There are several rare conditions that present the appearance of accelerated aging, the changes they cause extending far enough down into the fundamentals of human biochemistry that there yet remains much to learn about their operation and some debate over whether they are in fact forms of greatly accelerated aging. The best known of these conditions are Hutchinson-Gilford Progeria (HGPS, or just progeria) and Werner syndrome; significant progress has been made in identifying their root causes over the past decade, but that is still a way removed from knowing whether there is any great relevance there insofar as concerns research into ordinary aging.
A recent open access paper takes a look at the question, though the bottom line at this time is that more time and greater understanding is needed:
Hutchinson-Gilford Progeria (HGPS) and Werner syndromes are diseases that clinically resemble some aspects of accelerated aging. HGPS is caused by mutations in the LMNA gene resulting in post-translational processing defects that trigger Progeria in children. Werner syndrome, arising from mutations in the WRN helicase gene, causes premature aging in young adults. What are the molecular mechanism(s) underlying these disorders and what aspects of the diseases resemble physiological human aging?
In both diseases recent evidence indicates that mutations in the genes responsible for these premature aging diseases result in increased DNA damage, particularly at telomeres. Although shortening and/or damage to telomeres is associated with proliferative arrest of cells in vitro, it remains unclear how accurately these diseases recapitulate the processes of tissue aging in humans. Here we discuss recent advances, using in vitro cell culture and mouse models of progeroid syndromes to highlight important questions that remain: A) what is the molecular mechanism of how such seemingly unrelated proteins cause similar degenerative diseases? B) are these mechanisms representative of normal aging?
Like a fair amount of nonetheless interesting research, work aimed at understanding accelerated aging conditions - and mining that knowledge for material that may prove useful in the development of ways to intervene in ordinary aging - is something of a sideshow. The trouble with science in general is that you have to spend time on the sideshows in order to confirm that they are in fact sideshows; every presently major field of endeavor in the life sciences started off small, unpromising, and prospective. I don't think the odds are good that something spectacular will result from investigations of progeria: you can't completely rule it out at this stage, but there are other places to concentrate resources that have a much higher expectation of value.