Some interesting studies of rapamycin and resveratrol have emerged. Once study finds that it can slow down cellular senencence at high concentrations. Apparently, resveratrol also does. At this point many studies have shown resveratrol to (a) delay aging and (b) slow down the onset of age-related diseases (obviously not mutually exclusive events). Resveratrol activates sirtuins but it has other effects also, not all completely known. For a cell, and by extension a body, to age, you need (a) cell cycle arrest and (b) an active mTOR pathway. Basically mTOR causes aging by making cells proliferate more, and resveratrol can inhibit this via a mechanism of S6 phosphorylation.
Rapamycin can inhibit the mTOR pathway (see this study, the last line of the abstract of which I love - "Our data demonstrate that senescence can be pharmacologically suppressed."!). In addition, it prevents the loss of proliferative potential associated with cellular aging.
A conclusion of the above study was that resveratrol can be toxic, so it's a trade off between toxicity and anti-aging effects. Lower level can be quite effective however, the authors state, e.g. 2-3 fold preservation of proliferative potential (as opposed to 10-fold). Even transient inhibition of mTOR might be enough to have some effect on cellular senencence.
Various discussion about the exact interplay between mTOR, sirtuins, resveratrol etc. are then discussed. A bit over my head!
(a) sirtuins + mTOR = same pathway. Thus, activate one, inhibit the other...(evidence, e.g. that resveratrol inhibits PI3K, an upstream activator of mTOR)
(b) resveratrol, like anti-diabetic drug metaformin activated AMP-activated protein kinase which activates mTOR
So, one way or another resvertrol targets mTOR and the key is to use it at non-toxic doses. Up to 5g is apparently not toxic to humans - see this and this study.
Another study shown resveratrol increasing AMPK activity in mice (i.e. inhibiting mTOR).
The final conclusion if that rapamycin and resveratrol could work very well in tandem and at non-toxic doses to delay aging. Interestingly, here's the company of the authors.
See also this link and this link for some more info/discussion.