Mathematical modelling of Sec pathway mechanism in Escherichia coli: a case study for periplasmic translocation of maltose binding protein–glucose isomerase fusion protein

Abstract

Within the framework of reported information on the Sec pathway mechanism, a mathematical model for the periplasmic translocation of fusion proteins in bacteria was developed. The mathematical model includes all stages of the targeting stage and assume that the ATP-driven translocation stage is completed in a single step. The equations for the targeting stage involved cytoplasmic folding rate and SecB binding kinetics. Rate equations for the translocation stage were derived using King-Altman and network reduction techniques. Experimental data for maltose binding protein–glucose isomerase fusion protein (MBP-GI) translocation and reported data for MBP translocation were used to estimate the parameters. The simulation results show that the model fits well to the experimental data of cytoplasmic and periplasmic MBP-GI distributions. When the values of the targeting stage parameters, k 1 and k 3 or the concentration of SecB are changed, the model correctly predicts the expected changes in the MBP-GI distribution to the cytoplasmic and periplasmic spaces. The SecB complex and the preprotein concentrations predicted attain steady state immediately, within seconds, and their amounts are very low when compared to MBP-GI in either compartment. The model can be made applicable to any protein that uses the Sec pathway, and with ATP and Sec pathway protein limitations.