Parameter estimation in dynamic metabolic models applying a surrogate approximation

Abstract

Dynamic Flux Balance Analysis (dFBA) models are widely applied in the system biology field. The model connects the cellular genome information to the cell’s phenotype, it can therefore be applied to predict the effect of gene deletions or the insertion of new enzymes into the metabolic network. The dFBA model consists of a system of differential equations and an optimization problem that is performed to compute the internal flux distribution. Furthermore, kinetic equations (i.e. Michaelis-Menten) are used to model the uptake of substrates. The kinetic equations have some parameters that must be estimated from batch fermentation experimental data. When the dFBA model is inserted in a parameter estimation architecture, a bi-level optimization problem arises. As is well known, bi-level optimization problems are hard to solve and suffer from convergence problems. A recent method to replace the FBA optimization with a surrogate model was developed in our research group and applied to the simulation of a model predictive control of a bioreactor. Here, that recently developed surrogate dFBA model is applied to a parameter estimation problem. The approach was tested in a case study of Saccharomyces cerevisiae fermentation using glucose and xylose as substrates. S. cerevisiae is the main microorganism for industrial alcoholic fermentation and there is research to amplify the range of substrates that can be used, such as xylose. dFBA models can be applied to link possible genetic modifications strategies with the bioreactor performance. In order to achieve this aim, the kinetic parameters in the dFBA model must be well defined. First, the surrogate model was trained using Flux Balance Analysis simulations of the Yeast 8.3 genome-scale model. After that, the kinetic parameters on the surrogate dFBA were fitted to in silico data. The surrogate dFBA outperformed the sequential approach where the nested LP needs to be solved many times during the estimation. Furthermore, solving the parameter estimation with the surrogate model in a simultaneous approach can considerably reduce the computational time. The results indicated that the surrogate dFBA can be an important tool for the parameter estimation and optimal design of experiments of dynamic metabolic models.