In biomolecules, bifurcated H-bonds typically involve the interaction of two donor protons with the two lone pairs of oxygen. Here, we present direct NMR evidence for a bifurcated H-bonding arrangement involving nitrogen as the acceptor atom. Specifically, the H-bond network comprises the Nδ1 atom of histidine and both the backbone N–H and side-chain Oγ-H of threonine within the conserved TXXH motif of ankyrin repeat (AR) proteins. Identification of the H-bonding partners is achieved via solution NMR H-bond scalar coupling (HBC) and H/D isotope shift experiments. Quantitative determination of 2hJNN HBCs supports that Thr N–H···Nδ1 His H-bonds within internal repeats are stronger (∼4 Hz) than in the solvent exposed C-terminal AR (∼2 Hz). In agreement, pKa values for the buried histidines bridging internal ARs are several units lower than those of the C-terminus. Quantum chemical calculations show that the relevant 2hJ and 1hJ couplings are dominated by the Fermi contact interaction. Finally, a Thr-to-Val replacement, which eliminates the Thr Oγ-H···Nδ1 His H-bond and decreases protein stability, results in a 25% increase in 2hJNN, attributed to optimization of the Val N–H···Nδ1 His H-bond. Overall, the results provide new insights into the H-bonding properties of histidine, a refined structural rationalization for the folding cooperativity of AR proteins, and a challenging benchmark for the calculation of HBCs.

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.

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N-versus C-terminal) interfacial coupling freeenergies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs. 3

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N‐ vs. C‐terminal) interfacial coupling free‐energies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs.