“Starve a cold, feed a fever” is a myth—but according to new research, the timing of when we eat in the short term may play a role in how our bodies fight off infections.

Researchers analyzed blood samples taken before breakfast from 31 study participants and then taken again six hours later, after the participants had eaten breakfast and lunch. The researchers found that their T cells—a type of immune cell—in the postlunch blood draws appeared better prepared to fight off infection than their T cells upon waking—in other words, after not eating anything for hours.

The findings were published on Wednesday in the journal Nature.

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The “fed” T cells were “functionally better,” says Greg Delgoffe, the study’s senior author and an immunologist at the University of Pittsburgh. “They were better at doing the things that T cells do.”

In further experiments in mice, the researchers found that the type of food appeared to matter, too—eating a fat-rich diet (in this case, corn oil) emerged as key to boosting the T cells’ abilities when compared with carbohydrate- or protein-rich diets.

T cells, or T lymphocytes, Delgoffe explains, are like the immune system’s “soldiers.” They abide in the body’s tissues, ready to spring into action to fend off viruses, bacteria, cancer cells, and more. When T cells spot a pathogen, they activate and proliferate into an army of fighters, he explains. And in the T cells collected after a meal, those abilities were enhanced, he says.

Interestingly, the T cells seem to hold on to the advantage provided by a good meal, Delgoffe says. When he and his colleagues looked at the same cells a week later, after they’d divided, the T cells from the postmeal state still retained their edge. This finding was similar in mice.

The study doesn’t answer whether humans should eat a fatty meal if they are worried about getting sick, however. Rather, the results support the idea that a well-balanced diet—including healthy fats—may help strengthen our immune response to pathogens, Delgoffe says. “We don’t want somebody out there just chugging a gallon of corn oil.”

Ultimately, he hopes the findings could help scientists better design T cell therapies that target cancer cells, or diets that boost our body’s response to treatments such as vaccines.

“We’re very, very excited about where things are going next,” Delgoffe says.