How does DNA, the molecule containing genetic information, change its three-dimensional
shape during the complex cellular processes of replication, recombination and repair? This
is one of the core questions in molecular biology which cannot be answered without help
from mathematical modeling. Basic concepts of topology and geometry can be introduced in
undergraduate teaching to help students understand counterintuitive complex structural
transformations that occur in every living cell. Topoisomerases, a fascinating class of
enzymes involved in replication, recombination and repair, catalyze a change in DNA
topology through a series of highly coordinated mechanistic steps. Undergraduate biology
and mathematics students can visualize and explore the principles of topoisomerase action
by using easily available materials such as Velcro, ribbons, telephone cords, zippers and
tubing. These simple toys can be used as powerful teaching tools to engage students in
hands-on exploration with the goal of learning about both the mathematics and the biology
of DNA structure.