Systems view of the protein expression process - Gokhale, Sucheta A.; Nyayanit, Dimpal; Gadgil, Chetan J. (Systems and Synthetic Biology, 2011)
Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

Mathematical modeling of combinatorial regulation suggests that apparent positive regulation of targets by miRNA could be an artifact resulting from competition for mRNA - Nyayanit, Dimpal; Gadgil, Chetan J. (RNA-A Publication of the RNA Society, 2015)
MicroRNAs bind to and regulate the abundance and activity of target messenger RNA through sequestration, enhanced degradation, and suppression of translation. Although miRNA have a predominantly negative effect on the target protein concentration, several reports have demonstrated a positive effect of miRNA, i.e., increase in target protein concentration on miRNA overexpression and decrease in target concentration on miRNA repression. miRNA-target pair-specific effects such as protection of mRNA degradation owing to miRNA binding can explain some of these effects. However, considering such pairs in isolation might be an oversimplification of the RNA biology, as it is known that one miRNA interacts with several targets, and conversely target mRNA are subject to regulation by several miRNAs. We formulate a mathematical model of this combinatorial regulation of targets by multiple miRNA. Through mathematical analysis and numerical simulations of this model, we show that miRNA that individually have a negative effect on their targets may exhibit an apparently positive net effect when the concentration of one miRNA is experimentally perturbed by repression/overexpression in such a multi-miRNA multitarget situation. We show that this apparent unexpected effect is due to competition and will not be observed when miRNA interact noncompetitively with the target mRNA. This result suggests that some of the observed unusual positive effects of miRNA may be due to the combinatorial complexity of the system rather than due to any inherently unusual positive effect of the miRNA on its target.
Keywords: combinatorial binding; mathematical model; miRNA; post-transcriptional regulation

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.