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BIOMD0000000613 - Peterson2010 - Integrated calcium homeostasis and bone remodelling

 

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Reference Publication
Publication ID: 19732857
Peterson MC, Riggs MM.
A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling.
Bone 2010 Jan; 46(1): 49-63
Amgen, Inc., One Amgen Center Drive, MS 28-3-B, Thousand Oaks, CA 91320, USA. mark.peterson@biogenidec.com  [more]
Model
Original Model: BIOMD0000000613.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1604270004
Submission Date: 27 Apr 2016 15:35:15 UTC
Last Modification Date: 13 Jan 2017 16:02:07 UTC
Creation Date: 23 Jun 2016 12:56:40 UTC
Encoders:  Vijayalakshmi Chelliah
   Vincent Knight-Schrijver
   Mark Peterson
   Matthew M Riggs
set #1
bqbiol:hasProperty Human Disease Ontology hyperparathyroidism
Human Disease Ontology hypoparathyroidism
set #2
bqbiol:isVersionOf Gene Ontology regulation of parathyroid hormone secretion
Gene Ontology calcium ion homeostasis
Gene Ontology bone remodeling
bqbiol:hasTaxon Taxonomy Homo sapiens
Notes
Peterson2010 - integrated calcium homeostasis and bone remodelling
The original R code, obtained from the author can be downloaded from the link below: [ odm_CaBone_v1_2011_04_April.zip].

This model is described in the article:

Peterson MC, Riggs MM.
Bone 2010 Jan; 46(1): 49-63

Abstract:

Bone biology is physiologically complex and intimately linked to calcium homeostasis. The literature provides a wealth of qualitative and/or quantitative descriptions of cellular mechanisms, bone dynamics, associated organ dynamics, related disease sequela, and results of therapeutic interventions. We present a physiologically based mathematical model of integrated calcium homeostasis and bone biology constructed from literature data. The model includes relevant cellular aspects with major controlling mechanisms for bone remodeling and calcium homeostasis and appropriately describes a broad range of clinical and therapeutic conditions. These include changes in plasma parathyroid hormone (PTH), calcitriol, calcium and phosphate (PO4), and bone-remodeling markers as manifested by hypoparathyroidism and hyperparathyroidism, renal insufficiency, daily PTH 1-34 administration, and receptor activator of NF-kappaB ligand (RANKL) inhibition. This model highlights the utility of systems approaches to physiologic modeling in the bone field. The presented bone and calcium homeostasis model provides an integrated mathematical construct to conduct hypothesis testing of influential system aspects, to visualize elements of this complex endocrine system, and to continue to build upon iteratively with the results of ongoing scientific research.

