Poly-ubiquitin chains are flexible multidomain proteins, whose conformational dynamics enable their molecular recognition by a large number of partners in multiple biological pathways. By using alternative linkage, it is possible to obtain poly-ubiquitin molecules with different dynamical properties. This flexibility is further increased by the possibility to tune the length of poly-ubiquitin chains. Characterizing the dynamics of poly-ubiquitins as a function of their length is thus relevant to understand their biology. Structural characterization of poly-ubiquitin conformational dynamics is challenging both experimentally and computationally due to increasing system size and conformational variability. Here, by developing highly efficient and accurate small-angle X-ray scattering driven Martini coarse-grain simulations, we characterize the dynamics of linear M1-linked di-, tri- and tetra-ubiquitin chains. Our data show that the behavior of the di-ubiquitin subunits is independent of the presence of additional ubiquitin modules. We propose that the conformational space sampled by linear poly-ubiquitins, in general, may follow a simple self-avoiding polymer model. These results, combined with experimental data from small angle X-ray scattering, biophysical techniques and additional simulations show that binding of NEMO, a central regulator in the NF-κB pathway, to linear poly-ubiquitin obeys a 2:1 (NEMO:poly-ubiquitin) stoichiometry in solution, even in the context of four ubiquitin units. Eventually, we show how the conformational properties of long poly-ubiquitins may modulate the binding with their partners in a length-dependent manner.### Competing Interest StatementThe authors have declared no competing interest.

Molecular recognition and dynamics of linear poly-ubiquitins: integrating coarse-grain simulations and experiments