Kinetics of macroion coagulation induced by multivalent counterions

Deciphering the Assembly of Enveloped Viruses Using Model Lipid Membranes

The cell plasma membrane is mainly composed of phospholipids, cholesterol and embedded proteins, presenting a complex interface with the environment. It maintains a barrier to control matter fluxes between the cell cytosol and its outer environment. Enveloped viruses are also surrounded by a lipidic membrane derived from the host-cell membrane and acquired while exiting the host cell during the assembly and budding steps of their viral cycle. Thus, model membranes composed of selected lipid mixtures mimicking plasma membrane properties are the tools of choice and were used to decipher the first step in the assembly of enveloped viruses. Amongst these viruses, we choose to report the three most frequently studied viruses responsible for lethal human diseases, i.e., Human Immunodeficiency Type 1 (HIV-1), Influenza A Virus (IAV) and Ebola Virus (EBOV), which assemble at the host-cell plasma membrane. Here, we review how model membranes such as Langmuir monolayers, bicelles, large and small unilamellar vesicles (LUVs and SUVs), supported lipid bilayers (SLBs), tethered-bilayer lipid membranes (tBLM) and giant unilamellar vesicles (GUVs) contribute to the understanding of viral assembly mechanisms and dynamics using biophysical approaches.

Study of the conformation of polyelectrolyte aggregates using coarse-grained molecular dynamics simulations

The conformation of polyelectrolyte aggregates as a function of the backbone rigidity is investigated by coarse-grained molecular dynamics simulation. The polyelectrolyte is represented by a bead-spring chain with charged side chains. The simulations start from the uniform distributions of the polyelectrolytes, and the resultant polyelectrolyte conformation after a few microseconds exhibits spherical self-aggregates, clusters, or bending bundle-like aggregates, depending on the backbone rigidity. The interaggregate structures on a large scale are featured by the static structure factor (SSF). The simulated SSFs of the bending bundle-like aggregates are consistent with those of the small angle X-ray scattering (SAXS) measurement so we successfully assign the microscopic structures of polyelectrolytes to the SAXS measurement. The power-law of the SSFs for the bundle conditions is steeper than that of the conventional cylinder model. The present study finds that such discrepancy in the power-law results from the bending of the bundle-like aggregates. In addition, the relaxation behavior includes slow dynamics. The present study proposes that such slow dynamics results from diffusion-limited aggregation and from gliding processes to reduce local metastable folding within the aggregates.

Destabilization of colloidal suspensions by multivalent ions and polyelectrolytes: from screening to overcharging

The destabilization of charged colloidal suspensions is studied in the presence of polyelectrolytes and the corresponding oligomers. Two different systems are investigated, namely, negatively charged particles in the presence of polyamines and positively charged ones in the presence of polycarboxylates. Multivalent oligomers of low valence destabilize the particles by screening according to the Schulze-Hardy rule. Polyelectrolytes induce destabilization by overcharging. Both regimes can be observed for oligomers of intermediate valence. The stability data of any valence can be rather well described by the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO), indicating that the interactions are mainly governed by van der Waals and electrostatic double-layer forces.

Single-molecule stretching studies of RNA chaperones

RNA chaperone proteins play significant roles in diverse biological contexts. The most widely studied RNA chaperones are the retroviral nucleocapsid proteins (NC), also referred to as nucleic acid (NA) chaperones. Surprisingly, the biophysical properties of the NC proteins vary significantly for different viruses, and it appears that HIV-1 NC has optimal NA chaperone activity. In this review we discuss the physical nature of the NA chaperone activity of NC. We conclude that the optimal NA chaperone must saturate NA binding, leading to strong NA aggregation and slight destabilization of all NA duplexes. Finally, rapid kinetics of the chaperone protein interaction with NA is another primary component of its NA chaperone activity. We discuss these characteristics of HIV-1 NC and compare them with those of other NA binding proteins and ligands that exhibit only some characteristics of NA chaperone activity, as studied by single molecule DNA stretching.

Equilibrium polyelectrolyte bundles with different multivalent counterion concentrations

We present the results of molecular-dynamics simulations on the salt concentration dependence of the formation of polyelectrolyte bundles in thermodynamic equilibrium. Extending our results on salt-free systems we investigate here deficiency or excess of trivalent counterions in solution. Our results reveal that the trivalent counterion concentration significantly alters the bundle size and size distribution. The onset of bundle formation takes place at earlier Bjerrum length values with increasing trivalent counterion concentration. For the cases of 80%, 95%, and 100% charge compensation via trivalent counterions, the net charge of the bundles decreases with increasing size. We suggest that competition among two different mechanisms, counterion condensation and merger of bundles, leads to a nonmonotonic change in line-charge density with increasing Bjerrum length. The investigated case of having an abundance of trivalent counterions by 200% prohibits such a behavior. In this case, we find that the difference in effective line-charge density of different size bundles diminishes. In fact, the system displays an isoelectric point, where all bundles become charge neutral.

