BioModels Database

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.

Reactions (58)

PTH_production

→ [PTH];

Math:

(Details: $View Math$ )

PTH_administration

[TERISC] → [PTH];

Math:

(Details: $View Math$ )

PTH_degradation

[PTH] → ; {PTH}

Math:

(Details: $View Math$ )

PTH_gland_pool_production

→ [S]; {S}

Math:

(Details: $View Math$ )

PTH_gland_pool_degradation

[S] → ; {S}

Math:

(Details: $View Math$ )

PTH_max_capacity_increase

→ [PTmax];

Math:

(Details: $View Math$ )

PTH_max_capacity_decrease

[PTmax] → ; {PTmax}

Math:

(Details: $View Math$ )

Calcitriol_production

→ [B]; {A} , {A}

Math:

(Details: $View Math$ )

Calcitriol_degradation

[B] → ; {B}

Math:

(Details: $View Math$ )

SC_in

→ [SC];

Math:

(Details: $View Math$ )

SC_out

[SC] → ; {SC}

Math:

(Details: $View Math$ )

alpha_hydroxylase_production

→ [A];

Math:

(Details: $View Math$ )

alpha_hydroxylase_degradation

[A] → ; {A}

Math:

(Details: $View Math$ )

Ca_flux_from_Bone

[Q] → [P];

Math:

(Details: $View Math$ )

Ca_absorption

[T] → [P];

Math:

(Details: $View Math$ )

Ca_flux_to_Bone

[P] → [Q];

Math:

(Details: $View Math$ )

Ca_filtration

[P] → ;

Math:

(Details: $View Math$ )

Ca_oral_intake

→ [T];

Math:

(Details: $View Math$ )

PO4_transfer_from_bone

→ [ECCPhos];

Math:

(Details: $View Math$ )

PO4_absorption

[PhosGut] → [ECCPhos];

Math:

(Details: $View Math$ )

PO4_flux_from_intracellular

[IntraPO] → [ECCPhos];

Math:

(Details: $View Math$ )

PO4_transfer_to_bone

[ECCPhos] → ;

Math:

(Details: $View Math$ )

PO4_filtration

[ECCPhos] → ;

Math:

(Details: $View Math$ )

PO4_flux_to_intracellular

[ECCPhos] → [IntraPO];

Math:

(Details: $View Math$ )

PO4_oral_intake

→ [PhosGut];

Math:

(Details: $View Math$ )

Intestinal_calcium_in

→ [R]; {R}

Math:

(Details: $View Math$ )

Intestinal_calcium_out

[R] → ; {R}

Math:

(Details: $View Math$ )

HAp_prouction

→ [HAp];

Math:

(Details: $View Math$ )

HAp_out

[HAp] → ; {HAp}

Math:

(Details: $View Math$ )

OBfast_fraction

→ [OBfast];

Math:

(Details: $View Math$ )

OBfast_degradation

[OBfast] → ; {OBfast}

Math:

(Details: $View Math$ )

OBslow_fraction

→ [OBslow];

Math:

(Details: $View Math$ )

OBslow_degradation

[OBslow] → ; {OBslow}

Math:

(Details: $View Math$ )

Osteoclast_production

→ [OC];

Math:

(Details: $View Math$ )

Osteoclast_degradation

[OC] → ; {OC}

Math:

(Details: $View Math$ )

Responding_Osteoblast_production

→ [ROB1];

Math:

(Details: $View Math$ )

Responding_Osteoblast_degradation

[ROB1] → ; {ROB1}

Math:

(Details: $View Math$ )

TGFB_production

→ [TGFB];

Math:

(Details: $View Math$ )

TGFB_activation

[TGFB] → [TGFBact];

Math:

(Details: $View Math$ )

TGFB_degradation

[TGFBact] → ; {TGFBact}

Math:

(Details: $View Math$ )

RANKL_production

→ [L];

Math:

(Details: $View Math$ )

RANKL_degradation

[L] → ; {L}

Math:

(Details: $View Math$ )

RANK_production

→ [RNK]; {TGFBact} , {TGFBact}

Math:

(Details: $View Math$ )

RANK_degradation

[RNK] → ; {RNK}

Math:

(Details: $View Math$ )

OPG_production

→ [O];

Math:

(Details: $View Math$ )

OPG_degradation

[O] → ; {O}

Math:

(Details: $View Math$ )

RANKLRANKL_association

[L] + [RNK] → [M]; {RNK} , {L}

Math:

