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Do True Metabolic Pathway Models Exist?

Banff International Research Station for Mathematical Innovation and Discovery

Metabolic systems are among of the oldest applications of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring metabolic models and for formulating reactions has been growing constantly, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. This situation begs the question whether there are representations of metabolic processes that are true over reasonably wide ranges, yet mathematically tractable. A glimpse into such representations is provided by Dynamic Flux Estimation which, under ideal conditions, reveals the actual shapes of functions representing metabolic processes, although not their mathematical formats. While intriguing, DFE is only directly applicable if a pathway system contains as many dependent variables as fluxes. Because most actual systems contain more fluxes than metabolite pools, this requirement is seldom satisfied. Some auxiliary methods have been proposed to alleviate this issue, but they were quite ad hoc. Here I demonstrate a generic strategy that renders DFE applicable to moderately underdetermined pathway systems. A second challenge with DFE is the need to identify explicit functional formats that have shapes as close as possible to those inferred. Clearly, even if this inference is feasible, the result is necessarily biased. As an alternative, I demonstrate that good time series data allow us to circumvent this step and to develop nonlinear dynamic models in an entirely nonparametric fashion. The resulting nonparametric models offer a surprisingly wide range of analytic tools, including stability and sensitivity analyses. I will finish with some comments on dynamical model reduction, using power-law models. Goel, G., I-C. Chou, and E.O. Voit: System estimation from metabolic time series data. Bioinformatics 24, 2505-2511, 2008. Dolatshahi, S., and E.O. Voit: Identification of metabolic pathway systems. Frontiers in Genetics 7:6, 2016. Faraji, M. and E.O. Voit: Nonparametric dynamic modeling. Math. Biosc. 287, 130-146, 2017. Faraji, M. and E.O. Voit: Stepwise inference of likely dynamic flux distributions from metabolic time series data. Bioinformatics, 33 (14): 2165-2172; 2017. Voit, E.O.: The best models of metabolism. WIREs Systems Biology and Medicine. (in press)

Mathematics; Statistics; Partial differential equations

video/mp4

Author affiliation: Georgia Institute Technology

2018-03-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64973

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/