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J. Math. Biol. (2010) 60:313346 DOI 10.1007/s00285-009-0268-5
Mathematical Biology
Modelling of the activation of G-protein coupled receptors: drug free constitutive receptor activity
P. J. Woodroffe L. J. Bridge J. R. King
C. Y. Chen S. J. Hill
Received: 28 May 2008 / Revised: 13 March 2009 / Published online: 5 April 2009 Springer-Verlag 2009
Abstract G-protein coupled receptors (GPCRs) form a crucial component of approximately 80% of hormone pathways. In this paper, the most popular mechanism for activation of GPCRsthe shuttling mechanismis modelled mathematically. An asymptotic analysis of this model claries the dynamics of the system in the absence of drug, in particular which reactions dominate during the different timescales. Equilibrium analysis of the model demonstrates the models ability to predict constitutive receptor activity.
Keywords G-protein coupled receptors Mathematical modelling Asymptotic
analysis
Mathematics Subject Classication (2000) 92C45 92B05
1 Introduction
1.1 Motivation
Since multicellular organisms rst appeared on the earth, an essential factor in their success has been the effectiveness of communication between their component cells.
P. J. Woodroffe L. J. Bridge (B) J. R. King
Centre for Mathematical Medicine, Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham, UK e-mail: [email protected]
C. Y. ChenDepartment of Applied Mathematics, National University of Kaohsiung, Kaohsiung, Taiwan
S. J. HillInstitute of Cell Signalling, Medical School, Queens Medical Centre, Nottingham, UK
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Complex internal machinery is needed for the cells to coordinate their behaviour, allowing each individual cell to recognise its position and importance to the body as a whole: for example, having neighbouring cells control the rate of cell division is an important social control. The breakdown of such a control can lead to cancer, probably killing the organism (Alberts et al. 1994).
One specic type of intercellular communication involves the use of G-protein coupled receptors (GPCRs). It has been estimated that as much as 5% of the human genome codes for these receptors and approximately 80% of all known hormones, neurotransmitters and neuromodulators act through them. In addition, it is believed that between 45 and 60% of all pharmaceuticals used today act through GPCRs (Riccobene et al. 1999; Woolf et al. 2001).
Examples of GPCR systems include the 1-adrenoreceptor that adrenaline binds to, regulating heart contractility, and the...