We study the structural and energetic consequences of (α-helical) amphipathic peptide adsorption onto a lipid membrane and the subsequent formation of a transmembrane peptide pore. Initially, each peptide binds to the membrane surface, with the hydrophobic face of its cylinder-like body inserted into the hydrocarbon core. Pore formation results from subsequent peptide crowding, oligomerization, and eventually reorientation along the membrane normal. We have theoretically analyzed three peptide-membrane association states: interfacially-adsorbed monomeric and dimeric peptides, and the multi-peptide transmembrane pore state. Our molecular-level model for the lipid bilayer is based on a combination of detailed chain packing theory and a phenomenological description of the headgroup region. We show that the membrane perturbation free energy depends critically on peptide orientation: in the transmembrane pore state the lipid perturbation energy, per peptide, is smaller than in the adsorbed state. This suggests that the gain in conformational freedom of the lipid chains is a central driving force for pore formation. We also find a weak, lipid-mediated, gain in membrane perturbation free energy upon dimerization of interfacially-adsorbed peptides. Although the results pertain mainly to weakly-charged peptides, they reveal general properties of the interaction of amphipathic peptides with lipid membranes.

Cadherins constitute a family of cell-surface proteins that mediate intercellular adhesion through the association of protomers presented from juxtaposed cells. Differential cadherin expression leads to highly specific intercellular interactions in vivo. This cell-cell specificity is difficult to understand at the molecular level because individual cadherins within a given subfamily are highly similar to each other both in sequence and structure, and they dimerize with remarkably low binding affinities. Here, we provide a molecular model that accounts for these apparently contradictory observations. The model is based in part on the fact that cadherins bind to one another by ‘‘swapping’’ the N-terminal beta-strands of their adhesive domains. An inherent feature of strand swapping (or, more generally, the domain swapping phenomenon) is that ‘‘closed’’ monomeric conformations act as competitive inhibitors of dinner formation, thus lowering affinities even when the dimer interface has the characteristics of high-affinity complexes. The model describes quantitatively how small affinity differences between low-affinity cadherin dimers are amplified by multiple cadherin interactions to establish large specificity effects at the cellular level. It is shown that cellular specificity would not be observed if cadherins bound with high affinities, thus emphasizing the crucial role of strand swapping in cell-cell adhesion. Numerical estimates demonstrate that the strength of cellular adhesion is extremely sensitive to the concentration of cadherins expressed at the cell surface. We suggest that the domain swapping mechanism is used by a variety of cell-adhesion proteins and that related mechanisms to control affinity and specificity are exploited in other systems.

The ability of a mixed lipid bilayer composed of neutral and charged lipids to encapsulate an oppositely charged protein is studied with use of a simple theoretical model. The free energy of the bilayer-enveloped protein complex is expressed as a sum of electrostatic and curvature elasticity contributions, and compared to that of a protein adsorbed on a mixed planar bilayer. The electrostatic adsorption energy on the planar bilayer is calculated by using an extended Poisson-Boltzmann approach, which allows for local lipid charge modulation in the adsorption zone. We find that the electrostatic interactions favor the wrapped state, while the bending energy prefers the planar bilayer. To enable the transition from the adsorbed to enveloped protein geometry, there is a minimal necessary protein charge. This ‘‘crossover’’ charge depends on the bending rigidity of the lipid membrane and the (composition dependent) spontaneous curvature of its constituent monolayers. The values for the crossover charge predicted by the theory are in line with the charge necessary for peptide shuttles to penetrate cell membranes.

The structural and energetic characteristics of the interaction between interfacially adsorbed (partially inserted) a-helical, amphipathic peptides and the lipid bilayer substrate are studied using a molecular level theory of lipid chain packing in membranes. The peptides are modeled as ‘‘amphipathic cylinders’’ characterized by a well-defined polar angle. Assuming two-dimensional nematic order of the adsorbed peptides, the membrane perturbation free energy is evaluated using a cell-like model; the peptide axes are parallel to the membrane plane. The elastic and interfacial contributions to the perturbation free energy of the ‘‘peptide-dressed’’ membrane are evaluated as a function of: the peptide penetration depth into the bilayer’s hydrophobic core, the membrane thickness, the polar angle, and the lipid/peptide ratio. The structural properties calculated include the shape and extent of the distorted (stretched and bent) lipid chains surrounding the adsorbed peptide, and their orientational (C-H) bond order parameter profiles. The changes in bond order parameters attendant upon peptide adsorption are in good agreement with magnetic resonance measurements. Also consistent with experiment, our model predicts that peptide adsorption results in membrane thinning. Our calculations reveal pronounced, membrane-mediated, attractive interactions between the adsorbed peptides, suggesting a possible mechanism for lateral aggregation of membrane-bound peptides. As a special case of interest, we have also investigated completely hydrophobic peptides, for which we find a strong energetic preference for the transmembrane (inserted) orientation over the horizontal (adsorbed) orientation.

