Avinoam Ben-Shaul

Micelles, membranes, microemulsions, and monolayers

Contents: Statistical Thermodynamics of Amphiphile Self-Assembly (A. Ben-Shaul & W. Gelbart).- Micellar Growth, Flexibility and Polymorphism in Dilute Solutions (G. Porte).- Micellar Liquid Crystals (N. Boden).- Geometric Foundations of Mesomorphic Polymorphism (J. Charvolin & J.F. Sadoc).- Lamellar Phases: Effect of Fluctuations (Theory) (D. Sornette & N. Ostrowsky).- Lyotropic Lamellar Lx Phases (D. Roux, C.R. Safinya, & F. Nallet). Structure of Microemulsions: Experimenta (L. Auvray).- Lattice Theories of Microemulsions (G. Gompper & M. Schick).- Fluctuating Interfaces (S.A. Safran).- Interfacial Tension (D. Langevin & J. Meunier).- Critical Behavior of Surfactant Solutions (A-M. Bellocq).- Structures and Phase Transitions in Langmuir Monolayers (D. Andelman et al.).

DNA packaging and ejection forces in bacteriophage

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.

Molecular theory of curvature elasticity in surfactant films

We develop a microscopic‐level formulation for the curvature elasticity of monolayer and bilayer systems of typical surfactant molecules. It is argued that both the bending and saddle‐splay force constants k and k are determined primarily by the conformational entropy of the flexible hydrocarbon chain rather than by the electrostatic interactions associated with hydrophilic head groups. A priori estimates of the chain contributions are made for the first time, without the use of any adjustable parameters. Both k and k are shown to be calculable wholly from the conformational statistics describing the planar film. In particular, these constants are expressed in terms of the derivatives and moments of the lateral pressure profile characterizing chain packing in the unbent layers. By considering the dependence of the curvature elasticity on chain length, area per molecule, and composition in mixed films, we are able to account for the order‐of‐magnitude variations in k observed in a variety of different su...

The Extracellular Architecture of Adherens Junctions Revealed by Crystal Structures of Type I Cadherins

Adherens junctions, which play a central role in intercellular adhesion, comprise clusters of type I classical cadherins that bind via extracellular domains extended from opposing cell surfaces. We show that a molecular layer seen in crystal structures of E- and N-cadherin ectodomains reported here and in a previous C-cadherin structure corresponds to the extracellular architecture of adherens junctions. In all three ectodomain crystals, cadherins dimerize through a trans adhesive interface and are connected by a second, cis, interface. Assemblies formed by E-cadherin ectodomains coated on liposomes also appear to adopt this structure. Fluorescent imaging of junctions formed from wild-type and mutant E-cadherins in cultured cells confirm conclusions derived from structural evidence. Mutations that interfere with the trans interface ablate adhesion, whereas cis interface mutations disrupt stable junction formation. Our observations are consistent with a model for junction assembly involving strong trans and weak cis interactions localized in the ectodomain.

Forces and Pressures in DNA Packaging and Release from Viral Capsids

In a previous communication (Kindt et al., 2001) we reported preliminary results of Brownian dynamics simulation and analytical theory which address the packaging and ejection forces involving DNA in bacteriophage capsids. In the present work we provide a systematic formulation of the underlying theory, featuring the energetic and structural aspects of the strongly confined DNA. The free energy of the DNA chain is expressed as a sum of contributions from its encapsidated and released portions, each expressed as a sum of bending and interstrand energies but subjected to different boundary conditions. The equilibrium structure and energy of the capsid-confined and free chain portions are determined, for each ejected length, by variational minimization of the free energy with respect to their shape profiles and interaxial spacings. Numerical results are derived for a model system mimicking the lambda-phage. We find that the fully encapsidated genome is highly compressed and strongly bent, forming a spool-like condensate, storing enormous elastic energy. The elastic stress is rapidly released during the first stage of DNA injection, indicating the large force (tens of pico Newtons) needed to complete the (inverse) loading process. The second injection stage sets in when approximately 1/3 of the genome has been released, and the interaxial distance has nearly reached its equilibrium value (corresponding to that of a relaxed torus in solution); concomitantly the encapsidated genome begins a gradual morphological transformation from a spool to a torus. We also calculate the loading force, the average pressure on the capsids walls, and the anisotropic pressure profile within the capsid. The results are interpreted in terms of the (competing) bending and interaction components of the packing energy, and are shown to be in good agreement with available experimental data.

