Extreme stability in de novo-designed repeat arrays is determined by unusually stable short-range interactions

Significance We apply a statistical thermodynamic formalism to quantify the cooperativity of folding of de novo-designed helical repeat proteins (DHRs). This analysis provides a fundamental thermodynamic description of folding for de novo-designed proteins and permits comparison with naturally occurring repeat protein thermodynamics. We find that individual DHR units are intrinsically stable, unlike those of naturally occurring proteins. This observation reveals local (intrarepeat) interactions as a source of high stability in Rosetta-designed proteins and suggests that different types of DHR repeats may be combined in a single polypeptide chain, expanding the repertoire of folded DHRs for applications such as molecular recognition. Favorable intrinsic stability imparts a downhill shape to the energy landscape, suggesting that DHRs fold fast and through parallel pathways. Designed helical repeats (DHRs) are modular helix–loop–helix–loop protein structures that are tandemly repeated to form a superhelical array. Structures combining tandem DHRs demonstrate a wide range of molecular geometries, many of which are not observed in nature. Understanding cooperativity of DHR proteins provides insight into the molecular origins of Rosetta-based protein design hyperstability and facilitates comparison of energy distributions in artificial and naturally occurring protein folds. Here, we use a nearest-neighbor Ising model to quantify the intrinsic and interfacial free energies of four different DHRs. We measure the folding free energies of constructs with varying numbers of internal and terminal capping repeats for four different DHR folds, using guanidine-HCl and glycerol as destabilizing and solubilizing cosolvents. One-dimensional Ising analysis of these series reveals that, although interrepeat coupling energies are within the range seen for naturally occurring repeat proteins, the individual repeats of DHR proteins are intrinsically stable. This favorable intrinsic stability, which has not been observed for naturally occurring repeat proteins, adds to stabilizing interfaces, resulting in extraordinarily high stability. Stable repeats also impart a downhill shape to the energy landscape for DHR folding. These intrinsic stability differences suggest that part of the success of Rosetta-based design results from capturing favorable local interactions.