"This is the first concrete example in a fundamental biological process of such a sophisticated arithmetic calculation," said mathematical modeller Professor Martin Howard from the John Innes Centre.
Overnight, when a plant cannot use solar energy to convert carbon dioxide into sugars and starch, it regulates its starch reserves to make them last until dawn.
During the night, mechanisms inside the leaf measure the starch store and estimate the time until dawn, based on an internal clock similar to our own biological clocks.
The size of the starch store is divided by the time until dawn to set the correct rate of starch consumption, so that by dawn, about 95 percent of starch is used up even if night comes early or starch stores vary.
The researchers proposed that the process is mediated by two kinds of molecules, called "S" for starch and "T" for time.
If S molecules stimulate starch breakdown, and T molecules prevent it, then the rate of starch consumption is set by the ratio of S molecules to T molecules, or S divided by T.
"The calculations are precise so that plants prevent starvation but also make the most efficient use of their food," said Smith. "If the starch store is used too fast, plants will starve and stop growing during the night. If the store is used too slowly, some of it will be wasted."
"Understanding how plants continue to grow in the dark could help unlock new ways to boost crop yield," Smith said.