Solvation Effects on Chemical Shifts by Embedded Cluster Integral Equation Theory

The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of <i>N</i>-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute–solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute–solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent’s charge distribution

Structure and thermodynamics of nondipolar molecular liquids and solutions from integral equation theory

<p>Solvent-induced solute polarisation of nondipolar solvents originates mainly from specific directional interactions and higher electrostatic multipole moments. Popular continuum solvation models such as the polarisable continuum models ignore such interactions and, therefore, cannot adequately model solvation effects on electronic structure in these environments. Important examples of nondipolar solvents that are indistinguishable by continuum methods are benzene and hexafluorobenzene. Both substances have very similar macroscopic properties, while solutes dissolved in either benzene or hexafluorobenzene behave differently due to their inverted electrostatic quadrupole moments and slightly different size. As a first step towards a proper and computationally feasible description of nondipolar molecular solvents, we present here integral equation theory results based on various forms of the reference interaction site model coupled to quantum-chemical calculations for benzene and hexafluorobenzene solutions of small molecules. We analyse solvation structures, also in comparison with molecular dynamics simulations, and show that predictions of transfer Gibbs energies, which define partition constants, benefit substantially from considering the exact, wave function-derived electrostatic field distribution beyond a simple point charge solute model in comparison with experimental data. Moreover, by constructing artificial uncharged and charge-inverted toy models of the solvents, it is possible to dissect the relative importance of dispersion and quadrupolar electrostatic effects on the partitioning equilibria. Such insight can help to design specifically optimised solvents to control solubility and selectivity for a wide range of applications.</p> <p></p

Signatures of Solvation Thermodynamics in Spectra of Intermolecular Vibrations

This study explores the thermodynamic and vibrational properties of water in the three-dimensional environment of solvated ions and small molecules using molecular simulations. The spectrum of intermolecular vibrations in liquid solvents provides detailed information on the shape of the local potential energy surface, which in turn determines local thermodynamic properties such as the entropy. Here, we extract this information using a spatially resolved extension of the two-phase thermodynamics method to estimate hydration water entropies based on the local vibrational density of states (3D-2PT). Combined with an analysis of solute–water and water–water interaction energies, this allows us to resolve local contributions to the solvation enthalpy, entropy, and free energy. We use this approach to study effects of ions on their surrounding water hydrogen bond network, its spectrum of intermolecular vibrations, and resulting thermodynamic properties. In the three-dimensional environment of polar and nonpolar functional groups of molecular solutes, we identify distinct hydration water species and classify them by their characteristic vibrational density of states and molecular entropies. In each case, we are able to assign variations in local hydration water entropies to specific changes in the spectrum of intermolecular vibrations. This provides an important link for the thermodynamic interpretation of vibrational spectra that are accessible to far-infrared absorption and Raman spectroscopy experiments. Our analysis provides unique microscopic details regarding the hydration of hydrophobic and hydrophilic functional groups, which enable us to identify interactions and molecular degrees of freedom that determine relevant contributions to the solvation entropy and consequently the free energy

Thermodynamic Characterization of Hydration Sites from Integral Equation-Derived Free Energy Densities: Application to Protein Binding Sites and Ligand Series

Water molecules play an essential role for mediating interactions between ligands and protein binding sites. Displacement of specific water molecules can favorably modulate the free energy of binding of protein–ligand complexes. Here, the nature of water interactions in protein binding sites is investigated by 3D RISM (three-dimensional reference interaction site model) integral equation theory to understand and exploit local thermodynamic features of water molecules by ranking their possible displacement in structure-based design. Unlike molecular dynamics-based approaches, 3D RISM theory allows for fast and noise-free calculations using the same detailed level of solute–solvent interaction description. Here we correlate molecular water entities instead of mere site density maxima with local contributions to the solvation free energy using novel algorithms. Distinct water molecules and hydration sites are investigated in multiple protein–ligand X-ray structures, namely streptavidin, factor Xa, and factor VIIa, based on 3D RISM-derived free energy density fields. Our approach allows the semiquantitative assessment of whether a given structural water molecule can potentially be targeted for replacement in structure-based design. Finally, PLS-based regression models from free energy density fields used within a 3D-QSAR approach (CARMa - comparative analysis of 3D RISM Maps) are shown to be able to extract relevant information for the interpretation of structure–activity relationship (SAR) trends, as demonstrated for a series of serine protease inhibitors

Identification of Intrahelical Bifurcated H‑Bonds as a New Type of Gate in K⁺ Channels

