Emergence of Regular and Complex Calcium Oscillations by Inositol 1,4,5-Trisphosphate Signaling in Astrocytes

  • Valeri Matrosov
  • Susan GordleevaEmail author
  • Natalia Boldyreva
  • Eshel Ben-Jacob
  • Victor Kazantsev
  • Maurizio De Pittà
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI)


We use tools of bifurcation theory to characterize dynamics of astrocytic IP\(_3\) and Ca\(^{2+}\) for different IP\(_3\) regimes. We do so starting from a compact, well-stirred astrocyte model to first identify characteristic IP\(_3\) pathways whereby Ca\(^{2+}\) and IP\(_3\) dynamics “bifurcate,” namely their dynamics changes from stable (constant) concentration levels, to oscillating ones. Then, we extend our analysis to the elemental case of two astrocytes, coupled by IP\(_3\) diffusion mediated by gap junction channels, leveraging on the mechanisms of emergence of chaotic oscillations. Finally, we discuss spatiotemporal Ca\(^{2+}\) dynamics in a spatially extended astrocyte model, gaining insights on the possible physical mechanisms whereby random Ca\(^{2+}\) generation could be orchestrated into robust, spatially confined intracellular Ca\(^{2+}\) oscillations.


Chaotic calcium dynamics Compartmental astrocyte modeling Calcium spatial patterns 



Bogdanov-Takens bifurcation point


Calcium-induced calcium release


Cusp bifurcation point


Endoplasmic reticulum


Fold bifurcation point


Fold-flip bifurcation point


Generalized Andronov-Hopf bifurcation point


Andronov-Hopf bifurcation point


Homoclinic-to-hyperbolic saddle bifurcation point

\(\mathrm{{IP}_3}\) (\(\mathrm{{IP}_3}\) R)

Inositol 1,4,5-trisphosphate (receptor)

\(\mathrm{{IP}_3}\) 3K

\(\mathrm{{IP}_3}\) 3-kinase


Inositol polyphosphate 5-phosphatase


Fold bifurcation point of limit cycles

PLC\(\upbeta \)  (PLC\(\updelta \))

Phospholipase C\(\upbeta \) (C\(\updelta \))


Plasmalemma membrane \({\mathrm{Ca}^{2+}}\)-ATPase pump


(sarco)-endoplasmic reticulum \({\mathrm{Ca}^{2+}}\)-ATPase pump


Double Andronov-Hopf bifurcation point



This work was supported by the Russian Foundation for Basic Research (Grants No. 17-02-01103 and No. 16-32-60145) and by the Council of the President of the Russian Federation for State Support of Young Scientists and Leading Scientific Schools (Grant No. MK-2909.2017.4). MDP is a Junior Leader Postdoctoral Fellow sponsored by “la Caixa” Banking Foundation (LCF/BQ/LI18/11630006), and he was also previously supported by a FP7 Marie Sklodowska-Curie International Outgoing Fellowship by the European Commission (Project 331486 “Neuron-Astro-Nets”). MDP also wishes to acknowledge the support of the Basque Government by the BERC 2018–2021 program, as well as the support by the Spanish Ministry of Science, Innovation and Universities through the BCAM Severo Ochoa accreditation SEV-2017-0718.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Valeri Matrosov
    • 1
  • Susan Gordleeva
    • 1
    Email author
  • Natalia Boldyreva
    • 1
  • Eshel Ben-Jacob
    • 2
  • Victor Kazantsev
    • 1
  • Maurizio De Pittà
    • 3
    • 4
    • 5
  1. 1.N.I. Lobachevsky State University of Nizhni NovgorodNizhnyRussia
  2. 2.School of Physics and AstronomyTel Aviv UniversityRamat AvivIsrael
  3. 3.Department of NeurobiologyThe University of ChicagoChicagoUSA
  4. 4.EPI BEAGLE, INRIA Rhône-AlpesVilleurbanneFrance
  5. 5.Group of Mathematical, Computational and Experimental NeuroscienceBasque Center for Applied MathematicsBilbao, BiscaySpain

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