(142e) Biochemical Reaction Engineering: A Lumping Methodology

Biochemical reaction networks can be seen as the result of a long evolutionary process which, starting from the original compounds, and following optimisation routes, alters the carbon framework of the participating reactive species. As a consequence, one can extract two features which are important in the analysis of metabolic networks: a) the high number of species involved, and b) the high dimensionality and high degree of coupling of the reactions' system. The former characteristic has to deal with the composition of the mixture, whilst the first problem lies in identifying individual components: this can be accomplished by establishing some way of labelling the components. In discrete descriptions the label is simply some index (the kernel) i=1,?, N which should be chosen as some measurable quantity: in this specific case the carbon number emerges as the natural kernel.

Characteristic b), on the other hand, can be described by a continuous variable: as an example, in the case of linear kinetics, the kinetic behaviour of each species is entirely characterised by the value of the kinetic constant k, and hence k itself may be used as a label. The situation is significantly more complex in the case on nonlinear kinetics, but the feature remains that a continuous description results more appropriate.

In this paper, an example is presented where the reactions occurring in the metabolic pathways are studied by making use of the lumping methodology. One of the problems arising in studying the metabolic reactions has to do with the continuous discovery of new species (e.g. proteins). The methodology presented has the huge advantage, when compared to other analysis, to be flexible and amenable to the introduction of new compounds without changing drastically the system of equations to be solved.