Spontaneous bilayer wrapping of virus particles by a phospholipid Langmuir monolayer.

We report here the spontaneous formation of lipid-bilayer-wrapped virus particles, following the injection of "naked" virus particles into the subphase of a Langmuir trough with a liquid monolayer of lipids at its air-water interface. The virus particles are those of the well-studied cowpea chlorotic mottle virus, CCMV, which are negatively charged at the pH 6 of the subphase; the lipids are a 9:1 mix of neutral DMPC and cationic CTAB molecules. Before adding CCMV particles to the subphase we establish the mixed lipid monolayer in its liquid-expanded state at a fixed pressure (17.5 mN/m) and average area-per-molecule of (41Å2). Keeping the total area fixed, the surface pressure is observed to decrease at about 15 h after adding the virus particles in the subphase; by 37 h it has dropped to zero, corresponding to essentially all the lipid molecules having been removed from the air-water interface. By collecting particles from the subphase and measuring their sizes by atomic force microscopy, we show that the virus particles have been wrapped by lipid bilayers (or by two lipid bilayers). These results can be understood in terms of thermal fluctuations and electrostatic interactions driving the wrapping of the anionic virus particles by the cationic lipids. Spontaneous acquisition by a virus particle of, first, a hydrophobic lipid monolayer envelope and, then, a hydrophilic lipid bilayer envelope, as it interacts from the subphase with an oppositely charged Langmuir monolayer.

Controlling the surface charge of simple viruses.

The vast majority of plant viruses are unenveloped, i.e., they lack a lipid bilayer that is characteristic of most animal viruses. The interactions between plant viruses, and between viruses and surfaces, properties that are essential for understanding their infectivity and to their use as bionanomaterials, are largely controlled by their surface charge, which depends on pH and ionic strength. They may also depend on the charge of their contents, i.e., of their genes or-in the instance of virus-like particles-encapsidated cargo such as nucleic acid molecules, nanoparticles or drugs. In the case of enveloped viruses, the surface charge of the capsid is equally important for controlling its interaction with the lipid bilayer that it acquires and loses upon leaving and entering host cells. We have previously investigated the charge on the unenveloped plant virus Cowpea Chlorotic Mottle Virus (CCMV) by measurements of its electrophoretic mobility. Here we examine the electrophoretic properties of a structurally and genetically closely related bromovirus, Brome Mosaic Virus (BMV), of its capsid protein, and of its empty viral shells, as functions of pH and ionic strength, and compare them with those of CCMV. From measurements of both solution and gel electrophoretic mobilities (EMs) we find that the isoelectric point (pI) of BMV (5.2) is significantly higher than that of CCMV (3.7), that virion EMs are essentially the same as those of the corresponding empty capsids, and that the same is true for the pIs of the virions and of their cleaved protein subunits. We discuss these results in terms of current theories of charged colloidal particles and relate them to biological processes and the role of surface charge in the design of new classes of drug and gene delivery systems.

Electrophoretic mobilities of a viral capsid, its capsid protein, and their relation to viral assembly.

The self-assembly of many viral capsids is dominated by protein-protein electrostatic interactions. To have a better understanding of this process, it is important to know how the protein and the capsid surface charges vary as a function of the pH and ionic strength. In this work, using phase analysis light scattering, we measured the electrophoretic mobility (EM) of the cowpea chlorotic mottle virus (CCMV), its capsid protein (CP), and a cleaved CP that lacks its basic terminus, as a function of pH and ionic strength. The EM measurements of the CP are difficult to carry out due to its tendency to self-assemble into capsids; we show how to circumvent this problem by appropriately changing the CP concentration. We found that the isoelectric points (pIs) of the virion and of the CP are insensitive to ionic strength. The onset of multishell structures in the phase diagram of the CCMV CP as a function of ionic strength and pH (and its absence in the brome mosaic virus (BMV) CP phase diagram) can be related to the pI of the capsid. We propose that the transition from multiwall shells to nanotube structures is due to a change in the spontaneous curvature of the CP at its pI. A nonzero limit of the EM at high ionic strength is characteristic of a soft colloid, but a near identity of the EMs of empty capsids and those containing RNA indicates that the EM reflects only the charge distribution in the CP. The Henry equation has been used to provide approximate values of the capsid surface charge as a function of pH and I.

