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BIOMD0000000401 - Ayati2010_BoneRemodelingDynamics_NormalCondition

 

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Reference Publication
Publication ID: 20406449
Ayati BP, Edwards CM, Webb GF, Wikswo JP.
A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease.
Biol. Direct 2010; 5: 28
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA. ayati@math.uiowa.edu  [more]
Model
Original Model: BIOMD0000000401.xml.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1112060000
Submission Date: 07 Dec 2011 00:22:31 UTC
Last Modification Date: 11 Mar 2014 18:57:21 UTC
Creation Date: 07 Dec 2011 00:41:31 UTC
Encoders:  Vijayalakshmi Chelliah
   Bruce P Ayati
set #1
bqbiol:isVersionOf Gene Ontology regulation of bone remodeling
set #2
bqmodel:isDerivedFrom BioModels Database Komarova2005_PTHaction_OsteoclastOsteoblastCoupling
BioModels Database Komarova2003_BoneRemodeling
set #3
bqbiol:occursIn Taxonomy Chordata
set #4
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
Notes

This a model from the article:
A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease
Bruce P Ayati, Claire M Edwards, Glenn F Webb and John P Wikswo. Biology Direct2010 Apr 20;5(28). 20406449,
Abstract:
BACKGROUND: Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease. RESULTS: Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined. CONCLUSIONS: The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches.

Note:

The paper describes three models 1) Zero-dimensional Bone Model without Tumour, 2) Zero-dimensional Bone Model with Tumour and 3) Zero-dimensional Bone Model with Tumour and Drug Treatment. This model corresponds to the Zero-dimensional Bone Model without Tumour.

Typos in the publication:

Equation (4): The first term should be (β1/α1)^(g12/Γ) and not (β2/α2)^(g12/Γ)

Equation (14): The first term should be (β1/α1)^(((g12/(1+r12))/Γ) and not (β2/α2)^(((g12/(1+r12))/Γ)

Equation (13): The first term should be (β1/α1)^((1-g22+r22)/Γ) and not (β1/α1)^((1-g22-r22)/Γ)

All these corrections has been implemented in the model, with the authors agreement.

Beyond these, there are several mismatches between the equation numbers that are mentioned in for each equation and the reference that has been made to these equations in the figure legend.

Model
Publication ID: 20406449 Submission Date: 07 Dec 2011 00:22:31 UTC Last Modification Date: 11 Mar 2014 18:57:21 UTC Creation Date: 07 Dec 2011 00:41:31 UTC
Mathematical expressions
Rules
Rate Rule (variable: Osteoclasts) Rate Rule (variable: Osteoblasts) Rate Rule (variable: BoneMass) Assignment Rule (variable: maxC_Cbar)
Assignment Rule (variable: maxB_Bbar) Assignment Rule (variable: C_bar) Assignment Rule (variable: B_bar) Assignment Rule (variable: gamma)
Physical entities
Compartments Species
Compartment Osteoclasts Osteoblasts BoneMass
Global parameters
maxC_Cbar maxB_Bbar C_bar B_bar
alpha1 beta1 alpha2 beta2
k1 k2 g11 g21
g12 g22 gamma  
Reactions (0)
Rules (8)
 
 Rate Rule (name: C) d [ Osteoclasts] / d t= alpha1*C^g11*B^g21-beta1*C
 
 Rate Rule (name: B) d [ Osteoblasts] / d t= alpha2*C^g12*B^g22-beta2*B
 
 Rate Rule (name: z) d [ BoneMass] / d t= k2*y2-k1*y1
 
 Assignment Rule (name: y1) maxC_Cbar = piecewise(C-C_bar, C > C_bar, 0)
 
 Assignment Rule (name: y2) maxB_Bbar = piecewise(B-B_bar, B > B_bar, 0)
 
 Assignment Rule (name: C_bar) C_bar = (beta1/alpha1)^((1-g22)/gamma)*(beta2/alpha2)^(g21/gamma)
 
 Assignment Rule (name: B_bar) B_bar = (beta1/alpha1)^(g12/gamma)*(beta2/alpha2)^((1-g11)/gamma)
 
 Assignment Rule (name: gamma) gamma = g12*g21-(1-g11)*(1-g22)
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 Osteoclasts
Compartment: Compartment
Initial concentration: 11.06
 
 Osteoblasts
Compartment: Compartment
Initial concentration: 212.13
 
 BoneMass
Compartment: Compartment
Initial concentration: 100.0
 
Global Parameters (15)
 
   maxC_Cbar
Value: NaN
 
   maxB_Bbar
Value: NaN
 
   C_bar
Value: NaN
 
   B_bar
Value: NaN
 
 alpha1
Value: 3.0
Constant
 
 beta1
Value: 0.2
Constant
 
 alpha2
Value: 4.0
Constant
 
 beta2
Value: 0.02
Constant
 
 k1
Value: 0.24
Constant
 
 k2
Value: 0.0017
Constant
 
 g11
Value: 0.5
Constant
 
 g21
Value: -0.5
Constant
 
 g12
Value: 1.0
Constant
 
 g22
Constant
 
  gamma
Value: NaN
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000401

Curator's comment: (updated: 20 Dec 2011 14:40:38 PST)

This model corresponds to the "Zero-dimensional Bone Model without Tumour" described in the reference publication.
Figure 2 and Figure 3 plots for "Osteoclasts", "Osteoblasts" and "Bone Mass" of the reference publication, has been reproduced here.
The model as such reproduces figure 2. In order to get figure 3, set the parameters g11=1.1, k1=0.0748, k2=0.0006395 and initial conditions C=11.16 and B=231.72.
The model was simulated using Copasi v4.7 (Build 34).

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