Monte Carlo calculations of order parameter profiles in models of lipid-protein interactions in bilayers

The Monte Carlo method has been utilized to calculate lipid chain order parameters in model monomolecular layers (half-bilayers) containing several different model polypeptides. The systems all consist of a periodic array of identical cells, each containing 35 hydrocarbon chains and 1 "perturbant" (a small model polypeptide or protein). The lipid chains are each 10 CH2 subunits long, have one end constrained to lie in the bilayer plane, and interact via van der Waals forces between all subunits. The chains also interact with the perturbant via van der Waals forces. With standard Monte Carlo procedures order parameter profiles are calculated for chains that are close to the perturbant and for the nonneighboring chains. In order to examine a wide range of possibilities, several different model polypeptides are considered: (i) a rigid smooth cylinder, (ii) a cylinder with identical side chains at alpha-helical positions, (iii) a cylinder with nonidentical side chains at alpha-helical positions, and (iv) a cylinder identical with (ii) but which only extends about halfway through the monolayer. Although results differ for the different systems studied, in all cases only slight conformational differences between the bulk chains and the chains that are nearest the perturbants are found, and it is not possible to characterize the boundary chains as "more ordered" or "less ordered" than the nonboundary chains.     

Long range intermolecular forces between macroscopic bodies: macroscopic and microscopic approaches.

Van der Waals energies of interaction are calculated by two methods, the macroscopic method of Lifshitz and the microscopic method of London-Casimir and Polder-Hamaker for the case of two semi-infinite slabs separated by a thin film. When retardation effects may be neglected, the London-Hamaker approach yields values of dispersion interactions which almost coincide with those of the Lifshitz approach, the magnitude of the former values being larger by approximately 10–25%, which is attributed to the effect of the molecular environment in condensed media. At 50–100 Å film thicknesses where retardation effects are small, dispersion terms are generally the major part of van der Waals forces in the Lifshitz formulation. Hence, for 50–100 Å film thicknesses the Hamaker approach, which only includes dispersion interactions is generally adequate. By accounting for retardation effects, which significantly reduce the magnitude of dispersion interactions at several hundred Å, there is a reasonable agreement between the values obtained by the macroscopic and microscopic approaches. When polar substances are present and for film thicknesses of several hundred Å, where dispersion interactions are significantly reduced, the major contribution to van der Waals forces may arise from orientation and induction terms. For such cases the Hamaker approach may lead to critical underestimates of the calculated magnitude of van der Waals forces. An ad hoc way to overcome this difficulty which is applicable to any geometry is proposed. This study presents a simple procedure for the determination of free energies of interaction between macroscopic bodies of various shapes. The procedure, which is applicable when the molecules of bodies and surrounding medium are isotropic, yields results which closely approximate those obtained with the Lifshitz theory.     

Van der Waals forces. Special characteristics in lipid-water systems and a general method of calculation based on the Lifshitz theory

A practical method for examining and calculating van der Waals forces is derived from Lifshitz'' theory. Rather than treat the total van der Waals energy as a sum of pairwise interactions between atoms, the Lifshitz theory treats component materials as continua in which there are electromagnetic fluctuations at all frequencies over the entire body. It is necessary in principle to use total macroscopic dielectric data from component substances to analyze the permitted fluctuations; in practice it is possible to use only partial information to perform satisfactory calculations. The biologically interesting case of lipid-water systems is considered in detail for illustration. The method gives good agreement with measured van der Waals energy of interaction across a lipid film. It appears that fluctuations at infrared frequencies and microwave frequencies are very important although these are usually ignored in preference to UV contributions. “Retardation effects” are such as to damp out high frequency fluctuation contributions; if interaction specificity is due to UV spectra, this will be revealed only at interactions across <200 angstrom (A). Dependence of van der Waals forces on material electric properties is discussed in terms of illustrative numerical calculations.     

