One such harmful protein is beta-amyloid (Abeta), which accumulates in the brains of people with dementia.
US scientists who looked at data on 70 adults with an average age of 76 found that those who slept less, and who experienced low quality sleep, had higher levels of beta-amyloid.
Self-reported sleep duration in the participants ranged from five to seven hours a night.
The authors, led by Dr Adam Spira, from the Johns Hopkins Bloomberg School of Public Health in Baltimore, wrote in the journal JAMA Neurology: "In summary, our findings in a sample of community-dwelling older adults indicate that reports of shorter sleep duration and poorer sleep quality are associated with a greater Î'beta burden.
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"As evidence of this association accumulates, intervention trials will be needed to determine whether optimizing sleep can prevent or slow AD (Alzheimer's disease) progression."
The researchers pointed out that the study did not indicate whether sleep disturbance preceded beta-amyloid build-up. Nor were they able to assume that poor sleep causes Alzheimer's.
But other research published in the journal Science last week points to the importance of sleep in clearing toxic proteins such as beta-amyloid from the brain.
A system that flushes toxic waste out of the brain was found to be 10 times more active during sleep.
Scientists believe the brain has to take a break from mental processing while the clean-out is under way.