The study suggests that a male's life experience can be passed down through more than his genetic code alone.
Researchers link this difference to an epigenetic change in the stressed dad's sperm - a change that they could prevent by blocking the father's stress hormones.
Researchers confined male mice in plastic tubes for two hours a day, for two weeks straight, to induce stress.
Afterwards, the animals' glucose levels were increased, but the mice gained weight more slowly and had increased levels of stress hormones called glucocorticoids in their blood.
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"Paternal psychological stress can result in hyperglycemia in offspring in mice," said Xiaoying Li from Shanghai Jiao Tong University School of Medicine in China.
The root of the increased blood sugar was in a gene called Sfmbt2. When a male mouse is immobilised daily in a plastic tube, the spike of glucocorticoids causes extra methyl groups to be added to the Sfmbt2 gene in his sperm.
These epigenetic marks do not affect the underlying DNA, but they do control how Sfmbt2 and an associated microRNA (the intronic microRNA-466b-3p) are expressed.
This epigenetic change in stressed fathers showed up in their offspring's livers. The intronic microRNA-466b-3p in Sfmbt2 is supposed to help regulate an enzyme called PEPCK, which controls sugar production in the liver.
But when mammals reproduce, Sfmbt2 is turned off in the egg from the mother - meaning that offspring inherit their only working copy from the father's sperm.
And when the only functional Sfmbt2 gene carries these epigenetic tags, the intronic microRNA-466b-3p is silenced and can not keep watch over PEPCK as it normally would.
The father's offspring then develop livers with too much PEPCK, causing their blood glucose to increase.
The findings were published in the journal Cell Metabolism.