Roblitz2013 - Menstrual Cycle following GnRH analogue administration

  public model
Model Identifier
BIOMD0000000494
Short description
Roblitz2013 - Menstrual Cycle following GnRH analogue administration

The model describes the menstrual cycle feedback mechanisms. GnRH, FSH, LH, E2, P4, inbibins A and B, and follicular development are modelled. The model predicts hormonal changes following GnRH analogue administration. Simulation results agree with measurements of hormone blood concentrations. The model gives insight into mechanisms underlying gonadotropin supression.

This model is described in the article:

Röblitz S, Stötzel C, Deuflhard P, Jones HM, Azulay DO, van der Graaf PH, Martin SW.
J. Theor. Biol. 2013 Mar; 321: 8-27

Abstract:

The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Format
SBML (L2V4)
Related Publication
  • A mathematical model of the human menstrual cycle for the administration of GnRH analogues.
  • Röblitz S, Stötzel C, Deuflhard P, Jones HM, Azulay DO, van der Graaf PH, Martin SW
  • Journal of theoretical biology , 3/ 2013 , Volume 321 , pages: 8-27 , PubMed ID: 23206386
  • Computational Systems Biology Group, Zuse Institute Berlin (ZIB), Berlin, Germany. susanna.roeblitz@zib.de
  • The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.
Contributors
Susanna Röblitz

Metadata information

is
BioModels Database MODEL1311220000
BioModels Database BIOMD0000000494
isDescribedBy
PubMed 23206386
isVersionOf
hasProperty
Mathematical Modelling Ontology Ordinary differential equation model
Human Disease Ontology ovarian disease
hasTaxon
Experimental Factor Ontology female
Taxonomy Mammalia

Curation status
Curated


Original model(s)
gyncycle

Tags
Name Description Size Actions

Model files

BIOMD0000000494_url.xml SBML L2V4 representation of Roblitz2013 - Menstrual Cycle following GnRH analogue administration 430.05 KB Preview | Download

Additional files

BIOMD0000000494-biopax2.owl Auto-generated BioPAX (Level 2) 96.89 KB Preview | Download
BIOMD0000000494.xpp Auto-generated XPP file 37.47 KB Preview | Download
BIOMD0000000494.svg Auto-generated Reaction graph (SVG) 224.03 KB Preview | Download
BIOMD0000000494.sci Auto-generated Scilab file 67.00 bytes Preview | Download
BIOMD0000000494.vcml Auto-generated VCML file 923.00 bytes Preview | Download
BIOMD0000000494-biopax3.owl Auto-generated BioPAX (Level 3) 161.30 KB Preview | Download
BIOMD0000000494.m Auto-generated Octave file 42.08 KB Preview | Download
BIOMD0000000494.pdf Auto-generated PDF file 673.28 KB Preview | Download
BIOMD0000000494_urn.xml Auto-generated SBML file with URNs 428.88 KB Preview | Download
BIOMD0000000494.png Auto-generated Reaction graph (PNG) 1.93 MB Preview | Download

  • Model originally submitted by : Susanna Röblitz
  • Submitted: 22-Nov-2013 10:19:06
  • Last Modified: 10-Oct-2014 12:32:28
Revisions
  • Version: 2 public model Download this version
    • Submitted on: 10-Oct-2014 12:32:28
    • Submitted by: Susanna Röblitz
    • With comment: Current version of Roblitz2013 - Menstrual Cycle following GnRH analogue administration
  • Version: 1 public model Download this version
    • Submitted on: 22-Nov-2013 10:19:06
    • Submitted by: Susanna Röblitz
    • With comment: Original import of NoName
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
Lut4

corpus luteum
0.01385 dimensionless
OvF

follicular fluid formation in ovarian follicle antrum involved in fused antrum stage
7.652E-19 dimensionless
P4

progesterone ; blood
2.41 dimensionless
R FSH

Follicle-stimulating hormone receptor
6.341 dimensionless
R FSH des

receptor internalization ; Follicle-stimulating hormone receptor
1.497 dimensionless
s114 0.0 dimensionless
s115 0.0 dimensionless
s116 0.0 dimensionless
s66 1.0 dimensionless
s67 1.0 dimensionless
FSH pit

