Analysis of Interacting Nucleic Acids in Dilute Solutions

Motivated by the growing demand for analysis tools for diverse natural and engineered DNA and RNA systems, we develop a general theory and set of computational algorithms to perform thermodynamic analysis of dilute reactive solutions and then apply these techniques to interacting nucleic acids. The theory correctly accounts for the effects of indistinguishability in partition function calculations for complexes of interacting strands. With partition functions in hand, the unique complex concentrations corresponding to thermodynamic equilibrium are obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables corresponding to experimentally measurable properties. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality. To make these analysis tools available to researchers worldwide, we present NUPACK, a web-based software suite for thermodynamic analysis of nucleic acids. Its efficacy is demonstrated in example calculations and the results are shown to be in agreement with experiment. Finally, the thermodynamic properties of a DNA-based triggered self-assembly device [1] are analyzed using NUPACK and extensions of its tools. The computational results complement experimental studies, exposing novel properties about the system and dictating further research.