Misfolded proteins are tagged by ubiquitin and then are destroyed by proteasomes. How does ubiquitin know which protein to tag?
Ubiquitin is active as part of a complex of proteins. Other elements of the complex recognise the proteins to be degraded. These recognition or specificity proteins are responsible for targetting proteins for ubiquitination. They are called ubiquitin ligases.
Ubiquitin and the UPS
The ubiquitin proteasomal system (UPS) is a common method of regulation for many proteins in the cell. The modification is actually generated by E3 ubiquitin ligase, of which there are ~400-800 in the mammalian cell and the main source of specificity in the UPS (E2 ~40 and only 1 or 2 E1).
Ubiquitin gets its name from ubiquitous, meaning found everywhere. It's a 76 amino acid molecule that modifies proteins at lysine residues. Monoubiquitination can act as a signalling molecule whereas polyubiquitination leads to degradation. Ubiquitin is first activated via an ATP-dependent pathway to create a high energy thioester with E1. This is transthiolated to E2 and finally E3 allows the addition to the target protein. So really, your question is how E3 ubiquitin ligase recognises its target. 1
There are 3 classes of E3 ligases, according to whether they contain a RING, U-box or HECT domain. These domains are responsible for either directly catalysing the addition of ubiquitin or simply facilitating another E3 ligase to do so. RING and RING-like domains are by far the most common (<600). Exactly how these domains mediate the transmission of ubiquitin is not clear, but it can be via an E3-Ub intermediate or directly from E2 to the target. The domains are relatively standardised, due to the fact they bind to E2 proteins, which contain less diversity than target proteins. However, it's the combination of the E2 and substrate binding domains that generates the selection. 2
So how does the target come into all of this? Each E3 ligase recognises a specific sequence on the target protein due to it's own conformation and signal sequence creating a unique interface full of intermolecular interactions- just like any protein recognises any other protein. However, although individual cases vary, the tight control primarily comes from post translational modifications on the target. Phosphorylation in particular is common in signalling and may allow E3 to bind, inducing degradation of the target. I'll use some examples to demonstrate this point, but note that every case will be different.
Other regulations of the process that are linked but perhaps outside the scope of your question include E3 post translational modifications (eg. autoubiquitination), sequestration of E3 via binding partners (Cand1 and Roc1), pseudosubstrates and substrate competition. 7
Misfolded protein degradation
Making protein is a large investment for the cell and so there are several protective measures to prevent misfolding/aggregation. Whilst there are many different types, chaperones generally work by isolating the misfolded protein and undergoing a series of binding release steps, triggered by hydrolysis of ATP. The protein can still be released unfolded, and the cell will continually try to isolate it for refolding. However, certain chaperones form a complex with the proteasome, and can recruit other UPS components. The choice to give up on refolding appears to be a stochastic process, and will depend on the concentration of the appropriate chaperones. Misfolded proteins tend to have significant regions of exposed hydrophobic residues, and E3 ligases are therefore likely to recognise this less specifically than the degradation pathway described above.
The answer to your question is that there is no standard recognition sequence in E3 to know which protein to target, the binding needs to be diverse in order to give the control the cell needs. That means it could be anything, but each E3 is likely to be relatively specific for its target, and is often controlled by other post translation modifications on the substrate. Misfolded proteins can be recognised and degraded due to the association of the UPS with chaperones.
I think this video explains the ubiquitin system very well.