Diffusion Induced Oscillatory Insulin Secretion
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model contains partial differentials and as such can not currently be solved by existing CellML tools.
Model Structure
Insulin is secreted from pancreatic beta cells in an oscillatory fashion. In his 2001 paper (cited below), James Keener examines a mathematical model for in vitro insulin secretion from pancreatic beta cells in a one-dimensional chemical flow reactor, where the reaction region is represented by the volume occupied by the cells (see below). Glucose enters the cell through GLUT-1 and GLUT-2 transporters. Once inside the cell, intracellular glucose is metabolised, and this process activates insulin secretion via exocytosis of insulin containing granules. In the extracellular medium, insulin activates GLUT-1 transporters and inactivates GLUT-2 transporters.
In order to model the reactions, a steady flow of solution along the one-dimensional reactor is assumed, with insulin cells confined to a one-dimensional region. Keener found that the oscillations occur as a result of an important interplay between flow rate of the reactor and insulin diffusion. Without diffusion, the oscillations are eliminated.
The complete original paper reference is cited below:
Diffusion Induced Oscillatory Insulin Secretion, James P. Keener, 2001,
Bulletin of Mathematical Biology
, 63, 625-641. (A PDF version of the article is available to subscribers on the Bulletin of Mathematical Biology website.) PubMed ID: 11497161
cell_diagram
A schematic diagram representing the model of glucose uptake, glucose metabolism and insulin secretion by pancreatic beta cells. Red lines represent the inactivation of GLUT-2 transporters by extracellular insulin, blue arrows represent the activation of GLUT-1 transporters by extracellular insulin and the activation of insulin secretion by glucose metabolism.
The raw CellML descriptions of the model can be downloaded in various formats as described in .
$\frac{d \mathrm{G\_i}}{d \mathrm{time}}=\frac{\mathrm{R1}+\mathrm{R2}-\mathrm{Rm}}{\mathrm{rho}}$
$\frac{\partial^{1}G}{\partial \mathrm{time}}=\frac{-\mathrm{R1}+-\mathrm{R2}}{1.0-\mathrm{rho}}+\mathrm{D\_G}A+-(GB)\frac{\partial^{2.0}G}{\partial x^{2.0}}=A\frac{\partial^{1}G}{\partial x}=B$
$\frac{\partial^{1}I}{\partial \mathrm{time}}=\mathrm{Rs}+\mathrm{D\_I}C+-(VD)\frac{\partial^{2.0}I}{\partial x^{2.0}}=C\frac{\partial^{1}I}{\partial x}=D$
$\frac{d J}{d \mathrm{time}}=\mathrm{J\_tau}(\mathrm{J\_infinity}-J)\mathrm{J\_infinity}=\frac{\mathrm{K\_inh}}{\mathrm{K\_inh}+I}$
$\mathrm{Rm}=\mathrm{rho}\frac{\mathrm{Vm}\mathrm{G\_i}}{\mathrm{Km}+\mathrm{G\_i}}$
$\mathrm{R1}=\mathrm{rho}\frac{\mathrm{V1}(G-\mathrm{G\_i})}{(\mathrm{K1}+\mathrm{G\_i})(1.0+\frac{G}{\mathrm{K1}})}\frac{I}{\mathrm{Ki}+I}$
$\mathrm{R2}=\mathrm{rho}\frac{\mathrm{V2}(G\mathrm{Jm}-\mathrm{G\_i})}{(\mathrm{K2}+\mathrm{G\_i})(1.0+\frac{G}{\mathrm{K2}})}$
$\mathrm{Rs}=\frac{\mathrm{Vs}(\mathrm{Rm}^{4.0}+\mathrm{rho}^{4.0}L^{4.0})}{\mathrm{Rm}^{4.0}+\mathrm{rho}^{4.0}\mathrm{Ks}^{4.0}+\mathrm{rho}^{4.0}L^{4.0}}$
oscillator
beta cell
calcium dynamics
Pancreatic Beta-Cell
insulin
metabolism
The University of Auckland, Bioengineering Institute
Catherine Lloyd
Autumn
Cuellar
A
Catherine
Lloyd
May
James
Keener
P
The University of Auckland
The Bioengineering Institute
keyword
2002-11-20
11497161
c.lloyd@auckland.ac.nz
2003-04-09
2001-07
This is the CellML description of James Keener's 2001 mathematical
model of insulin secretion oscillations in pancreatic beta cells.
Added publication date information.
Diffusion Induced Oscillatory Insulin Secretion
63
625
641
Bulletin of Mathematical Biology
James Keener's 2001 mathematical model of insulin secretion oscillations in pancreatic beta cells.
Pancreatic Beta Cell