Abstract:The Nucleic Acid Package (NUPACK) is a growing software suite for the analysis and design of nucleic acid systems. The NUPACK web server (http://www.nupack.org) currently enables:• Analysis: thermodynamic analysis of dilute solutions of interacting nucleic acid strands.• Design: sequence design for complexes of nucleic acid strands intended to adopt a target secondary structure at equilibrium.• Utilities: evaluation, display, and annotation of equilibrium properties of a complex of nucleic acid strands.NUPACK algorithms are formulated in terms of nucleic acid secondary structure. In most cases, pseudoknots are excluded from the structural ensemble.

DESIGNSEQ(s)m leafopt ← 0 φ, n ← OPTIMIZELEAF(s) while n > fstop|s| and m leafopt < M leafopt φ,n ← OPTIMIZELEAF(s)Algorithm S1: Single-scale ensemble defect optimization with uniform mutation sampling.Algorithm S2: Single-scale ensemble defect optimization with defect-weighted mutation sampling.

We describe a framework for designing the sequences of multiple nucleic acid strands intended to hybridize in solution via a prescribed reaction pathway. Sequence design is formulated as a multistate optimization problem using a set of target test tubes to represent reactant, intermediate, and product states of the system, as well as to model crosstalk between components. Each target test tube contains a set of desired "on-target" complexes, each with a target secondary structure and target concentration, and a set of undesired "off-target" complexes, each with vanishing target concentration. Optimization of the equilibrium ensemble properties of the target test tubes implements both a positive design paradigm, explicitly designing for on-pathway elementary steps, and a negative design paradigm, explicitly designing against off-pathway crosstalk. Sequence design is performed subject to diverse user-specified sequence constraints including composition constraints, complementarity constraints, pattern prevention constraints, and biological constraints. Constrained multistate sequence design facilitates nucleic acid reaction pathway engineering for diverse applications in molecular programming and synthetic biology. Design jobs can be run online via the NUPACK web application.

We describe an algorithm for designing the equilibrium base-pairing properties of a test tube of interacting nucleic acid strands. A target test tube is specified as a set of desired "on-target" complexes, each with a target secondary structure and target concentration, and a set of undesired "off-target" complexes, each with vanishing target concentration. Sequence design is performed by optimizing the test tube ensemble defect, corresponding to the concentration of incorrectly paired nucleotides at equilibrium evaluated over the ensemble of the test tube. To reduce the computational cost of accepting or rejecting mutations to a random initial sequence, the structural ensemble of each on-target complex is hierarchically decomposed into a tree of conditional subensembles, yielding a forest of decomposition trees. Candidate sequences are evaluated efficiently at the leaf level of the decomposition forest by estimating the test tube ensemble defect from conditional physical properties calculated over the leaf subensembles. As optimized subsequences are merged toward the root level of the forest, any emergent defects are eliminated via ensemble redecomposition and sequence reoptimization. After successfully merging subsequences to the root level, the exact test tube ensemble defect is calculated for the first time, explicitly checking for the effect of the previously neglected off-target complexes. Any off-target complexes that form at appreciable concentration are hierarchically decomposed, added to the decomposition forest, and actively destabilized during subsequent forest reoptimization. For target test tubes representative of design challenges in the molecular programming and synthetic biology communities, our test tube design algorithm typically succeeds in achieving a normalized test tube ensemble defect ≤1% at a design cost within an order of magnitude of the cost of test tube analysis.

Information technologies enable programmers and engineers to design and synthesize systems of startling complexity that nonetheless behave as intended. This mastery of complexity is made possible by a hierarchy of formal abstractions that span from high-level programming languages down to low-level implementation specifications, with rigorous connections between the levels. DNA nanotechnology presents us with a new molecular information technology whose potential has not yet been fully unlocked in this way. Developing an effective hierarchy of abstractions may be critical for increasing the complexity of programmable DNA systems. Here, we build on prior practice to provide a new formalization of ‘domain-level’ representations of DNA strand displacement systems that has a natural connection to nucleic acid biophysics while still being suitable for formal analysis. Enumeration of unimolecular and bimolecular reactions provides a semantics for programmable molecular interactions, with kinetics given by an approximate biophysical model. Reaction condensation provides a tractable simplification of the detailed reactions that respects overall kinetic properties. The applicability and accuracy of the model is evaluated across a wide range of engineered DNA strand displacement systems. Thus, our work can serve as an interface between lower-level DNA models that operate at the nucleotide sequence level, and high-level chemical reaction network models that operate at the level of interactions between abstract species.