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BIOMD0000000494 - Roblitz2013 - Menstrual Cycle following GnRH analogue administration

 

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Reference Publication
Publication ID: 23206386
Röblitz S, Stötzel C, Deuflhard P, Jones HM, Azulay DO, van der Graaf PH, Martin SW.
A mathematical model of the human menstrual cycle for the administration of GnRH analogues.
J. Theor. Biol. 2013 Mar; 321: 8-27
Computational Systems Biology Group, Zuse Institute Berlin (ZIB), Berlin, Germany. susanna.roeblitz@zib.de  [more]
Model
Original Model: gyncycle
Submitter: Susanna Röblitz
Submission ID: MODEL1311220000
Submission Date: 22 Nov 2013 10:19:06 UTC
Last Modification Date: 10 Oct 2014 12:32:28 UTC
Creation Date: 22 Nov 2013 12:55:36 UTC
Encoders:  Vijayalakshmi Chelliah
   Susanna Röblitz
set #1
bqbiol:hasTaxon Taxonomy Mammalia
Experimental Factor Ontology female
bqbiol:isVersionOf Gene Ontology response to gonadotropin-releasing hormone
Gene Ontology ovulation cycle
set #2
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
set #3
bqbiol:hasProperty Human Disease Ontology ovarian disease
Notes
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.

Model
Publication ID: 23206386 Submission Date: 22 Nov 2013 10:19:06 UTC Last Modification Date: 10 Oct 2014 12:32:28 UTC Creation Date: 22 Nov 2013 12:55:36 UTC
Mathematical expressions
Reactions
re2 re3 re4 re5
re6 re8 re11 re15
re24 re25 re26 re28
re29 re35 re36 re37
re38 re39 re40 re42
re43 re44 re45 re46
re49 re50 re51 re52
re53 re54 re56 re57
re58 re59 re60 re61
re62 re64 re65 re66
re67 re69 re71 re72
re73 re74 re75 re76
re78 re82 re83 re84
re85 re87 re90 re93
re94 re95 re97 re98
re99 re100 re101 re102
re103 re104 re105 re106
re107 re108 re109  
Rules
Assignment Rule (variable: freq) Assignment Rule (variable: mass)    
Events
ago_admin ant_admin    
Physical entities
Compartments Species
default AF1 AF2 E2
FSH_R FSH_bld FSH_pit
GnRH GnRH_R-a GnRH_R-i
InhA InhA_delay InhB
LH_Pit LH_R LH_bld
Lut1 Lut2 Lut3
Lut4 OvF P4
PrF R_FSH R_FSH_des
R_Foll R_GnRH-a R_GnRH-i
R_LH R_LH_des csa1_degraded
s33 s38 s62
s64 s66 s67
s69 s71 s72
s74 s76 s78
s82 s85 s87
s92 s93 s94
s95 sa1_degraded sa28_degraded
sa31_degraded sa35_degraded sa3_degraded
sa52_degraded sa53_degraded sa61_degraded
sa75_degraded sa78_degraded sa86_degraded
Sc1 Sc2 AF3
AF4 Ago_c Ago_d
s102 s106 s108
s107 Ago_R-i Ago_R-a
Ant_d Ant_c Ant_p
Ant_R s113 s114
s115 s116  
Global parameters
b_syn_LH k_E2_LH k_AF2_IhB b_IhB
T_E2_LH T_P4_LH n_E2_LH n_P4_LH
k_Sc2_IhB k_AF2_E2 b_E2 k_AF3_E2
k_AF4_E2 k_PrF_E2 k_Lut1_E2 k_Lut4_E2
k_cl_E2 b_IhA k_PrF_IhA k_Lut2_IhA
k_Lut3_IhA k_Lut4_IhA k_Sc1_IhA k_Lut1_IhA
b_P4 k_Lut4_P4 k_cl_P4 a_0
T_P4_freq n_P4_freq T_E2_freq n_E2_freq
T_E2_mass_1 n_E2_mass_1 T_E2_mass_2 n_E2_mass_2
V_blood k_degr_G k_cl_IhAe k_Ih_FSH
T_IhA T_IhB n_IhA n_IhB
T_freq_FSH n_freq_FSH T_GR_LH n_GR_LH
b_rel_LH k_GR_LH k_on_G k_recy_RG
k_inter_RG k_degr_RG k_syn_RG k_off_G
k_inact_GR k_act_GR k_diss_GRi k_cl_LH
k_on_LH k_des_LH k_recy_LH b_rel_FSH
k_GR_FSH T_GR_FSH n_GR_FSH k_on_FSH
k_recy_FSH k_des_FSH k_s T_FSH_s
n_FSH_s k_cl_s T_P4_s n_P4_s
k_AF1 T_FSHR_AF1 n_FSHR_AF1 k_AF1_AF2
k_AF2_AF3 SF_LHR n_AF2_AF3 k_AF3_AF4
n_AF3_AF4 k_AF3_AF3 SeF_max k_A42_AF4
n_AF4 k_AF4_PrF k_cl_PrF n_OvF
k_OvF T_PrF_OvF n_PrF_OvF k_cl_OvF
k_Sc1 T_OvF_Sc1 n_OvF_Sc1 k_Sc1_Sc2
k_Sc2_Lut1 k_Lut1_Lut2 T_GR_Lut n_GR_Lut
k_Lut2_Lut3 k_Lut3_Lut4 k_cl_Lut4 k_IhA
k_cl_IhB k_degr_GRi k_cl_FSH m_GR_Lut
freq mass facE2 facP4
facLH facFSH f_0 m_E2_freq
k_A_Ago cl_Ago V_c_F_Ago k_off_Ago
k_on_Ago k_degr_AgoR k_diss_AgoR k_inact_AgoR
k_act_AgoR t_0_Ago dose_Ago k_on_ant
k_off_Ant k_degr_Ant k_A_Ant cl_Ant
V_c_F_Ant k_cp_Ant k_pc_Ant t_0_Ant
dose_Ant      
Reactions (71)
 
