Theoretical conformational analysis of phospholipids. I. Study of the interactions between phospholipid molecules by use of semi-empirical methods with the explicit introduction of polar headgroup interactions

We present a theoretical conformational analysis of a system composed of seven dipalmitoylphosphatidylethanolamine molecules in interaction. The combined use of classical semi-empirical methods for the polar headgroup region with mechanical statistical calculations for the aliphatic chains permits the evaluation of the free energy for a phospholipids molecule. The free energy variation in function of the mean intermolecular interchain distance gives information about the main lipid bilayer phase transition. It appears, however, necessary to take into account the hydration of the polar headgroups.     

Nonspecific interactions in dye binding to DNA. Influence of alcohols and amides

The binding of a few drugs (ethidium bromide, propidium diiodide, proflavine and actinomycin D) to DNA has been investigated in aqueous solutions to which cosolvents of different polarity have been added. It is found that both alcohols (less polar than water) and amides (more polar) lower the binding constant according to a linear relationship between the intercalation free energy and cosolvent concentration. The main action of cosolvents cannot be described in terms of electrostatic effects, since they predict much smaller changes in the binding constant than those observed. It appears instead that relevant solvation effects are responsible for the binding strength of the different dyes to DNA. As a general result, it is found that solvation effects largely contribute to the intercalation free energy, thereby weakening the influence of nonspecific interactions at the intercalation site.     

Energetics of hydrophobic matching in lipid-protein interactions

Lipid chain length modulates the activity of transmembrane proteins by mismatch between the hydrophobic span of the protein and that of the lipid membrane. Relative binding affinities of lipids with different chain lengths are used to estimate the excess free energy of lipid-protein interaction that arises from hydrophobic mismatch. For a wide range of integral proteins and peptides, the energy cost is much less than the elastic penalty of fully stretching or compressing the lipid chains to achieve complete hydrophobic matching. The chain length dependences of the free energies of lipid association are described by a model that combines elastic chain extension with a free energy term that depends linearly on the extent of residual mismatch. The excess free energy densities involved lie in the region of 0.5-2.0 k_BT.nm⁻². Values of this size could arise from exposure of hydrophobic groups to polar portions of the lipid or protein, but not directly to water, or alternatively from changes in tilt of the transmembrane helices that are energetically comparable to those activating mechanosensitive channels. The influence of hydrophobic mismatch on dimerization of transmembrane helices and their transfer between lipid vesicles, and on shifts in chain-melting transitions of lipid bilayers by incorporated proteins, is analyzed by using the same thermodynamic model. Segmental order parameters confirm that elastic lipid chain distortions are insufficient to compensate fully for the mismatch, but the dependence on chain length with tryptophan-anchored peptides requires that the free energy density of hydrophobic mismatch should increase with increasing extent of mismatch.     

Stabilizing nonpolar/polar side-chain interactions in the alpha-helix.

A simplistic, yet often used, view of protein stability is that amino acids attract other amino acids with similar polarity, whereas nonpolar and polar side chains repel. Here we show that nonpolar/polar interactions, namely Val or Ile bonding to Lys or Arg in alpha-helices, can in fact be stabilizing. Residues spaced i, i + 4 in alpha-helices are on the same face of the helix, with potential to favorably interact and stabilize the structure. We observe that the nonpolar/polar pairs Ile-Lys, Ile-Arg, and Val-Lys occur in protein helices more often than expected when spaced i, i + 4. Partially helical peptides containing pairs of nonpolar/polar residues were synthesized. Controls with i, i + 5 spacing have the residues on opposite faces of the helix and are less helical than the test peptides with the i, i + 4 interactions. Experimental circular dichroism results were analyzed with helix-coil theory to calculate the free energy for the interactions. All three stabilize the helix with DeltaG between -0.14 and -0.32 kcal x mol(-1). The interactions are hydrophobic with contacts between Val or Ile and the alkyl groups in Arg or Lys. Side chains such as Lys and Arg can thus interact favorably with both polar and nonpolar residues.     

