Shrestha2010_HypoCalcemia_PTHresponse

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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 hypocalcemic 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, Ca0, Ca1, t0 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 1.2550 1.2369 1.2475
Ca1 0.1817 0.2211 0.1985
t0 575 577 575
alpha 0.0442 0.0488 0.0472

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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.

Format
SBML (L2V4)
Related Publication
  • 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
  • Mathematical biosciences , 7/ 2010 , Volume 226 , pages: 46-57
  • Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA.
  • 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.
Contributors
Vijayalakshmi Chelliah

Metadata information

is
BioModels Database MODEL1011170001
BioModels Database BIOMD0000000276
isDescribedBy
PubMed 20406649
hasTaxon
Taxonomy Homo sapiens
isVersionOf
hasProperty
Human Disease Ontology calcium metabolism disease
Curation status
Curated
  • Model originally submitted by : Vijayalakshmi Chelliah
  • Submitted: Nov 17, 2010 2:15:24 PM
  • Last Modified: Oct 9, 2014 5:15:39 PM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Oct 9, 2014 5:15:39 PM
    • Submitted by: Vijayalakshmi Chelliah
    • With comment: Current version of Shrestha2010_HypoCalcemia_PTHresponse
  • Version: 1 public model Download this version
    • Submitted on: Nov 17, 2010 2:15:24 PM
    • Submitted by: Vijayalakshmi Chelliah
    • With comment: Original import of Shrestha2010_HypoCalcemia_PTHresponse
Curator's comment:
(added: 09 Dec 2010, 16:49:39, updated: 09 Dec 2010, 16:49:39)
This model corresponds to the PTH response to Hypocalcemia model, described in the reference publication. The model as such has the parameter values that correspond to Subject 1 and reproduces Figure 7 & 10 (Figure "a) Subject 1" in here) of the reference publication. Figure 8 & 11 (Figure "b) Subject 2" in here) and Figure 9 & 12 (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).