title: Optimal control of metabolic networks with saturable enzyme kinetics.
abstract: This note addresses the optimal control of non-linear metabolic networks by means of time-dependent enzyme synthesis rates. The authors consider 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 authors provide 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 authors use 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.
authors.affiliation: Imperial College London, Centre for Synthetic Biology and Innovation, Department of Bioengineering, UK. d.oyarzun@imperial.ac.uk
authors.forename: D A
authors.initials: DA
authors.lastname: Oyarzuun
mesh_terms: D000465:Algorithms; D004798:Enzymes / Q000235:genetics / Q000378:metabolism*; D007700:Kinetics; D016014:Linear Models; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D049490:Systems Biology / Q000379:methods*
chemical_list: D004798:Enzymes