We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots – closed loops in three-dimensional space equipped with additional bonds that connect different segments of the knot. We extend the Kauffman bracket polynomial (which is closely related to the Jones polynomial) to bonded knots through the introduction of the bonded version of the Kauffman bracket skein module. We show that this module is infinitely generated and torsion-free for both the rigid and topological case of bonded knots. In the rigid case, evaluating a bonded knot in the basis of this module yields an bonded knot invariant closely related to the APS bracket and the Simplified RNA polynomial.
