Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis

In this report we describe an accurate numerical method for calculating the total electrostatic energy of molecules of arbitrary shape and charge distribution, accounting for both Coulombic and solvent polarization terms. In addition to the solvation energies of individual molecules, the method can be used to calculate the electrostatic energy associated with conformational changes in proteins as well as changes in solvation energy that accompany the binding of charged substrates. The validity of the method is examined by calculating the hydration energies of acetate, methyl ammonium, ammonium, and methanol. The method is then used to study the relationship between the depth of a charge within a protein and its interaction with the solvent. Calculations of the relative electrostatic energies of crystal and misfolded conformations of Themiste dyscritum hemerythrin and the VL domain of an antibody are also presented. The results indicate that electrostatic charge-solvent interactions strongly favor the crystal structures. More generally, it is found that charge-solvent interactions, which are frequently neglected in protein structure analysis, can make large contributions to the total energy of a macromolecular system.     

Aromatic cluster mutations produce focal modulations of β-sheet structure

Site-directed mutagenesis is a powerful tool for altering the structure and function of proteins in a focused manner. Here, we examined how a model β-sheet protein could be tuned by mutation of numerous surface-exposed residues to aromatic amino acids. We designed these aromatic side chain “clusters” at highly solvent-exposed positions in the flat, single-layer β-sheet of Borrelia outer surface protein A (OspA). This unusual β-sheet scaffold allows us to interrogate the effects of these mutations in the context of well-defined structure but in the absence of the strong scaffolding effects of globular protein architecture. We anticipated that the introduction of a cluster of aromatic amino acid residues on the β-sheet surface would result in large conformational changes and/or stabilization and thereby provide new means of controlling the properties of β-sheets. Surprisingly, X-ray crystal structures revealed that the introduction of aromatic clusters produced only subtle conformational changes in the OspA β-sheet. Additionally, despite burying a large degree of hydrophobic surface area, the aromatic cluster mutants were slightly less stable than the wild-type scaffold. These results thereby demonstrate that the introduction of aromatic cluster mutations can serve as a means for subtly modulating β-sheet conformation in protein design.     

Modeling of peptides and proteins in a membrane environment: II. Structural and energetic aspects of glycophorin A in a lipid bilayer

The conformational space of a hydrophobic peptide fragment of glycophorin A in a lipid membrane was studied with the Monte Carlo method using the solvation model described in the first communication of this series. The simulation was performed for various starting orientations of the peptide relative the membrane bilayer: outside, inside, partially immersed, and transbilayer. We showed that the membrane substantially stabilizes the α-helical conformation of the central hydrophobic part of the glycophorin A molecule, which for the most part is immersed in the apolar core of the bilayer. For various conformational states, energy values were calculated and the orientations of the peptide relative to the membrane were characterized. Depending on the thickness of the bilayer, either an entirely α-helical conformation in transbilayer orientation or a conformation with a kink in the central part of the helix with theN- andC-termini exposed on one side of the membrane corresponds to the minimal-energy structure. The transmembrane orientation of glycophorin A is energetically advantageous when the membrane thickness is close to the length of its hydrophobic helical portion, which is consistent with the effect ofhydrophobic match observed experimentally. The prospects for further refinement of the model are discussed. For communication I, see [1].     

Investigation of a side-chain-side-chain hydrogen bond by mutagenesis, thermodynamics, and NMR spectroscopy.

Anomalous NMR behavior of the hydroxyl proton resonance for Ser 31 has been reported for histidine-containing protein (HPr) from two microorganisms: Escherichia coli and Staphylococcus aureus. The unusual slow exchange and chemical shift exhibited by the resonance led to the proposal that the hydroxyl group is involved in a strong hydrogen bond. To test this hypothesis and to characterize the importance of such an interaction, a mutant in which Ser 31 is replaced by an alanine was generated in HPr from Escherichia coli. The activity, stability, and structure of the mutant HPr were assessed using a reconstituted assay system, analysis of solvent denaturation curves, and NMR, respectively. Substitution of Ser 31 yields a fully functional protein that is only slightly less stable (delta delta G(folding) = 0.46 +/- 0.15 kcal mol-1) than the wild type. The NMR results confirm the identity of the hydrogen bond acceptor as Asp 69 and reveal that it exists as the gauche- conformer in wild-type HPr in solution but exhibits conformational averaging in the mutant protein. The side chain of Asp 69 interacts with two main-chain amide proteins in addition to its interaction with the side chain of Ser 31 in the wild-type protein. These results indicate that removal of the serine has led to the loss of all three hydrogen bond interactions involving Asp 69, suggesting a cooperative network of interactions. A complete analysis of the thermodynamics was performed in which differences in side-chain hydrophobicity and conformational entropy between the two proteins are accounted for.(ABSTRACT TRUNCATED AT 250 WORDS)     

Calculation of the free energy of association for protein complexes.

