Optimal control of metabolic networks with saturable enzyme kinetics

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This note addresses the optimal control of non-linear metabolic networks by means of time-dependent enzyme synthesis rates. The author considers networks with general topologies described by a control-affine dynamical system coupled with a linear model for enzyme synthesis and degradation. The problem formulation accounts for transitions between two metabolic equilibria, which typically arise in metabolic adaptations to environmental changes, and the minimisation of a quadratic functional that weights the cost/benefit relation between the transcriptional effort required for enzyme synthesis and the transition to the new phenotype. Using a linear time-variant approximation of the non-linear dynamics, the problem is recast as a sequence of linear-quadratic problems, the solution of which involves a sequence of differential Lyapunov equations. The author provides conditions for convergence to an approximate solution of the original problem, which are naturally satisfied by a wide class of models for saturable enzyme kinetics. As a case study the author uses the method to examine the robustness of an optimal just-in-time gene expression pattern with respect to heterogeneity in the biosynthetic costs of individual proteins.
Original languageEnglish
Pages (from-to)110-119
Number of pages10
JournalSystems Biology, IET
Issue number2
Publication statusPublished - 1 Mar 2011


  • biochemistry
  • enzymes
  • genetics
  • nonlinear dynamical systems
  • reaction kinetics
  • saturable enzyme kinetics
  • nonlinear metabolic networks
  • time-dependent enzyme synthesis rate
  • control-affine dynamical system
  • enzyme degradation
  • metabolic equilibria
  • quadratic functional minimisation
  • phenotype
  • nonlinear dynamics
  • differential Lyapunov equations
  • just-in-time gene expression pattern


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