Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

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.

Biochemical Systems Theory: A Review

“…MCMC was also applied to different classes of metabolic pathways [467][468][469][470][471][472][473][474][475][476], the evolutionary development of different designs of enzyme systems and moiety-transfer cycles [477][478][479][480][481][482][483][484], bacterial growth phenomena [485], two-component sensing systems with and without bistable switches and hysteresis [387][388][389][390]475], a stress response system in yeast [486], higher plant systems [487], and even control systems for lymphocytes and their responses to antigens [462,463]. Puigjaner and colleagues compared MCMC for BST and metabolic control analysis (MCA; [488]).…”

“…A different extension of methods for the discovery of design principles was the corresponding analysis of operating principles, where the focus is not so much on the structural design of systems, but on their operation in response to stimuli [76,77,380,484]. A recent review of design and operating principles can be found in [78].…”

“…Voit and Radivoyevitch demonstrated that the glycolytic gene expression pro�le following heat stress is all but intuitive, yet appropriate for the required metabolic response [543]. Sorribas' group analyzed the same phenomenon and showed that the cellular response is essentially optimal, given the constraints within which it has to be mounted [484,[544][545][546].…”

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

“…For example, in the minlp.org problem GMA ethanol model CH [80,81], there are seven signomial terms with nonnegative variables natural to the model formulation; all seven participate in both a convex and concave direction:…”

“…The remaining terms are convex in one direction and concave in the other. The reinforcing exponential transformation, convex hulls, and RLT equations allow the MISO framework to solve GMA ethanol model CH [80,81] to a relative optimality tolerance of 1 × 10 −4 % in 1.1 CPU s.…”