DNA release dynamics from bioreducible poly(amido amine) polyplexes

The DNA release dynamics of bioreducible poly(amido amine) polyplexes were studied in real time by atomic force microscopy (AFM). DNA release is triggered by a depolymerization of high-molecular-weight polycations into low-molecular-weight oligocations that occurs by means of the thiol and disulfide exchange reaction mechanism. AFM images were captured in a simulated physiological reducing environment that used dithiothreitol. Distinctive stages of disassembly are common among various polyplexes that have different disulfide content, molecular weight, and polymer architecture, while the DNA release rate depends upon the disulfide content. In the first stage, polyplexes evolve from metastable structures into the more stable toroid structure upon the depolymerization. In the second stage, toroids either aggregate or fuse into larger toroids. In the last stage, DNA wormlike chains and loops are held by a central compact core. The results confirm the prospect of bioreducible poly(amido amine)s as controlled DNA delivery vectors. The study offers new physical insights into the DNA release pathway including intermediate structures that have a high degree of structural heterogeneity and disassembly induced particle growth. The study identifies disassembly induced colloidal and morphological instability as an important issue to be addressed.

Salt-induced aggregation of stiff polyelectrolytes

Molecular dynamics simulation techniques are used to study the process of aggregation of highly charged stiff polyelectrolytes due to the presence of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one polyelectrolyte meeting others at right angles, and the kinetic pathway to bundle formation is found to be similar to that of flocculation dynamics of colloids as described by Smoluchowski. The aggregation process is found to favor the formation of finite bundles of 10-11 filaments at long times. Comparing the distribution of the cluster sizes with the Smoluchowski formula suggests that the energy barrier for the aggregation process is negligible. Also, the formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration.

Role of microtubules in stress granule assembly: microtubule dynamical instability favors the formation of micrometric stress granules in cells

Following exposure to various stresses (arsenite, UV, hyperthermia, and hypoxia), mRNAs are assembled into large cytoplasmic bodies known as "stress granules," in which mRNAs and associated proteins may be processed by specific enzymes for different purposes like transient storing, sorting, silencing, or other still unknown processes. To limit mRNA damage during stress, the assembly of micrometric granules has to be rapid, and, indeed, it takes only approximately 10-20 min in living cells. However, such a rapid assembly breaks the rules of hindered diffusion in the cytoplasm, which states that large cytoplasmic bodies are almost immobile. In the present work, using HeLa cells and YB-1 protein as a stress granule marker, we studied three hypotheses to understand how cells overcome the limitation of hindered diffusion: shuttling of small messenger ribonucleoprotein particles from small to large stress granules, sliding of messenger ribonucleoprotein particles along microtubules, microtubule-mediated stirring of large stress granules. Our data favor the two last hypotheses and underline that microtubule dynamic instability favors the formation of micrometric stress granules.

Polyelectrolyte-induced aggregation of liposomes: a new cluster phase with interesting applications

Different charged colloidal particles have been shown to be able to self-assemble, when mixed in an aqueous solvent with oppositely charged linear polyelectrolytes, forming long-lived finite-size mesoscopic aggregates. On increasing the polyelectrolyte content, with the progressive reduction of the net charge of the primary polyelectrolyte-decorated particles, larger and larger clusters are observed. Close to the isoelectric point, where the charge of the adsorbed polyelectrolytes neutralizes the original charge of the particles' surface, the aggregates reach their maximum size, while beyond this point any further increase of the polyelectrolyte-particle charge ratio causes the formation of aggregates whose size is progressively reduced. This re-entrant condensation behavior is accompanied by a significant overcharging. Overcharging, or charge inversion, occurs when more polyelectrolyte chains adsorb on a particle than are needed to neutralize its original charge so that, eventually, the sign of the net charge of the polymer-decorated particle is inverted. The stability of the finite-size long-lived clusters that this aggregation process yields results from a fine balance between long-range repulsive and short-range attractive interactions, both of electrostatic nature. For the latter, besides the ubiquitous dispersion forces, whose supply becomes relevant only at high ionic strength, the main contribution appears due to the non-uniform correlated distribution of the charge on the surface of the polyelectrolyte-decorated particles ('charge-patch' attraction). The interesting phenomenology shown by these system has a high potential for biotechnological applications, particularly when the primary colloidal particles are bio-compatible lipid vesicles. Possible applications of these systems as multi-compartment vectors for the simultaneous intra-cellular delivery of different pharmacologically active substances will be briefly discussed.

