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.