_n]^* is uncovered, leading to a more refined view of the manifestation of electron solvation in small gas-phase clusters.     

The solvation of bromide anion in acetonitrile: a structural study based on the combination of theoretical calculations and X-ray absorption spectroscopy

This work studies the solvation of bromide in acetonitrile by combining quantum mechanics, computer simulations and X-ray absorption near edge structure (XANES) spectroscopy. Three different sets of interaction potentials were tested, one of them derived from literature and the other two are simple modifications of the previous one to include specificities of the bromide–acetonitrile interactions. Results for microsolvation of bromide were obtained by quantum mechanical optimization and classical minimization of small clusters [Br(ACN) _n ]^?  (n = 9, 20). Analysis of molecular dynamics (MD) simulations has provided structural, dynamic and energetic aspects of the solvation phenomenon. The theoretical computation of Br K-edge XANES spectrum in solution using the structural information obtained from the different simulations has allowed the comparison among the three different potentials, as well as the examination of the main structural and dynamic factors determining the shape of the experimental spectrum.     

Zinc finger protein binding to DNA: an energy perspective using molecular dynamics simulation and free energy calculations on mutants of both zinc finger domains and their specific DNA bases

Energy calculations based on MM-GBSA were employed to study various zinc finger protein (ZF) motifs binding to DNA. Mutants of both the DNA bound to their specific amino acids were studied. Calculated energies gave evidence for a relationship between binding energy and affinity of ZF motifs to their sites on DNA. ΔG values were ?15.82(12), ?3.66(12), and ?12.14(11.6) kcal/mol for finger one, finger two, and finger three, respectively. The mutations in the DNA bases reduced the value of the negative energies of binding (maximum value for ΔΔG = 42Kcal/mol for F1 when GCG mutated to GGG, and ΔΔG = 22 kcal/mol for F2, the loss in total energy of binding originated in the loss in electrostatic energies upon mutation (r = .98). The mutations in key amino acids in the ZF motif in positions-1, 2, 3, and 6 showed reduced binding energies to DNA with correlation coefficients between total free energy and electrostatic was .99 and with Van der Waal was .93. Results agree with experimentally found selectivity which showed that Arginine in position-1 is specific to G, while Aspartic acid (D) in position 2 plays a complicated role in binding. There is a correlation between the MD calculated free energies of binding and those obtained experimentally for prepared ZF motifs bound to triplet bases in other reports (), our results may help in the design of ZF motifs based on the established recognition codes based on energies and contributing energies to the total energy.     

Synthesis of poly(ε-caprolactone) by an immobilized lipase coated with ionic liquids in a solvent-free condition

Polycaprolactone (PCL) was synthesized by ring-opening polymerization of ε-caprolactone through two different enzymatic processes. The lipase from Candida antarctica B, immobilized on macroporous acrylic acid beads, was employed either untreated or coated with small amounts of ionic liquids (ILs). Monocationic ionic liquids, [C _n MIm][NTf₂] (n = 2, 6, 12), as well as a dicationic ionic liquid, ([C₄(C₆Im)₂][NTf₂]₂), were used to coat the immobilized lipase and also as the reaction medium. In both methods, the polarity, anion of the ILs concentration and viscosity strongly influenced the reaction. Coating the immobilized enzyme with ILs improved catalytic activity and less ILs was required to produce PCL with a higher molecular weight and reaction yield. At 60 °C and ILs/Novozyme-435 coating ratio of 3:1 (w/w) for 48 h, the highest M _w and reaction yield of PCL were 35,600 g/mol and 62 % in the case of [C₁₂MIm][NTf₂], while the M _w and reaction yield of PCL was 20,300 g/mol and 54 % with [C₁₂MIm][NTf₂] and catalyzed by untreated lipase.     