A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch.

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness dP, embedded in a lipid bilayer of unperturbed thickness doL. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when dP > doL) in order to bridge over the lipid-protein hydrophobic mismatch (dP-doL). The bilayers hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isometric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy delta F is calculated as a function of dP-doL. Most calculations are for C14 amphiphiles which, in the absence of a protein, pack at an average area per head-group ao approximately equal to 32 A2 (doL approximately 24.5 A), corresponding to the fluid state of the membrane. When dP = doL, delta F > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When dP > doL, the interaction free energy is further increased due to the enhanced stretching of the tails. When dP < doL, chain flexibility (entropy) increases, but this contribution to delta F is overcounted by the increase in the interfacial free energy. Thus, delta F obtains a minimum at dP-doL approximately 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the discussion.

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.

Transforming binding affinities from three dimensions to two with application to cadherin clustering

Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells and extracellular matrix proteins. For example, the association of membrane proteins with proteins on different cells (trans-interactions) can drive the oligomerization of proteins on the same cell (cis-interactions). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional solution and are thus difficult to relate to the two-dimensional environment of a membrane surface. Here we present a theoretical treatment that converts three-dimensional affinities to two dimensions, accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multiscale simulation approach, we apply the theory to explain the formation of ordered, junction-like clusters by classical cadherin adhesion proteins. The approach features atomic-scale molecular dynamics simulations to determine interdomain flexibility, Monte Carlo simulations of multidomain motion and lattice simulations of junction formation. A finding of general relevance is that changes in interdomain motion on trans-binding have a crucial role in driving the lateral, cis-, clustering of adhesion receptors.

Chain organization and thermodynamics in micelles and bilayers. I. Theory

Starting from the partition function of a micellar aggregate, the various assumptions involved in decomposing the aggregate’s standard chemical potential into surface and core terms are explicitly stated and discussed. The conformational statistics of the amphiphiles’ hydrocarbon chains (tails) composing the hydrophobic core is assumed to be governed by the hard core repulsive interactions between chain segments. The density within the core is assumed uniform and liquid‐like. By appropriate expansion of the aggregate’s configurational integral, explicit expressions are derived for the (singlet) distribution function of chain conformations and the chain’s conformational partition function (free energy). These quantities depend on the thickness and curvature (geometry) of the hydrophobic core via the lateral pressures representing the geometric packing constraints. (The same distribution function has been previously derived by us using the maximal entropy formalism.) It is argued that the variations in the ...

Linking molecular affinity and cellular specificity in cadherin-mediated adhesion

Many cell–cell adhesive events are mediated by the dimerization of cadherin proteins presented on apposing cell surfaces. Cadherin-mediated processes play a central role in the sorting of cells into separate tissues in vivo, but in vitro assays aimed at mimicking this behavior have yielded inconclusive results. In some cases, cells that express different cadherins exhibit homotypic cell sorting, forming separate cell aggregates, whereas in other cases, intermixed aggregates are formed. A third pattern is observed for mixtures of cells expressing either N- or E-cadherin, which form distinct homotypic aggregates that adhere to one another through a heterotypic interface. The molecular basis of cadherin-mediated cell patterning phenomena is poorly understood, in part because the relationship between cellular adhesive specificity and intermolecular binding free energies has not been established. To clarify this issue, we have measured the dimerization affinities of N-cadherin and E-cadherin. These proteins are similar in sequence and structure, yet are able to mediate homotypic cell patterning behavior in a variety of tissues. N-cadherin is found to form homodimers with higher affinity than does E-cadherin and, unexpectedly, the N/E-cadherin heterophilic binding affinity is intermediate in strength between the 2 homophilic affinities. We can account for observed cell aggregation behaviors by using a theoretical framework that establishes a connection between molecular affinities and cell–cell adhesive specificity. Our results illustrate how graded differences between different homophilic and heterophilic cadherin dimerizaton affinities can result in homotypic cell patterning and, more generally, show how proteins that are closely related can, nevertheless, be responsible for highly specific cellular adhesive behavior.