Phase diagram of self-assembled viral capsid protein polymorphs.

We present an experimental study of the self-assembly of capsid proteins of the cowpea chlorotic mosaic virus (CCMV), in the absence of the viral genome, as a function of pH and ionic strength. In accord with previous measurements, a wide range of polymorphs can be identified by electron microscopy, among them single and multiwalled shells and tubes. The images are analyzed with respect to size and shape of aggregates, and evidence is given that equilibrium has been achieved, allowing a phase diagram to be constructed. Some previously unreported structures are also described. The range and stability of the polymorphs can be understood in terms of electrostatic interactions and the way they affect the spontaneous curvature of protein networks and the relative stabilities of pentamers and hexamers.

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.

Statics and dynamics of polymer-wrapped colloids.

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.

Osmotic force resisting chain insertion in a colloidal suspension.

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accommodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fractions of a few tenths. These magnitudes are argued to be important for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm.

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.

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.

DNA folding: structural and mechanical properties of the two-angle model for chromatin.

We present a theoretical analysis of the structural and mechanical properties of the 30-nm chromatin fiber. Our study is based on the two-angle model introduced by Woodcock et al. (Woodcock, C. L., S. A. Grigoryev, R. A. Horowitz, and N. Whitaker. 1993. Proc. Natl. Acad. Sci. USA. 90:9021-9025) that describes the chromatin fiber geometry in terms of the entry-exit angle of the nucleosomal DNA and the rotational setting of the neighboring nucleosomes with respect to each other. We analytically explore the different structures that arise from this building principle, and demonstrate that the geometry with the highest density is close to the one found in native chromatin fibers under physiological conditions. On the basis of this model we calculate mechanical properties of the fiber under stretching. We obtain expressions for the stress-strain characteristics that show good agreement with the results of recent stretching experiments (Cui, Y., and C. Bustamante. 2000. Proc. Natl. Acad. Sci. USA. 97:127-132) and computer simulations (Katritch, V., C. Bustamante, and W. K. Olson. 2000. J. Mol. Biol. 295:29-40), and which provide simple physical insights into correlations between the structural and elastic properties of chromatin.

DNA delivery by phage as a strategy for encapsulating toroidal condensates of arbitrary size into liposomes.

We report a strategy for encapsulating and condensing DNA. When T5 phage binds to its membrane protein receptor, FhuA, its double stranded DNA (120,000 bp) is progressively released base pair after base pair in the surrounding medium. Using cryoelectron microscopy, we have visualized the structures formed after T5 phage DNA is released into neutral unilamellar proteoliposomes reconstituted with the receptor FhuA. In the presence of spermine, toroidal condensates of circumferentially wrapped DNA were formed. Most significantly, the sizes of these toroids were shown to vary, from 90 to 200 nm in their outer diameters, depending on the number of DNA stands transferred. We have also analyzed T5 DNA release in bulk solution containing the detergent-solubilized FhuA receptor. After DNA release in a spermine containing solution, huge DNA condensates with a diameter of about 300 nm were formed containing the DNAs from as many as 10-20 capsids. At alkaline pH, the condensates appeared as large hollow cylinders with a diameter of 200 nm and a height of 100-200 nm. Overall, the striking feature of our experiments is that, because of the progressive release of DNA from the phage capsid, the mechanism of toroid formation is fundamentally different from that in the classical studies in which highly dilute, "naked" DNA is condensed by direct addition of polyvalent cations; as a consequence, our method leads to toroids of arbitrary size.

Comparative genomics of the eukaryotes.