 re2 [GnRH_R-a] → [GnRH_R-i];   {GnRH_R-a}
 
 re3 [GnRH_R-i] → [GnRH_R-a];   {GnRH_R-i}
 
 re4 [R_GnRH-i] → [R_GnRH-a];   {R_GnRH-i}
 
 re5 [R_GnRH-a] → [R_GnRH-i];   {R_GnRH-a}
 
 re6 [GnRH_R-i] → [R_GnRH-i];   {GnRH_R-i}
 
 re8 [GnRH] + [R_GnRH-a] → [GnRH_R-a];   {GnRH} , {R_GnRH-a}
 
 re11 [R_GnRH-i] → [sa1_degraded];   {R_GnRH-i}
 
 re15 [GnRH_R-a] → [GnRH] + [R_GnRH-a];   {GnRH_R-a}
 
 re24 [GnRH] → [sa3_degraded];   {GnRH}
 
 re25 [s33] → [LH_Pit];   {E2} , {P4} , {E2} , {P4}
 
 re26 [s38] → [FSH_pit];   {InhA_delay} , {InhB} , {InhA_delay} , {InhB}
 
 re28 [LH_Pit] → [s92];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {LH_Pit}
 
 re29 [FSH_pit] → [s94];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {FSH_pit} , {GnRH_R-a}
 
 re35 [LH_bld] + [R_LH] → [LH_R];   {LH_bld} , {R_LH}
 
 re36 [LH_R] → [R_LH_des];   {LH_R}
 
 re37 [R_LH_des] → [R_LH];   {R_LH_des}
 
 re38 [LH_bld] → [sa28_degraded];   {LH_bld}
 
 re39 [FSH_R] → [R_FSH_des];   {FSH_R}
 
 re40 [R_FSH_des] → [R_FSH];   {R_FSH_des}
 
 re42 [AF1] → [AF2];   {FSH_R} , {AF1} , {FSH_R}
 
 re43 [s62] → [AF1];   {FSH_R} , {FSH_R}
 
 re44 [AF2] → [AF3];   {LH_R} , {R_Foll} , {AF2} , {LH_R} , {R_Foll}
 
 re45 [AF3] → [AF4];   {R_Foll} , {LH_R} , {AF3} , {LH_R} , {R_Foll}
 
 re46 [AF4] → [PrF];   {LH_R} , {R_Foll} , {AF4} , {LH_R} , {R_Foll}
 
 re49 [Sc1] → [Sc2];   {Sc1}
 
 re50 [Sc2] → [Lut1];   {Sc2}
 
 re51 [Lut1] → [Lut2];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {Lut1}
 
 re52 [Lut2] → [Lut3];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {Lut2}
 
 re53 [Lut3] → [Lut4];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {Lut3}
 
 re54 [s64] → [R_Foll];   {FSH_bld} , {FSH_bld}
 
 re56 [R_Foll] → [sa61_degraded];   {P4} , {P4} , {R_Foll}
 
 re57 [s66] → [AF3];   {FSH_R} , {AF3} , {AF3} , {FSH_R}
 
 re58 [s67] → [AF4];   {LH_R} , {AF4} , {AF4} , {LH_R}
 
 re59 [PrF] → [sa52_degraded];   {R_Foll} , {LH_R} , {LH_R} , {PrF} , {R_Foll}
 
 re60 [s69] → [OvF];   {R_Foll} , {LH_R} , {PrF} , {LH_R} , {PrF} , {R_Foll}
 
 re61 [OvF] → [sa53_degraded];   {OvF}
 
 re62 [s71] → [Sc1];   {OvF} , {OvF}
 
 re64 [Lut4] → [s72];   {GnRH_R-a} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {Lut4}
 
