Statistical thermodynamic analysis and designof DNA-based computers

A principal research area in biomolecular computing is the development of analytical methods for evaluating computational fidelity and efficiency. In this work, the equilibrium theory of the DNA helix-coil transition is reviewed and expanded, as applied to the analysis and design of oligonucleotide-based computers. After a review of the equilibrium apparatus for modeling the helix-coil transition for single dsDNA species, application to complex hybridizing systems is discussed, via decomposition into component equilibria, which are presumed to proceed independently. The alternative approach, which involves estimation of a mean error probability per hybridized structure, or computational incoherence, ε is then presented, along with a discussion of a special-case exact solution (directed dimer formation), and an approximate general solution, applicable to conditions of uniform fractional-saturation. In order to clarify the opposing nature of the predictions of these two models, simulations are presented for the uniform saturation solution for ε, as applied to a small Tag–Antitag (TAT) system, along with the behavior expected via isolated melting curves. By a comparison with the predictions of a recent, TAT-specific solution for ε, the views provided by these generalized approximate models are shown to define the opposing limits of a more general error-response.