Polynomial time dynamic programming algorithms play a crucial role in the design, analysis and engineering of nucleic acid systems including DNA computers and DNA/RNA nanostructures. However, in complex multistranded or pseudoknotted systems, computing the minimum free energy (MFE), and partition function of nucleic acid systems is NP-hard. Despite this, multistranded and/or pseudoknotted systems represent some of the most utilised and successful systems in the field. This leaves open the tempting possibility that many of the kinds of multistranded and/or pseudoknotted systems we wish to engineer actually fall into restricted classes, that do in fact have polynomial time algorithms, but we've just not found them yet. Here, we give polynomial time algorithms for MFE and partition function calculation for a restricted kind of multistranded system called the 1D scaffolded DNA computer. This model of computation thermodynamically favours correct outputs over erroneous states, simulates finite state machines in 1D and Boolean circuits in 2D, and is amenable to DNA storage applications. In an effort to begin to ask the question of whether we can naturally compare the expressivity of nucleic acid systems based on the computational complexity of prediction of their preferred energetic states, we show our MFE problem is in logspace (the complexity class L), making it perhaps one of the simplest known, natural, nucleic acid MFE problems. Finally, we provide a stochastic kinetic simulator for the 1D scaffolded DNA computer and evaluate strategies for efficiently speeding up this thermodynamically favourable system in a constant-temperature kinetic regime.

Given multiple nucleic acid strands, what is the minimum free energy (MFE) secondary structure that they can form? As interacting nucleic acid strands are the basis for DNA computing and molecular programming, e.g., in DNA self-assembly and DNA strand displacement systems, determining the MFE structure is an important step in the design and verification of these systems. Efficient dynamic programming algorithms are well known for predicting the MFE pseudoknot-free secondary structure of a single nucleic acid strand. In contrast, we prove that for a simple energy model, the problem of predicting the MFE pseudoknot-free secondary structure formed from multiple interacting nucleic acid strands is NP-hard and also APX-hard. The latter result implies that there does not exist a polynomial time approximation scheme for this problem, unless 𝖯 = NP, and it suggests that heuristic methods should be investigated.

The emerging fields of genetic engineering, synthetic biology, DNA computing, DNA nanotechnology, and molecular programming herald the birth of a new information technology that acquires information by directly sensing molecules within a chemical environment, stores information in molecules such as DNA, RNA, and proteins, processes that information by means of chemical and biochemical transformations, and uses that information to direct the manipulation of matter at the nanometer scale. To scale up beyond current proof-of-principle demonstrations, new methods for managing the complexity of designed molecular systems will need to be developed. Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a well-mixed “soup” of molecules is stochastic, asynchronous, concurrent, and often involves multiple intermediate steps in the implementation, parallel pathways, and side reactions. This problem relates to the verification of Petri nets, but existing approaches are not sufficient for providing a single guarantee covering an infinite set of possible initial states (molecule counts) and an infinite state space potentially explored by the system given any initial state. We address these issues by formulating a new theory of pathway decomposition that provides an elegant formal basis for comparing chemical reaction network implementations, and we present an algorithm that computes this basis. Our theory naturally handles certain situations that commonly arise in molecular implementations, such as what we call “delayed choice,” that are not easily accommodated by other approaches. We further show how pathway decomposition can be combined with weak bisimulation to handle a wider class that includes most currently known enzyme-free DNA implementation techniques. We anticipate that our notion of logical equivalence between chemical reaction network implementations will be valuable for other molecular implementations such as biochemical enzyme systems, and perhaps even more broadly in concurrency theory.

BACKGROUND: Existing algorithms and methods for forming diverse core subsets currently address either allele representativeness (breeder's preference) or allele richness (taxonomist's preference). The main objective of this paper is to propose a powerful yet flexible algorithm capable of selecting core subsets that have high average genetic distance between accessions, or rich genetic diversity overall, or a combination of both. RESULTS: We present Core Hunter, an advanced stochastic local search algorithm for selecting core subsets. Core Hunter is able to find core subsets having more genetic diversity and better average genetic distance than the current state-of-the-art algorithms for all genetic distance and diversity measures we evaluated. Furthermore, Core Hunter can attempt to optimize any number of genetic measures simultaneously, based on the preference of the user. Notably, Core Hunter is able to select significantly smaller core subsets, which retain all unique alleles from a reference collection, than state-of-the-art algorithms. CONCLUSION: Core Hunter is a highly effective and flexible tool for sampling genetic resources and establishing core subsets. Our implementation, documentation, and source code for Core Hunter is available at http://corehunter.org.

Methods for reliable synthesis of long genes offer great promise for protein synthesis via expression of synthetic genes, with applications to improved analysis of protein structure and function, as well as engineering of novel proteins. Current technologies for gene synthesis use computational methods for design of short oligos, which can then be reliably synthesized and assembled into the desired target gene. For collision-oblivious oligo design -when mishybridizations between oligos are ignored -we give a simple and efficient dynamic programming algorithm. We conjecture that the collision-aware oligo design problem is NP-hard and provide evidence that mishybridizations between oligos occur infrequently in the designs from the collision-oblivious algorithm. We extend our dynamic programming algorithm to achieve collision-aware oligo design, when the target gene can be partitioned into independently-assembled short segments. We evaluate our methods on a large biological gene set.

BACKGROUND: The ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics. The ab initio protein folding problem is computationally challenging and has been shown to be NuRho -hard even when conformations are restricted to a lattice. In this work, we implement and evaluate the replica exchange Monte Carlo (REMC) method, which has already been applied very successfully to more complex protein models and other optimization problems with complex energy landscapes, in combination with the highly effective pull move neighbourhood in two widely studied Hydrophobic Polar (HP) lattice models. RESULTS: We demonstrate that REMC is highly effective for solving instances of the square (2D)and cubic (3D) HP protein folding problem. When using the pull move neighbourhood, REMCoutperforms current state-of-the-art algorithms for most benchmark instances. Additionally, we show that this new algorithm provides a larger ensemble of ground-state structures than the existing state-of-the-art methods. Furthermore, it scales well with sequence length, and it finds significantly better conformations on long biological sequences and sequences with a provably unique ground-state structure, which is believed to be a characteristic of real proteins. We also present evidence that our REMC algorithm can fold sequences which exhibit significant interaction between termini in the hydrophobic core relatively easily. CONCLUSION: We demonstrate that REMC utilizing the pull move neighbourhood significantly outperforms current state-of-the-art methods for protein structure prediction in the HP model on 2D and 3D lattices. This is particularly noteworthy, since so far, the state-of-the-art methods for2D and 3D HP protein folding - in particular, the pruned-enriched Rosenbluth method (PERM) and,to some extent, Ant Colony Optimisation (ACO) - were based on chain growth mechanisms. To the best of our knowledge, this is the first application of REMC to HP protein folding on the cubic lattice, and the first extension of the pull move neighbourhood to a 3D lattice.