A New Approach for the Calculation of the Energy of van der Waals Interactions in Macromolecules of Globular Proteins

Abstract

Van der Waals interaction energy in globular proteins is presented by the interaction energies between regions of protein spatial structure with homogenous medium density distribution. We introduce a notion of the local medium permittivity as a function of absorptance of molecular groups with particular conformation. Proposed theory avoids shortcomings which are typical for the calculations on the basis of the pairwise additive approximation. The approach takes into account local peculiarities of protein spatial structure and physical-chemical characteristics of amino acid residues and molecular groups.     

Quantitative Characterization of Local Protein Solvation To Predict Solvent Effects on Protein Structure

Characterization of solvent preferences of proteins is essential to the understanding of solvent effects on protein structure and stability. Although it is generally believed that solvent preferences at distinct loci of a protein surface may differ, quantitative characterization of local protein solvation has remained elusive. In this study, we show that local solvation preferences can be quantified over the entire protein surface from extended molecular dynamics simulations. By subjecting microsecond trajectories of two proteins (lysozyme and antibody fragment D1.3) in 4 M glycerol to rigorous statistical analyses, solvent preferences of individual protein residues are quantified by local preferential interaction coefficients. Local solvent preferences for glycerol vary widely from residue to residue and may change as a result of protein side-chain motions that are slower than the longest intrinsic solvation timescale of ～10 ns. Differences of local solvent preferences between distinct protein side-chain conformations predict solvent effects on local protein structure in good agreement with experiment. This study extends the application scope of preferential interaction theory and enables molecular understanding of solvent effects on protein structure through comprehensive characterization of local protein solvation.     

Conversion of albumin into a transmitter of the ultra long-range interaction of human erythrocytes

Previous experiments in our laboratory and elsewhere have shown that extended macromolecules of high molecular weight are needed in the suspending medium to transmit the quantum-mechanical coherent interaction of human erythrocytes. Albumin, a globular protein, does not transmit the interaction at physiological concentrations. Albumin can be converted into a transmitter by preheating a solution of albumin to 62 degrees C for 20 min. Such treatment unravels the tertiary structure of albumin and allows it to polymerize.     

Conversion of albumin into a transmitter of the ultra long-range interaction of human erythrocytes

Previous experiments in our laboratory and elsewhere have shown that extended macromolecules of high molecular weight are needed in the suspending medium to transmit the quantum-mechanical coherent interaction of human erythrocytes. Albumin, a globular protein, does not transmit the interaction at physiological concentrations. Albumin can be converted into a transmitter by preheating a solution of albumin to 62°C for 20 min. Such treatment unravels the tertiary structure of albumin and allows it to polymerize.     

A new approach to calculation of the energy from van der Waals interactions in macromolecular proteins. Dielectric permeability as a physical parameter for calculations

The problem in the calculation of Van der Waals interactions in protein globules based on the theory of condensed media was considered. The Van der Waals interactions are represented as energies of interaction of regions with a uniform density distribution. A definition of the local dielectric constant as a function of coefficients of absorption of molecular groups with a particular conformation was introduced. The applicability of this approach was estimated. The theory enables one to circumvent the problems arising in calculations based on pairwise additive approximation. The methods provides a high accuracy in determining the local features of spatial structures of globular proteins and physicochemical characteristics of their constituent amino acids and molecular groups.     

Study of the structure of streptokinase conjugates with a hydrophilic vinylpyrrolidone copolymer

The modification of streptokinase by a synthetic N-vinylpyrrolidone copolymer leads to formation of conjugates varying in structures according to the proportions of the components in the reaction medium. Based on data obtained from spectrophotometry, as well as sedimentation and diffusion analyses, it is shown that in the presence of excess protein in the reaction medium, formation of the main chain takes place via the copolymer associated with several protein globules. Under conditions of excess modifier copolymer, either single-site and/or multiple-site bonding is possible for the protein backbone, depending on the molecular weight of the copolymer. One of the models for the conjugates obtained in this manner has been corroborated by small-angle X-ray scattering data. CD spectral analyses has been performed in order to demonstrate that covalent modification does not alter the secondary structure of streptokinase in the conjugate whereas the tertiary structure undergoes local changes in conformation.     

