Abstract
In contrast to electronic computation, chemical computation is noisy and susceptible to a variety of sources of error, which has prevented the construction of robust complex systems. To be effective, chemical algorithms must be designed with an appropriate error model in mind. Here we consider the model of chemical reaction networks that preserve molecular count (population protocols), and ask whether computation can be made robust to a natural model of unintended “leak” reactions. Our definition of leak is motivated by both the particular spurious behavior seen when implementing chemical reaction networks with DNA strand displacement cascades, as well as the unavoidable side reactions in any implementation due to the basic laws of chemistry. We develop a new “Robust Detection” algorithm for the problem of fast (logarithmic time) single molecule detection, and prove that it is robust to this general model of leaks. Besides potential applications in single molecule detection, the error-correction ideas developed here might enable a new class of robust-by-design chemical algorithms. Our analysis is based on a non-standard hybrid argument, combining ideas from discrete analysis of population protocols with classic Markov chain techniques.
D. Alistarh—Supported by an SNF Ambizione Fellowship.
A. Kosowski—Supported by Inria project GANG, ANR project DESCARTES, and NCN grant 2015/17/B/ST6/01897.
D. Soloveichik—Supported by NSF grants CCF-1618895 and CCF-1652824.
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References
Gopalkrishnan, M.: Catalysis in reaction networks. Bull. Math. Biol. 73(12), 2962–2982 (2011)
Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107(12), 5393–5398 (2010)
Cardelli, L.: Two-domain DNA strand displacement. Math. Struct. Comput. Sci. 23(02), 247–271 (2013)
Chen, Y.-J., Dalchau, N., Srinivas, N., Phillips, A., Cardelli, L., Soloveichik, D., Seelig, G.: Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8(10), 755–762 (2013)
Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853), 1121–1125 (2007)
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18, 235–253 (2006). Preliminary version appeared in PODC 2004
Karp, R.M., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: 41st Annual Symposium on Foundations of Computer Science, FOCS 2000, pp. 565–574, IEEE Computer Society (2000)
Hopfield, J.J.: Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. Proc. Natl. Acad. Sci. 71(10), 4135–4139 (1974)
Thachuk, C., Winfree, E., Soloveichik, D.: Leakless DNA strand displacement systems. In: Phillips, A., Yin, P. (eds.) DNA 2015. LNCS, vol. 9211, pp. 133–153. Springer, Cham (2015)
Angluin, D., Aspnes, J., Eisenstat, D.: A simple population protocol for fast robust approximate majority. Distrib. Comput. 21(2), 87–102 (2008)
Cardelli, L.: Morphisms of reaction networks that couple structure to function. BMC Syst. Biol. 8(1), 84 (2014)
Pittel, B.: On spreading a rumor. SIAM J. Appl. Math. 47(1), 213–223 (1987)
Doerr, B., Doerr, C., Moran, S., Moran, S.: Simple and optimal randomized fault-tolerant rumor spreading. Distrib. Comput. 29(2), 89–104 (2016)
Boczkowski, L., Korman, A., Natale, E.: Minimizing message size in stochastic communication patterns: fast self-stabilizing protocols with 3 bits. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, pp. 2540–2559
Dudek, B., Kosowski, A.: Spreading a confirmed rumor: A case for oscillatory dynamics, CoRR, vol. abs/1705.09798 (2017)
Soloveichik, D.: Robust stochastic chemical reaction networks and bounded tau-leaping. J. Comput. Biol. 16(3), 501–522 (2009)
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We thank Lucas Boczkowski and Luca Cardelli for helpful comments on the manuscript.
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Alistarh, D., Dudek, B., Kosowski, A., Soloveichik, D., Uznański, P. (2017). Robust Detection in Leak-Prone Population Protocols. In: Brijder, R., Qian, L. (eds) DNA Computing and Molecular Programming. DNA 2017. Lecture Notes in Computer Science(), vol 10467. Springer, Cham. https://doi.org/10.1007/978-3-319-66799-7_11
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