Leveraging Steric Moieties for Kinetic Control of DNA Strand Displacement Reactions.

DNA strand displacement networks are a critical part of dynamic DNA nanotechnology and are proven primitives for implementing chemical reaction networks. Precise kinetic control of these networks is important for their use in a range of applications. Among the better understood and widely leveraged kinetic properties of these networks are toehold sequence, length, composition, and location. While steric hindrance has been recognized as an important factor in such systems, a clear understanding of its impact and role is lacking. Here, a systematic investigation of steric hindrance within a DNA toehold-mediated strand displacement network was performed through tracking kinetic reactions of reporter complexes with incremental concatenation of steric moieties near the toehold. Two subsets of steric moieties were tested with systematic variation of structures and reaction conditions to isolate sterics from electrostatics. Thermodynamic and coarse-grained computational modeling was performed to gain further insight into the impacts of steric hindrance. Steric factors yielded up to 3 orders of magnitude decrease in the reaction rate constant. This pronounced effect demonstrates that steric moieties can be a powerful tool for kinetic control in strand displacement networks while also being more broadly informative of DNA structural assembly in both DNA-based therapeutic and diagnostic applications that possess elements of steric hindrance through DNA functionalization with an assortment of chemistries.

Speed and Correctness Guarantees for Programmable Enthalpy-Neutral DNA Reactions†.

Molecular control circuits embedded within chemical systems to direct molecular events have transformative applications in synthetic biology, medicine, and other fields. However, it is challenging to understand the collective behavior of components due to the combinatorial complexity of possible interactions. Some of the largest engineered molecular systems to date have been constructed using DNA strand displacement reactions, in which signals can be propagated without a net change in base pairs (enthalpy neutral). This flexible and programmable component has been used for constructing molecular logic circuits, smart structures and devices, for systems with complex autonomously generated dynamics, and for diagnostics. Limiting their utility, however, strand displacement systems are susceptible to the spurious release of output in the absence of the proper combination of inputs (leak), as well as reversible unproductive binding (toehold occlusion) and spurious displacement that slow down desired kinetics. We systematize the properties of the simplest enthalpy-neutral strand displacement cascades (logically linear topology), and develop a taxonomy for the desired and undesired properties affecting speed and correctness, and trade-offs between them based on a few fundamental parameters. We also show that enthalpy-neutral linear cascades can be engineered with stronger thermodynamic guarantees to leak than non-enthalpy-neutral designs. We confirm our theoretical analysis with laboratory experiments comparing the properties of different design parameters. Our method of tackling the combinatorial complexity using mathematical proofs can guide the engineering of robust and efficient molecular algorithms.

Digital nanoreactors to control absolute stoichiometry and spatiotemporal behavior of DNA receptors within lipid bilayers.

Interactions between membrane proteins are essential for cell survival but are often poorly understood. Even the biologically functional ratio of components within a multi-subunit membrane complex-the native stoichiometry-is difficult to establish. Here we demonstrate digital nanoreactors that can control interactions between lipid-bound molecular receptors along three key dimensions: stoichiometric, spatial, and temporal. Each nanoreactor is based on a DNA origami ring, which both templates the synthesis of a liposome and provides tethering sites for DNA-based receptors (modelling membrane proteins). Receptors are released into the liposomal membrane using strand displacement and a DNA logic gate measures receptor heterodimer formation. High-efficiency tethering of receptors enables the kinetics of receptors in 1:1 and 2:2 absolute stoichiometries to be observed by bulk fluorescence, which in principle is generalizable to any ratio. Similar single-molecule-in-bulk experiments using DNA-linked membrane proteins could determine native stoichiometry and the kinetics of membrane protein interactions for applications ranging from signalling research to drug discovery.

Absolute and arbitrary orientation of single-molecule shapes.

DNA origami is a modular platform for the combination of molecular and colloidal components to create optical, electronic, and biological devices. Integration of such nanoscale devices with microfabricated connectors and circuits is challenging: Large numbers of freely diffusing devices must be fixed at desired locations with desired alignment. We present a DNA origami molecule whose energy landscape on lithographic binding sites has a unique maximum. This property enabled device alignment within 3.2° on silica surfaces. Orientation was absolute (all degrees of freedom were specified) and arbitrary (the orientation of every molecule was independently specified). The use of orientation to optimize device performance was shown by aligning fluorescent emission dipoles within microfabricated optical cavities. Large-scale integration was demonstrated with an array of 3456 DNA origami with 12 distinct orientations that indicated the polarization of excitation light.

