How much of a role tuition revenue plays in underwriting research?

I knew that TA positions in American schools are usually borne out of tuition revenue. Tuition revenue (that is, the cash that comes from the sometimes exorbitant undergraduate tuition) is usually unrestricted so one would wonder whether tuition money is directly used in order to fund research.

But other than start-up research funds, what other research expenditures are borne out of tuition money, if any? Would a university use tuition revenue to make up for a shortfall in research grants?