(714b) Computational Strategies for the Global Optimization of Kinetic Models of Metabolic Networks

Mathematical optimization has evolved from a methodology of academic interest into a technology with extensive use in areas of very different nature [1]. One of these areas is systems biology. The complexity associated with the holistic approach of this discipline is specially suited for computational methods. In particular, the capabilities, opportunities and benefits that mathematical optimization can bring to research in systems biology were recently reviewed elsewhere [2].

One of these contributions focuses on the field of metabolic engineering [3-5]. Here, optimization is used to predict enzymatic changes that maximize a given objective function, typically the synthesis rate of a specific metabolite. The nature of the problem addressed depends on the model selected to describe the metabolic network of interest. For instance, in flux balance analysis, problems arise in the form of LP whereas the use of kinetic models (i.e., GMA, Michaelis-Menten) gives rise to NLP problems. Besides, particular considerations such as gene knock-outs or the definition of an upper limit on the number of reactions that can be modified may require the introduction of integer variables, which increases the associated complexity. An important issue in NLP formulation is the presence of non-convexities the can lead the existence of multiple local optima in which traditional solvers may get trapped during the search. These problems require then the use of global optimization techniques that guarantee convergence to the global optimum within a specified tolerance.

Although considerable work has been done in the area of global optimization over the last 25 years, there is still a need to develop faster algorithms for particular applications [2, 6]. In this work, we explore the application of global optimization methods to the area of metabolic engineering. Particularly, we present two different customized solution algorithms based on spatial branch and bound and outer-approximation schemes. A common key ingredient in both these solution methods is the derivation of a lower bounding problem, which in our case is constructed by exploiting some recent results on convexification of problems with signomial terms [7,8]. This lower bounding problem takes the form of a mixed-integer linear program (MILP) that provides a rigorous lower bound on the global optimum. We show how the solution time associated with this MILP can be expedited through the addition of cutting planes that are derived by applying an exponential transformation on some constraints of the original non-convex formulation. The capabilities of both algorithms are tested through their application to the citric acid production by Aspergillus Niger considering different biological constraints. Results are presented for each instance and the advantages and disadvantages of each methodology are extensively discussed.

References

[1] Biegler LT and Grossmann IE. Retrospective on optimization. Computers and Chemical Engineering. 2004, 28:1169-1192.

[2] Banga JR: Optimization in computational systems biology. BMC Syst Biol. 2008, 2:47.

[3] Pozo C, Guillén-Gosálbez G, Sorribas A and Jiménez L. Outer approximation-based algorithm for biotechnology studies in systems biology. Computers and Chemical Engineering. Article in press, Corrected proof.

[4] Sorribas A, Pozo C, Vilaprinyo E, Guillén-Gosálbez G, Jiménez L and Alves R. Optimization and evolution in metabolic pathways: Global optimization techniques in Generalized Mass Action models. Journal of biotechnology. Article in Press, Corrected proof.

[5] Guillén-Gosálbez G and Sorribas A. Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses. BMC Bioinformatics. 2009, 10(386).

[6] Grossmann IE, Biegler LT. Part II. Future perspective on optimization. Computers and Chemical Engineering. 2004, 28:1193-1218.

[7] Bjork KM, Lindberg PO and Westerlund T. Some convexifications in global optimization of problems containing signomial terms. Computers and Chemical Engineering. 2003, 27:669-679.

[8] Pörn R, Bjork KM and Westerlund T. Global solution of optimization problems with signomial parts. Discrete optimization. 2008, 5:108-120.