Interaction sign patterns in biological networks: from qualitative to quantitative criteria
(2017) 56th IEEE Annual Conference on Decision and Control, CDC 2017- Abstract
- In stable biological and ecological networks, the steady-state influence matrix gathers the signs of steady-state responses to step-like perturbations affecting the variables. Such signs are difficult to predict a priori, because they result from a combination of direct effects (deducible from the Jacobian of the network dynamics) and indirect effects. For stable monotone or cooperative networks, the sign pattern of the influence matrix can be qualitatively determined based exclusively on the sign pattern of the system Jacobian. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for Jacobians with a given sign pattern to admit a fully positive influence matrix, and we also provide... (More)
- In stable biological and ecological networks, the steady-state influence matrix gathers the signs of steady-state responses to step-like perturbations affecting the variables. Such signs are difficult to predict a priori, because they result from a combination of direct effects (deducible from the Jacobian of the network dynamics) and indirect effects. For stable monotone or cooperative networks, the sign pattern of the influence matrix can be qualitatively determined based exclusively on the sign pattern of the system Jacobian. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for Jacobians with a given sign pattern to admit a fully positive influence matrix, and we also provide quantitative conditions for Jacobians that are translated eventually nonnegative matrices. We present a computational test to check whether the influence matrix has a constant sign pattern in spite of parameter variations, and we apply this algorithm to quasi-Metzler Jacobian matrices, to assess whether positivity of the influence matrix is preserved in spite of deviations from cooperativity. When the influence matrix is fully positive, we give a simple vertex algorithm to test robust stability. The devised criteria are applied to analyse the steady-state behaviour of ecological and biomolecular networks. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/a1d759e6-de24-4e66-b9d6-984012a6a78e
- author
- Giordano, Giulia LU and Altafini, Claudio
- organization
- publishing date
- 2017
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 56th IEEE Conference on Decision and Control
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 56th IEEE Annual Conference on Decision and Control, CDC 2017
- conference location
- Melbourne, Australia
- conference dates
- 2017-12-12 - 2017-12-15
- external identifiers
-
- scopus:85046164926
- DOI
- 10.1109/CDC.2017.8264451
- language
- English
- LU publication?
- yes
- id
- a1d759e6-de24-4e66-b9d6-984012a6a78e
- date added to LUP
- 2017-08-22 11:35:51
- date last changed
- 2022-04-25 01:54:54
@inproceedings{a1d759e6-de24-4e66-b9d6-984012a6a78e,
abstract = {{In stable biological and ecological networks, the steady-state influence matrix gathers the signs of steady-state responses to step-like perturbations affecting the variables. Such signs are difficult to predict a priori, because they result from a combination of direct effects (deducible from the Jacobian of the network dynamics) and indirect effects. For stable monotone or cooperative networks, the sign pattern of the influence matrix can be qualitatively determined based exclusively on the sign pattern of the system Jacobian. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for Jacobians with a given sign pattern to admit a fully positive influence matrix, and we also provide quantitative conditions for Jacobians that are translated eventually nonnegative matrices. We present a computational test to check whether the influence matrix has a constant sign pattern in spite of parameter variations, and we apply this algorithm to quasi-Metzler Jacobian matrices, to assess whether positivity of the influence matrix is preserved in spite of deviations from cooperativity. When the influence matrix is fully positive, we give a simple vertex algorithm to test robust stability. The devised criteria are applied to analyse the steady-state behaviour of ecological and biomolecular networks.}},
author = {{Giordano, Giulia and Altafini, Claudio}},
booktitle = {{Proceedings of the 56th IEEE Conference on Decision and Control}},
language = {{eng}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Interaction sign patterns in biological networks: from qualitative to quantitative criteria}},
url = {{http://dx.doi.org/10.1109/CDC.2017.8264451}},
doi = {{10.1109/CDC.2017.8264451}},
year = {{2017}},
}