Bulletin of Mathematical Biology

, Volume 80, Issue 7, pp 1900–1936 | Cite as

Signal Propagation in Sensing and Reciprocating Cellular Systems with Spatial and Structural Heterogeneity

  • Arran Hodgkinson
  • Gilles Uzé
  • Ovidiu Radulescu
  • Dumitru Trucu
Original Article


Sensing and reciprocating cellular systems (SARs) are important for the operation of many biological systems. Production in interferon (IFN) SARs is achieved through activation of the Jak-Stat pathway, and downstream upregulation of IFN regulatory factor (IRF)-7 and IFN transcription, but the role that high- and low-affinity IFNs play in this process remains unclear. We present a comparative between a minimal spatio-temporal partial differential equation model and a novel spatio-structural-temporal (SST) model for the consideration of receptor, binding, and metabolic aspects of SAR behaviour. Using the SST framework, we simulate single- and multi-cluster paradigms of IFN communication. Simulations reveal a cyclic process between the binding of IFN to the receptor, and the consequent increase in metabolism, decreasing the propensity for binding due to the internal feedback mechanism. One observes the effect of heterogeneity between cellular clusters, allowing them to individualise and increase local production, and within clusters, where we observe ‘subpopular quiescence’; a process whereby intra-cluster subpopulations reduce their binding and metabolism such that other such subpopulations may augment their production. Finally, we observe the ability for low-affinity IFN to communicate a long range signal, where high affinity cannot, and the breakdown of this relationship through the introduction of cell motility. Biological systems may utilise cell motility where environments are unrestrictive and may use fixed system, with low-affinity communication, where a localised response is desirable.


Population dynamics Structured models Interferon signalling 

Mathematics Subject Classification

22E46 53C35 57S20 



AH would like to acknowledge the PhD training funding provided by the École Doctorale I2S de l’Université de Montpellier. OR thanks the programme Emergence of the Canceropole Grand Sud-Ouest and the Labex EpigenMed for supporting this research. dt would like to acknowledge the position of Invited Distinguished Research Scholar and associated funding awarded by the Université de Montpellier (France), for the period 28 Nov. to 14 Dec. 2016.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.DIMNP - UMR 5235Université de MontpellierMontpellierFrance
  2. 2.Division of MathematicsUniversity of DundeeDundeeScotland, UK

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