Mathematical model for the ubiquitin activating enzyme E1

The ubiquitin-activating enzyme E1 (EC 6.3.2.19) represents the first step in the degradation of proteins by the ubiquitin proteasome pathway. E1 transfers ubiquitin from the ubiquitinated E1 to the ubiquitin carrier proteins (E2), ubiquitin-protein ligases (E3) and proteins. This process is rather complex, and known from the work of Haas, Ciechanover, Hershko, Rose and others. The occurrence of 19 hypothetical intermediate enzyme forms (EFs) and 22 different reactions were considered in the presence of ubiquitin (Ub), ATP, adenosine 5’-tetraphosphate (p4A), pyrophosphate (P2), and tripolyphosphate (P3) as substrates, and iodoacetamide (IAA) and dithiothreitol (DTT) as inhibitors. Inspired by the work of Cha (Cha (1968) J. Biol. Chem., 243, 820-825) we have treated these reactions in two complementary ways: in rapid equilibrium and in steady state. The kinetics of both types of reactions were simulated and solved with a system of ordinary differential equations using the Mathematica Program. The ubiquitination of E1 has been also theoretically coupled to the ubiquitination of E2, E3 and proteins. This makes the model useful to predict the theoretical influence of inhibitors (or of changes in some parameters of the reaction) on the ubiquitination of proteins. The Program responds to changes in the concentration of ATP or ubiquitin and has predictive properties as shown by the influence of AMP on the synthesis of p4A, calculated theoretically and confirmed experimentally.