A Unified Dynamic Programming Framework for the Analysis of Interacting Nucleic Acid Strands: Enhanced Models, Scalability, and Speed.

Dynamic programming algorithms within the NUPACK software suite enable analysis of nucleic acid sequences over complex and test tube ensembles containing arbitrary numbers of interacting strand species, serving the needs of researchers in molecular programming, nucleic acid nanotechnology, synthetic biology, and across the life sciences. Here, to enhance the underlying physical model, ensure scalability for large calculations, and achieve dramatic speedups when calculating diverse physical quantities over complex and test tube ensembles, we introduce a unified dynamic programming framework that combines three ingredients: (1) recursions that specify the dependencies between subproblems and incorporate the details of the structural ensemble and the free energy model, (2) evaluation algebras that define the mathematical form of each subproblem, (3) operation orders that specify the computational trajectory through the dependency graph of subproblems. The physical model is enhanced using new recursions that operate over the complex ensemble including coaxial and dangle stacking subensembles.

Constrained Multistate Sequence Design for Nucleic Acid Reaction Pathway Engineering.

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.