Polyubiquitination, a critical protein post-translational modification, signals for a diverse set of cellular events via the different isopeptide linkages formed between C-terminus of one ubiquitin (Ub) and the ε-amine of K6, K11, K27, K29, K33, K48, or K63 of a second Ub. We assembled di-ubiquitins (Ub2) comprised of every lysine linkage and examined them biochemically and structurally. Of these, K27-Ub2 is unique as it is not cleaved by most deubiquitinases. As this remains the only structurally uncharacterized lysine-linkage, we comprehensively examined the structures and dynamics of K27-Ub2 using NMR, small-angle neutron scattering, and in silico ensemble modeling. Our structural data provide insights into functional properties of K27-Ub2, in particular, that K27-Ub2 may be specifically recognized by K48-selective receptor UBA2 domain from proteasomal shuttle protein hHR23a. Binding studies and mutagenesis confirmed this prediction, further highlighting structural/recognition versatility of polyubiquitins and the potential power of determining function from elucidation of conformational ensembles.