Wang, Yi-Fang, Khan, Michael and Berg, Hugo van den, 1968-. (2012) Interaction of fast and slow dynamics in endocrine control systems with an application to β-cell dynamics. Mathematical Biosciences, Vol.235 (No.1). pp. 8-18. ISSN 0025-5564

Preview

PDF WRAP_Van_Den_Berg_fastslow.pdf - Submitted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (3426Kb)

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 non-linear averaging procedure to extract the slower dynamics in a way that accounts properly for the non-linear 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 epsilon-quantity 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 slow-time 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 insulin-glucose feedback system: the significance of pulsatile insulin secretion, J. Theor. Biol. 207 (2000) 361-375.] for ultradian dynamics of the glucose-insulin homeostasis feedback system, extended to include beta-cell dynamics. We find that the dynamics of the beta-cell 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 beta-cell mass in check without compromising regulatory function. We also find that replenishment of beta-cells from a rapidly proliferating pool of cells, as opposed to the slow turn-over which characterises fully differentiated beta-cells, 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:	0025-5564
Date:	January 2012
Volume:	Vol.235
Number:	No.1
Number of Pages:	11
Page Range:	pp. 8-18
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. β-cell proliferation, but not neogenesis, following 60% partial pancreatomy is impaired in the absence of FoxM1. Diabetes 57, 3069{3077. Akirav, E., Kushner, J. A., Herold, K. C., 2008. β-cell mass and Type 1 diabetes. Diabetes 57, 2883{2888. Beith, J. L., Alejandro, E. U., Johnson, J. D., 1998. Insulin stimulates primary β-cell proliferation via Raf-1 kinase. Endocrinology 149, 2251{2260. Bonner-Weir, S., 2000. Perspective: Postnatal pancreatic β cell growth. Endocrinology 141, 1926{ 1928. Bouwens, L., Rooman, I., 2005. Regulation of pancreatic beta-cell mass. Physiol. Rev. 85, 1255{ 1270. Brook, C. G. D., Marshall, N. J., 2001. Essential Endocrinology. Blackwell Science. De Leon, D. D., Deng, S., Madani, R., Ahima, R. S., Drucker, D. J., Stoffers, D. A., 2003. Role of endogenous glucagon-like peptide-1 in islet regeneration after partial pancreatectomy. Diabetes 52, 365{371. De Winter, W., DeJongh, J., Post, T., Ploeger, B., Urquhart, R., Moules, I., Eckland, D., Danhof, M., 2006. A mechanism-based disease progression model for comparison of long-term effects of prioglitazone, metformin and gliclazide on disease processes underlying type 2 diabetes mellitus. J. Pharmacokin. Pharmacodyn. 33 (3), 313{343. Dor, Y., Brown, J., Martinez, O. I., Melton, D. A., 2004. Adult pancreatic β-cells are formed by self-duplication rather than stem-cell differentiation. Nature 429, 41{46. Efanova, I., Zaitsev, S., B., Z., Kohler, M., Efendic, S., Orrenius, S., Berggren, P. O., 1998. Glucose and tolbutamide induce apoptosis in pancreatic β-cells. A process dependent on intracellular Ca2+ concentration. J. Biol. Chem. 273, 33501{33507. Frayn, K. N., 2003. Metabolic Regulation: A Human Perspective. W. B. Saunders. Grossman, E. J., Lee, D. D., Tao, J., Wilson, R. A., Park, S.-Y., Bell, G. I., Chong, A. S., 2010. Glycemic control promotes pancreatic beta-cell regeneration in streptozotocin-induced diabetic mice. PLoS ONE 5, e8749. URL doi:10.1371/journal.pone.0008749 Holmes, M. H., 1995. Introduction to Perturbation Methods. Springer. Hope, K. M., Tran, P. O. T., Zhou, H., Oseid, E., Leroy, E., Robertson, R. P., 2004. Regulation of β-cell function by the β-cell in isolated human and rat islets deprived of glucose: the \switch-of" hypothesis. Diabetes 53, 1488{1495. Imagawa, A., Hanafusa, T., Miyagawa, J.-I., Matsuzawa, Y., 2000. A novel subtype of type 1 diabetes mellitus characterized by a rapid onset and an absence of diabetes-related antibodies. N. Engl. J. Med. 342, 301{307. Johnson, J. D., Alejandro, E. U., 2008. Control of pancreatic β-cell fate by insulin signaling: The sweet spot hypothesis. Cell Cycle 7, 1343{1347. Johnson, J. D., Bernal-Mizrachi, E., Alejandro, E. U., Han, Z., Kalynyak, T. B., Li, H., Beith, J. L., Gross, J., Warnock, G. L., Townsend, R. R., Permutt, M. A., Polonsky, K. S., 2006. Insulin protects islets from apoptosis via Pdx1 and specific changes in the human islet proteome. Proc. Natl. Acad. Sci. USA 103, 19575{19580. Jonas, J.-C., Laybutt, D. R., Steil, G. M., Trivedi, N., Pertusa, J. G., Van de Casteele, M., Weir, G. C., Henquin, J.