Double Electron-Electron Resonance (DEER) is a popular technique that exploits attached spin-labels to probe the collective dynamics of biomolecules in a native environment. Like most spectroscopic approaches, DEER detects an ensemble of states accounting for biomolecular dynamics as well as the intrinsic spin-labels flexibility. Therefore, the DEER data alone does not provide high-resolution structural information. To disentangle this variability, we introduce a minimally-biased simulation method to sample a structural ensemble that reproduces multiple experimental signals within the uncertainty. In contrast to previous approaches, our method targets the raw data itself, thereby it opens the possibility of an unbiased molecular interpretation of the experiments. After validation on the T4-Lysozyme, we applied this technique to interpret recent DEER data on a membrane transporter binding-protein (VcSiaP). The results highlight the large-scale conformational movement that occurs upon substrate binding and reveal that the unbound VcSiaP is more open in solution than the X-ray structure.