BIOMD0000000277
type: SBMLModel
parameter: metaid_0000017
rule: metaid_0000040
parameter: metaid_0000035
species: metaid_0000019
rule: metaid_0000027
rule: metaid_0000028
parameter: metaid_0000010
created:
  W3 CDTF: Mon Nov 15 14:42:27 GMT 2010
name: Shrestha2010_HyperCalcemia_PTHresponse
curated: true
parameter: metaid_0000009
parameter: metaid_0000011
is described by: http://identifiers.org/pubmed/20406649
parameter: metaid_0000023
rule: metaid_0000039
parameter: metaid_0000018
time units: metaid_0000004
volume units: 773761
is version of: GO:0071107
area units: metaid_0000005
parameter: metaid_0000020
length unit: 879216
parameter: metaid_0000036
parameter: metaid_0000015
species: metaid_0000006
species: metaid_0000005
substance units: metaid_0000060
parameter: metaid_0000012
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 lamb…
is: MODEL1011170002
parameter: metaid_0000013
creator:
  ORG:
    orgname: EMBL-EBI
  n:
    given: Vijayalakshmi
    family: Chelliah
parameter: metaid_0000007
rule: metaid_0000025
compartment: metaid_0000003
rule: metaid_0000026
parameter: metaid_0000021
parameter: metaid_0000037
parameter: metaid_0000016
occurs in: http://identifiers.org/taxonomy/9606
rule: metaid_0000034
rule: metaid_0000029
parameter: metaid_0000014
creator:
  ORG:
    orgname: Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA
  n:
    given: Rajiv P
    family: Shrestha
parameter: metaid_0000008
rule: metaid_0000024
compartment: metaid_0000004
parameter: metaid_0000022
parameter: metaid_0100038
modified:
  W3 CDTF: Tue May 15 22:56:24 BST 2012
parameter: metaid_0000038

metaid_0000017
type: Parameter
constant: false
value: 4.9E-4
name: B

metaid_0000035
type: Parameter
notes: For subject1, x1_n=490.78; subject2, x1_n=452.82; subject3, x1_n=298.82
constant: true
value: 490.78
name: x1_n

metaid_0000019
type: Species
initial concentration: 1.22
is version of: C00076
constant: false
is: SBO:0000247
has only substance units: false
initial amount: NaN
name: Ca_in_Plasma
is version of: CHEBI:29108
in compartment: metaid_0000004
boundary condition: false

metaid_0000004
type: Compartment
is version of: BTO:0000131
is: SBO:0000290
constant: true
size: 1.0
spatial dimensions: 3.0
name: Plasma_pool

metaid_0000010
type: Parameter
notes: For subject1, m1=112.52; subject2, m1=150.0; subject3, m1=90.857
is: SBO:0000002
constant: true
value: 112.52
name: m1

metaid_0000009
type: Parameter
constant: false
value: 170.0
name: m_Ca

metaid_0000011
type: Parameter
notes: For subject 1, 2, and 3, m2=15.0
is: SBO:0000002
constant: true
value: 15.0
name: m2

metaid_0000023
type: Parameter
notes: For subject1, alpha=0.0569; subject2, alpha=0.0563; subject3, alpha=0.0421
constant: true
value: 0.0569
name: alpha

metaid_0000018
type: Parameter
constant: false
value: 1.2159
name: S

metaid_0000020
type: Parameter
notes: For subject1, Ca0=1.22; subject2, Ca0=1.2513; subject3, Ca0=1.2480
constant: true
value: 1.22
name: Ca0

metaid_0000036
type: Parameter
notes: For subject1, x2_n=6.629; subject2, x2_n=9.5894; subject3, x2_n=5.46
constant: true
value: 6.629
name: x2_n

metaid_0000015
type: Parameter
notes: For subject1, lambda_2=0.5595; subject2, lambda_2=0.4642; subject3, lambda_2=0.4935
is: SBO:0000002
constant: true
value: 0.5595
name: lambda_2

metaid_0000006
type: Species
initial concentration: 0.0
in compartment: metaid_0000004
name: PTH_in_Plasma
constant: false
initial amount: NaN
is version of: P01270
has only substance units: false
boundary condition: false
is: SBO:0000245

metaid_0000005
type: Species
initial concentration: 0.0
is: SBO:0000245
boundary condition: false
initial amount: NaN
constant: false
is version of: P01270
name: PTH_in_PTG
has only substance units: false
in compartment: metaid_0000003

metaid_0000003
type: Compartment
is part of: BTO:0000997
is: SBO:0000290
constant: true
size: 1.0
spatial dimensions: 3.0
name: PTG_pool

metaid_0000012
type: Parameter
notes: For subject1, 2 and 3, beta= 1000000
is: SBO:0000002
constant: true
value: 1000000.0
name: beta

metaid_0000013
type: Parameter
notes: For subject1, R=1.2162; subject2, R=1.1627; subject3, R=1.1889
is: SBO:0000002
constant: true
value: 1.2162
name: R

metaid_0000007
type: Parameter
is: SBO:0000002
constant: false
value: 9.8436755
name: k

metaid_0000021
type: Parameter
notes: For subject1, Ca1=0.2624; subject2, Ca1=0.2267; subject3, Ca1=0.2132
constant: true
value: 0.2624
name: Ca1

metaid_0000037
type: Parameter
notes: For subject1, x2_min=0.6697; subject2, x2_min=1.4813; subject3, x2_n=0.8287
constant: true
value: 0.6697
name: x2_min

metaid_0000016
type: Parameter
constant: false
value: 0.04945
name: A

metaid_0000014
type: Parameter
notes: For subject1, lambda_1=0.0125; subject2, lambda_1=0.0122; subject3, lambda_1=0.0269
is: SBO:0000002
constant: true
value: 0.0125
name: lambda_1

metaid_0000008
type: Parameter
constant: false
value: 170.0
name: lambda_Ca

metaid_0000022
type: Parameter
notes: For subject1, t0=575; subject2, t0=575; subject3, t0=575
constant: true
value: 575.0
name: t0

metaid_0100038
type: Parameter
constant: true
value: 1.255
name: Ca0_baseline

metaid_0000038
type: Parameter
notes: For subject1, x2_max=14.043; subject2, x2_max=17.871; subject3, x2_max=15.199
constant: true
value: 14.043
name: x2_max