We have developed a method for calculating the association energy of quaternary complexes starting from their atomic coordinates. The association energy is described as the sum of two solvation terms and an energy term to account for the loss of translational and rotational entropy. The calculated solvation energy, using atomic solvation parameters and the solvent accessible surface areas, has a correlation of 96% with experimentally determined values. We have applied this methodology to examine intermediates in viral assembly and to assess the contribution isomerization makes to the association energy of molecular complexes. In addition, we have shown that the calculated association can be used as a predictive tool for analyzing modeled molecular complexes.     

Optimal ratio between the average conformational entropy and the average energy of interaction between residues for fast protein folding

Based on available experimental data and using a theoretical model of protein folding, we demonstrate that there is an optimal ratio between the average conformational entropy and the average contact energy per residue for fast protein folding. A statistical analysis of the conformational entropy and the number of contacts per residue for 5829 protein domains from four main classes (α, β, α/β, α+β) shows that each class has its own characteristic average number of contacts per residue and average conformational entropy per residue. These class-specific characteristics determine the protein folding rates: α-proteins are the fastest to fold, β-proteins are the second fastest, α+β-proteins are the third, and α/β-proteins are the last to fold.     

Why do protein architectures have boltzmann-like statistics?

A theoretical study has shown that the occurrence of various structural elements in stable folds of random copolymers is exponentially dependent on the own energy of the element. A similar occurrence-on-energy dependence is observed in globular proteins¹ from the level of amino acid conformations to the level of overall architectures. Thus, the structural features stabilized by many random sequences are typical of globular proteins while the features rarely observed in proteins are those which are stabilized by only a minor part of the random sequences. © 1995 Wiley-Liss, Inc.     

Changes in Conformation and Stability upon Formation of Complexes of Erythropoietin (EPO) and Soluble EPO Receptor

Erythropoietin (EPO) is a glycoprotein hormone which belongs to the four-helical-bundle cytokine family and regulates the level of circulating red blood cells. The EPO receptor (EPOR) belongs to the cytokine-receptor family of proteins. While many of the downstream events following receptor/ligand interaction have been defined, both ligand-induced receptor dimerization and conformational changes induced by binding have been implicated as the initial step in signal transduction. In a recent paper [Philo et al. (1996), Biochemistry38, 1681–1691] we described the formation of both 1:1 and 2:1 EPOR/EPO complexes. In this paper, we examine changes in protein conformation and stability resulting from the formation of both 1:1 and 2:1 complexes of the soluble extracellular domain of EPOR and the recombinant EPO derived from either Chinese hamster ovary cells or from Escherichia coli cells. Occupation of the first binding site results in a slight conformational change that is apparent in both the far- and near-UV circular dichroism spectra. Formation of the 2:1 complex results in an even greater change in conformation which involves the local environment of one or more aromatic amino acids, accompanied perhaps by a small increase in helical content of the complex. This change in local conformation could occur in the EPO molecule, in the EPOR, in both EPOR molecules due to dimerization, or in all molecules in the trimer. The 1:1 complex exhibits increased stability to thermal-induced denaturation relative to the individual protein component; indeed, the E. coli-derived (nonglycosylated) EPO stays folded in the complex at temperatures where the EPO alone would have unfolded and precipitated. Glycosylation of the receptor increases the reversibility of thermal denaturation, but does not affect the temperature at which this unfolding reaction occurs.     

Interaction of Cardiotoxin A5 with Membrane: Role of Conformational Heterogeneity and Hydrophobic Properties

The hypothesis that local conformational differences of the snake venom cardiotoxins (cytotoxins, CT) may play a significant role in their interaction with membrane was tested by molecular modeling of the behavior of the CT A5 from the venom of Naja atra in water and at the water–membrane interface. Two models of the CT A5 spatial structure are known: the first was obtained by X-ray analysis and the second, by NMR studies in solution. A molecular dynamics (MD) analysis demonstrated that loop II of the toxin has a fixed -like shape in water, which does not depend on its initial structure. An interaction of the experimentally derived (X-ray and NMR) conformations and MD simulated conformations of CT A5 with the lipid bilayer was studied by the Monte Carlo method using the previously developed model of the implicit membrane. It is found that: (1) unlike the previously studied CT2 from the venom of cobra Naja oxiana, CT A5 has only loops I and II bound to the membrane with the involvement of a lesser number of hydrophobic residues. (2) A long hydrophobic area is formed on the surface of CT A5 due to the -like shape of loop II and the arrangement of loop I in proximity to loop II. This hydrophobic area favors the toxin embedding into the lipid bilayer. (3) The toxin retains its conformation upon interaction with the membrane. (4) The CT A5 molecule has close values of the potential energy in the membrane and in aqueous environment, which suggests dynamic character of the binding. The results of the molecular modeling indicate a definite configuration of loops I and II and, consequently, a specific character of distribution of polar and apolar properties on the toxin surface, which turns out to be the most energetically favorable.