 re65 [s74] → [E2];   {AF3} , {AF4} , {Lut1} , {Lut4} , {AF2} , {PrF} , {LH_bld} , {AF2} , {AF3} , {AF4} , {LH_bld} , {Lut1} , {Lut4} , {PrF}
 
 re66 [E2] → [sa75_degraded];   {E2}
 
 re67 [s76] → [P4];   {Lut4} , {Lut4}
 
 re69 [s78] → [InhA];   {PrF} , {Sc1} , {Lut1} , {Lut2} , {Lut3} , {Lut4} , {Lut1} , {Lut2} , {Lut3} , {Lut4} , {PrF} , {Sc1}
 
 re71 [P4] → [sa78_degraded];   {P4}
 
 re72 [s82] → [InhB];   {AF2} , {Sc2} , {AF2} , {Sc2}
 
 re73 [InhB] → [sa86_degraded];   {InhB}
 
 re74 [InhA_delay] → [sa35_degraded];   {InhA_delay}
 
 re75 [s85] → [R_GnRH-i];  
 
 re76 [GnRH_R-i] → [csa1_degraded];   {GnRH_R-i}
 
 re78 [s87] → [GnRH];   {E2} , {P4}
 
 re82 [FSH_bld] → [sa31_degraded];   {FSH_bld}
 
 re83 [s93] → [LH_bld];   {GnRH_R-a} , {LH_Pit} , {Ago_R-a} , {Ago_R-a} , {GnRH_R-a} , {LH_Pit}
 
 re84 [s95] → [FSH_bld];   {GnRH_R-a} , {FSH_pit} , {Ago_R-a} , {Ago_R-a} , {FSH_pit} , {GnRH_R-a}
 
 re85 [FSH_bld] + [R_FSH] → [FSH_R];   {FSH_bld} , {R_FSH}
 
 re87 [InhA] → [InhA_delay];   {InhA}
 
 re90 [Ago_c] → [s102];   {Ago_c}
 
 re93 [Ago_R-a] → [Ago_R-i];   {Ago_R-a}
 
 re94 [Ago_R-i] → [Ago_R-a];   {Ago_R-i}
 
 re95 [Ago_R-i] → [s106];   {Ago_R-i}
 
 re97 [R_GnRH-a] + [Ago_c] → [Ago_R-a];   {Ago_c} , {R_GnRH-a}
 
 re98 [Ago_R-a] → [Ago_c] + [R_GnRH-a];   {Ago_R-a}
 
 re99 [Ago_R-i] → [R_GnRH-i];   {Ago_R-i}
 
 re100 [Ago_d] → [s107];   {Ago_d}
 
 re101 [s108] → [Ago_c];   {Ago_d} , {Ago_d}
 
 re102 [Ant_d] → [s113];   {Ant_d}
 
 re103 [s114] → [Ant_c];   {Ant_d} , {Ant_d}
 
 re104 [Ant_c] → [s115];   {Ant_c}
 
 re105 [Ant_R] → [R_GnRH-a] + [Ant_c];   {Ant_R}
 
 re106 [R_GnRH-a] + [Ant_c] → [Ant_R];   {Ant_c} , {R_GnRH-a}
 
 re107 [Ant_R] → [s116];   {Ant_R}
 
 re108 [Ant_c] → [Ant_p];   {Ant_c}
 
 re109 [Ant_p] → [Ant_c];   {Ant_p}
 
Rules (2)
 
 Assignment Rule (name: freq) freq = p202/(1+(P4*p201*default/p7/(p203*facP4))^p204)*(1+p201*(E2*p201*default/p7/(p205*facE2))^p206/(1+(E2*p201*default/p7/(p205*facE2))^p206))
 
 Assignment Rule (name: mass) mass = p301*((E2*p201*default/p7/(p208*facE2))^p209/(1+(E2*p201*default/p7/(p208*facE2))^p209)+1/(1+(E2*p201*default/p7/(p210*facE2))^p211))
 
Events (2)
 
 ago_admin
Ago_d = p272/default
 
 ant_admin
Ant_d = Ant_d+p472
 
Functions (71)
 
 Function for re2 lambda(GnRH_R_a, default, p309, p309*GnRH_R_a*default/default)
 
 Function for re3 lambda(GnRH_R_i, default, p310, p310*GnRH_R_i*default/default)
 
 Function for re4 lambda(R_GnRH_i, default, p307, p307*R_GnRH_i*default/default)
 
 Function for re5 lambda(R_GnRH_a, default, p306, p306*R_GnRH_a*default/default)
 
 Function for re6 lambda(GnRH_R_i, default, p305, p305*GnRH_R_i*default/default)
 
 Function for re8 lambda(GnRH, R_GnRH_a, default, p302, p302*GnRH*default*R_GnRH_a*default/default)
 
 Function for re11 lambda(R_GnRH_i, default, p308, p308*R_GnRH_i*default/default)
 