How Flexible Polymers Interact with Proteins and Its Relationship with the Protein Separation Method by Protein–Polymer Complex Formation

Bovine serum albumin was selected as a model protein to study the molecular mechanism of interaction between flexible polymer with net negative electrical charge (polyvinylsulphonate and polyacrylic acid) and a non-charged polymer such as poly(ethylene) poly(propylene) oxide (molecular mass 8,400) by using spectroscopies techniques combination: fluorescence emission and circular dichroism. Polyvinylsulphonate and polyacrylic acid interact with the protein due to the coulombic interaction between positive charged protein groups such as amine of lysine and histydine. The poly(ethylene)-poly(propylene) oxide increased the hydrophobic microenvironment around the tryptophan residues. This polymer preserved the secondary and tertiary structure of the protein and did not induce any significant modification in the protein surface area exposed to the solvent.     

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg²⁺) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg²⁺ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg²⁺ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg²⁺-excess concentrations and comparison with fluorescence titration measurements shows that on average 20–30% of the Mg²⁺ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.     

MCSS functionality maps for a flexible protein

The Multiple Copy Simultaneous Search (MCSS) methodology for finding energetically favorable positions and orientations of small functional groups in a binding site is extended to include flexibility of the target. This makes possible the finding of novel minima not present in a fixed structure and so extends the diversity of inhibitors that can be constructed starting with the MCSS procedure. Quenched molecular dynamics is used to generate energetically favorable positions and orientations of the functional groups in the field of a flexible protein. The method is applied to the viral protein HIV-1 protease with methanol and methyl ammonium as a test case. If the protein is quenched with many copies of functional groups randomly distributed in the binding site, the resulting minima have ligand-protein interaction energies that are, on average, less favorable than those obtained with standard MCSS. This is a consequence of the renormalized potential function employed in the Locally Enhanced Sampling (LES) approximation. However, local optimizations of existing MCSS minima with a flexible protein results in lower energy minima in regions of the protein that are of particular interest. Their use in constructing a consensus protein model for ligand design is discussed.     

The intraglobular electrostatic field of an enzyme. 1. The primary field created by the polypeptide core, functional groups and ions of the alpha-chymotrypsin molecule

The electric field set up by the dipoles of peptide groups ad other dipoles at the atoms of substrate and catalytic groups of alpha-chymotrypsin is considered. It is shown that substantial electric potentials reaching some tenths of volts exist in the active center of the enzyme, the fact which must influence significantly the reactivity of corresponding groups. In contrast to low molecular weight liquids, the contribution to the total potential of dipoles located at different distances from the point under consideration often changes nonmonotonically with the distance, sometimes the predominant influence being exerted not by the nearest polar groups but by the more distant ones. The existence of electric fields having a complex spatial configuration determined by the protein structure can be defined as the effect of the polar medium preorganization. Emphasis is placed on the necessity of taking into account the polarization of the external medium by charges of protein atoms and ions (the difference of primary and secondary electric fields).     

Structural stability of short subsequences of the tropomyosin chain

The native tropomyosin molecule is a parallel, registered, α-helical coiled coil made from two 284-residiic chains. Long excised subsequences (≥ 95 residues) form the same structure with comparable thermal stability. Here, we investigate local stability using shorter subsequences (20-50 residues) that are chemically synthesized or excised from various regions along the protein chain. Thermal unfolding studies of such shorter peptides by CD in the same solvent medium used in extant studies of the parent protein indicate very low helix content, almost no coiled-coil formation, and high thermal lability of such secondary structure as does form. This behavior is in stark contrast to extant data on leucine-zipper peptides and short “designed” synthetic peptides, many of which have high α-helix content and form highly stable coiled coils. The existence of short coiled coils calls into question the older idea that short subsequences of a protein have little structure. The present study supports the older view, at least in its application to tropomyosin. The intrinsic local α-helical propensity and helix–helix interaction in this prototypical α-helical protein is sufficiently weak as to require not only dimerization, but macro-molecular amplification in order to attain its native conformation in common benign media near neutral pH. © 1995 John Wiley & Sons, Inc.     

