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In this paper, we investigate the two-way communication between two users assisted by a re-configurable intelligent surface (RIS). The scheme that two users communicate simultaneously in the same time slot over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at $\left(\log(\rho)/\rho\right)^L$ rate where $L$ is the number of elements, whereas the spectral efficiency increases at $\log(\rho)$ rate at large average SINR $\rho$. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solutions are derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter is relaxed to be a semidefinite programming problem, whose optimal solution is achievable and serves as a sub-optimal solution.

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Size‐constrained gold nanoparticles are successfully synthesized within the cavity of native horse spleen ferritin by using a two‐step process relying on the initial formation of nanoclusters. The particles co‐elute with the nanocage ferritin by chromatography, indicating that the particles are associated with intact protein cages. Further characterization reveals that the growth of the monodisperse particles is limited by the protein cage.

The fundamental process of protein self-assembly is governed by protein-protein interactions between subunits, which combine to form structures that are often on the nano-scale. The nano-cage protein, bacterioferritin from Escherichia coli, a maxi-ferritin made up of 24 subunits, was chosen as the basis for an alanine-shaving mutagenesis study to discover key amino acid residues at symmetry-related protein-protein interfaces that control protein stability and self-assembly. By inspection of these interfaces and "virtual alanine scanning," nine mutants were designed, expressed, purified, and characterized using transmission electron microscopy, size exclusion chromatography, dynamic light scattering, native PAGE, and temperaturedependent CD. Many of the selected amino acids act as hot spot residues. Four of these (Arg-30, which is located at the two-fold axis, and Arg-61, Tyr-114, and Glu-128, which are located at the three-fold axis), when individually mutated to alanine, completely shut down detectable solution formation of 24-mer, favoring a cooperatively folded dimer, suggesting that they may be oligomerization "switch residues." Furthermore, two residues, Arg-30 and Arg-61, when changed to alanine form mutants that are more thermodynamically stable than the native protein. This investigation into the structure and energetics of this self-assembling nano-cage protein not only can act as a jumping off point for the eventual design of novel protein nanostructures but can also help to understand the role that structure plays on the function of this important class of proteins.