# Computation with finite stochastic chemical reaction networks

## Abstract

A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates, that are composed into larger circuits, with each logic gate in the circuit corresponding to one or more molecular species. With this paradigm, designing and producing new molecular species is necessary to perform larger computations. An alternative approach begins by noticing that chemical systems on the small scale are fundamentally discrete and stochastic. In particular, the exact molecular counts of each molecular species present, is an intrinsically available form of information. This might appear to be a very weak form of information, perhaps quite difficult for computations to utilize. Indeed, it has been shown that error-free Turing universal computation is impossible in this setting. Nevertheless, we show a design of a chemical computer that achieves fast and reliable Turing-universal computation using molecular counts. Our scheme uses only a small number of different molecular species to do computation of arbitrary complexity. The total probability of error of the computation can be made arbitrarily small (but not zero) by adjusting the initial molecular counts of certain species. While physical implementations would be difficult, these results demonstrate that molecular counts can be a useful form of information for small molecular systems such as those operating within cellular environments.

## Keywords

Stochastic chemical kinetics Molecular counts Turing-universal computation Probabilistic computation## Notes

### Acknowledgments

We thank G. Zavattaro for pointing out an error in an earlier version of this manuscript. This work is supported in part by the “Alpha Project” at the Center for Genomic Experimentation and Computation, an NIH Center of Excellence (Grant No. P50 HG02370), as well as NSF Grant No. 0523761 and NIMH Training Grant MH19138-15.

## Supplementary material

## References

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