A structural classification of candidate oscillatory and multistationary biochemical systems
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Abstract
Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas' conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.
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The mutual inhibition between HPG and HPA axes gives rise to a positive loop; therefore, the dynamic system is a candidate multistable system that can admit multiple equilibria.
“The mutual inhibition between HPG and HPA axes gives rise to a positive loop; therefore, the dynamic system is a candidate multistable system that can admit multiple equilibria [130].”
From Fibromyalgia pathogenesis explained by a neuroendocrine multistable model (2024) · cites this paper as [130]
Figure 1b describes mutual inhibition as an overall positive feedback loop, and Proposition 3 (under Definition 9; page unavailable) says a non-critical system with a positive cycle is a candidate multistationary system. The paper does not establish mutual inhibition between the HPG and HPA axes or assess that particular system; its conclusion about possible multiple equilibria is therefore a conditional application, not a finding about those axes. (LLM, conf=0.85)
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Cites
A synthetic oscillatory network of transcriptional regulators
Elowitz, M., & Leibler, S. (2000) · Nature · doi:10.1038/35002125 · Cited by 4,812 · see citing works
Strogatz, S. H. (1998) · doi:10.1142/3481 · Cited by 4,542 · see citing works
Construction of a genetic toggle switch in Escherichia coli
Gardner, T. S., Cantor, C. R., & Collins, J. J. (2000) · Nature · doi:10.1038/35002131 · Cited by 4,310 · see citing works
An Introduction to Systems Biology: Design Principles of Biological Circuits
Alon, U. (2006) · doi:10.1201/9781420011432 · Cited by 2,825 · see citing works
Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
Smith, H. L. (2008) · Mathematical surveys and monographs · doi:10.1090/surv/041 · Cited by 2,345 · see citing works
Strogatz, S. H. (2018) · CRC Press eBooks · doi:10.1201/9780429492563 · Cited by 2,247 · see citing works
Mathematical Models in Biology
Edelstein‐Keshet, L. (2005) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719147 · Cited by 2,053 · see citing works
(1962) · Journal of the Franklin Institute · doi:10.1016/0016-0032(62)91109-2 · Cited by 2,001 · see citing works
A genomic regulatory network for development
Davidson, E. H., Rast, J. P., Oliveri, P., Ransick, A., Calestani, C., Yuh, C.-H., Minokawa, T., Amore, G., Hinman, V., Arenas-Mena, C., et al. (2002) · Science · doi:10.1126/science.1069883 · Cited by 1,567 · see citing works
Set-Theoretic Methods in Control
Blanchini, F., & Miani, S. (2007) · Systems & control · doi:10.1007/978-0-8176-4606-6 · Cited by 1,510 · see citing works
Self-citationDesign principles of biochemical oscillators
Novák, B., & Tyson, J. J. (2008) · Nature Reviews Molecular Cell Biology · doi:10.1038/nrm2530 · Cited by 1,137 · see citing works
A fast, robust and tunable synthetic gene oscillator
Stricker, J., Cookson, S., Bennett, M. R., Mather, W., Tsimring, L. S., & Hasty, J. (2008) · Nature · doi:10.1038/nature07389 · Cited by 1,102 · see citing works
Angeli, D., Ferrell, J. E., & Sontag, E. D. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0308265100 · Cited by 1,007 · see citing works
Autoinhibition with Transcriptional Delay
Lewis, J. H. (2003) · Current Biology · doi:10.1016/s0960-9822(03)00534-7 · Cited by 736 · see citing works
Feinberg, M. (1987) · Chemical Engineering Science · doi:10.1016/0009-2509(87)80099-4 · Cited by 729 · see citing works
Atkinson, M. R., Savageau, M. A., Myers, J. T., & Ninfa, A. J. (2003) · Cell · doi:10.1016/s0092-8674(03)00346-5 · Cited by 710 · see citing works
Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops
Tsai, T. Y.-C., Choi, Y. S., Ma, W., Pomerening, J. R., Tang, C., & Ferrell, J. E. (2008) · Science · doi:10.1126/science.1156951 · Cited by 689 · see citing works
Angeli, D., & Sontag, E. D. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.817920 · Cited by 683 · see citing works
A primer of nonlinear analysis
Ambrosetti, A., & Prodi, G. A. (1993) · Cited by 597 · see citing works
A tunable synthetic mammalian oscillator
Tigges, M., Marquez‐Lago, T. T., Stelling, J., & Fussenegger, M. (2009) · Nature · doi:10.1038/nature07616 · Cited by 568 · see citing works
Differential Dynamical Systems
Meiss, J. D. (2007) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718232 · Cited by 424 · see citing works
Thomas, R. (1981) · Springer series in synergetics · doi:10.1007/978-3-642-81703-8_24 · Cited by 358 · see citing works
Stability and convergence in strongly monotone dynamical systems.
