Identification of Unintuitive Features of Sumoylation through Mathematical Modeling.

Abstract Sumoylation is a multi-step multi-enzymatic 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 auto-sumoylation of E2 and multifunctional nature of SENP. Simulations and analysis reveal three non-obvious 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 auto-sumoylation 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 levels is maximum. These results are qualitatively different for 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 timescales. We thus use this mechanism-based model to explain system properties and generate testable hypotheses for existence and mechanism of unexpected responses.