Flexible docking using tabu search and an empirical estimate of binding affinity

This article describes the implementation of a new docking approach. The method uses a Tabu search methodology to dock flexibly ligand molecules into rigid receptor structures. It uses an empirical objective function with a small number of physically based terms derived from fitting experimental binding affinities for crystallographic complexes. This means that docking energies produced by the searching algorithm provide direct estimates of the binding affinities of the ligands. The method has been tested on 50 ligand-receptor complexes for which the experimental binding affinity and binding geometry are known. All water molecules are removed from the structures and ligand molecules are minimized in vacuo before docking. The lowest energy geometry produced by the docking protocol is within 1.5 Å root-mean square of the experimental binding mode for 86% of the complexes. The lowest energies produced by the docking are in fair agreement with the known free energies of binding for the ligands. Proteins 33:367–382, 1998. © 1998 Wiley-Liss, Inc.     

Hydration properties of DNA-lysine gels by microwave dielectric measurements as a function of temperature

Dielectric measurements by a cavity perturbation method at 10 GHz in the temperature range from-20°C to +45°C are reported for aqueous gels of herring sperm DNA in the presence of 1 or 3 lysine molecules per nucleotide. Measurements for lysine-water and DNA-water systems are also reported. The experimental results can be accounted for by the presence of interfacial water, with dielectric properties different from those of bulk water, and are analyzed in terms of a three component equation (solute molecules, interfacial water and bulk water) to calculate hydration parameters of the systems. The lysine molecule is found to coordinate a particular number of water molecules, in agreement with the literature. The specific hydration of DNA is reduced by the presence of lysine, indicating a direct interaction between the polyion and the aminoacid: a decrease to about 50% was observed at a ratio of one molecule of lysine per nucleotide. A suggestion is made that the interaction is mainly electrostatic in nature.     

Simple combined explicit/implicit water model

A simple combined water model (SCW model) for the calculation of the hydration free energy is presented. In the frame of the model a solute is placed in the centre of the spherical cavity with explicit water molecules, which are considered at the atomistic level. Rigid wall potential at the boundary of the cavity restricts the moving of the explicit water molecules. Water outside the sphere is considered as the conducting continuum (implicit part of the model). Simulation is performed in the frame of the NVT ensemble (constant number of particles, volume and temperature), density of water is fixed and equal to experimental value 1 g/cm³. The energy of electrostatic interaction of atomic point charges of the explicit water molecules with conducting continuum is calculated analytically by means of the image charges method. It provides high computational efficiency of the SCW model. For the averaging of the calculated thermodynamic and structural values over microstates of the system the thermodynamic integration method is used. The possible using of SCW for the docking problem is discussed.     

Water structure and interactions with protein surfaces

The structure of liquid water and its interaction with biological molecules is a very active area of experimental and theoretical research. The chemically complex surfaces of protein molecules alter the structure of the surrounding layer of hydrating water molecules. The dynamics of hydration water can be detected by a series of experimental techniques, which show that hydration waters typically have slower correlation times than water in bulk. Specific water-mediated interactions in protein complexes have been studied in detail, and these interactions have been incorporated into potential energy functions for protein folding and design. The subtle changes in the structure of hydration water have been investigated by theoretical studies.     

Determination of the positions of bound water molecules in the solution structure of reduced human thioredoxin by heteronuclear three-dimensional nuclear magnetic resonance spectroscopy.

The presence of bound water molecules in the solution structure of reduced human thioredoxin has been investigated using three-dimensional 1H rotating frame Overhauser 1H-15N multiple quantum coherence spectroscopy. It is demonstrated that the backbone amide protons of Lys21, Lys39, Lys82, Gly83 and Asn102, as well as the side-chain amide group of Asn102, are in close proximity to bound water molecules. Examination of the high-resolution solution structure of reduced human thioredoxin reveals that these results are best accounted for by four bound water molecules. Subsequent simulated annealing calculations carried out on the basis of interproton distance and hydrogen bonding restraints to the bound water molecules, supplemented by the original set of experimental restraints used in the calculation of the three-dimensional structure of human thioredoxin, permit a more precise localization of the bound water positions. Potential hydrogen bonds to these water molecules are described and a comparison is made to corresponding bound water molecules in the crystal structure of oxidized Escherichia coli thioredoxin.     

Dowser++, a new method of hydrating protein structures

A new method of hydrating protein structures, which we call Dowser++, is presented. The method is based on a semi‐empirical modification of a popular program for protein hydration Dowser, and the usage of protocols AutoDock Vina, and WaterDock. The positions of water molecules predicted by Dowser++ were compared with experimental data for a set of 14 high‐resolution crystal structures of oligopeptide‐binding protein (OppA) containing a large number of resolved internal water molecules, as well as for the D‐ and K‐channels of cytochrome c oxidase, and the recent data on PSII. Comparison is also made with the predictions of the original Dowser, and its improved version, Dowser+, described in our previous publication. We also present a model for quantitative estimation of the quality of water molecules placement made by a program, which includes an assumption of possible false negative data from the crystallographic analysis. The comparison of predictions made by Dowser++, Dowser and Dowser+ demonstrates significant improvement of predictive power of the new method. Proteins 2016; 84:1347–1357. © 2016 Wiley Periodicals, Inc.     

