JWS Online

demin1

demin1

 Detail
 Download

Reactions

v1

v1

∅ > AA_b

v10in

v10in

LTC4_b > ∅

v10out

v10out

∅ > LTC4_b_out

v11

v11

LTC4_b_out > LTD4_b

v12

v12

LTD4_b > LTE4_b

v13

v13

LTC4_b_out > ∅

v14

v14

LTD4_b > ∅

v15

v15

LTE4_b > ∅

v16

v16

EO_b > EO_i_b

v17

v17

EO_i_b > EO_a_b

v18

v18

EO_a_b > EO_b

v19

v19

EO_b > ∅

v2

v2

AA_b > ∅

v20

v20

EO_a_b > ∅

v21

v21

EO_i_b > EO_i_aw

v22

v22

EO_a_b > EO_a_aw

v23

v23

EO_b > EO_aw

v24

v24

∅ > Hn_b

v25

v25

Hn_b > ∅

v26

v26

∅ > IL_b

v27

v27

IL_b > ∅

v28

v28

IL_b > IL_bm

v29

v29

∅ > EO_bm

v3

v3

∅ > HPETE_b

v30

v30

EO_bm > EO_b

v31

v31

∅ > AA_aw

v32

v32

AA_aw > ∅

v33

v33

∅ > HPETE_aw

v34

v34

HPETE_aw > HETE_aw

v35

v35

HPETE_aw > HETE_aw

v36

v36

∅ > LTA4_aw

v37

v37

LTA4_aw > LTC4_aw

v38

v38

HETE_aw > ∅

v39

v39

LTA4_aw > ∅

v4

v4

HPETE_b > HETE_b

v40in

v40in

LTC4_aw > ∅

v40out

v40out

∅ > LTC4_aw_out

v41

v41

LTC4_aw_out > LTD4_aw

v42

v42

LTD4_aw > LTE4_aw

v43

v43

LTE4_aw > LTE4_b

v44

v44

LTD4_aw > LTD4_b

v45

v45

LTC4_aw_out > LTC4_b_out

v46

v46

EO_aw > EO_i_aw

v47

v47

EO_i_aw > EO_a_aw

v48

v48

EO_a_aw > EO_aw

v49

v49

EO_aw > ∅

v5

v5

HPETE_b > HETE_b

v50

v50

EO_a_aw > ∅

v51

v51

∅ > Hn_aw

v52

v52

Hn_aw > Hn_b

v53

v53

∅ > IL_aw

v54

v54

IL_aw > IL_b

v55

v55

LTE4_aw > ∅

v56

v56

LTD4_aw > ∅

v57

v57

LTC4_aw_out > ∅

v58

v58

IL_aw > ∅

v59

v59

Hn_aw > ∅

v6

v6

∅ > LTA4_b

v60

v60

ZF_intes > ZF_blood

v61

v61

ZF_blood > ZF_airways

v62

v62

ZF_blood > ∅

v63

v63

ML_intes > ML_blood

v64

v64

ML_blood > ∅

v7

v7

LTA4_b > LTC4_b

v8

v8

HETE_b > ∅

v9

v9

LTA4_b > ∅

Parameters

Global parameters

Fixed species

Initial values

Functions and Rules

Assignment rules

ft_ml = ceil(time / T)

ZF_blood_conc = fup_ZF * ZF_blood

ZF_airways_conc = ZF_airways

ML_blood_conc = fup_ML * ML_blood

ML_airways_conc = fup_ML * ML_blood

w_EO = npi * pow(diam_EO, 3.000000e+00) / 6.000000e+00

V_aCB = EO_a_b * N_A_pmole * w_EO * V_B

V_aCAW = EO_a_aw * N_A_pmole * w_EO * V_AW

GSSG_b = (GS_pool_b - GSH_b) / 2.000000e+00

PLA2_D = 1.000000e+00 + Ca / K_PLA2_Ca

Ki_AA_AA = Ki_AA

Ki_HPETE_AA = Ki_AA

OOH_b = HPETE_b + LOOH_b

OH_b = HETE_b + LOH_b

r1 = k_ox + k_ox2 * Ca / K_Ca2

r2 = k_red + k_red2 * Ca / K_Ca2

RELFLO5_b = (k_lo * AA_b / K_AA + k3 * HPETE_b * (1.000000e+00 + AA_b / Ki_AA)) / (k_lta_syn + k_3 * (1.000000e+00 + AA_b / Ki_HPETE_AA))

