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The authors review recent advances in the physics of strongly interacting charged systems functioning in water at room temperature. In these systems, many phenomena go beyond the framework of mean-field theories, whether linear Debye-H\"uckel or nonlinear Poisson-Boltzmann, culminating in charge inversion---a counterintuitive phenomenon in which a strongly charged particle, called a macroion, binds so many counterions that its net charge changes sign. The review discusses the universal theory of charge inversion based on the idea of a strongly correlated liquid of adsorbed counterions, similar to a Wigner crystal. This theory has a vast array of applications, particularly in biology and chemistry; for example, in the presence of positive multivalent ions (e.g., polycations), the DNA double helix acquires a net positive charge and drifts as a positive particle in an electric field. This simplifies DNA uptake by the cell as needed for gene therapy, because the cell membrane is negatively charged. Analogies of charge inversion to other fields of physics are also discussed.

The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetra-valent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions., 4 pages, 3 figures, accepted for publication in Phys. Rev. Lett. (2010)

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

The problem of RNA genomes packaged inside spherical viruses is studied. The viral capsid is modeled as a hollowed sphere. The attraction between RNA molecules and the inner viral capsid is assumed to be non-specific and occurs at the inner capsid surface only. For small capsid attraction, it is found that monomer concentration of RNA molecules is maximum at the center of the capsid to maximize their configurational entropy. For stronger capsid attraction, RNA concentration peaks at some distance near the capsid. In the latter case, the competition between the branching of RNA secondary struture and its adsorption to the inner capsid results in the formation of a dense layer of RNA near capsid surface. The layer thickness is a slowly varying (logarithmic) function of the capsid inner radius. Consequently, for immediate strength of RNA-capsid interaction, the amount of RNA packaged inside a virus is proportional to the capsid {\em area} (or the number of proteins) instead of its volume. The numerical profiles describe reasonably well the experimentally observed RNA nucleotide concentration profiles of various viruses., Comment: 5 pages, 2 figures. Abstract, introduction rewritten. Comparison to actual virus profiles added. Submitted to PRL

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.

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of DMPC$-$POPG and DPPC$-$POPG surfactants. We suggested it has the same physics as the well-known Raleigh instability under the action of the bilayer surface tension whose magnitude is dictated by the electrostatic interaction between charged surfactants. In this paper, we calculate the relaxation of charge molecules during the deformation of the tubes into pearling structure. We find the functional dependence of the relaxation energy on the screening length $\kappa^{-1}$ explicitly. Relaxation effect lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for weak screening case where the tube radius is smaller than the screening length of the solution, this relaxation effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show this relaxation effect remains small. It gives less than 20% contribution to the total electrostatic energy., Comment: 7 pages, 3 figures, to be submitted to PRE

We present a model supported by simulation to explain the effect of temperature on the conduction threshold in disordered systems. Arrays with randomly distributed local thresholds for conduction occur in systems ranging from superconductors to metal nanocrystal arrays. Thermal fluctuations provide the energy to overcome some of the local thresholds, effectively erasing them as far as the global conduction threshold for the array is concerned. We augment this thermal energy reasoning with percolation theory to predict the temperature at which the global threshold reaches zero. We also study the effect of capacitive nearest-neighbor interactions on the effective charging energy. Finally, we present results from Monte Carlo simulations that find the lowest-cost path across an array as a function of temperature. The main result of the paper is the linear decrease of conduction threshold with increasing temperature: $V_t(T) = V_t(0) (1 - 4.8 k_BT P(0)/ p_c) $, where $1/P(0)$ is an effective charging energy that depends on the particle radius and interparticle distance, and $p_c$ is the percolation threshold of the underlying lattice. The predictions of this theory compare well to experiments in one- and two-dimensional systems., 14 pages, 10 figures, submitted to PRB

Adsorption of multivalent counterions on the charged surface of a macroion is known to lead to inversion of the macroion charge due to the strong lateral correlations of counterions. We consider a nontrivial role of the excluded volume of counterions on this effect. It is shown analytically that when the bare charge of the macroion increases, its net charge including the adsorbed counterions oscillates with the number of their layers. Charge inversion vanishes every time the top layer of counterions is completely full and becomes incompressible. These oscillations of charge inversion are confirmed by Monte Carlo simulations. Another version of this phenomenon is studied for a metallic electrode screened by multivalent counterions when the potential of the electrode is controlled instead of its charge. In this case, oscillations of the compressibility and charge inversion lead to oscillations of capacitance of this electrode with the number of adsorbed layers of multivalent counterions.