Ideses Y, Brill-Karniely Y, Haviv L, Ben-Shaul A, Bernheim-Groswasser A. Arp2/3 Branched Actin Network Mediates Filopodia-Like Bundles Formation In Vitro. PLOS ONE. 2008;3.Abstract

During cellular migration, regulated actin assembly takes place at the cell leading edge, with continuous disassembly deeper in the cell interior. Actin polymerization at the plasma membrane results in the extension of cellular protrusions in the form of lamellipodia and filopodia. To understand how cells regulate the transformation of lamellipodia into filopodia, and to determine the major factors that control their transition, we studied actin self-assembly in the presence of Arp2/3 complex, WASp-VCA and fascin, the major proteins participating in the assembly of lamellipodia and filopodia. We show that in the early stages of actin polymerization fascin is passive while Arp2/3 mediates the formation of dense and highly branched aster-like networks of actin. Once filaments in the periphery of an aster get long enough, fascin becomes active, linking the filaments into bundles which emanate radially from the aster's surface, resulting in the formation of star-like structures. We show that the number of bundles nucleated per star, as well as their thickness and length, is controlled by the initial concentration of Arp2/3 complex ([Arp2/3]). Specifically, we tested several values of [Arp2/3] and found that for given initial concentrations of actin and fascin, the number of bundles per star, as well as their length and thickness are larger when [Arp2/3] is lower. Our experimental findings can be interpreted and explained using a theoretical scheme which combines Kinetic Monte Carlo simulations for aster growth, with a simple mechanistic model for bundles' formation and growth. According to this model, bundles emerge from the aster's (sparsely branched) surface layer. Bundles begin to form when the bending energy associated with bringing two filaments into contact is compensated by the energetic gain resulting from their fascin linking energy. As time evolves the initially thin and short bundles elongate, thus reducing their bending energy and allowing them to further associate and create thicker bundles, until all actin monomers are consumed. This process is essentially irreversible on the time scale of actin polymerization. Two structural parameters, L, which is proportional to the length of filament tips at the aster periphery and b, the spacing between their origins, dictate the onset of bundling; both depending on [Arp2/3]. Cells may use a similar mechanism to regulate filopodia formation along the cell leading edge. Such a mechanism may allow cells to have control over the localization of filopodia by recruiting specific proteins that regulate filaments length (e. g., Dia2) to specific sites along lamellipodia.

Tzlil S, Murray D, Ben-Shaul A. The ``Electrostatic-Switch'' mechanism: Monte Carlo study of MARCKS-membrane interaction. BIOPHYSICAL JOURNAL. 2008;95 :1745-1757.Abstract

The binding of the myristoylated alanine-rich C kinase substrate (MARCKS) to mixed, fluid, phospholipid membranes is modeled with a recently developed Monte Carlo simulation scheme. The central domain of MARCKS is both basic (zeta = +13) and hydrophobic (five Phe residues), and is flanked with two long chains, one ending with the myristoylated N-terminus. This natively unfolded protein is modeled as a flexible chain of ``beads'' representing the amino acid residues. The membranes contain neutral (zeta = 0), monovalent (zeta = -1), and tetravalent (zeta = -4) lipids, all of which are laterally mobile. MARCKS-membrane interaction is modeled by Debye-Huckel electrostatic potentials and semiempirical hydrophobic energies. In agreement with experiment, we find that membrane binding is mediated by electrostatic attraction of the basic domain to acidic lipids and membrane penetration of its hydrophobic moieties. The binding is opposed by configurational entropy losses and electrostatic membrane repulsion of the two long chains, and by lipid demixing upon adsorption. The simulations provide a physical model for how membrane-adsorbed MARCKS attracts several PIP2 lipids (zeta = -4) to its vicinity, and how phosphorylation of the central domain (zeta = +13 to zeta = +7) triggers an ``electrostatic switch'', which weakens both the membrane interaction and PIP(2) sequestration. This scheme captures the essence of ``discreteness of charge'' at membrane surfaces and can examine the formation of membrane-mediated multicomponent macromolecular complexes that function in many cellular processes.

