Interaction sign patterns in biological networks: From qualitative to quantitative criteria

Giulia Giordano, Claudio Altafini

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

4 Citations (Scopus)
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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.

Original languageEnglish
Title of host publicationProceedings of the 2017 IEEE 56th Annual Conference on Decision and Control
EditorsA Astolfi
Place of PublicationPiscataway, NJ, USA
ISBN (Electronic)978-150902873-3
Publication statusPublished - 2017
EventCDC 2017: 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017


ConferenceCDC 2017: 56th IEEE Annual Conference on Decision and Control
OtherThe CDC is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control. The CDC annually brings together an international community of researchers and practitioners in the field of automatic control to discuss new research results, perspectives on future developments, and innovative applications relevant to decision making, systems and control, and related areas.
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