Right. If they already produced, they can bind each other even if genes are turned off, as long as proteins not inactivated or degraded.

Yes, I also confirm above answer. E.Coli can encode approximately 4300 proteins, but not all of them are made at any single time, expression is often controlled. If you make proteins and turn off gene, as long as proteins are made and have affinity towards each other they will bind - Only exception is if you have truncated or degraded proteins in that case only they will not bind.

Mahesh Chandak Timur Yergaliyev can you, by any chance, cite a paper that will validate this claim or is this a well-known fact?

It's common sense, but I am sure that there are a lot of articles, where you can find a confirmation of it. Antibodies, some DNA and RNA binding proteins, enzymes are acting independently from their genes as long as they keep active conformation. You can take artificially produced enzyme and it will still be working in different cells, independently from the presence or absence of the coding gene in an organism.

Transcription factors bind to the regulatory regions of a gene and increase or decrease its expression, and amount of protein made by particular gene at any given time is determined in this process. This process / your question is an established concept, you will have to read gene regulation chapter from any book.

if two molecules bind or not is a result of the competition between

entropy and energy.

If we bring a small system “a” into thermal and mechanical contact with a big system“B”, then “B” will stay in equilibrium at its original temperature T and pressure p, but “a” will come to a new equilibrium, which minimizes

Ga ≡ Ea + pVa − TSa. Gibbs free energy