 Function for re15 lambda(GnRH_R_a, default, p303, p303*GnRH_R_a*default/default)
 
 Function for re24 lambda(GnRH, default, p300, p300*GnRH*default/default)
 
 Function for re25 lambda(E2, P4, default, facE2, facP4, p1, p2, p3, p4, p6, p7, (p1+p2*(E2*default/(p3*facE2))^p6/(1+(E2*default/(p3*facE2))^p6))/(1+(P4*default/(p4*facP4))^p7)/default)
 
 Function for re26 lambda(InhA_delay, InhB, default, freq, p11, p13, p21, p22, p23, p24, p25, p21/(1+(InhA_delay*default/p22)^p24+(InhB*default/p23)^p25)*1/(1+(freq/p11)^p13)/default)
 
 Function for re28 lambda(Ago_R_a, GnRH_R_a, LH_Pit, default, p16, p5, p8, p9, (p16+p5*((GnRH_R_a*default+Ago_R_a*default)/p8)^p9/(1+((GnRH_R_a*default+Ago_R_a*default)/p8)^p9))*LH_Pit*default/default)
 
 Function for re29 lambda(Ago_R_a, FSH_pit, GnRH_R_a, default, p17, p18, p20, p28, (p17+p28*((GnRH_R_a*default+Ago_R_a*default)/p18)^p20/(1+((GnRH_R_a*default+Ago_R_a*default)/p18)^p20))*FSH_pit*default/default)
 
 Function for re35 lambda(LH_bld, R_LH, default, facLH, p230, p230/facLH*LH_bld*default*R_LH*default/default)
 
 Function for re36 lambda(LH_R, default, p234, p234*LH_R*default/default)
 
 Function for re37 lambda(R_LH_des, default, p232, p232*R_LH_des*default/default)
 
 Function for re38 lambda(LH_bld, default, p231, p231*LH_bld*default/default)
 
 Function for re39 lambda(FSH_R, default, p244, p244*FSH_R*default/default)
 
 Function for re40 lambda(R_FSH_des, default, p242, p242*R_FSH_des*default/default)
 
 Function for re42 lambda(AF1, FSH_R, default, p50, p50*FSH_R*default*AF1*default/default)
 
 Function for re43 lambda(FSH_R, default, p47, p48, p49, p49*(FSH_R*default/p48)^p47/(1+(FSH_R*default/p48)^p47)/default)
 
 Function for re44 lambda(AF2, LH_R, R_Foll, default, p46, p51, p52, p51*(LH_R*default/p52)^p46*R_Foll*default*AF2*default/default)
 
 Function for re45 lambda(AF3, LH_R, R_Foll, default, p32, p43, p52, p32*(LH_R*default/p52)^p43*R_Foll*default*AF3*default/default)
 
 Function for re46 lambda(AF4, LH_R, R_Foll, default, p34, p52, p34*LH_R*default/p52*R_Foll*default*AF4*default/default)
 
 Function for re49 lambda(Sc1, default, p37, p37*Sc1*default/default)
 
 Function for re50 lambda(Sc2, default, p38, p38*Sc2*default/default)
 
 Function for re51 lambda(Ago_R_a, GnRH_R_a, Lut1, default, p39, p80, p83, p84, p39*(1+p80*((GnRH_R_a*default+Ago_R_a*default)/p83)^p84/(1+((GnRH_R_a*default+Ago_R_a*default)/p83)^p84))*Lut1*default/default)
 
 Function for re52 lambda(Ago_R_a, GnRH_R_a, Lut2, default, p40, p80, p83, p84, p40*(1+p80*((GnRH_R_a*default+Ago_R_a*default)/p83)^p84/(1+((GnRH_R_a*default+Ago_R_a*default)/p83)^p84))*Lut2*default/default)
 
 Function for re53 lambda(Ago_R_a, GnRH_R_a, Lut3, default, p41, p80, p83, p84, p41*(1+p80*((GnRH_R_a*default+Ago_R_a*default)/p83)^p84/(1+((GnRH_R_a*default+Ago_R_a*default)/p83)^p84))*Lut3*default/default)
 
 Function for re54 lambda(FSH_bld, default, p90, p91, p94, p94*(FSH_bld*default/p90)^p91/(1+(FSH_bld*default/p90)^p91)/default)
 
 Function for re56 lambda(P4, R_Foll, default, facP4, p92, p93, p95, p95*(P4*default/(p92*facP4))^p93/(1+(P4*default/(p92*facP4))^p93)*R_Foll*default/default)
 
 Function for re57 lambda(AF3, FSH_R, default, p31, p55, p31*FSH_R*default*AF3*default*(1-AF3*default/p55)/default)
 
 Function for re58 lambda(AF4, LH_R, default, p33, p44, p52, p55, p33*(LH_R*default/p52)^p44*AF4*default*(1-AF4*default/p55)/default)
 
