Leptin is released by fat cells and travels through the blood to the brain. The more fat on a person’s body, the more leptin is released. When fat levels are low, leptin levels in the brain are low, and the brain responds by increasing the person’s appetite, prompting the person to eat and gain weight. For someone like Ms. Johnson, who has almost no fat cells to signal the brain, the brain gets almost no leptin. To the brain, it seems as if she is starving. As a result, she receives continuous signals to eat.

With leptin treatment, Ms. Johnson’s brain was tricked into responding as though she had abundant fat. Her insatiable hunger vanished. Fat disappeared from her liver, her blood glucose became normal, and so did her cholesterol and triglyceride levels.

But why did she and other lipodystrophy patients have these conditions in the first place, and why did they vanish? What was going on?

A couple of studies involving mice produced some clues. Dr. Marc Reitman, the chief of the diabetes, endocrinology and obesity branch at the National Institute of Diabetes and Digestive and Kidney Diseases and his colleague, Dr. Charles Vinson, of the National Cancer Institute, genetically engineered mice to have lipodystrophy. The mice, like Ms. Johnson, had almost no fat tissue. And like her, they developed all of the conditions associated with obesity.

What would happen, the researchers asked, if the mice had a bit more fat tissue?

They transplanted fat tissue into the rodents, and two weeks later, the mice had normal levels of glucose, insulin and triglycerides. Their livers and muscles went back to normal, too.

If that worked, the scientists wondered, could a limitless amount of fat tissue prevent the syndrome, even if copious amounts of fat were stored in that tissue?

Philipp E. Scherer, the director of the Touchstone Diabetes Center at the University of Texas Southwestern Medical Center in Dallas, and his colleagues tested the idea. They engineered mice that could make an almost limitless amount of fat tissue. As a result, there was no end to the amount of fat the animals could store. They were, Dr. Scherer said, “the fattest mice under the sun, the mouse equivalent of an 800-pound human being.”