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Nucleic acid secondary structure models usually exclude pseudoknots due to the difficulty of treating these nonnested structures efficiently in structure prediction and partition function algorithms. Here, the standard secondary structure energy model is extended to include the most physically relevant pseudoknots. We describe an O(N(5)) dynamic programming(More)
In nature, self-assembling and disassembling complexes of proteins and nucleic acids bound to a variety of ligands perform intricate and diverse dynamic functions. In contrast, attempts to rationally encode structure and function into synthetic amino acid and nucleic acid sequences have largely focused on engineering molecules that self-assemble into(More)
Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the(More)
Biologists working in the area of computational protein design have never doubted the seriousness of the algorithmic challenges that face them in attempting in silico sequence selection. It turns out that in the language of the computer science community, this discrete optimization problem is NP-hard. The purpose of this paper is to explain the context of(More)
The rst half of this paper derives the adjoint equations for inviscid and viscous compressible ow, with the emphasis being on the correct formulation of the adjoint boundary conditions and restrictions on the permissible choice of operators in the linearised functional. It is also shown that the boundary conditions for the adjoint problem can be simpliied(More)
Hybridization chain reaction (HCR) provides multiplexed, isothermal, enzyme-free, molecular signal amplification in diverse settings. Within intact vertebrate embryos, where signal-to-background is at a premium, HCR in situ amplification enables simultaneous mapping of multiple target mRNAs, addressing a longstanding challenge in the biological sciences.(More)
Dead-end elimination (DEE) is a powerful theorem for selecting optimal protein side-chain orientations from a large set of discrete conformations. The present work describes a new approach to dead-end elimination that effectively splits conformational space into partitions to more efficiently eliminate dead-ending rotamers. Split DEE makes it possible to(More)
We present two error estimation approaches for bounding or correcting the error in functional estimates such as lift or drag. Adjoint methods quantify the error in a particular output functional that results from residual errors in approximating the solution to the partial differential equation. Defect methods can be used to bound or reduce the error in the(More)
UNLABELLED 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(More)
We introduce the concept of hybridization chain reaction (HCR), in which stable DNA monomers assemble only upon exposure to a target DNA fragment. In the simplest version of this process, two stable species of DNA hairpins coexist in solution until the introduction of initiator strands triggers a cascade of hybridization events that yields nicked double(More)