Lipid-mediated interactions between intrinsic membrane proteins: dependence on protein size and lipid composition.

The present study is an application of an approach recently developed by the authors for describing the structure of the hydrocarbon chains of lipid-bilayer membranes (LBMs) around embedded protein inclusions ( Biophys. J. 79:2867-2879). The approach is based on statistical mechanical integral equation theories developed for the study of dense liquids. First, the configurations extracted from molecular dynamics simulations of pure LBMs are used to extract the lateral density-density response function. Different pure LBMs composed of different lipid molecules were considered: dioleoyl phosphatidylcholine (DOPC), palmitoyl-oleoyl phosphatidylcholine (POPC), dipalmitoyl phosphatidylcholine (DPPC), and dimyristoyl phosphatidylcholine (DMPC). The results for the lateral density-density response function was then used as input in the integral equation theory. Numerical calculations were performed for protein inclusions of three different sizes. For the sake of simplicity, protein inclusions are represented as hard smooth cylinders excluding the lipid hydrocarbon core from a small cylinder of 2.5 A radius, corresponding roughly to one aliphatic chain, a medium cylinder of 5 A radius, corresponding to one alpha-helix, and a larger cylinder of 9 A radius, representing a small protein such as the gramicidin channel. The lipid-mediated interaction between protein inclusions was calculated using a closed-form expression for the configuration-dependent free energy. This interaction was found to be repulsive at intermediate range and attractive at short range for two small cylinders in POPC, DPPC, and DMPC bilayers, whereas it oscillates between attractive and repulsive values in DOPC bilayers. For medium size cylinders, it is again repulsive at intermediate range and attractive at short range, but for every model LBM considered here. In the case of a large cylinder, the lipid-mediated interaction was shown to be repulsive for both short and long ranges for the DOPC, POPC, and DPPC bilayers, whereas it is again repulsive and attractive for DMPC bilayers. The results indicate that the packing of the hydrocarbon chains around protein inclusions in LBMs gives rise to a generic (i.e., nonspecific) lipid-mediated interaction which favors the association of two alpha-helices and depends on the lipid composition of the membrane.     

Interaction of alamethicin pores in DMPC bilayers

We have investigated the x-ray scattering signal of highly aligned multilayers of the zwitterionic lipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine containing pores formed by the antimicrobial peptide alamethicin as a function of the peptide/lipid ratio. We are able to obtain information on the structure factor of the pore fluid, which then yields the interaction potential between pores in the plane of the bilayers. Aside from a hard core with a radius corresponding to the geometric radius of the pore, we find a repulsive lipid-mediated interaction with a range of approximately 30 A and a contact value of 2.4 k(B)T. This result is in qualitative agreement with recent theoretical models.     

Electrostatics of membrane adhesion.

We consider electrical double layer interaction under the conditions typically encountered during membrane fusion. Within the physiological concentration range of monovalent electrolytes the interaction is repulsive and the Poisson-Boltzmann calculation may be used to evaluate the force. When divalent counterions are added, strong ion-ion correlations make the Poisson-Boltzmann approximation inapplicable. We use the anisotropic hypernetted chain method to show that in the presence of small amounts of divalent counterions in adsorption equilibrium with the surfaces, the double layer interaction turns into attraction. This attractive electrostatic force may be the balancing contribution controlling membrane adhesion.     

