Roi Asor

RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism.

Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using time-resolved small-angle X-ray scattering (TR-SAXS), we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly one-third complete within 35 ms, following a two-state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 10(9) M(-1) s(-1). The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.

The structure of ions and zwitterionic lipids regulates the charge of dipolar membranes.

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ∼10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.

Following the structural changes during zinc-induced crystallization of charged membranes using time-resolved solution X-ray scattering

Zinc ions are highly abundant in biological systems and interact with various enzymes, proteins and biomembranes. In this paper, an in-house state-of-the-art time-resolved solution X-ray scattering setup was used to study the interactions of divalent ions with charged membranes. We show that unlike calcium ions that strongly couple and crystallize charged membranes very rapidly, zinc ions exhibit a fast time scale (seconds) for the strong coupling of the bilayers and a much slower one (hours) for the 2D lateral crystallization of the bilayers. This is attributed to the smaller zinc ion size (compared to calcium ions), which requires higher energy to shed its hydration shells. The rate of crystallization depends on the structure of the lipid tails and is slower for the unsaturated lipid, DOPS, than the saturated lipid, DLPS. We attribute this to the stronger steric repulsion between unsaturated DOPS tails, which have kinks, and to the weaker cohesive electrostatic energy, induced by the zinc ions, due to the larger area per head-group of DOPS. The Avrami model for a 2D growth mechanism with an instantaneous nucleation describes well the crystallization process. The crystallization involves various structural changes in the bilayer structure and lipid conformations within each bilayer. In this paper, we present those structural changes as a function of time.

Effect of temperature on the structure of charged membranes.

Interactions between charged and neutral self-assembled phospholipid membranes are well understood and take into account temperature dependence. Yet, the manner in which the structure of the membrane is affected by temperature was hardly studied. Here we study the effect of temperature on the thickness, area per lipid, and volume per lipid of charged membranes. Two types of membranes were studied: membranes composed of charged lipids and dipolar (neutral) membranes that adsorbed divalent cations and became charged. Small-angle X-ray scattering data demonstrate that the thickness of charged membranes decreases with temperature. Wide-angle X-ray scattering data show that the area per headgroup increases with temperature. Intrinsically charged membranes linearly thin with temperature, whereas neutral membranes that adsorb divalent ions and become charged show an exponential decrease of their thickness. The data indicate that, on average, the tails shorten as the temperature rises. We attribute this behavior to higher lipid tail entropy and to the weaker electrostatic screening of the charged headgroups, by their counterions, at elevated temperatures. The latter effect leads to stronger electrostatic repulsion between the charged headgroups that increases the area per headgroup and decreases the bilayer thickness.

Effect of capsid confinement on the chromatin organization of the SV40 minichromosome

Using small-angle X-ray scattering, we determined the three-dimensional packing architecture of the minichromosome confined within the SV40 virus. In solution, the minichromosome, composed of closed circular dsDNA complexed in nucleosomes, was shown to be structurally similar to cellular chromatin. In contrast, we find a unique organization of the nanometrically encapsidated chromatin, whereby minichromosomal density is somewhat higher at the center of the capsid and decreases towards the walls. This organization is in excellent agreement with a coarse-grained computer model, accounting for tethered nucleosomal interactions under viral capsid confinement. With analogy to confined liquid crystals, but contrary to the solenoid structure of cellular chromatin, our simulations indicate that the nucleosomes within the capsid lack orientational order. Nucleosomes in the layer adjacent to the capsid wall, however, align with the boundary, thereby inducing a ‘molten droplet’ state of the chromatin. These findings indicate that nucleosomal interactions suffice to predict the genome organization in polyomavirus capsids and underscore the adaptable nature of the eukaryotic chromatin architecture to nanoscale confinement.

Entropic Attraction Condenses Like-Charged Interfaces Composed of Self-Assembled Molecules

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.

Effect of temperature on the interactions between dipolar membranes.

It is well-known that phospholipids in aqueous environment self-assemble into lamellar structures with a repeat distance governed by the interactions between them. Yet, the understanding of these interactions is incomplete. In this paper, we study the effect of temperature on the interlamellar interactions between dipolar membranes. Using solution small-angle X-ray scattering (SAXS), we measured the repeat distance between 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) bilayers at different temperatures and osmotic stresses. We found that when no pressure is applied the lamellar repeat distance, D, decreases and then increases with increasing temperature. As the osmotic stress increases, D decreases with temperature and then increases to a limited extent, until at sufficiently high pressure D decreases with temperature in all the examined range. We then reconstructed experimentally the equation of state and fit it with a modified interaction model that takes into account the temperature dependence of the fluctuation term. Finally, we showed how the thickness of DLPC membranes decreases with temperature.

