If the fund charges investors 2% of AUM and 20% of profits, factoring in the actual fund costs, hypothetically I'd estimate you'd need an AUM of 2.5B-5B to fund the scientists just on half the management fees.

Practically, you wouldn't do it on mgmt fees and you could do it much smaller, distributed differently, and grow/shrink the research division using fund profits instead of management fees. Using fund money to invest in a seed venture arm for the spinoff startups would just be another investment theme.

the main question would be, if you're making money on the investment side, what do you need the researchers for, and does that research mission (and their expenses) conflict with being a fiduciary. speculatively you'd need to have the fund as a separate entity owned by a partnership who took profits and invested in the research side separately.

at that point, you're back to the original basic problem, where instead of using the profits of a single private fund to support a research team, just make it a bluesky company of researchers who also generate investment strategies, and use venture funding.

the essential pattern is: make a large low-risk financial economic engine to fuel a small high risk one. if a VC firm put 80% of their LP's money in an index fund and just did a bunch of small seed investments, the effect could be similar. I'm not an expert in this, but nobody has invented another bell labs since, so the field seems open to new ideas and it's fun to think about.