Model of human immunodeficiency virus budding and self-assembly: role of the cell membrane

Budding from the plasma membrane of the host cell is an indispensable step in the life cycle of the human immunodeficiency virus (HIV), which belongs to a large family of enveloped RNA viruses, retroviruses. Unlike regular enveloped viruses, retrovirus budding happens concurrently with the self-assembly of the main retrovirus protein subunits (called Gag protein after the name of the genetic material that codes for this protein: Group-specific AntiGen) into spherical virus capsids on the cell membrane. Led by this unique budding and assembly mechanism, we study the free energy profile of retrovirus budding, taking into account the Gag-Gag attraction energy and the membrane elastic energy. We find that if the Gag-Gag attraction is strong, budding always proceeds to completion. During early stage of budding, the zenith angle of partial budded capsids, alpha , increases with time as alpha proportional t1/2. However, if the Gag-Gag attraction is weak, a metastable state of partial budding appears. The zenith angle of these partially spherical capsids is given by alpha0 approximately (tau2/kappasigma)1/4 in a linear approximation, where kappa and sigma are the bending modulus and the surface tension of the membrane, and tau is a line tension of the capsid proportional to the strength of Gag-Gag attraction. Numerically, we find alpha0<0.3pi without any approximations. Using experimental parameters, we show that HIV budding and assembly always proceed to completion in normal biological conditions. On the other hand, by changing Gag-Gag interaction strength or membrane rigidity, it is relatively easy to tune it back and forth between complete budding and partial budding. Our model agrees reasonably well with experiments observing partial budding of retroviruses including HIV.

Aggregation kinetics of stiff polyelectrolytes in the presence of multivalent salt

Using molecular dynamics simulations, the kinetics of bundle formation for stiff polyelectrolytes such as actin is studied in the solution of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one rod meeting others at a right angle due to electrostatic interactions. The kinetic pathway to bundle formation involves a hierarchical structure of small clusters forming initially and then feeding into larger clusters, which is reminiscent of the flocculation dynamics of colloids. For the first few cluster sizes, the Smoluchowski formula for the time evolution of the cluster size gives a reasonable account of the results of our simulation without a single fitting parameter. The description using the Smoluchowski formula provides evidence for the aggregation time scale to be controlled by diffusion, with no appreciable energy barrier to overcome.

Toroidal DNA Condensates: Unraveling the Fine Structure and the Role of Nucleation in Determining Size

Toroidal DNA condensates have attracted the attention of biophysicists, biochemists, and polymer physicists for more than thirty years. In the biological community, the quest to understand DNA toroid formation has been motivated by its relevance to gene packing in certain viruses and by the potential use of DNA toroids in artificial gene delivery (e.g., gene therapy). In the physical sciences, DNA toroids are appreciated as a superb model system for studying particle formation by the collapse of a semiflexible, polyelectrolyte polymer. This review focuses on experimental studies from the past few years that have significantly increased our understanding of DNA toroid structure and the mechanism of their formation. Highlights include structural studies that show the DNA strands within toroids to be packed in an ideal hexagonal lattice, and also in regions with a nonhexagonal lattice that are required by the topological constraints associated with winding DNA into a toroid. Recent studies of DNA toroid formation have also revealed that toroid size limits result from a complex interplay between kinetic and thermodynamic factors that govern both toroid nucleation and growth. The work discussed in this review indicates that it will ultimately be possible to obtain substantial control over DNA toroid dimensions.

Charging and aggregation of latex particles by oppositely charged dendrimers

Poly(amidoamine) (PAMAM) dendrimers were shown to adsorb strongly on negatively charged latex particles, and their effect on the particle charge and aggregation behavior was investigated by light scattering and electrophoretic mobility measurements. Time-resolved simultaneous static and dynamic light scattering was used to measure absolute aggregation rate constants. With increasing dendrimer dose, the overall charge could be tuned from negative to positive values through the isoelectric point (IEP). The aggregation is fast near the IEP and slows down further away. With decreasing ionic strength, the region of fast aggregation narrows and the dependence of the aggregation rate on the dendrimer dose is more pronounced. Surface charge heterogeneities become important for higher dendrimer generations. They widen the fast aggregation region, reduce the dependence of the aggregation rate on the dendrimer dose, and lead to an acceleration of the rate in the fast aggregation regime near the IEP. The ratio of the dendrimer charge and the particle charge exceeds the stoichiometric ratio of unity substantially and further increases with increasing generation. The tentative interpretation of such superstoichiometric charge neutralization involves coadsorption of anions and the finite thickness of the adsorbed dendrimer layer.

Evidence That Both Kinetic and Thermodynamic Factors Govern DNA Toroid Dimensions: Effects of Magnesium(II) on DNA Condensation by Hexammine Cobalt(III)

Millimolar concentrations of divalent cations are shown to affect the size of toroids formed when DNA is condensed by multivalent cations. The origins of this effect were explored by varying the order in which MgCl(2) was added to a series of DNA condensation reactions with hexammine cobalt chloride. The interplay between Mg(II), temperature, and absolute cation concentration on DNA condensation was also investigated. These studies reveal that DNA condensation is extremely sensitive to whether Mg(II) is associated with DNA prior to condensation or Mg(II) is added concurrently with hexammine cobalt(III) at the time of condensation. It was also found that, in the presence of Mg(II), temperature and dilution can have opposite effects on the degree of DNA condensation. A systematic comparison of DNA condensates observed in this study clearly illustrates that, under our low-salt conditions, toroid size is determined by the kinetics of toroid nucleation and growth. However, when Mg(II) is present during condensation, toroid size can also be limited by a thermodynamic parameter (e.g., undercharging). The path dependence of DNA condensation presented here illustrates that regardless of which particular factors limit toroid growth, toroids formed under the various conditions of this study are largely nonequilibrium structures.