Oyarzun Rodriguez, Diego Antonio
A control-theoretic approach to
dynamic optimization of metabolic
PhD thesis, National University of Ireland Maynooth.
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.
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