Van der Waals locks: loop-n-lock structure of globular proteins

In a globular protein the polypeptide chain returns to itself many times, making numerous chain-to-chain contacts. The stability of these contacts is maintained primarily by van der Waals interactions. In this work we isolated and analysed van der Waals contacts that stabilise spatial structures of nine major folds. We suggest a specific way to identify the tightest contacts of prime importance for the stability of a given crystallized protein and introduce the notion of the van der Waals lock. The loops closed by the van der Waals interactions provide a basically novel view of protein globule organization: the loop-n-lock structure. This opens a new perspective in understanding protein folding as well: the consecutive looping of the polypeptide chain and the locking of the loop ends by tight van der Waals interactions.     

Interrod forces in aqueous gels of tobacco mosaic virus.

The lateral separation of virus rod particles of tobacco mosaic virus has been studied as a function of externally applied osmotic pressure using an osmotic stress technique. The results have been used to test the assumption that lattice equilibrium in such gels results from a balance between repulsive (electrostatic) and attractive (van der Waals and osmotic) forces. Results have been obtained at different ionic strengths (0.001 to 1.0 M) and pH's (5.0 to 7.2) and compared with calculated curves for electrostatic nad van der Waals pressure. Under all conditions studied, interrod spacing decreased with increasing applied pressure, the spacings being smaller at higher ionic strengths. Only small differences were seen when the pH was changed. At ionic strengths near 0.1 M, agreement between theory and experiment is good, but the theory appears to underestimate electrostatic forces at high ionic strengths and to underestimate attractive forces at large interrod spacings (low ionic strengths). It is concluded that an electrostatic-van der Waals force balance can explain stability in tobacco mosaic virus gels near physiological conditions and can provide a good first approximation elsewhere.     

Van der Waals interactions involving proteins.

Van der Waals (dispersion) forces contribute to interactions of proteins with other molecules or with surfaces, but because of the structural complexity of protein molecules, the magnitude of these effects is usually estimated based on idealized models of the molecular geometry, e.g., spheres or spheroids. The calculations reported here seek to account for both the geometric irregularity of protein molecules and the material properties of the interacting media. Whereas the latter are found to fall in the generally accepted range, the molecular shape is shown to cause the magnitudes of the interactions to differ significantly from those calculated using idealized models, with important consequences. First, the roughness of the molecular surface leads to much lower average interaction energies for both protein-protein and protein-surface cases relative to calculations in which the protein molecule is approximated as a sphere. These results indicate that a form of steric stabilization may be an important effect in protein solutions. Underlying this behavior is appreciable orientational dependence, one reflection of which is that molecules of complementary shape are found to exhibit very strong attractive dispersion interactions. Although this has been widely discussed previously in the context of molecular recognition processes, the broader implications of these phenomena may also be important at larger molecular separations, e.g., in the dynamics of aggregation, precipitation, and crystal growth.     

Membrane-Mediated Interactions Measured Using Membrane Domains

Cell membrane organization is the result of the collective effect of many driving forces. Several of these, such as electrostatic and van der Waals forces, have been identified and studied in detail. In this article, we investigate and quantify another force, the interaction between inclusions via deformations of the membrane shape. For electrically neutral systems, this interaction is the dominant organizing force. As a model system to study membrane-mediated interactions, we use phase-separated biomimetic vesicles that exhibit coexistence of liquid-ordered and liquid-disordered lipid domains. The membrane-mediated interactions between these domains lead to a rich variety of effects, including the creation of long-range order and the setting of a preferred domain size. Our findings also apply to the interaction of membrane protein patches, which induce similar membrane shape deformations and hence experience similar interactions.     

Repulsive stabilization in black lipid membranes. A hydrodynamic model

A linear stability analysis is performed for a black lipid membrane. The hydrodynamic model consists of a viscous hydrocarbon film sandwiched between two aqueous phases. Attractive forces (van der Waals and electrical) and repulsive forces (steric) are expressed as body forces in the equations of fluid motion in the three phases. The steric repulsion due to overlap of the hydrocarbon chains of the lipids at small film thicknesses is described via an exponentially decaying interaction potential. The dispersion equation displays two modes of vibrations: the bending mode with the two Film surfaces transversely in phase, and the squeezing mode with the two surfaces 180 degrees out of phase. For symmetrical films, these two modes are uncoupled, and the squeezing mode (with thickness variations) is stabilized by the repulsive interactions. For nonsymmetrical films (different surface tensions, surface charges, etc.). these two modes are coupled and the asymmetry induces a shift of the marginal stability curve to shorter wavelengths.     