 Function for re59 lambda(LH_R, PrF, R_Foll, default, p35, p45, p52, p35*(LH_R*default/p52)^p45*R_Foll*default*PrF*default/default)
 
 Function for re60 lambda(LH_R, PrF, R_Foll, default, p27, p45, p52, p53, p54, p27*R_Foll*default*(LH_R*default/p52)^p45*(PrF*default/p53)^p54/(1+(PrF*default/p53)^p54)/default)
 
 Function for re61 lambda(OvF, default, p36, p36*OvF*default/default)
 
 Function for re62 lambda(OvF, default, p26, p56, p57, p26*(OvF*default/p56)^p57/(1+(OvF*default/p56)^p57)/default)
 
 Function for re65 lambda(AF2, AF3, AF4, LH_bld, Lut1, Lut4, PrF, default, facE2, p152, p158, p159, p160, p161, p164, p165, facE2*(p158+p152*AF2*default+p159*AF3*default*LH_bld*default+p160*AF4*default+p161*PrF*default*LH_bld*default+p164*Lut1*default+p165*Lut4*default)/default)
 
 Function for re64 lambda(Ago_R_a, GnRH_R_a, Lut4, default, p42, p80, p83, p84, 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)
 
 Function for re66 lambda(E2, default, p154, p154*E2*default/default)
 
 Function for re67 lambda(Lut4, default, facP4, p166, p167, facP4*(p166+p167*Lut4*default)/default)
 
 Function for re69 lambda(Lut1, Lut2, Lut3, Lut4, PrF, Sc1, default, p168, p169, p170, p171, p172, p177, p178, (p168+p169*PrF*default+p177*Sc1*default+p178*Lut1*default+p170*Lut2*default+p171*Lut3*default+p172*Lut4*default)/default)
 
 Function for re71 lambda(P4, default, p155, p155*P4*default/default)
 
 Function for re72 lambda(AF2, Sc2, default, p173, p174, p175, (p173+p174*AF2*default+p175*Sc2*default)/default)
 
 Function for re73 lambda(InhB, default, p157, p157*InhB*default/default)
 
 Function for re74 lambda(InhA_delay, default, p30, p30*InhA_delay*default/default)
 
 Function for re75 lambda(default, p311, p311/default)
 
 Function for re76 lambda(GnRH_R_i, default, p304, p304*GnRH_R_i*default/default)
 
 Function for re78 lambda(default, freq, mass, freq*mass/default)
 
 Function for re82 lambda(FSH_bld, default, p241, p241*FSH_bld*default/default)
 
 Function for re83 lambda(Ago_R_a, GnRH_R_a, LH_Pit, default, facLH, p12, p16, p5, p8, p9, facLH/p12*(p16+p5*((GnRH_R_a*default+Ago_R_a*default)/p8)^p9/(1+((GnRH_R_a*default+Ago_R_a*default)/p8)^p9))*LH_Pit*default/default)
 
 Function for re84 lambda(Ago_R_a, FSH_pit, GnRH_R_a, default, facFSH, p12, p17, p18, p20, p28, facFSH/p12*(p17+p28*((GnRH_R_a*default+Ago_R_a*default)/p18)^p20/(1+((GnRH_R_a*default+Ago_R_a*default)/p18)^p20))*FSH_pit*default/default)
 
 Function for re85 lambda(FSH_bld, R_FSH, default, facFSH, p240, p240/facFSH*FSH_bld*default*R_FSH*default/default)
 
 Function for re87 lambda(InhA, default, p156, p156*InhA*default/default)
 
 Function for re90 lambda(Ago_c, default, p275, p275*Ago_c*default/default)
 
 Function for re93 lambda(Ago_R_a, default, p319, p319*Ago_R_a*default/default)
 
 Function for re94 lambda(Ago_R_i, default, p320, p320*Ago_R_i*default/default)
 
 Function for re95 lambda(Ago_R_i, default, p314, p314*Ago_R_i*default/default)
 
 Function for re97 lambda(Ago_c, R_GnRH_a, default, p312, p312*R_GnRH_a*default*Ago_c*default/default)
 
 Function for re98 lambda(Ago_R_a, default, p313, p313*Ago_R_a*default/default)
 
 Function for re99 lambda(Ago_R_i, default, p315, p315*Ago_R_i*default/default)
 
 Function for re100 lambda(Ago_d, default, p274, p274*Ago_d*default/default)
 
 Function for re101 lambda(Ago_d, default, p273, p274, p274/p273*Ago_d*default/default)
 
 Function for re102 lambda(Ant_d, default, p474, p474*Ant_d/default)
 
 Function for re103 lambda(Ant_d, default, p473, p474, p474/p473*Ant_d/default)
 
 Function for re104 lambda(Ant_c, default, p475, p475*Ant_c/default)
 
 Function for re105 lambda(Ant_R, default, p513, p513*Ant_R/default)
 
