In vivo, DNA and proteins can form knotted structures, and recent experiments have demonstrated that the knotting affects biological functions. It remains unclear how DNA knots and protein knots are formed and how the knotting affects the dynamics of DNA and proteins. In this talk, I will present our recent research results about DNA knots and protein knots based on statistical physics and computer simulations. We found that DNA knots can spontaneously tighten themselves due to an entropic effect. The predicted tight DNA knots have been observed in recent nanopore experiments. Regarding protein knots, we found that the interactions between several critical sites along peptide chains may be the key factors that determine knot formation in protein knots. In addition to revealing the physical mechanisms underlying DNA knots and protein knots, our results can be used to guide the rational control of DNA knots and protein knots to utilize their special properties.
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