Force Balances in Systems of Cylindrical Polyelectrolytes

A detailed analysis is made of the model system of two parallel cylindrical polyelectrolytes which contain ionizable groups on their surfaces and are immersed in an ionic bathing medium. The interaction between the cylinders is examined by considering the interplay between repulsive electrostatic forces and attractive forces of electrodynamic origin. The repulsive force arises from the screened coulomb interaction between the surface charge distributions on the cylinders and has been treated by developing a solution to the linearized Poisson-Boltzmann equation. The boundary condition at the cylinder surfaces is determined as a self-consistent functional of the potential, with the input consisting of the density of ionizable groups and their dissociation constants. It is suggested that a reasonably accurate representation for the form of the attractive force can be obtained by performing a pairwise summation of the individual interatomic forces. A quantitative estimate is obtained using a Hamaker constant chosen on the basis of rigorous calculations on simpler systems. It is found that a balance exists between these repulsive and attractive forces at separations in good agreement with those observed in arrays of tobacco mosaic virus and in the A band myosin lattice in striated muscle. The behavior of the balance point as a function of the pH and ionic strength of the bathing medium closely parallels that seen experimentally.     

Molecular simulation of the effect of cholesterol on lipid-mediated protein-protein interactions

Experiments and molecular simulations have shown that the hydrophobic mismatch between proteins and membranes contributes significantly to lipid-mediated protein-protein interactions. In this article, we discuss the effect of cholesterol on lipid-mediated protein-protein interactions as function of hydrophobic mismatch, protein diameter and protein cluster size, lipid tail length, and temperature. To do so, we study a mesoscopic model of a hydrated bilayer containing lipids and cholesterol in which proteins are embedded, with a hybrid dissipative particle dynamics-Monte Carlo method. We propose a mechanism by which cholesterol affects protein interactions: protein-induced, cholesterol-enriched, or cholesterol-depleted lipid shells surrounding the proteins affect the lipid-mediated protein-protein interactions. Our calculations of the potential of mean force between proteins and protein clusters show that the addition of cholesterol dramatically reduces repulsive lipid-mediated interactions between proteins (protein clusters) with positive mismatch, but does not affect attractive interactions between proteins with negative mismatch. Cholesterol has only a modest effect on the repulsive interactions between proteins with different mismatch.     

The heme redox center of chloroplast cytochrome f is linked to a buried five-water chain.

The crystal structure of the 252-residue lumen-side domain of reduced cytochrome f, a subunit of the proton-pumping integral cytochrome b6f complex of oxygenic photosynthetic membranes, was determined to a resolution of 1.96 A from crystals cooled to -35 degrees. The model was refined to an R-factor of 15.8% with a 0.013-A RMS deviation of bond lengths from ideality. Compared to the structure of cytochrome f at 20 degrees, the structure at -35 degrees has a small change in relative orientation of the two folding domains and significantly lower isotropic temperature factors for protein atoms. The structure revealed an L-shaped array of five buried water molecules that extend in two directions from the N delta 1 of the heme ligand His 25. The longer branch extends 11 A within the large domain, toward Lys 66 in the prominent basic patch at the top of the large domain, which has been implicated in the interaction with the electron acceptor, plastocyanin. The water sites are highly occupied, and their temperature factors are comparable to those of protein atoms. Virtually all residues that form hydrogen bonds with the water chain are invariant among 13 known cytochrome f sequences. The water chain has many features that optimize it as a proton wire, including insulation from the protein medium. It is suggested that this chain may function as the lumen-side exit port for proton translocation by the cytochrome b6f complex.     

van der Waals forces between cylinders: Arrays of thin cylinders and three body forces

We study the van der Waals energy of interaction of an array of parallel dielectric cylinders immersed in a dielectric medium. We consider only “thin” cylinders which have radius small compared to the separation of the cylinders. The energy is calculated as a sum of two body plus three body interactions. The case of hexagonally close packed cylinders is studied in more detail. Some biophysical applications are discussed and in particular the van der Waals energy of the myosin lattice in striated muscle is examined.     

Curvature properties of novel forms of phosphatidylcholine with branched acyl chains.

