Towards Real-Time Control of Gene Expression at the Single Cell Level: A Stochastic Control Approach

  • Lakshmeesh R. M. Maruthi
  • Ilya Tkachev
  • Alfonso Carta
  • Eugenio Cinquemani
  • Pascal Hersen
  • Gregory Batt
  • Alessandro Abate
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8859)


Recent works have demonstrated the experimental feasibility of real-time gene expression control based on deterministic controllers. By taking control of the level of intracellular proteins, one can probe single-cell dynamics with unprecedented flexibility. However, single-cell dynamics are stochastic in nature, and a control framework explicitly accounting for this variability is presently lacking. Here we devise a stochastic control framework, based on Model Predictive Control, which fills this gap. Based on a stochastic modelling of the gene response dynamics, our approach combines a full state-feedback receding-horizon controller with a real-time estimation method that compensates for unobserved state variables. Using previously developed models of osmostress-inducible gene expression in yeast, we show in silico that our stochastic control approach outperforms deterministic control design in the regulation of single cells. The present new contribution leads to envision the application of the proposed framework to wetlab experiments on yeast.


Model Predictive Control Stochastic Control Unscented Kalman Filter Regression Algorithm Stochastic Simulation Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35(3), 407–427 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Carta, A., Cinquemani, E.: State estimation for gene networks with intrinsic and extrinsic noise: a case study on E.coli arabinose uptake dynamics. In: European Control Conference, ECC 2013, Zurich, Suisse, pp. 3658–3663 (2013)Google Scholar
  3. 3.
    Caruana, R., Niculescu-Mizil, A.: An empirical comparison of supervised learning algorithms. In: Proc. of the 23rd International Conference on Machine Learning, pp. 161–168. ACM (2006)Google Scholar
  4. 4.
    Ernst, D., Geurts, P., Wehenkel, L.: Tree-based batch mode reinforcement learning. Journal of Machine Learning Research, 503–556 (2005)Google Scholar
  5. 5.
    Espinoza, M., Suykens, J.A.K., De Moor, B.: Fixed-size least squares support vector machines: A large scale application in electrical load forecasting. Computational Management Science 3(2), 113–129 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22(4), 403–434 (1976)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gillespie, D.T.: The chemical Langevin equation. Journal of Chemical Physics 113(1), 297–306 (2000)CrossRefGoogle Scholar
  8. 8.
    Gonzalez, A.M., Uhlendorf, J., Cinquemani, E., Batt, G., Ferrari-Trecate, G.: Identification of biological models from single-cell data: A comparison between mixed-effects and moment-based inference. In: European Control Conference, ECC 2013, pp. 3652–3657 (2013)Google Scholar
  9. 9.
    Haesaert, S., Babuska, R., Abate, A.: Sampling-based approximations with quantitative performance for the probabilistic reach-avoid problem over general Markov processes. arXiv preprint, arXiv:1409.0553 (2014)Google Scholar
  10. 10.
    Kallenberg, O.: Foundations of modern probability. Probability and its Applications. Springer, New York (2002)CrossRefzbMATHGoogle Scholar
  11. 11.
    Menolascina, F., Fiore, G., Orabona, E., De Stefano, L., Ferry, M., Hasty, J., di Bernardo, M., di Bernardo, D.: In-vivo real-time control of protein expression from endogenous and synthetic gene networks. PLoS Computational Biology 10(5), e1003625 (2014)Google Scholar
  12. 12.
    Milias-Argeitis, A., Summers, S., Stewart-Ornstein, J., Zuleta, I., Pincus, D., El-Samad, H., Khammash, M., Lygeros, J.: In silico feedback for in vivo regulation of a gene expression circuit. Nature Biotechnology 29, 1114–1116 (2011)CrossRefGoogle Scholar
  13. 13.
    Muzzey, D., Gómez-Uribe, C.A., Mettetal, J.T., van Oudenaarden, A.: A systems-level analysis of perfect adaptation in yeast osmoregulation. Cell 138(1), 160–171 (2009)CrossRefGoogle Scholar
  14. 14.
    Olson, E.J., Hartsough, L.L., Landry, B.P., Shroff, R., Tabor, J.J.: Characterizing bacterial gene circuit dynamics with optically programmed gene expression signals. Nature Methods 11, 449–455 (2014)CrossRefGoogle Scholar
  15. 15.
    Pelckmans, K., Suykens, J.A.K., Van Gestel, T., De Brabanter, J., Lukas, L., Hamers, B., De Moor, B., Vandewalle, J.: LS-SVMlab: a matlab/c toolbox for least squares support vector machines. Tutorial, Leuven, Belgium (2002)Google Scholar
  16. 16.
    Toettcher, J.E., Gong, D., Lim, W.A., Weiner, O.D.: Light-based feedback for controlling intracellular signaling dynamics. Nature Methods 8, 837–839 (2011)CrossRefGoogle Scholar
  17. 17.
    Uhlendorf, J., Bottani, S., Fages, F., Hersen, P., Batt, G.: Towards real-time control of gene expression: controlling the HOG signaling cascade. In: 16th Pacific Symposium of Biocomputing, pp. 338–349 (2011)Google Scholar
  18. 18.
    Uhlendorf, J., Miermont, A., Delaveau, T., Charvin, G., Fages, F., Bottani, S., Batt, G., Hersen, P.: Long-term model predictive control of gene expression at the population and single-cell levels. PNAS 109(35), 14271–14276 (2012)CrossRefGoogle Scholar
  19. 19.
    Wan, E.A., Van Der Merwe, R.: The unscented kalman filter for nonlinear estimation. In: Adaptive Systems for Signal Processing, Communications, and Control Symposium, AS-SPCC 2000, pp. 153–158. IEEE (2000)Google Scholar
  20. 20.
    Yang, X., Payne-Tobin Jost, A., Weiner, O.D., Tang, C.: A light-inducible organelle-targeting system for dynamically activating and inactivating signaling in budding yeast. Molecular Biology of the Cell 24(15), 2419–2430 (2013)CrossRefGoogle Scholar
  21. 21.
    Zechner, C., Ruess, J., Krenn, P., Pelet, S., Peter, M., Lygeros, J., Koeppl, H.: Moment-based inference predicts bimodality in transient gene expression. PNAS 109(21), 8340–8345 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lakshmeesh R. M. Maruthi
    • 1
  • Ilya Tkachev
    • 1
  • Alfonso Carta
    • 2
  • Eugenio Cinquemani
    • 3
  • Pascal Hersen
    • 4
  • Gregory Batt
    • 5
  • Alessandro Abate
    • 1
    • 6
  1. 1.Delft Center for Systems and ControlTU DelftThe Netherlands
  2. 2.INRIA Sophia-AntipolisMéditerranéeFrance
  3. 3.INRIA GrenobleRhône-AlpesFrance
  4. 4.UMR 7057Laboratoire Matière et Systèmes ComplexesParisFrance
  5. 5.INRIA Paris-RocquencourtFrance
  6. 6.Department of Computer ScienceUniversity of OxfordUK

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