Macroion adsorption on a mixed, fluid, lipid membrane containing oppositely charged lipids induces local changes in lipid composition at the interaction zones, and gradients at their boundaries. Including these effects in the free energy of the macroion-dressed membrane we derive its spinodal equation, and show that nonideal lipid mixing can lead to (lipid-mediated) attraction between macroions and lateral phase separation in the composite membrane. The critical nonideality for this transition is substantially smaller than that of the bare lipid membrane, decreasing with macroion size and charge. That is, the lipid membrane is destabilized by macroion adsorption.

We calculate the forces required to package (or, equivalently, acting to eject) DNA into (from) a bacteriophage capsid, as a function of the loaded (ejected) length, under conditions for which the DNA is either self-repelling or self-attracting. Through computer simulation and analytical theory, we find the loading force to increase more than 10-fold (to tens of piconewtons) during the final third of the loading process; correspondingly, the internal pressure drops 10-fold to a few atmospheres (matching the osmotic pressure in the cell) upon ejection of just a small fraction of the phage genome. We also determine an evolution of the arrangement of packaged DNA from toroidal to spool-like structures.

We present a molecular-level theory for amphiphile packing in linear micelles, focusing on the early stages of micellar elongation, i.e., on small and ‘‘intermediate-size’’ micelles, whose endcaps are not yet molded into a final shape. The internal free energy of a micelle of given size and shape is expressed as an integral over local molecular packing free energies in different regions of the micelle. The free energy per molecule is expressed as a sum of interfacial (’’opposing forces’’) and chain conformational contributions, both depending on the local geometry. The equilibrium shape and energy of the micelle is determined by functional minimization of the total free energy. For amphiphiles exhibiting strong preference for packing in the cylindrical geometry, we show that the early stages of growth involve an energetic barrier, resulting in a ‘‘gap’’ in the micellar size distribution. That is, at low total amphiphile concentrations only small (globular) micelles appear in solution. Their concentration reaches a well-defined saturation value, beyond which, all added amphiphiles are incorporated in long micelles, whose ‘‘non-interacting’’ endcaps are well separated by the cylindrical middle part. This, ‘‘second CMC’’ behavior is demonstrated by numerical calculations of micellar size distributions and average aggregation numbers as a function of the total concentration. The conditions necessary for the appearance of a second CMC are analyzed theoretically, with explicit reference to the underlying molecular packing characteristics. In particular, it is shown that a necessary condition for the appearance of a sharply defined second CMC is that the endcap energies (of at least some) of the small or intermediate-size micelles must be considerably lower than the asymptotic (long micelle) value of this quantity. The diameter of the minimal, spherical micelles, as well as that of the final endcaps, is found to be larger than the diameter of the cylindrical body of the very long micelles. Our results are in good qualitative agreement with recent cryo-TEM imaging studies of micellar shape and growth, as well as with previous (less direct) experiments revealing second CMC behavior.

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, Delta S degrees, have been derived from the root-mean-square fluctuations in protein crystals, suggesting Delta S degrees approximate to -50 e.u., i.e., T Delta S degrees approximate to -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane. obtaining T Delta S degrees approximate to -1.7 kT approximate to -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much ‘‘softer.’’

The cooperative condensation of DNA and cationic liposomes to form ordered aggregates in aqueous solution is associated with the release of partially bound counterions. We directly determine the extent of counterion release by separating the supernatant from the precipitated condensates, measuring the conductivity of the solution before and after the phase transition. The extent of counterion release is calculated for a range of lipid/DNA concentration ratios based on the nonlinear Poisson-Boltzmann theory. Both experiment and theory show maximal, essentially complete, release of counterions at the isoelectric point, where the positive (lipid)/negative (DNA) charge ratio is 1:1. Furthermore, at this point the entropic contribution to the condensation free energy is maximal and dominant.

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is ‘‘saturated’’ by adsorbed proteins), the membrane charges are ‘‘overcompensated’’ by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.

The loss of conformational freedom experienced by lipid chains in the vicinity of one, or two, impenetrable walls, representing the surfaces of hydrophobic transmembrane proteins, is calculated using a mean-field molecular-level chain packing theory. The hydrophobic thickness of the protein is set equal to that of the unperturbed lipid membrane (i.e., no ‘‘hydrophobic mismatch’’). The probability distributions of chain conformations, at all distances from the walls, are calculated by generating all conformations according to the rotational-isomeric-state model, and subjecting the system free energy to the requirement that the hydrophobic core of the membrane is liquid-like, and hence uniformly packed by chain segments. As long as the two protein surfaces are far apart, their interaction zones do not overlap, each extending over several molecular diameters. When the interaction zones begin to overlap, inter-protein repulsion sets in. At some intermediate distance the interaction turns strongly attractive, resulting from the depletion of (highly constrained) lipid tails from the volume separating the two surfaces. The chains confined between the hydrophobic surfaces are tilted away from the walls. Their tilt angle decreases monotonically with the distance from the walls, and with the distance between the walls. A nonmonotonic variation of the lipid-mediated interaction free energy between hydrophobic surfaces in membranes is also obtained using a simple, analytical, model in which chain conformations are grouped according to their director (end-to-end vector) orientations.

We present a theoretical analysis of the phase behavior of solutions containing DNA, cationic lipids, and nonionic (helper) lipids. Our model allows for five possible structures, treated as incompressible macroscopic phases: two lipid-DNA composite (lipoplex) phases, namely, the lamellar (L-alpha(C)) and hexagonal (H-II(C)) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L-alpha) and inverse-hexagonal (H-II) structures, and uncomplexed DNA. The free energy of the four lipid-containing phases is expressed as a sum of composition-dependent electrostatic, elastic, and mixing terms. The electrostatic free energies of all phases are calculated based on Poisson-Boltzmann theory. The phase diagram of the system is evaluated by minimizing the total free energy of the three-component mixture with respect to all the compositional degrees of freedom. We show that the phase behavior, in particular the preferred lipid-DNA complex geometry, is governed by a subtle interplay between the electrostatic, elastic, and mixing terms, which depend, in turn, on the lipid composition and lipid/DNA ratio. Detailed calculations are presented for three prototypical systems, exhibiting markedly different phase behaviors. The simplest mixture corresponds to a rigid planar membrane as the lipid source, in which case, only lamellar complexes appear in solution. When the membranes are ‘‘soft’’ (i.e., low bending modulus) the system exhibits the formation of both lamellar and hexagonal complexes, sometimes coexisting with each other, and with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity toward the inverse-hexagonal phase. Here, again, the phase diagram is rather complex, revealing a multitude of phase transitions and coexistences. Lamellar and hexagonal complexes appear, sometimes together, in different regions of the phase diagram.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (L-alpha to the inverse-hexagonal (H-II phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., ‘‘cylinder-like,’’ ‘‘barrel-like,’’ or ‘‘vase-like.’’ We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions. the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape. and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the H-II lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the L-alpha –> H-II transition. At the transition, a peptide-poor L-alpha phase coexists with a peptide-rich H-II phase.