Charged membranes under confinement induced by polymer-, salt-, or ionic liquid solutions

Osmotic pressure confines and decreases the lamellar distance between membranes in a stack and may also change the phase or structure of lipid bilayers. Using solution X-ray scattering, we determined the structure and interactions of saturated (DLPS) and unsaturated (DOPS) charged lipids under osmotic stress, generated by osmolyte solutions consisting of polyethylene glycol (PEG), NaCl, or the ionic liquid EMIES. The measured pressure–distance curves were fit to the theoretical free energy of charged liquid membranes that included numerical solutions of the Poisson–Boltzmann theory, modified to account for nonelectrostatic interactions between counterions and the surface and between lipid molecules on the surface. Charged membranes exhibit a non-ideal swelling behaviour that is consistent with partial melting of the lamellar phase into a coexisting, disordered phase. The disordered phase applies an osmotic stress to the lamellar phase and decreases the spacing between bilayers in the lamellar phase. We showed that in pure water, the pressure of the disordered phase increased with the lipid volume fraction or temperature. Addition of osmolytes reduced the lamellar spacing. The numerical solutions that fit the data showed that at the critical osmolyte concentration, a small, sharp drop in the water spacing between bilayers is expected owing to massive adsorption of the counterions onto the membrane. The adsorption increases with the osmolyte concentration, and is accompanied by a lateral phase separation into domains of neutral (counterion adsorbing) and charged (non-adsorbing) lipid molecules. In the case of the ionic liquid, this transition was followed by a liquid-to-crystal phase transition of the bilayers. With NaCl the transition to the crystal phase required a significantly higher osmolyte concentration. In the crystal phase that was induced by the ionic liquid, the lipid molecules were more tilted than in the crystal phase formed by NaCl. A further increase of the ionic liquid concentration melted the lipid crystal phase into the gel phase.

Reciprocal Grids: A Hierarchical Algorithm for Computing Solution X-ray Scattering Curves from Supramolecular Complexes at High Resolution

In many biochemical processes large biomolecular assemblies play important roles. X-ray scattering is a label-free bulk method that can probe the structure of large self-assembled complexes in solution. As we demonstrate in this paper, solution X-ray scattering can measure complex supramolecular assemblies at high sensitivity and resolution. At high resolution, however, data analysis of larger complexes is computationally demanding. We present an efficient method to compute the scattering curves from complex structures over a wide range of scattering angles. In our computational method, structures are defined as hierarchical trees in which repeating subunits are docked into their assembly symmetries, describing the manner subunits repeat in the structure (in other words, the locations and orientations of the repeating subunits). The amplitude of the assembly is calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the grids of larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures, we developed a hybrid method that sums grids of smaller subunits in order to avoid numerical artifacts. We developed protocols for obtaining high-resolution solution X-ray scattering data from taxol-free microtubules at a wide range of scattering angles. We then validated our method by adequately modeling these high-resolution data. The higher speed and accuracy of our method, over existing methods, is demonstrated for smaller structures: short microtubule and tobacco mosaic virus. Our algorithm may be integrated into various structure prediction computational tools, simulations, and theoretical models, and provide means for testing their predicted structural model, by calculating the expected X-ray scattering curve and comparing with experimental data.

Crystallization, Reentrant Melting, and Resolubilization of Virus Nanoparticles

Crystallization is a fundamental and ubiquitous process that is well understood in the case of atoms or small molecules, but its outcome is still hard to predict in the case of nanoparticles or macromolecular complexes. Controlling the organization of virus nanoparticles into a variety of 3D supramolecular architectures is often done by multivalent ions and is of great interest for biomedical applications such as drug or gene delivery and biosensing, as well as for bionanomaterials and catalysis. In this paper, we show that slow dialysis, over several hours, of wild-type Simian Virus 40 (wt SV40) nanoparticle solution against salt solutions containing MgCl2, with or without added NaCl, results in wt SV40 nanoparticles arranged in a body cubic center crystal structure with Im3m space group, as a thermodynamic product, in coexistence with soluble wt SV40 nanoparticles. The nanoparticle crystals formed above a critical MgCl2 concentrations. Reentrant melting and resolubilization of the virus nanoparticles took place when the MgCl2 concentrations passed a second threshold. Using synchrotron solution X-ray scattering we determined the structures and the mass fraction of the soluble and crystal phases as a function of MgCl2 and NaCl concentrations. A thermodynamic model, which balances the chemical potentials of the Mg2+ ions in each of the possible states, explains our observations. The model reveals the mechanism of both the crystallization and the reentrant melting and resolubilization and shows that counterion entropy is the main driving force for both processes.