Effect of branching in 4-alkylpyrazoles on liver alcohol dehydrogenase inhibition: A shape analysis study

Shape analysis methodology is applied to the study of 4-alkylpyrazoles which are known inhibitors of liver alcohol dehydrogenase. Elongation of the alkyl chain increases the inhibitory power, whereas branching of the chain diminishes the activity. These two counterpoised effects are studied simultaneously in a selected set of 4-alkylpyrazoles. A systematic conformational analysis followed by topological characterization of the van der Waals surfaces of all the local minima restricts the conformational space to potential bioactive structures. The analysis of the interrelation between the molecular electrostatic potential and van der Waals surfaces provides certain shape codes characteristic of each 4-alkylpyrazole. In both topological analyses van der Waals surfaces and molecular electrostatic potential van der Waals surface interrelations) graphical representations and analytical methods were used. A good correlation between the shape codes and the inhibitory activity is found for the linear derivatives. For branched pyrazoles, a tendency in their inhibitory power is predicted. Isopentylpyrazole is suggested to have the same inhibitory profile as 4-butylpyrazole, the linear derivative with one less carbon atom.     

A facile synthesis of ceramides.

Lateral diffusion of phosphatide molecules in liquid crystalline bilayers has been analysed as a case of co-operative lattice diffusion. The potential energy of interaction between two molecules is assumed to arise from Van der Waals interactions of the hydrocarbon chains, and to have the form suggested by Salem [6]. From the observed values of the self-diffusion constant (of the order of 10^?8 cm² sec^?1) the depth of the potential “well” for two molecules at the equilibrium separation was estimated to have a lower limit of 1.95 kcal per mole, and the energy barrier to lateral motion was estimated to have an upper limit of 7.21 kcal per mole.     

Swelling of phospholipids by monovalent salt

Critical to biological processes such as membrane fusion and secretion, ion-lipid interactions at the membrane-water interface still raise many unanswered questions. Using reconstituted phosphatidylcholine membranes, we confirm here that multilamellar vesicles swell in salt solutions, a direct indication that salt modifies the interactions between neighboring membranes. By varying sample histories, and by comparing with data from ion carrier-containing bilayers, we eliminate the possibility that swelling is an equilibration artifact. Although both attractive and repulsive forces could be modified by salt, we show experimentally that swelling is driven primarily by weakening of the van der Waals attraction. To isolate the effect of salt on van der Waals interactions, we focus on high salt concentrations at which any possible electrostatic interactions are screened. By analysis of X-ray diffraction data, we show that salt does not alter membrane structure or bending rigidity, eliminating the possibility that repulsive fluctuation forces change with salt. By measuring changes in interbilayer separation with applied osmotic stress, we have determined, using the standard paradigm for bilayer interactions, that 1 M concentrations of KBr or KCl decrease the van der Waals strength by 50%. By weakening van der Waals attractions, salt increases energy barriers to membrane contact, possibly affecting cellular communication and biological signaling.     

Direct measurement of the intermolecular forces between counterion-condensed DNA double helices. Evidence for long range attractive hydration forces.

Rather than acting by modifying van der Waals or electrostatic double layer interactions or by directly bridging neighboring molecules, polyvalent ligands bound to DNA double helices appear to act by reconfiguring the water between macromolecular surfaces to create attractive long range hydration forces. We have reached this conclusion by directly measuring the repulsive forces between parallel B-form DNA double helices pushed together from the separations at which they have self organized into hexagonal arrays of parallel rods. For all of the wide variety of "condensing agents" from divalent Mn to polymeric protamines, the resulting intermolecular force varies exponentially with a decay rate of 1.4-1.5 A, exactly one-half that seen previously for hydration repulsion. Such behavior qualitatively contradicts the predictions of all electrostatic double layer and van der Waals force potentials previously suggested. It fits remarkably well with the idea, developed and tested here, that multivalent counterion adsorption reorganizes the water at discrete sites complementary to unadsorbed sites on the apposing surface. The measured strength and range of these attractive forces together with their apparent specificity suggest the presence of a previously unexpected force in molecular organization.     

Mapping interaction forces with the atomic force microscope.