Implicit solvent model studies of the interactions of the influenza hemagglutinin fusion peptide with lipid bilayers

The "fusion peptide," a segment of approximately 20 residues of the influenza hemagglutinin (HA), is necessary and sufficient for HA-induced membrane fusion. We used mean-field calculations of the free energy of peptide-membrane association (DeltaG(tot)) to deduce the most probable orientation of the fusion peptide in the membrane. The main contributions to DeltaG(tot) are probably from the electrostatic (DeltaG(el)) and nonpolar (DeltaG(np)) components of the solvation free energy; these were calculated using continuum solvent models. The peptide was described in atomic detail and was modeled as an alpha-helix based on spectroscopic data. The membrane's hydrocarbon region was described as a structureless slab of nonpolar medium embedded in water. All the helix-membrane configurations, which were lower in DeltaG(tot) than the isolated helix in the aqueous phase, were in the same (wide) basin in configurational space. In each, the helix was horizontally adsorbed at the water-bilayer interface with its principal axis parallel to the membrane plane, its hydrophobic face dissolved in the bilayer, and its polar face in the water. The associated DeltaG(tot) value was approximately -8 to -10 kcal/mol (depending on the rotameric state of one of the phenylalanine residues). In contrast, the DeltaG(tot) values associated with experimentally observed oblique orientations were found to be near zero, suggesting they are marginally stable at best. The theoretical model did not take into account the interactions of the polar headgroups with the peptide and peptide-induced membrane deformation effects. Either or both may overcompensate for the DeltaG(tot) difference between the horizontal and oblique orientations.     

On the role of electrostatic interactions in the design of protein-protein interfaces

Here, the methods of continuum electrostatics are used to investigate the contribution of electrostatic interactions to the binding of four protein-protein complexes; barnase-barstar, human growth hormone and its receptor, subtype N9 influenza virus neuraminidase and the NC41 antibody, the Ras binding domain (RBD) of kinase cRaf and a Ras homologue Rap1A. In two of the four complexes electrostatics are found to strongly oppose binding (hormone-receptor and neuraminidase-antibody complexes), in one case the net effect is close to zero (barnase-barstar) and in one case electrostatics provides a significant driving force favoring binding (RBD-Rap1A). In order to help understand the wide range of electrostatic contributions that were calculated, the electrostatic free energy was partitioned into contributions of individual charged and polar residues, salt bridges and networks involving salt bridges and hydrogen bonds. Although there is no one structural feature that accounts for the differences between the four interfaces, the extent to which the desolvation of buried charges is compensated by the formation of hydrogen bonds and ion pairs appears to be an important factor. Structural features that are correlated with contribution of an individual residue to stability are also discussed. These include partial burial of a charged group in the free monomer, the formation of networks involving charged and polar amino acids, and the formation of partially exposed ion-pairs. The total electrostatic contribution to binding is found to be inversely correlated with buried total and non-polar surface area. This suggests that different interfaces can be designed to exploit electrostatic and hydrophobic forces in very different ways.     

Electric interactions at the lipid membrane surface

This work presents the results of an experimental study and of computer simulations concerning electric interactions in the surface layer of egg yolk lecithin (EYL) liposome membranes. The surface layer is formed by EYL polar heads, which possess features of electric dipoles, and positive charged polar heads belonging to admixtures of quaternary ammonium salts (AS). The results of the experimental study are in good agreement with the ones of the computer simulations. It was found that fluidity of the membranes, at a given concentration of AS, obtains the extremal (minimal) value. Similarly, the binding energy of the dipoles-positive charges system behaves like that in computer simulations. Moreover, the locations of the fluidity extremum and those of the binding energy depend on the charge of the AS polar heads as well as on the degree of electric interactions screening by the environment. At a certain optimal value of the screening coefficient, the energy of the system is the lowest (the most negative) and together with the rise in AS charge, the minimum of the energy moves towards its higher concentrations.     

Probing weakly polar interactions in cytochrome c.

