Specificity of protein degradation by cellular proteasomes comes from tetra-ubiquitin recognition. We carry out molecular dynamics simulations to characterize how the ubiquitin receptor Rpn10 recognizes in the 26S proteasome K-48-linked tetra-ubiquitin. In the binding pose, ubiquitin and Rpn10 interact primarily through hydrophobic patches. However, K-48-linked tetra-ubiquitin mostly assumes a closed form in solution prior to binding, in which its hydrophobic patches are not exposed to solvent. Likewise, the hydrophobic ubiquitin interacting motifs (UIMs) of Rpn10 are mostly protected prior to binding. As a result, ubiquitin recognition in the proteasome requires refolding of both K-48-linked tetra-ubiquitin and Rpn10. Simulations suggest that conserved complementary electrostatic patterns of Rpn10 and ubiquitins guide protein association (stage 1 in the recognition process), which induces refolding (stage 2), and then facilitates formation of hydrophobic contacts (stage 3). The simulations also explain why Rpn10 has a higher affinity for K48-linked tetra-ubiquitin than for mono-ubiquitin and K-48-linked di- and tri-ubiquitins. Simulation results expand on the current view that the flexible arm of Rpn10 acts as an extended fragment of alpha-helices and flexible coils in the recognition process.