Ph.D. Position Opening


Analysis and Control of models of biological regulatory systems

Application: growth control in E. coli



Biological networks play a major the role in the regulation of living organisms and raise many control questions, such as stabilization towards a desired state. However, classical control problems have to be revisited in a new light [7,8], as the control laws should satisfy biological constraints as well as be liable to experimental implementation. Synthetic biology experiments [1] have shown that it is possible to design and implement systems that exhibit a particular dynamical behavior, by assembling molecular components with the corresponding properties.


This project will address the problem of controlling the class of piecewise affine systems, under biologically appropriate restrictions. Piecewise affine (PWA) systems constitute an intuitive theoretical framework for the study of genetic regulatory networks, as they are based on a qualitative description of the systems that can be easily compared with the experimental data obtained from gene and protein expression [5]. In general, the parameters of PWA systems represent synthesis and degradation rates of the molecular components of the biological network, and can be used as experimentally controlled “inputs” to the system. Possible control functions will be in the form of piecewise constant inputs to the system (constant in time intervals or in regions of space), and ranging in a qualitative scale. In a more advanced stage, control laws that depend on the variables of the system or dynamic feedback laws will also be explored.


The current project will focus on studying control problems for small circuits (motifs such as simple positive and negative loops, feedforward loops) and then investigate the insertion of each motif and its control method into a larger network. Control problems can be related to generating invariant regions, stabilization to a given steady state, or generating periodic solutions. The methods developed in this project will be applied to the genetic network that regulates growth in E. coli [6], with the goal of limiting growth rate under high nutrient availability. The aim is to biologically implement the theoretical control in a biologically feasible form.





  1. E. Andrianantoandro, S. Basu, D.K. Karig and R. Weiss. Synthetic biology: New engineering rules for an emerging discipline. Molecular Systems Biology, 2:2006.0028, 2006

  2. G. Batt, B. Yordanov, R. Weiss and C. Belta. Robustness analysis and tuning of synthetic gene networks. Bioinformatics, 23(18):2415:2422, 2007

  3. C. Belta and L.C.G.J.M. Habets, Controlling a class of nonlinear systems on rectangles, IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1749-1759, 2006

  4. E. Farcot and J.-L. Gouze. A mathematical framework for the control of piecewise affine models of gene networks. Automatica, 44(9):2326-2332, 2008

  5. H. de Jong, J.L. Gouze, C. Hernandez, M. Page, T. Sari and J. Geiselmann. Qualitative simulation of genetic regulatory networks using piecewise linear models. Bull. Math. Biol. 66:301-340, 2004

  6. D. Ropers, H. de Jong, M. Page, D. Schneider, J. Geiselmann (2006), Qualitative simulation of the carbon starvation response in Escherichia coli. BioSystems, 84(2):124-152.

  7. E.D. Sontag. Some new directions in control theory inspired by systems biology. IET Systems Biology, 1:9-18, 2004

  8. E.D. Sontag. Mathematical Control Theory (2nd ed.). Springer, 1998



Requirements:

You are an ideal candidate for this position if you have a degree in applied mathematics (or similar) with a background in the analysis of dynamical systems, preferably familiar with control theory (and/or hybrid systems theory), you are enthusiastic for international and multidisciplinary work, and have a strong motivation to work on applications in biology and genomics.

Collaboration is planned with other INRIA teams (G. Batt, INRIA CONTRAINTES) as well as a biology laboratories.


Contact:

Please send a CV and provide 2 or 3 names for reference to

JL Gouzé, INRIA COMORE, gouze@sophia.inria.fr



Practical informations :


Team: COMORE Modelling and Control of Renewable Resources, see http://www- sop.inria.fr/comore/main_en.html



Supervisors : JL Gouzé and M. Chaves, INRIA COMORE


Place : INRIA Research Unit, Sophia -Antipolis, near Nizza, South of France.

See http://www-sop.inria.fr/index_en.php


Salary: approx. 2000 euros (gross) per month. Duration 3 years.




More informations :




Web page of JL Gouze http://www-sop.inria.fr/members/Jean-Luc.Gouze/JLGouze-eng.html


Web page of M. Chaves http://www-sop.inria.fr/members/Madalena.Chaves/