Ser/Thr Motifs in Transmembrane Proteins: Conservation Patterns and Effects on Local Protein Structure and Dynamics

We combined systematic bioinformatics analyses and molecular dynamics simulations to assess the conservation patterns of Ser and Thr motifs in membrane proteins, and the effect of such motifs on the structure and dynamics of α-helical transmembrane (TM) segments. We find that Ser/Thr motifs are often present in β-barrel TM proteins. At least one Ser/Thr motif is present in almost half of the sequences of α-helical proteins analyzed here. The extensive bioinformatics analyses and inspection of protein structures led to the identification of molecular transporters with noticeable numbers of Ser/Thr motifs within the TM region. Given the energetic penalty for burying multiple Ser/Thr groups in the membrane hydrophobic core, the observation of transporters with multiple membrane-embedded Ser/Thr is intriguing and raises the question of how the presence of multiple Ser/Thr affects protein local structure and dynamics. Molecular dynamics simulations of four different Ser-containing model TM peptides indicate that backbone hydrogen bonding of membrane-buried Ser/Thr hydroxyl groups can significantly change the local structure and dynamics of the helix. Ser groups located close to the membrane interface can hydrogen bond to solvent water instead of protein backbone, leading to an enhanced local solvation of the peptide.     

Role of the cytosolic factor in the interaction of [3H] alpha-tocopherol with rat liver nuclei

A protein fraction (Mr = 30-70 kD) specifically binding [3H]alpha-tocopherol was isolated from rat liver cytosol. Using high performance ion exchange chromatography, this fraction was separated into acid and alkaline protein subfractions. Acid proteins make up to 41% of the total protein pool and they bind the label 8 times more intensively than the alkaline ones. Cytosol and its protein fraction with an average molecular mass increase 2.2-2.5-fold the binding of labeled vitamin E to isolated liver nuclei. It is concluded that the cytosolic proteins having a medium molecular mass are involved in tocopherol interaction with the nuclei.     

Molecular dynamics study of the structure and dynamics of a protein molecule in a crystalline ionic environment, Streptomyces griseus protease A

A large-scale molecular dynamics simulation of the behavior of a serine protease (Streptomyces griseus protease A) in a crystalline environment has been performed. All atoms (including hydrogens) of two protein molecules and the surrounding solvent of crystallization, consisting of both water and salt ions, were explicitly represented, and a relatively long range of interactions (up to 15 A) were included. The simulation is the longest so far reported for a protein in such an environment (60 ps). The use of the full crystalline environment allows a direct comparison of the structure and dynamic properties of the protein and surrounding solvent to be made with the experimental X-ray structure. Here we report the comparison of the protein structures and analyze the energetics of the system, including interaction with the aqueous environment. Subsequent papers will deal with other aspects of the simulation. The overall root mean square differences between the time-averaged molecular dynamics structure and that from crystallography, for all well-ordered, non-hydrogen atoms, are 1.67 and 1.25 A for the two molecules taken as the asymmetric unit. An extensive analysis of the conformation of substructural elements and individual residues and their deviation from experiment has revealed a strong influence of the ionic medium on their behavior. Implications of the results for free energy calculations and for future directions are also discussed.     

X-ray structure determination and comparison of two crystal forms of a variant (Asn115Arg) of the alkaline protease from Bacillus alcalophilus refined at 1.85 A resolution.

The X-ray structure determination, refinement and comparison of two crystal forms of a variant (Asn115Arg) of the alkaline protease from Bacillus alcalophilus is described. Under identical conditions crystals were obtained in the orthorhombic space group P2(1)2(1)2(1) (form I) and the rhombohedral space group R32 (form II). For both space groups the structures of the protease were solved by molecular replacement and refined at 1.85 A resolution. The final R-factors are 17.9% and 17.1% for form I and form II, respectively. The root-mean-square deviation between the two forms is 0.48 A and 0.86 A for main-chain and side-chain atoms, respectively. Due to differences in crystal lattice contacts and packing, the structures of the two crystal forms differ in intermolecular interaction affecting the local conformation of three flexible polypeptide sequences (Ser50-Glu55, Ser99-Gly102, Gly258-Ser259) at the surface of the protein. While the two overall structures are very similar, the differences are significantly larger than the errors inherent in the structure determination. As expected, the differences in the temperature factors in form I and II are correlated with the solvent accessibility of the corresponding amino acid residues. In form II, two symmetry-related substrate binding sites face each other, forming a tight intermolecular interaction. Some residues contributing to this intermolecular interaction are also found to be involved in the formation of the complex between subtilisin Carlsberg and the proteinaceous inhibitor eglin C. This demonstrates that the two symmetry-related molecules interact with each other at the same molecular surface area that is used for binding of substrates and inhibitors.     

