Challenges of Inversely Estimating Jacobian from Metabolomics Data

Xiaoliang Sun (Corresponding author), Bettina Länger, Wolfram Weckwerth

    Publications: Contribution to journalArticlePeer Reviewed

    Abstract

    Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJ(T)  = -2D, called Lyapunov Equation in its generic form, where J is the Jacobian, C is the covariance matrix of metabolomics data, and D is the fluctuation matrix. Lyapunov Equation can be further simplified as the linear form Ax = b. Frequently, this linear equation system is ill-conditioned, i.e., a small variation in the right side b results in a big change in the solution x, thus making the solution unstable and error-prone. At the same time, inaccurate estimation of covariance matrix and uncertainties in the fluctuation matrix bring biases to the solution x. Here, we first reviewed common approaches to circumvent the ill-conditioned problems, including total least squares, Tikhonov regularization, and truncated singular value decomposition. Then, we benchmarked these methods on several in silico kinetic models with small to large perturbations on the covariance and fluctuation matrices. The results identified that the accuracy of the reverse Jacobian is mainly dependent on the condition number of A, the perturbation amplitude of C, and the stiffness of the kinetic models. Our research contributes a systematical comparison of methods to inversely solve Jacobian from metabolomics data.

    Original languageEnglish
    Article number188
    Pages (from-to)188
    JournalFrontiers in bioengineering and biotechnology
    Volume3
    DOIs
    Publication statusPublished - 2015

    Austrian Fields of Science 2012

    • 106005 Bioinformatics
    • 101004 Biomathematics
    • 102009 Computer simulation

    Keywords

    • metabolomics
    • ill-posed problems
    • Jacobian
    • Lyapunov Equation
    • inverse engineering
    • Inverse engineering
    • Metabolomics
    • Ill-posed problems

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