Anion–π interactions: CP-corrected vs. standard optimisation,AIM and NBO analyses

The anion–π interactions between Br^? , Cl^? , F^?  and H^?  anions and hexafluorobenzene (HFB), 1,2,4,5-tetracyanobenzene (TCB) and tetracyanopyrazine (TCP) have been studied by standard and counterpoise (CP) corrected methods at HF, B3LYP and MP2/6-31+ + G (d,p) levels of theory. The complexation energies were corrected for basis set superposition error (ΔE _BSSE) and zero point energy (ΔE _BSSE + ZPE). Also, the B3LYP results were corrected by single-point calculation at B3LYP/aug-cc-PVTZ level of theory. Although the CP-corrected method results in higher distances between anions and rings, the standard method gives lower complexation energies. TCP…X^?  series gives higher complexation energies in both CP-corrected and standard methods. Topological analysis of the charge density ρ(r) has been performed by the means of atoms in molecules method on the wave functions obtained at MP2/6-31+ + G (d,p) level of theory. The number and the nature of critical points depend on aromatic ring and anion. Natural bond orbital analysis indicates that n_X → π*_CC and n_X → π*_CN interactions are the most important interactions for TCB (and HFB)…X^?  and TCP…X^?  complexes, respectively.     

Enzymatic synthesis of poly(ε-caprolactone) in monocationic and dicationic ionic liquids

Enzymatic polymerization can offer metal-free routes to polymer materials that could be used in biomedical applications. To take advantage of the unique properties of ionic liquids (ILs) for enzyme stability, monocationic ionic liquid (MIL) and dicationic ionic liquid (DIL) were used to promote the ring-opening polymerization of ε-caprolactone (ε-CL) using Candida antarctica lipase B as catalyst. Considering the molecular weight (M _n ) and reaction yield of the resulting polymer (PCL), high density and viscosity of ILs would be good, especially in the case of DIL. With the same total alkyl chain length, the density and viscosity of [C₄(C₆Im)₂][PF₆]₂ were higher than that of [C₁₂MIm][PF₆]. Using a lipase/CL/ILs ratio of 1:20:20 (by wt) for 48 h at 90 °C, the highest M _n and reaction yield of PCL were 26,200 g/mol and 62 % with [C₄(C₆Im)₂][PF₆]₂, while the M _n and reaction yield of PCL obtained in [C₁₂MIm][PF₆] were 11,700 g/mol and 37 %.     

Helix coil transitions of d (A)n·d(T)n,d(A-T)n·d(A-T)n,and d(A-A-T)n·d(A-T-T)n; evaluation of parameters governing DNA stability

The thermally induced helix-coil transitions of three A-T DNAs, d(A)_n·d(T)_n, d(A-T)_n·d(A-T)_n, and d(A-A-T)_n·d(A-T-T)_n, were studied. Experimental transition curves of the DNAs were analyzed using the loop entropy model of DNA melting. The calculation of the melting curve of d(A-A-T)_n·d(A-T-T)_n is presented using the integral equation formalism of Goel and Montroll. The aim of this work was to evaluate thermodynamic parameters which govern DNA stability and to test the theoretical model employed in the analysis. Our results show (1) an excellent over-all agreement between theory and experiment, (2) a loop entropy exponent k = 1.55 ± 0.05 provided the best fit to all the polymer transition curves, (3) the evaluated stacking free energies reflect the relative stability of the DNAs, and (4) the stacking energies of the ApA·TpT dimer evaluated from d(A)_n·d(T)_n and d(A-A-T)_n·d(A-T-T)_n differ. The last result is consistent with different conformations for the dimer in these two polymers.     

Ab initio investigations on planar (MgO)n clusters (n = 1–5) and their hydrogen adsorption behaviour

Ab initio calculations (B3LYP and PBE-D3) of the structures, stabilities, vibrational, electronic and hydrogen adsorption behaviour of (MgO)_n clusters are performed using 6-311+ + G(d,p) basis set. The planar (MgO)_n clusters are found to be global minima for n ≤ 3 and local minima for n = 4 and 5. In addition, we have also analysed global minimum structures of (MgO)₄ and (MgO)₅. The binding energies suggest that their stabilities increase successively. Vibrational frequencies and IR intensities further support the enhanced stability with an increase in the size of (MgO)_n clusters. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) surfaces are used to explain and discuss the electronic properties. Finally, we have demonstrated hydrogen storage capacity of (MgO)_n clusters, considering hydrogen adsorption on planar as well as global minimum (MgO)₄ and (MgO)₅ clusters. We have noticed that four and five H₂ molecules can be easily adsorbed by (MgO)₄ and (MgO)₅ clusters having adsorption energy of 0.13–0.14 eV with mass ratio of 4.76%. Thus, the present study is expected to motivate further the applications of small clusters for efficient hydrogen energy storage.     

