A complete rule set for designing symmetry combination materials from protein molecules

Significance Building nanoscale materials in a predictable way is a major goal in broad fields of molecular engineering. In pursuing that goal, protein molecules are gaining interest as a source of structurally defined, self-assembling building blocks, but methods and geometric rules for how they might be combined into novel materials have not been fully laid out yet. This work brings together ideas from structural biology, geometry, and group theory to articulate a complete rule set that describes all the kinds of protein-based materials that can be created by combining separate oligomeric components, thereby laying the foundation for an emerging area of science and biotechnology.