Let n be the number of different protein complexes (as defined here) that a protein may be a stable part of for a considerable amount of time (and not only transiently). Which proteins have the largest n?

An answer should include the number of different protein complexes the protein is part of.

Or where should I start doing my own research? I have no clue.

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    $\begingroup$ Can you better define "protein complex"? Are you asking which proteins have the greatest number of distinct binding partners? Are you asking which proteins are most promiscuous in their binding to other proteins? While I appreciate your thought-provoking questions, Hans-Peter, I feel that you've made no attempt at research for this one. $\endgroup$ – Dirigible Mar 5 at 19:27
  • $\begingroup$ @Dirigible, thanks for asking. But are your paraphrases more unambiguous than my "simple" question? I agree that "of the most different protein complexes" doesn't sound perfectly right. I'll try to do better. $\endgroup$ – Hans-Peter Stricker Mar 5 at 19:46
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    $\begingroup$ @Hans-PeterStricker As an example of what Dirigible might mean: all proteins are translated by ribosomes, along with a bunch of accessory proteins and chaperones to assist in properly folding proteins. Therefore, the ribosomal proteins (and associates) may be said to be complexed with every other protein. I haven't checked but this almost certainly gives them the highest degree in a protein-protein interaction network. This is a trivially true answer to your question, but it's almost certainly not what you mean. $\endgroup$ – Maximilian Press Mar 5 at 19:54
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    $\begingroup$ Also: I would suggest reading a little bit more about protein-protein interaction networks, which I'm pretty sure are what you are interested in: ebi.ac.uk/training/online/course/… $\endgroup$ – Maximilian Press Mar 5 at 19:56

This answer does not address the number of complexes that a protein participates in, but rather a related question -- With how many proteins does a protein interact?
I acknowledge this is a fundamentally different question, though I think it's a good starting point on which other people can build a better answer.

Taking the data from STRING v11 for all protein-protein interactions (PPIs) in Escherichia coli str. K-12 substr. MG1655, we can subset these PPIs to include only those of action type "binding". This database provides PPI scores between 0 and 1 based upon experiments (co-purification, co-crystallization, Y2H), textmining, co-occurence, co-expression, and co-localization of coding genes across genomes.

If we set no cutoff for the confidence in these binding interactions, we see that 2585 proteins have ≥1 binding partner, and one protein has an astonishing 273 binding partners (pfo, a putative pyruvate-flavodoxin oxidoreductase). Note that this database collapses splice variants and post-transcriptionally modified proteins into single nodes in the interaction network, so all gene product variants are represented by one coding sequence. Also, this database states this E. coli strain has 4127 distinct protein-coding genes, so approximately 63% (2585/4127) of genes encode a protein that interacts with at least one other distinct protein. Note also that this database does not include self-interactions (e.g. dimerization), which are a valid type of protein complex per OP's question.

If we limit the interactions to those with a "high confidence" score (≥0.900), only 656 proteins (~16%) are seen to have ≥1 binding partner, with a maximum of 55 binding partners seen for 4 proteins. Unsurprisingly, and consistent with the comment from Maximilian Press, these proteins are all associated with the ribosome (sra, rpsP, rpsI, and rpsR). The spike in the graph below at 54 interacting partners for the high-confidence PPIs is a group of of ribosomal proteins, most of which are annotated as co-interactors.

histogram of number of protein-protein binding partners for distinct E. coli proteins

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