(Details: $View Math$ )

RANKLRANKL_dissociation

[M] → [L] + [RNK]; {M}

Math:

(Details: $View Math$ )

OPGRANKL_association

→ [N]; {O} , {L} , {O} , {L}

Math:

(Details: $View Math$ )

OPGRANKL_dissociation

[N] → ; {N}

Math:

(Details: $View Math$ )

Ca_to_intracellular_transfer

[Qbone] → [Q];

Math:

(Details: $View Math$ )

Ca_to_extracellular_transfer

[Q] → [Qbone];

Math:

(Details: $View Math$ )

RunX2_production

→ [RX2];

Math:

(Details: $View Math$ )

RunX2_degradation

[RX2] → ; {RX2}

Math:

(Details: $View Math$ )

CREB_production

→ [CREB];

Math:

(Details: $View Math$ )

CREB_degradation

[CREB] → ; {CREB}

Math:

(Details: $View Math$ )

Bcl2_production

→ [BCL2];

Math:

(Details: $View Math$ )

Bcl2_degradation

[BCL2] → ; {BCL2}

Math:

(Details: $View Math$ )

Rules (141)

Assignment Rule (name: T13)

T13 = CaDay/24/Q0

Math:

(Details: $View Math$ )

Assignment Rule (name: T15)

T15 = CaDay/(2.35*14*24)

Math:

(Details: $View Math$ )

Assignment Rule (name: T17)

T17 = 3.85*T16-3.85

Math:

(Details: $View Math$ )

Assignment Rule (name: Osteoclast)

Osteoclast = OC

Math:

(Details: $View Math$ )

Assignment Rule (name: J14OC50)

J14OC50 = exp(ln(J14OCmax*OC0^J14OCgam/T13-OC0^J14OCgam)/J14OCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: OCeqn)

OCeqn = J14OCmax*Osteoclast^J14OCgam/(Osteoclast^J14OCgam+J14OC50^J14OCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: kinRNK)

kinRNK = ((koutRNK*RNK0+k3*RNK0*RANKL0)-k4*M0)/TGFBact0^kinRNKgam

Math:

(Details: $View Math$ )

Assignment Rule (name: MOCratio)

MOCratio = M/Osteoclast

Math:

(Details: $View Math$ )

Assignment Rule (name: MOCratio0)

MOCratio0 = M0/OC0

Math:

(Details: $View Math$ )

Assignment Rule (name: MOCratioEff)

MOCratioEff = (MOCratio/MOCratio0)^MOCratioGam

Math:

(Details: $View Math$ )

Assignment Rule (name: J14OCdepend)

J14OCdepend = OCeqn*Q0*FracJ14*MOCratioEff

Math:

(Details: $View Math$ )

Assignment Rule (name: J14)

J14 = T13*Q0*(1-FracJ14)+J14OCdepend

Math:

(Details: $View Math$ )

Assignment Rule (name: J41)

J41 = 0.464*J14

Math:

(Details: $View Math$ )

Assignment Rule (name: PicOCkin)

PicOCkin = Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: bigDb)

bigDb = kb*OB0*Pic0/ROB0

Math:

(Details: $View Math$ )

Assignment Rule (name: kinTGF)

kinTGF = koutTGF0*TGFB0

Math:

(Details: $View Math$ )

Assignment Rule (name: koutTGF)

koutTGF = koutTGF0

Math:

(Details: $View Math$ )

Assignment Rule (name: koutTGFact)

koutTGFact = koutTGF0*1000

Math:

(Details: $View Math$ )

Assignment Rule (name: koutTGFeqn)

koutTGFeqn = koutTGF*TGFB*(Osteoclast/OC0)^OCtgfGAM

Math:

(Details: $View Math$ )

Assignment Rule (name: E0PicROB)

E0PicROB = FracPicROB*Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicROBparen)

EC50PicROBparen = EmaxPicROB*TGFBact0^PicROBgam/(Pic0-E0PicROB)-TGFBact0^PicROBgam

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicROB)

EC50PicROB = exp(ln(EC50PicROBparen)/PicROBgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: Dr)

Dr = kb*OB0/Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: PicROB)

PicROB = E0PicROB+EmaxPicROB*TGFBact^PicROBgam/(TGFBact^PicROBgam+EC50PicROB^PicROBgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: ROBin2)

ROBin2 = Dr*PicROB

Math:

(Details: $View Math$ )

Assignment Rule (name: ROBin)

ROBin = ROBin2

Math:

(Details: $View Math$ )

Assignment Rule (name: E0PicOB)

E0PicOB = FracPicOB*Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOBparen)

EC50PicOBparen = EmaxPicOB*TGFBact0^PicOBgam/(Pic0-E0PicOB)-TGFBact0^PicOBgam

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOB)

EC50PicOB = exp(ln(EC50PicOBparen)/PicOBgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PicOB)

PicOB = E0PicOB+EmaxPicOB*TGFBact^PicOBgam/(TGFBact^PicOBgam+EC50PicOB^PicOBgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: KPT)

KPT = 1*bigDb/PicOB

Math:

(Details: $View Math$ )

Assignment Rule (name: D)

D = ROB1

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50MeffOC)

EC50MeffOC = exp(ln(M0^kinOCgam*EmaxMeffOC/(1-E0Meff)-M0^kinOCgam)/kinOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: MeffOC)

MeffOC = E0Meff+EmaxMeffOC*M^kinOCgam/(M^kinOCgam+EC50MeffOC^kinOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: kinOC2)

kinOC2 = Da*PicOCkin*MeffOC*OC0

Math:

(Details: $View Math$ )

Assignment Rule (name: E0PicOC)

E0PicOC = FracPicOC*Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOCparen)

EC50PicOCparen = EmaxPicOC*TGFBact0^PicOCgam/(Pic0-E0PicOC)-TGFBact0^PicOCgam

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOC)

EC50PicOC = exp(ln(EC50PicOCparen)/PicOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PicOC)

PicOC = E0PicOC+EmaxPicOC*TGFBact^PicOCgam/(TGFBact^PicOCgam+EC50PicOC^PicOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PiL0)

PiL0 = k3/k4*RANKL0

Math:

(Details: $View Math$ )

Assignment Rule (name: PiL)

PiL = M/10

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50survInPar)

EC50survInPar = (E0RANKL-EmaxL)*PiL0^LsurvOCgam/(E0RANKL-1)-PiL0^LsurvOCgam

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50surv)

EC50surv = exp(ln(EC50survInPar)/LsurvOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: LsurvOC)

LsurvOC = E0RANKL-(E0RANKL-EmaxL)*PiL^LsurvOCgam/(PiL^LsurvOCgam+EC50surv^LsurvOCgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: KLSoc)

KLSoc = Da*PicOC*LsurvOC

Math:

(Details: $View Math$ )

Assignment Rule (name: C4)

C4 = PTH/V1

Math:

(Details: $View Math$ )

Assignment Rule (name: T66)

T66 = (T67^AlphOHgam+3.85^AlphOHgam)/3.85^AlphOHgam

Math:

(Details: $View Math$ )

Assignment Rule (name: k15a)

k15a = k14a*QboneInit/Q0

Math:

(Details: $View Math$ )

Assignment Rule (name: J14a)

J14a = k14a*Qbone

Math:

(Details: $View Math$ )

Assignment Rule (name: J15a)

J15a = k15a*Q

Math:

(Details: $View Math$ )

Assignment Rule (name: kLShap)

kLShap = 1/HApMRT

Math:

(Details: $View Math$ )

Assignment Rule (name: kHApIn)

kHApIn = kLShap/OB0

Math:

(Details: $View Math$ )

Assignment Rule (name: J15)

J15 = T15*P*(1-FracJ15)+T15*P*FracJ15*HAp

Math:

(Details: $View Math$ )

Assignment Rule (name: J42)

J42 = 0.464*J15

Math:

(Details: $View Math$ )

Assignment Rule (name: OBfast0)

OBfast0 = OB0*FracOBfast

Math:

(Details: $View Math$ )

Assignment Rule (name: Osteoblast)

Osteoblast = OBfast+OBslow

Math:

(Details: $View Math$ )

Assignment Rule (name: kinLbase)

kinLbase = koutL*RANKL0

Math:

(Details: $View Math$ )

Assignment Rule (name: OsteoEffect)

OsteoEffect = (Osteoblast/OB0)^OsteoEffectGam

Math:

(Details: $View Math$ )

Assignment Rule (name: PTH50)

PTH50 = EmaxLpth*3.85-3.85

Math:

(Details: $View Math$ )

Assignment Rule (name: PTHconc)

PTHconc = C4

Math:

(Details: $View Math$ )

Assignment Rule (name: LpthEff)

LpthEff = EmaxLpth*PTHconc/(PTH50*OsteoEffect^TESTPOWER+PTHconc)

