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BIOMD0000000277 - Shrestha2010_HyperCalcemia_PTHresponse

 

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Reference Publication
Publication ID: 20406649
Shrestha RP, Hollot CV, Chipkin SR, Schmitt CP, Chait Y.
A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans.
Math Biosci 2010 Jul; 226(1): 46-57
Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA.  [more]
Model
Original Model: BIOMD0000000277.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1011170002
Submission Date: 17 Nov 2010 14:15:53 UTC
Last Modification Date: 09 Oct 2014 16:16:35 UTC
Creation Date: 15 Nov 2010 14:42:27 UTC
Encoders:  Vijayalakshmi Chelliah
   Rajiv P Shrestha
set #1
bqbiol:hasProperty Human Disease Ontology calcium metabolism disease
set #2
bqbiol:occursIn Taxonomy Homo sapiens
set #3
bqbiol:isVersionOf Gene Ontology response to parathyroid hormone
Notes

This a model from the article:
A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans.
Shrestha RP, Hollot CV, Chipkin SR, Schmitt CP, Chait Y. Math Biosci.2010 Jul;226(1):46-57. 20406649,
Abstract:
A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis.

The model corresponds to hypercalcemic clamp test explained in the paper and parameter values used in the model are that of "subject 1". In order to obtain the plots corresponding to "subject 2" and "subject 3" the following parameters to be changed: lambda_1, lambda_2, m1, m2, R, beta, x1_n, x2_n, x2_min, x2_max, t0, Ca0, Ca1 and alpha.

parameter Subject 1 Subject 2 Subject 3
lambda_1 0.0125 0.0122 0.0269
lambda_2 0.5595 0.4642 0.4935
m1 112.5200 150.0000 90.8570
m2 15.0000 15.0000 15.0000
R 1.2162 1.1627 1.1889
beta 10e+06 10e+06 10e+06
x1_n 490.7800 452.8200 298.8200
x2_n 6.6290 9.5894 5.4600
x2_min 0.6697 1.4813 0.8287
x2_max 14.0430 17.8710 15.1990
Ca0 1.2200 1.2513 1.2480
Ca1 0.2624 0.2267 0.2132
t0 575 575 575
alpha 0.0569 0.0563 0.0421

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: 20406649 Submission Date: 17 Nov 2010 14:15:53 UTC Last Modification Date: 09 Oct 2014 16:16:35 UTC Creation Date: 15 Nov 2010 14:42:27 UTC
Mathematical expressions
Rules
Assignment Rule (variable: lambda_Ca) Assignment Rule (variable: m_Ca) Assignment Rule (variable: Ca_in_Plasma) Rate Rule (variable: PTH_in_PTG)
Rate Rule (variable: PTH_in_Plasma) Assignment Rule (variable: S) Assignment Rule (variable: k) Assignment Rule (variable: A)
Assignment Rule (variable: B)      
Physical entities
Compartments Species
PTG_pool PTH_in_PTG    
Plasma_pool PTH_in_Plasma Ca_in_Plasma  
Global parameters
k lambda_Ca m_Ca m1
m2 beta R lambda_1
lambda_2 A B S
Ca0 Ca1 t0 alpha
x1_n x2_n x2_min x2_max
Ca0_baseline      
Reactions (0)
Rules (9)
 
 Assignment Rule (name: lambda_Ca) lambda_Ca = (A-B)/(1+(Ca/S)^m_Ca)+B
 
 Assignment Rule (name: m_Ca) m_Ca = m1/(1+exp((-beta)*(R-Ca)))+m2
 
 Assignment Rule (name: Ca) Ca_in_Plasma = piecewise(Ca0, time < t0, Ca0+Ca1*(1-exp((-alpha)*(time-t0))))
 
 Rate Rule (name: x1) d [ PTH_in_PTG] / d t= k-lambda_Ca*x1-lambda_1*x1
 
 Rate Rule (name: x2) d [ PTH_in_Plasma] / d t= lambda_Ca*x1-lambda_2*x2
 
 Assignment Rule (name: S) S = Ca0_baseline*((-(x1_n*B-lambda_2*x2_n))/(x1_n*A-lambda_2*x2_n))^(1/m_Ca)
 
 Assignment Rule (name: k) k = lambda_2*x2_n+lambda_1*x1_n
 
 Assignment Rule (name: A) A = lambda_1*lambda_2*x2_max/(k-lambda_2*x2_max)
 
 Assignment Rule (name: B) B = lambda_1*lambda_2*x2_min/(k-lambda_2*x2_min)
 
 PTG_pool Spatial dimensions: 3.0  Compartment size: 1.0
 
 PTH_in_PTG
Compartment: PTG_pool
Initial concentration: 0.0
 
 Plasma_pool Spatial dimensions: 3.0  Compartment size: 1.0
 
 PTH_in_Plasma
Compartment: Plasma_pool
Initial concentration: 0.0
 
  Ca_in_Plasma
Compartment: Plasma_pool
Initial concentration: 1.22
 
Global Parameters (21)
 
  k
Value: 9.8436755
 
   lambda_Ca
Value: 170.0
 
   m_Ca
Value: 170.0
 
 m1
Value: 112.52
Constant
 
 m2
Value: 15.0
Constant
 
 beta
Value: 1000000.0
Constant
 
 R
Value: 1.2162
Constant
 
 lambda_1
Value: 0.0125
Constant
 
 lambda_2
Value: 0.5595
Constant
 
   A
Value: 0.04945
 
   B
Value: 4.9E-4
 
   S
Value: 1.2159
 
 Ca0
Value: 1.22
Constant
 
 Ca1
Value: 0.2624
Constant
 
 t0
Value: 575.0
Constant
 
 alpha
Value: 0.0569
Constant
 
 x1_n
Value: 490.78
Constant
 
 x2_n
Value: 6.629
Constant
 
 x2_min
Value: 0.6697
Constant
 
 x2_max
Value: 14.043
Constant
 
   Ca0_baseline
Value: 1.255
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000277

Curator's comment: (updated: 09 Dec 2010 16:49:02 GMT)

This model corresponds to the PTH response to Hypercalcemia model, described in the reference publication. The model as such has the parameter values that correspond to Subject 1 and reproduces Figure 13 & 16 (Figure "a) Subject 1" in here) of the reference publication. Figure 14 & 17 (Figure "b) Subject 2" in here) and Figure 15 & 18 (Figure "c) Subject 3" in here) of the reference publication are also reproduced by changing the values of the parameters lambda_1, lambda_2, m1, m2, R, beta, x1_n, x2_n, x2_min, x2_max, Ca0, Ca1, t0 and alpha (see the model header or the publication for details about the parameter values). The model was integrated and simulated using Copasi v4.6 (Build 32).

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