Hirsch, M. W. (1988) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1988.383.1 · Cited by 353 · see citing works
Construction of an in vitro bistable circuit from synthetic transcriptional switches
Kim, J., White, K. S., & Winfree, E. (2006) · Molecular Systems Biology · doi:10.1038/msb4100099 · Cited by 316 · see citing works
Synthetic in vitro transcriptional oscillators
Kim, J., & Winfree, E. (2011) · Molecular Systems Biology · doi:10.1038/msb.2010.119 · Cited by 316 · see citing works
Recasting nonlinear differential equations as S-systems: a canonical nonlinear form
Savageau, M. A., & Voit, E. O. (1987) · Mathematical Biosciences · doi:10.1016/0025-5564(87)90035-6 · Cited by 310 · see citing works
Understanding bistability in complex enzyme-driven reaction networks
Crăciun, G., Tang, Y., & Feinberg, M. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0602767103 · Cited by 310 · see citing works
Stability theory for nonnegative and compartmental dynamical systems with time delay
Haddad, W. M., & Chellaboina, V.-S. (2003) · Systems & Control Letters · doi:10.1016/j.sysconle.2003.09.006 · Cited by 294 · see citing works
Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property
Crăciun, G., & Feinberg, M. (2005) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139904440278 · Cited by 292 · see citing works
Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph
Crăciun, G., & Feinberg, M. (2006) · SIAM Journal on Applied Mathematics · doi:10.1137/050634177 · Cited by 287 · see citing works
Programming an in vitro DNA oscillator using a molecular networking strategy
Montagne, K., Plasson, R., Sakai, Y., Fujii, T., & Rondelez, Y. (2011) · Molecular Systems Biology · doi:10.1038/msb.2010.120 · Cited by 285 · see citing works
Positive and Negative Circuits in Dynamical Systems
Gouzé, J. (1998) · Journal of Biological Systems · doi:10.1142/s0218339098000054 · Cited by 273 · see citing works
Stability Analysis for Continuous-Time Positive Systems With Time-Varying Delays
Liu, X., Yu, W., & Wang, L. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2041982 · Cited by 271 · see citing works
Smith, H. L. (2008) · Mathematical surveys and monographs · doi:10.1090/surv/041/01 · Cited by 264 · see citing works
Necessary Conditions for Multistationarity and Stable Periodicity
Snoussi, E. H. (1998) · Journal of Biological Systems · doi:10.1142/s0218339098000042 · Cited by 239 · see citing works
Graphic Requirements for Multistationarity
Soulé, C. (2003) · Complexus · doi:10.1159/000076100 · Cited by 237 · see citing works
Timing molecular motion and production with a synthetic transcriptional clock
Franco, E., Friedrichs, E., Kim, J., Jungmann, R., Murray, R. M., Winfree, E., & Simmel, F. C. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1100060108 · Cited by 233 · see citing works
Self-citationBistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling
Qiao, L., Nachbar, R. B., Kevrekidis, I. G., & Shvartsman, S. Y. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030184 · Cited by 210 · see citing works
Monotone and near-monotone biochemical networks
Sontag, E. D. (2007) · Systems and Synthetic Biology · doi:10.1007/s11693-007-9005-9 · Cited by 201 · see citing works
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
Watkins, D. S. (2008) · Cited by 174 · see citing works
Bottom-up construction of in vitro switchable memories
Padirac, A., Fujii, T., & Rondelez, Y. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1212069109 · Cited by 170 · see citing works
Qualitative Problems in Matrix Theory
Maybe, J., & Quirk, J. (1969) · SIAM Review · doi:10.1137/1011004 · Cited by 141 · see citing works
Watkins, D. S. (2007) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898717808 · Cited by 131 · see citing works
A new necessary condition on interaction graphs for multistationarity
Kaufman, M., Soulé, C., & Thomas, R. (2007) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2007.06.016 · Cited by 112 · see citing works
Systems biology of cellular rhythms
Goldbeter, A., Gérard, C., Gonze, D., Leloup, J., & Dupont, G. (2012) · FEBS Letters · doi:10.1016/j.febslet.2012.07.041 · Cited by 110 · see citing works
Topological Methods in Differential Equations and Inclusions
Granas, A., Frigon, M., & Sabidussi, G. (1995) · Springer eBooks · doi:10.1007/978-94-011-0339-8 · Cited by 102 · see citing works
Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements
Banaji, M., & Crăciun, G. (2009) · Communications in Mathematical Sciences · doi:10.4310/cms.2009.v7.n4.a4 · Cited by 96 · see citing works
Zeines, B., & Gates, A. B. (1973) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.3426706 · Cited by 83 · see citing works
On the Global Stability of Cooperative Systems
Ji-Fa, J. (1994) · Bulletin of the London Mathematical Society · doi:10.1112/blms/26.5.455 · Cited by 81 · see citing works
Structurally robust biological networks
Blanchini, F., & Franco, E. (2011) · BMC Systems Biology · doi:10.1186/1752-0509-5-74 · Cited by 80 · see citing works
Self-citationBistability and oscillations in chemical reaction networks
