Abstract
BackgroundOptimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements.ResultsWe first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer-approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shockConclusionOur results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.
Highlights
Optimization methods allow designing changes in a system so that specific goals are attained
One may argue that the adaptive response of the cellular metabolism to different situations is shaped by physiological requirements that must be met by tuning gene expression and enzyme activity [18,19,20]
Feasible enzyme activity patterns in the adaptive response of yeast to heat shock stress Using the same model as in the second optimization example, we have investigated the feasibility regions for changing enzyme activities in yeast metabolism so that specific physiological constraints are met
Summary
Optimization methods allow designing changes in a system so that specific goals are attained. The identification of design principles through controlled mathematical comparisons that evaluate different functional criteria in metabolic networks has led to a better understanding of adaptation and design emergence [5,6,7,8,9,10,11,12]. Such principles enable building new gene and metabolic networks that accomplish specific requirements which is the main goal of Synthetic Biology [13,14,15]. Understanding the evolution of the adaptive strategies that assure cell survival in different conditions is, an important goal in Systems Biology [18,19,20,21,22]
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