hypophysis ; Glycoprotein hormones alpha chain
48627.2 dimensionless
GnRH

Progonadoliberin-1
0.00326 dimensionless
GnRH R a

Gonadotropin-releasing hormone receptor
1.447E-5 dimensionless
Reactions
Reactions Rate Parameters
default*p42*(1+p80*((GnRH_R_a*default+Ago_R_a*default)/p83)^p84/(1+((GnRH_R_a*default+Ago_R_a*default)/p83)^p84))*Lut4*default/default

default*p42*(1+p80*((GnRH_R_a*default+Ago_R_a*default)/p83)^p84/(1+((GnRH_R_a*default+Ago_R_a*default)/p83)^p84))*Lut4*default/default
p80 = 20.0; p42 = 0.542840522641847; p83 = 8.0E-4; p84 = 5.0
default*p27*R_Foll*default*(LH_R*default/p52)^p45*(PrF*default/p53)^p54/(1+(PrF*default/p53)^p54)/default

default*p27*R_Foll*default*(LH_R*default/p52)^p45*(PrF*default/p53)^p54/(1+(PrF*default/p53)^p54)/default
p53 = 3.0; p52 = 2.7262; p54 = 10.0; p45 = 6.0; p27 = 7.98433864327904
default*p36*OvF*default/default

default*p36*OvF*default/default
p36 = 12.2060139609808
default*facP4*(p166+p167*Lut4*default)/default

default*facP4*(p166+p167*Lut4*default)/default
p166 = 0.9426346876678; p167 = 761.643100053696; facP4 = 1.0
default*p242*R_FSH_des*default/default

default*p242*R_FSH_des*default/default
p242 = 61.0291748702345
default*p240/facFSH*FSH_bld*default*R_FSH*default/default

default*p240/facFSH*FSH_bld*default*R_FSH*default/default
facFSH = 1.0; p240 = 3.52890638983354
default*p244*FSH_R*default/default

default*p244*FSH_R*default/default
p244 = 138.303203866118
default*p474/p473*Ant_d/default

default*p474/p473*Ant_d/default
p474 = 45.56; p473 = 34.9
default*p475*Ant_c/default

default*p475*Ant_c/default
p475 = 5.0
default*p514*Ant_R/default

default*p514*Ant_R/default
p514 = 0.009
default*p31*FSH_R*default*AF3*default*(1-AF3*default/p55)/default

default*p31*FSH_R*default*AF3*default*(1-AF3*default/p55)/default
p55 = 10.0; p31 = 0.122060139609808
default*p33*(LH_R*default/p52)^p44*AF4*default*(1-AF4*default/p55)/default

default*p33*(LH_R*default/p52)^p44*AF4*default*(1-AF4*default/p55)/default
p52 = 2.7262; p44 = 2.0; p55 = 10.0; p33 = 12.2060139609808
default*p21/(1+(InhA_delay*default/p22)^p24+(InhB*default/p23)^p25)*1/(1+(freq/p11)^p13)/default

default*p21/(1+(InhA_delay*default/p22)^p24+(InhB*default/p23)^p25)*1/(1+(freq/p11)^p13)/default
p24 = 5.0; p22 = 95.81; p21 = 22129.0495793807; freq = 3.17876449742659; p11 = 10.0; p13 = 3.0; p23 = 70.0; p25 = 2.0
default*p302*GnRH*default*R_GnRH_a*default/default

default*p302*GnRH*default*R_GnRH_a*default/default
p302 = 322.176481116879
default*p309*GnRH_R_a*default/default

default*p309*GnRH_R_a*default/default
p309 = 32.2176481116879
Curator's comment:
(added: 22 Nov 2013, 12:55:18, updated: 22 Nov 2013, 12:55:18)
The model reproduces figures 6-11, 13 and 15 from the reference publication. Here figure 7 has been reproduced. The model was simulation using Copasi v4.11 (Build 64) and the plots were generated using gnuplot.