Abstract
In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (<300 h) and are able to reduce the system to an 8-equation delay differential equation model. In addition to demonstrating congruency between the two models, we also show that a similar stability is only reproducible when the delay in gastrin transport is approximately 30 min. This suggests that gastric acid secretion homeostasis likely depends strongly on the delay in gastrin transport from the antrum to the corpus.
Similar content being viewed by others
References
Arnold, R., H. Koop, H. Schwarting, K. Tuch and B. Willemer (1986). Effect of acid inhibition on gastric endocrine cells. Scand. J. Gastroenterol Suppl. 125, 14–19.
Blair, A. J. d., C. T. Richardson, M. Vasko, J. H. Walsh and M. Feldman (1986). Comparison of acid secretory responsiveness to gastrin heptadecapeptide and of gastrin heptadecapeptide pharmacokinetics in duodenal ulcer patients and normal subjects. J. Clin. Invest. 78, 779–783.
Busenberg, S. and B. Tang (1994). Mathematical models of the early embryonic cell cycle: the role of MPF activation and cyclin degradation. J. Math. Biol. 32, 573–596.
Campos, R. V., A. M. Buchan, R. M. Meloche, R. A. Pederson, Y. N. Kwok and D. H. Coy (1990). Gastrin secretion from human antral G cells in culture. Gastroenterology 99, 36–44.
Chen, D., C. M. Zhao, E. Lindstrom and R. Hakanson (1999a). Rat stomach ECL cells up-date of biology and physiology. Gen. Pharmacol. 32, 413–422.
Chen, T., H. L. He and G. M. Church (1999b). Modeling gene expression with differential equations. Pac. Symp. Biocomput. 29–40.
Chew, C. S. (1983). Inhibitory action of somatostatin on isolated gastric glands and parietal cells. Am. J. Physiol. 245, G221–G229.
Chew, C. S. and S. J. Hersey (1982). Gastrin stimulation of isolated gastric glands. Am. J. Physiol. 242, G504–G512.
Culshaw, R. V. and S. Ruan (2000). A delay-differential equation model of HIV infection of CD4(+) T-cells. Math. Biosci. 165, 27–39.
D’Adda, T., A. Bertele, F. P. Pilato and C. Bordi (1989). Quantitative electron microscopy of endocrine cells in oxyntic mucosa of normal human stomach. Cell Tissue Res. 255, 41.
de Beus, A. M., T. L. Fabry and H. M. Lacker (1993). A gastric acid secretion model. Biophys. J. 65, 362–378.
Debas, H. T. and S. H. Carvajal (1994). Vagal regulation of acid secretion and gastrin release. Yale J. Biol. Med. 67, 145–151.
De Gaetano, A. and O. Arino (2000). Mathematical modelling of the intravenous glucose tolerance test. J. Math. Biol. 40, 136–168.
Dockray, G. J. (1999). Topical review. Gastrin and gastric epithelial physiology. J. Physiol. (Lond) 518, 315–324.
Engel, E. Jr., A. Peskoff, G. L. Kauffman and M. I. Grossman (1984). Analysis of hydrogen ion concentration in the gastric gel mucus layer. Am. J. Physiol. 247, G321–G338.
Hakanson, R., D. Chen, E. Lindstrom, P. Norlen, M. Bjorkqvist and D. Lehto-Axtelius (1998). Physiology of the ECL cells. Yale J. Biol. Med. 71, 163–171.
Hansen, C. P., F. Stadil, L. Yucun and J. F. Rehfeld (1996). Pharmacokinetics and organ metabolism of carboxyamidated and glycine-extended gastrins in pigs. Am. J. Physiol. 271, G156.
Hattori, T. and N. Arizono (1988). Cell kinetics and secretion of mucus in the gastrointestinal mucosa, and their diurnal rhythm. J. Clin. Gastroenterol. 10, S1–S6.
Helander, H. F., K. Rutgersson, K. G. Helander, J. P. Pisegna, J. D. Gardner, R. T. Jensen and P. N. Maton (1992). Stereologic investigations of human gastric mucosa. II. Oxyntic mucosa from patients with Zollinger-Ellison syndrome. Scand. J. Gastroenterol. 27, 875.
Hersey, S. J. and G. Sachs (1995). Gastric acid secretion. Physiol. Rev. 75, 155–189.
Hildebrand, P., J. W. Ensinck, J. Buettiker, J. Drewe, B. Burckhardt, K. Gyr and C. Beglinger (1994). Circulating somatostatin-28 is not a physiologic regulator of gastric acid production in man. Eur. J. Clin. Invest. 24, 50.