Structural change in lipid bilayers and water penetration induced by shock waves: molecular dynamics simulations

The structural change of a phospholipid bilayer in water under the action of a shock wave is numerically studied with unsteady nonequilibrium molecular dynamics simulations. The action of shock waves is modeled by the momentum change of water molecules, and thereby we demonstrate that the resulting collapse and rebound of the bilayer are followed by the penetration of water molecules into the hydrophobic region of the bilayer. The high-speed phenomenon that occurs during the collapse and rebound of the bilayer is analyzed in detail, particularly focusing on the change of bilayer thickness, the acyl chain bend angles, the lateral fluidity of lipid molecules, and the penetration rate of water molecules. The result shows that the high-speed phenomenon can be divided into two stages: in the first stage the thickness of bilayer and the order parameter are rapidly reduced, and then in the second stage they are recovered relatively slowly. It is in the second stage that water molecules are steadily introduced into the hydrophobic region. The penetration of water molecules is enhanced by the shock wave impulse and this qualitatively agrees with a recent experimental result.     

Water-protein interactions from high-resolution protein crystallography

To understand the role of water in life at molecular and atomic levels, structures and interactions at the protein-water interface have been investigated by cryogenic X-ray crystallography. The method enabled a much clearer visualization of definite hydration sites on the protein surface than at ambient temperature. Using the structural models of proteins, including several hydration water molecules, the characteristics in hydration structures were systematically analysed for the amount, the interaction geometries between water molecules and proteins, and the local and global distribution of water molecules on the surface of proteins. The tetrahedral hydrogen-bond geometry of water molecules in bulk solvent was retained at the interface and enabled the extension of a three-dimensional chain connection of a hydrogen-bond network among hydration water molecules and polar protein atoms over the entire surface of proteins. Networks of hydrogen bonds were quite flexible to accommodate and/or to regulate the conformational changes of proteins such as domain motions. The present experimental results may have profound implications in the understanding of the physico-chemical principles governing the dynamics of proteins in an aqueous environment and a discussion of why water is essential to life at a molecular level.     

A novel way to calculate the diffusivity of water in carbon nanotubes

Theoretical studies on water diffusion in carbon nanotubes have been challenged because the diffusivities calculated by molecular simulations are much lower than what experiments show. This paper proposes a new way to estimate transport diffusivity in such systems directly by simply inspecting the long term behaviors of the velocity autocorrelation functions of water molecules. The results from simulation of molecular dynamics based on this method show that the new method can generate much higher diffusivities, in accordance with experimental measurements, and of the correct order of magnitude.     

Quantifying the Entropy of Binding for Water Molecules in Protein Cavities by Computing Correlations

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.     

Intermolecular interactions between protein and other molecules including hydration effects

The structural aspects of protein functions, e.g., molecular recognition such as enzyme-substrate and antibody-antigen interactions, are elucidated in terms of dehydration and atomic interactions. When a protein interacts with some target molecule, water molecules at the interacting regions of both molecules are removed, with loss of the hydration free energy, but gaining atomic interactions between atoms of the contact sites in both molecules. The free energies of association originating from the dehydration and interactions between the atoms can be computed from changes in the accessible surface areas of the atoms involved. The free energy due to interactions between atomic groups at the contact sites is estimated as the sum of those estimated from the changes in the accessible surface area of 7 atomic groups, assuming that the interactions are proportional to the change of the area. The chain enthalpies and entropies evaluated from experimental thermodynamic properties and hydration quantities at the standard temperature for 10 proteins were available to determine the proportional constants for the atomic groups. This method was applied to the evaluation of association constants for the dimerization of proteins and the formation of proteolytic enzyme-inhibitor complexes, and the computed constants were in agreement with the experimental ones. However, the method is not accurate enough to account quantitatively for the change in the thermal stability of mutants of T4 lysozyme. Nevertheless, this method provides a way to elucidate the interactions between molecules in solution.     

Conformational analysis of dipeptides in aqueous solution. II. Molecular structure of glycine and alanine dipeptides by depolarized rayleigh scattering and laser Raman spectroscopy

A new approach to the experimental conformational analysis of peptides in aqueous solution is presented and discussed. The basic idea is to combine laser Raman spectroscopy and depolarized Rayleigh scattering in order to interpret scattering properties of the dissolved molecule in terms of both local and global structure. We outline a simple method (anisotropic perturbation treatment) appropriate for solving conformational problems in large molecules by studying together slightly perturbed homologous compounds. This method is applied to the study of the molecular structure of simple glycine and alanine dipeptides. The preferred conformation for such molecules is the seven-membered chelated ring (C₇) additionally stabilized by two intermolecular hydrogen bonds involving one molecule of water.     

