In nature, protein molecules have evolved as building blocks for the assembly of diverse and complex structures, many of which exhibit a high degree of symmetry. This observation has motivated a number of recent engineering efforts in which the advantages of symmetry have been exploited to design novel self-assembling protein structures of great size. Materials ranging from cages to extended two and three-dimensional arrays have been demonstrated. Especially for extended arrays, a vast number of geometrically different design types are possible. A table of geometric rules is provided for designing a universe of novel materials by combining two component symmetries.

Diverse efforts in protein engineering are beginning to produce novel kinds of symmetric self-assembling architectures, from protein cages to extended two-dimensional (2D) and three-dimensional (3D) crystalline arrays. Partial theoretical frameworks for creating symmetric protein materials have been introduced, but no complete system has been articulated. Only a minute fraction of the possible design space has been explored experimentally, in part because that space has not yet been described in theory. Here, in the form of a multiplication table, we lay out a complete rule set for materials that can be created by combining two chiral oligomeric components (e.g., proteins) in precise configurations. A unified system is described for parameterizing and searching the construction space for all such symmetry-combination materials (SCMs). In total, 124 distinct types of SCMs are identified, and then proven by computational construction. Mathematical properties, such as minimal ring or circuit size, are established for each case, enabling strategic predictions about potentially favorable design targets. The study lays out the theoretical landscape and detailed computational prescriptions for a rapidly growing area of protein-based nanotechnology, with numerous underlying connections to mathematical networks and chemical materials such as metal organic frameworks.

Theoretical and experimental advances in protein engineering have led to the creation of precisely defined, novel protein assemblies of great size and complexity, with diverse applications. One powerful approach involves designing a new attachment or binding interface between two simpler symmetric oligomeric protein components. The required methods of design, which present both similarities and key differences compared to problems in protein docking, remain challenging and are not yet routine. With the aim of more fully enabling this emerging area of protein material engineering, we developed a computer program, nanohedra, to introduce two key advances. First, we encoded in the program the construction rules (i.e. the search space parameters) that underlie all possible symmetric material constructions. Second, we developed algorithms for rapidly identifying favorable docking/interface arrangements based on tabulations of empirical patterns of known protein fragment-pair associations. As a result, the candidate poses that nanohedra generates for subsequent amino acid interface design appear highly native-like (at the protein backbone level), while simultaneously conforming to the exacting requirements for symmetry-based assembly. A retrospective computational analysis of successful vs failed experimental studies supports the expectation that this should improve the success rate for this challenging area of protein engineering.

Protein molecules bring a rich functionality to the field of designed nanoscale architectures. High-symmetry protein cages are rapidly finding diverse applications in biomedicine, nanotechnology, and imaging, but methods for their reliable and predictable construction remain challenging. In this study we introduce an approach for designing protein assemblies that combines ideas and favorable elements adapted from recent work. Cubically symmetric cages can be created by combining two simpler symmetries, following recently established principles. Here, two different oligomeric protein components are brought together in a geometrically specific arrangement by their separate genetic fusion to individual components of a heterodimeric coiled-coil polypeptide motif of known structure. Fusions between components are made by continuous α-helices to limit flexibility. After a computational design, we tested 10 different protein cage constructions experimentally, two of which formed larger assemblies. One produced the intended octahedral cage, ∼26 nm in diameter, while the other appeared to produce the intended tetrahedral cage as a minor component, crystallizing instead in an alternate form representing a collapsed structure of lower stoichiometry and symmetry. Geometric distinctions between the two characterized designs help explain the different degrees of success, leading to clearer principles and improved prospects for the routine creation of nanoscale protein architectures using diverse methods.

Theoretical and experimental advances in protein engineering have led to the creation of precisely defined, novel protein assemblies of great size and complexity, with diverse applications. One powerful approach involves designing a new attachment or binding interface between two simpler symmetric oligomeric protein components. The required methods of design, which present both similarities and key differences compared to problems in protein docking, remain challenging, and are not yet routine. With the aim of more fully enabling this emerging area of protein material engineering, we developed a computer program, Nanohedra, to introduce two key advances. First, we encoded in the program the construction rules (i.e. the search space parameters) that underlie all possible symmetric material constructions. Second, we developed algorithms for rapidly identifying favorable docking/interface arrangements based on tabulations of empirical patterns of known protein fragment-pair associations. As a result, the candidate poses that Nanohedra generates for subsequent amino acid interface design appear highly native-like (at the protein backbone level), while simultaneously conforming to the exacting requirements for symmetry-based assembly. A retrospective computational analysis of successful vs failed experimental studies supports the expectation that this should improve the success rate for this challenging area of protein engineering.