Holst, J. J., S. Knuhtsen, C. Orskov, T. Skak-Nielsen, S. S. Poulsen and O. V. Nielsen (1987). GRP-producing nerves control antral somatostatin and gastrin secretion in pigs. Am. J. Physiol. 253, G767.
Inokuchi, H., S. Fujimoto and K. Kawai (1983). Cellular kinetics of gastrointestinal mucosa, with special reference to gut endocrine cells. Arch. Histol. Jpn. 46, 137–157.
Joseph, I. M., Y. Zavros, J. Merchant and D. Kirschner (2002). A model for integrative study of human gastric acid secretion. J. Appl. Physiol. 8, 8.
Karam, S. M. (1993). Dynamics of epithelial cells in the corpus of the mouse stomach. IV. Bidirectional migration of parietal cells ending in their gradual degeneration and loss. Anat. Rec. 236, 314–332.
Karam, S. M. (1995). New insights into the stem cells and the precursors of the gastric epithelium. Nutrition 11, 607–613.
Karam, S. M. (1999). Lineage commitment and maturation of epithelial cells in the gut. Front. Biosci. 4, D286–D298.
Karam, S. M. and C. P. Leblond (1993a). Dynamics of epithelial cells in the corpus of the mouse stomach. I. Identification of proliferative cell types and pinpointing of the stem cell. Anat. Rec. 236, 259–279.
Karam, S. M. and C. P. Leblond (1993b). Dynamics of epithelial cells in the corpus of the mouse stomach. II. Outward migration of pit cells. Anat. Rec. 236, 280–296.
Karam, S. M. and C. P. Leblond (1993c). Dynamics of epithelial cells in the corpus of the mouse stomach. III. Inward migration of neck cells followed by progressive transformation into zymogenic cells. Anat. Rec. 236, 297–313.
Karam, S. M. and C. P. Leblond (1993d). Dynamics of epithelial cells in the corpus of the mouse stomach. V. Behavior of entero-endocrine and caveolated cells: general conclusions on cell kinetics in the oxyntic epithelium. Anat. Rec. 236, 333–340.
Karam, S. and C. P. Leblond (1995). Origin and migratory pathways of the eleven epithelial cell types present in the body of the mouse stomach. Microsc. Res. Tech. 31, 193–214.
Karam, S. M., Q. Li and J. I. Gordon (1997). Gastric epithelial morphogenesis in normal and transgenic mice. Am. J. Physiol. 272, G1209–G1220.
Keener, J. P. and J. Sneyd (1998). Mathematical Physiology, New York: Springer.
Koh, T. J. and D. Chen (2000). Gastrin as a growth factor in the gastrointestinal tract [In Process Citation]. Regul. Pept. 93, 37–44.
Konturek, S. J. (1982). Cholinergic control of gastric acid secretion in man. Scand. J. Gastroenterol. Suppl. 72, 1–5.
Koop, H., I. Behrens, E. Bothe, C. H. McIntosh, R. A. Pederson, R. Arnold and W. Creutzfeldt (1982). Adrenergic and cholinergic interactions in rat gastric somatostatin and gastrin release. Digestion 25, 96–102.
Kuang, Y. (1993). Delay Differential Equations: With Applications in Population Dynamics, Cambridge, MA: Academic Press.
Lambert, J. D. (1991). Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, Chichester, New York: Wiley.
Licko, V. and E. B. Ekblad (1992a). Dynamics of a metabolic system: what single-action agents reveal about acid secretion. Am. J. Physiol. 262, G581–G592.
Licko, V. and E. B. Ekblad (1992b). What dual-action agents reveal about acid secretion: a combined experimental and modeling analysis. Biochim. Biophys. Acta 1137, 19–28.
Lindstrom, E., D. Chen, P. Norlen, K. Andersson and R. Hakanson (2001). Control of gastric acid secretion: the gastrin-ECL cell-parietal cell axis. Comp. Biochem. Physiol. A Mol. Integr. Physiol. 128, 505–514.
Lindstrom, E. and R. Hakanson (2001). Neurohormonal regulation of secretion from isolated rat stomach ECL cells: a critical reappraisal. Regul. Pept. 97, 169–180.
Lundell, L., G. Lindstedt and L. Olbe (1987). Origin of gastrin liberated by gastrin releasing peptide in man. Gut 28, 1128–1133.
Makhlouf, G. M. and M. L. Schubert (1990). Gastric somatostatin: a paracrine regulator of acid secretion. Metabolism 39, 138.
Matsuno, M., T. Matsui, A. Iwasaki and Y. Arakawa (1997). Role of acetylcholine and gastrin-releasing peptide (GRP) in gastrin secretion. J. Gastroenterol. 32, 579–586.
