<i>BDC</i>-Decomposition for Global Influence Analysis

Blanchini, Franco; Giordano, Giulia

doi:10.1109/lcsys.2018.2866903

Cited by 7 publications

(10 citation statements)

References 28 publications

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“…The system is also shown to be a candidate oscillator [5], [6], consistently with glycolytic oscillations reported in the literature, not only for yeast [2], [11], but also for E. coli [22], [23], [31] and even for human pancreatic beta-cells [33]. The steady-state influences among the system variables (i.e., the variations in the steady state of a variable due to a persistent positive perturbation added to the differential equation of another variable) are also assessed [9], [14], [15], to reveal influences whose sign is preserved regardless of the parameters, and to analyse sensitivity to parameter variations; it turns out that the variation of [AT P ] due to additive perturbations affecting the other metabolites is particularly small, which supports the evidence of energy homeostasis (Section III). Finally, the theoretical predictions obtained with the proposed model are compared to experimental observations from E. coli cultivations: the model is able to reproduce very well the qualitative evolution of concentrations over time, and the observed energy homeostasis (Section IV).…”

Section: Introductionmentioning

confidence: 60%

“…Assumption 2: In the system in Table I, D = µ = 0. If D = µ = 0, the system admits a BDC-decomposition [4], [7], [8], [9], [14]: Then, the steady state can be proven to be unique. Proposition 2: Under Assumptions 1 and 2, the system in Table I admits a unique steady statex ∈ B, which does not have zero components.…”

Section: B Uniqueness Of the Steady Statementioning

confidence: 99%

“…How does the new steadystate differ from the previous one? For systems admitting a BDC-decomposition, the sign of the variation between the old and the new steady-states can be computed based on the algorithm proposed in [14] (see also the extension [9] and the applications to biological systems in [13], [15], [16], [17]).…”

Section: Steady-state Influencesmentioning

confidence: 99%

See 2 more Smart Citations

Unraveling energy homeostasis in a dynamic model of glycolysis in Escherichia coli

Giordano

Graaf

Vasilakou

et al. 2019

2019 18th European Control Conference (ECC)

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Section: Introductionmentioning

confidence: 60%

Section: B Uniqueness Of the Steady Statementioning

confidence: 99%

See 1 more Smart Citation

Unraveling energy homeostasis in a dynamic model of glycolysis in Escherichia coli

Giordano

Graaf

Vasilakou

et al. 2019

2019 18th European Control Conference (ECC)

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“…The following proposition provides a necessary and sufficient condition for the steady state (14) to be well defined. Proposition 4 (Existence of a steady state): A is robustly nonsingular, namely det(A) = 0 for all A ∈ A, if and only if det(A) has the same sign on all the vertices of A.…”

Section: Static Linear Casementioning

confidence: 99%

“…Proposition 5 (Positivity of the steady state): The steady statex defined in (14) is positive for all A ∈ A if and only if −A −1 b > 0 for all the vertices of A.…”

Section: Static Linear Casementioning

confidence: 99%

A switched model for mixed cooperative-competitive social dynamics

Blanchini

Casagrande

Giordano

et al. 2019

2019 18th European Control Conference (ECC)

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A multi-agent continuous-time nonlinear model of social behaviour allowing for both competition and cooperation is presented and analysed. The state of each agent is represented by its payoff, which the agent aims at maximising. The role of control variables is played by the model parameters, which account for the agents' decisions to either cooperate with or boycott the other agents and can vary in time within assigned intervals. Alliances and enmities can be established at any time, according to either a greedy or a longsighted criterion. The general nonlinear case is first considered. It is proved that, under realistic assumptions, the system evolution is bounded positive (no extinction) and there is a unique globallystable equilibrium point. As is somehow expected, the optimal decision for all agents corresponds to full cooperation (decision parameters kept at their positive maximum value) in the case of both shortsighted and farsighted criteria. This is not true if some parameters have negative upper bounds (meaning that some agents systematically boycott some others). Then, in the linear case, it is shown that the system is stable for arbitrarilyvarying decision parameters, provided that a Metzler matrix associated with full cooperation is Hurwitz. A characterisation of the long-term behaviour of the linear system is also provided. In particular, it is proved that, under stability conditions, a Nash equilibrium exists if a steady strategy is adopted. G.G. acknowledges support from the Aspasia grant and the DTF grant.

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Vertex results for the robust analysis of uncertain biochemical systems

et al. 2022

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We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

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BDC-Decomposition for Global Influence Analysis

Cited by 7 publications

References 28 publications

Unraveling energy homeostasis in a dynamic model of glycolysis in Escherichia coli

Unraveling energy homeostasis in a dynamic model of glycolysis in Escherichia coli

A switched model for mixed cooperative-competitive social dynamics

Vertex results for the robust analysis of uncertain biochemical systems

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