Comparison of the structures and electronic properties of sodalites containing alkali metals and alkali-earth metals and their hydrates

The effects of different alkali and alkali-earth metal ions on the electronic structures and properties of sodalite M_n[AlSiO₄]₆ (M-SOD) and their hydrates M_n[AlSiO₄]₆?8H₂O (M=Li, Na, K, n = 6; M=Ca, n = 3) were studied using density functional theory method. Theoretical calculations predicted that the Al–O–Si bond angle and cation-framework oxide distance in sodalites with alkali metal cations are correlated with cell volumes. The reduced bandwidths in M-SOD (M=Li, Na and K) show that the inter-atomic orbital overlap in sodalites is weaker than those in the hydrate phases. Frontier molecular orbital analysis indicated that oxygen atoms in the frameworks and most metal ions of SOD and their corresponding hydrates exhibit high reactivity. The interactions existing in sodalites and hydrates were qualitative described. The calculated combination energies of metal ions with framework of sodalites are in the order of K⁺< Na⁺< Li⁺< Ca²⁺. This finding confirms the experimental observation for ion exchange.     

Model assembly study of the ligand binding by p-hydroxybenzoate hydroxylase: Correlation between the calculated binding energies and the experimental dissociation constants

The energies of binding of seven ligands by p-hydroxybenzoate hydroxylase (PHBH) were calculated theoretically. Direct enzyme–ligand interaction energies were calculated using the ab initio quantum mechanical model assembly of the active site at the 3-21G level. Solvation energies of the ligands needed in the evaluation of the binding energies were calculated with the semiempirical AM1–SM2 method and the long-range electrostatic interaction energies between the ligands and the protein matrix classically using the static charge distributions of the ligands and the protein. Energies for proton-transfer between the ligands OH or SH substituent at position 4 and the active-site tyrosine within the ab initio model assemblies were calculated and compared to the corresponding pK_as in aqueous solution. Excluding 3,4-dihydroxybenzoate, the natural product of PHBH, a linear relationship between the calculated binding energies and the experimental binding free energies was found with a correlation coefficient of 0.90. Contributions of the direct enzyme–ligand interaction energies, solvation energies and the long-range electrostatic interaction energies to the calculated binding energies were analyzed. The proton-transfer energies of the ligands with substituents ortho to the ionized OH were found to be perturbed less in the model calculations than the energies of their meta isomers as deduced from the corresponding pK_as. © 1995 Wiley-Liss, Inc.     

On the Charge and Molecule Based Summations of Solvent Electrostatic Potentials and the Validity of Electrostatic Linear Response in Water

Solvent-induced electrostatic potentials and field components at thesolute sites of model Na^+q–Cs^-q molecules were computed bysumming over either solvent charges (q-summation) or solventmolecular centers (M-summation) from molecular dynamics simulations.These were compared with values obtained by solving Poisson equation withthe dielectric boundary defined by R _eff = (R _atom +R _gmax )/2.q-summation using cut-offs that are 10 Å generallyunderestimates or overestimates the magnitude of (a) the potentials and field components atNa^+q and Cs^-q relative to the theoretical values and (b)electrostatic solvation free energies of the dipolar solutes assuminglinear solvent response relative to the respective values from free energysimulations. Furthermore, the q-summed electric potentials showedsignificant oscillations even beyond the second hydration shell. Incontrast, the corresponding M-summed potentials plateaued after thefirst hydration shell. Although the different water molecular centersyielded different converged potential values, the dipole center producedvalues in remarkable agreement with the theoretical values for solutecharges ranging from 1 to 0.1e, indicating the existence of an a convenient molecular center for computing these quantities. In contrast to theM-summed potentials, the electrostatic field components andelectrostatic solvation free energies from linear response relationshipswere found not to be sensitive to the choice of the molecular centerfor typical cut-off distances (8 to 12 Å) used in most simulations.     