Hydration of nucleic acid fragments: comparison of theory and experiment for high-resolution crystal structures of RNA, DNA, and DNA-drug complexes.

A computationally efficient method to describe the organization of water around solvated biomolecules is presented. It is based on a statistical mechanical expression for the water-density distribution in terms of particle correlation functions. The method is applied to analyze the hydration of small nucleic acid molecules in the crystal environment, for which high-resolution x-ray crystal structures have been reported. Results for RNA [r(ApU).r(ApU)] and DNA [d(CpG).d(CpG) in Z form and with parallel strand orientation] and for DNA-drug complexes [d(CpG).d(CpG) with the drug proflavine intercalated] are described. A detailed comparison of theoretical and experimental data shows positional agreement for the experimentally observed water sites. The presented method can be used for refinement of the water structure in x-ray crystallography, hydration analysis of nuclear magnetic resonance structures, and theoretical modeling of biological macromolecules such as molecular docking studies. The speed of the computations allows hydration analyses of molecules of almost arbitrary size (tRNA, protein-nucleic acid complexes, etc.) in the crystal environment and in aqueous solution.     

A near-infrared analysis of water-macromolecule interactions: Hydration and the spectra of aqueous solutions of intact proteins

A procedure utilizing a variable path length absorption cell has made possible the recording of what appear to be the first well-resolved, compensated near-infrared spectra of intact proteins in aqueous solution. Individual spectra, corresponding to (1) absorbance by the protein plus bound water, and (2) the solvent volume excluded by the hydrated protein, were obtained using the same experimental sample. Calculations of bound water and excluded volume from these spectra were compared to other results in the literature. The validity of this spectral method was supported by comparisons with the spectra of proteins in films, where there is no excluded volume effect and where the amount of water present has been determined independently by gravimetric measurements. The results indicate that the bound water detected by the near-infrared spectra has an absence or deficiency of molecules with quasi-free OH groups (relative to bulk water), and that in conjunction with results of other methods, these water molecules may represent those that are most firmly or more completely bonded to the protein surface.     

A view of the three dimensional structure of globular proteins

A view of the three dimensional structure of globular proteins based on continuous networks of hydrogen bonds is proposed. Active sites of enzymes and ion sites are prominent and, within the networks, there are islands of hydrophobic regions giving an overall piebald effect to the appearance of the molecule. This point of view was originally suggested by the results of quantum mechanical computations on the coupling between hydrogen bonds. A formalism for the total energy of a globular protein in water is also suggested.The study of five lines of experimental evidence supports this suggestion. The analysis of the experimental X-ray data for ten globular proteins, using the NETWORK program, revealed the existence of these hydrogen bond networks; X-ray data showed that water molecules tend to occupy fixed positions relative to the protein molecule; a survey has shown that water molecules tend to occupy specific positions relative to the hydrogen bonding side chains; experimental evidence on the bulk properties of lysozyme showed that there exist tightly bound water molecules; graphics studies of the ribonucleaseA molecule demonstrated the networks and the piebald effect. This point of view is pictorially simple and, to illustrate the use of such networks, we discuss the simple ion pairs which occur as substructures within the networks.     

On the possible permeation of water across the glucose transporter

The possibility that the glucose transporter may serve as water channel is explored with the help of theoretical and experimental arguments. A model for a pore is drawn based on a hypothetical water channel structure, subject to the constraints that: molecules will bind to the channel wall in successive rings, forming a hollow sleeve; an integer number of molecules will exist in each ring; the pore radius will not be large enough to allow water molecules along its center, but will be large enough to allow glucose molecules across. The only configurations that meet these conditions exhibit either 5 or 6 water molecules abreast in each ring, with pore radii of 4.1 and 4.5 Å, respectively. The kinetic characteristics of such pores are estimated and found to conform to available evidence.     

Determination of Equivalent Pore Radius for Human Red Cells by Osmotic Pressure Measurement

A new method has been developed to measure the equivalent pore radius in cellular membranes, and has been applied to human red cells. When red cells are suddenly introduced into a non-isosmolar concentration of non-lipid-soluble non-electrolyte molecules, water will enter or leave the cell. The rate of cell swelling or shrinking is determined and extrapolated to zero time to give the initial rate of volume change. By suitable adjustment of the concentration of the external solution the initial rate may be brought to zero. The transient equilibrium concentration, determined by interpolation from experimental data, gives a measure of Staverman's reflection coefficient, σ. The zero time method has enabled us to determine σ for nine permeant molecules. σ is directly related to the equivalent pore radius; the experimental data lead to a value of 4.2 Å for the equivalent pore radius in man, in good agreement with the previous figure of 3.5 Å given by Paganelli and Solomon. The zero time method offers a number of advantages over previous methods for determination of this parameter. It requires no measurement of the rate of water entrance into the cell, and is essentially independent of the kinetics of cell swelling. It may be applied to a variety of living cells so that many additional membranes may now be characterized in terms of their equivalent pore radius.