Kinetic Aspects and Mathematical Modeling of PHA Biosynthesis

Process/strain optimization procedures are unavoidable in the improvement of large-scale bioproduction processes. These procedures are necessary on macroscopic (bioreactor) level and on biochemical/genetic level of producing strains. Inter alia, mathematical modeling is one of the applicable and useful methods in such procedures. Mathematical models applied for PHA biosynthesis (classified as both structured and unstructured) are denominated as formal kinetic, low-structured, dynamic, metabolicor high-structured, cybernetic, and hybrid type models, or neural networks. In the chapter at hand, each specific group of models is discussed in the light of its applicability and benefit for increased productivity, enhancing of the specific PHA biosynthesis rate, and better understanding of the intracellular metabolic regulation systems. Characteristics of production strains, particularities of mixed microbial cultures and features of industrial-scale plants cannot be described by a single type of mathematical model since it is not possible to address all the different requirements by a single model type. Therefore, it is more than necessary to fine-tune the modeling approach to each actual case in a sophisticated way. Formal-kinetic and “lowstructured” models that are relatively simple and display low computational demand, are applicable for simple cases and are beneficial for mathematical embodiment of “standard microbial cultivations and practices”. Hybrid models are used by some authors to address certain deficiencies of diverse types of models. In this context, satisfying, compromised, perhaps most promising solutions can be reached if mechanistic, cybernetic, computational fluid dynamics (CFD) and neural models were combined. A hybrid modeling strategy like this generates a holistic representation of solutions for the total PHA biosynthesis process, including all advantages of the different modeling schemes. For example, application of growth media of complex composition usually entails a higher degree of model organization. For the future, really existent biotechnological systems are expected to be expressed by hybrid models of high organization.

Major attention was dedicated to the use of elementary flux modes (EFMs) and yield space analysis (YSA) to develop metabolic models of PHA biosynthesis. The implementation of these methods is reported for numerous case studies which involve modeling of metabolic networks. The chapter concludes with some case studies, where the implementation of EFMs and YSA performed as a powerful modeling tool. It includes the description of intracellular PHA generation and mobilization in the organism Cupriavidus necator, the limitation-based picture of the steady-state flux cone of the organism´s metabolic network, the detailed analysis of a multi-stage bioreactor cascade dedicated to continuous PHA production, and metabolic flux investigation in the metabolism of C. necator cultivated using glycerol.

Keywords: Bioreactor cascade, Cybernetic models, Dynamic models, Elementary flux modes (EFM), Formal kinetic modelling, Hybrid models, Mathematical modelling, Metabolic models, Network modelling, Neural networks, Polyhydroxyalkanoates (PHA), Yield space analysis (YSA).