We studied the properties of a series of phosphatidylcholine molecules with branched acyl chains. These lipids have previously been shown to have marked stimulatory effects on the side-chain cleavage activity of cytochrome P450SCC (CYP11A1), an enzyme of the inner mitochondrial membrane. The synthetic lipids used were diacyl phosphatidylcholines with the decanoyl, dodecanoyl or tetradecanoyl chain having a hexyl, octyl or decyl straight chain aliphatic branch at the 2-position. All three lipids lowered the bilayer to hexagonal phase transition temperature of dielaidoyl phosphatidylethanolamine, the lipids with longer acyl chains being more effective in this regard. As pure lipids all of the forms were found by X-ray diffraction to be predominantly in the hexagonal phase (HII) over the entire temperature range of 7-75 degrees C. The properties of the HII phase were unusual with regard to the small size of the lattice spacings and the small temperature dependence of the spacings. We used tetradecane to relieve hydrocarbon packing constraints to determine the intrinsic radius of curvature of the lipid monolayer. The elastic bending modulus was measured in the presence of tetradecane by introducing an osmotic gradient across the hexagonal phase cylinders with aqueous solutions of poly(ethylene glycol). The elastic bending modulus was found to be higher than that observed with other lipids and to increase with temperature. Both the small intrinsic radius of curvature and the high elastic bending modulus indicate that the presence of these lipids in bilayer membranes will impose a high degree of negative curvature strain.     

Comparison of polyelectrolyte theories of the binding of cations to DNA.

Predictions of the binding of counterions to DNA made using the counterion condensation theory developed by Manning are compared with those made using the Poisson-Boltzmann equation, solved numerically by the Runge-Kutta procedure. Ions are defined as territorially or atmospherically bound if they fall within a given distance, defined by counterion condensation theory, from the DNA surface. Two types of experimental situations are considered. The first is the delocalized binding of a single type of counterion to DNA. In this case the Poisson-Boltzmann treatment predicts somewhat lower extents of binding TO DNA, modeled as a 10-A radius cylinder, than does Manning theory. The two theories converge as the radius decreases. The second type of experiment is the competition of ions of different valence for binding to DNA. The theories are compared with literature values of binding constants of divalent ions in the presence of monovalent ions, and of spermidine 3+ in the presence of Na+ or Mg2+. Both predict with fair accuracy the salt dependence of the equilibrium constants.     

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.     

Small-Angle Neutron Scattering Characterization of Monoclonal Antibody Conformations and Interactions at High Concentrations

Small-angle neutron scattering (SANS) is used to probe the solution structure of two protein therapeutics (monoclonal antibodies 1 and 2 (MAb1 and MAb2)) and their protein-protein interaction (PPI) at high concentrations. These MAbs differ by small sequence alterations in the complementarity-determining region but show very large differences in solution viscosity. The analyses of SANS patterns as a function of different solution conditions suggest that the average intramolecular structure of both MAbs in solution is not significantly altered over the studied protein concentrations and experimental conditions. Even though a strong repulsive interaction is expected for both MAbs due to their net charges and low solvent ionic strength, analysis of the SANS data shows that the effective PPI for MAb1 is dominated by a very strong attraction at small volume fraction that becomes negligible at large concentrations. The MAb1 PPI cannot be modeled simply by a spherically symmetric central forces model. It is proposed that an anisotropic attraction strongly affects the local interprotein structure and leads to an anomalously large viscosity of concentrated MAb1 solutions. Conversely, MAb2 displays a repulsive interaction potential throughout the concentration series probed and a comparatively small solution viscosity.     

Small-Angle Neutron Scattering Characterization of Monoclonal Antibody Conformations and Interactions at High Concentrations

