A statistical mechanical treatment of error in the annealing biostep of DNA computation

Abstract

The relaxation of an ensemble of ss-DNA oligonucleotides to an equilibrium of annealed, or hybridized, double-stranded molecules has been harnessed for massively parallel computation. The annealing reactions, however, have the potential to produce error. Various heuristic methods for generating sets of single-stranded DNA (encodings) with minimal potential for hybridization error have emerged. Nevertheless, an adequate model of error demands not only implementation details that minimize the impact of physical uncertainties on the computational process, but also an unambiguous, quantitative measure of confidence with which to associate computational results. In this study, the principles of equilibrium statistical mechanics are used to derive an expression for the ensemble average equilibrium probability of an error hybridization per annealing event, given a specified set of planned hybridizations, a set of encodings, and a reaction temperature.