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BIOMD0000000341 - Topp2000_BetaCellMass_Diabetes

 

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Reference Publication
Publication ID: 11013117
Topp B, Promislow K, deVries G, Miura RM, Finegood DT.
A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes.
J. Theor. Biol. 2000 Oct; 206(4): 605-619
Diabetes Research Laboratory, Simon Fraser University, Burnaby, BC, Canada V5A IS6.  [more]
Model
Original Model: BIOMD0000000341.xml.origin
Submitter: Ishan Ajmera
Submission ID: MODEL1106270000
Submission Date: 27 Jun 2011 11:49:35 UTC
Last Modification Date: 07 Jun 2013 15:37:12 UTC
Creation Date: 07 Jul 2011 15:51:17 UTC
Encoders:  Ishan Ajmera
set #1
bqbiol:isVersionOf Gene Ontology regulation of insulin secretion involved in cellular response to glucose stimulus
set #2
bqbiol:occursIn Taxonomy Homo sapiens
Notes

This model is from the article:
A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes.
Topp B, Promislow K, deVries G, Miura RM, Finegood DT. J Theor Biol. 2000 Oct 21;206(4):605-19. 11013117 ,
Abstract:
Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).

Model
Publication ID: 11013117 Submission Date: 27 Jun 2011 11:49:35 UTC Last Modification Date: 07 Jun 2013 15:37:12 UTC Creation Date: 07 Jul 2011 15:51:17 UTC
Mathematical expressions
Rules
Rate Rule (variable: glucose) Rate Rule (variable: insulin) Rate Rule (variable: Mass)  
Physical entities
Compartments Species
cell glucose insulin Mass
Global parameters
si Eg0 R0 sigma
alpha k d0 r1
r2      
Reactions (0)
Rules (3)
 
 Rate Rule (name: G) d [ glucose] / d t= R0-(Eg0+si*I)*G
 
 Rate Rule (name: I) d [ insulin] / d t= B*sigma*G^2/(alpha+G^2)-k*I
 
 Rate Rule (name: B) d [ Mass] / d t= (-d0+r1*G-r2*G^2)*B
 
   cell Spatial dimensions: 3.0  Compartment size: 1.0
 
 glucose
Compartment: cell
Initial concentration: 250.0
 
 insulin
Compartment: cell
Initial concentration: 2.8
 
 Mass
Compartment: cell
Initial concentration: 37.0
 
Global Parameters (9)
 
 si
Value: 0.72
Constant
 
 Eg0
Value: 1.44
Constant
 
 R0
Value: 864.0
Constant
 
 sigma
Value: 43.2
Constant
 
 alpha
Value: 20000.0
Constant
 
 k
Value: 432.0
Constant
 
 d0
Value: 0.06
Constant
 
 r1
Value: 8.4E-4
Constant
 
 r2
Value: 2.4E-6
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000341

Curator's comment: (updated: 27 Jun 2011 13:03:35 BST)

Figure 3 ( Global behaviour of the beta-insulin-glucose model) of the reference publication has been reproduced here. The model as such has the initial concentration corresponding to saddle point (beta Cell Mass = 37; Insulin= 2.8; Glucose = 250). In order to obtain figure 3, the initial concentration of beta Cell Mass, Insulin and Glucose was changed to 0, 0 and 600, respectively.

The model was integrated and simulated using Copasi v4.6 (Build 33).

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