Abstract
The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform a statistical operation known as Information Projection or E projection with stochastic mass-action kinetics. Our scheme encodes desired conditional distributions as the equilibrium distributions of reaction systems. To our knowledge this is a first scheme to exploit the inherent stochasticity of reaction networks for information processing. We apply this to the problem of an artificial cell trying to infer its environment from partial observations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson, D.F., Craciun, G., Kurtz, T.G.: Product-form stationary distributions for deficiency zero chemical reaction networks. Bull. Math. Biol. 72(8), 1947–1970 (2010)
Buisman, H.J., ten Eikelder, H.M.M., Hilbers, P.A.J., Liekens, A.M.L., Liekens, A.M.L.: Computing algebraic functions with biochemical reaction networks. Artif. Life 15(1), 5–19 (2009)
Cardelli, L., Kwiatkowska, M.Z., Laurenti, L.: Programming discrete distributions with chemical reaction networks. CoRR, abs/1601.02578 (2016)
Cencov, N.N.: Statistical Decision Rules and Optimal Inference. Translations of Mathematical Monographs. American Mathematical Society, New York (2000)
Craciun, G., Toric differential inclusions, a proof of the global attractor conjecture. arXiv preprint arXiv:1501.02860 (2015)
Csiszár, I., Shields, P.C., et al.: Information theory and statistics: a tutorial. Found. Trends® Commun. Inf. Theor. 1(4), 417–528 (2004)
Daniel, R., Rubens, J.R., Sarpeshkar, R., Lu, T.K.: Synthetic analog computation in living cells. Nature 497(7451), 619–623 (2013)
Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Stochastic Modelling and Applied Probability, vol. 38. Springer, Heidelberg (2010)
Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations, vol. 902. Wiley, New York (2011)
Feinberg, M.: On chemical kinetics of a certain class. Arch. Rational Mech. Anal. 46, 1–41 (1972)
Feinberg, M.: Lectures on chemical reaction networks (1979). http://www.che.eng.ohio-state.edu/FEINBERG/LecturesOnReactionNetworks/
Gopalkrishnan, M.: Catalysis in reaction networks. Bull. Math. Biol. 73(12), 2962–2982 (2011)
Gopalkrishnan, M.: A scheme for molecular computation of maximum likelihood estimators for log-linear models. In: Rondelez, Y., Woods, D. (eds.) DNA 2016. LNCS, vol. 9818, pp. 3–18. Springer, Cham (2016). doi:10.1007/978-3-319-43994-5_1
Horn, F.J.M.: Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Rational Mech. Anal. 49(3), 172–186 (1972)
Amari, S.: Information Geometry and its Applications, 7th edn. Springer, Osaka (2016)
Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620 (1957)
Kullback, S.: Information Theory and Statistics. Courier Corporation, New York (1997)
Miller, E.: Theory and applications of lattice point methods for binomial ideals. In: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry, pp. 99–154. Springer, Heidelberg (2011)
Napp, N.E., Adams, R.P.: Message passing inference with chemical reaction networks. In: Advances in Neural Information Processing Systems, pp. 2247–2255 (2013)
Oishi, K., Klavins, E.: Biomolecular implementation of linear I/O systems. Syst. Biol. IET 5(4), 252–260 (2011)
Qian, L., Winfree, E.: A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8(62), 1281–1297 (2011)
Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034), 1196–1201 (2011)
Whittle, P.: Systems in Stochastic Equilibrium. Wiley, New York (1986)
Zwicker, D., Murugan, A., Brenner, M.P.: Receptor arrays optimized for natural odor statistics. In: Proceedings of the National Academy of Sciences, p. 201600357 (2016)
Acknowledgements
Work of Abhishek Behera was supported in part by Bharti Centre for Communication in IIT Bombay.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Virinchi, M.V., Behera, A., Gopalkrishnan, M. (2017). A Stochastic Molecular Scheme for an Artificial Cell to Infer Its Environment from Partial Observations. 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_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-66799-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66798-0
Online ISBN: 978-3-319-66799-7
eBook Packages: Computer ScienceComputer Science (R0)