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: 19732857 Submission Date: 27 Apr 2016 15:35:15 UTC Last Modification Date: 13 Jan 2017 16:02:07 UTC Creation Date: 23 Jun 2016 12:56:40 UTC
Mathematical expressions
Reactions
PTH_production PTH_administration PTH_degradation PTH_gland_pool_production
PTH_gland_pool_degradation PTH_max_capacity_increase PTH_max_capacity_decrease Calcitriol_production
Calcitriol_degradation SC_in SC_out alpha_hydroxylase_production
alpha_hydroxylase_degradation Ca_flux_from_Bone Ca_absorption Ca_flux_to_Bone
Ca_filtration Ca_oral_intake PO4_transfer_from_bone PO4_absorption
PO4_flux_from_intracellular PO4_transfer_to_bone PO4_filtration PO4_flux_to_intracellular
PO4_oral_intake Intestinal_calcium_in Intestinal_calcium_out HAp_prouction
HAp_out OBfast_fraction OBfast_degradation OBslow_fraction
OBslow_degradation Osteoclast_production Osteoclast_degradation Responding_Osteoblast_production
Responding_Osteoblast_degradation TGFB_production TGFB_activation TGFB_degradation
RANKL_production RANKL_degradation RANK_production RANK_degradation
OPG_production OPG_degradation RANKLRANKL_association RANKLRANKL_dissociation
OPGRANKL_association OPGRANKL_dissociation Ca_to_intracellular_transfer Ca_to_extracellular_transfer
RunX2_production RunX2_degradation CREB_production CREB_degradation
Bcl2_production Bcl2_degradation    
Rules
Assignment Rule (variable: T13) Assignment Rule (variable: T15) Assignment Rule (variable: T17) Assignment Rule (variable: Osteoclast)
Assignment Rule (variable: J14OC50) Assignment Rule (variable: OCeqn) Assignment Rule (variable: kinRNK) Assignment Rule (variable: MOCratio)
Assignment Rule (variable: MOCratio0) Assignment Rule (variable: MOCratioEff) Assignment Rule (variable: J14OCdepend) Assignment Rule (variable: J14)
Assignment Rule (variable: J41) Assignment Rule (variable: PicOCkin) Assignment Rule (variable: bigDb) Assignment Rule (variable: kinTGF)
Assignment Rule (variable: koutTGF) Assignment Rule (variable: koutTGFact) Assignment Rule (variable: koutTGFeqn) Assignment Rule (variable: E0PicROB)
Assignment Rule (variable: EC50PicROBparen) Assignment Rule (variable: EC50PicROB) Assignment Rule (variable: Dr) Assignment Rule (variable: PicROB)
Assignment Rule (variable: ROBin2) Assignment Rule (variable: ROBin) Assignment Rule (variable: E0PicOB) Assignment Rule (variable: EC50PicOBparen)
Assignment Rule (variable: EC50PicOB) Assignment Rule (variable: PicOB) Assignment Rule (variable: KPT) Assignment Rule (variable: D)
Assignment Rule (variable: EC50MeffOC) Assignment Rule (variable: MeffOC) Assignment Rule (variable: kinOC2) Assignment Rule (variable: E0PicOC)
Assignment Rule (variable: EC50PicOCparen) Assignment Rule (variable: EC50PicOC) Assignment Rule (variable: PicOC) Assignment Rule (variable: PiL0)
Assignment Rule (variable: PiL) Assignment Rule (variable: EC50survInPar) Assignment Rule (variable: EC50surv) Assignment Rule (variable: LsurvOC)
Assignment Rule (variable: KLSoc) Assignment Rule (variable: C4) Assignment Rule (variable: T66) Assignment Rule (variable: k15a)
Assignment Rule (variable: J14a) Assignment Rule (variable: J15a) Assignment Rule (variable: kLShap) Assignment Rule (variable: kHApIn)
Assignment Rule (variable: J15) Assignment Rule (variable: J42) Assignment Rule (variable: OBfast0) Assignment Rule (variable: Osteoblast)
Assignment Rule (variable: kinLbase) Assignment Rule (variable: OsteoEffect) Assignment Rule (variable: PTH50) Assignment Rule (variable: PTHconc)
Assignment Rule (variable: LpthEff) Assignment Rule (variable: kinL) Assignment Rule (variable: pObase) Assignment Rule (variable: pO)
Assignment Rule (variable: RX2Kin) Assignment Rule (variable: EC50PTHRX2x) Assignment Rule (variable: RX2Kout) Assignment Rule (variable: EC50PTHcreb)
Assignment Rule (variable: crebKin0) Assignment Rule (variable: crebKin) Assignment Rule (variable: bcl2Kin) Assignment Rule (variable: CaConc)
Assignment Rule (variable: C2) Assignment Rule (variable: PO4inhPTH) Assignment Rule (variable: PhosEffTop) Assignment Rule (variable: PhosEffBot)
Assignment Rule (variable: PhosEffMax) Assignment Rule (variable: PhosEff) Assignment Rule (variable: PhosEffect) Assignment Rule (variable: T68)
Assignment Rule (variable: SE) Assignment Rule (variable: C8) Assignment Rule (variable: C1) Assignment Rule (variable: T36)
Assignment Rule (variable: T37) Assignment Rule (variable: CaFilt) Assignment Rule (variable: ReabsMax) Assignment Rule (variable: ReabsPTHeff)
Assignment Rule (variable: CaReabsActive) Assignment Rule (variable: T20) Assignment Rule (variable: T10) Assignment Rule (variable: J27a)
Assignment Rule (variable: J27) Assignment Rule (variable: ScaEff) Assignment Rule (variable: T72) Assignment Rule (variable: T73)
Assignment Rule (variable: T74) Assignment Rule (variable: T75) Assignment Rule (variable: T76) Assignment Rule (variable: T47)
Assignment Rule (variable: J48a) Assignment Rule (variable: J48) Assignment Rule (variable: J53) Assignment Rule (variable: J54)
Assignment Rule (variable: J56) Assignment Rule (variable: E0PicOBkb) Assignment Rule (variable: EmaxPicOBkb) Assignment Rule (variable: EC50PicOBparenKb)
Assignment Rule (variable: EC50PicOBkb) Assignment Rule (variable: PicOBkb) Assignment Rule (variable: PicOBkbEff) Assignment Rule (variable: E0RUNX2kbEff)
Assignment Rule (variable: RUNX2) Assignment Rule (variable: RUNkbMax) Assignment Rule (variable: INparen) Assignment Rule (variable: RUNkb50)
Assignment Rule (variable: RUNX2kbPrimeEff) Assignment Rule (variable: kbprime) Assignment Rule (variable: kbslow) Assignment Rule (variable: kbfast)
Assignment Rule (variable: Frackb2) Assignment Rule (variable: T29) Assignment Rule (variable: T31) Assignment Rule (variable: T83)
Assignment Rule (variable: J40) Assignment Rule (variable: T85Rpart) Assignment Rule (variable: T85) Assignment Rule (variable: F11)
Assignment Rule (variable: INparenCtriol) Assignment Rule (variable: Ctriol50) Assignment Rule (variable: CtriolPTeff) Assignment Rule (variable: PTin)
Assignment Rule (variable: INparenCa) Assignment Rule (variable: T60) Assignment Rule (variable: FCTD) Assignment Rule (variable: T63)
Assignment Rule (variable: EPTH) Assignment Rule (variable: IPTH) Assignment Rule (variable: SPTH) Assignment Rule (variable: kout)
Assignment Rule (variable: TERIPK)      
Events
Event      
Physical entities
Compartments Species
Gut T R PhosGut
     
Vasculature PTH B SC
P ECCPhos TERISC
     
Bone HAp OB OC
ROB1 L RNK
O Q Qbone
TGFB TGFBact OBfast
OBslow M N
PTH_Gland S PTmax  
Kidney A    
Intracellular IntraPO    
Osteoblast_Intracellular RX2 CREB BCL2
     
Global parameters
Pic0 FracOBfast k3 k4
k1 k2 V1 CaDay
FracJ14 J14OCmax J14OCgam FracJ15
kinRNKgam koutRNK MOCratioGam Da
OBtgfGAM koutTGF0 koutTGFGam OCtgfGAM
EmaxPicROB PicROBgam FracPicROB PicOBgam
FracPicOB EmaxPicOB E0Meff EmaxMeffOC
kinOCgam EmaxPicOC FracPicOC PicOCgam
E0RANKL EmaxL GFR T16
T64 T65 T67 AlphOHgam
k14a HApMRT koutL OsteoEffectGam
TESTPOWER opgPTH50 IO RX2Kout0
E0rx2Kout EmaxPTHRX2x E0crebKin EmaxPTHcreb
crebKout bcl2Kout ScaEffGam PhosEff0
PhosEff50 PhosEffGam PO4inhPTHgam T69
Reabs50 T7 T9 T70
T71 T33 T34 T35
CaPOgam T46 T52 OralPhos
F12 T49 T55 PicOBgamkb
MultPicOBkb FracPic0kb E0RUNX2kbEffFACT RUNkbGAM
RUNkbMaxFact RUNX20 Frackb T81
T87 T0 T28 OralCa
T77 T80 CtriolPTgam CtriolMax
CtriolMin PTout T57 T58
T59 T61 IPTHint IPTHinf
LsurvOCCgam EmaxLpth kO kb
LsurvOCgam TERIVC TERICL TERIKA
Q0 OC0 RNK0 RANKL0
RNKL0 OB0 ROB0 QboneInit
OPG0 RX20 CREB0 M0
TGFBact0 TGFB0 T13 T15
T17 Osteoclast J14OC50 OCeqn
kinRNK MOCratio MOCratio0 MOCratioEff
J14OCdepend J14 J41 PicOCkin
bigDb kinTGF koutTGF koutTGFact
koutTGFeqn E0PicROB EC50PicROBparen EC50PicROB
Dr PicROB ROBin2 ROBin
E0PicOB EC50PicOBparen EC50PicOB PicOB
KPT D EC50MeffOC MeffOC
kinOC2 E0PicOC EC50PicOCparen EC50PicOC
PicOC PiL0 PiL EC50survInPar
EC50surv LsurvOC KLSoc C4
T66 k15a J14a J15a
kLShap kHApIn J15 J42
OBfast0 Osteoblast kinLbase OsteoEffect
PTH50 PTHconc LpthEff kinL
pObase pO RX2Kin EC50PTHRX2x
RX2Kout EC50PTHcreb crebKin0 crebKin
bcl2Kin CaConc C2 PO4inhPTH
PhosEffTop PhosEffBot PhosEffMax PhosEff
PhosEffect T68 SE C8
C1 T36 T37 CaFilt
ReabsMax ReabsPTHeff CaReabsActive T20
T10 J27a J27 ScaEff
T72 T73 T74 T75
T76 T47 J48a J48
J53 J54 J56 E0PicOBkb
EmaxPicOBkb EC50PicOBparenKb EC50PicOBkb PicOBkb
PicOBkbEff E0RUNX2kbEff RUNX2 RUNkbMax
INparen RUNkb50 RUNX2kbPrimeEff kbprime
kbslow kbfast Frackb2 T29
T31 T83 J40 T85Rpart
T85 F11 INparenCtriol Ctriol50
CtriolPTeff PTin INparenCa T60
FCTD T63 EPTH IPTH
SPTH kout TERIPK event_counter
teri_times_interval teri_times_initial teri_number_of_doses teri_dose_mcg
Reactions (58)
 
