Levels of the essential amino acid methionine in the diet appear to be involved in generating the beneficial effects of calorie restriction on health and longevity. Some portion of the resulting changes in the operation of metabolism is based on sensing low levels of methionine. It is thus possible that humans might obtain benefits comparable to those generated by calorie restriction from a sensibly constructed low-methionine diet with a normal calorie intake. The research in support of this supposition is still sparse in comparison to that for calorie restriction, however.
It was first reported in 1993 that rats subjected to a diet restricted in methionine (MR) enjoyed comparable life spans to rats that were on caloric restriction (CR). In the first experiments, methionine was reduced to ⅕ its normal level in the diet, and growth of the rats was severely stunted. We can't live entirely without methionine - the body would not be able to make any proteins at all. Restricting methionine is likely to have impacts on growth, health, and wellbeing that are as yet unstudied in humans. Rats fed a diet without methionine developed steatohepatitis (fatty liver), anemia and lost two thirds of their body weight over 5 weeks. In one experiment where methionine was severely restricted but not eliminated entirely, ⅕ of the mice died, and the other ⅘ went on to live longer than control mice.
Here's a clue about why methionine is special. The instructions for making proteins is coded into DNA, via the genetic code, which specifies words of 3 DNA letters, each corresponding to one of the 20 amino acids. The genetic code also contains "punctuation", instructions to start and stop. The "start codon" is also the word for methionine. Every chain of amino acids that the body constructs begins with methionine. No methionine - no protein synthesis. A shortage of methionine means that the body is inhibited in making every kind of protein. More genes are expressed (more proteins synthesized) as the body grows older. Perhaps methionine restriction is putting a brake on this production of extra proteins that are not produced when we're young, and that contribute to aging.
Methionine restriction in practice involves eating foods that are low in methionine. Though all protein has methionine, some protein sources are much lower in methionine than others. All animal sources (including milk and especially eggs) are high in methionine. So a methionine-restricted diet is a vegan diet, not just any vegan diet, but a subset of vegan protein sources. There appear to be no general rules. For example, almonds are a good source of low-methionine protein, but Brazil nuts are terrible. Even a strict vegan diet would only reduce methionine intake by about 1/2. Extrapolating from the rodent experiments, we may need to reduce by ~ 3/4 before crossing a threshold where benefits kick in.