Theoretical, statistical, and model studies suggest that proteins are stabilized by weakly polar attractions between sulfur atoms and properly oriented aromatic rings. The two sulfur-containing amino acids, methionine and cysteine, occur frequently among functional alleles in random mutant libraries of Saccharomyces cerevisiae iso-1-cytochrome c genes at positions that form a weakly polar aromatic-aromatic interaction, the wild-type protein. To determine if a weakly polar sulfur-aromatic interaction replaced the aromatic-aromatic interaction, the structure and stability of two variants were examined. Phenylalanine 10, which interacts with tyrosine 97, was replaced by methionine and cysteine. The cysteine was modified to form the methionine and cysteine analog, S-methyl cysteine (CysSMe). Proton NMR studies indicate that changing Phe 10 to Met or CysSMe affects only local structure and that the structures of sulfur-containing variants are nearly identical. Analysis of chemical shifts and nuclear Overhauser effect data indicates that both sulfur-containing side chains are in position to form a weakly polar interaction with Tyr 97. The F10M and F10CSMe variants are 2-3 kcal mol-1 less stable than iso-1-cytochrome c at 300 K. Comparison of the stabilities of the F10M and F10CSMe variants allows evaluation of the potential weakly polar interaction between the additional sulfur atom of F10CSMe and the aromatic moiety of Tyr 97. The F10CSMe;C102T variant is 0.7 +/- 0.3 kcal mol-1 more stable than the F10M;C102T protein. The increased stability is explained by the difference in hydrophobicity of the sulfur-containing side chains. We conclude that any weakly polar interaction between the additional sulfur and the aromatic ring is too weak to detect or is masked by destabilizing contributions to the free energy of denaturation.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Dissection of the protein G B1 domain binding site for human IgG Fc fragment.

The contribution to the free energy of binding of each of the residues forming the binding site for a human IgG Fc fragment on the surface of the B1 domain of protein G was determined by alanine-scanning mutagenesis. The interface between these two proteins is atypical in that it is smaller than usual, polar in character, and involves two well-defined "knobs-into-holes" interactions. The bulk of the free energy of binding is contributed by three central residues, which make hydrogen bonds across the interface. Of these, the most critical interaction is formed by Glu27, which acts as a charged knob on the surface of the B1 domain, inserting into a polar hole on the Fc fragment. A single alanine mutation of this residue virtually abolishes stable complex formation. Formation of a stable interface between these two proteins is therefore dominated by a small, polar "hot spot."     

A comparison of thermodynamic approaches to predict the adhesion of dairy microorganisms to solid substrata.

Four different thermodynamic approaches were compared on their usefulness to predict correctly the adhesion of two fouling microogranisms from dairy processing to various solid substrata. The surface free energies of the interacting surfaces were derived from measured contact angles according to: 1. The equation of state; 2. The geometric-mean equation using dispersion and polar components neglecting spreading pressures; 3. The geometric-mean equation using dispersion and polar components while accounting for spreading pressures; and 4. The Lifshitz-van der Waals/Acid-Base approach. All approaches yielded similar surface free energies for the low energy surfaces. Application of approach 1 with different liquids did not give consistent values for the high surface free energy substrata. The dispersion or Lifshiftz-van der Waals components were nearly equal for approaches 2, 3, and 4; however, the polar or acid-base components differed greatly according to the approach followed. Approaches 1 and 2 correctly predicted that adhesion should occur, although the trend with respect to the various solid substrata was opposite the one experimentally observed, as was also the trend predicted by approach 4. Only approach 3 correctly predicted the observed bacterial adhesion with respect to the various solid substrata. In approach 3 and 4, adhesion was frequently found, despite a positive free energy of adhesion. This was attributed to either possible local attractive electrostatic interactions, inadequate weighing of surface free energy components in the calculation of free energies of adhesion, or to additional forces arising from structured interfacial water.     

Analysis of the heat capacity dependence of protein folding.

