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BIOMD0000000274 - Rattanakul2003_BoneFormationModel

 

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Reference Publication
Publication ID: 12753937
Rattanakul C, Lenbury Y, Krishnamara N, Wollkind DJ.
Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy.
BioSystems 2003 Jun; 70(1): 55-72
Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand.  [more]
Model
Original Model: CellML logo
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL7909987998
Submission Date: 25 Mar 2009 12:01:00 UTC
Last Modification Date: 08 Jun 2014 18:07:01 UTC
Creation Date: 25 Mar 2009 12:01:00 UTC
Encoders:  Catherine Lloyd
   Vijayalakshmi Chelliah
   Chontita Rattanakul
   Yongwimon Lenbury
set #1
bqbiol:occursIn Taxonomy Chordata
set #2
bqbiol:isVersionOf Gene Ontology ossification
Gene Ontology bone resorption
Notes

This a model from the article:
Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy.
Rattanakul C, Lenbury Y, Krishnamara N, Wollkind DJ. Biosystems 2003:70(1):55-72. 12753937,
Abstract:
Bone, a major reservoir of body calcium, is under the hormonal control of the parathyroid hormone (PTH). Several aspects of its growth, turnover, and mechanism, occur in the absence of gonadal hormones. Sex steroids such as estrogen, nonetheless, play an important role in bone physiology, and are extremely essential to maintain bone balance in adults. In order to provide a basis for understanding the underlying mechanisms of bone remodeling as it is mediated by PTH, we propose here a mathematical model of the process. The nonlinear system model is then utilized to study the temporal effect of PTH as well as the action of estrogen replacement therapy on bone turnover. Analysis of the model is done on the assumption, supported by reported clinical evidence, that the process is characterized by highly diversified dynamics, which warrants the use of singular perturbation arguments. The model is shown to exhibit limit cycle behavior, which can develop into chaotic dynamics for certain ranges of the system's parametric values. Effects of estrogen and PTH administrations are then investigated by extending on the core model. Analysis of the model seems to indicate that the paradoxical observation that intermittent PTH administration causes net bone deposition while continuous administration causes net bone loss, and certain other reported phenomena may be attributed to the highly diversified dynamics which characterizes this nonlinear remodeling process.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: rattananakul, lenbury, krishnamara, wollkind. (2003) - version01
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use.
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Model
Publication ID: 12753937 Submission Date: 25 Mar 2009 12:01:00 UTC Last Modification Date: 08 Jun 2014 18:07:01 UTC Creation Date: 25 Mar 2009 12:01:00 UTC
Mathematical expressions
Rules
Rate Rule (variable: PTH) Rate Rule (variable: active osteoclasts) Rate Rule (variable: active osteoblasts)  
Physical entities
Compartments Species
Compartment PTH active osteoclasts active osteoblasts
Global parameters
epsilon delta a1 a2
a3 a4 a5 b1
b2 b3 k1 k2
k3      
Reactions (0)
Rules (3)
 
 Rate Rule (name: x) d [ PTH] / d t= a1/(k1+y)-b1*x
 
 Rate Rule (name: y) d [ active osteoclasts] / d t= epsilon*((a2+a3*x)*y*z/(k2+x^2)-b2*y)
 
 Rate Rule (name: z) d [ active osteoblasts] / d t= epsilon*delta*(a4*x-(b3*z+a5*x*z/(k3+x)))
 
  Spatial dimensions: 3.0  Compartment size: 1.0  (Units: litre)
 
 PTH
Compartment: Compartment
Initial concentration: 2.0
 
 active osteoclasts
Compartment: Compartment
Initial concentration: 1.0
 
 active osteoblasts
Compartment: Compartment
Initial concentration: 0.15
 
Global Parameters (13)
 
 epsilon
Value: 0.1
Constant
 
 delta
Value: 0.9
Constant
 
 a1
Value: 0.05
Constant
 
 a2
Value: 0.0090
Constant
 
 a3
Value: 0.675
Constant
 
 a4
Value: 0.01
Constant
 
 a5
Value: 0.0050
Constant
 
 b1
Value: 0.1
Constant
 
 b2
Value: 0.3
Constant
 
 b3
Value: 0.01
Constant
 
 k1
Value: 0.1
Constant
 
 k2
Value: 0.5
Constant
 
 k3
Value: 0.025
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000274

Curator's comment: (updated: 10 Nov 2010 14:34:42 GMT)

Figure 3 of the reference publication has been reproduced. The model was integrated and simulated using Copasi v4.6 (Build 32).

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