DNA as a universal substrate for chemical kinetics

Abstract

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka-Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior. . Whereas the use of mass-action kinetics to describe existing chemical systems is well established, the inverse problem of experimentally implementing a given set of chemical reactions has not been considered in full generality. Here, we ask: Given a set of formal chemical reaction equations, involving formal species X 1 ; X 2 ; …; X n , can we find a set of actual molecules M 1 ; M 2 ; …; M m that interact in an appropriate buffer to approximate the formal system's mass-action kinetics? If this were possible, the formalism of chemical reaction networks (CRNs) could be treated as an effective programming language for the design of complex network behavior (5-9).Unfortunately, a formally expressed system of coupled chemical equations may not have an obvious realization in known chemistry. In a formal system of chemical reactions, a species may participate in multiple reactions, both as a reactant and/or as a product, and these reactions progress at relative rates determined by the corresponding rate constants, all of which imposes formidable constraints on the chemical properties of the species participating in the reactions. For example, it is likely hard to find a physical implementation of arbitrary chemical reaction equations using small molecules, because small molecules have a limited set of reactivities.Thus, formal CRNs may appear to be an unforgiving target for general implementation strategies. Indeed, most experimental work in chemical and biological engineering has started with particular molecular systems-genetic regulatory networks (10), RNA folding and processing (11), metabolic pathways (12), signal transduction pathways (13), cell-free enzyme systems (14, 15), and small molecules (16, 17)-and found ways to modify or rewire the components to achieve particular functions. Attempts to systematically understand what functional behaviors can be obtained by using such components have targeted connections to analog and digital electronic circuits (10,18,19), neural networks (20)(21)(22), and computing machines (...

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“…It has been shown that such arbitrary systems of chemical reactions can be faithfully implemented in a biochemical setting by compiling them into an enlarged system of DNA strand displacement reactions [50]. By contrast, our design is influenced by more practical considerations and is targeted to a specific implementation framework using DNAzymes.…”

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“…Note that while we have found numerically conditions in which a WTA effect occurs in DNA-only circuits, it is not guaranteed that a unique winner will exist whenever competition for fuel occurs. Strand displacement is prone to leak, which is thought to arise mainly from blunt-end displacement (displacement of a strand from a duplex without the assistance of a toehold) [32,65,66]. Leak is especially problematic for first-order rsif.royalsocietypublishing.org J R Soc Interface 10: 20130212 autocatalytic circuits because they amplify exponentially even a miniscule leak (contrary to second-order amplification which occurs only above a threshold, in the presence of first-order degradation) [31].…”