Sylvio May

Structure, Stability, and Thermodynamics of Lamellar DNA-Lipid Complexes

We develop a statistical thermodynamic model for the phase evolution of DNA-cationic lipid complexes in aqueous solution, as a function of the ratios of charged to neutral lipid and charged lipid to DNA. The complexes consist of parallel strands of DNA intercalated in the water layers of lamellar stacks of mixed lipid bilayers, as determined by recent synchrotron x-ray measurements. Elastic deformations of the DNA and the lipid bilayers are neglected, but DNA-induced spatial inhomogeneities in the bilayer charge densities are included. The relevant nonlinear Poisson-Boltzmann equation is solved numerically, including self-consistent treatment of the boundary conditions at the polarized membrane surfaces. For a wide range of lipid compositions, the phase evolution is characterized by three regions of lipid to DNA charge ratio, rho: 1) for low rho, the complexes coexist with excess DNA, and the DNA-DNA spacing in the complex, d, is constant; 2) for intermediate rho, including the isoelectric point rho = 1, all of the lipid and DNA in solution is incorporated into the complex, whose inter-DNA distance d increases linearly with rho; and 3) for high rho, the complexes coexist with excess liposomes (whose lipid composition is different from that in the complex), and their spacing d is nearly, but not completely, independent of rho. These results can be understood in terms of a simple charging model that reflects the competition between counterion entropy and inter-DNA (rho < 1) and interbilayer (rho > 1) repulsions. Finally, our approach and conclusions are compared with theoretical work by others, and with relevant experiments.

Interactions of Cholesterol with Lipid Bilayers: The Preferred Configuration and Fluctuations

The free energy difference associated with the transfer of a single cholesterol molecule from the aqueous phase into a lipid bilayer depends on its final location, namely on its insertion depth and orientation within the bilayer. We calculated desolvation and lipid bilayer perturbation contributions to the water-to-membrane transfer free energy, thus allowing us to determine the most favorable location of cholesterol in the membrane and the extent of fluctuations around it. The electrostatic and nonpolar contributions to the solvation free energy were calculated using continuum solvent models. Lipid layer perturbations, resulting from both conformational restrictions of the lipid chains in the vicinity of the (rigid) cholesterol backbone and from cholesterol-induced elastic deformations, were calculated using a simple director model and elasticity theory, respectively. As expected from the amphipathic nature of cholesterol and in agreement with the available experimental data, our results show that at the energetically favorable state, cholesterols hydrophobic core is buried within the hydrocarbon region of the bilayer. At this state, cholesterol spans approximately one leaflet of the membrane, with its OH group protruding into the polar (headgroup) region of the bilayer, thus avoiding an electrostatic desolvation penalty. We found that the transfer of cholesterol into a membrane is mainly driven by the favorable nonpolar contributions to the solvation free energy, whereas only a small opposing contribution is caused by conformational restrictions of the lipid chains. Our calculations also predict a strong tendency of the lipid layer to elastically respond to (thermally excited) vertical fluctuations of cholesterol so as to fully match the hydrophobic height of the solute. However, orientational fluctuations of cholesterol were found to be accompanied by both an elastic adjustment of the surrounding lipids and by a partial exposure of the hydrophobic cholesterol backbone to the polar (headgroup) environment. Our calculations of the molecular order parameter, which reflects the extent of orientational fluctuations of cholesterol in the membrane, are in good agreement with available experimental data.

Interaction between two cylindrical inclusions in a symmetric lipid bilayer

We calculate the membrane-mediated interaction between two cylindrical inclusions in a symmetric lipid bilayer. Our theory takes two contributions to the free energy into account, the elastic behavior of the membrane and the conformational restrictions that the flexible hydrocarbon chains of the lipids experience in the vicinity of a rigid inclusion. The description of the elastic behavior is based on two order parameters, the hydrophobic thickness of the membrane and a director field that characterizes the average tilt of the lipid chains. Conformational restrictions of the lipid chains are taken into account by a simple director model. We show that the short-range interaction potential between two inclusions sensitively depends on the degree of hydrophobic mismatch and on the spontaneous curvature of the lipid layers. In particular, we find pronounced attraction if the hydrophobic mismatch is positive. For negative mismatch the attraction is much less pronounced and, additionally, an energetic barrier appears. The inclusions prefer a small but notable negative hydrophobic mismatch. Positive spontaneous curvature amplifies these behaviors.

Modulation of the spontaneous curvature and bending rigidity of lipid membranes by interfacially adsorbed amphipathic peptides.

Amphipathic alpha-helical peptides are often ascribed an ability to induce curvature stress in lipid membranes. This may lead directly to a bending deformation of the host membrane, or it may promote the formation of defects that involve highly curved lipid layers present in membrane pores, fusion intermediates, and solubilized peptide-micelle complexes. The driving force is the same in all cases: peptides induce a spontaneous curvature in the host lipid layer, the sign of which depends sensitively on the peptides structural properties. We provide a quantitative account for this observation on the basis of a molecular-level method. To this end, we consider a lipid membrane with peptides interfacially adsorbed onto one leaflet at high peptide-to-lipid ratio. The peptides are modeled generically as rigid cylinders that interact with the host membrane through a perturbation of the conformational properties of the lipid chains. Through the use of a molecular-level chain packing theory, we calculate the elastic properties, that is, the spontaneous curvature and bending stiffness, of the peptide-decorated lipid membrane as a function of the peptides insertion depth. We find a positive spontaneous curvature (preferred bending of the membrane away from the peptide) for small penetration depths of the peptide. At a penetration depth roughly equal to half-insertion into the hydrocarbon core, the spontaneous curvature changes sign, implying negative spontaneous curvature (preferred bending of the membrane toward the peptide) for large penetration depths. Despite thinning of the membrane upon peptide insertion, we find an increase in the bending stiffness. We discuss these findings in terms of how the peptide induces elastic stress.