A comparative analysis of the genomes of Drosophila melanogaster, Caenorhabditis elegans, and Saccharomyces cerevisiae-and the proteins they are predicted to encode-was undertaken in the context of cellular, developmental, and evolutionary processes. The nonredundant protein sets of flies and worms are similar in size and are only twice that of yeast, but different gene families are expanded in each genome, and the multidomain proteins and signaling pathways of the fly and worm are far more complex than those of yeast. The fly has orthologs to 177 of the 289 human disease genes examined and provides the foundation for rapid analysis of some of the basic processes involved in human disease.

Spontaneous patterning of quantum dots at the air-water interface.

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications.

Databases in genomic research.

Genome-related databases have already become an invaluable part of the scientific landscape. The role played by these databases will only increase as the volume and complexity of relevant biology data rapidly expand. We are far enough into the genome project and into the development of these databases to assess their attributes and to reexamine some of the conceptual organizations and approaches they are taking. It is clear that there are needs for both highly detailed and simplified database views, the latter being especially needed to make expert domain data more accessible to nonspecialists.

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.

Topological defects and the optimum size of DNA condensates.

Under a wide variety of conditions, the addition of condensing agents to dilute solutions of random-coil DNA gives rise to highly compact particles that are toroidal in shape. The size of these condensates is remarkably constant and is largely independent of DNA molecular weight and basepair sequence, and of the nature of condensing agent (e.g., multivalent cation, polymers, or added cosolvent). We show how this optimum size is determined by the interactions between topological defects, which unavoidably strain the circumferentially wound DNA strands in the torus.

Identification of chromosomal regions involved in decapentaplegic function in Drosophila.

Signaling molecules of the transforming growth factor beta (TGF-beta) family contribute to numerous developmental processes in a variety of organisms. However, our understanding of the mechanisms which regulate the activity of and mediate the response to TGF-beta family members remains incomplete. The product of the Drosophila decapentaplegic (dpp) locus is a well-characterized member of this family. We have taken a genetic approach to identify factors required for TGF-beta function in Drosophila by testing for genetic interactions between mutant alleles of dpp and a collection of chromosomal deficiencies. Our survey identified two deficiencies that act as maternal enhancers of recessive embryonic lethal alleles of dpp. The enhanced individuals die with weakly ventralized phenotypes. These phenotypes are consistent with a mechanism whereby the deficiencies deplete two maternally provided factors required for dpp's role in embryonic dorsal-ventral pattern formation. One of these deficiencies also appears to delete a factor required for dpp function in wing vein formation. These deficiencies remove material from the 54F-55A and 66B-66C polytene chromosomal regions, respectively. As neither of these regions has been previously implicated in dpp function, we propose that each of the deficiencies removes a novel factor or factors required for dpp function.

Mothers against dpp participates in a DDP/TGF-beta responsive serine-threonine kinase signal transduction cascade.

Mothers against dpp (Mad) is the prototype of a family of genes required for signaling by TGF-beta related ligands. In Drosophila, Mad is specifically required in cells responding to Decapentaplegic (DPP) signals. We further specify the role of Mad in DPP-mediated signaling by utilizing tkvQ199D, an activated form of the DPP type I receptor serine-threonine kinase thick veins (tkv). In the embryonic midgut, tkvQ199D mimics DPP-mediated inductive interactions. Homozygous Mad mutations block signaling by tkvQ199D. Appropriate responses to signaling by tkvQ199D are restored by expression of MAD protein in DPP-target cells. Endogenous MAD is phosphorylated in a ligand-dependent manner in Drosophila cell culture. DPP overexpression in the embryonic midgut induces MAD nuclear accumulation; after withdrawal of the overexpressed DPP signal, MAD is detected only in the cytoplasm. However, in three different tissues and developmental stages actively responding to endogenous DPP, MAD protein is detected in the cytoplasm but not in the nucleus. From these observations, we discuss possible roles for MAD in a DPP-dependent serine-threonine kinase signal transduction cascade integral to the proper interpretation of DPP signals.