The Robust Assembly of Small Symmetric Nanoshells

Abstract

Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine.

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

“…We use en masse simulations with small cores(R 0 = 1.2), comparable to the capsids filled with PSS. The smaller structure looks like a tennis ball, previously observed in the self-assembly studies of clathrin shells [44,63]. Fig.…”

“…The structure formed in the simulations when the size of the core is R0 = 1.2. This structure looks like a tennis ball and has been observed in the clathrin shell experiments too[44,63]. Phase diagram of structures obtained from en masse simulations in the presence of smaller core size comparing to…”

“…The fact that most spherical viruses adopt structures with icosahedral symmetry reveals the important role of elasticity in the energetics of viral shells [44,53,54]. Nevertheless, it has remained a mystery how an error-free shell formed out of 90 dimers or 60 trimers grows with perfect icosahedral symmetry under many different in vitro assembly conditions.…”

The equilibrium structure of self-assembled protein nano-cages

“…While the dynamical structures of protein shells under non-equilibrium conditions as a function of bending rigidity and stretching modulus of building blocks have been thoroughly investigated in Ref. [25], due to irreversible steps in the shell growth, the structures obtained in those simulations might be completely far from equilibrium.…”

“…Nevertheless, we find some differences between two phase diagrams too. A few symmetric structures grown in irreversible simulations [25] do not constitute the minimum free energy structures. Furthermore, we obtain additional symmetric structures in the equilibrium simulations, which were not observed in the growth simulations under non-equilibrium conditions.…”