  Macrochains of topologically interlocked rings with unique physical
properties have recently gained considerable interest in supramolecular
chemistry, biology, and soft matter. Most of the work has been, so far, focused
on linear chains and on their variety of conformational properties compared to
standard polymers. Here we go beyond the linear case and show that, by
circularizing such macrochains, one can exploit the topology of the local
interlockings to store torsional stress in the system, altering significantly
its metric and local properties. Moreover, by properly defining the twist (Tw)
and writhe (Wr) of these macrorings we show the validity of a relation
equivalent to the C\v{a}lug\v{a}reanu-White-Fuller theorem $Tw + Wr$=const,
originally proved for ribbon like structures such as ds-DNA. Our results
suggest that circular structures of topologically linked rings with storable
and tunable torsion can form a new category of highly designable multiscale
structures with potential applications in supramolecular chemistry and material
science
