Smectic viral capsids and the aneurysm instability.

The capsids of certain Archaea-infecting viruses undergo large shape changes, while maintaining their integrity against rupture by osmotic pressure. We propose that these capsids are in a smectic liquid crystalline state, with the capsid proteins assembling along spirals. We show that smectic capsids are intrinsically stabilized against the formation of localized bulges with non-zero Gauss curvature while still allowing for large-scale cooperative shape transformation that involves global changes in the Gauss curvature.

Useful scars: Physics of the capsids of archaeal viruses.

We propose a physical model for the capsids of tailed archaeal viruses as viscoelastic membranes under tension. The fluidity is generated by thermal motion of scarlike structures that are an intrinsic feature of the ground state of large particle arrays covering surfaces with nonzero Gauss curvature. The tension is generated by a combination of the osmotic pressure of the enclosed genome and an extension force generated by filamentous structure formation that drives the formation of the tails. In continuum theory, the capsid has the shape of a surface of constant mean curvature: an unduloid. Particle arrays covering unduloids are shown to exhibit pronounced subdiffusive and diffusive single-particle transport at temperatures that are well below the melting temperature of defect-free particle arrays on a surface with zero Gauss curvature.

Equilibrium self-assembly of small RNA viruses.

We propose a description for the quasiequilibrium self-assembly of small, single-stranded (ss) RNA viruses whose capsid proteins (CPs) have flexible, positively charged, disordered tails that associate with the negatively charged RNA genome molecules. We describe the assembly of such viruses as the interplay between two coupled phase-transition-like events: the formation of the protein shell (the capsid) by CPs and the condensation of a large ss viral RNA molecule. Electrostatic repulsion between the CPs competes with attractive hydrophobic interactions and attractive interaction between neutralized RNA segments mediated by the tail groups. An assembly diagram is derived in terms of the strength of attractive interactions between CPs and between CPs and the RNA molecules. It is compared with the results of recent studies of viral assembly. We demonstrate that the conventional theory of self-assembly, which does describe the assembly of empty capsids, is in general not applicable to the self-assembly of RNA-encapsidating virions.

Statistical Physics of Viral Capsids with Broken Symmetry.

We present a model to understand quantitatively the role of symmetry breaking in assembly of macromolecular aggregates in general, and the protein shells of viruses in particular. A simple dodecahedral lattice model with a quadrupolar order parameter allows us to demonstrate how symmetry breaking may reduce the probability of assembly errors and, consequently, enhance assembly efficiency. We show that the ground state is characterized by large-scale cooperative zero-energy modes. In analogy with other models, this suggests a general physical principle: the tendency of biological molecules to generate symmetric structures competes with the tendency to break symmetry in order to achieve specific functional goals.

Elasticity theory of macromolecular aggregates.

We present a version of continuum elasticity theory applicable to aggregates of functional biomolecules at length scales comparable to that of the component molecules. Unlike classical elasticity theory, the stress and strain fields have mathematical discontinuities along the interfaces of the macromolecules, due to conformational incompatibility and large scale conformational transitions. The method is applied to the P-II to EI shape transition of the protein shell of the virus HK97. We show that protein residual stresses generated by incompatibility drive a "reverse buckling" transition from an icosahedral to a dodecahedral shape via a "critical" spherical shape, which can be identified as the P-II state.

Continuum theory of lipid bilayer electrostatics.

In order to address the concerns about the applicability of the continuum theory of lipid bilayers, we generalize it by including a film with uniaxial dielectric properties representing the polar head groups of the lipid molecules. As a function of the in-plane dielectric constant κ|| of this film, we encounter a sequence of different phases. For low values of κ||, transmembrane pores have aqueous cores, ions are repelled by the bilayer, and the ion permeability of the bilayer is independent of the ion radius as in the existing theory. For increasing κ||, a threshold is reached--of the order of the dielectric constant of water--beyond which ions are attracted to the lipid bilayer by generic polarization attraction, transmembrane pores collapse, and the ion permeability becomes sensitively dependent on the ion radius, results that are more consistent with experimental and numerical studies of the interaction of ions with neutral lipid bilayers. At even higher values of κ||, the ion/pore complexes are predicted to condense in the form of extended arrays. The generalized continuum theory can be tested quantitatively by studies of the ion permeability as a function of salt concentration and co-surfactant concentration.

Structural transitions of encapsidated polyelectrolytes.

