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Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations
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dc.contributor.author | Chaplain, Mark | |
dc.contributor.author | Ptashnyk, Mariya | |
dc.contributor.author | Sturrock, Marc | |
dc.date.accessioned | 2015-09-29T15:10:00Z | |
dc.date.available | 2015-09-29T15:10:00Z | |
dc.date.issued | 2015-01-08 | |
dc.identifier.citation | Chaplain , M , Ptashnyk , M & Sturrock , M 2015 , ' Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations ' , Mathematical Models and Methods in Applied Sciences , vol. 25 , no. 6 , pp. 1179-1215 . https://doi.org/10.1142/S021820251550030X | en |
dc.identifier.issn | 0218-2025 | |
dc.identifier.other | PURE: 206431985 | |
dc.identifier.other | PURE UUID: 3eb6bacf-4f3b-4c52-aff0-53fd43b75552 | |
dc.identifier.other | RIS: urn:E69CE837219A40C22A225F5D19E103EF | |
dc.identifier.other | Scopus: 84928548767 | |
dc.identifier.other | ORCID: /0000-0001-5727-2160/work/55378988 | |
dc.identifier.uri | https://hdl.handle.net/10023/7564 | |
dc.description | M.A.J.C. and M.S. gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS — From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”. M.S. would also like to thank the support from the Mathematical Biosciences Institute at the Ohio State University and NSF Grant DMS0931642. | en |
dc.description.abstract | Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a one-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NF-κB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer. | |
dc.format.extent | 37 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematical Models and Methods in Applied Sciences | en |
dc.rights | Copyright 2015 The Authors. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 3.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. | en |
dc.subject | Gene regulatory network | en |
dc.subject | Transcription factor | en |
dc.subject | Negative feedback loop | en |
dc.subject | Oscillations | en |
dc.subject | Hopf bifurcation | en |
dc.subject | Center manifold and normal form | en |
dc.subject | Weakly nonlinear analysis | en |
dc.subject | QA Mathematics | en |
dc.subject | QH301 Biology | en |
dc.subject | NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject | SDG 3 - Good Health and Well-being | en |
dc.subject.lcc | QA | en |
dc.subject.lcc | QH301 | en |
dc.title | Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | https://doi.org/10.1142/S021820251550030X | |
dc.description.status | Peer reviewed | en |
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