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

摘要

The importance of DNA microarrays 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 (ε). Although predictions for dilute inputs indicate the easy attainment of excellent fidelity, recently a sharp 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, 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, ε_(e(i)) for the single-tag, excess limit. The temperature-dependence 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 ε_(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 ε. 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.