FLO3_b = FLOa / DFLOa_b

FLO2_b = FLO3_b * REDOX_b

FLO3t_b = FLO3_b * (1.000000e+00 + Ca / K_Ca3)

FLO2t_b = FLO2_b * (1.000000e+00 + Ca / K_Ca2)

FLO5HP_b = FLO3t_b * RELFLO5_b

C_b = HPETE_b * GSH_b * GSH_b / (Km_gpx_HPETE5 * Km_gpx_GSH * Km_gpx_GSH)

delta_LTCs_b = 1.000000e+00 + LTA4_b / K_LTA + GSH_b / K_GSH + LTA4_b * GSH_b / K_LTA / K_LTA_GSH + LTC4_b / K_LTC

C_hedh_b = (1.000000e+00 + HETE_b / Kd_hedh_HETE5 + NADPH_b / Kd_hedh_NADPH) * (k_hedh_3 * oxoETE_b / Kd_hedh_oxoETE5 + k_hedh_2 * NADP_b / Kd_hedh_NADP)

GSSG_aw = (GS_pool_aw - GSH_aw) / 2.000000e+00

NADPH_aw = NP_pool_aw - NADP_aw

OOH_aw = HPETE_aw + LOOH_aw

OH_aw = HETE_aw + LOH_aw

RELFLO5_aw = (k_lo * AA_aw / K_AA + k3 * HPETE_aw * (1.000000e+00 + AA_aw / Ki_AA)) / (k_lta_syn + k_3 * (1.000000e+00 + AA_aw / Ki_HPETE_AA))

FLO3_aw = FLOa / DFLOa_aw

FLO2_aw = FLO3_aw * REDOX_aw

FLO3t_aw = FLO3_aw * (1.000000e+00 + Ca / K_Ca3)

FLO2t_aw = FLO2_aw * (1.000000e+00 + Ca / K_Ca2)

FLO5HP_aw = FLO3t_aw * RELFLO5_aw

C_aw = HPETE_aw * GSH_aw * GSH_aw / (Km_gpx_HPETE5 * Km_gpx_GSH * Km_gpx_GSH)

B_aw = k_gpx_cat * HPETE_aw * GSH_aw * GSH_aw / (Km_gpx_HPETE5 * Km_gpx_GSH * Km_gpx_GSH)

den_LTCs_aw = delta_LTCs_aw * K_LTA_GSH * K_GSH * K_LTC

C_hedh_aw = (1.000000e+00 + HETE_aw / Kd_hedh_HETE5 + NADPH_aw / Kd_hedh_NADPH) * (k_hedh_3 * oxoETE_aw / Kd_hedh_oxoETE5 + k_hedh_2 * NADP_aw / Kd_hedh_NADP)

B_hedh_aw = k_hedh_1 * k_hedh_2 * HETE_aw * NADP_aw / (Kd_hedh_HETE5 * Kd_hedh_NADP) - oxoETE_aw * NADPH_aw * k_hedh_3 * k_hedh_4 / (Kd_hedh_oxoETE5 * Kd_hedh_NADPH)

Rec_occup_migr = portion_migr * fup_LT * LTE4_b / (Kd_LTE_migr + fup_LT * LTE4_b) + (1.000000e+00 - portion_migr) * IL_b / (Kd_IL_migr + IL_b)

r_in_FEV = r_out_FEV - (R_FEV - R_in_relax_FEV) * pow(R_FEV / r_out_FEV, 5.000000e-01)

FEV1 = MAX_FEV * pow(r_in_FEV / R_in_relax_FEV, 2.000000e+00)

time_hour = time / 6.000000e+01

time_day = time / 1.440000e+03

N_EO_bm = EO_bm * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

N_EO_b = EO_b * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

N_EO_i_b = EO_i_b * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

EO_b_tot = EO_b + EO_i_b + EO_a_b

N_EO_b_tot = (EO_b + EO_i_b + EO_a_b) * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

N_EO_aw = EO_aw * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

N_EO_i_aw = EO_i_aw * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

N_EO_a_aw = EO_a_aw * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

EO_aw_tot = EO_aw + EO_i_aw + EO_a_aw

N_EO_aw_tot = (EO_aw + EO_i_aw + EO_a_aw) * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

