Abstract
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.
Highlights
The analysis of metabolic fluxes in quasi-steady state has helped to increase the understanding of cell metabolism [1,2,3,4]
Where cex is a vector of extracellular concentrations that comprises the biomass concentration x, V is the volume of the broth, q is a vector of specific rates, u is a vector of compound specific feeding rates, c is a vector of intracellular concentrations, v is a vector of intracellular fluxes, and S and Sq are the stoichiometric matrices, which are obtained from the metabolic network
If the solution space of the time integrated Flux Variability Analysis is to be constrained, e.g., by the optimum obtained from time integrated Flux Balance Analysis, additional constraints that account for this can be added to the set of constraints
Summary
The analysis of metabolic fluxes in quasi-steady state has helped to increase the understanding of cell metabolism [1,2,3,4]. For the analysis of experimental data with these flux analysis methods, estimation of the fluxes that cross the cell boundary from the concentration measurements is required This flux estimation can be accomplished in two different ways: differential or integral [10,11]. The parameters contained in these functions can be fitted by numerically integrating the material balance and minimizing the residual between the predicted and measured concentration values. The macroscopic material balance can be numerically or analytically integrated and the residuals between the measured and predicted concentrations can be minimized by adapting the flux values. A new approach for flux analysis is proposed that adopts the time-integrated form of the macroscopic material balances (without any assumption on the flux values or the kinetic functions) to estimate the amount of material that is transformed by the intracellular pathways. The sparse FBA adaptation is applied to an experimental example to showcase the practical relevance of the approach
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