Murray, J. D. (2001). Mathematical Biology, New York: Springer.
Naik, S. R., S. C. Bajaj, R. K. Goyal, D. N. Gupta and H. K. Chuttani (1971). Parietal cell mass in healthy human stomach. Gastroenterology 61, 682.
Nishi, S., Y. Seino, J. Takemura, H. Ishida, M. Seno, T. Chiba, C. Yanaihara, N. Yanaihara and H. Imura (1985). Vagal regulation of GRP, gastric somatostatin, and gastrin secretion in vitro. Am. J. Physiol. 248, E425–E431.
Nomiyama, S., B. Nishioka, T. Ishii, K. Nakamura and S. Majima (1981). Comparative study of G-and D-cell population in the dog stomach. Jpn. J. Surg. 11, 346.
Pansu, D., A. Berard and R. Lambert (1977). Regulation of cell renewal in the gastrointestinal mucosa (author’s transl). Pathol. Biol. (Paris) 25, 119–133.
Rocheville, M., D. C. Lange, U. Kumar, R. Sasi, R. C. Patel and Y. C. Patel (2000). Subtypes of the somatostatin receptor assemble as functional homo-and hetero-dimers. J. Biol. Chem. 275, 7862.
Royston, C. M., J. Polak, S. R. Bloom, W. M. Cooke, R. C. Russell, A. G. Pearse, J. Spencer, R. B. Welbourn and J. H. Baron (1978). G cell population of the gastric antrum, plasma gastrin, and gastric acid secretion in patients with and without duodenal ulcer. Gut 19, 689.
Saffouri, B., G. C. Weir, K. N. Bitar and G. M. Makhlouf (1980). Gastrin and somatostatin secretion by perfused rat stomach: functional linkage of antral peptides. Am. J. Physiol. 238, G495–G501.
Sato, F., S. Muramatsu, S. Tsuchihashi, A. Shiragai, T. Hiraoka, T. Inada, K. Kawashima, H. Matsuzawa, W. Nakamura, E. Trucco and G. A. Sacher (1972). Radiation effects on cell populations in the intestinal epithelium of mice and its theory. Cell Tissue Kinet. 5, 227–235.
Schaffer, K., H. Herrmuth, J. Mueller, D. H. Coy, H. C. Wong, J. H. Walsh, M. Classen, V. Schusdziarra and W. Schepp (1997). Bombesin-like peptides stimulate somatostatin release from rat fundic D cells in primary culture. Am. J. Physiol. 273, G686.
Schubert, M. L., N. F. Edwards, A. Arimura and G. M. Makhlouf (1987). Paracrine regulation of gastric acid secretion by fundic somatostatin. Am. J. Physiol. 252, G485.
Schwarting, H., H. Koop, G. Gellert and R. Arnold (1986). Effect of starvation on endocrine cells in the rat stomach. Regul. Pept. 14, 33–39.
Simonsson, M., S. Eriksson, R. Hakanson, T. Lind, H. Lonroth, L. Lundell, D. T. O’Connor and F. Sundler (1988). Endocrine cells in the human oxyntic mucosa. A histochemical study. Scand. J. Gastroenterol. 23, 1089.
Solcia, E., C. Capella, F. Sessa, G. Rindi, M. Cornaggia, C. Riva and L. Villani (1986). Gastric carcinoids and related endocrine growths. Digestion 35, 3.
Takahashi, T., H. Shimazu, T. Yamagishi and M. Tani (1979). G-cell population in antral mucosa of the dog. Dig. Dis. Sci. 24, 921.
Tam, J. (1999). Delay effect in a model for virus replication. IMA J. Math. Appl. Med. Biol. 16, 29–37.
Weigert, N., Y. Y. Li, R. R. Schick, D. H. Coy, M. Classen and V. Schusdziarra (1997). Role of vagal fibers and bombesin/gastrin-releasing peptide-neurons in distention-induced gastrin release in rats. Regul. Pept. 69, 33–40.
Wollin, A. (1987). Regulation of gastric acid secretion at the cellular level. Clin. Invest. Med. 10, 209–214.
Author information
Authors and Affiliations
Corresponding author
Additional information
Equal contribution.
Rights and permissions
About this article
Cite this article
Marino, S., Ganguli, S., Joseph, I.M.P. et al. The importance of an inter-compartmental delay in a model for human gastric acid secretion. Bull. Math. Biol. 65, 963–990 (2003). https://doi.org/10.1016/S0092-8240(03)00046-6
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1016/S0092-8240(03)00046-6