Error Propagation Analysis for Quantitative Intracellular Metabolomics

Abstract

Model-based analyses have become an integral part of modern metabolic engineering and systems biology in order to gain knowledge about complex and not directly observable cellular processes. For quantitative analyses, not only experimental data, but also measurement errors, play a crucial role. The total measurement error of any analytical protocol is the result of an accumulation of single errors introduced by several processing steps. Here, we present a framework for the quantification of intracellular metabolites, including error propagation during metabolome sample processing. Focusing on one specific protocol, we comprehensively investigate all currently known and accessible factors that ultimately impact the accuracy of intracellular metabolite concentration data. All intermediate steps are modeled, and their uncertainty with respect to the final concentration data is rigorously quantified. Finally, on the basis of a comprehensive metabolome dataset of Corynebacterium glutamicum, an integrated error propagation analysis for all parts of the model is conducted, and the most critical steps for intracellular metabolite quantification are detected.

Less Sacrifice, More Insight: Repeated Low‐Volume Sampling of Microbioreactor Cultivations Enables Accelerated Deep Phenotyping of Microbial Strain Libraries

“…Random error propagation was conducted by a parametric bootstrap approach . Input variables (i.e., experimental raw data) are assumed to follow Gaussian distributions.…”

“…Random error propagation was conducted by a parametric bootstrap approach. [37,38] Input variables (i.e., experimental raw data) are assumed to follow Gaussian distributions. For each culture replicate (n biol ¼ 24 for C. glutamicum WT and n biol ¼ 8 for each genome-reduced strain) 5000 bootstrap samples were generated by sampling the assumed Gaussian distributions according to a Latin Hypercube Sampling plan by applying MATLAB's lhsnorm function.…”

Metabolic profile of 1,5‐diaminopentane producing Corynebacterium glutamicum under scale‐down conditions: Blueprint for robustness to bioreactor inhomogeneities

“…Deviation of intracellular concentrations was determined using error propagation integrated in a MATLAB (MathWorks, Natick, MA) tool described (Tillack et al, 2012). Further required are the volumes of the taken samples (V s ), quenching supernatants (V qs ), extraction fluent (V es ), and the determined BV in the sample (V bv ).…”

To be certain about the uncertainty: Bayesian statistics for13C metabolic flux analysis

“…A second concern about the χ 2 −test was the need for accurate measurement uncertainties, represented by the covariance matrix , which is used when calculating the residual in Equation . In 13 C MFA, data are obtained in a multi‐step procedure, where each step is associated with an error (Tillack et al, ). Therefore, accurate measurement uncertainty quantification means to generate a large number of independent data assessments, where each representative for all errors that arise during the sampling process.…”

“…The growing awareness of the importance of measurement errors (Antoniewicz, Kelleher, & Stephanopoulos, ; Tillack, Paczia, Nöh, Wiechert, & Noack, ) has led to the advise that flux uncertainty analysis should become, if it not yet is, part of the routine analysis 13 C MFA workflow (Crown and Antoniewicz, ; Wiechert, ). Practically, quantification of the uncertainty in the flux estimates has proven to be of high importance, since typically, only part of the fluxes addressed in a 13 C MFA can be determined with high precision, whereas other fluxes can only be determined up to their order of magnitude and still others remain non‐identifiable (Kappelmann, Wiechert, & Noack, ; McCloskey et al, ; Wiechert et al, ; Zamboni, Fendt, Rühl, & Sauer, ).…”