 Function for re106 lambda(Ant_c, R_GnRH_a, default, p512, p512*R_GnRH_a*default*Ant_c/default)
 
 Function for re107 lambda(Ant_R, default, p514, p514*Ant_R/default)
 
 Function for re108 lambda(Ant_c, default, p476, p476*Ant_c/default)
 
 Function for re109 lambda(Ant_p, default, p477, p477*Ant_p/default)
 
 default Spatial dimensions: 3.0  Compartment size: 1.0
 
 AF1
Compartment: default
Initial concentration: 2.26
 
 AF2
Compartment: default
Initial concentration: 19.92
 
 E2
Compartment: default
Initial concentration: 45.0
 
 FSH_R
Compartment: default
Initial concentration: 0.662
 
 FSH_bld
Compartment: default
Initial concentration: 4.1
 
 FSH_pit
Compartment: default
Initial concentration: 48627.2
 
 GnRH
Compartment: default
Initial concentration: 0.00326
 
 GnRH_R-a
Compartment: default
Initial concentration: 1.447E-5
 
 GnRH_R-i
Compartment: default
Initial concentration: 1.294E-5
 
 InhA
Compartment: default
Initial concentration: 1.07
 
 InhA_delay
Compartment: default
Initial concentration: 86.84
 
 InhB
Compartment: default
Initial concentration: 52.18
 
 LH_Pit
Compartment: default
Initial concentration: 261119.0
 
 LH_R
Compartment: default
Initial concentration: 0.263
 
 LH_bld
Compartment: default
Initial concentration: 2.667
 
 Lut1
Compartment: default
Initial concentration: 2.762E-5
 
 Lut2
Compartment: default
Initial concentration: 3.772E-4
 
 Lut3
Compartment: default
Initial concentration: 0.00334
 
 Lut4
Compartment: default
Initial concentration: 0.01385
 
 OvF
Compartment: default
Initial concentration: 7.652E-19
 
 P4
Compartment: default
Initial concentration: 2.41
 
 PrF
Compartment: default
Initial concentration: 0.244
 
 R_FSH
Compartment: default
Initial concentration: 6.341
 
 R_FSH_des
Compartment: default
Initial concentration: 1.497
 
 R_Foll
Compartment: default
Initial concentration: 0.119
 
 R_GnRH-a
Compartment: default
Initial concentration: 0.00928
 
 R_GnRH-i
Compartment: default
Initial concentration: 9.409E-4
 
 R_LH
Compartment: default
Initial concentration: 8.41
 
 R_LH_des
Compartment: default
Initial concentration: 0.699
 
 csa1_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 s33
Compartment: default
Initial concentration: 1.0
Constant
 
 s38
Compartment: default
Initial concentration: 1.0
Constant
 
 s62
Compartment: default
Initial concentration: 1.0
Constant
 
 s64
Compartment: default
Initial concentration: 1.0
Constant
 
 s66
Compartment: default
Initial concentration: 1.0
Constant
 
 s67
Compartment: default
Initial concentration: 1.0
Constant
 
 s69
Compartment: default
Initial concentration: 1.0
Constant
 
 s71
Compartment: default
Initial concentration: 1.0
Constant
 
 s72
Compartment: default
Initial concentration: 1.0
Constant
 
 s74
Compartment: default
Initial concentration: 1.0
Constant
 
 s76
Compartment: default
Initial concentration: 1.0
Constant
 
 s78
Compartment: default
Initial concentration: 1.0
Constant
 
 s82
Compartment: default
Initial concentration: 1.0
Constant
 
 s85
Compartment: default
Initial concentration: 1.0
Constant
 
 s87
Compartment: default
Initial concentration: 1.0
Constant
 
 s92
Compartment: default
Initial concentration: 1.0
Constant
 
 s93
Compartment: default
Initial concentration: 1.0
Constant
 
 s94
Compartment: default
Initial concentration: 1.0
Constant
 
 s95
Compartment: default
Initial concentration: 1.0
Constant
 
 sa1_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa28_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa31_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa35_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa3_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa52_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa53_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa61_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa75_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa78_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 sa86_degraded
Compartment: default
Initial concentration: 1.0
Constant
 
