The fidelity of the tag-antitag system: Characterization of the stringent temperature for robustness in the excess limit

Abstract

The importance of DNA microarrays and Tag-Antitag (TAT) systems in biotechnology and DNA computing has prompted the development of various approaches for high-fidelity design, including analytical methods based on an ensemble average error probability per conformation, or computational incoherence (ε). Although system biasing for dilute input has been reported to allow the attainment of high fidelity, recently a sharp pseudo-phase transition from the low-error ε-behavior predicted for dilute inputs, to a high-error ε-behavior was predicted to accompany an asymmetric (i.e., single-tag) excess input. This error-response, likely to be the critical test of TAT system robustness for DNA-based computing applications that employ multiple merge operations and/or non-linear amplification, is here examined more closely, via derivation of an approximate closed-form expression, ${\mathit{\epsilon }}_{\mathit{e}\mathrm{(}\mathit{i}\mathrm{)}}$ for the single-tag, excess input. The temperature-dependence of this expression is characterized, and applied to derive an expression for a novel TAT system error-parameter, ${\mathit{T}}_{\mathit{i}}^{\mathrm{†}}$ which defines the temperature of minimal ${\mathit{\epsilon }}_{\mathit{e}\mathrm{(}\mathit{i}\mathrm{)}}$ . ${\mathit{T}}_{\mathit{i}}^{\mathrm{†}}$ is taken to provide a more precise definition of the stringent reaction temperature previously discussed conceptually in the literature. A similar analysis is also undertaken for a uniform excess multi-tag input, which indicates the absence of an accompanying pseudo-phase transition in ε. The validity of ${\mathit{\epsilon }}_{\mathit{e}\mathrm{(}\mathit{i}\mathrm{)}}$ is discussed via simulation, with comparison to the predictions of the general model. Applicability of $\{{\mathit{T}}_{\mathit{i}}^{\mathrm{†}}\}$ to both TAT system design and selection of a reaction temperature optimally robust to an asymmetric excess input is discussed.