The accommodation index measures the perturbation associated with insertions and deletions in coiled‐coils: Application to understand signaling in histidine kinases

Coiled‐coils are essential components of many protein complexes. First discovered in structural proteins such as keratins, they have since been found to figure largely in the assembly and dynamics required for diverse functions, including membrane fusion, signal transduction and motors. Coiled‐coils have a characteristic repeating seven‐residue geometric and sequence motif, which is sometimes interrupted by the insertion of one or more residues. Such insertions are often highly conserved and critical to interdomain communication in signaling proteins such as bacterial histidine kinases. Here we develop the “accommodation index” as a parameter that allows automatic detection and classification of insertions based on the three dimensional structure of a protein. This method allows precise identification of the type of insertion and the “accommodation length” over which the insertion is structurally accommodated. A simple theory is presented that predicts the structural perturbations of 1, 3, 4 residue insertions as a function of the length over which the insertion is accommodated. Analysis of experimental structures is in good agreement with theory, and shows that short accommodation lengths give rise to greater perturbation of helix packing angles, changes in local helical phase, and increased structural asymmetry relative to long accommodation lengths. Cytoplasmic domains of histidine kinases in different signaling states display large changes in their accommodation lengths, which can now be seen to underlie diverse structural transitions including symmetry/asymmetry and local variations in helical phase that accompany signal transduction.