Design,synthesis, MTT assay,DNA interaction studies of platinum(II) complexes

The square planar Pt(II) complexes of the type [Pt(Lⁿ)(Cl₂)] (where Lⁿ = L^1?3 = thiophene-2-carboxamide derivatives and L^4?6 = thiophene-2-carbothioamide derivatives) have been synthesized and characterized by physicochemical and various spectroscopic studies. MIC method was employed to inference the antibacterial potency of complexes in reference to free ligands and metal salt. Characteristic binding constant (K_b) and binding mode of complexes with calf thymus DNA (CT-DNA) were determined using absorption titration (0.76–1.61 × 10⁵ M^?1), hydrodynamic chain length assay and fluorescence quenching analysis, deducing the partial intercalative mode of binding. Molecular docking calculation displayed free energy of binding in the range of –260.06 to –219.63 kJmol^?1. The nuclease profile of complexes towards pUC19 DNA shows that the complexes cleave DNA more efficiently compared to their respective metal salt. Cytotoxicity profile of the complexes on the brine shrimp shows that all the complex exhibit noteworthy cytotoxic activity with LC₅₀ values ranging from 7.87 to 15.94 μg/mL. The complexes have been evaluated for cell proliferation potential in human colon carcinoma cells (HCT 116) and IC₅₀ value of complexes by MTT assay (IC₅₀ = 125–1000 μg/mL).     

Exploring the structure and dynamics of nano-confined water molecules using molecular dynamics simulations

Confinement effects can lead to drastic changes in the structural and dynamical properties of water molecules. In this work, we have performed classical molecular dynamics simulations of endohedral fullerenes of type (H₂O)_n@C_m (n = 1, 12, 21, 62, 108 and m = 60, 180, 240, 500 and 720) to explore the effects of spherical confinement on water properties. It is shown that these confined water molecules can form distinct solvation pattern depending upon the available space inside the fullerene cavity. For the systems with smaller diameter, cage-like structure is predominant whereas bulk-like structure is observed for larger fullerenes. The orientational relaxation of these confined water molecules showed slower relaxation as the cavity diameter increases except for the (H₂O)₂₁@C₂₄₀. In this case, stable cage-like structure hinders the overall dynamics of the trapped water molecules. Finally, we have calculated the hydrogen bond lifetimes from the hydrogen bond time correlation functions and compared with that of bulk water.     

Aromaticity of azines through dyotropic double hydrogen transfer reaction

The thermodynamic stabilities and IR spectra of the three water clusters (H₂O)_20, (H₂O)_54,, and (H₂O)₁₀₀ are studied by quantum-chemical computations. After full optimization of the (H₂O)_20,54,100 structures using the hybrid density functional B3LYP together with the 6-31+G(d,p) basis set, the electronic energies, zero-point energies, internal energies, enthalpies, entropies, and Gibbs free energies of the water clusters at 298 K are investigated. The OH stretching vibrational IR spectra of (H₂O)_20,54,100 are simulated and split into sub-spectra for different H-bond groups depending on the conformations of the hydrogen bonds. From the computed spectra the different spectroscopic fingerprint features of water molecules in different H-bond conformations in the water clusters are inferred.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Relativistic theoretical studies on hydrogen bonds and the electronic structure of aqueous solvated bis(uranyl) complex: an insight into explicit and/or implicit solvent effects

To understand the chemical behavior of uranyl complexes in water, a bis-uranyl [(phen)(UO₂)(μ₂–F)(F)]₂ (A; phen?=?phenanthroline, μ₂?=?doubly bridged) and its hydrated form A?·?(H₂O)_n (n?=?2, 4 and 6) were examined using scalar relativistic density functional theory. The addition of water caused the phen ligands to deviate slightly from the U₂(μ₂–F)₂ plane, and red-shifts the U–F-terminal and U?=?O stretching vibrations. Four types of hydrogen bonds are present in the optimized hydrated A?·?(H₂O)_n complexes; their energies were calculated to fall within the range 4.37–6.77 kcal mol^-1, comparable to the typical values of 5.0 kcal mol^-1 reported for hydrogen bonds. An aqueous environment simulated by explicit and/or implicit models lowers and re-arranges the orbitals of the bis-uranyl complex.