 PTH_production  → [PTH];  
 
 PTH_administration [TERISC] → [PTH];  
 
 PTH_degradation [PTH] → ;   {PTH}
 
 PTH_gland_pool_production  → [S];   {S}
 
 PTH_gland_pool_degradation [S] → ;   {S}
 
 PTH_max_capacity_increase  → [PTmax];  
 
 PTH_max_capacity_decrease [PTmax] → ;   {PTmax}
 
 Calcitriol_production  → [B];   {A} , {A}
 
 Calcitriol_degradation [B] → ;   {B}
 
 SC_in  → [SC];  
 
 SC_out [SC] → ;   {SC}
 
 alpha_hydroxylase_production  → [A];  
 
 alpha_hydroxylase_degradation [A] → ;   {A}
 
 Ca_flux_from_Bone [Q] → [P];  
 
 Ca_absorption [T] → [P];  
 
 Ca_flux_to_Bone [P] → [Q];  
 
 Ca_filtration [P] → ;  
 
 Ca_oral_intake  → [T];  
 
 PO4_transfer_from_bone  → [ECCPhos];  
 
 PO4_absorption [PhosGut] → [ECCPhos];  
 
 PO4_flux_from_intracellular [IntraPO] → [ECCPhos];  
 
 PO4_transfer_to_bone [ECCPhos] → ;  
 
 PO4_filtration [ECCPhos] → ;  
 
 PO4_flux_to_intracellular [ECCPhos] → [IntraPO];  
 
 PO4_oral_intake  → [PhosGut];  
 
 Intestinal_calcium_in  → [R];   {R}
 
 Intestinal_calcium_out [R] → ;   {R}
 
 HAp_prouction  → [HAp];  
 
 HAp_out [HAp] → ;   {HAp}
 
 OBfast_fraction  → [OBfast];  
 
 OBfast_degradation [OBfast] → ;   {OBfast}
 
 OBslow_fraction  → [OBslow];  
 
 OBslow_degradation [OBslow] → ;   {OBslow}
 
 Osteoclast_production  → [OC];  
 
 Osteoclast_degradation [OC] → ;   {OC}
 
 Responding_Osteoblast_production  → [ROB1];  
 
 Responding_Osteoblast_degradation [ROB1] → ;   {ROB1}
 
 TGFB_production  → [TGFB];  
 
 TGFB_activation [TGFB] → [TGFBact];  
 
 TGFB_degradation [TGFBact] → ;   {TGFBact}
 
 RANKL_production  → [L];  
 
 RANKL_degradation [L] → ;   {L}
 
 RANK_production  → [RNK];   {TGFBact} , {TGFBact}
 
 RANK_degradation [RNK] → ;   {RNK}
 
 OPG_production  → [O];  
 
 OPG_degradation [O] → ;   {O}
 
 RANKLRANKL_association [L] + [RNK] → [M];   {RNK} , {L}
 
 RANKLRANKL_dissociation [M] → [L] + [RNK];   {M}
 
 OPGRANKL_association  → [N];   {O} , {L} , {O} , {L}
 
 OPGRANKL_dissociation [N] → ;   {N}
 
 Ca_to_intracellular_transfer [Qbone] → [Q];  
 
 Ca_to_extracellular_transfer [Q] → [Qbone];  
 
 RunX2_production  → [RX2];  
 
 RunX2_degradation [RX2] → ;   {RX2}
 
 CREB_production  → [CREB];  
 
 CREB_degradation [CREB] → ;   {CREB}
 
 Bcl2_production  → [BCL2];  
 
 Bcl2_degradation [BCL2] → ;   {BCL2}
 
Rules (141)
 
 Assignment Rule (name: T13) T13 = CaDay/24/Q0
 
 Assignment Rule (name: T15) T15 = CaDay/(2.35*14*24)
 
 Assignment Rule (name: T17) T17 = 3.85*T16-3.85
 
 Assignment Rule (name: Osteoclast) Osteoclast = OC
 
 Assignment Rule (name: J14OC50) J14OC50 = exp(ln(J14OCmax*OC0^J14OCgam/T13-OC0^J14OCgam)/J14OCgam)
 
 Assignment Rule (name: OCeqn) OCeqn = J14OCmax*Osteoclast^J14OCgam/(Osteoclast^J14OCgam+J14OC50^J14OCgam)
 
 Assignment Rule (name: kinRNK) kinRNK = ((koutRNK*RNK0+k3*RNK0*RANKL0)-k4*M0)/TGFBact0^kinRNKgam
 
