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.

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. [ACS Nano 4 (2010), 3853-3860] 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.

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.

Preparation of homogeneous endoderm cells and culture is a prerequisite to understanding the cellular and molecular mechanism of endosymbiosis in the cnidarian-dinoflagellate association. During the cell isolation from the stony coral Euphyllia glabrescens, various amounts of symbiotic endoderm cells were found to release their symbionts (Symbiodinium spp., or zooxanthellae in generic usage) into the culture. Due to the bulky occupation by zooxanthellae inside the endoderm cell, the symbiotic endoderm cells, or zooxanthellae in hospite, are difficult to be distinguished from released zooxanthellae by microscopic examination. We now report a method for this identification using a fluorescent analogue of sphingomyelin, N-[5-(5,7-dimethyl boron dipyrromethene difluoride)-1-pentanoyl]-D-erythro-sphingosylphosphorylcholine (C(5)-DMB-SM). Incubation of symbiotic endoderm cells with C(5)-DMB-SM-defatted bovine serum albumin (DF-BSA) complex results in bright fluorescent membrane staining. Nevertheless, the membrane staining of free-living or released zooxanthellae by this complex is significantly decreased or even diminished. This method has provided a fast and reliable assay to identify symbiotic endoderm cells and will greatly accelerate the progress of endosymbiosis research.