Teif VB, Harries D, Lando DY, Ben-Shaul A. Matrix formalism for site-specific binding of unstructured proteins to multicomponent lipid membranes. JOURNAL OF PEPTIDE SCIENCE. 2008;14 :368-373.Abstract

We describe a new approach to calculate the binding of flexible peptides and unfolded proteins to multicomponent lipid membranes. The method is based on the transfer matrix formalism of statistical mechanics recently described as a systematic tool to study DNA-protein-drug binding in gene regulation. Using the energies of interaction of the individual polymer segments with different membrane lipid species and the scaling corrections due to polymer looping, we calculate polymer adsorption characteristics and the degree of sequestration of specific membrane lipids. The method is applied to the effector domain of the MARCKS (myristoylated alanine rich C kinase substrate) protein known to be involved in signal transduction through membrane binding. The calculated binding constants of the MARCKS(151-175) peptide and a series of related peptides to mixed PC/PS/PIP2 membranes are in satisfactory agreement with in vitro experiments. Copyright (c) 2008 European Peptide Society and John Wiley & Sons, Ltd.

Zemel A, Ben-Shaul A, May S. Modulation of the spontaneous curvature and bending rigidity of lipid membranes by interfacially adsorbed amphipathic peptides. JOURNAL OF PHYSICAL CHEMISTRY B. 2008;112 :6988-6996.Abstract

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 peptide's 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 peptide's 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.

Yoffe AM, Prinsen P, Gopal A, Knobler CM, Gelbart WM, Ben-Shaul A. Predicting the sizes of large RNA molecules. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. 2008;105 :16153-16158.Abstract

We present a theory of the dependence on sequence of the three-dimensional size of large single-stranded (ss) RNA molecules. The work is motivated by the fact that the genomes of many viruses are large ssRNA molecules-often several thousand nucleotides long-and that these RNAs are spontaneously packaged into small rigid protein shells. We argue that there has been evolutionary pressure for the genome to have overall spatial properties-including an appropriate radius of gyration, R-g-that facilitate this assembly process. For an arbitrary RNA sequence, we introduce the (thermal) average maximum ladder distance (< MLD >) and use it as a measure of the ``extendedness'' of the RNA secondary structure. The < MLD > values of viral ssRNAs that package into capsids of fixed size are shown to be consistently smaller than those for randomly permuted sequences of the same length and base composition, and also smaller than those of natural ssRNAs that are not under evolutionary pressure to have a compact native form. By mapping these secondary structures onto a linear polymer model and by using < MLD > as a measure of effective contour length, we predict the R-g values of viral ssRNAs are smaller than those of nonviral sequences. More generally, we predict the average < MLD > values of large nonviral ssRNAs scale as N-0.67 +/- 0.01, where N is the number of nucleotides, and that their R-g values vary as < MLD >(0.5) in an ideal solvent, and hence as N-0.34. An alternative analysis, which explicitly includes all branches, is introduced and shown to yield consistent results.

Haviv L, Brill-Karniely Y, Mahaffy R, Backouche F, Ben-Shaul A, Pollard TD, Bernheim-Groswasser A. Reconstitution of the transition from lamellipodium to filopodium in a membrane-free system. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. 2006;103 :4906-4911.Abstract

The cellular cytoskeleton is a complex dynamical network that constantly remodels as cells divide and move. This reorganization process occurs not only at the cell membrane, but also in the cell interior (bulk). During locomotion, regulated actin assembly near the plasma membrane produces lamellipodia and filopodia. Therefore, most in vitro experiments explore phenomena taking place in the vicinity of a surface. To understand how the molecular machinery of a cell self-organizes in a more general way, we studied bulk polymerization of actin in the presence of actin-related protein 2/3 complex and a nucleation promoting factor as a model for actin assembly in the cell interior separate from membranes. Bulk polymerization of actin in the presence of the verprolin homology, cofilin homology, and acidic region, domain of Wiskott-Aldrich syndrome protein, and actin-related protein 2/3 complex results in spontaneous formation of diffuse aster-like structures. In the presence of fascin these asters transition into stars with bundles of actin filaments growing from the surface, similar to star-like structures recently observed in vivo. The transition from asters to stars depends on the ratio [fascin]/[G actin]. The polarity of the actin filaments during the transition is preserved, as in the transition from lamellipodia to filopodia. Capping protein inhibits star formation. Based on these experiments and kinetic Monte Carlo simulations, we propose a model for the spontaneous self-assembly of asters and their transition into stars. This mechanism may apply to the transition from lamellipodia to filopodia in vivo.