Trans-monolayer coupling of fluid domains in lipid bilayers

Lipid membranes that exhibit fluid–fluid phase coexistence are widely studied as models for the physical state of lipids in raft-forming biomembranes. Yet, whereas model membranes are typically symmetric, biomembranes maintain different lipid compositions in their two leaflets. In the plasma membrane, only the extracellular but not the cytoplasmic leaf contains a raft-competent lipid mixture. This raises the question if a raft-like state in the extracellular layer is able to induce a similar state also on the cytoplasmic side. Recent studies have thus begun to investigate the problem of trans-monolayer domain coupling in model membranes. Experimental work on asymmetric membranes has revealed that a tendency to phase-separate in one leaf can induce phase separation on the other leaf. Conversely, the lack of such a tendency can prevent phase separation in the apposed leaf. The strength of the coupling between domains can be described by a composition-dependent surface tension or, for small compositional changes, by a single coupling constant. Theoretical work has demonstrated how the coupling constant affects the phase behavior of a binary membrane. We summarize previous experimental findings and modeling efforts. In addition, three possible physical mechanisms of trans-monolayer domain coupling are discussed: electrostatic coupling, cholesterol flip-flop, and dynamic chain interdigitation. We argue that dynamic chain interdigitation likely provides the main contribution to the coupling constant. The charges of acidic lipids tend to reduce the coupling constant – but the reduction is insignificant even at low salt content.

Influence of Monolayer-Monolayer Coupling on the Phase Behavior of a Fluid Lipid Bilayer

We suggest a minimal model for the coupling of the lateral phase behavior in an asymmetric lipid membrane across its two monolayers. Our model employs one single order parameter for each monolayer leaflet, namely its composition. Regular solution theory on the mean-field level is used to describe the free energy in each individual leaflet. Coupling between monolayers entails an energy penalty for any local compositional differences across the membrane. We calculate and analyze the phase behavior of this model. It predicts a range of possible scenarios. A monolayer with a propensity for phase separation is able to induce phase separation in the apposed monolayer. Conversely, a monolayer without this propensity is able to prevent phase separation in the apposed monolayer. If there is phase separation in the membrane, it may lead to either complete or partial registration of the monolayer domains across the membrane. The latter case which corresponds to a three-phase coexistence is only found below a critical coupling strength. We calculate that critical coupling strength. Above the critical coupling strength, the membrane adopts a uniform compositional difference between its two monolayers everywhere in the membrane, implying phase coexistence between only two phases and thus perfect spatial registration of all domains on the apposed membrane leafs. We use the lattice Boltzmann simulation method to also study the morphologies that form during phase separation within the three-phase coexistence region. Generally, domains in one monolayer diffuse but remain fully enclosed within domains in the other monolayer.

Theories on structural perturbations of lipid bilayers

Structural perturbations of fluid lipid bilayers can be caused by various processes, such as the insertion of transmembrane inclusions, protein and peptide adsorption, the formation of membrane pores, or even by the transition to the inverse hexagonal phase. Theoretical concepts for their energetic description are often based on membrane elasticity theory. New insights have emerged from both applying this theory to inclusion-containing membranes and from relating membrane elasticity theory to microscopic models of perturbed lipid layers.

Perturbation of a lipid membrane by amphipathic peptides and its role in pore formation

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.

Structure and Energy of Fusion Stalks: The Role of Membrane Edges

Fusion of lipid bilayers proceeds via a sequence of distinct structural transformations. Its early stage involves a localized, hemifused intermediate in which the proximal but not yet the distal monolayers are connected. Whereas the so-called stalk model most successfully accounts for the properties of the hemifused intermediate, there is still uncertainty about its microscopic structure and energy. We reanalyze fusion stalks using the theory of membrane elasticity. In our calculations, a short (cylindrical micelle-like) tether connects the two proximal monolayers of the hemifused membranes. The shape of the stalk and the length of the tether are calculated such as to minimize the overall free energy and to avoid the formation of voids within the hydrocarbon core. Our free energy expression is based on three internal degrees of freedom of a perturbed lipid layer: thickness, splay, and tilt deformations. Based on exactly the same model, we compare fusion stalks with and without the ability included to form sharp edges at the interfacial region between the hydrocarbon core and the polar environment. Requiring the interface to be smooth everywhere, our detailed calculations recover previous results: the stalk energies are far too high to account for the experimental observation of fusion intermediates. However, if we allow the interface to be nonsmooth, we find a remarkable reduction of the stalk free energy down to more realistic values. The corresponding structure of a nonsmooth stalk exhibits sharp edges at the transition regions between the bilayer and tether parts. In addition to that, a corner is formed at each of the two distal monolayers. We discuss the mechanism how membrane edges reduce the energy of fusion stalks.

Spontaneous curvature and thermodynamic stability of mixed amphiphilic layers

The elastic behavior of mixed bilayers composed of two amphiphilic components with different chain length (and identical head groups) is studied using two molecular level models. In both, the bilayer free energy is expressed as a sum of chain, head group and interfacial contributions as well as a mixing entropy term. The head group and interfacial terms are modeled using simple phenomenological but general expressions. The models differ in their treatment of the chain conformational free energy. In one it is calculated using a detailed mean‐field molecular theory. The other is based on a simple ‘‘compression’’ model. Both models lead to similar conclusions. Expressing the bilayer free energy as a sum of its two monolayer contributions, a thermodynamic stability analysis is performed to examine the possibility of spontaneous vesicle formation. To this end, we expand the bilayer free energy as a power series (up to second order) in terms of the monolayer curvatures, their amphiphilic compositions and the av...