Effective design principles for leakless strand displacement systems.

Artificially designed molecular systems with programmable behaviors have become a valuable tool in chemistry, biology, material science, and medicine. Although information processing in biological regulatory pathways is remarkably robust to error, it remains a challenge to design molecular systems that are similarly robust. With functionality determined entirely by secondary structure of DNA, strand displacement has emerged as a uniquely versatile building block for cell-free biochemical networks. Here, we experimentally investigate a design principle to reduce undesired triggering in the absence of input (leak), a side reaction that critically reduces sensitivity and disrupts the behavior of strand displacement cascades. Inspired by error correction methods exploiting redundancy in electrical engineering, we ensure a higher-energy penalty to leak via logical redundancy. Our design strategy is, in principle, capable of reducing leak to arbitrarily low levels, and we experimentally test two levels of leak reduction for a core "translator" component that converts a signal of one sequence into that of another. We show that the leak was not measurable in the high-redundancy scheme, even for concentrations that are up to 100 times larger than typical. Beyond a single translator, we constructed a fast and low-leak translator cascade of nine strand displacement steps and a logic OR gate circuit consisting of 10 translators, showing that our design principle can be used to effectively reduce leak in more complex chemical systems.

Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components.

Biochemical circuits made of rationally designed DNA molecules are proofs of concept for embedding control within complex molecular environments. They hold promise for transforming the current technologies in chemistry, biology, medicine and material science by introducing programmable and responsive behaviour to diverse molecular systems. As the transformative power of a technology depends on its accessibility, two main challenges are an automated design process and simple experimental procedures. Here we demonstrate the use of circuit design software, combined with the use of unpurified strands and simplified experimental procedures, for creating a complex DNA strand displacement circuit that consists of 78 distinct species. We develop a systematic procedure for overcoming the challenges involved in using unpurified DNA strands. We also develop a model that takes synthesis errors into consideration and semi-quantitatively reproduces the experimental data. Our methods now enable even novice researchers to successfully design and construct complex DNA strand displacement circuits.

Less haste, less waste: on recycling and its limits in strand displacement systems.

We study the potential for molecule recycling in chemical reaction systems and their DNA strand displacement realizations. Recycling happens when a product of one reaction is a reactant in a later reaction. Recycling has the benefits of reducing consumption, or waste, of molecules and of avoiding fuel depletion. We present a binary counter that recycles molecules efficiently while incurring just a moderate slowdown compared with alternative counters that do not recycle strands. This counter is an n-bit binary reflecting Gray code counter that advances through 2(n) states. In the strand displacement realization of this counter, the waste-total number of nucleotides of the DNA strands consumed-is polynomial in n, the number of bits of the counter, while the waste of alternative counters grows exponentially in n. We also show that our n-bit counter fails to work correctly when many (Θ(n)) copies of the species that represent the bits of the counter are present initially. The proof applies more generally to show that in chemical reaction systems where all but one reactant of each reaction are catalysts, computations longer than a polynomial function of the size of the system are not possible when there are polynomially many copies of the system present.

An algorithm for the energy barrier problem without pseudoknots and temporary arcs.

We make two new contributions to the problem of calculating pseudoknot-free folding pathways with minimum energy barrier between pairs (Α,Β) of RNA secondary structures. Our first contribution pertains to a problem posed by Morgan and Higgs: find a min-barrier direct folding pathway for a simple energy model in which each base pair contributes -1. In a direct folding pathway, intermediate structures contain only base pairs in Α and Β and are of length |AΔB| (the size of the symmetric difference of the two structures). We show how to solve this problem exactly, using techniques for deconstructing bipartite graphs. The problem is NP-hard and so our algorithm requires exponential time in the worst case but performs quite well empirically on pairs of structures that are hundreds of nucleotides long. Our second contribution shows that for the simple energy model, repeatedly adding or removing a base pair from A U B along a pathway is not useful in minimizing the energy barrier. Two consequences of this result are that (i) the problem of determining the min-barrier pseudoknot-free folding pathway from the space of direct pathways with repeats is NP-hard and (ii) our new algorithm finds the min-barrier pathway not only from the space of direct folding pathways but in fact from the space of direct pathways with repeats.

Core Hunter: an algorithm for sampling genetic resources based on multiple genetic measures.

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.

A replica exchange Monte Carlo algorithm for protein folding in the HP model.

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.