1. A toehold exchange catalyst system comprising: a substrate molecule defining a plurality of binding sites including at least one first toehold binding site that is in an initial, single-stranded state and at least one second toehold binding site that is in an initial, double-stranded state; a plurality of distinct ligand molecules pre-hybridized onto said substrate molecule, each of said pre-hybridized ligand molecules having binding sites that are complementary to at least one of the plurality of binding sites on said substrate molecule such that the pre-hybridized ligand molecules do not overlap each other, and such that said distinct pre-hybridized ligand molecules jointly occupy all of the plurality of binding sites on said substrate molecule except the first toehold binding site; a plurality of distinct reactant ligand molecules each of said reactant ligand molecules having binding sites that are complementary to at least one of the plurality of binding sites on said substrate molecule, and wherein at least one of the reactant ligand molecules additionally possesses a binding site complementary to the second toehold binding site; a catalyst molecule having at least one binding site complementary to the first toehold binding site of the substrate molecule and at least one additional, binding site on said substrate molecule identical, in sequence to the binding sites of at least one of the pre-hybridized ligand molecules on said substrate molecule, but wherein said at least one additional, binding site is not complementary to the second toehold binding site such that when the catalyst molecule is bound to the substrate molecule it triggers an exchange reaction that dislodges at least an output molecule formed from at least one pre-hybridized ligand molecule, thereby converting the second toehold binding site into a single-stranded state; and such that when the second toehold is bound by a reactant ligand molecule the second toehold binding site is converted back into a double-stranded state and the bound catalyst molecule is released thereby converting the first toehold binding site back into a single-stranded state.