A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available