Math:

(Details: $View Math$ )

Assignment Rule (name: kinL)

kinL = kinLbase*OsteoEffect*LpthEff

Math:

(Details: $View Math$ )

Assignment Rule (name: pObase)

pObase = kO*OPG0

Math:

(Details: $View Math$ )

Assignment Rule (name: pO)

pO = pObase*D/ROB0*(PTHconc+opgPTH50*D/ROB0)/(2*PTHconc)+IO

Math:

(Details: $View Math$ )

Assignment Rule (name: RX2Kin)

RX2Kin = RX2Kout0*RX20

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PTHRX2x)

EC50PTHRX2x = EmaxPTHRX2x*3.85/(RX2Kout0-E0rx2Kout)-3.85

Math:

(Details: $View Math$ )

Assignment Rule (name: RX2Kout)

RX2Kout = E0rx2Kout+EmaxPTHRX2x*PTHconc/(PTHconc+EC50PTHRX2x)

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PTHcreb)

EC50PTHcreb = EmaxPTHcreb*3.85/(1-E0crebKin)-3.85

Math:

(Details: $View Math$ )

Assignment Rule (name: crebKin0)

crebKin0 = crebKout*CREB0

Math:

(Details: $View Math$ )

Assignment Rule (name: crebKin)

crebKin = crebKin0*(E0crebKin+EmaxPTHcreb*PTHconc/(PTHconc+EC50PTHcreb))

Math:

(Details: $View Math$ )

Assignment Rule (name: bcl2Kin)

bcl2Kin = RX2*CREB*0.693

Math:

(Details: $View Math$ )

Assignment Rule (name: CaConc)

CaConc = P/14

Math:

(Details: $View Math$ )

Assignment Rule (name: C2)

C2 = ECCPhos/V1

Math:

(Details: $View Math$ )

Assignment Rule (name: PO4inhPTH)

PO4inhPTH = (C2/1.2)^PO4inhPTHgam

Math:

(Details: $View Math$ )

Assignment Rule (name: PhosEffTop)

PhosEffTop = (PhosEff0-1)*(1.2^PhosEffGam+PhosEff50^PhosEffGam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PhosEffBot)

PhosEffBot = PhosEff0*1.2^PhosEffGam

Math:

(Details: $View Math$ )

Assignment Rule (name: PhosEffMax)

PhosEffMax = PhosEffTop/PhosEffBot

Math:

(Details: $View Math$ )

Assignment Rule (name: PhosEff)

PhosEff = PhosEff0-PhosEffMax*PhosEff0*C2^PhosEffGam/(C2^PhosEffGam+PhosEff50^PhosEffGam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PhosEffect)

PhosEffect = piecewise(PhosEff, C2 > 1.2, 1)

Math:

(Details: $View Math$ )

Assignment Rule (name: T68)

T68 = T66*C4^AlphOHgam/(T67^AlphOHgam*PO4inhPTH+C4^AlphOHgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: SE)

SE = T65*T68*PhosEffect

Math:

(Details: $View Math$ )

Assignment Rule (name: C8)

C8 = B/V1

Math:

(Details: $View Math$ )

Assignment Rule (name: C1)

C1 = P/V1

Math:

(Details: $View Math$ )

Assignment Rule (name: T36)

T36 = T33+(T34-T33)*C8^CaPOgam/(T35^CaPOgam+C8^CaPOgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: T37)

T37 = T34-(T34-T33)*C8^CaPOgam/(T35^CaPOgam+C8^CaPOgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: CaFilt)

CaFilt = 0.6*0.5*GFR*C1

Math:

(Details: $View Math$ )

Assignment Rule (name: ReabsMax)

ReabsMax = (0.3*GFR*2.35-0.149997)*(Reabs50+2.35)/2.35

Math:

(Details: $View Math$ )

Assignment Rule (name: ReabsPTHeff)

ReabsPTHeff = T16*C4/(C4+T17)

Math:

(Details: $View Math$ )

Assignment Rule (name: CaReabsActive)

CaReabsActive = ReabsMax*C1/(Reabs50+C1)*ReabsPTHeff

Math:

(Details: $View Math$ )

Assignment Rule (name: T20)

T20 = CaFilt-CaReabsActive

Math:

(Details: $View Math$ )

Assignment Rule (name: T10)

T10 = T7*C8/(C8+T9)

Math:

(Details: $View Math$ )

Assignment Rule (name: J27a)

J27a = (2-T10)*T20

Math:

(Details: $View Math$ )

Assignment Rule (name: J27)

J27 = piecewise(0, J27a < 0, J27a)

Math:

(Details: $View Math$ )

Assignment Rule (name: ScaEff)

ScaEff = (2.35/CaConc)^ScaEffGam

Math:

(Details: $View Math$ )

Assignment Rule (name: T72)

T72 = 90*ScaEff

Math:

(Details: $View Math$ )

Assignment Rule (name: T73)

T73 = T71*(C8-T72)

Math:

(Details: $View Math$ )

Assignment Rule (name: T74)

T74 = (exp(T73)-exp(-T73))/(exp(T73)+exp(-T73))

Math:

(Details: $View Math$ )

Assignment Rule (name: T75)

T75 = T70*(0.85*(1+T74)+0.15)

Math:

(Details: $View Math$ )

Assignment Rule (name: T76)

T76 = T70*(0.85*(1-T74)+0.15)

Math:

(Details: $View Math$ )

Assignment Rule (name: T47)

T47 = T46*0.88*GFR

Math:

(Details: $View Math$ )

Assignment Rule (name: J48a)

J48a = 0.88*GFR*C2-T47

Math:

(Details: $View Math$ )

Assignment Rule (name: J48)

J48 = piecewise(0, J48a < 0, J48a)

Math:

(Details: $View Math$ )

Assignment Rule (name: J53)

J53 = T52*PhosGut

Math:

(Details: $View Math$ )

Assignment Rule (name: J54)

J54 = T49*C2

Math:

(Details: $View Math$ )

Assignment Rule (name: J56)

J56 = T55*IntraPO

Math:

(Details: $View Math$ )

Assignment Rule (name: E0PicOBkb)

E0PicOBkb = MultPicOBkb*Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: EmaxPicOBkb)

EmaxPicOBkb = FracPic0kb*Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOBparenKb)

EC50PicOBparenKb = (E0PicOBkb-EmaxPicOBkb)*TGFBact0^PicOBgamkb/(E0PicOBkb-Pic0)-TGFBact0^PicOBgamkb

Math:

(Details: $View Math$ )

Assignment Rule (name: EC50PicOBkb)

EC50PicOBkb = exp(ln(EC50PicOBparenKb)/PicOBgamkb)

Math:

(Details: $View Math$ )

Assignment Rule (name: PicOBkb)

PicOBkb = E0PicOBkb-(E0PicOBkb-EmaxPicOBkb)*TGFBact^PicOBgamkb/(TGFBact^PicOBgamkb+EC50PicOBkb^PicOBgamkb)

Math:

(Details: $View Math$ )

Assignment Rule (name: PicOBkbEff)

PicOBkbEff = PicOBkb/Pic0

Math:

(Details: $View Math$ )

Assignment Rule (name: E0RUNX2kbEff)

E0RUNX2kbEff = E0RUNX2kbEffFACT*kb

Math:

(Details: $View Math$ )

Assignment Rule (name: RUNX2)

RUNX2 = piecewise(BCL2-90, BCL2 > 105, 10)

Math:

(Details: $View Math$ )

Assignment Rule (name: RUNkbMax)

RUNkbMax = E0RUNX2kbEff*RUNkbMaxFact

Math:

(Details: $View Math$ )

Assignment Rule (name: INparen)

INparen = RUNkbMax*RUNX20^RUNkbGAM/(E0RUNX2kbEff-kb)-RUNX20^RUNkbGAM

Math:

(Details: $View Math$ )

Assignment Rule (name: RUNkb50)

RUNkb50 = exp(ln(INparen)/RUNkbGAM)

Math:

(Details: $View Math$ )

Assignment Rule (name: RUNX2kbPrimeEff)

RUNX2kbPrimeEff = RUNkbMax*RUNX2^RUNkbGAM/(RUNX2^RUNkbGAM+RUNkb50^RUNkbGAM)

Math:

(Details: $View Math$ )

Assignment Rule (name: kbprime)

kbprime = E0RUNX2kbEff*PicOBkbEff-RUNX2kbPrimeEff

Math:

(Details: $View Math$ )

Assignment Rule (name: kbslow)

kbslow = kbprime*Frackb

Math:

(Details: $View Math$ )

Assignment Rule (name: kbfast)

kbfast = ((kb*OB0+kbslow*OBfast0)-kbslow*OB0)/OBfast0

Math:

(Details: $View Math$ )

Assignment Rule (name: Frackb2)