Conformations and structural transitions of polyelectrolytes strictly confined onto a spherical 2D surface have been investigated by scaling descriptions based on physical arguments concerning polyelectrolyte adsorption onto planar surface and liquid crystals as well as by Monte Carlo simulations using a bead-spring model with short-range and electrostatic repulsions. In case of the electrostatic screened regime, a disordered-ordered (spiral) transition at increasing persistence length of the chain was found. It was predicted that the transition occurred when the persistence length is comparable with the mean spacing between adjacent strands of the ordered chain. The presence of a non-screened electrostatic repulsion led to a more complex behavior with i) a re-entrant order-disorder transition and ii) a tennis ball texture as an additional smectic/nematic structure. The various competing structures given by the theory were recovered by the Monte Carlo simulations, which also indicated that the tennis ball texture was favored over the spiral structure by the long-range interactions for semi-flexible chains.

Continuum theory of retroviral capsids.

We present a self-assembly phase diagram for the shape of retroviral capsids, based on continuum elasticity theory. The spontaneous curvature of the capsid proteins drives a weakly first-order transition from spherical to spherocylindrical shapes. The conical capsid shape which characterizes the HIV-1 retrovirus is never stable under unconstrained energy minimization. Only under conditions of fixed volume and/or fixed spanning length can the conical shape be a minimum energy structure. Our results indicate that, unlike the capsids of small viruses, retrovirus capsids are not uniquely determined by the molecular structure of the constituent proteins but depend in an essential way on physical constraints present during assembly.

Physics of RNA and viral assembly.

The overview discusses the application of physical arguments to structure and function of single-stranded viral RNA genomes.

Structural polymorphism of DNA-dendrimer complexes.

DNA condensation in vivo relies on electrostatic complexation with small cations or large histones. We report a synchrotron x-ray study of the phase behavior of DNA complexed with synthetic cationic dendrimers of intermediate size and charge. We encounter unexpected structural transitions between columnar mesophases with in-plane square and hexagonal symmetries, as well as liquidlike disorder. The isoelectric point is a locus of structural instability. A simple model is proposed based on competing long-range electrostatic interactions and short-range entropic adhesion by counterion release.

Raft instability of biopolymer gels.

Following recent x-ray diffraction experiments by Wong, Li, and Safinya on biopolymer gels, we apply Onsager excluded volume theory to a nematic mixture of rigid rods and strong " pi/2" cross-linkers obtaining a long-ranged, highly anisotropic depletion attraction between the linkers. This attraction leads to breakdown of the percolation theory for this class of gels, to breakdown of Onsager's second-order virial method, and to formation of heterogeneities in the form of raftlike ribbons.

Polymer reptation and nucleosome repositioning.

We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem arises in the case of globular aggregates of proteins (histones) that are wound by DNA in the chromosomes of plants and animals; these beads (nucleosomes) are multiply wrapped and yet are able to reposition themselves over long distances, while remaining bound by the DNA chain.

Elastically driven linker aggregation between two semiflexible polyelectrolytes.

The behavior of mobile linkers connecting two semiflexible charged polymers, such as polyvalent counterions connecting DNA or F-actin chains, is studied theoretically. The chain bending rigidity induces an effective repulsion between linkers at large distances while the interchain electrostatic repulsion leads to an effective short-range interlinker attraction. We find a rounded phase transition from a dilute linker gas where the chains form large loops between linkers to a dense disordered linker fluid connecting parallel chains. The onset of chain pairing occurs within the rounded transition.

Spontaneous-curvature theory of clathrin-coated membranes.

Clathrin-coated membranes are precursors to coated vesicles in the receptor-mediated endocytic pathway. In this paper we present a physical model for the first steps of the transformation of a clathrin-coated membrane into a coated vesicle. The theory is based on in vitro cytoplasmic acidification experiments of Heuser (J. Cell Biol. 108:401-411) that suggest the transformation proceeds by changes in the chemical environment of the clathrin lattice, wherein the chemical environment determines the amount of intrinsic, or spontaneous, curvature of the network. We show that a necessary step of the transformation, formation of free pentagons in the clathrin network, can proceed via dislocation unbinding, driven by changes in the spontaneous curvature. Dislocation unbinding is shown to favor formation of coated vesicles that are quite small compared to those predicted by the current continuum theories, which do not include the topology of the clathrin lattice.

Structure of membrane surfactant and liquid crystalline smectic lamellar phases under flow.

Synchrotron x-ray scattering studies were performed to probe the nonequilibrium structures of two layered systems at high shear rates: the smectic-A phase of the thermotropic liquid crystal 4-cyano-4'-octylbiphenyl (8CB) and the lamellar L(alpha) phases of surfactant membranes composed of sodium dodecyl sulfate and pentanol. Whereas the lamellar surfactant phases oriented primarily with their layers parallel to the shearing plates, as expected intuitively, in the corresponding high shear regime, the smectic-A liquid crystalline material oriented with the layers perpendicular to the shearing plates. A careful numerical study revealed that this surprising layer orientation results from nonlinear dynamics of the liquid crystal director and is caused by the flow distortion of thermal fluctuations.