Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of th...Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of the Alexander polynomial.However,the Alexander polynomial cannot directly discriminate knot chirality,while knot chirality plays important roles in many physical,chemical,and biological properties.In this work,we discover a new relationship for knot chirality and accordingly,develop a new algorithm to extend the applicability of the Alexander polynomial to the identification of knot chirality.Our algorithm adds an extra step in the ordinary calculation of the Alexander polynomial.This extra step only slightly increases the computational cost.The correctness of our algorithm has been proved mathematically by us.The implication of this algorithm in physical research has been demonstrated by our studies of the tube model for polymer knots.Without this algorithm,we would be unable to obtain the tubes for polymer knots.展开更多
基金This work was financially supported by the National Natural Science Foundation of China(No.21973080)Research Grants Council of Hong Kong(Nos.21302520,11313322 and 14301819)Guangdong Basic and Applied Basic Research Fund(No.2022A1515010484).
文摘Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of the Alexander polynomial.However,the Alexander polynomial cannot directly discriminate knot chirality,while knot chirality plays important roles in many physical,chemical,and biological properties.In this work,we discover a new relationship for knot chirality and accordingly,develop a new algorithm to extend the applicability of the Alexander polynomial to the identification of knot chirality.Our algorithm adds an extra step in the ordinary calculation of the Alexander polynomial.This extra step only slightly increases the computational cost.The correctness of our algorithm has been proved mathematically by us.The implication of this algorithm in physical research has been demonstrated by our studies of the tube model for polymer knots.Without this algorithm,we would be unable to obtain the tubes for polymer knots.
