A constrained wavelet smoother for pathway identification tasks in systems biology

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, 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. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

Stepwise inference of likely dynamic flux distributions from metabolic time series data

MOTIVATION

Most metabolic pathways contain more reactions than metabolites and therefore have a wide stoichiometric matrix that corresponds to infinitely many possible flux distributions that are perfectly compatible with the dynamics of the metabolites in a given dataset. This under-determinedness poses a challenge for the quantitative characterization of flux distributions from time series data and thus for the design of adequate, predictive models. Here we propose a method that reduces the degrees of freedom in a stepwise manner and leads to a dynamic flux distribution that is, in a statistical sense, likely to be close to the true distribution.

RESULTS

We applied the proposed method to the lignin biosynthesis pathway in switchgrass. The system consists of 16 metabolites and 23 enzymatic reactions. It has seven degrees of freedom and therefore admits a large space of dynamic flux distributions that all fit a set of metabolic time series data equally well. The proposed method reduces this space in a systematic and biologically reasonable manner and converges to a likely dynamic flux distribution in just a few iterations. The estimated solution and the true flux distribution, which is known in this case, show excellent agreement and thereby lend support to the method.

AVAILABILITY AND IMPLEMENTATION

The computational model was implemented in MATLAB (version R2014a, The MathWorks, Natick, MA). The source code is available at https://github.gatech.edu/VoitLab/Stepwise-Inference-of-Likely-Dynamic-Flux-Distributions and www.bst.bme.gatech.edu/research.php .

CONTACT

mojdeh@gatech.edu or eberhard.voit@bme.gatech.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Nonparametric dynamic modeling

Challenging as it typically is, the estimation of parameter values seems to be an unavoidable step in the design and implementation of any dynamic model. Here, we demonstrate that it is possible to set up, diagnose, and simulate dynamic models without the need to estimate parameter values, if the situation is favorable. Specifically, it is possible to establish nonparametric models for nonlinear compartment models, including metabolic pathway models, if sufficiently many high-quality time series data are available that describe the biological phenomenon under investigation in an appropriate and representative manner. The proposed nonparametric strategy is a variant of the method of Dynamic Flux Estimation (DFE), which permits the estimation of numerical flux profiles from metabolic time series data. However, instead of attempting to formulate these numerical profiles as explicit functions and to optimize their parameter values, as it is done in DFE, the metabolite and flux profiles are used here directly as a scaffold for a library from which values are interpolated and retrieved for the simulation of the differential equations describing the model. Beyond simulations, the proposed methods render it possible to determine steady states from non-steady state data, perform sensitivity analyses, and estimate the Jacobian of the system at a steady state.

Identification of Metabolic Pathway Systems

The estimation of parameters in even moderately large biological systems is a significant challenge. This challenge is greatly exacerbated if the mathematical formats of appropriate process descriptions are unknown. To address this challenge, the method of dynamic flux estimation (DFE) was proposed for the analysis of metabolic time series data. Under ideal conditions, the first phase of DFE yields numerical representations of all fluxes within a metabolic pathway system, either as values at each time point or as plots against their substrates and modulators. However, this numerical result does not reveal the mathematical format of each flux. Thus, the second phase of DFE selects functional formats that are consistent with the numerical trends obtained from the first phase. While greatly facilitating metabolic data analysis, DFE is only directly applicable if the pathway system contains as many dependent variables as fluxes. Because most actual systems contain more fluxes than metabolite pools, this requirement is seldom satisfied. Auxiliary methods have been proposed to alleviate this issue, but they are not general. Here we propose strategies that extend DFE toward general, slightly underdetermined pathway systems.

New insights into the complex regulation of the glycolytic pathway in Lactococcus lactis. I. Construction and diagnosis of a comprehensive dynamic model

This article and the companion paper use computational systems modeling to decipher the complex coordination of regulatory signals controlling the glycolytic pathway in the dairy bacterium Lactococcus lactis.