Other groups have since found similar patterns in mice and primates. One study, for example, found that many genes turned on in the brains of old monkeys and humans are the same as those expressed in young brains, suggesting that ageing and development are controlled by some of the same gene networks.

Perhaps most provocative of all, some studies of worms have shown that shutting down essential development genes in adults significantly prolongs life. “We’ve found quite a lot of genes in which this happened – several dozen,” de Magalhaes says.

Nobody knows whether the same sort of developmental-programme genes exist in people. But say that they do exist. If someone was born with a mutation that completely destroyed this programme, Walker reasoned, that person would undoubtedly die. But if a mutation only partially destroyed it, it might lead to a condition like what he saw in Brooke Greenberg or Gabby Williams. So if Walker could identify the genetic cause of Syndrome X, then he might also have a driver of the ageing process in the rest of us.

And if he found that, then could it lead to treatments that slow – or even end – ageing? “There’s no doubt about it,” he says.

Public stage

After agreeing to participate in Walker’s research, the Williamses, just like the Greenbergs before them, became famous. In January 2011, when Gabby was six, the television channel TLC featured her on a one-hour documentary. The Williams family also appeared on Japanese television and in dozens of newspaper and magazine articles.

Other than becoming a local celebrity, though, Gabby’s everyday life hasn’t changed much since getting involved in Walker’s research. She spends her days surrounded by her large family. She’ll usually lie on the floor, or in one of several cushions designed to keep her spine from twisting into a C shape. She makes noises that would make an outsider worry: grunting, gasping for air, grinding her teeth. Her siblings think nothing of it. They play boisterously in the same room, somehow always careful not to crash into her. Once a week, a teacher comes to the house to work with Gabby. She uses sounds and shapes on an iPad to try to teach cause and effect. When Gabby turned nine, last October, the family made her a birthday cake and had a party, just as they always do. Most of her gifts were blankets, stuffed animals and clothes, just as they are every year. Her aunt Jennie gave her make-up.

Walker teamed up with geneticists at Duke University and screened the genomes of Gabby, John and MaryMargret. This test looked at the exome, the 2% of the genome that codes for proteins. From this comparison, the researchers could tell that Gabby did not inherit any exome mutations from her parents – meaning that it wasn’t likely that her siblings would be able to pass on the condition to their kids. “It was a huge relief – huge,” MaryMargret says.

Still, the exome screening didn’t give any clues as to what was behind Gabby’s disease. Gabby carries several mutations in her exome, but none in a gene that would make sense of her condition. All of us have mutations littering our genomes. So it’s impossible to know, in any single individual, whether a particular mutation is harmful or benign – unless you can compare two people with the same condition.

All girls

Luckily for him, Walker’s continued presence in the media has led him to two other young girls who he believes have the same syndrome. One of them, Mackenzee Wittke, of Alberta, Canada, is now five years old, with has long and skinny limbs, just like Gabby. “We have basically been stuck in a time warp,” says her mother, Kim Wittke. The fact that all of these possible Syndrome X cases are girls is intriguing – it could mean that the crucial mutation is on their X chromosome. Or it could just be a coincidence.

Walker is working with a commercial outfit in California to compare all three girls’ entire genome sequences – the exome plus the other 98% of DNA code, which is thought to be responsible for regulating the expression of protein-coding genes.

For his theory, Walker says, “this is do or die – we’re going to do every single bit of DNA in these girls. If we find a mutation that’s common to them all, that would be very exciting.”

But that seems like a very big if.

Why we get nicer as we get older