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Typical DNA storage schemes do not allow in-memory computation, and instead transformation of the stored data requires DNA sequencing, electronic computation of the transformation, followed by synthesizing new DNA. In contrast we propose a model of in-memory computation that avoids the time consuming and expensive sequencing and synthesis steps, with computation carried out by DNA strand displacement. We demonstrate the flexibility of our approach by developing schemes for massively parallel binary counting and elementary cellular automaton Rule 110 computation. 

Synthetic biology is a rapidly emerging research area, with expected wide-ranging impact in biology, nanofabrication, and medicine. A key technical challenge lies in embedding computation in molecular contexts where electronic micro-controllers cannot be inserted. This necessitates effective representation of computation using molecular components. While previous work established the Turing-completeness of chemical reactions, defining representations that are faithful, efficient, and practical remains challenging. This paper introduces CRN++, a new language for programming deterministic (mass-action) chemical kinetics to perform computation. We present its syntax and semantics, and build a compiler translating CRN++ programs into chemical reactions, thereby laying the foundation of a comprehensive framework for molecular programming. Our language addresses the key challenge of embedding familiar imperative constructs into a set of chemical reactions happening simultaneously and manipulating real-valued concentrations. Although some deviation from ideal output value cannot be avoided, we develop methods to minimize the error, and implement error analysis tools. We demonstrate the feasibility of using CRN++ on a suite of well-known algorithms for discrete and real-valued computation. CRN++ can be easily extended to support new commands or chemical reaction implementations, and thus provides a foundation for developing more robust and practical molecular programs. 

Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model idealizes chemical interactions, abstracting away specifics of the molecular implementation, and allowing rigorous reasoning about the computational power of chemical kinetics. Here we focus on function computation with CRNs, where we think of the initial concentrations of some species as the input and the eventual steady-state concentration of another species as the output. Specifically, we are concerned with CRNs that are rate-independent (the computation must be correct independent of the reaction rate law) and composable (𝑓∘𝑔 can be computed by concatenating the CRNs computing f and g). Rate independence and composability are important engineering desiderata, permitting implementations that violate mass-action kinetics, or even “well-mixedness”, and allowing the systematic construction of complex computation via modular design. We show that to construct composable rate-independent CRNs, it is necessary and sufficient to ensure that the output species of a module is not a reactant in any reaction within the module. We then exactly characterize the functions computable by such CRNs as superadditive, positive-continuous, and piecewise rational linear. Our results show that composability severely limits rate-independent computation unless more sophisticated input/output encodings are used.