Stochastic model for first order reaction networks - Gadgil, Chetan J.; Lee, Chang Hyeong; Othmer, Hans G. (Bulletin of Mathematical Biology, 2005)
A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived.

Stochastic modeling of biological reactions - Gadgil, Chetan J. (Journal of the Indian Institute of Science, 2008)
Several biological systems comprise of reaction networks where the low number of molecules makes it inappropriate to completely characterize system behavior using a continuous approach. Biological systems are also characterized by discrete states (e.g. infected, dead) that are not amenable to the use of a continuous descriptor. This review discusses the need for adopting a discrete stochastic modeling approach for analyzing biological reactions networks. Various stochastic simulation procedures and theoretical studies are presented. The challenges in the theoretical and computational analysis of discrete stochastic biological reaction networks are discussed.

Size-independent differences between the mean of discrete stochastic systems and the corresponding continuous deterministic systems - Gadgil, Chetan J. (Bulletin of Mathematical Biology, 2009)
In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.
Keywords: Biochemical reaction kinetics; Continuous systems; Deterministic chemical kinetics; Discrete systems; Stochastic reaction kinetics

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.

Simple method for incorporating dynamic effects of intronic miRNA mediated regulation - Gokhale, Sucheta A.; Hariharan, Manoj; Brahmachari, Samir K.; Gadgil, Chetan J. (Molecular Biosystems, 2012)
The importance of microRNA (miRNA) in modulating gene expression at the post-transcriptional level is well known. Such regulation has been shown to influence the dynamics of several regulatory networks including the cell cycle. In this study we incorporated regulatory effects of intronic miRNA into an existing mathematical model of the cell cycle through the use of an existing `proxy' protein - the host protein. It was observed that the incorporation of intronic miRNA mediated regulation improved the performance of the model resulting in a closer match to experimental results. To test the universality of this approach we compared the effects of intronic miRNA mediated regulation and host protein mediated regulation. Further, we compared miRNA mediated and protein mediated positive and negative feedback regulations of the target protein. We found that the target protein profiles were predominantly similar. These observations show the applicability of our method for incorporating intronic miRNA mediated dynamic effects in models for regulation of gene expression.

Systematic comparison of the response properties of protein and RNA mediated gene regulatory motifs - Iyengar, Bharat Ravi; Pillai, Beena; Venkatesh, K. V.; Gadgil, Chetan J. (Molecular BioSystems, 2017)
We present a framework enabling the dissection of the effects of motif structure (feedback or feedforward), the nature of the controller (RNA or protein), and the regulation mode (transcriptional, post-transcriptional or translational) on the response to a step change in the input. We have used a common model framework for gene expression where both motif structures have an activating input and repressing regulator, with the same set of parameters, to enable a comparison of the responses. We studied the global sensitivity of the system properties, such as steady-state gain, overshoot, peak time, and peak duration, to parameters. We find that, in all motifs, overshoot correlated negatively whereas peak duration varied concavely with peak time. Differences in the other system properties were found to be mainly dependent on the nature of the controller rather than the motif structure. Protein mediated motifs showed a higher degree of adaptation i.e. a tendency to return to baseline levels; in particular, feedforward motifs exhibited perfect adaptation. RNA mediated motifs had a mild regulatory effect; they also exhibited a lower peaking tendency and mean overshoot. Protein mediated feedforward motifs showed higher overshoot and lower peak time compared to the corresponding feedback motifs.

SUMOylation of dorsal attenuates Toll/NF-kappa B signaling - Hegde, Sushmitha; Sreejan, Ashley; Gadgil, Chetan J.; Ratnaparkhi, Girish S. (Genetics, 2022)
In Drosophila, Toll/NF-kappa B signaling plays key roles in both animal development and in host defense. The activation, intensity, and kinetics of Toll signaling are regulated by posttranslational modifications such as phosphorylation, SUMOylation, or ubiquitination that target multiple proteins in the Toll/NF-kappa B cascade. Here, we have generated a CRISPR-Cas9 edited Dorsal (DL) variant that is SUMO conjugation resistant. Intriguingly, embryos laid by dl(SCR) mothers overcome dl haploinsufficiency and complete the developmental program. This ability appears to be a result of higher transcriptional activation by DLSCR. In contrast, SUMOylation dampens DL transcriptional activation, ultimately conferring robustness to the dorso-ventral program. In the larval immune response, dl(SCR) animals show an increase in crystal cell numbers, stronger activation of humoral defense genes, and high cactus levels. A mathematical model that evaluates the contribution of the small fraction of SUMOylated DL (1-5%) suggests that it acts to block transcriptional activation, which is driven primarily by DL that is not SUMO conjugated. Our findings define SUMO conjugation as an important regulator of the Toll signaling cascade, in both development and host defense. Our results broadly suggest that SUMO attenuates DL at the level of transcriptional activation. Furthermore, we hypothesize that SUMO conjugation of DL may be part of a Ubc9-dependent mechanism that restrains Toll/NF-kappa B signaling.
Keywords: Drosophila; haploinsufficiency; innate immunity; SUMO; transcription