Frackb2 = kbfast/kbprime

Math:

(Details: $View Math$ )

Assignment Rule (name: T29)

T29 = (T28*T0-0.17533*T0)/0.17533

Math:

(Details: $View Math$ )

Assignment Rule (name: T31)

T31 = T28*T/(T+T29)

Math:

(Details: $View Math$ )

Assignment Rule (name: T83)

T83 = R/0.5

Math:

(Details: $View Math$ )

Assignment Rule (name: J40)

J40 = T31*T*T83/(T+T81)+T87*T

Math:

(Details: $View Math$ )

Assignment Rule (name: T85Rpart)

T85Rpart = R^T80/(R^T80+T81^T80)

Math:

(Details: $View Math$ )

Assignment Rule (name: T85)

T85 = T77*T85Rpart

Math:

(Details: $View Math$ )

Assignment Rule (name: F11)

F11 = T85

Math:

(Details: $View Math$ )

Assignment Rule (name: INparenCtriol)

INparenCtriol = (CtriolMax-CtriolMin)*C8^CtriolPTgam/(CtriolMax-1)-C8^CtriolPTgam

Math:

(Details: $View Math$ )

Assignment Rule (name: Ctriol50)

Ctriol50 = exp(ln(INparenCtriol)/CtriolPTgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: CtriolPTeff)

CtriolPTeff = CtriolMax-(CtriolMax-CtriolMin)*C8^CtriolPTgam/(C8^CtriolPTgam+Ctriol50^CtriolPTgam)

Math:

(Details: $View Math$ )

Assignment Rule (name: PTin)

PTin = PTout*CtriolPTeff

Math:

(Details: $View Math$ )

Assignment Rule (name: INparenCa)

INparenCa = (T58-T61)*2.35^T59/(T58-385)-2.35^T59

Math:

(Details: $View Math$ )

Assignment Rule (name: T60)

T60 = exp(ln(INparenCa)/T59)

Math:

(Details: $View Math$ )

Assignment Rule (name: FCTD)

FCTD = S/0.5*PTmax

Math:

(Details: $View Math$ )

Assignment Rule (name: T63)

T63 = T58-(T58-T61)*CaConc^T59/(CaConc^T59+T60^T59)

Math:

(Details: $View Math$ )

Assignment Rule (name: EPTH)

EPTH = T63*FCTD

Math:

(Details: $View Math$ )

Assignment Rule (name: IPTH)

IPTH = 0.693*SC+IPTHinf

Math:

(Details: $View Math$ )

Assignment Rule (name: SPTH)

SPTH = EPTH+IPTH

Math:

(Details: $View Math$ )

Assignment Rule (name: kout)

kout = T57/14

Math:

(Details: $View Math$ )

Assignment Rule (name: TERIPK)

TERIPK = TERISC*TERICL/TERIVC

Math:

(Details: $View Math$ )

Events (1)

Event

event_counter = event_counter+teri_times_interval

TERISC = teri_dose_mcg*1000000/4117.8

Trigger:

(time == teri_times_initial) || ((time == (event_counter+teri_times_initial)) && (time < (teri_times_interval*teri_number_of_doses+teri_times_initial)))

Delay:

Global Parameters (268)

Pic0

Value: 0.228142

Constant

FracOBfast

Value: 0.797629

Constant

Value: 6.24E-6

Constant

Value: 0.112013

Constant

Value: 6.24E-6

Constant

Value: 0.112013

Constant

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

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

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

Value: 2.0

Constant

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

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

Value: 15.8885

Constant

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

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

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

PicROB

Value: NaN

ROBin2

Value: NaN

ROBin

Value: NaN

E0PicOB

Value: NaN

EC50PicOBparen

Value: NaN

EC50PicOB

Value: NaN

PicOB

Value: NaN

KPT

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

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

RX2Kin

Value: NaN

EC50PTHRX2x

Value: NaN

RX2Kout

Value: NaN

EC50PTHcreb

Value: NaN

crebKin0

Value: NaN

crebKin

Value: NaN

bcl2Kin

Value: NaN

CaConc

Value: NaN

PO4inhPTH

Value: NaN

PhosEffTop

Value: NaN

PhosEffBot

Value: NaN

PhosEffMax

Value: NaN

PhosEff

Value: NaN

PhosEffect

Value: NaN

T68

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

BioModels Database

BIOMD0000000613 - Peterson2010 - Integrated calcium homeostasis and bone remodelling

EMBL-EBI

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