 Sc1
Compartment: default
Initial concentration: 1.098E-8
 
 Sc2
Compartment: default
Initial concentration: 2.171E-6
 
 AF3
Compartment: default
Initial concentration: 0.504
 
 AF4
Compartment: default
Initial concentration: 1.604E-5
 
 Ago_c
Compartment: default
Initial concentration: 0.0
 
 Ago_d
Compartment: default
Initial concentration: 0.0
 
 s102
Compartment: default
Initial concentration: 1.0
Constant
 
 s106
Compartment: default
Initial concentration: 1.0
Constant
 
 s108
Compartment: default
Initial concentration: 1.0
Constant
 
 s107
Compartment: default
Initial concentration: 1.0
Constant
 
 Ago_R-i
Compartment: default
Initial concentration: 0.0
 
 Ago_R-a
Compartment: default
Initial concentration: 0.0
 
 Ant_d
Compartment: default
Initial concentration: 0.0
 
 Ant_c
Compartment: default
Initial concentration: 0.0
 
 Ant_p
Compartment: default
Initial concentration: 0.0
 
 Ant_R
Compartment: default
Initial concentration: 0.0
 
 s113
Compartment: default
Initial concentration: 0.0
 
 s114
Compartment: default
Initial concentration: 0.0
 
 s115
Compartment: default
Initial concentration: 0.0
 
 s116
Compartment: default
Initial concentration: 0.0
 
Global Parameters (141)
 