Mbamala EC, Ben-Shaul A, May S. Domain formation induced by the adsorption of charged proteins on mixed lipid membranes. BIOPHYSICAL JOURNAL. 2005;88 :1702-1714.Abstract

Peripheral proteins can trigger the formation of domains in mixed. uid- like lipid membranes. We analyze the mechanism underlying this process for proteins that bind electrostatically onto a. at two- component membrane, composed of charged and neutral lipid species. Of particular interest are membranes in whichthe hydrocarbon lipid tails tend to segregate owing to nonideal chain mixing,but the ( protein- free) lipid membrane is nevertheless stable due to the electrostatic repulsion between the charged lipid headgroups. The adsorption of charged, say basic, proteins onto a membrane containing anionic lipids induces local lipid demixing, whereby charged lipids migrate toward ( or away from) the adsorption site, so as to minimize the electrostatic binding free energy. Apart from reducing lipid headgroup repulsion, this process creates a gradient in lipid composition around the adsorption zone, and hence a line energy whose magnitude depends on the protein's size and charge and the extent of lipid chain nonideality. Above a certain critical lipid nonideality, the line energy islarge enough to induce domain formation, i. e., protein aggregation and, concomitantly, macroscopic lipid phase separation. We quantitatively analyze the thermodynamic stability of the dressed membrane based on nonlinear Poisson- Boltzmann theory, accounting for both the microscopic characteristics of the proteins and lipid composition modulations at and around the adsorption zone. Spinodal surfaces and critical points of the dressed membranes are calculated for several different model proteins of spherical and disklike shapes. Among the models studied we. nd the most substantial protein- induced membrane destabilization for disk- like proteins whose charges are concentrated in the membrane- facing surface. If additional charges reside on the side faces of the proteins, direct protein- protein repulsion diminishes considerably the propensity fordomain formation. Generally, a highly charged. at face of a macroion appears most ef. cient in inducing large compositional gradients, hence a large and unfavorable line energy and consequently lateral macroion aggregation and, concomitantly, macroscopic lipid phase separation.

Tzlil S, Ben-Shaul A. Flexible charged macromolecules on mixed fluid lipid membranes: Theory and Monte Carlo simulations. BIOPHYSICAL JOURNAL. 2005;89 :2972-2987.Abstract

Fluid membranes containing charged lipids enhance binding of oppositely charged proteins by mobilizing these lipids into the interaction zone, overcoming the concomitant entropic losses due to lipid segregation and lower conformational freedom upon macromolecule adsorption. We study this energetic-entropic interplay using Monte Carlo simulations and theory. Our model system consists of a flexible cationic polyelectrolyte, interacting, via Debye-Huckel and short-ranged repulsive potentials, with membranes containing neutral lipids, 1% tetravalent, and 10% ( or 1%) monovalent anionic lipids. Adsorption onto a fluid membrane is invariably stronger than to an equally charged frozen or uniform membrane. Although monovalent lipids may suffice for binding rigid macromolecules, polyvalent counter-lipids ( e. g., phosphatidylinositol 4,5 bisphosphate), whose entropy loss upon localization is negligible, are crucial for binding flexible macromolecules, which lose conformational entropy upon adsorption. Extending Rosenbluth's Monte Carlo scheme we directly simulate polymer adsorption on fluid membranes. Yet, we argue that similar information could be derived from a biased superposition of quenched membrane simulations. Using a simple cell model we account for surface concentration effects, and show that the average adsorption probabilities on annealed and quenched membranes coincide at vanishing surface concentrations. We discuss the relevance of our model to the electrostatic-switch mechanism of, e. g., the myristoylated alanine-rich C kinase substrate protein.

Zemel A, Ben-Shaul A, May S. Perturbation of a lipid membrane by amphipathic peptides and its role in pore formation. EUROPEAN BIOPHYSICS JOURNAL WITH BIOPHYSICS LETTERS. 2005;34 :230-242.Abstract

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.

Chen CP, Posy S, Ben-Shaul A, Shapiro L, Honig BH. Specificity of cell-cell adhesion by classical cadherins: Critical role for low-affinity dimerization through beta-strand swapping. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. 2005;102 :8531-8536.Abstract

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.

Harries D, Ben-Shaul A, Szleifeo I. Enveloping of charged proteins by lipid bilayers. JOURNAL OF PHYSICAL CHEMISTRY B. 2004;108 :1491-1496.Abstract

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.

Zemel A, Ben-Shaul A, May S. Membrane perturbation induced by interfacially adsorbed peptides. BIOPHYSICAL JOURNAL. 2004;86 :3607-3619.Abstract

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.