Cationic lipid-DNA complexes, often referred to as lipoplexes, are formed spontaneously in aqueous solutions upon mixing DNA and liposomes composed of cationic and nonionic lipids. Understanding the mechanisms underlying lipoplex formation, structure and phase behavior is crucial for their further development and design as non-viral transfection vectors in gene therapy. From a physical point of view, lipoplexes are ordered, self-assembled, composite aggregates. Their preferred spatial geometry and phase behavior are governed by a delicate coupling between the electrostatic interactions which drive lipoplex formation and the elastic properties of the constituent lipid layers, both depending on the molecular nature and composition of the lipid mixture. In this review we outline some recent efforts to model the microscopic structure, energetic and phase behavior of cationic lipid-DNA mixtures, focusing on the two principal aggregation geometries: the lamellar (L-alpha(C)), or ‘‘sandwich’’ complexes, and the hexagonal (H-II(C)), or ‘‘honeycomb’’ complexes. We relate the structural and thermodynamic properties of these two ‘‘canonical’’ lipoplex morphologies to their appearance in phase diagrams of DNA-lipid mixtures, emphasizing the crucial role fulfilled by the molecular packing characteristics of the cationic and neutral lipids, as reflected in the curvature elastic properties of the mixed lipid layer.

We present a simple statistical thermodynamic model for budding of viral nucleocapsids at the cell membrane. The membrane is modeled as a flexible lipid bilayer embedding linker (spike) proteins, which serve to anchor and thus wrap the membrane around the viral capsids. The free energy of a single bud is expressed as a sum of the bending energy of its membrane coat, the spike-mediated capsid-membrane adhesion energy, and the line energy associated with the bud’s rim, all depending on the extent of wrapping (i.e., bud size), and density of spikes in the curved membrane. This self-energy is incorporated into a simple free energy functional for the many-bud system, allowing for different spike densities, and hence entropy, in the curved (budding) and planar membrane regions, as well as for the configurational entropy of the polydisperse bud population. The equilibrium spike densities in the coexisting, curved and planar, membrane regions are calculated as a function of the membrane bending energy and the spike-mediated adhesion energy, for different spike and nucleocapsid concentrations in the membrane plane, as well as for several values of the bud’s rim energy. We show that complete budding (full wrapping of nucleocapsids) can only take place if the adhesion energy exceeds a certain, critical, bending free energy. Whenever budding takes place, the spike density in the mature virions is saturated, i.e., all spike adhesion sites are occupied. The rim energy plays an important role in determining the size distribution of buds. The fraction of fully wrapped buds increases as this energy increases, resulting eventually in an all-or-nothing mechanism, whereby nucleocapsids at the plasma membrane are either fully enveloped or completely naked (just touching the membrane). We also find that at low concentrations all capsids arriving at the membrane get tightly and fully enveloped. Beyond a certain concentration, corresponding approximately to a stoichiometric spike/capsid ratio, newly arriving capsids cannot be fully wrapped; i.e., the budding yield decreases.

In addition to the familiar bending and stretching deformations, lipid monolayers and bilayers in their disordered state are often subjected to tilt deformations, occurring for instance in structural rearrangements accompanying membrane fusion, or upon insertion of ‘‘oblique’’ hydrophobic proteins into lipid bilayers. We study the elastic response of a flat lipid monolayer to a tilt deformation, using the spatial and conformational average of the chain end-to-end vector from the membrane normal to define a macroscopic membrane tilt. The physical origin and magnitude of the corresponding tilt modulus k(t) is analyzed using two complementary theoretical approaches. The first is a phenomenological model showing that the tilt and bending deformations are decoupled and the effects of inter-chain correlations on the tilt modulus is small. The second is based on a molecular-level mean-field theory of chain packing, enabling numerical evaluation of the tilt modulus for realistic, multi-conformation, chain models. Both approaches reveal that the tilt modulus involves two major contributions. The first is elastic in origin, arising from the stretching of the hydrocarbon chains upon a tilt deformation and reflecting the loss of chain conformational freedom associated with chain stretching. The second, purely entropic, contribution results from the constraints imposed by a tilt deformation on the fluctuations of chain director orientations. Using the chain-packing theory we compute the two contributions numerically as a function of the cross-sectional area per chain. The elastic and entropic terms are shown to dominate the value of k(t) for small and large areas per chain, respectively. For typical cross-sectional areas of lipid chains in biological membranes they areof comparable magnitude, yielding k(t) approximate to 0.2k(B)T/Angstrom(2).