This paper presents an analysis of plots of enthalpy versus heat capacity change at 25 degrees C for the unfolding of proteins and for the dissolution of gaseous, liquid and solid solutes, first reported by Murphy, Privalov & Gill. The negative slope in the enthalpy plot for proteins is interpreted as arising from a large penalty associated with burying polar groups in the protein interior. The small enthalpy changes that accompany protein unfolding at 25 degrees C are also discussed. It is argued that the combined effects of hydrogen bond formation and close packing predict a large positive enthalpy of unfolding. Electrostatic calculations indicate that the penalty associated with burying polar groups is large enough to effectively cancel these terms, leading to the small net enthalpy changes that are observed. The free energy changes associated with protein folding are also discussed. The free energy cost of burying polar groups largely compensates for the stabilizing contribution of the hydrophobic effect and would appear to account for the fact that proteins are marginally stable, independent of their size and of their relative hydrophobicities.     

Standardizing the free energy change of transmembrane helix-helix interactions

Side-to-side associations of transmembrane alpha-helices are integral components of the structure and function of helical membrane proteins. A fundamental unknown in the understanding of the chemical principles driving the lateral interactions between transmembrane alpha-helices is the balance of forces arising from the polypeptide sequence versus the hydrophobic solvent. To begin to address this question, a consideration of basic thermodynamic principles has been applied to assess the experimental free energy change associated with transmembrane helix dimerization in micelles. This analysis demonstrates the ability to partition the apparent free energy of transmembrane helix-helix association into two components. The first component is a statistical energy term, which arises from the fact that there are an unequal number of reactants and products. The second component is a standard state free energy change, which informs on the molecular details of the transmembrane helix self-association reaction. The advantage of separating these two energy terms arises from the fact that extrapolation to the standard state free energy change normalizes the statistical energy term so that it applies equivalently in all experimental systems. Accompanying experimental results for the glycophorin A transmembrane alpha-helix dimer measured in micelles are well described by these theoretical components assuming an ideal-dilute solution.     

城市绿化植物叶片表面特征对滞尘能力的影响

以西安市21种常见绿化植物为对象,采用人工降尘方法测定植物叶片的最大滞尘量,研究植物叶片表面绒毛、润湿性、表面自由能及其分量对滞尘能力的影响.结果表明： 21种供试植物叶片的最大滞尘量在0.8～38.6 g·m^-2,不同树种最大滞尘量差异显著,物种间相差40倍以上.叶片表面绒毛数量及其形态、分布特征对滞尘能力具有重要影响,可能与绒毛和颗粒物间的作用方式有关.除叶片表面着生绒毛的悬铃木、国槐、榆叶梅和毛梾4个物种外,其他植物叶片接触角与最大滞尘量均呈显著负相关.接触角较小、易润湿的植物叶片最大滞尘量在2.0～8.0 g·m^-2,而接触角较大的银杏、三叶草、紫叶小檗和鸡爪槭的最大滞尘量均＜2.0 g·m^-2.叶片表面自由能主要表现分子间色散力的作用,而极性分量对表面自由能的贡献低于20%,可能与叶片表面含有的非极性或弱极性物质有关.最大滞尘量与叶片表面自由能及其色散分量呈显著正相关,而与极性分量的相关关系不显著.     

Solvent effects and polar interactions in the structural stability and dynamics of globular proteins.

Using detailed hydrogen bonding, surface exposure, internal environment, and solvent interaction calculations on several proteins, in conjunction wit data from quantum mechanical hydrogen-bonding studies, various contributions to the free energy of globular estimated and their likely relative significance discussed. A picture emerges of globular proteins as extremely well-fitting jigsaw-puzzles, in which no single driving force dominates the marginal stability of the native conformation. Rather, the folded structure is seen as the result of a complex global maximization of several strongly-interacting driving forces. In particular, the necessity to maintain very efficient internal hydrogen-bonding, and the role of the solvent as a hydrogen-bond sink, are stressed as strong constraints on the (incomplete) maximization of hydrophobic effects. The possible significance of internal dipole-induced dipole interactions is discussed tentatively. Although quantitative estimates of the various contributions remain uncertain, consideration of effective force constants suggests that polar, including solvent, interactions may largely determine the overall curvatures of the native conformation's potential well, and be important in controlling the flexibility of local regions which are important for the exact positioning of groups during enzyme catalysis, as well as the molecule's overall dynamics. In contrast, hydrophobic interactions change less for small geometrical perturbations, and seem more relevant to directing the folding protein. along a path to a region in configurational space where the polar interactions can switch on for the final "docking".     

