Sensitivity analysis and adaptive mutation strategy differential evolution algorithm for optimizing enzymes' turnover numbers in metabolic models

Abstract

Genome-scale metabolic network model (GSMM) based on enzyme constraints greatly improves general metabolic models. The turnover number ( $k_{\mathrm{cat}}$ ) of enzymes is used as a parameter to limit the reaction when extending GSMM. Therefore, turnover number plays a crucial role in the prediction accuracy of cell metabolism. In this work, we proposed an enzyme-constrained GSMM parameter optimization method. First, sensitivity analysis of the parameters was carried out to select the parameters with the greatest influence on predicting the specific growth rate. Then, differential evolution (DE) algorithm with adaptive mutation strategy was adopted to optimize the parameters. This algorithm can dynamically select five different mutation strategies. Finally, the specific growth rate prediction, flux variability, and phase plane of the optimized model were analyzed to further evaluate the model. The enzyme-constrained GSMM of Saccharomyces cerevisiae, ecYeast8.3.4, was optimized. Results of the sensitivity analysis showed that the optimization variables can be divided into three groups based on sensitivity: most sensitive (149 $k_{\mathrm{cat}}$ c), highly sensitive (1759 $k_{\mathrm{cat}}$ ), and nonsensitive (2502 $k_{\mathrm{cat}}$ ) groups. Six optimization strategies were developed based on the results of the sensitivity analysis. The results showed that the DE with adaptive mutation strategy can indeed improve the model by optimizing highly sensitive parameters. Retaining all parameters and optimizing the highly sensitive parameters are the recommended optimization strategy.

Keywords: Saccharomyces cerevisiae; adaptive mutation strategy; enzyme-constrained genome-scale metabolic network model; sensitivity analysis.