An engineered protein nanocage is designed to encapsulate and deliver the synthetic drug molecule, Micillin, directly to target cells. The nanocage consists of multiple protein subunits assembled into a hollow spherical shell.
A single nanocage has a hollow inner cavity with a total volume of 520 nm3520\text{ nm}^3520 nm3.
This inner cavity can hold a maximum of 450045004500 Micillin molecules.
The volume of a single Micillin molecule is 4.20×10−3 nm34.20 \times 10^{-3}\text{ nm}^34.20×10−3 nm3.
Calculate the volume of the inner cavity that is not occupied by Micillin molecules when the cavity is fully loaded.
Explain how hydrophobic and hydrophilic interactions of the amino acid R-groups stabilize the tertiary and quaternary structure of this spherical protein nanocage in an aqueous environment.
