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 (...

Time-Complexity of Multilayered DNA Strand Displacement Circuits

“…More recent papers have implemented a variety of improvements including gates for fast catalytic amplification [11,9], and reversible logic gates based on a simple catalytic gate motif [3]. This technology provides a starting point for building large-scale molecular circuitry with quantitatively predictable behavior using standardized off-the-shelf components [6].…”

Molecular circuits for dynamic noise filtering

“…Strand displacement is a competitive hybridization reaction where an incoming single-stranded DNA molecule binds to a complementary strand, in the process displacing an incumbent strand. This elementary mechanism allows one to directly synthesize arbitrary chemical reaction networks (30). Furthermore, because individual DSD reactions can be described by conventional bimolecular rate laws at a remarkably high precision (31), they provide a higher degree of quantitative control compared with cellular systems.…”

Robustness of Expressivity in Chemical Reaction Networks

“…CRNs have only recently been considered as a model of computation [21], motivated partially by the ability to implement them using a basic experimental technique called DNA strand displacement [22]. Discrete CRNs are Turing…”