Robustness of DNA Strand Displacement Systems⋆^⁎

How to construct a reliable deoxyribonucleic acid (DNA) circuit is one of the most important issues in the field of molecular programming and computing. Such a circuit frequently suffers from various kinds of unintended binding reactions on account of a lower specificity of the molecular interaction emerging from base complementarity between DNA strands, which results in low reliability of the molecular circuit. In this study, we propose a method to quantitatively evaluate the robustness of a DNA circuit created by DNA strand displacement reactions. The highlight of our method is representing the circuit system contaminated by unintended reactions by a standard form of a disturbed nonlinear system and evaluating the robustness with the L₂ gain by solving the Hamilton–Jacobi inequality.