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Interaction of fast and slow dynamics in endocrine control systems with an application to βcell dynamics
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Wang, YiFang, Khan, Michael and Berg, Hugo van den. (2012) Interaction of fast and slow dynamics in endocrine control systems with an application to βcell dynamics. Mathematical Biosciences, Vol.235 (No.1). pp. 818. ISSN 00255564

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Official URL: http://dx.doi.org/10.1016/j.mbs.2011.10.003
Abstract
Endocrine dynamics spans a wide range of time scales, from rapid responses to physiological challenges to with slow responses that adapt the system to the demands placed on it. We outline a nonlinear averaging procedure to extract the slower dynamics in a way that accounts properly for the nonlinear dynamics of the faster time scale and is applicable to a hierarchy of more than two time scales, although we restrict our discussion to two scales for the sake of clarity. The procedure is exact if the slow time scale is infinitely slow (the dimensionless epsilonquantity is the period of the fast time scale fluctuation times an upper bound to the slow time scale rate of change). However, even for an imperfect separation of time scales we find that this construction provides an excellent approximation for the slowtime dynamics at considerably reduced computational cost. Besides the computation advantage, the averaged equation provided a qualitative insight into the interaction of the time scales. We demonstrate the procedure and its advantages by applying the theory to the model described by Tolic et al. [I.M. Tolic, E. Mosekilde, J. Stuns, Modeling the insulinglucose feedback system: the significance of pulsatile insulin secretion, J. Theor. Biol. 207 (2000) 361375.] for ultradian dynamics of the glucoseinsulin homeostasis feedback system, extended to include betacell dynamics. We find that the dynamics of the betacell mass are dependent not only on the glycemic load (amount of glucose administered to the system), but also on the way this load is applied (i.e. three meals daily versus constant infusion), effects that are lost in the inappropriate methods used by the earlier authors. Furthermore, we find that the loss of the protection against apoptosis conferred by insulin that occurs at elevated levels of insulin has a functional role in keeping the betacell mass in check without compromising regulatory function. We also find that replenishment of betacells from a rapidly proliferating pool of cells, as opposed to the slow turnover which characterises fully differentiated betacells, is essential to the prevention of type 1 diabetes.
Item Type:  Journal Article 

Subjects:  Q Science > QP Physiology 
Divisions:  Faculty of Science > Life Sciences (2010 ) Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Endocrinology  Mathematical models, Biological control systems  Mathematical models, Pancreatic beta cells  Mathematical models 
Journal or Publication Title:  Mathematical Biosciences 
Publisher:  Elsevier Science Inc. 
ISSN:  00255564 
Official Date:  January 2012 
Volume:  Vol.235 
Number:  No.1 
Number of Pages:  11 
Page Range:  pp. 818 
Identification Number:  10.1016/j.mbs.2011.10.003 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  University of Warwick, Engineering and Physical Sciences Research Council (EPSRC) 
References:  Ackermann Misfeldt, A., Costa, R. H., Gannon, M., 2008. βcell proliferation, but not neogenesis, 
URI:  http://wrap.warwick.ac.uk/id/eprint/42182 
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