| Abstract: | Knots can occur in real and model biological macromolecules. We describe a program for determining whether or not any knots are present in model structures and for classifying those knots that do occur. The program computes the Alexander polynomial, Δ(t), for any model. This polynomial characterizes the knot in the sense that if two knots have different Alexander polynomials, then the knots are topologically distinct. The Alexander polynomial of the circle, or trivial knot, is Δ(t)≡1. If the computed Alexander polynomial is not identically equal to unity, then the structure is nontrivially knotted, and the program will then determine a lower bound on the minimum number of path crossings. The program is entirely general, and may be used to analyze any closed polygonal path. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 813–818, 1999 |