Gating of ion channels is based on structural transitions between open and closed states. To uncover the chemical basis of individual gates, we performed a comparative experimental and computational analysis between two K⁺ channels, Kcv_S and Kcv_NTS. These small viral encoded K⁺ channel proteins, with a monomer size of only 82 amino acids, resemble the pore module of all complex K⁺ channels in terms of structure and function. Even though both proteins share about 90% amino acid sequence identity, they exhibit different open probabilities with ca. 90% in Kcv_NTS and 40% in Kcv_S. Single channel analysis, mutational studies and molecular dynamics simulations show that the difference in open probability is caused by one long closed state in Kcv_S. This state is structurally created in the tetrameric channel by a transient, Ser mediated, intrahelical hydrogen bond. The resulting kink in the inner transmembrane domain swings the aromatic rings from downstream Phes in the cavity of the channel, which blocks ion flux. The frequent occurrence of Ser or Thr based helical kinks in membrane proteins suggests that a similar mechanism could also occur in the gating of other ion channels

<i>s</i>PB1-F2 generates Ca²⁺ and anion fluxes into liposomes.

<p>(A) Fluorescence of liposomes with Ca²⁺ sensitive dye Fluo3 was recorded before and after adding (at arrow) ionophore Valinomycin (triangle), sPB1-F2_pr8 alone (filled squares) or together with Valinomycin (open squares). Peptide and ionophore were added during the time gap of ca. 1 min indicated in the graph. The presence of the peptide results in an increase in fluorescence indicating an influx of Ca²⁺ into the liposomes. The ionophore enhances Ca²⁺ influx because it prevents building up of a charge, which hinders net Ca²⁺ influx. (B) Fluorescence of liposomes filled with Ca²⁺ sensitive dye Fluo-3 before and after addition (at arrow) of 1 µM peptide to incubation medium. The truncated peptide sPB1-F2_pr8^50–87 results in a fast rise in Fluo3 fluorescence. (C) Fluorescence of liposomes filled with anion sensitive dye lucigenin was measured before and after adding of anion specific ionophore TBT (filled squares, added at arrow 1), sPB1-F2_pr8 (open triangle, arrow 2). The control was left untreated (filled circles); the stepwise drop of the control signal is due to an unspecific drift of the signal. Both ionophore and sPB1-F2_pr8 generate a strong quenching of the lucigenin fluorescence well beyond the control indicating an influx of anions. Peptide and ionophore were added during the time gap of ca. 1 min indicated in the graph.</p

Snapshots of the simulation system after removal of the center-of-mass constraint (set to 0 ns).

<p>The protein is shown in cartoon representation with explicit depiction of positively charged residues (arginine: blue, lysine: red). Lipid molecules have been removed except for the head groups that are depicted as grey spheres. Potassium ions are shown in green, chloride ions in blue. The c-terminus is located on the bottom side.</p

Dependence of various measures for protein stability over the simulation time after removal of the center-of-mass (c.o.m.) constraint (set to 0 ns).

<p>From top to bottom: Root mean square deviation (RMSD) of the protein backbone, <i>z</i> coordinate (membrane normal) of the c.o.m. of the protein (corrected by removing the total membrane drift), the protein's radius of gyration (<i>R_g</i>), and the helical fraction recognized for the fold.</p

I/V relation of the small (o₁) and large (o₂) <i>s</i>PB1-F2 generated current fluctuation.

<p>(A) Unitary currents were recorded in bilayer with 500 mM KCl on <i>trans</i> side and 500 mM NaCl on trans (open circles) or with 500 mM KCl on cis and 500 mM K-gluconate on trans (filled squares). (B) I/V relation obtained with 500 mM KCl on trans side and 50 mM KCl on cis side. (C) I/V relation obtained with 500 mM KCl on cis and 500 mM CaCl₂ on trans side. Currents were elicited upon adding <i>s</i>PB1-F2_pr8 (in A-C) and sPB1-F2_sf (in C) to trans side.</p

Alignment of predicted amino acid sequences of PB1-F2 proteins.

<p>The proteins from A/Puerto Rico/8/34 (H1N1) strain (PB1-F2_pr8), the Spanish flu isolate (PB1-F2_sf) and the bird flu virus (H5N1) (PB1-F2_bf) have an overall identity (*) of ca 60%. The domains, which are predicted by structural prediction algorithms to have a high propensity for α-helixes are marked in gray. The truncated peptide sPB1-F2_pr8^50–87 is underlined.</p