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The ends of your chromosomes are capped, and the cap gets shorter every time a cell divides.

Biology Facts, sourced to National Human Genome Research Institute.

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The machinery that copies DNA cannot quite finish the very end of a strand, so a little is lost each round. Telomeres are repetitive sequences that carry nothing important and take that loss instead of a gene. They also stop the cell from reading a chromosome end as a broken strand in need of emergency repair. When they run down far enough the cell stops dividing, which is a defense against runaway growth as much as a clock.

The claim comes from National Human Genome Research Institute.

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