Parameter estimation and network identification in metabolic pathway systems
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Cells are able to function and survive due to a delicate orchestration of the expression of genes and their downstream products at the genetic, transcriptomic, proteomic, and metabolic levels. Since metabolites are ultimately the causative agents for physiological responses and responsible for much of the functionality of the organism, a comprehensive understanding of cellular functioning mandates deep insights into how metabolism works. Gaining these insights is impeded by the fact that the regulation and dynamics of metabolic networks are often too complex to allow intuitive predictions, which thus renders mathematical modeling necessary as a means for assessing and understanding metabolic systems. The most difficult step of the modeling process is the extraction of information regarding the structure and regulation of the system from experimental data. The work presented here addresses this "inverse" task with three new methods that are applied to models within Biochemical Systems Theory (BST). Alternating Regression (AR) dissects the nonlinear estimation task into iterative steps of linear regression by utilizing the fact that power-law functions are linear in logarithmic space. Eigenvector Optimization (EO) is an extension of AR that is particularly well suited for the identification of model structure. Dynamic Flux Estimation (DFE) is a more general approach that can involve AR and EO and resolves open issues of model validity and quality beyond residual data fitting errors. The necessity of fast solutions to biological inverse problems is discussed in the context of concept map modeling, which allows the conversion of hypothetical network diagrams into mathematical models.