Recent proteomic profiling of mouse brain preparations using the ubiquitin receptor, Rpn10 proteasome subunit, as an affinity ligand revealed a representative group of proteins bound to this sorbent (Medvedev, A. E., et al. (2017) Biochemistry (Moscow), 82, 330-339). In the present study, we investigated interaction of the Rpn10 subunit of proteasomes with some of these identified proteins: glyceraldehyde-3-phosphate dehydrogenase (GAPDH), pyruvate kinase, and histones H2A and H2B. The study revealed: (i) quantitative affinity interaction of the proteasome subunit immobilized on a Biacore-3000 optical biosensor cuvette with both the GAPDH (Kd = 2.4·10-6 M) and pyruvate kinase (Kd = 2.8·10-5 M); (ii) quantitative high-affinity interaction of immobilized histones H2A and H2B with the Rpn10 subunit (Kd values of 6.5·10-8 and 3.2·10-9 M, respectively). Mass spectrometric analysis revealed the presence of the ubiquitin signature (GG) only in a highly purified preparation of GAPDH. We suggest that binding (especially high-affinity binding) of non-ubiquitinated proteins to the Rpn10 proteasome subunit can both regulate the functioning of this proteasomal ubiquitin receptor (by competing with ubiquitinated substrates) and promote activation of other pathways for proteolytic degradation of proteins destined to the proteasome.