Identification of Unintuitive Features of Sumoylation through Mathematical Modeling

Sumoylation is a multistep, multienzymatic post-translational modification in which a small ubiquitin-like modifier protein (SUMO) is attached to the target. We present the first mathematical model for sumoylation including enzyme mechanism details such as autosumoylation of E2 and multifunctional nature of SENP. Simulations and analysis reveal three nonobvious properties for the long term response, modeled as an open system: (i) the steady state sumoylation level is robust to variation in several enzyme properties; (ii) even when autosumoylation of E2 results in equal or higher activity, the target sumoylation levels are lower; and (iii) there is an optimal SENP concentration at which steady state target sumoylation level is maximum. These results are qualitatively different for a short term response modeled as a closed system, where e.g. sumoylation always decreases with increasing SENP levels. Simulations with multiple targets suggest that the available SUMO is limiting, indicating a possible explanation for the experimentally observed low fractional sumoylation. We predict qualitative differences in system responses at short post-translational and longer transcriptional time scales. We thus use this mechanism-based model to explain system properties and generate testable hypotheses for existence and mechanism of unexpected responses.

Pedagogical view of model metabolic cycles

The main purpose of this study was to present a simplified view of model metabolic cycles. Although the models have been elaborated with the Mathematica Program, and using a system of differential equations, the main conclusions were presented in a rather intuitive way, easily understandable by students of general courses of Biochemistry, and without any need of mathematical support. A change in any kinetic constant (Km or Vmax) of only one enzyme affected the metabolic profile of all the substrates of the cycle. In addition, it is shown how an increase in the Km or a decrease in the Vmax values of any particular enzyme promoted an increase of its substrate; the contrary occurred decreasing the Km or increasing the Vmax values.