Yeah, BRM is discussed in depth here in several articles. Here is but one:
https://www.cardschat.com/f49/bankroll-management-71029
It varies from person to person, and different top players or authors will advise different BR levels. It can vary according to your playing style, the type of game you play (e.g. NL vs FL), and whether you have a "virtual" bankroll behind, meaning you have the resources to deposit to cover any losses and keep your account topped off.
All that said, there is a general rule of thumb for NL that you want to have somewhere between 30-100 buy-ins for the stakes you play. Assuming 50 buy-ins, then you're looking at $200 for 4NL (.04 x 100 x 50). For full limit, you can get away with a good bit less than that, since your entire BI is seldom at risk in any one hand.