A Stochastic Molecular Scheme for an Artificial Cell to Infer Its Environment from Partial Observations

  • Muppirala Viswa Virinchi
  • Abhishek Behera
  • Manoj GopalkrishnanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10467)


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.



Work of Abhishek Behera was supported in part by Bharti Centre for Communication in IIT Bombay.


  1. 1.
    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)Google Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Cardelli, L., Kwiatkowska, M.Z., Laurenti, L.: Programming discrete distributions with chemical reaction networks. CoRR, abs/1601.02578 (2016)Google Scholar
  4. 4.
    Cencov, N.N.: Statistical Decision Rules and Optimal Inference. Translations of Mathematical Monographs. American Mathematical Society, New York (2000)Google Scholar
  5. 5.
    Craciun, G., Toric differential inclusions, a proof of the global attractor conjecture. arXiv preprint arXiv:1501.02860 (2015)
  6. 6.
    Csiszár, I., Shields, P.C., et al.: Information theory and statistics: a tutorial. Found. Trends® Commun. Inf. Theor. 1(4), 417–528 (2004)Google Scholar
  7. 7.
    Daniel, R., Rubens, J.R., Sarpeshkar, R., Lu, T.K.: Synthetic analog computation in living cells. Nature 497(7451), 619–623 (2013)Google Scholar
  8. 8.
    Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Stochastic Modelling and Applied Probability, vol. 38. Springer, Heidelberg (2010)Google Scholar
  9. 9.
    Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations, vol. 902. Wiley, New York (2011)Google Scholar
  10. 10.
    Feinberg, M.: On chemical kinetics of a certain class. Arch. Rational Mech. Anal. 46, 1–41 (1972)Google Scholar
  11. 11.
    Feinberg, M.: Lectures on chemical reaction networks (1979).
  12. 12.
    Gopalkrishnan, M.: Catalysis in reaction networks. Bull. Math. Biol. 73(12), 2962–2982 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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 CrossRefGoogle Scholar
  14. 14.
    Horn, F.J.M.: Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Rational Mech. Anal. 49(3), 172–186 (1972)Google Scholar
  15. 15.
    Amari, S.: Information Geometry and its Applications, 7th edn. Springer, Osaka (2016)Google Scholar
  16. 16.
    Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620 (1957)Google Scholar
  17. 17.
    Kullback, S.: Information Theory and Statistics. Courier Corporation, New York (1997)Google Scholar
  18. 18.
    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)Google Scholar
  19. 19.
    Napp, N.E., Adams, R.P.: Message passing inference with chemical reaction networks. In: Advances in Neural Information Processing Systems, pp. 2247–2255 (2013)Google Scholar
  20. 20.
    Oishi, K., Klavins, E.: Biomolecular implementation of linear I/O systems. Syst. Biol. IET 5(4), 252–260 (2011)CrossRefGoogle Scholar
  21. 21.
    Qian, L., Winfree, E.: A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8(62), 1281–1297 (2011)Google Scholar
  22. 22.
    Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034), 1196–1201 (2011)CrossRefGoogle Scholar
  23. 23.
    Whittle, P.: Systems in Stochastic Equilibrium. Wiley, New York (1986)Google Scholar
  24. 24.
    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)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Muppirala Viswa Virinchi
    • 1
  • Abhishek Behera
    • 1
  • Manoj Gopalkrishnan
    • 1
    Email author
  1. 1.India Institute of Technology BombayMumbaiIndia

Personalised recommendations