-C., 2001. High glucose stimulates early response gene c-Myc expression in rat pancreatic cells. J. Biol. Chem. 276, 35375{35381. Keener, J., Sneyd, J., 1998. Mathematical Physiology. Springer. Lee, C. S., Leon, D. D. D., Kaestner, K. H., Stoffers, D. A., 2006. Regeneration of pancreatic islets after partial pancreatectomy in mice does not involve the reactivation of neurogenin-3. Diabetes 55, 269{272. Lingohr, M. K., Buettner, R., Rhodes, C. J., 2002. Pancreatic β-cell growth and survival|a role in obesity-linked type 2 diabetes? TRENDS Mol. Med., 375{384. Lipsett, M., Finegood, D. T., 2002. β-cell neogenesis during prolonged hyperglycemia in rats. Diabetes 51, 1834{1841. Mentlein, R., Gallwitz, B., Schmidt, W. E., 1993. Dipeptidyl peptidase IV hydrolyses gastric inhibitory polypeptide, glucagon-like peptide-1(7-36)amide, peptide histidine methionine and is responsible for their degradation in human serum. Eur. J. Biochem. 214, 829{835. Nielsen, J. H., Svensson, C., Galsgaard, E. D., Moldrup, A., Billestrup, N., 1999. Beta cell proliferation and growth factors. J. Mol. Med. 77, 62{66. Nir, T., Melton, D. A., Dor, Y., 2007. Recovery from diabetes in mice by β cell regeneration. J. Clin. Invest. 117, 2553{2561. Okada, T., Liew, C. W., Hu, J., Hinault, C., Michael, M. D., Krutzfeldt, J., Yin, C., abd Markus Stoffel, M. H., Kulkarni, R. N., 2007. Insulin receptors in β-cells are critical for islet compensatory growth response to insulin resistance. Proc. Natl. Acad. Sci. USA 104, 8977{8892. Pattaranit, R., van den Berg, H. A., 2008. Mathematical models of energy homeostasis. J. R. Soc. Interface 5, 1119{1135. Pavliotis, G., Stuart, A., 2008. Multiscale Methods: Averaging and Homogenization. Springer. Pelengaris, S., Khan, M., 2003. The many faces of c-Myc. Arch. Biochem. and Biophys. 416, 129{ 136. Pelengaris, S., Khan, M., Evan, G. I., 2002. Suppression of Myc-induced apoptosis in β cells exposes multiple oncogenic properties of Myc and triggers carcinogenic progression. Cell 109, 321{334. Protter, M. H., Morrey, C. B., 1970. College Calculus with Analytic Geometry. Addison-Wesley. Raju, B., Cryer, P. E., 2005. Maintenance of the postabsorptive plasma glucose concentration: Insulin or insulin plus glucagon? Am. J. Physiol. Endocrinol. Metab. 289, E181{E186. Ribbing, J., Hamren, B., Svensson, M. K., Karlsson, M. O., 2010. A model for glucose, insulin, and beta-cell dynamics in subjects with insulin resistance and patients with Type 2 diabetes. J. Clin. Pharmacol. 50, 861{872. Rooman, I., Lardon, J., Bouwens, L., 2002. Gastrin stimulates β-cell neogenesis and increases islet mass from transdifferentiated but not from normal exocrine pancreas tissue. Diabetes 51, 686{690. Salway, J. G., 1999. Metabolism at a Glance. Blackwell Science. Schmidt, R. F., Thews, G. (Eds.), 1989. Human Physiology, 2nd Edition. Springer. Sofroniou, M., Spaletta, G., 2004. Construction of explicit Runge{Kutta pairs with stiffness detection. Math. Computer Modell. 40, 1157{1169. Steil, G. M., Trivedi, N., Jonas, J.-C., Hasenkamp, W. M., Sharma, A., Bonner-Weir, S., Weir, G. C., 2001. Adaptation of β-cell mass to substrate oversupply: Enhanced function with normal gene expression. Am. J. Physiol. Endocrinol. Metab. 280, E788{E796. Sturis, J., Polonsky, K. S., Mosekilde, E., Cauter, E. V., 1991. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. Am. J. Physiol. Endocrinol. Metab. 260, E801{E809. Tolic, I. M., Mosekilde, E., Sturis, J., 2000. Modeling the insulin{glucose feedback system: The significance of pulsatile insulin secretion. J. Theor. Biol. 207, 361{375. Topp, B., Promislow, K., Vries, G. D., Miura, R. M., Finegood, D. T., 2000. A model of β-cell mass, insulin, and glucose kinetics: Pathways to diabetes. J. Theor. Biol 206, 605 { 619. Van de Casteele, M., Kefas, B. A., Cai, Y., Heimberg, H., Scott, D. K., Henquin, J. C., Pipeleers, D., Jonas, J, C., 2003. Prolonged culture in low glucose induces apoptosis of rat pancreatic β-cells through induction of c-myc. Biochem. Biophys. Res. Commun. 312, 937{944. Watkins, P. J., 2003. ABC of Diabetes. BMJ Books. Weir, G. C., Laybutt, D. R., Kaneto, H., Bonner-Weir, S., Sharma, A., 2001. β-cell adaptation and decompensation during the progression of diabetes. Diabetes, S154{S159. Young, J., Pelengaris, S., Chipperfield, A., Heath, W. P., Khan, M., 2008. Engineering beta cell mass regulation in diabetes. Curr. Topics Biochem. Res. 10, 47{78.
URI:	http://wrap.warwick.ac.uk/id/eprint/42182

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item