A system-level mathematical description of metabolic regulation combining aspects of elementary mode analysis with cybernetic control laws

Jamey Dale Young, Purdue University


Cybernetic modeling strives to uncover the in-built regulatory programs of biological systems and leverage them to develop concise mathematical representations of cellular phenomena. Because of their focus on incorporating the global aims of metabolism, cybernetic models provide a systems-oriented approach for approximating regulatory inputs and inferring the impact of regulation within biochemical networks. This thesis revisits the fundamental cybernetic control laws that have been used to describe regulation of enzyme synthesis (Matching Law) and enzyme activity (Proportional Law). The current treatment reveals how these laws are obtained as the solution to a well-defined optimal control problem that seeks to maximize a quadratic performance index subject to the constraints imposed by the linearized system dynamics. The resulting control policies extend and generalize earlier cybernetic treatments and infuse them with mathematical rigor, which has been sorely lacking. The Matching and Proportional Laws are further evaluated in comparison to alternate control policies and are shown to be superior in describing the qualitative and quantitative features of biological control circuits. Combining cybernetic control laws with elementary mode analysis provides a systematic approach for the formulation and identification of cybernetic models. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. Because of the stabilizing influence of the included control variables, the resulting cybernetic models tend to be more robust and reliable in comparison to other dynamic models when simulating the network response to imposed perturbations. The main concepts are illustrated within a cybernetic model of anaerobic E. coli central carbon metabolism. The model successfully describes the metabolic shift that occurs upon deletion of the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions, both of an interpolative and extrapolative nature, that are consistent with experimental results on various mutant strains.




Ramkrishna, Purdue University.

Subject Area

Chemical engineering|Microbiology

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