   b_syn_LH
Value: 7309.91587614104
Constant
 
   k_E2_LH
Value: 7309.91587614104
Constant
 
   k_AF2_IhB
Value: 447.467334884553
Constant
 
   b_IhB
Value: 89.4934669769107
Constant
 
   T_E2_LH
Value: 192.2041
Constant
 
   T_P4_LH
Value: 2.3708
Constant
 
   n_E2_LH
Value: 10.0
Constant
 
   n_P4_LH
Value: 1.0
Constant
 
   k_Sc2_IhB
Value: 134240.200465366
Constant
 
   k_AF2_E2
Value: 2.09450510112762
Constant
 
   b_E2
Value: 51.558081260068
Constant
 
   k_AF3_E2
Value: 9.28
Constant
 
   k_AF4_E2
Value: 3480.27
Constant
 
   k_PrF_E2
Value: 0.972
Constant
 
   k_Lut1_E2
Value: 1713.71039914086
Constant
 
   k_Lut4_E2
Value: 8675.13871487382
Constant
 
   k_cl_E2
Value: 5.23500984428137
Constant
 
   b_IhA
Value: 1.44522999821013
Constant
 
   k_PrF_IhA
Value: 2.28494719885448
Constant
 
   k_Lut2_IhA
Value: 28.2110255951316
Constant
 
   k_Lut3_IhA
Value: 216.85
Constant
 
   k_Lut4_IhA
Value: 114.247359942724
Constant
 
   k_Sc1_IhA
Value: 60.0
Constant
 
   k_Lut1_IhA
Value: 180.0
Constant
 
   b_P4
Value: 0.9426346876678
Constant
 
   k_Lut4_P4
Value: 761.643100053696
Constant
 
   k_cl_P4
Value: 5.12958654018257
Constant
 
   a_0
Value: 0.005593
Constant
 
   T_P4_freq
Value: 1.2
Constant
 
   n_P4_freq
Value: 2.0
Constant
 
   T_E2_freq
Value: 220.0
Constant
 
   n_E2_freq
Value: 10.0
Constant
 
   T_E2_mass_1
Value: 220.0
Constant
 
   n_E2_mass_1
Value: 2.0
Constant
 
   T_E2_mass_2
Value: 9.6
Constant
 
   n_E2_mass_2
Value: 1.0
Constant
 
   V_blood
Value: 5.0
Constant
 
   k_degr_G
Value: 0.447467334884553
Constant
 
   k_cl_IhAe
Value: 0.1989
Constant
 
   k_Ih_FSH
Value: 22129.0495793807
Constant
 
   T_IhA
Value: 95.81
Constant
 
   T_IhB
Value: 70.0
Constant
 
   n_IhA
Value: 5.0
Constant
 
   n_IhB
Value: 2.0
Constant
 
   T_freq_FSH
Value: 10.0
Constant
 
   n_freq_FSH
Value: 3.0
Constant
 
   T_GR_LH
Value: 3.0E-4
Constant
 
   n_GR_LH
Value: 5.0
Constant
 
   b_rel_LH
Value: 0.00476024700196886
Constant
 
   k_GR_LH
Value: 0.190415249686773
Constant
 
   k_on_G
Value: 322.176481116879
Constant
 
   k_recy_RG
Value: 32.2176481116879
Constant
 
   k_inter_RG
Value: 3.22176481116878
Constant
 
   k_degr_RG
Value: 0.0894934669769107
Constant
 
   k_syn_RG
Value: 8.94934669769107E-5
Constant
 
   k_off_G
Value: 644.352962233757
Constant
 
   k_inact_GR
Value: 32.2176481116879
Constant
 
   k_act_GR
Value: 3.222
Constant
 
   k_diss_GRi
Value: 32.2176481116879
Constant
 
   k_cl_LH
Value: 74.8505459101486
Constant
 
   k_on_LH
Value: 2.1430105602291
Constant
 
   k_des_LH
Value: 183.363164488992
Constant
 
   k_recy_LH
Value: 68.9493466976911
Constant
 
   b_rel_FSH
Value: 0.0569894397708967
Constant
 
   k_GR_FSH
Value: 0.27201539287632
Constant
 
   T_GR_FSH
Value: 3.0E-4
Constant
 
   n_GR_FSH
Value: 2.0
Constant
 
   k_on_FSH
Value: 3.52890638983354
Constant
 
   k_recy_FSH
Value: 61.0291748702345
Constant
 
   k_des_FSH
Value: 138.303203866118
Constant
 
   k_s
Value: 0.2186056917845
Constant
 
   T_FSH_s
Value: 3.0
Constant
 
   n_FSH_s
Value: 5.0
Constant
 
   k_cl_s
Value: 1.34267048505459
Constant
 
   T_P4_s
Value: 1.2348
Constant
 
   n_P4_s
Value: 5.0
Constant
 
   k_AF1
Value: 3.66180418829425
Constant
 
   T_FSHR_AF1
Value: 0.608121
Constant
 
   n_FSHR_AF1
Value: 3.0
Constant
 
   k_AF1_AF2
Value: 1.22060139609808
Constant
 
   k_AF2_AF3
Value: 4.88231609092536
Constant
 
   SF_LHR
Value: 2.7262
Constant
 
   n_AF2_AF3
Value: 3.68896
Constant
 
   k_AF3_AF4
Value: 122.060139609808
Constant
 
   n_AF3_AF4
Value: 5.0
Constant
 
   k_AF3_AF3
Value: 0.122060139609808
Constant
 
   SeF_max
Value: 10.0
Constant
 
   k_A42_AF4
Value: 12.2060139609808
Constant
 
   n_AF4
Value: 2.0
Constant
 
   k_AF4_PrF
Value: 332.754608913549
Constant
 
   k_cl_PrF
Value: 122.060139609808
Constant
 
   n_OvF
Value: 6.0
Constant
 
   k_OvF
Value: 7.98433864327904
Constant
 
   T_PrF_OvF
Value: 3.0
Constant
 
   n_PrF_OvF
Value: 10.0
Constant
 
   k_cl_OvF
Value: 12.2060139609808
Constant
 
   k_Sc1
Value: 1.20834079112225
Constant
 
   T_OvF_Sc1
Value: 0.02
Constant
 
   n_OvF_Sc1
Value: 10.0
Constant
 
   k_Sc1_Sc2
Value: 1.22060139609808
Constant
 
   k_Sc2_Lut1
Value: 0.958117057454806
Constant
 
   k_Lut1_Lut2
Value: 0.924735994272418
Constant
 
   T_GR_Lut
Value: 8.0E-4
Constant
 
   n_GR_Lut
Value: 5.0
Constant
 
   k_Lut2_Lut3
Value: 0.756765706103455
Constant
 
   k_Lut3_Lut4
Value: 0.610291748702345
Constant
 
   k_cl_Lut4
Value: 0.542840522641847
Constant
 
   k_IhA
Value: 4.28718453552891
Constant
 
   k_cl_IhB
Value: 172.453910864507
Constant
 
   k_degr_GRi
Value: 0.00894934669769107
Constant
 
   k_cl_FSH
Value: 114.247359942724
Constant
 
   m_GR_Lut
Value: 20.0
Constant
 
   freq
Value: 3.17876449742659
 
   mass
Value: 0.00120799195301476
 
   facE2
Value: 1.0
Constant
 
   facP4
Value: 1.0
Constant
 
   facLH
Value: 1.0
Constant
 
   facFSH
Value: 1.0
Constant
 
   f_0
Value: 16.0
Constant
 
   m_E2_freq
Value: 1.0
Constant
 
   k_A_Ago
Value: 54.2
Constant
 
   cl_Ago
Value: 2.65
Constant
 
   V_c_F_Ago
Value: 38.12
Constant
 
   k_off_Ago
Value: 644.35
Constant
 
   k_on_Ago
Value: 322.18
Constant
 
   k_degr_AgoR
Value: 0.009
Constant
 
   k_diss_AgoR
Value: 32.22
Constant
 
   k_inact_AgoR
Value: 32.22
Constant
 
   k_act_AgoR
Value: 3.22
Constant
 
   t_0_Ago
Value: 91.0
Constant
 
   dose_Ago
Value: 100.0
Constant
 
   k_on_ant
Value: 322.18
Constant
 
   k_off_Ant
Value: 644.35
Constant
 
   k_degr_Ant
Value: 0.009
Constant
 
   k_A_Ant
Value: 45.56
Constant
 
   cl_Ant
Value: 5.0
Constant
 
   V_c_F_Ant
Value: 34.9
Constant
 
   k_cp_Ant
Value: 3.216
Constant
 
   k_pc_Ant
Value: 4.76
Constant
 
   t_0_Ant
Value: 34.0
Constant
 
   dose_Ant
Value: 500.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000494

Curator's comment: (updated: 22 Nov 2013 12:55:18 GMT)

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.

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