The Fidelity of the Tag-Antitag System III. Robustness in the Excess Limit: The Stringent Temperature

The importance of DNAmicroarrays and Tag-Antitag (TAT) systems has prompted the recent development of various approaches for high-fidelity design, including analytical methods based on an ensemble average error probability per conformation, or computational incoherence ( ). Although predictions for dilute inputs indicate the easy attainment of excellent fidelity, recently a sharp phase transition from the low-error -behavior predicted for dilute inputs, to a high-error -behavior was predicted to accompany an asymmetric (i.e., single-tag) excess input. This error-response, which is likely to be the critical test of TAT system robustness for DNA-based computing applications that employ non-linear amplification, is examined more closely, via derivation of an approximate expression, e(i) for the single-tag, excess limit. The temperaturedependence of this expression is then characterized, and applied to derive an expression for a novel TAT system error-parameter, T † i which defines the temperature of minimal e(i). T † i is taken to provide a precise definition of the stringent reaction temperature previously discussed conceptually in the literature. A similar analysis, undertaken for a uniform excess multi-tag input, indicates the absence of a phase transition in . The validity of each expression is discussed via simulation, with comparison to the general model. Applicability of {T † i } to both TAT system design and selection of an optimal reaction temperature is discussed.