Estimating the energy expenditure of free‐ranging polar bears using tri‐axial accelerometers: A validation with doubly labeled water

Measures of energy expenditure can be used to inform animal conservation and management, but methods for measuring the energy expenditure of free‐ranging animals have a variety of limitations. Advancements in biologging technologies have enabled the use of dynamic body acceleration derived from accelerometers as a proxy for energy expenditure. Although dynamic body acceleration has been shown to strongly correlate with oxygen consumption in captive animals, it has been validated in only a few studies on free‐ranging animals. Here, we use relationships between oxygen consumption and overall dynamic body acceleration in resting and walking polar bears Ursus maritimus and published values for the costs of swimming in polar bears to estimate the total energy expenditure of 6 free‐ranging polar bears that were primarily using the sea ice of the Beaufort Sea. Energetic models based on accelerometry were compared to models of energy expenditure on the same individuals derived from doubly labeled water methods. Accelerometer‐based estimates of energy expenditure on average predicted total energy expenditure to be 30% less than estimates derived from doubly labeled water. Nevertheless, accelerometer‐based measures of energy expenditure strongly correlated (r² = 0.70) with measures derived from doubly labeled water. Our findings highlight the strengths and limitations in dynamic body acceleration as a measure of total energy expenditure while also further supporting its use as a proxy for instantaneous, detailed energy expenditure in free‐ranging animals.     

Free energy decomposition of protein-protein interactions.

A free energy decomposition scheme has been developed and tested on antibody-antigen and protease-inhibitor binding for which accurate experimental structures were available for both free and bound proteins. Using the x-ray coordinates of the free and bound proteins, the absolute binding free energy was computed assuming additivity of three well-defined, physical processes: desolvation of the x-ray structures, isomerization of the x-ray conformation to a nearby local minimum in the gas-phase, and subsequent noncovalent complex formation in the gas phase. This free energy scheme, together with the Generalized Born model for computing the electrostatic solvation free energy, yielded binding free energies in remarkable agreement with experimental data. Two assumptions commonly used in theoretical treatments; viz., the rigid-binding approximation (which assumes no conformational change upon complexation) and the neglect of vdW interactions, were found to yield large errors in the binding free energy. Protein-protein vdW and electrostatic interactions between complementary surfaces over a relatively large area (1400--1700 A(2)) were found to drive antibody-antigen and protease-inhibitor binding.     

Use of restrained molecular dynamics in water to determine three-dimensional protein structure: prediction of the three-dimensional structure of Ecballium elaterium trypsin inhibitor II

Refinement of distance geometry (DG) structures of EETI-II (Heitz et al.: Biochemistry 28:2392-2398, 1989), a member of the squash family trypsin inhibitor, have been carried out by restrained molecular dynamics (RMD) in water. The resulting models show better side chain apolar/polar surface ratio and estimated solvation free energy than structures refined "in vacuo." The consistent lower values of residual NMR constraint violations, apolar/polar surface ratio, and solvation free energy for one of these refined structures allowed prediction of the 3D folding and disulfide connectivity of EETI-II. Except for the few first residues for which no NMR constraints were available, this computer model fully agreed with X-ray structures of CMTI-I (Bode et al.: FEBS Lett. 242:285-292, 1989) and EETI-II complexed with trypsin that appeared after the RMD simulation was completed. Restrained molecular dynamics in water is thus proved to be highly valuable for refinement of DG structures. Also, the successful use of apolar/polar surface ratio and of solvation free energy reinforce the analysis of Novotny et al. (Proteins 4:19-30, 1988) and shows that these criteria are useful indicators of correct versus misfolded models.