Optimization of biochemical systems through mathematical programming: Methods and applications

In this work we present a general (mono and multiobjective) optimization framework for the technological improvement of biochemical systems. The starting point of the method is a mathematical model in ordinary differential equations (ODEs) of the investigated system, based on qualitative biological knowledge and quantitative experimental data. In the method we take advantage of the special structural features of a family of ODEs called power-law models to reduce the computational complexity of the optimization program. In this way, the genetic manipulation of a biochemical system to meet a certain biotechnological goal can be expressed as an optimization program with some desired properties such as linearity or convexity. The general method of optimization is presented and discussed in its linear and geometric programming versions. We furthermore illustrate the use of the method by several real case studies. We conclude that the technological improvement of microorganisms can be afforded using the combination of mathematical modelling and optimization. The systematic nature of this approach facilitates the redesign of biochemical systems and makes this a predictive exercise rather than a trial-and-error procedure.