BackgroundDuring the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been succesfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework.ResultsIn this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results.ConclusionsThe proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.

BackgroundAdjusting the capacity of metabolic pathways in response to rapidly changing environmental conditions is an important component of microbial adaptation strategies to stochastic environments. In this work, we use advanced dynamic optimization techniques combined with theoretical models to study which reactions in pathways are optimally targeted by regulatory interactions in order to minimize the regulatory effort that is required to adjust the flux through a complex metabolic network. Moreover, we analyze how constraints in the speed at which an organism can respond on a proteomic level influences these optimal targets of pathway control.ResultsWe find that limitations in protein biosynthetic rates have a strong influence. With increasing protein biosynthetic rates the regulatory effort targeting the initial enzyme in a pathway is reduced while the regulatory effort in the terminal enzyme is increased. Studying the impact of allosteric regulation for different pathway topologies, we find that the presence of feedback inhibition by products of metabolic pathways allows organisms to reduce the regulatory effort that is required to control a metabolic pathway in all cases. In a linear pathway this even leads to the case where the sole transcriptional regulatory control of the terminal enzyme is sufficient to control flux through the entire pathway. We confirm the utilization of these pathway regulation strategies through the large-scale analysis of transcriptional regulation in several hundred prokaryotes.ConclusionsThis work expands our knowledge about optimal programs of pathway control. Optimal targets of pathway control strongly depend on the speed at which proteins can be synthesized. Moreover, post-translational regulation such as allosteric regulation allows to strongly reduce the number of transcriptional regulatory interactions required to control a metabolic pathway across different pathway topologies.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0587-z) contains supplementary material, which is available to authorized users.

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.

Current fishing practices result in the waste of 20 million tonnes of valuable resources every year. However, from now on, vessels must keep on board and land both target and those non-target species subject to quota regulations, as regulated by recent EU legislation, in the reform of the Common Fisheries Policy (CFP). Therefore, an important quantity of low-value marine biomass has to be managed in an efficient manner to avoid its waste. Several added value products apart from fishmeal and oil (like enzymes or nutraceuticals) can be obtained from the wide variety of discarded species trough different valorisation processes. The challenge arises when these species can be handled by more than one processing route. The selection of the best alternatives has to fulfil often-opposite sustainability criteria, considering also the constraints associated to each resource and process. This was achieved by a multiobjective framework using a suitable and efficient optimization approach based on scatter-search. The results from the obtained Pareto fronts show that, in general, the valorisation of specific fish parts rather than the use of the whole specimen is more optimal from both points of view. It is also demonstrated that the most suitable products to be obtained are biopeptides, chondroitin sulphate and fish enzymes, due to their high sales price and relative low environmental impact. On the other hand, alternative technologies to present state-of-the-art ones should be considered for the production of chitin, gelatine and fishmeal due to their high environmental cost. Furthermore, a high number of the most optimal valorisation pathways leave biomass unprocessed and therefore, its treatment as solid waste must be included in the economic and environmental costs.