Domijan, M., & Kirkilionis, M. (2008) · Journal of Mathematical Biology · doi:10.1007/s00285-008-0234-7 · Cited by 61 · see citing works
Some applications of the topological degree to stability theory
Ortega, R. (1995) · Springer eBooks · doi:10.1007/978-94-011-0339-8_8 · Cited by 59 · see citing works
On rest points of dynamical systems
Srzednicki, R. (1985) · Fundamenta Mathematicae · doi:10.4064/fm-126-1-69-81 · Cited by 50 · see citing works
An index theorem for dissipative semiflows
Hofbauer, J. (1990) · Rocky Mountain Journal of Mathematics · doi:10.1216/rmjm/1181073059 · Cited by 50 · see citing works
Thomas, R. (1994) · Berichte der Bunsengesellschaft für physikalische Chemie · doi:10.1002/bbpc.19940980916 · Cited by 49 · see citing works
Modeling and Analyzing Biological Oscillations in Molecular Networks
Wang, R., Li, C. G., Chen, L., & Aihara, K. (2008) · Proceedings of the IEEE · doi:10.1109/jproc.2008.925448 · Cited by 38 · see citing works
A fixed point theorem for bounded dynamical systems
Richeson, D. S., & Wiseman, J. (2002) · Illinois Journal of Mathematics · doi:10.1215/ijm/1258136205 · Cited by 37 · see citing works
Mincheva, M., & Crăciun, G. (2008) · Proceedings of the IEEE · doi:10.1109/jproc.2008.925474 · Cited by 36 · see citing works
Erratum To: Programming an in vitro DNA oscillator using a molecular networking strategy
Montagne, K., Plasson, R., Sakai, Y., Fujii, T., & Rondelez, Y. (2011) · Molecular Systems Biology · doi:10.1038/msb.2011.12 · Cited by 36 · see citing works
Stable periodicity and negative circuits in differential systems
Richard, A., & Comet, J. (2010) · Journal of Mathematical Biology · doi:10.1007/s00285-010-0388-y · Cited by 20 · see citing works
Multistability, oscillations and bifurcations in feedback loops
Leite, M. C. A., & Wang, Y. (2010) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2010.7.83 · Cited by 18 · see citing works
The interaction graph structure of mass-action reaction networks
Domijan, M., & Pécou, E. (2011) · Journal of Mathematical Biology · doi:10.1007/s00285-011-0462-0 · Cited by 18 · see citing works
Merkin, J. H., & Sleeman, B. D. (2004) · Journal of Mathematical Biology · doi:10.1007/s00285-004-0308-0 · Cited by 16 · see citing works
Oscillations in Biochemical Reaction Networks Arising from Pairs of Subnetworks
Mincheva, M. (2011) · Bulletin of Mathematical Biology · doi:10.1007/s11538-010-9620-6 · Cited by 16 · see citing works
Structural properties of the MAPK pathway topologies in PC12 cells
Franco, E., & Blanchini, F. (2012) · Journal of Mathematical Biology · doi:10.1007/s00285-012-0606-x · Cited by 11 · see citing works
Self-citationDifferential Dynamical Systems (Monographs on Mathematical Modeling and Computation)
Meiss, J. D. (2007) · Society for Industrial and Applied Mathematics eBooks · Cited by 10 · see citing works
Oscillations in I/O Monotone Systems Under Negative Feedback
Angeli, D., & Sontag, E. D. (2009) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2007.911320 · Cited by 6 · see citing works
Hori, Y., & Hara, S. (2011) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2011.5990877 · Cited by 6 · see citing works
An Attack Against the Revised Murthy–Swamy Cryptosystem
Youssef, A. (2008) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2007.911833 · Cited by 5 · see citing works
Positive feedback circuits are a necessary condition for positive eigenvalues of the jacobian matrix
Thomas, R. (1994) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · Cited by 4 · see citing works
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Self-citation
- Authors
- Blanchini, F., Franco, E., & Giordano, G.
- Affiliations
- University of Udine (IT)
- University of California, Riverside (US)
- Corresponding author
- Blanchini, Franco
- Venue
- Bulletin of Mathematical Biology
- Published
- 2014-09-18
- Volume
- 76
- Issue
- 10
- Pages
- 2542-2569
- ISSN
- 0092-8240 (ISSN-L)
- 1522-9602
- OpenAlex
- W1980077650
- Cited by
- 54
- References
- 70
- Citations by year
- 2025: 5 · 2024: 4 · 2023: 2 · 2022: 6 · 2021: 3 · 2020: 4 · 2019: 6 · 2018: 5 · 2017: 6 · 2016: 4 · 2015: 6 · 2014: 3
- FWCI
- 2.60
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by-nc-nd
- www.springer.com/tdm (tdm)
- Locations
- Bulletin of Mathematical Biology (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Institutional Research Information System (University of Udine) (submittedVersion)
- Iris (University of Trento) (submittedVersion)
- Lund University Publications (Lund University) (submittedVersion)
- Funders
- National Science Foundation (1266402)
- Division of Civil, Mechanical and Manufacturing Innovation (1266402, CMMI-1266402)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Keywords
- multistationarity, bistability, eigenvalue analysis, complex eigenvalues, real eigenvalues
- MeSH terms
- Biochemical Phenomena, Models, Chemical, Models, Genetic, Feedback, Physiological, Systems Biology, Gene Regulatory Networks, Mathematical Concepts, Synthetic Biology
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