Small-angle neutron scattering (SANS) is used to probe the solution structure of two protein therapeutics (monoclonal antibodies 1 and 2 (MAb1 and MAb2)) and their protein-protein interaction (PPI) at high concentrations. These MAbs differ by small sequence alterations in the complementarity-determining region but show very large differences in solution viscosity. The analyses of SANS patterns as a function of different solution conditions suggest that the average intramolecular structure of both MAbs in solution is not significantly altered over the studied protein concentrations and experimental conditions. Even though a strong repulsive interaction is expected for both MAbs due to their net charges and low solvent ionic strength, analysis of the SANS data shows that the effective PPI for MAb1 is dominated by a very strong attraction at small volume fraction that becomes negligible at large concentrations. The MAb1 PPI cannot be modeled simply by a spherically symmetric central forces model. It is proposed that an anisotropic attraction strongly affects the local interprotein structure and leads to an anomalously large viscosity of concentrated MAb1 solutions. Conversely, MAb2 displays a repulsive interaction potential throughout the concentration series probed and a comparatively small solution viscosity.     

Passive Membrane Potentials: A Generalization of the Theory of Electrotonus

The theory of electrotonus, which has been well developed for small cylinders, is extended: the fundamental potential equations for a membrane of arbitrary shape are derived, and solutions are found for cylindrical and spherical geometries. If two purely conductive media are separated by a resistance-capacitance membrane, then Laplace's equation describes the potential in either medium, and two boundary equations relate the transmembrane potential to applied currents and to currents flowing into the membrane from each medium. The core conductor model, on which most previous work on cylindrical electrotonus has been based, gives rise to a one dimensional diffusion equation, the cable equation, for the transmembrane potential in a small cylinder. Under the assumptions of the core conductor model the more general equations developed here are shown to reduce to the cable equation. The two theories agree well in predicting the transmembrane potential in a small cylinder owing to an applied current step, and the extracellular potential for this cylinder is estimated numerically from the general theory. A detailed proof is given for the isopotentiality of a spherical soma membrane.     

Motion of a doublet of two cylinders in contact in a narrow channel flow.

The motion of two rigid circular cylinders in contact immersed in an incompressible Newtonian fluid in a channel is examined numerically in the zero Reynolds number limit, for various values of the cylinder radius/channel width ratio. Analyses of the time courses of the lateral position and the orientation of the doublet showed that, depending on the initial condition and the doublet/channel size ratio, the doublet exhibit one of the three types of motion: a continuous rotation in the same direction during a period, and a rotation changing its direction at every half period with a large or a small variation of the orientation.     

The radial decline of nerve impulses in a restricted cylindrical extracellular space

In order to increase the potentials recorded extracellularly from nerve fibres, peripheral nerves are often placed in restricted space with cylindrical geometry. Equations are derived for computing the potentials expected at the surface of the cylinder, based on the potentials at the external surface of a small nerve fibre located on the long axis of the cylinder. These equations are evaluated numerically, using two formulae for a nerve impulse given in the literature. In both cases there is little attenuation for cylinders with radii less than 0.5 mm, but the potential declines approximately as a power of radius b for 1<b<10 mm. Various factors which might affect these results under different experimental conditions are discussed.     

Direct, sequence-specific binding of the human U1-70K ribonucleoprotein antigen protein to loop I of U1 small nuclear RNA.

We have studied the interaction of two of the U1 small nuclear ribonucleoprotein (snRNP)-specific proteins, U1-70K and U1-A, with U1 small nuclear RNA (snRNA). The U1-70K protein is a U1-specific RNA-binding protein. Deletion and mutation analyses of a beta-galactosidase/U1-70K partial fusion protein indicated that the central portion of the protein, including the RNP sequence domain, is both necessary and sufficient for specific U1 snRNA binding in vitro. The highly conserved eight-amino-acid RNP consensus sequence was found to be essential for binding. Deletion and mutation analyses of U1 snRNA showed that both the U1-70K fusion protein and the native HeLa U1-70K protein bound directly to loop I of U1 snRNA. Binding was sequence specific, requiring 8 of the 10 bases in the loop. The U1-A snRNP protein also interacted specifically with U1 snRNA, principally with stem-loop II.     