 Assignment Rule (name: MOCratio) MOCratio = M/Osteoclast
 
 Assignment Rule (name: MOCratio0) MOCratio0 = M0/OC0
 
 Assignment Rule (name: MOCratioEff) MOCratioEff = (MOCratio/MOCratio0)^MOCratioGam
 
 Assignment Rule (name: J14OCdepend) J14OCdepend = OCeqn*Q0*FracJ14*MOCratioEff
 
 Assignment Rule (name: J14) J14 = T13*Q0*(1-FracJ14)+J14OCdepend
 
 Assignment Rule (name: J41) J41 = 0.464*J14
 
 Assignment Rule (name: PicOCkin) PicOCkin = Pic0
 
 Assignment Rule (name: bigDb) bigDb = kb*OB0*Pic0/ROB0
 
 Assignment Rule (name: kinTGF) kinTGF = koutTGF0*TGFB0
 
 Assignment Rule (name: koutTGF) koutTGF = koutTGF0
 
 Assignment Rule (name: koutTGFact) koutTGFact = koutTGF0*1000
 
 Assignment Rule (name: koutTGFeqn) koutTGFeqn = koutTGF*TGFB*(Osteoclast/OC0)^OCtgfGAM
 
 Assignment Rule (name: E0PicROB) E0PicROB = FracPicROB*Pic0
 
 Assignment Rule (name: EC50PicROBparen) EC50PicROBparen = EmaxPicROB*TGFBact0^PicROBgam/(Pic0-E0PicROB)-TGFBact0^PicROBgam
 
 Assignment Rule (name: EC50PicROB) EC50PicROB = exp(ln(EC50PicROBparen)/PicROBgam)
 
 Assignment Rule (name: Dr) Dr = kb*OB0/Pic0
 
 Assignment Rule (name: PicROB) PicROB = E0PicROB+EmaxPicROB*TGFBact^PicROBgam/(TGFBact^PicROBgam+EC50PicROB^PicROBgam)
 
 Assignment Rule (name: ROBin2) ROBin2 = Dr*PicROB
 
 Assignment Rule (name: ROBin) ROBin = ROBin2
 
 Assignment Rule (name: E0PicOB) E0PicOB = FracPicOB*Pic0
 
 Assignment Rule (name: EC50PicOBparen) EC50PicOBparen = EmaxPicOB*TGFBact0^PicOBgam/(Pic0-E0PicOB)-TGFBact0^PicOBgam
 
 Assignment Rule (name: EC50PicOB) EC50PicOB = exp(ln(EC50PicOBparen)/PicOBgam)
 
 Assignment Rule (name: PicOB) PicOB = E0PicOB+EmaxPicOB*TGFBact^PicOBgam/(TGFBact^PicOBgam+EC50PicOB^PicOBgam)
 
 Assignment Rule (name: KPT) KPT = 1*bigDb/PicOB
 
 Assignment Rule (name: D) D = ROB1
 
 Assignment Rule (name: EC50MeffOC) EC50MeffOC = exp(ln(M0^kinOCgam*EmaxMeffOC/(1-E0Meff)-M0^kinOCgam)/kinOCgam)
 
 Assignment Rule (name: MeffOC) MeffOC = E0Meff+EmaxMeffOC*M^kinOCgam/(M^kinOCgam+EC50MeffOC^kinOCgam)
 
 Assignment Rule (name: kinOC2) kinOC2 = Da*PicOCkin*MeffOC*OC0
 
 Assignment Rule (name: E0PicOC) E0PicOC = FracPicOC*Pic0
 
 Assignment Rule (name: EC50PicOCparen) EC50PicOCparen = EmaxPicOC*TGFBact0^PicOCgam/(Pic0-E0PicOC)-TGFBact0^PicOCgam
 
 Assignment Rule (name: EC50PicOC) EC50PicOC = exp(ln(EC50PicOCparen)/PicOCgam)
 
 Assignment Rule (name: PicOC) PicOC = E0PicOC+EmaxPicOC*TGFBact^PicOCgam/(TGFBact^PicOCgam+EC50PicOC^PicOCgam)
 
 Assignment Rule (name: PiL0) PiL0 = k3/k4*RANKL0
 
 Assignment Rule (name: PiL) PiL = M/10
 
 Assignment Rule (name: EC50survInPar) EC50survInPar = (E0RANKL-EmaxL)*PiL0^LsurvOCgam/(E0RANKL-1)-PiL0^LsurvOCgam
 
 Assignment Rule (name: EC50surv) EC50surv = exp(ln(EC50survInPar)/LsurvOCgam)
 
 Assignment Rule (name: LsurvOC) LsurvOC = E0RANKL-(E0RANKL-EmaxL)*PiL^LsurvOCgam/(PiL^LsurvOCgam+EC50surv^LsurvOCgam)
 
 Assignment Rule (name: KLSoc) KLSoc = Da*PicOC*LsurvOC
 
 Assignment Rule (name: C4) C4 = PTH/V1
 
 Assignment Rule (name: T66) T66 = (T67^AlphOHgam+3.85^AlphOHgam)/3.85^AlphOHgam
 
 Assignment Rule (name: k15a) k15a = k14a*QboneInit/Q0
 
 Assignment Rule (name: J14a) J14a = k14a*Qbone
 
 Assignment Rule (name: J15a) J15a = k15a*Q
 
 Assignment Rule (name: kLShap) kLShap = 1/HApMRT
 
 Assignment Rule (name: kHApIn) kHApIn = kLShap/OB0
 
 Assignment Rule (name: J15) J15 = T15*P*(1-FracJ15)+T15*P*FracJ15*HAp
 
 Assignment Rule (name: J42) J42 = 0.464*J15
 
 Assignment Rule (name: OBfast0) OBfast0 = OB0*FracOBfast
 
 Assignment Rule (name: Osteoblast) Osteoblast = OBfast+OBslow
 
 Assignment Rule (name: kinLbase) kinLbase = koutL*RANKL0
 
 Assignment Rule (name: OsteoEffect) OsteoEffect = (Osteoblast/OB0)^OsteoEffectGam
 
