Impact of charge variation on the encapsulation of nanoparticles by virus coat proteins.

Electrostatic interaction is the driving force for the encapsulation by virus coat proteins of nanoparticles such as quantum dots, gold particles and magnetic beads for, e.g., imaging and therapeutic purposes. In recent experimental work, Daniel et al (2010 ACS Nano 4 3853-60) found the encapsulation efficiency to sensitively depend on the interplay between the surface charge density of negatively charged gold nanoparticles and the number of positive charges on the RNA binding domains of the proteins. Surprisingly, these experiments reveal that despite the highly cooperative nature of the co-assembly at low pH, the efficiency of encapsulation is a gradual function of their surface charge density. We present a simple all-or-nothing mass action law combined with an electrostatic interaction model to explain the experiments. We find quantitative agreement with experimental observations, supporting the existence of a natural statistical charge distribution between nanoparticles.

Fluctuation-induced forces between inclusions in a fluid membrane under tension.

We develop an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each object's shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.

Attachment and detachment rate distributions in deep-bed filtration.

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long-time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability, and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.

Role of charge regulation and size polydispersity in nanoparticle encapsulation by viral coat proteins.

Nanoparticles can be encapsulated by virus coat proteins if their surfaces are functionalized to acquire a sufficiently large negative charge. A minimal surface charge is required to overcome (i) repulsive interactions between the positively charged RNA-binding domains on the proteins and (ii) the loss of mixing and translational entropy of RNA and capsid coat proteins. Here, we present a model describing the encapsulation of spherical particles bearing weakly acidic surface groups and investigate how charge regulation and size polydispersity impact upon the encapsulation efficiency of gold nanoparticles by model coat proteins. We show that the surface charge density of these particles cannot be assumed fixed, but that it adjusts itself to minimize electrostatic repulsion between the charges on them and maximize the attractive interaction with the RNA binding domains on the proteins. Charge regulation in combination with the natural variation of particle radii has a large effect on the encapsulation efficiency: it makes it much more gradual despite its inherently cooperative nature. Our calculations rationalize recent experimental observations on the coassembly of gold nanoparticles by brome mosaic virus coat proteins.