Intrinsically disordered proteins (IDP) and intrinsically disordered regions (IDR) are at the center of numerous regulation and control pathways in the cell, and attract consequently extreme interest nowadays in structural biology. The optimization problem that arises for protein structure determination is more complex for such objects as the convergence criterion is more difficult to set up and the size of the conformational space is a obstacle to exhaustive exploration. The threading-augmented interval Branch-and-Prune (TAiBP), based on a reformulating of the Distance Geometry Problem (DGP), provides a theoretical frame for the fast generation of protein conformations, Combinatorial explosion of the Branch-and-Prune approach due to exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by systematic solutions clustering.<br/>A pipeline is proposed to exhaustively sample protein conformations with TAiBP using backbone angle limits obtained by nuclear magnetic resonance (NMR), and to determine the populations of conformations by fitting small angle X-ray scattering (SAXS) data or Ramachandran probability maps. This pipeline was applied to a whirlin tandem domain, in which two PDZ domains are connected by a disordered linker (IDR). The most populated conformation of the tandem domain is a semi-closed one, fully closed and more extended conformations being in minority, in agreement with previous observations. A similar pipeline was applied on the proteins Sic1 and pSic1, corresponding to unphosphorylated and phosphorylated states of an IDP. The populated conformations were obtained by fitting SAXS curves as well as Ramachandran probability maps, the original finite mixture approach RamaMix being developed for this second task. The similarity between profiles of local gyration radii provided to a certain extend a converged view of the Sic1 and pSic1 conformational space. Profiles and populations are thus proposed for describing IDP conformations. Overall, SAXS and NMR data display different influences on the populations determination.

Exploring the conformational space of disordered proteins using a geometric approach

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