 Assignment Rule (name: PTH50) PTH50 = EmaxLpth*3.85-3.85
 
 Assignment Rule (name: PTHconc) PTHconc = C4
 
 Assignment Rule (name: LpthEff) LpthEff = EmaxLpth*PTHconc/(PTH50*OsteoEffect^TESTPOWER+PTHconc)
 
 Assignment Rule (name: kinL) kinL = kinLbase*OsteoEffect*LpthEff
 
 Assignment Rule (name: pObase) pObase = kO*OPG0
 
 Assignment Rule (name: pO) pO = pObase*D/ROB0*(PTHconc+opgPTH50*D/ROB0)/(2*PTHconc)+IO
 
 Assignment Rule (name: RX2Kin) RX2Kin = RX2Kout0*RX20
 
 Assignment Rule (name: EC50PTHRX2x) EC50PTHRX2x = EmaxPTHRX2x*3.85/(RX2Kout0-E0rx2Kout)-3.85
 
 Assignment Rule (name: RX2Kout) RX2Kout = E0rx2Kout+EmaxPTHRX2x*PTHconc/(PTHconc+EC50PTHRX2x)
 
 Assignment Rule (name: EC50PTHcreb) EC50PTHcreb = EmaxPTHcreb*3.85/(1-E0crebKin)-3.85
 
 Assignment Rule (name: crebKin0) crebKin0 = crebKout*CREB0
 
 Assignment Rule (name: crebKin) crebKin = crebKin0*(E0crebKin+EmaxPTHcreb*PTHconc/(PTHconc+EC50PTHcreb))
 
 Assignment Rule (name: bcl2Kin) bcl2Kin = RX2*CREB*0.693
 
 Assignment Rule (name: CaConc) CaConc = P/14
 
 Assignment Rule (name: C2) C2 = ECCPhos/V1
 
 Assignment Rule (name: PO4inhPTH) PO4inhPTH = (C2/1.2)^PO4inhPTHgam
 
 Assignment Rule (name: PhosEffTop) PhosEffTop = (PhosEff0-1)*(1.2^PhosEffGam+PhosEff50^PhosEffGam)
 
 Assignment Rule (name: PhosEffBot) PhosEffBot = PhosEff0*1.2^PhosEffGam
 
 Assignment Rule (name: PhosEffMax) PhosEffMax = PhosEffTop/PhosEffBot
 
 Assignment Rule (name: PhosEff) PhosEff = PhosEff0-PhosEffMax*PhosEff0*C2^PhosEffGam/(C2^PhosEffGam+PhosEff50^PhosEffGam)
 
 Assignment Rule (name: PhosEffect) PhosEffect = piecewise(PhosEff, C2 > 1.2, 1)
 
 Assignment Rule (name: T68) T68 = T66*C4^AlphOHgam/(T67^AlphOHgam*PO4inhPTH+C4^AlphOHgam)
 
 Assignment Rule (name: SE) SE = T65*T68*PhosEffect
 
 Assignment Rule (name: C8) C8 = B/V1
 
 Assignment Rule (name: C1) C1 = P/V1
 
 Assignment Rule (name: T36) T36 = T33+(T34-T33)*C8^CaPOgam/(T35^CaPOgam+C8^CaPOgam)
 
 Assignment Rule (name: T37) T37 = T34-(T34-T33)*C8^CaPOgam/(T35^CaPOgam+C8^CaPOgam)
 
 Assignment Rule (name: CaFilt) CaFilt = 0.6*0.5*GFR*C1
 
 Assignment Rule (name: ReabsMax) ReabsMax = (0.3*GFR*2.35-0.149997)*(Reabs50+2.35)/2.35
 
 Assignment Rule (name: ReabsPTHeff) ReabsPTHeff = T16*C4/(C4+T17)
 
 Assignment Rule (name: CaReabsActive) CaReabsActive = ReabsMax*C1/(Reabs50+C1)*ReabsPTHeff
 
 Assignment Rule (name: T20) T20 = CaFilt-CaReabsActive
 
 Assignment Rule (name: T10) T10 = T7*C8/(C8+T9)
 
 Assignment Rule (name: J27a) J27a = (2-T10)*T20
 
 Assignment Rule (name: J27) J27 = piecewise(0, J27a < 0, J27a)
 
 Assignment Rule (name: ScaEff) ScaEff = (2.35/CaConc)^ScaEffGam
 
 Assignment Rule (name: T72) T72 = 90*ScaEff
 
 Assignment Rule (name: T73) T73 = T71*(C8-T72)
 
 Assignment Rule (name: T74) T74 = (exp(T73)-exp(-T73))/(exp(T73)+exp(-T73))
 
 Assignment Rule (name: T75) T75 = T70*(0.85*(1+T74)+0.15)
 
 Assignment Rule (name: T76) T76 = T70*(0.85*(1-T74)+0.15)
 
 Assignment Rule (name: T47) T47 = T46*0.88*GFR
 
 Assignment Rule (name: J48a) J48a = 0.88*GFR*C2-T47
 
 Assignment Rule (name: J48) J48 = piecewise(0, J48a < 0, J48a)
 
 Assignment Rule (name: J53) J53 = T52*PhosGut
 
 Assignment Rule (name: J54) J54 = T49*C2
 
 Assignment Rule (name: J56) J56 = T55*IntraPO
 
 Assignment Rule (name: E0PicOBkb) E0PicOBkb = MultPicOBkb*Pic0
 
 Assignment Rule (name: EmaxPicOBkb) EmaxPicOBkb = FracPic0kb*Pic0
 
 Assignment Rule (name: EC50PicOBparenKb) EC50PicOBparenKb = (E0PicOBkb-EmaxPicOBkb)*TGFBact0^PicOBgamkb/(E0PicOBkb-Pic0)-TGFBact0^PicOBgamkb
 
 Assignment Rule (name: EC50PicOBkb) EC50PicOBkb = exp(ln(EC50PicOBparenKb)/PicOBgamkb)
 
 Assignment Rule (name: PicOBkb) PicOBkb = E0PicOBkb-(E0PicOBkb-EmaxPicOBkb)*TGFBact^PicOBgamkb/(TGFBact^PicOBgamkb+EC50PicOBkb^PicOBgamkb)
 