Force curves were recorded as the sample was raster-scanned under the tip. This opens new opportunities for imaging with the atomic force microscope: several characteristics of the samples can be measured simultaneously, for example, topography, adhesion forces, elasticity, van der Waals, and electrostatic interactions. The new opportunities are illustrated by images of several characteristics of thin metal films, aggregates of lysozyme, and single molecules of DNA.     

Temperature-dependent van der Waals forces

Biological systems can experience a strong van der Waals interaction involving electromagnetic fluctuations at the low frequency limit. In lipid-water mixtures the free energy of this interaction is proportional to temperature, primarily involves an entropy change, and has qualitative features of a “hydrophobic bond.” Protein-protein attraction in dilute solution is due as much to low frequency proton fluctuation (Kirkwood-Shumaker forces) and permanent dipole forces as to high frequency (infrared and UV) van der Waals intreactions. These conclusions are described in terms of numerical calculations via the Lifshitz theory of van der Waals forces.     

Anthracycline antibiotic arugomycin binds in both grooves of the DNA helix simultaneously: an NMR and molecular modelling study.

Perturbations to the 1H and 31P chemical shifts of DNA resonances together with twenty-four intermolecular nuclear Overhauser effects show that the anthracycline antibiotic arugomycin intercalates between the basepairs of the hexamer duplex d(5'-GCATGC)2 at the 5'-CpA and 5'-TpG binding sites. In the complex two drug molecules are bound per duplex with full retention of the dyad symmetry. Arugomycin adopts a threaded binding orientation with chains of sugars positioned in both the major and minor groove of the helix simultaneously. The complex is stabilized by hydrogen bonding, electrostatic and van der Waals interactions principally in the major groove and involving substituents on the rigidly oriented bicycloamino-glucose sugar of the antibiotic. A specific hydrogen bond is identified between the C2'-hydroxyl and the guanine N7 at the intercalation site. Together, interactions in the major groove appear to account for the intercalation specificity of arugomycin that requires both a guanine and thymine at the intercalation site. We are unable to identify any sequence specific interactions between the minor groove and the arugarose sugar (S1) which binds only weakly, through van der Walls contacts, over the d(GCA).d(TGC) trinucleotide sequence. The data indicate that the sugar chains of arugomycin are flexible and play little part in the interaction of the antibiotic with DNA. The intensity of sequential internucleotide NOEs identifies the intercalation site as being assymmetric. A family of conformers computed using restrained energy minimisation and molecular dynamics indicate that basepair buckling is a feature of the anthracycline intercalation site that may serve to maximise intermolecular van der Waals interactions by wrapping the basepairs around the antibiotic chromophore.     

A dissipative particle dynamics model of carbon nanotubes

A mesoscale dissipative particle dynamics model of single wall carbon nanotubes (CNTs) is designed and demonstrated. The coarse-grained model is produced by grouping together carbon atoms and by bonding the new lumped particles through pair and triplet forces. The mechanical properties of the simulated tube are determined by the bonding forces, which are derived by virtual experiments. Through the introduction of van der Waals interactions, tube–tube interactions were studied. Owing to the reduced number of particles, this model allows the simulation of relatively large systems. The applicability of the presented scheme to model CNT based mechanical devices is discussed.     

Refinement of the structure of Escherichia coli-derived rat intestinal fatty acid binding protein with bound oleate to 1.75-A resolution. Correlation with the structures of the apoprotein and the protein with bound palmitate.

