Time Integrated Flux Analysis: Exploiting the Concentration Measurements Directly for Cost-Effective Metabolic Network Flux Analysis

Background: Flux analyses, such as Metabolic Flux Analysis (MFA), Flux Balance Analysis (FBA), Flux Variability Analysis (FVA) or similar methods, can provide insights into the cellular metabolism, especially in combination with experimental data. The most common integration of extracellular concentration data requires the estimation of the specific fluxes (/rates) from the measured concentrations. This is a time-consuming, mathematically ill-conditioned inverse problem, raising high requirements for the quality and quantity of data. Method: In this contribution, a time integrated flux analysis approach is proposed which avoids the error-prone estimation of specific flux values. The approach is adopted for a Metabolic time integrated Flux Analysis and (sparse) time integrated Flux Balance/Variability Analysis. The proposed approach is applied to three case studies: (1) a simulated bioprocess case studying the impact of the number of samples (experimental points) and measurements’ noise on the performance; (2) a simulation case to understand the impact of network redundancies and reaction irreversibility; and (3) an experimental bioprocess case study, showing its relevance for practical applications. Results: It is observed that this method can successfully estimate the time integrated flux values, even with relatively low numbers of samples and significant noise levels. In addition, the method allows the integration of additional constraints (e.g., bounds on the estimated concentrations) and since it eliminates the need for estimating fluxes from measured concentrations, it significantly reduces the workload while providing about the same level of insight into the metabolism as classic flux analysis methods.