EO_b_tot_per_ss = 1.000000e+02 * (EO_b_tot - 5.330000e-04) / 5.330000e-04

N_EO_aw_tot_perc = N_EO_aw_tot / 8.187350e+05 * 1.000000e+02

N_EO_b_tot_perc = N_EO_b_tot / 4.266021e+06 * 1.000000e+02

LTC4_b_pM = LTC4_b * 1.000000e+06

N_EO_a = (N_EO_a_b * V_B + N_EO_a_aw * V_AW) / (V_B + V_AW)

N_EO = (N_EO_b_tot * V_B + N_EO_aw_tot * V_AW) / (V_B + V_AW)

N_EO_aw_perc = 1.000000e+02 * N_EO_aw_tot / 8.187350e+05

Hn_aw_perc = 1.000000e+02 * Hn_aw / 1.416200e+04

N_EO_perc = 1.000000e+02 * N_EO / 3.587580e+05

OL_ASM = R1_portion_FEV * (LTD4_aw / Kd_LTR1_FEV) / (1.000000e+00 + LTD4_aw / Kd_LTR1_FEV + ML_airways_conc / EC50_ML_FEV) + R2_portion_FEV * ((LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) / (1.000000e+00 + (LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) + (1.000000e+00 - R1_portion_FEV - R2_portion_FEV) * (Hn_aw / Kd_Hn_FEV) / (1.000000e+00 + Hn_aw / Kd_Hn_FEV)

Ca_FEV_LTR2 = k_fev_eff * (R2_portion_FEV * ((LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) / (1.000000e+00 + (LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) + (1.000000e+00 - R1_portion_FEV - R2_portion_FEV) * (Hn_aw / Kd_Hn_FEV) / (1.000000e+00 + Hn_aw / Kd_Hn_FEV)) / (Ca_FEV - Cao_FEV)

Ca_FEV_LTR1 = k_fev_eff * (R1_portion_FEV * (LTD4_aw / Kd_LTR1_FEV) / (1.000000e+00 + LTD4_aw / Kd_LTR1_FEV + ML_airways_conc / EC50_ML_FEV)) / (Ca_FEV - Cao_FEV)

LTD4_aw_pers = 1.000000e+02 * LTD4_aw / 2.057600e+02

ML_uM = ML_blood / 1.000000e+06

LTD4_b_free = LTD4_b * fup_LT

LTs_aw_pg = (LTC4_aw_out / fup_LT * M_LTC + LTD4_aw / fup_LT * M_LTD + LTE4_aw / fup_LT * M_LTE) / 1.000000e+03

N_EO_a_b = EO_a_b * 6.020000e+00 * pow(1.000000e+01, 8.000000e+00)

FEV1_percent = (FEV1 - 3.528000e+00) / 3.528000e+00 * 1.000000e+02

TSN_Hn = TSN_0 * (R_FEV - pow(R_FEV * pow(R_FEV - R_in_relax_FEV, 2.000000e+00), 1.000000e+00 / 3.000000e+00)) * pow(Ca_FEV, n_FEV) / (pow(K_Ca_FEV, n_FEV) + pow(Ca_FEV, n_FEV))

TSN = TSN_0 * (R_FEV - pow(R_FEV * pow(R_FEV - R_in_relax_FEV, 2.000000e+00), 1.000000e+00 / 3.000000e+00)) * pow(Ca_FEV_ex, n_FEV) / (pow(K_Ca_FEV, n_FEV) + pow(Ca_FEV_ex, n_FEV))

r_out_FEV = R_FEV - (R_FEV - pow(R_FEV * pow(R_FEV - R_in_relax_FEV, 2.000000e+00), 1.000000e+00 / 3.000000e+00)) * pow(Ca_FEV, n_FEV) / (pow(K_Ca_FEV, n_FEV) + pow(Ca_FEV, n_FEV))

Ca_FEV = Cao_FEV + k_fev_eff * (R1_portion_FEV * (LTD4_aw / Kd_LTR1_FEV) / (1.000000e+00 + LTD4_aw / Kd_LTR1_FEV + ML_airways_conc / EC50_ML_FEV) + R2_portion_FEV * ((LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) / (1.000000e+00 + (LTD4_aw + LTC4_aw_out) / Kd_LTR2_FEV) + (1.000000e+00 - R1_portion_FEV - R2_portion_FEV) * (Hn_aw / Kd_Hn_FEV) / (1.000000e+00 + Hn_aw / Kd_Hn_FEV))

