Tightness of random knotting

Long polymers in solution frequently adopt knotted configurations. To under stand the physical properties of knotted polymers, it is important to find out whether the knots formed at thermodynamic equilibrium are spread over t he whole polymer chain or rather are localized as tight knots. We present h ere a method to analyze the knottedness of short linear portions of simulat ed random chains. Using this method, we observe that knot-determining domai ns are usually very tight, so that, for example, the preferred size of the trefoil-determining portions of knotted polymer chains corresponds to just seven freely jointed segments.