Fig. 3. Underlying mechanisms used in dynamic DNA circuits. (A) Schematic representation of the toehold-mediated strand displacement reaction. Input A binds to the toehold-sequence 1* present on complex X, initiating subsequent branch migration. Completion of branch migration results in the release of output B and the formation of complex Y. Since the resulting complex Y has no available toehold, the reverse reaction is effectively not taking place. (B) The rate of toehold-mediated strand displacement is highly dependent on the length and sequence of the toehold domain. Increasing the stability of the toehold results in an enhanced displacement rate (adapted with permission from ref. 21, copyright 2009, American Chemical Society). (C) Schematic representation of the toehold-exchange mechanism. Input A binds to the toehold-sequence 1* present on complex X, initiating subsequent branch migration. After branch migration output B is bound to the complex via toehold-sequence 3*, which has to spontaneously dissociate for the toehold exchange reaction to complete, resulting in the release of output B and the formation of complex Y. Since complex Y contains a toehold-sequence to which output B can bind, the reverse reaction can also take place.