OL_aw = R1_portion_EOa * (LTD4_aw / Kd_LT) / (1.000000e+00 + LTD4_aw / Kd_LT + ML_airways_conc / Ki_ML_EOa) + (1.000000e+00 - R1_portion_EOa) * ((LTC4_aw_out + LTD4_aw) / Kd_LT_2) / (1.000000e+00 + (LTC4_aw_out + LTD4_aw) / Kd_LT_2)

OL_b = R1_portion_EOa * (fup_LT * LTD4_b / Kd_LT) / (1.000000e+00 + fup_LT * LTD4_b / Kd_LT + ML_blood_conc / Ki_ML_EOa) + (1.000000e+00 - R1_portion_EOa) * (fup_LT * (LTC4_b_out + LTD4_b) / Kd_LT_2) / (1.000000e+00 + fup_LT * (LTC4_b_out + LTD4_b) / Kd_LT_2)

A_hedh_aw = (1.000000e+00 + NADP_aw / Kd_hedh_NADP + oxoETE_aw / Kd_hedh_oxoETE5) * (k_hedh_1 * HETE_aw / Kd_hedh_HETE5 + k_hedh_4 * NADPH_aw / Kd_hedh_NADPH) + C_hedh_aw

nom_LTCs_aw = Et_LTCs * (K_LTC * k_LTCs_fow * LTA4_aw * GSH_aw - k_LTCs_back * K_LTA_GSH * K_GSH * LTC4_aw)

delta_LTCs_aw = 1.000000e+00 + LTA4_aw / K_LTA + GSH_aw / K_GSH + LTA4_aw * GSH_aw / K_LTA / K_LTA_GSH + LTC4_aw / K_LTC

A_aw = GSH_aw * GSH_aw / (Km_gpx_GSH * Km_gpx_GSH) * (1.000000e+00 + GSSG_aw / Kd_gpx_GSSG) + HPETE_aw / Km_gpx_HPETE5 * (1.000000e+00 + HETE_aw / Kd_gpx_HETE5) + C_aw

DFLOa_aw = (1.000000e+00 + Ca / K_Ca3) * (1.000000e+00 + REDOX_aw * (1.000000e+00 + Ca / K_Ca2) / (1.000000e+00 + Ca / K_Ca3) + AA_aw / K_AA * (1.000000e+00 + AA_aw / Ki_AA_AA) + AA_aw / Ki_AA * (1.000000e+00 + HETE_aw / K_AA_HETE) + RELFLO5_aw * (1.000000e+00 + AA_aw / Ki_HPETE_AA) + HETE_aw / Ki_HETE + al * ZF_airways_conc / KdZ)

REDOX_aw = (r2 / Ke_red + r1 * OH_aw / Ke_ox + al * ki * ZF_airways_conc / KdZ * (1.000000e+00 + Ca / K_Ca3)) / (r2 + r1 * OOH_aw)

B_hedh_b = k_hedh_1 * k_hedh_2 * HETE_b * NADP_b / (Kd_hedh_HETE5 * Kd_hedh_NADP) - oxoETE_b * NADPH_b * k_hedh_3 * k_hedh_4 / (Kd_hedh_oxoETE5 * Kd_hedh_NADPH)

A_hedh_b = (1.000000e+00 + NADP_b / Kd_hedh_NADP + oxoETE_b / Kd_hedh_oxoETE5) * (k_hedh_1 * HETE_b / Kd_hedh_HETE5 + k_hedh_4 * NADPH_b / Kd_hedh_NADPH) + C_hedh_b

den_LTCs_b = delta_LTCs_b * K_LTA_GSH * K_GSH * K_LTC

nom_LTCs_b = Et_LTCs * (K_LTC * k_LTCs_fow * LTA4_b * GSH_b - k_LTCs_back * K_LTA_GSH * K_GSH * LTC4_b)

B_b = k_gpx_cat * HPETE_b * GSH_b * GSH_b / (Km_gpx_HPETE5 * Km_gpx_GSH * Km_gpx_GSH)

