I could tell you to buy "Stryer: Biochemistry". It has many chapters that you need, which are:
- Gene regulation (Regulation on DNA, RNA, Protein level, etc.)
- Signaltransduction (JAK/STAT pathway & general concepts)
- Regulatory strategies (Product inhibition etc.)
- Stem cell differentiation (French Flag model, specification vs determination)
Stryer also explains the biochemical machinery behind that, which is interesting. Your other paper mentions interferon signalling, which is part of the immune system. So you could buy "Janeway: Immunology" for that. You also mentioned cell fate determination, for that the best book imo is "Scott F Gilbert: Developmental Biology".
They are awesome books, with tons of awesome pictures and are simply very very fun to read!
HOWEVER, these books are huge and contain many chapters that you will never need. So I might also tell you to just google stuff. For biology purposes my goto strategy is hammering this query into the search bar:
"pubmed review <biologic term I don't understand>"
For example when I google "genetic regulation network pubmed review" I get this pubmed link. Then you press "full text links". Then you realize there's a paywall. I would never recommend visiting a certain page (starts with sci and ends with hub) to circumvent that paywall.
So I keep searching and find another review from 2012. However it lacks those biological terms that you need. I tried finding some comprehensive reviews online about biological topics, however this kind of literature often focuses on flashy state-of-the-art topics that go into too much detail. So you might want to consider buying "Stryer Biochemistry", after all!
Or just ask your supervisor to buy those books and keep them in your research group. They are definitely worth it. And these books definitely know a lot more than anyone in a physical research group (including your PI). Yes, it will take you some time to look up those topics and read them, but I promise, they're written in the best and most understandable way possible (no background knowledge is necessary, unlike published papers!) and might save you and your whole research group a trip to the library or a lot of time and frustration trying to google terms that no one taught them.
It doesn't have to be the Stryer, maybe there are books that specialize on regulatory strategies in living beings. But it's a good start.