Interaction between bound water molecules and local protein structures: A statistical analysis of the hydrogen bond structures around bound water molecules

Water molecules play an important role in protein folding and protein interactions through their structural association with proteins. Examples of such structural association can be found in protein crystal structures, and can often explain protein functionality in the context of structure. We herein report the systematic analysis of the local structures of proteins interacting with water molecules, and the characterization of their geometric features. We first examined the interaction of water molecules with a large local interaction environment by comparing the preference of water molecules in three regions, namely, the protein–protein interaction (PPI) interfaces, the crystal contact (CC) interfaces, and the non‐interfacial regions. High preference of water molecules to the PPI and CC interfaces was found. In addition, the bound water on the PPI interface was more favorably associated with the complex interaction structure, implying that such water‐mediated structures may participate in the shaping of the PPI interface. The pairwise water‐mediated interaction was then investigated, and the water‐mediated residue–residue interaction potential was derived. Subsequently, the types of polar atoms surrounding the water molecules were analyzed, and the preference of the hydrogen bond acceptor was observed. Furthermore, the geometries of the structures interacting with water were analyzed, and it was found that the major structure on the protein surface exhibited planar geometry rather than tetrahedral geometry. Several previously undiscovered characteristics of water–protein interactions were unfolded in this study, and are expected to lead to a better understanding of protein structure and function. Proteins 2016; 84:43–51. © 2015 Wiley Periodicals, Inc.     

Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.     

Theory of protein secondary structure and algorithm of its prediction

A molecular theory of protein secondary structure is presented that takes account of both local interactions inside each chain region and long-range interactions between different regions, incorporating all these interactions in a single Ising-like model. Local interactions are evaluated from the stereochemical theory describing the relative stabilities of α- and β-structures for different residues in synthetic polypeptides, while long-range effects are approximated by the interaction of each chain region with the averaged hydrophobic template. Based on this theory, an algorithm of protein secondary structure prediction is proposed and examples are given of “blind” predictions made before the x-ray structural data became available.     

Inactivation of the ribosomal protein S1 in polyuridylate binding by reductive methylation of the lysyl-ammonium groups.

The ribosomal protein S1 was modified by reductive methylation of some of its lysyl ammonium groups (S1). With 6 out of 30 groups methylated the protein lost its capacity to form stable complexes with polyuridylate. Addition of excess polyuridylate inhibited the methylation of the lysyl groups. In equilibrium dialysis experiments it was shown that the binding constant between S1 and U15 was lowered 10-fold as compared to the native protein. The pH-dependence of the complex formation between S1 and U15 confirms a participation of the lysyl residues. When S1 depleted 30-S ribosomes were reconstituted with methylated S1 these ribosomes were inactive in the poly(U) stimulated Phe-tRNA binding. The data are discussed with respect to a grid-like interaction between the lysyl groups of the protein and the phosphodiester bonds of the polynucleotide as a molecular basis of protein nucleic acid interaction.     

Computational approach for the design of AP1867 analogs: aiming at new synthetic routes for potential immunosuppressant agents

Molecular modelling and synthetic arguments are valuable tools for the design of potential immunosuppressant agents. In this paper, eight proline-based compounds related to the AP1867 structure are studied and at least one of them is found to be a structurally good candidate for the inhibition of FKBP protein. Theoretical calculations were carried out to locate the most energetically favorable chemical substituent group relative to a core skeleton group on interaction with the FKBP binding cavity. Connolly accessible surface calculations have complemented the molecular mechanics and dynamics approaches. Calculated results were also analyzed on the basis of hydrogen bond interactions, relative energies of interaction, root-mean square deviations of amino acid residues of the crystallized protein, and orientation of the substituent groups within the active site. The results show a significant reduction in the relative interaction energies and very good shape complementarities between our final analog compound and the FKBP binding pocket.