 Assignment Rule (name: PicOBkbEff) PicOBkbEff = PicOBkb/Pic0
 
 Assignment Rule (name: E0RUNX2kbEff) E0RUNX2kbEff = E0RUNX2kbEffFACT*kb
 
 Assignment Rule (name: RUNX2) RUNX2 = piecewise(BCL2-90, BCL2 > 105, 10)
 
 Assignment Rule (name: RUNkbMax) RUNkbMax = E0RUNX2kbEff*RUNkbMaxFact
 
 Assignment Rule (name: INparen) INparen = RUNkbMax*RUNX20^RUNkbGAM/(E0RUNX2kbEff-kb)-RUNX20^RUNkbGAM
 
 Assignment Rule (name: RUNkb50) RUNkb50 = exp(ln(INparen)/RUNkbGAM)
 
 Assignment Rule (name: RUNX2kbPrimeEff) RUNX2kbPrimeEff = RUNkbMax*RUNX2^RUNkbGAM/(RUNX2^RUNkbGAM+RUNkb50^RUNkbGAM)
 
 Assignment Rule (name: kbprime) kbprime = E0RUNX2kbEff*PicOBkbEff-RUNX2kbPrimeEff
 
 Assignment Rule (name: kbslow) kbslow = kbprime*Frackb
 
 Assignment Rule (name: kbfast) kbfast = ((kb*OB0+kbslow*OBfast0)-kbslow*OB0)/OBfast0
 
 Assignment Rule (name: Frackb2) Frackb2 = kbfast/kbprime
 
 Assignment Rule (name: T29) T29 = (T28*T0-0.17533*T0)/0.17533
 
 Assignment Rule (name: T31) T31 = T28*T/(T+T29)
 
 Assignment Rule (name: T83) T83 = R/0.5
 
 Assignment Rule (name: J40) J40 = T31*T*T83/(T+T81)+T87*T
 
 Assignment Rule (name: T85Rpart) T85Rpart = R^T80/(R^T80+T81^T80)
 
 Assignment Rule (name: T85) T85 = T77*T85Rpart
 
 Assignment Rule (name: F11) F11 = T85
 
 Assignment Rule (name: INparenCtriol) INparenCtriol = (CtriolMax-CtriolMin)*C8^CtriolPTgam/(CtriolMax-1)-C8^CtriolPTgam
 
 Assignment Rule (name: Ctriol50) Ctriol50 = exp(ln(INparenCtriol)/CtriolPTgam)
 
 Assignment Rule (name: CtriolPTeff) CtriolPTeff = CtriolMax-(CtriolMax-CtriolMin)*C8^CtriolPTgam/(C8^CtriolPTgam+Ctriol50^CtriolPTgam)
 
 Assignment Rule (name: PTin) PTin = PTout*CtriolPTeff
 
 Assignment Rule (name: INparenCa) INparenCa = (T58-T61)*2.35^T59/(T58-385)-2.35^T59
 
 Assignment Rule (name: T60) T60 = exp(ln(INparenCa)/T59)
 
 Assignment Rule (name: FCTD) FCTD = S/0.5*PTmax
 
 Assignment Rule (name: T63) T63 = T58-(T58-T61)*CaConc^T59/(CaConc^T59+T60^T59)
 
 Assignment Rule (name: EPTH) EPTH = T63*FCTD
 
 Assignment Rule (name: IPTH) IPTH = 0.693*SC+IPTHinf
 
 Assignment Rule (name: SPTH) SPTH = EPTH+IPTH
 
 Assignment Rule (name: kout) kout = T57/14
 
 Assignment Rule (name: TERIPK) TERIPK = TERISC*TERICL/TERIVC
 
Events (1)
 
 Event
event_counter = event_counter+teri_times_interval
TERISC = teri_dose_mcg*1000000/4117.8
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 T
Compartment: Gut
Initial concentration: 1.2375
 
 R
Compartment: Gut
Initial concentration: 0.5
 
 PhosGut
Compartment: Gut
Initial concentration: 0.839
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 PTH
Compartment: Vasculature
Initial concentration: 53.9
 
 B
Compartment: Vasculature
Initial concentration: 1260.0
 
 SC
Compartment: Vasculature
Initial concentration: 0.0
 
 P
Compartment: Vasculature
Initial concentration: 32.9
 
 ECCPhos
Compartment: Vasculature
Initial concentration: 16.8
 
 TERISC
Compartment: Vasculature
Initial concentration: 0.0
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 HAp
Compartment: Bone
Initial concentration: 1.0
 
 OB
Compartment: Bone
Initial concentration: 0.00501324
 
 OC
Compartment: Bone
Initial concentration: 0.00115398
 
 ROB1
Compartment: Bone
Initial concentration: 0.00104122
 
 L
Compartment: Bone
Initial concentration: 0.4
 
 RNK
Compartment: Bone
Initial concentration: 10.0
 
 O
Compartment: Bone
Initial concentration: 4.0
 
 Q
Compartment: Bone
Initial concentration: 100.0
 
 Qbone
Compartment: Bone
Initial concentration: 24900.0
 
 TGFB
Compartment: Bone
 
 TGFBact
Compartment: Bone
 
 OBfast
Compartment: Bone
 
 OBslow
Compartment: Bone
 
 M
Compartment: Bone
 
 N
Compartment: Bone
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 S
Compartment: PTH_Gland
Initial concentration: 0.5
 
 PTmax
Compartment: PTH_Gland
Initial concentration: 1.0
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 A
Compartment: Kidney
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 IntraPO
Compartment: Intracellular
Initial concentration: 3226.0
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 RX2
Compartment: Osteoblast_Intracellular
Initial concentration: 10.0
 
 CREB
Compartment: Osteoblast_Intracellular
Initial concentration: 10.0
 
 BCL2
Compartment: Osteoblast_Intracellular
Initial concentration: 100.0
 
Global Parameters (268)
 
