Semidefinite programming for Turing instability analysis in molecular communication networks

Yutaka Hori, Hiroki Miyazako

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes a computationally tractable algebraic condition for Turing instability, a type of local instability inducing self-organized spatial pattern formation, in molecular communication networks. The molecular communication networks consist of spatially distributed homogeneous compartments, or biological cells, that interact with neighbor compartments using a small number of diffusible chemical species. Thus, the underlying spatio-temporal dynamics of the system can be modeled by reaction-diffusion equations whose diffusion terms are zero for some chemical species. We show that the molecular communication networks are not Turing unstable if and only if certain polynomials are non-negative. This leads to sum-of-squares optimizations for Turing instability analysis. The proposed approach is capable of predicting the formation of spatial patterns in molecular communication networks based on the mathematically rigorous analysis of Turing instability.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1874-1880
Number of pages7
ISBN (Electronic)9781728113982
DOIs
Publication statusPublished - 2019 Dec
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: 2019 Dec 112019 Dec 13

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period19/12/1119/12/13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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  • Cite this

    Hori, Y., & Miyazako, H. (2019). Semidefinite programming for Turing instability analysis in molecular communication networks. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 1874-1880). [9029976] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029976