The Energy Landscapes of Repeat-Containing Proteins: Topology, Cooperativity, and the Folding Funnels of One-Dimensional Architectures

Repeat-proteins are made up of near repetitions of 20– to 40–amino acid stretches. These polypeptides usually fold up into non-globular, elongated architectures that are stabilized by the interactions within each repeat and those between adjacent repeats, but that lack contacts between residues distant in sequence. The inherent symmetries both in primary sequence and three-dimensional structure are reflected in a folding landscape that may be analyzed as a quasi–one-dimensional problem. We present a general description of repeat-protein energy landscapes based on a formal Ising-like treatment of the elementary interaction energetics in and between foldons, whose collective ensemble are treated as spin variables. The overall folding properties of a complete “domain” (the stability and cooperativity of the repeating array) can be derived from this microscopic description. The one-dimensional nature of the model implies there are simple relations for the experimental observables: folding free-energy (ΔGwater) and the cooperativity of denaturation (m-value), which do not ordinarily apply for globular proteins. We show how the parameters for the “coarse-grained” description in terms of foldon spin variables can be extracted from more detailed folding simulations on perfectly funneled landscapes. To illustrate the ideas, we present a case-study of a family of tetratricopeptide (TPR) repeat proteins and quantitatively relate the results to the experimentally observed folding transitions. Based on the dramatic effect that single point mutations exert on the experimentally observed folding behavior, we speculate that natural repeat proteins are “poised” at particular ratios of inter- and intra-element interaction energetics that allow them to readily undergo structural transitions in physiologically relevant conditions, which may be intrinsically related to their biological functions.Author Summary: Repeat-proteins are coded in repetitions of similar amino acid stretches. Unlike typical globular domains, repeat-protein domains fold into elongated superhelical shapes of stacked elements, stabilized only by interactions within each repeat or between adjacent repeats. This architecture allows folding to be treated as a quasi–one-dimensional problem. We introduce an analytical model that describes the folding energy landscape of repeat-proteins, based on a representation in terms of spin variables. This representation groups together conformations on the basis of the degree of order in local quasi-independent folding units, often called foldons. We derive simple relations between the experimentally observed stability and cooperativity of denaturation of the whole repeat-domain, which differ from those found in three-dimensionally connected globular proteins. Folding simulations on perfectly funneled landscapes reproduce these relations. We document that these relations are experimentally observed in a variety of repeat-protein systems. We show the parameters in the foldon spin description can be predicted on the basis, largely, of protein topology, reflecting the funneled energy landscape.