1. V. H. Nagaraj, J. M. Greene, A. M. Sengupta, and E.D. Sontag. Translation inhibition and resource balance in the TX-TL cell-free gene expression system. Synthetic Biology, 2:ysx005, 2017. [PDF] Keyword(s): tx/tl, cell-free systems, in vitro synthetic biology, synthetic biology, systems biology. Abstract:

   Utilizing the synthetic transcription-translation (TX-TL) system, this paper studies the impact of nucleotide triphosphates (NTPs) and magnesium (Mg2+), on gene expression, in the context of the counterintuitive phenomenon of suppression of gene expression at high NTP concentration. Measuring translation rates for different Mg2+ and NTP concentrations, we observe a complex resource dependence. We demonstrate that translation is the rate-limiting process that is directly inhibited by high NTP concentrations. Additional Mg2+ can partially reverse this inhibition. In several experiments, we observe two maxima of the translation rate viewed as a function of both Mg2+ and NTP concentration, which can be explained in terms of an NTP-independent effect on the ribosome complex and an NTP- Mg2+ titration effect. The non-trivial compensatory effects of abundance of different vital resources signals the presence of complex regulatory mechanisms to achieve optimal gene expression.




2. M. Chaves, A. M. Sengupta, and E.D. Sontag. Geometry and topology of parameter space: investigating measures of robustness in regulatory networks. J. of Mathematical Biology, 59:315-358, 2009. [PDF] Keyword(s): identifiability, robust, robustness, geometry. Abstract:

   The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task, but mathematical models have often associated it to the volume of the space of admissible parameters. Not only the volume of the space but also its topology and geometry contain information on essential aspects of the network, including feasible pathways, switching between two parallel pathways or distinct/disconnected active regions of parameters. A method is presented here to characterize the space of admissible parameters, by writing it as a semi-algebraic set, and then theoretically analyzing its topology and geometry, as well as volume. This method provides a more objective and complete measure of the robustness of a developmental module. As a detailed case study, the segment polarity gene network is analyzed.




3. A. Dayarian, M. Chaves, E.D. Sontag, and A. M. Sengupta. Shape, Size and Robustness: Feasible Regions in the Parameter Space of Biochemical Networks. PLoS Computational Biology, 5:e10000256, 2009. [PDF] Keyword(s): identifiability, robust, robustness, geometry. Abstract:

   The concept of robustness of regulatory networks has received much attention in the last decade. One measure of robustness has been associated with the volume of the feasible region, namely, the region in the parameter space in which the system is functional. In recent work, we emphasized that topology and geometry matter, as well as volume. In this paper, and using the segment polarity gene network to illustrate our approach, we show that random walks in parameter space and how they exit the feasible region provide a rich perspective on the different modes of failure of a model. In particular, for the segment polarity network, we found that, between two alternative ways of activating Wingless, one is more robust. Our method provides a more complete measure of robustness to parameter variation. As a general modeling strategy, our approach is an interesting alternative to Boolean representation of biochemical networks.

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