Beyond icosahedral symmetry in packings of proteins in spherical shells

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations, and (ii) that optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties.Comment: 8 pages, 5 figure

Influence of Metal, Ligand and Solvent on Supramolecular Polymerizations with Transition-Metal Compounds: A Theoretical Study

The nature of intermolecular interactions governing supramolecular polymerizations is very important to control their cooperativity. In order to address this problem, supramolecular columns made of Pt(II) and Pd(II) complexes of oligo(phenyleneethynylene)-based pyridine (OPE) and tetrazolyl-pyridine ligands (TEP) were investigated through the dispersion-corrected PM6 method. Aromatic, CH-π, M-Cl and metallophilic interactions helped stabilize the supramolecules studied, and their geometries and associated cooperativities were in excellent agreement with experimental data. The OPE ligand and/or the presence of Pt(II) have led to stronger metallophilic interactions and also to cooperative supramolecular polymerizations, which clearly suggests that metallophilic interactions are a key factor to control cooperativity. The results indicate that sequential monomer addition is in general less spontaneous than the combination of two larger pre-formed stacks. The present theoretical investigations contribute to the further understanding of the relation between the thermodynamics of supramolecular polymerizations and the nature of different synthons