The structure of rat intestinal fatty acid binding protein (I-FABP) with bound oleate (C18:1) has been refined with x-ray diffraction data to a resolution of 1.75 A. The protein contains 10 anti-parallel beta strands composed of 99 residues and 2 short helices of 14 residues. Oleate is located in the interior of the protein in a bent conformation with C1-C12 more ordered than C13-C18. Two of the eight ordered waters in I-FABP:oleate are part of a hydrogen bond network that includes the carboxylate of oleate, the guanidinium group of Arg106, the nitrogen of the indole group of Trp82, and the side chain of Gln115. Most of the methylenes of bound oleate reside in a crevice formed by hydrophobic and aromatic side chains. Tyr70 and Tyr117 envelop the acyl chain from C3 to C8 forming contacts with both the convex and concave faces of its van der Waals surface. The hydroxyls of each phenolic side chain hydrogen bond to ordered water molecules. Two ordered waters make van der Waals contact with the concave face of the bound fatty acid. The omega-terminal methyl of oleate is oriented so that it points toward the center of the benzene of Phe55 allowing it to form van der Waals interactions with its component methylenes. Comparison of the structure of I-FABP:oleate with a recently refined 1.19-A model of apoI-FABP and an earlier 2.0-A model of I-FABP:palmitate revealed a remarkable degree of similarity in the positions of their main chain and side chain atoms and in the conformations of the bound oleate and palmitate. The principal differences were confined to a few discrete regions of the protein. The helical domain, the type I turn between beta strands C and D, and the ring of Phe55 together form a solvent-accessible portal to the interior of the protein. They are repositioned in I-FABP:oleate (and I-FABP:palmitate) so that the binding cavity is even more accessible to solvent and its volume is increased. The side chain of Phe55 which shows discrete disorder in the apoprotein functions as an omega-terminal "sensing device": moving progressively outward toward the surface as the chain length of the bound fatty acid increases by 2 methylenes. Tyr70 and Tyr117 which also show discrete disorder in the apoprotein structure due to rotation around their C alpha-C beta bonds, are stabilized in a single, well ordered position in the holoproteins.(ABSTRACT TRUNCATED AT 400 WORDS)     

Binding to δ and μ opioid receptors by deltorphin I/II analogues modified at the Phe and Asp/Glu side chains: a report of 32 new analogues and a QSAR study

The synthesis and binding affinities of 32 X³Gly⁴ dual-substitution analogues of the natural opioid heptapeptides deltorphin I and II are reported. A multiple regression QSAR analysis was performed using those results along with literature data for the X³Asp⁴ and Phe³X⁴ side chain analogues. Fitting to a three-term potential well model with hydrophobic and van der Waals attraction terms and a steric repulsion term indicates that the δ and μ receptor sites for binding the residue three side chain are similar, and that the binding interaction is primarily van der Waals and secondarily hydrophobic. Further analysis indicates that both sites are more constrained with respect to side chain length than width or thickness, and the μ site appears to be somewhat larger. A binding model consistent with these findings pictures the native third residues Phe ring laying on a step notched out of the receptor surface, pointing toward the back (riser) of the step, and sandwiched between the receptor and ligand. However, the binding sites for the residue four side chains are quite different on δ and μ receptors. Binding to the δ site appears to involve both electrostatic attraction (probably to a partial positive charge) and van der Waals attraction, but not necessarily hydrogen bonding, and more constraint with respect to side chain length than width or thickness. In contrast, there is no evidence for any kind of binding attraction between the side chain of residue four and the μ site, which acts more as steric repulsion site, as though the space that is a pocket on the δ receptor is filled in on the μ receptor. A regression model based only on steric repulsion by van der Waals bulk and/or the effective bulk of a hydration layer accounts for over 80% of the residue four related variation in μ affinity.

Abstract

Thirty-two new X³Gly⁴ analogues of deltrophin I/II opioid peptides are described. A QSAR study of the X³Gly⁴, X³Asp⁴, and Phe³X⁴ analogue series using a potential well model reveals the roles of hydrophobic, van der Waals, electrostatic, hydrogen bonding and steric interactions in δ and μ receptor binding of X³ and X⁴ side chains.     

Cholesterol effects on the phospholipid condensation and packing in the bilayer: a molecular simulation study

A 15-ns molecular dynamics simulation of the fully hydrated liquid-crystalline dimyristoylphosphatidylcholine-cholesterol (DMPC-Chol) bilayer containing approximately 22 mol% Chol was carried out. The generated trajectory was analysed to investigate the mechanism of the Chol condensing effect on DMPC hydrocarbon chains and the influence of Chol on the chain packing in the membrane. Chol was found to induce stronger van der Waals interactions among the chains, whereas its interactions with the chains were weak. In the DMPC-Chol bilayer, as in the DMPC bilayer, DMPC chains were regularly packed around a chosen chain but around a Chol molecule they were not. DMPC gamma chains made closer contacts with Chol than the beta chains.