Workaholics are fooling themselves if they think a weekend lie-in can make up for lost sleep.

The first hard evidence has emerged that we are unable to catch up on lost sleep if it happens night after night - increasing the risk of obesity, heart disease and depression, while cutting mental dexterity.

While our bodies try to catch up on occasional loss by making us sleep more and/or more deeply the following night, this mechanism breaks down when there is chronic deprivation, say researchers at Northwestern University, Illinois.

They report in the Proceedings of the National Academy of Sciences shows that when rats are partially sleep deprived over consecutive days they no longer attempt to catch up, despite an accumulating sleep deficit. "The ability to compensate for lost sleep is itself lost, which is damaging both physically and mentally," said Prof Fred Turek.

Scientists estimate that in the 1960s people slept for more than eight hours. Now we are sleeping for about six. Symptoms of deprivation include weight gain, irritability, hallucinations and depression, said Prof Russell Foster, of Oxford University. It also impairs the ability of the brain to innovate.

The effect is pernicious, he said, because sleep-restricted people report not feeling sleepy, even though their performance on tasks declines markedly.

Prof Foster argues that we are turning into a "zombie nation" with sleep deprivation harming mental dexterity, memory and health, as well as leading to greater risk of accidents.

He said: "Our 24/7 society assumes we can free ourselves from our biology - we cannot."

He added: "The consequences of sleep-deprived brains in an increasingly intelligence-dependent economy is a serious issue and not fully appreciated by our business leaders. We need to embrace sleep and stop treating sleep as an illness in want of a cure."