Speaker
Description
Fundamental properties and emergent behaviours of biochemical systems often depend exclusively on the system structure (the graph topology along with qualitative information), regardless of parameter values. We first provide an overview of the parameter-free assessment of important properties, including the stability of equilibria and the sign of steady-state input-output influences. Then, we focus on the emergence of sustained oscillations via convergence to periodic orbits, a complex question with important applications in systems biology, including the understanding of biomolecular oscillators that rule cell life cycle and metabolism, as well as circadian rhythms in hormone secretion, body temperature and metabolic functions. The study of sustained oscillations in a dynamical system requires first showing that at least one periodic orbit exists and then assessing the stability of periodic orbits and characterising the initial conditions from which the solutions converge to periodic trajectories. For a class of strongly 2-cooperative nonlinear dynamical systems, leveraging results from the theory of cones, the spectral theory of totally positive matrices and Perron-Frobenius theory, we show that every solution emanating from an explicit set of initial conditions of positive measure converges to a periodic orbit. The result applies to well-known biological systems, including the n-dimensional Goodwin oscillator and biological oscillators based on RNA-mediated regulation.
Bibliography
@article{Katz_Giordano_Margaliot_2025,
title={Instability of equilibrium and convergence to periodic orbits in strongly 2-cooperative systems},
volume={444},
DOI={10.1016/j.jde.2025.113651},
journal={Journal of Differential Equations},
author={Katz, Rami and Giordano, Giulia and Margaliot, Michael},
year={2025},
month=nov,
pages={113651},
}
@article{Proverbio_Katz_Giordano_2025,
title={Robustness and Resilience of Dynamical Networks in Biology and Epidemiology},
volume={12},
url={http://www.nowpublishers.com/article/Details/SYS-036},
DOI={10.1561/2600000036},
number={2–3},
journal={Foundations and Trends® in Systems and Control},
author={Proverbio, Daniele and Katz, Rami and Giordano, Giulia},
year={2025},
pages={112–360},
}
@article{Blanchini_Giordano_2021,
title={Structural analysis in biology: A control-theoretic approach},
volume={126},
DOI={10.1016/j.automatica.2020.109376},
journal={Automatica},
author={Blanchini, Franco and Giordano, Giulia},
year={2021},
month=apr,
pages={109376}
}
@article{Blanchini_Samaniego_Franco_Giordano_2018,
title={Aggregates of Monotonic Step Response Systems: A Structural Classification},
volume={5},
DOI={10.1109/TCNS.2017.2746343},
number={2},
journal={IEEE Transactions on Control of Network Systems},
author={Blanchini, Franco and Cuba Samaniego, Christian and Franco, Elisa and Giordano, Giulia},
year={2018},
month=june,
pages={782–792}
}
@article{Blanchini_Franco_Giordano_2014,
title={A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems},
volume={76},
DOI={10.1007/s11538-014-0023-y},
number={10},
journal={Bulletin of Mathematical Biology},
author={Blanchini, Franco and Franco, Elisa and Giordano, Giulia},
year={2014},
month=oct,
pages={2542–2569},
}