May S, Ben-Shaul A. Modeling of cationic lipid-DNA complexes. CURRENT MEDICINAL CHEMISTRY. 2004;11 :151-167.Abstract

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.

Tzlil S, Deserno M, Gelbert WM, Ben-Shaul A. A statistical-thermodynamic model of viral budding. BIOPHYSICAL JOURNAL. 2004;86 :2037-2048.Abstract

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.

May S, Kozlovsky Y, Ben-Shaul A, Kozlov MM. Tilt modulus of a lipid monolayer. EUROPEAN PHYSICAL JOURNAL E. 2004;14 :299-308.Abstract

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).

May S, Ben-Shaul A. Membrane-Macromolecule Interactions and their Structural Consequences. In: Tien HT, Ottowa-Leitmanova AL Planar Lipid Bilayers (BLM's) and their Applications. Vol. 7. 1st ed. Amsterdam: Elsevier Science ; 2003. pp. 315-346. 2003.smabs_adobetien.pdf
Harries D, May S, Ben-Shaul A. Curvature and charge modulations in lamellar DNA-lipid complexes. JOURNAL OF PHYSICAL CHEMISTRY B. 2003;107 :3624-3630.Abstract

To model the possible formation of coupled spatial corrugations and charge density modulations in lamellar DNA-lipid complexes, we use a free energy functional which includes the electrostatic, lipid mixing, and elastic degrees of freedom in a self-consistent manner. We find that the balance of forces favors membrane corrugations that are expected to be stable with respect to thermal membrane undulations for a certain range of lipid (charged and uncharged) composition. This may lead to locking between DNA strands in adjacent galleries of the complex. Furthermore, the possibility of membrane corrugations renders the lamellar complex more stable with respect to another, hexagonal, DNA-lipid phase.

Zemel A, Fattal DR, Ben-Shaul A. Energetics and self-assembly of amphipathic peptide pores in lipid membranes. BIOPHYSICAL JOURNAL. 2003;84 :2242-2255.Abstract

We present a theoretical study of the energetics, equilibrium size, and size distribution of membrane pores composed of electrically charged amphipathic peptides. The peptides are modeled as cylinders (mimicking alpha-helices) carrying different amounts of charge, with the charge being uniformly distributed over a hydrophilic face, defined by the angle subtended by polar amino acid residues. The free energy of a pore of a given radius, R, and a given number of peptides, s, is expressed as a sum of the peptides' electrostatic charging energy (calculated using Poisson-Boltzmann theory), and the lipid-perturbation energy associated with the formation of a membrane rim (which we model as being semitoroidal) in the gap between neighboring peptides. A simple phenomenological model is used to calculate the membrane perturbation energy. The balance between the opposing forces (namely, the radial free energy derivatives) associated with the electrostatic free energy that favors large R, and the membrane perturbation term that favors small R, dictates the equilibrium properties of the pore. Systematic calculations are reported for circular pores composed of various numbers of peptides, carrying different amounts of charge (1-6 elementary, positive charges) and characterized by different polar angles. We find that the optimal R's, for all (except, possibly, very weakly) charged peptides conform to the ``toroidal'' pore model, whereby a membrane rim larger than similar to1 nm intervenes between neighboring peptides. Only weakly charged peptides are likely to form ``barrel-stave'' pores where the peptides essentially touch one another. Treating pore formation as a two-dimensional self-assembly phenomenon, a simple statistical thermodynamic model is formulated and used to calculate pore size distributions. We find that the average pore size and size polydispersity increase with peptide charge and with the amphipathic polar angle. We also argue that the transition of peptides from the adsorbed to the inserted (membrane pore) state is cooperative and thus occurs rather abruptly upon a change in ambient conditions.

Tzlil S, Kindt JT, Gelbart WM, Ben-Shaul A. Forces and pressures in DNA packaging and release from viral capsids. BIOPHYSICAL JOURNAL. 2003;84 :1616-1627.Abstract

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 similar to1/3 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 capsid's 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.

Cordova A, Deserno M, Gelbart WM, Ben-Shaul A. Osmotic shock and the strength of viral capsids. BIOPHYSICAL JOURNAL. 2003;85 :70-74.Abstract

Osmotic shock is a familiar means for rupturing viral capsids and exposing their genomes intact. The necessary conditions for providing this shock involve incubation in high-concentration salt solutions, and lower permeability of the capsids to salt ions than to water molecules. We discuss here how values of the capsid strength can be inferred from calculations of the osmotic pressure differences associated with measured values of the critical concentration of incubation solution.