The phase behavior of mixed lipid membranes in the presence of the rippled phase.

We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is used as an order parameter. As function of temperature, this model properly accounts for the phase behavior of the three possible membrane phases: solid, liquid and the rippled phase. Our primary aim is to explore extensions of this model to binary lipid mixtures by considering the composition dependence of important model parameters. The obtained phase diagrams show various liquid, solid and rippled phase coexistence regions, and are in quantitative agreement with the experimental ones for some specific lipid mixtures.

Tension-induced morphological transition in mixed lipid bilayers.

Recently, Rozovsky et al. reported on the morphology and dynamics of superstructures in three-component lipid bilayers containing saturated lipid, unsaturated lipid, and cholesterol (Rozovsky, S.; Kaizuka, Y.; Groves, J. T. J. Am. Chem. Soc. 2005, 127, 36). We suggest that the observed sequence of the striped-to-hexagonal morphological transition in mixed bilayers can be attributed to an enhanced membrane surface tension that is induced by the vesicle adhesion onto the solid surface.

Polyelectrolyte multilayer formation: electrostatics and short-range interactions.

We investigate the phenomenon of multilayer formation via layer-by-layer deposition of alternating charged polyelectrolytes. Using mean-field theory, we find that a strong short-range attraction between the two types of polymer chains is essential for the formation of multilayers. For strong enough short-range attraction, the adsorbed amount per layer increases (after an initial decrease), and finally it stabilizes in the form of a polyelectrolyte multilayer that can be repeated hundreds of times. For weak short-range attraction between any two adjacent layers, the adsorbed amount (per added layer) decays as the distance from the surface increases, until the chains stop adsorbing altogether. The dependence of the threshold value of the short-range attraction as function of the polymer charge fraction and salt concentration is calculated.

Adhesion of membranes with competing specific and generic interactions.

Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. The membranes contain specific adhesion molecules (stickers) which are attracted by the second surface. In the absence of stickers, the trans-interaction between the membrane and the second surface is assumed to be repulsive at short separations. It is shown that the interplay of specific attractive and generic repulsive interactions can lead to the formation of a potential barrier. This barrier induces a line tension between bound and unbound membrane segments which results in lateral phase separation during adhesion. The mechanism for adhesion-induced phase separation is rather general, as is demonstrated by considering two distinct cases involving: i) stickers with a linear attractive potential, and ii) stickers with a short-ranged square-well potential. In both cases, membrane fluctuations reduce the potential barrier and, therefore, decrease the tendency of phase separation.

Supported membranes on chemically structured and rough surfaces.

We present a general linear response description of membrane adhesion at rough or chemically structured surfaces. Our method accounts for nonlocal Van der Waals effects and contains the more approximate (and local) Deryagin approach in a simple limit. Specializing to supported membranes we consider the effects of substrate structure on the membrane adhesion energy and configuration. Adhesion is usually less favorable for rough substrates and the membrane shape tends to follow that of the surface contours. Chemical patterning (described by a spatially varying Van der Waals force), however, favors adhesion with the membrane configuration being out of phase with the surface structure. Finally, considering a surface indented with "V"-shaped trenches, we show that our approach is in good agreement with an exact numerical solution.

Binding of molecules to DNA and other semiflexible polymers.

A theory is presented for the binding of small molecules such as surfactants to semiflexible polymers. The persistence length is assumed to be large compared to the monomer size but much smaller than the total chain length. Such polymers (e.g., DNA) represent an intermediate case between flexible polymers and stiff, rodlike ones, whose association with small molecules was previously studied. The chains are not flexible enough to actively participate in the self-assembly, yet their fluctuations induce long-range attractive interactions between bound molecules. In cases where the binding significantly affects the local chain stiffness, those interactions lead to a very sharp, cooperative association. This scenario is of relevance to the association of DNA with surfactants and compact proteins such as RecA. External tension exerted on the chain is found to significantly modify the binding by suppressing the fluctuation-induced interaction.

Hydration interactions: aqueous solvent effects in electric double layers

A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic nonlocal term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar electric double layer. The counterion density is found to increase near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analytically in the case where the ion distribution near the plate is dominated only by counterions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory, with an effective surface charge that is smaller than the actual one.

Domain shapes and patterns: the phenomenology of modulated phases.

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.

Theory of spontaneous vesicle formation in surfactant mixtures.

The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lameliar structures only when interactions or complexing of the two surfactants is taken into account.