Observability and observers for mathematical models of bacterial growth

To monitor and optimize bioreactors (tanks where bacteria are growing), the main limitation is the lack of reliable measurements of biological variables. For example, for two strains of bacteria, it will be possible to estimate the total biomass (by optical density), but not the biomass of each species.

Observers [1] (also called software sensors) are mathematical systems that are able to reconstruct missing measurements from the outputs of the biological system (effective measurements) and from a mathematical model of this system. They are based on observability properties of the system.

In this internship, we consider several problems of observability and observation for different biological systems:

  • A classical model of two competing species of bacteria in a bioreactor [2]
  • A new model of allocation of resources to optimize bacterial growth of a bacterium [3]

For each case, the goal will be to study the observability properties and to build observers.

  1. E.D. Sontag. Mathematical Control Theory (2nd ed.). Springer, 1998
  2. Smith, H. L., & Waltman, P. (1995). The theory of the chemostat: dynamics of microbial competition (Vol. 13). Cambridge university press.
  3. Giordano, N., Mairet, F., Gouzé, J. L., Geiselmann, J., & de Jong, H. (2016). Dynamical allocation of cellular resources as an optimal control problem: novel insights into microbial growth strategies. PLoS computational biology, 12(3), e1004802.

 

Requirements: background in dynamical systems, and control theory; strong motivation to work on applications in biology

Collaboration between McTAO and Biocore teams in Sophia.

Contact: Ludovic Sacchelli (Inria McTAO), Jean Luc Gouzé (Inria Biocore)

Location : INRIA Research Unit, Sophia -Antipolis, near Nice, South of France.

Wage: approx. 550 euros per month.