 Pic0
Value: 0.228142
Constant
 
 FracOBfast
Value: 0.797629
Constant
 
 k3
Value: 6.24E-6
Constant
 
 k4
Value: 0.112013
Constant
 
 k1
Value: 6.24E-6
Constant
 
 k2
Value: 0.112013
Constant
 
 V1
Value: 14.0
Constant
 
 CaDay
Value: 88.0
Constant
 
 FracJ14
Value: 0.107763
Constant
 
 J14OCmax
Value: 0.543488
Constant
 
 J14OCgam
Value: 1.6971
Constant
 
 FracJ15
Value: 0.114376
Constant
 
 kinRNKgam
Value: 0.151825
Constant
 
 koutRNK
Value: 0.00323667
Constant
 
 MOCratioGam
Value: 0.603754
Constant
 
 Da
Value: NaN
Constant
 
 OBtgfGAM
Value: 0.0111319
Constant
 
 koutTGF0
Value: 2.98449E-5
Constant
 
 koutTGFGam
Value: 0.919131
Constant
 
 OCtgfGAM
Value: 0.593891
Constant
 
 EmaxPicROB
Value: 3.9745
Constant
 
 PicROBgam
Value: 1.80968
Constant
 
   FracPicROB
Value: 0.883824
Constant
 
 PicOBgam
Value: 0.122313
Constant
 
   FracPicOB
Value: 2.44818E-4
Constant
 
 EmaxPicOB
Value: 0.251636
Constant
 
 E0Meff
Value: 0.388267
Constant
 
   EmaxMeffOC
Value: 3.15667
Constant
 
 kinOCgam
Value: 8.53065
Constant
 
   EmaxPicOC
Value: 1.9746
Constant
 
   FracPicOC
Value: 0.878215
Constant
 
 PicOCgam
Value: 1.0168
Constant
 
 E0RANKL
Value: 3.80338
Constant
 
 EmaxL
Value: 0.469779
Constant
 
 GFR
Value: NaN
Constant
 
 T16
Value: 1.06147
Constant
 
 T64
Value: 0.05
Constant
 
 T65
Value: 6.3
Constant
 
 T67
Value: 1.54865
Constant
 
 AlphOHgam
Value: 0.111241
Constant
 
 k14a
Value: 2.44437E-5
Constant
 
   HApMRT
Value: 3.60609
Constant
 
 koutL
Value: 0.00293273
Constant
 
 OsteoEffectGam
Value: 0.173833
Constant
 
   TESTPOWER
Value: 1.0
Constant
 
 opgPTH50
Value: 3.85
Constant
 
   IO
Constant
 
 RX2Kout0
Value: 0.693
Constant
 
 E0rx2Kout
Value: 0.125
Constant
 
   EmaxPTHRX2x
Value: 5.0
Constant
 
 E0crebKin
Value: 0.5
Constant
 
   EmaxPTHcreb
Value: 3.39745
Constant
 
 crebKout
Value: 0.00279513
Constant
 
 bcl2Kout
Value: 0.693
Constant
 
 ScaEffGam
Value: 0.9
Constant
 
 PhosEff0
Value: 1.52493
Constant
 
 PhosEff50
Value: 1.3021
Constant
 
 PhosEffGam
Value: 8.25229
Constant
 
   PO4inhPTHgam
Constant
 
 T69
Value: 0.1
Constant
 
 Reabs50
Value: 1.57322
Constant
 
 T7
Value: 2.0
Constant
 
 T9
Value: 90.0
Constant
 
 T70
Value: 0.01
Constant
 
 T71
Value: 0.03
Constant
 
 T33
Value: 0.003
Constant
 
 T34
Value: 0.037
Constant
 
 T35
Value: 90.0
Constant
 
   CaPOgam
Value: 1.0
Constant
 
 T46
Value: 1.142
Constant
 
 T52
Value: 0.365
Constant
 
 OralPhos
Value: NaN
Constant
 
 F12
Value: 0.7
Constant
 
 T49
Value: 51.8
Constant
 
 T55
Value: 0.019268
Constant
 
 PicOBgamkb
Value: 2.92375
Constant
 
   MultPicOBkb
Value: 3.11842
Constant
 
   FracPic0kb
Value: 0.764028
Constant
 
 E0RUNX2kbEffFACT
Value: 1.01
Constant
 
   RUNkbGAM
Value: 3.67798
Constant
 
   RUNkbMaxFact
Value: 0.638114
Constant
 
 RUNX20
Value: 10.0
Constant
 
 Frackb
Value: 0.313186
Constant
 
 T81
Value: 0.75
Constant
 
 T87
Value: 0.0495
Constant
 
   T0
Value: 1.58471
Constant
 
 T28
Value: 0.9
Constant
 
 OralCa
Value: NaN
Constant
 
   T77
Value: 0.909359
Constant
 
 T80
Value: 4.0
Constant
 
 CtriolPTgam
Value: 12.5033
Constant
 
 CtriolMax
Value: 4.1029
Constant
 
 CtriolMin
Value: 0.9
Constant
 
 PTout
Value: 1.604E-4
Constant
 
   T57
Value: 100.0
Constant
 
 T58
Value: 6249.09
Constant
 
 T59
Value: 11.7387
Constant
 
 T61
Value: 96.25
Constant
 
   IPTHint
Constant
 
   IPTHinf
Constant
 
 LsurvOCCgam
Value: 3.0923
Constant
 
 EmaxLpth
Value: 1.30721
Constant
 
 kO
Value: 15.8885
Constant
 
 kb
Value: 6.05516E-4
Constant
 
   LsurvOCgam
Value: 3.09023
Constant
 
   TERIVC
Value: 133.0
Constant
 
   TERICL
Value: 94.3
Constant
 
   TERIKA
Value: 16.4
Constant
 
 Q0
Value: NaN
Constant
 
 OC0
Value: NaN
Constant
 
 RNK0
Value: NaN
Constant
 
 RANKL0
Value: NaN
Constant
 
 RNKL0
Value: NaN
Constant
 
 OB0
Value: NaN
Constant
 
 ROB0
Value: NaN
Constant
 
 QboneInit
Value: NaN
Constant
 
 OPG0
Value: NaN
Constant
 
 RX20
Value: NaN
Constant
 
 CREB0
Value: NaN
Constant
 
 M0
Value: NaN
Constant
 
 TGFBact0
Value: NaN
Constant
 
 TGFB0
Value: NaN
Constant
 
   T13
Value: NaN
 
   T15
Value: NaN
 
   T17
Value: NaN
 
   Osteoclast
Value: NaN
 
   J14OC50
Value: NaN
 
   OCeqn
Value: NaN
 
   kinRNK
