The belief that a good night's sleep boosts memory has been shown in countless tests. But up until now, direct evidence has been lacking on how exactly sleep strengthens the brains' neural connections. The study, published in Science, provides the first physical evidence of how sleep helps to consolidate and strengthen new memories. Professor Wen-Biao Gan, of New York University, said: 'We have known for a long time sleep plays an important role in learning and memory. If you do not sleep well you will not learn well. Here we have shown how sleep helps neurons form very specific connections on dendritic branches that may facilitate long-term memory’.

The researchers trained one set of mice to sleep for seven hours and another to stay awake for the same period of time. They found learning led to the formation of new dendritic spines - tiny structures that project from the end of nerve cells and help pass electric signals from one neuron to another - but only in the mice left to sleep. The mice lacking in sleep experienced significantly less dendritic spine growth than the well rested ones.

Dr Gan said: 'Now we know when we learn something new, a neuron will grow new connections on a specific branch.

The finding adds to research that a lack of shut eye causes rogue proteins to build up in the eye, increasing the risk for Alzheimer’s disease.