Abstract
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 2n 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.
Highlights
DNA strand displacement is a form of chemical reaction in which one or more single-stranded DNA molecules— the reactants—bind to a multi-stranded complex, thereby displacing other single-stranded molecules—the products
Can chemical reactions and their strand displacement system realizations recycle strands in more general ways? We show that the answer is yes: we describe chemical reaction system computations and their strand displacement realizations in which recycling of strands significantly reduces waste and avoids fuel depletion while incurring just a moderate slowdown relative to comparable computations that do not recycle strands
We have introduced the concept of recycling, or molecule reuse, in strand displacement systems and chemical reaction systems
Summary
DNA strand displacement is a form of chemical reaction in which one or more single-stranded DNA molecules— the reactants—bind to a multi-stranded complex, thereby displacing other single-stranded molecules—the products. The second contribution of the paper is to demonstrate a limit to recycling: recycling is not possible in certain classes of chemical reaction systems, which include certain classes of strand displacement systems that should work correctly even when many copies of the initial state of the system are present in the same environment. The rest of this introduction illustrates the concept of strand recycling and gives an overview of our results and related work.
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