Value: NaN
 
   MOCratio
Value: NaN
 
   MOCratio0
Value: NaN
 
   MOCratioEff
Value: NaN
 
   J14OCdepend
Value: NaN
 
  J14
Value: NaN
 
  J41
Value: NaN
 
   PicOCkin
Value: NaN
 
   bigDb
Value: NaN
 
  kinTGF
Value: NaN
 
  koutTGF
Value: NaN
 
  koutTGFact
Value: NaN
 
  koutTGFeqn
Value: NaN
 
   E0PicROB
Value: NaN
 
   EC50PicROBparen
Value: NaN
 
   EC50PicROB
Value: NaN
 
   Dr
Value: NaN
 
   PicROB
Value: NaN
 
   ROBin2
Value: NaN
 
  ROBin
Value: NaN
 
   E0PicOB
Value: NaN
 
   EC50PicOBparen
Value: NaN
 
   EC50PicOB
Value: NaN
 
   PicOB
Value: NaN
 
   KPT
Value: NaN
 
   D
Value: NaN
 
   EC50MeffOC
Value: NaN
 
   MeffOC
Value: NaN
 
   kinOC2
Value: NaN
 
   E0PicOC
Value: NaN
 
   EC50PicOCparen
Value: NaN
 
   EC50PicOC
Value: NaN
 
   PicOC
Value: NaN
 
   PiL0
Value: NaN
 
   PiL
Value: NaN
 
   EC50survInPar
Value: NaN
 
   EC50surv
Value: NaN
 
   LsurvOC
Value: NaN
 
  KLSoc
Value: NaN
 
  C4
Value: NaN
 
   T66
Value: NaN
 
   k15a
Value: NaN
 
  J14a
Value: NaN
 
  J15a
Value: NaN
 
   kLShap
Value: NaN
 
  kHApIn
Value: NaN
 
  J15
Value: NaN
 
  J42
Value: NaN
 
  OBfast0
Value: NaN
 
  Osteoblast
Value: NaN
 
   kinLbase
Value: NaN
 
   OsteoEffect
Value: NaN
 
   PTH50
Value: NaN
 
  PTHconc
Value: NaN
 
   LpthEff
Value: NaN
 
  kinL
Value: NaN
 
   pObase
Value: NaN
 
   pO
Value: NaN
 
  RX2Kin
Value: NaN
 
   EC50PTHRX2x
Value: NaN
 
  RX2Kout
Value: NaN
 
   EC50PTHcreb
Value: NaN
 
   crebKin0
Value: NaN
 
  crebKin
Value: NaN
 
  bcl2Kin
Value: NaN
 
  CaConc
Value: NaN
 
  C2
Value: NaN
 
   PO4inhPTH
Value: NaN
 
   PhosEffTop
Value: NaN
 
   PhosEffBot
Value: NaN
 
   PhosEffMax
Value: NaN
 
   PhosEff
Value: NaN
 
   PhosEffect
Value: NaN
 
   T68
Value: NaN
 
  SE
Value: NaN
 
  C8
Value: NaN
 
  C1
Value: NaN
 
   T36
Value: NaN
 
   T37
Value: NaN
 
   CaFilt
Value: NaN
 
   ReabsMax
Value: NaN
 
   ReabsPTHeff
Value: NaN
 
  CaReabsActive
Value: NaN
 
   T20
Value: NaN
 
   T10
Value: NaN
 
   J27a
Value: NaN
 
  J27
Value: NaN
 
   ScaEff
Value: NaN
 
   T72
Value: NaN
 
   T73
Value: NaN
 
   T74
Value: NaN
 
   T75
Value: NaN
 
   T76
Value: NaN
 
   T47
Value: NaN
 
   J48a
Value: NaN
 
  J48
Value: NaN
 
   J53
Value: NaN
 
   J54
Value: NaN
 
   J56
Value: NaN
 
   E0PicOBkb
Value: NaN
 
   EmaxPicOBkb
Value: NaN
 
   EC50PicOBparenKb
Value: NaN
 
   EC50PicOBkb
Value: NaN
 
   PicOBkb
Value: NaN
 
   PicOBkbEff
Value: NaN
 
   E0RUNX2kbEff
Value: NaN
 
   RUNX2
Value: NaN
 
   RUNkbMax
Value: NaN
 
   INparen
Value: NaN
 
   RUNkb50
Value: NaN
 
   RUNX2kbPrimeEff
Value: NaN
 
   kbprime
Value: NaN
 
   kbslow
Value: NaN
 
   kbfast
Value: NaN
 
   Frackb2
Value: NaN
 
   T29
Value: NaN
 
   T31
Value: NaN
 
   T83
Value: NaN
 
   J40
Value: NaN
 
   T85Rpart
Value: NaN
 
   T85
Value: NaN
 
   F11
Value: NaN
 
   INparenCtriol
Value: NaN
 
   Ctriol50
Value: NaN
 
   CtriolPTeff
Value: NaN
 
   PTin
Value: NaN
 
   INparenCa
Value: NaN
 
   T60
Value: NaN
 
   FCTD
Value: NaN
 
   T63
Value: NaN
 
   EPTH
Value: NaN
 
   IPTH
Value: NaN
 
  SPTH
Value: NaN
 
  kout
Value: NaN
 
  TERIPK
Value: NaN
 
 event_counter  
 
 teri_times_interval
Value: 24.0
Constant
 
 teri_times_initial
Value: 12.0
Constant
 
 teri_number_of_doses
Value: 3.0
Constant
 
 teri_dose_mcg
Value: 20.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000613

Curator's comment: (updated: 22 Jun 2016 16:16:18 BST)

Figures 3 and 4 were reproduced.

SBML L3V1 was constructed in QTAntimony and the simulations were carried out in Copasi. Figures were generated in R.

Some disagreement was seen in peak TERISC values between both R and SBML models, this appeared to be of little or no consequence to the other variables.

Peak PTH levels were also seen to be different in Figure 3B. However, it is unclear whether this is the result of simulation, data manipulation or plotting.
Despite this, the values of PTH in Figure 4, in both the original paper and the SBML model simulation, were identical (the same simulation data was used here in curation to plot in both figure 3 and 4) which implies either of the latter two reasons.

Vince

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