TY - GEN
T1 - Optimal adaptation of metabolic networks in dynamic equilibrium
AU - OyarzĂșn, D. A.
AU - Middleton, R. H.
PY - 2011/6/1
Y1 - 2011/6/1
N2 - We consider the dynamic optimization of enzyme expression rates to drive a metabolic network between two given equilibrium fluxes. The formulation is based on a nonlinear control-affine model for a metabolic network coupled with a linear model for enzyme expression and degradation, whereby the expression rates are regarded as control inputs to be optimized. The cost function is a quadratic functional that accounts for the deviation of the species concentrations and expression rates from their target values, together with the genetic effort required for enzyme synthesis. If the network is in dynamic equilibrium along the whole adaptation process, the metabolite levels are constant and the nonlinear dynamics can be recast as a nonregular descriptor system. The structure of the reduced system can be exploited to decouple the algebraic and differential parts of the dynamics, so as to parameterize the controls that satisfy the algebraic constraint in terms of a lower-dimensional control. The problem is then solved as a standard Linear Quadratic Regulator problem for an uncon strained lower dimensional system. This solution allows for a systematic computation of the optimal flux trajectories between two prescribed dynamic equilibrium regimes for networks with general topologies and kinetics.
AB - We consider the dynamic optimization of enzyme expression rates to drive a metabolic network between two given equilibrium fluxes. The formulation is based on a nonlinear control-affine model for a metabolic network coupled with a linear model for enzyme expression and degradation, whereby the expression rates are regarded as control inputs to be optimized. The cost function is a quadratic functional that accounts for the deviation of the species concentrations and expression rates from their target values, together with the genetic effort required for enzyme synthesis. If the network is in dynamic equilibrium along the whole adaptation process, the metabolite levels are constant and the nonlinear dynamics can be recast as a nonregular descriptor system. The structure of the reduced system can be exploited to decouple the algebraic and differential parts of the dynamics, so as to parameterize the controls that satisfy the algebraic constraint in terms of a lower-dimensional control. The problem is then solved as a standard Linear Quadratic Regulator problem for an uncon strained lower dimensional system. This solution allows for a systematic computation of the optimal flux trajectories between two prescribed dynamic equilibrium regimes for networks with general topologies and kinetics.
KW - algebra
KW - biotechnology
KW - enzymes
KW - linear quadratic control
KW - nonlinear control systems
KW - nonlinear dynamical systems
KW - quadratic programming
KW - reduced order systems
KW - dynamic equilibrium flux
KW - metabolic networks
KW - dynamic optimization
KW - enzyme expression rates
KW - nonlinear control affine model
KW - linear model
KW - enzyme degradation
KW - cost function
KW - quadratic functional
KW - species concentration
KW - enzyme synthesis
KW - adaptation process
KW - nonregular descriptor system
KW - reduced system
KW - differential parts
KW - algebraic constraint
KW - lower-dimensional control
KW - standard linear quadratic regulator problem
KW - unconstrained lower dimensional system
KW - systematic computation
KW - optimal flux trajectories
KW - metabolite levels
KW - nonlinear dynamics
KW - Biochemistry
KW - Steady-state
KW - Optimization
KW - Kinetic theory
KW - Degradation
KW - Equations
U2 - 10.1109/ACC.2011.5990744
DO - 10.1109/ACC.2011.5990744
M3 - Conference contribution
SP - 2897
EP - 2902
BT - Proceedings of the 2011 American Control Conference
T2 - 2011 American Control Conference
Y2 - 29 June 2011 through 1 July 2011
ER -