An example metabolic network for reactions among substances X0, X1, S1, S2 with corresponding fluxes equal to E1, E2, E3, E4.

With yves sucaet, peter vedell, eunmee yoonann, ...

The studies on genetic and metabolic networks are expanding as more and more genes and proteins are discovered and descriptions on the relationships among genes and proteins at a system level become more feasible. A metabolic network can be modeled by using a system of reaction equations. Many related mathematical problems then arise from the solution of the equations such as the inverse problem for the determination of the system parameters, the initial and boundary value problems for time-resolved simulations, steady-state flux balancing, control, and optimization, etc. Investigations on these issues present various new challenges to the mathematical as well as the biological fields.

The steady-state flux equations form an underdetermined linear system of equations. The solutions of the system relate to all the pathways that are allowed by the network. The network can be optimized to increase or decrease certain network output subject to the flux balancing requirements.

 

A metabolic network is not exactly a graph-theoretic network, and therefore, cannot be optimized immediately using standard network optimization algorithms. A general linear programming method can be used, but is not as efficient especially for large-scale cases

 

We are developing an efficient algorithm for large-scale metabolic network optimization. By using the Bender’s and Danzig-Wolfe decompositions, we are able to reduce a metabolic network to a graphic-theoretic network and then apply standard network optimization algorithms.

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