Evaluation of ricin A-chain immunotoxins directed against human T cells

We have synthesized four immunotoxins (ITs) by covalently coupling the A chain of ricin to murine monoclonal antibodies that recognize surface antigens on human T cells. Treatment of human peripheral blood lymphocytes with either 10.2-A, directed against the CD5 (Tp67) antigen, or 64.1-A, directed against the CD3 (Tp19) antigen, abolished protein synthesis in cells subsequently cultured with phytohemagglutinin (PHA). In contrast, two other ITs (9.6-A and 35.1-A), both directed against the CD2 (Tp50) antigen, had minimal effects on protein synthesis in PHA-stimulated cells. The binding of each IT to T cells was shown by immunofluorescence with fluorescein-conjugated goat anti-mouse immunoglobulin (FITC-GAMIg) and fluorescein-conjugated rabbit anti-ricin A-chain (FITC-RAR) antibodies. Activity of the ricin A chain in each IT was demonstrated by its ability to inhibit protein synthesis in a cell-free reticulocyte lysate assay. Ultrastructural immunoperoxidase analysis of IT internalization showed that ineffective and effective ITs were endocytosed at the same rate (50% of cells had labeled endosomes after 15 min). However, ineffective IT 35.1-A was more rapidly delivered to lysosomes (15-30 min) than effective ITs (10.2-A and 64.1-A) (greater than or equal to 30 min). The data support the hypothesis that there are several distinct pathways for internalization of ITs and that the ability of ricin A chain to reach and inactivate ribosomes may depend upon the specific membrane receptor involved in binding a given IT, its route of internalization, and the rate of entry of the IT into lysosomes.     

The influence of lysolipids on the spontaneous curvature and bending elasticity of phospholipid membranes.

The effects of lysolipids on phospholipid layer curvature and bending elasticity were examined using x-ray diffraction and the osmotic stress method. Lysolipids with two different head groups, phosphatidylcholine (PC) and phosphatidylethanolamine (PE), and differing hydrocarbon chains were mixed with the hexagonal-forming lipid, dioleoylphosphatidylethanolamine (DOPE). With up to 30 mole% lysolipid in DOPE, the mixture maintains the inverted hexagonal (H(II)) phase in excess water, where increasing levels of lysolipid result in a systematic increase in the H(II) lattice dimension. Analysis of the structural changes imposed by lysolipids show that, opposite to DOPE itself, which has an spontaneous radius of curvature (R(0)) of -30 A, PC lysolipids add high positive curvature, with R(0) = +38 to +60 A, depending on chain length. LysoPEs, in contrast, add very small curvatures. When both polar group and hydrocarbon chains of the added lysolipid mismatch those of DOPE, the structural effects are qualitatively different from otherwise. Such mismatched lysolipids "reshape" the effective combination molecule into a longer and more cylindrical configuration compared to those lysolipids with either matching polar group or hydrocarbon chain.     

Dynamic Light Scattering Application to Study Protein Interactions in Electrolyte Solutions

The concentration dependence of the diffusion coefficient of particles suspended in solution depends primarily on the occupied volume fraction and on repulsive and attractive forces. This dependency is expressed by the interaction parameter, which can be assessed experimentally by light scattering measurements and have been determined for the diffusion coefficient of BSA under different salt concentration conditions in the present work. The result shows that the diffusion coefficient of protein grows up with increasing protein concentration, and when the ionic strength turns up gradually the diffusion coefficient decreases with protein concentrations increasing. The concentration dependence of BSA diffusion coefficients is interpreted in the context of a two-body potential of mean force, which includes repulsive hard-sphere and Coulombic interactions and attractive dispersion. With the increase of ionic strength, Debye screening decreases, protein interaction changes from repulsion to attraction, and protein begins to aggregate. By means of the concentration dependence of BSA diffusion coefficients, one can obtain the parameters of protein interactions and can find that protein bears a net effective charge of –9.0 e and has a Hamaker constant of 2.8k_BT. This work demonstrates that DLS is an effective technique of studying protein interactions.