A mathematical investigation of the consequences of metabolic regulation in complex pathways: The cybernetic approach

Abhijit Anand Namjoshi, Purdue University


Advances in biology have resulted in bioprocesses competing increasingly with chemical technologies for the manufacture of chemical and pharmaceutical products. Thus, chemical engineers have to assume new roles to design reactors with living cells which comprise intricate networks of enzyme catalyzed reactions. The cellular enzymes are themselves manipulated in response to environmental stimuli. This phenomenon, termed metabolic regulation, is a defining feature of biosystems as cells can not only change the extents of different reactions, but also decide which reactions to activate or exclude. The consequence of this versatility is extreme non-linearity with which engineering models must contend with for bioreactor optimization and control. Cellular environmental changes can cause variation in fluxes throughout the network and drastically affect the production of a desired secondary metabolite. Clearly, existing coarse models that rely on small sets of reactions, such as the uptake of selected substrates, to account for regulation cannot capture detailed pathways. This thesis, therefore, focuses on a much needed rational approach for large-scale metabolic modeling. The strategy presented builds on the cybernetic framework successful at predicting different substrate utilization patterns and expands it to address detailed pathway modeling. ^ The cybernetic framework perceives cells as optimal strategists which allocate limited cellular resources to groups of reactions. Objective functions are identified for elementary convergent, divergent, cyclic and linear pathways. This thesis projects a systematic algorithmic approach to identify elementary pathways in large networks The accompanying cybernetic competitions are identified using experimental flux measurements. The strategy has been applied to a hybridoma reactor problem of practical importance. Metabolic fluxes are used to construct a model which is successful in explaining the observed multiplicity of steady states with varying biomass, antibody and waste metabolite concentrations. The significant finding is that the cells seem to maximize substrate uptake leading to different metabolic states depending on the batch or fed-batch startup strategy employed. These metabolic states correspond to multiple steady states in continuous culture. Bifurcation analysis carried out on this and other cybernetic models suggests novel reactor start-up strategies beyond revealing interesting non-linear phenomena such as multiple steady states and periodic behavior. ^




Major Professor: Doraiswami Ramkrishna, Purdue University.

Subject Area

Biology, Cell|Engineering, Chemical

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