From evolution to folding of repeat proteins

Abstract

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Due to their symmetry, these proteins constitute excellent model systems to investigate how evolution relates to structure, folding and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat-proteins. We model the energetics by a combination of an inverse Potts model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at single residue level. This is used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrinrepeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transition are obtained for arrays with enough sequence-similar elements and strong interactions between them, while non-cooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. In between, we characterised nucleation-propagation and multi-domain folding mechanisms. Finally, we showed that stability and cooperativity of a repeat-array can be quantitatively predicted from a simple energy score, paving the way for guiding protein folding design with a co-evolutionary model.

Error Estimates For A Linear Folding Model

“…Due to the appearance in natural processes and their importance to modern technical devices, foldable structures have attracted a lot of attention in recent decades. Applications include flapping mechanisms in biology [14,1], protein folding [30,19], movable structures in architecture [27,29], sheet (metal) pressing and wrapping [22,24] or origami and kirigami [25,15,11,21]. We address in this article the numerical discretization of a linear folding model.…”

Resolving the fine structure in the energy landscapes of repeat proteins

“…When the local energetics are similar along the assemblage, parallel folding routes can be identified (Werbeck and Itzhaki, 2007;Aksel and Barrick, 2014) and the routes can be switched by (de)stabilising regions along the array (Tripp and Barrick, 2008;Werbeck et al, 2008). Thus, the energy landscapes of repeat proteins can be very rich and amenable to design (Galpern et al, 2022). Most importantly, in various cases, the detailed folding mechanism of repeat arrays has been identified to play a major role in their biological function (Löw et al, 2008;Barrick, 2009;Ferreiro and Komives, 2010;Kumar and Balbach, 2021).…”