Identification of unintuitive features of sumoylation through mathematical modeling - Puntambekar, Shraddha S.; Nyayanit, Dimpal; Saxena, Priyanka; Gadgil, Chetan J. (Journal of Biological Chemistry, 2016)
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.

Network motifs exhibiting a differential response to spaced and massed inputs - Sreejan, Ashley; Saxena, Priyanka; Gadgil, Chetan J. (Learning & Memory, 2024)
One characteristic of long-term memory is the existence of an inverted U-shaped response to increasing intervals between training sessions, and consequently, an optimal spacing that maximizes memory formation. Current models of this spacing effect focus on specific molecular components and their interactions. Here, we computationally study the underlying network architecture, in particular, the potential of motif dynamics in qualitatively capturing the spacing effect in a manner that is independent of the animal model, biomolecular components, and the timescales involved. We define a common training and test protocol, and computationally identify network topologies that can qualitatively replicate the experimentally observed characteristics of the spacing effect. For 41 motifs derived from fundamental network architectures such as autoregulation, feedback, and feedforward motifs, we tested their capacity to manifest the spacing effect in terms of an inverted U-shaped response curve, using different combinations of stimulation protocols, response metrics, and kinetic parameters. Our findings indicate that positive feedback motifs where the stimulus enhances conversion reaction in the loop replicate the spacing effect across all response metrics, while feedforward motifs exhibit a metric-specific spacing effect. For some parameter combinations, linear cascades of activation and conversion reactions were found sufficient to qualitatively exhibit spacing effect characteristics.