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Linear control analysis of the autocatalytic glycolysis system

Linear control analysis of the autocatalytic glycolysis system,10.1109/ACC.2009.5159925,Fiona A. Chandra,Gentian Buzi,John C. Doyle

Linear control analysis of the autocatalytic glycolysis system   (Citations: 5)
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Autocatalysis is necessary and ubiquitous in both engineered and biological systems but can aggravate control performance and cause instability. We analyze the properties of autocatalysis in the universal and well studied glycolytic pathway. A simple two-state model incorporating ATP autocatalysis and inhibitory feedback control captures the essential dynamics, including limit cycle oscillations, observed experimentally. System performance is limited by the inherent autocatalytic stoichiometry and higher levels of autocatalysis exacerbate stability and performance. We show that glycolytic oscillations are not merely a ldquofrozen accidentrdquo but a result of the intrinsic stability tradeoffs emerging from the autocatalytic mechanism. This model has pedagogical value as well as appearing to be the simplest and most complete illustration yet of Bode's integral formula.
Conference: American Control Conference - ACC , pp. 319-324, 2009
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    • ...In [1], the effect of autocatalysis in a glycolytic pathway model is studied by tools from linear control theory...
    • ...In this example, we consider the nominal regulated autocatalytic glycolysis model, which is studied in [1], as follows...

    Nader Moteeet al. Stability analysis of a class of biological network models

    • ...An example of such a pathway is the glycolysis pathway [1], [2], [3]...

    Gentian Buziet al. Compositional analysis of autocatalytic networks in biology

    • ...We use glycolysis as our motivating example and look at a simplified model of glycolysis previously presented in [11]...
    • ...We consider the two-state model from [11] with ATP (denoted by variable y) and a lumped intermediate metabolite (denoted by variable x) as states...

    Nader Moteeet al. Performance limitations in autocatalytic networks in biology

    • ...Using tools from linear systems theory, our previous work on a simple two-state pathway (figure 2a) showed that autocatalysis can aggravate controller performance [13]...
    • ...metabolites. In the topologies we investigate, the plants P have right half-plane (RHP) zeros which introduce theoretical limits on performance captured by a special form of the Bode’s integral formula [13],...
    • ...Notice that these limits are exacerbated by smaller magnitude RHP zeros, since it severely penalizes performance in frequencies below z. Reference [13] characterizes the limits and the tradeoffs involved for a special form of the two-state model shown in figure 2a. In particular it shows that performance improves as the concentration of the intermediate enzyme increases (higher intermediate reaction rate)...
    • ...As shown in [13], high concentration of catalyzing enzymes leads to an increase in the rates of the intermediate reactions (ki), which makes the pathway more stable (i.e., there is a larger range of stable gains available) and increases the magnitude of z (i.e., “softens” the hard limits on performance)...

    Gentian Buziet al. Topological tradeoffs in autocatalytic metabolic pathways

    • ...Using tools from linear systems theory, our previous work on a simple two dimensional model of glycolysis demonstrated that autocatalysis can aggravate control performance and contribute to instability [3]...
    • ...Define the parameter ˆ := +1 h that captures the strength of feedback in the linearized dynamics (see [3] for a detailed discussion on ˆ h)...

    Gentian Buziet al. Quantitative nonlinear analysis of autocatalytic pathways with applica...

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