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US Scientists That Found Shoelaces Come Undone Due To A Combination Of The Foot Striking The Ground And The Swinging Motion Of The Leg, Which Loosen The Knot And Pull The Lace Ends. Their Study May Help Explain How Other Knotted Systems Such As Complex Microstructures And DNA. Fail Under Repetitive Motion And Stress.

Mystery of why shoelaces come undone unravelled by science – BBC News

http://www.bbc.com/news/science-environment-39573642

The authors say the research can be applied to other structures, such as DNA.