A_b = GSH_b * GSH_b / (Km_gpx_GSH * Km_gpx_GSH) * (1.000000e+00 + GSSG_b / Kd_gpx_GSSG) + HPETE_b / Km_gpx_HPETE5 * (1.000000e+00 + HETE_b / Kd_gpx_HETE5) + C_b

DFLOa_b = (1.000000e+00 + Ca / K_Ca3) * (1.000000e+00 + REDOX_b * (1.000000e+00 + Ca / K_Ca2) / (1.000000e+00 + Ca / K_Ca3) + AA_b / K_AA * (1.000000e+00 + AA_b / Ki_AA_AA) + AA_b / Ki_AA * (1.000000e+00 + HETE_b / K_AA_HETE) + RELFLO5_b * (1.000000e+00 + AA_b / Ki_HPETE_AA) + HETE_b / Ki_HETE + al * ZF_blood_conc / KdZ)

REDOX_b = (r2 / Ke_red + r1 * OH_b / Ke_ox + al * ki * ZF_blood_conc / KdZ * (1.000000e+00 + Ca / K_Ca3)) / (r2 + r1 * OOH_b)

K_AA_HETE = Ki_HETE

PLA2_Ca = Ca / K_PLA2_Ca / PLA2_D

NADPH_b = NP_pool_b - NADP_b

V_LTC_CAW = (naEO_LTCsyn * (EO_aw + EO_i_aw) + EO_a_aw) * N_A_pmole * w_EO * V_AW

V_CAW = (EO_a_aw + EO_aw + EO_i_aw) * N_A_pmole * w_EO * V_AW

V_LTC_CB = (naEO_LTCsyn * (EO_b + EO_i_b) + EO_a_b) * N_A_pmole * w_EO * V_B

V_CB = (EO_a_b + EO_b + EO_i_b) * N_A_pmole * w_EO * V_B

ft_zf = ceil(time / T) + ceil((time - 3.600000e+02) / T) + ceil((time - 6.600000e+02) / T) + ceil((time - 9.600000e+02) / T)

Function definitions

Events

Constraints

Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.


Species:

Reactions:

Middle-click: pin/unpin nodes
Shift-click: pool/unpool species
Right-click: context menu
Apply alternate model layout to overlapping elements in current model:

log scales

y-axis min/max

x-axis min/max

Systems pharmacology models can be used to understand complex pharmacokinetic-pharmacodynamic behavior: an example using 5-lipoxygenase inhibitors.

  • T Karelina
  • D Svetlichniy
  • E Metelkin
  • G Speshilov
  • O Demin
  • D Fairman
  • Piet H van der Graaf
  • BM Agoram
CPT Pharmacometrics Syst Pharmacol 2013; 2 :
Abstract
Zileuton, a 5-lipoxygenase (5LO) inhibitor, displays complex pharmaokinetic (PK)-pharmacodynamic (PD) behavior. Available clinical data indicate a lack of dose-bronchodilatory response during initial treatment, with a dose response developing after ~1-2 weeks. We developed a quantitative systems pharmacology (QSP) model to understand the mechanism behind this phenomenon. The model described the release, maturation, and trafficking of eosinophils into the airways, leukotriene synthesis by the 5LO enzyme, leukotriene signaling and bronchodilation, and the PK of zileuton. The model provided a plausible explanation for the two-phase bronchodilatory effect of zileuton-the short-term bronchodilation was due to leukotriene inhibition and the long-term bronchodilation was due to inflammatory cell infiltration blockade. The model also indicated that the theoretical maximum bronchodilation of both 5LO inhibition and leukotriene receptor blockade is likely similar. QSP modeling provided interesting insights into the effects of leukotriene modulation.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e74; doi:10.1038/psp.2013.49; advance online publication 11 September 2013.
The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000490) Biomodels notes: Figure 2 of the reference publication has been reproduced here. To simulate the curves of Figure 2, (i) set a=1 ("1" corresponds to multiple dose administration, "0" corresponds to single dose administration), (ii) set DOSE_zf to 400 or 600 (this corresponds to the dosage of Zileuton in mg), and (iii) set DOSE_ml to 10 or 50 (this corresponds to the dosage of Montelukast in mg). The model was simulated using Copasi v4.10 (Build 55) and the plots were generated using Gnuplot. The Copasi file corresponding to each of these four conditions (i.e.,DOSE_zf=400,600mg and DOSE_ml=10,50mg) that can be used to generate the plots, can be downloaded (see below). JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.