Analysis of autocatalytic networks in biology

Buzi, Gentian; Topcu, Ufuk; Doyle, John C.

doi:10.1016/j.automatica.2011.02.040

Cited by 6 publications

(11 citation statements)

References 24 publications

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“…This means that the pathway is not activated by an increase in glucose if there is no overexpression of the upper glycolytic enzymes. Such a clear division in active flux through glycolysis vs. equilibrium has been found before in a small core model, including essentially only reactions v 1 , v 2 and v 6 [1,3]. Here we show in a more involved core model with two side-branches and ATP and NADH householding that this bifurcation value persists; the expression of the other enzymes in fermentative glycolysis do not influence the activation threshold.…”

Section: Without Overexpression Of Its Upper Part Glycolysis Will Nosupporting

confidence: 83%

“…As mentioned in Section 4.1, this simple transition had been reported before in a small core model of essentially the v 1 , v 2 and v 6 reactions [1,3]. However, the bifurcation behaviour was found to be more complicated when adding glycerol production in the v 3 and phosphate householding in the v 7 reaction [13].…”

Section: A Simple Condition For the Transcritical Bifurcationsupporting

confidence: 69%

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Understanding start-up problems in yeast glycolysis

Overal

Teusink

Bruggeman

et al. 2018

Mathematical Biosciences

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Yeast glycolysis has been the focus of research for decades, yet a number of dynamical aspects of yeast glycolysis remain poorly understood at present. If nutrients are scarce, yeast will provide its catabolic and energetic needs with other pathways, but the enzymes catalysing upper glycolytic fluxes are still expressed. We conjecture that this overexpression facilitates the rapid transition to glycolysis in case of a sudden increase in nutrient concentration. However, if starved yeast is presented with abundant glucose, it can enter into an imbalanced state where glycolytic intermediates keep accumulating, leading to arrested growth and cell death. The bistability between regularly functioning and imbalanced phenotypes has been shown to depend on redox balance. We shed new light on these phenomena with a mathematical analysis of an ordinary differential equation model, including NADH to account for the redox balance. In order to gain qualitative insight, most of the analysis is parameter-free, i.e., without assigning a numerical value to any of the parameters. The model has a subtle bifurcation at the switch between an inviable equilibrium state and stable flux through glycolysis. This switch occurs if the ratio between the flux through upper glycolysis and ATP consumption rate of the cell exceeds a fixed threshold. If the enzymes of upper glycolysis would be barely expressed, our model predicts that there will be no glycolytic flux, even if external glucose would be at growth-permissable levels. The existence of the imbalanced state can be found for certain parameter conditions independent of the mentioned bifurcation. The parameter-free analysis proved too complex to directly gain insight into the imbalanced states, but the starting point of a branch of imbalanced states can be shown to exist in detail. Moreover, the analysis offers the key ingredients necessary for successful numerical continuation, which highlight the existence of this bistability and the influence of the redox balance.

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Section: Without Overexpression Of Its Upper Part Glycolysis Will Nosupporting

confidence: 83%

Section: A Simple Condition For the Transcritical Bifurcationsupporting

confidence: 69%

Understanding start-up problems in yeast glycolysis

Overal

Teusink

Bruggeman

et al. 2018

Mathematical Biosciences

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“…It is important that a perturbation is chosen that efficiently triggers turbulence. In many earlier studies, such as (10,25), turbulence was induced by insertion of a static obstacle close to the pipe inlet. Such obstacles provide a continuous perturbation, and at high Reynolds numbers the flow downstream is fully turbulent, whereas in the transitional…”

Section: The Onset Of Turbulence In Pipe Flowmentioning

confidence: 99%

Glycolytic Oscillations and Limits on Robust Efficiency

Chandra

Buzi

Doyle

2011

Science

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205

208

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“…We denote by π(y, z; ǫ) the solution of the HJB PDE corresponding to the cheap optimal control problem to (9). We apply the power series method [31], [32] by first expanding π(y, z; ǫ) in series as follows π(y, z; ǫ) = π [2] (y, z; ǫ) + π [3] (y, z; ǫ) + . .…”

Section: Fundamental Limits On the Performance Measuresmentioning

confidence: 99%

Fundamental Limits and Tradeoffs in Autocatalytic Pathways

Siami

Motee

Buzi

et al. 2020

IEEE Trans. Automat. Contr.

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This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. We consider a simplified model of Glycolysis pathway as our motivating application. First, the properties of these class of pathways are investigated through a simplified twostate model, which is obtained by lumping all the intermediate reactions into a single intermediate reaction. Then, we generalize our results to autocatalytic pathways that are composed of a chain of enzymatically catalyzed intermediate reactions. We explicitly derive a hard limit on the minimum achievable L 2 -gain disturbance attenuation and a hard limit on its minimum required output energy. Finally, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production.

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Analysis of autocatalytic networks in biology

Cited by 6 publications

References 24 publications

Understanding start-up problems in yeast glycolysis

Understanding start-up problems in yeast glycolysis

Glycolytic Oscillations and Limits on Robust Efficiency

Fundamental Limits and Tradeoffs in Autocatalytic Pathways

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