Robustness in <i>Escherichia coli</i> glutamate and glutamine synthesis studied by a kinetic model

Abstract

Metabolic control of glutamine and glutamate synthesis from ammonia and oxoglutarate in Escherichia coli is tight and complex. In this work, the role of glutamine synthetase (GS) and glutamate dehydrogenase (GDH) regulation in this control was studied. Both enzymes form a linear pathway, which can also have a cyclic topology if glutamate–oxoglutarate amino transferase (GOGAT) activity is included. We modelled the metabolic pathways in the linear or cyclic topologies using a coupled nonlinear differential equations system. To simulate GS regulation by covalent modification, we introduced a relationship that took into account the levels of oxoglutarate and glutamine as signal inputs, as well as the ultrasensitive response of enzyme adenylylation. Thus, by including this relationship or not, we were able to model the system with or without GS regulation. In addition, GS and GDH activities were changed manually. The response of the model in different stationary states, or under the influence of N-input exhaustion or oscillation, was analyzed in both pathway topologies. Our results indicate a metabolic control coefficient for GDH ranging from 0.94 in the linear pathway with GS regulation to 0.24 in the cyclic pathway without regulation, employing a default GDH concentration of 8 μM. Thus, in these conditions, GDH seemed to have a high degree of control in the linear pathway while having limited influence in the cyclic one. When GS was regulated, system responses to N-input perturbations were more sensitive, especially in the cyclic pathway. Furthermore, we found that effects of regulation against perturbations depended on the relative values of the glutamine and glutamate output first-order kinetic constants, which we named k6 and k7, respectively. Effects of regulation grew exponentially with a factor around 2, with linear increases of (k7 − k6). These trends were sustained but with lower differences at higher GS concentration. Hence, GS regulation seemed important for metabolic stability in a changing environment, depending on the cell’s metabolic status.