The fact that limited calorie diets enable mice and rats to life as much as 25% longer was first published in 1935. This effect was later seen with other animals and, even though similar studies on humans are obviously not possible, there is likely a similar effect. Basically, a severely restricted low-calorie diet that just provides all the essential nutrients extends the life of most animals. However, it is not been clear why. Researchers at University of California's Gladstone Institutes may have just figured it out though.
Dr. Eric Verdin's laboratory has uncovered a connection between a restricted diet and aging. The lab found that one type of ketone body appears to increase the levels of two genes that have been associated with increased longevity and protection against oxidative stress. Ketone bodies are produced when the body starts to run out of carbohydrates and begins breaking down fat to generate energy. The β-hydroxybutyrate ketone body, a by-product of fat breakdown, acts to increase levels of both Foxo3a and Mt2. The Foxo3a gene, in particular, has been previously associated with human longevity.
High levels of ketone bodies, of course, are toxic in other ways, and so, not generally healthy. However, this study indicates that low levels of at least one type may help protect against age-related diseases such as Alzheimer's. This link "connects the dots" between nutrient metabolism and the aging process.
You can find more on this study in the press release from the Gladstone Institutes, and an overview on Science Daily. Also, you can read more about the food metabolism connection to aging in related article on this site discussing Linda Partridge's research. The article was published in Science on December 6.