Abstract
Information technologies enable programmers and engineers to design and synthesize systems of startling complexity that nonetheless behave as intended. This mastery of complexity is made possible by a hierarchy of formal abstractions that span from high-level programming languages down to low-level implementation specifications, with rigorous connections between the levels. DNA nanotechnology presents us with a new molecular information technology whose potential has not yet been fully unlocked in this way. Developing an effective hierarchy of abstractions may be critical for increasing the complexity of programmable DNA systems. Here, we build on prior practice to provide a new formalization of ‘domain-level’ representations of DNA strand displacement systems that has a natural connection to nucleic acid biophysics while still being suitable for formal analysis. Enumeration of unimolecular and bimolecular reactions provides a semantics for programmable molecular interactions, with kinetics given by an approximate biophysical model. Reaction condensation provides a tractable simplification of the detailed reactions that respects overall kinetic properties. The applicability and accuracy of the model is evaluated across a wide range of engineered DNA strand displacement systems. Thus, our work can serve as an interface between lower-level DNA models that operate at the nucleotide sequence level, and high-level chemical reaction network models that operate at the level of interactions between abstract species.
Highlights
The evolution of DNA nanotechnology during the last few decades has shown DNA to be a robust and versatile substrate for nanoscale construction and computation [1]
This approximation is valid for low species concentrations, and can be performed either with or without reference to specific reaction rates, e.g. those that Peppercorn provides for domain-level DNA systems. Peppercorn uses this timescale separation to condense the detailed enumerated network with fast and slow reactions into a considerably smaller chemical reaction networks (CRNs) with only overall slow reactions. We prove that those two CRNs are equivalent in terms of overall slow reaction pathways, and we provide a corresponding reaction rate condensation algorithm to simulate domain-level strand displacement (DSD) systems on the more compact, condensed level
We present a rigorous self-contained theory that is independent of DSD enumeration, but requires certain properties of the original, detailed CRN to which the coarse-graining and condensation algorithm is applied: (i) Reactions can have any arity (n, m), as long as 1 ≤ n ≤ 2 and m > 0
Summary
The evolution of DNA nanotechnology during the last few decades has shown DNA to be a robust and versatile substrate for nanoscale construction and computation [1]. In contrast to other enumerators, it provides an exhaustive set of intramolecular domain-level reactions within the space of pseudoknot-free nucleic acid secondary structures (opening and closing of helix domains, as well as three-way and four-way branch migration via proximal and remote toeholds; see §2.2) This class of secondary structures (see definition 2.3) is important, as the vast majority of conformations will be sterically feasible and well modelled by a well-established DNA and RNA thermodynamic energy model [21], which is used by standard nucleic acid structure prediction software [22,23,24]. Combinatorial explosion due to implausible polymerization (figure 3) is controlled by enforcing a separation of timescales: assuming some reactions are much faster than others This approximation is valid for low species concentrations, and can be performed either with or without reference to specific reaction rates, e.g. those that Peppercorn provides for domain-level DNA systems. Badelt et al [44] use Nuskell (and Peppercorn) to enumerate and compare 13 different DSD systems implementing a DNA-only oscillator [7]
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