benson1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000512) Biomodels notes: Figure 5 of the reference publication has been reproduced here. The plots shows cannabinoid receptor (CB1) occupancy (in percentage) in the brain with the increasing dosage of drug (0.1 to 40mg). The model as such reproduces the plot corresponding to 10mg dose. Other plots were obtained by varying the value of the parameter "Dose". JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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A systems pharmacology perspective on the clinical development of Fatty Acid amide hydrolase inhibitors for pain.

  • N Benson
  • E Metelkin
  • O Demin
  • GL Li
  • D Nichols
  • Piet H van der Graaf
CPT Pharmacometrics Syst Pharmacol 2014; 3 :
Abstract
The level of the endocannabinoid anandamide is controlled by fatty acid amide hydrolase (FAAH). In 2011, PF-04457845, an irreversible inhibitor of FAAH, was progressed to phase II clinical trials for osteoarthritic pain. This article discusses a prospective, integrated systems pharmacology model evaluation of FAAH as a target for pain in humans, using physiologically based pharmacokinetic and systems biology approaches. The model integrated physiological compartments; endocannabinoid production, degradation, and disposition data; PF-04457845 pharmacokinetics and pharmacodynamics, and cannabinoid receptor CB1-binding kinetics. The modeling identified clear gaps in our understanding and highlighted key risks going forward, in particular relating to whether methods are in place to demonstrate target engagement and pharmacological effect. The value of this modeling exercise will be discussed in detail and in the context of the clinical phase II data, together with recommendations to enable optimal future evaluation of FAAH inhibitors.CPT: Pharmacometrics Systems Pharmacology (2014) 3, e91; doi:10.1038/psp.2013.72; published online 15 January 2014.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
BRAIN 3.0 1.45000004768372
Default 3.0 1.0
MEC 3.0 0.0000149999996210681
PLASMA 3.0 2.6489999294281
ROB 3.0 65.3000030517578
Id Name Initial quantity Compartment Fixed
A_b A_b 0.7493309 BRAIN
A_m A_m 0.97761 MEC
A_p A_p 0.8740574 PLASMA
A_r A_r 0.5419204 ROB
FAAH_b FAAH_b 15.366 BRAIN
FAAH_m FAAH_m 10.686 MEC
FAAH_r FAAH_r 2.165868 ROB
FAAHinh_b FAAHinh_b 0.0 BRAIN
FAAHinh_m FAAHinh_m 0.0 MEC
FAAHinh_r FAAHinh_r 0.0 ROB
L_b L_b 2.319571 BRAIN
L_m L_m 0.0 MEC
L_p L_p 1.916254 PLASMA
L_r L_r 1.705466 ROB
NAPE_b NAPE_b 0.00003879041 BRAIN
NAPE_r NAPE_r 0.000004241633 ROB
NLPE_b NLPE_b 0.00007550331 BRAIN
NLPE_r NLPE_r 0.000008256095 ROB
NOPE_b NOPE_b 0.0008814287 BRAIN
NOPE_r NOPE_r 0.00009638198 ROB
NPPE_b NPPE_b 0.0001732296 BRAIN
NPPE_r NPPE_r 0.00001894222 ROB
NSPE_b NSPE_b 0.0001272629 BRAIN
NSPE_r NSPE_r 0.00001391587 ROB
O_b O_b 20.77858 BRAIN
O_m O_m 16.3219 MEC
O_p O_p 5.085073 PLASMA
O_r O_r 14.23822 ROB
PFM_gut PFM_gut 0.0 Default
PFM_p PFM_p 0.0 Default
PFM_r PFM_r 0.0 Default
P_b P_b 6.541209 BRAIN
P_m P_m 5.809415 MEC
P_p P_p 4.849307 PLASMA
P_r P_r 4.121915 ROB
S_b S_b 3.427807 BRAIN
S_m S_m 2.968774 MEC
S_p S_p 0.273772 PLASMA
S_r S_r 2.515968 ROB

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
absorp absorp PFM_gut > PFM_p

kabs_PFM * MD
dist dist PFM_p > PFM_r

kout_PFM * PFM_p - kin_PFM * PFM_r
elim elim PFM_p > ∅

klinear_PFM * PFM_p + Vm_PFM * PFM_p / (Km_PFM + PFM_p / Vss_PFM) / Vss_PFM
vA_UE_b vA_UE_b A_b > ∅

BRAIN * b_FAAH_Brain * kcl_A * A_b
vA_UE_r vA_UE_r A_r > ∅

c_NAAA_ROB * kcl_A * A_r
vA_b_m vA_b_m A_b > A_m

MEC * ktr_m_p_A * (A_b - A_m) / (A_m + A_b + Km_p_m_A)
vA_degr_b vA_degr_b A_b > ∅

BRAIN * FAAH_b * kcat_FAAH * a_FAAH_A * A_b / (Km_FAAH_A * FAAH_D_b)
vA_degr_m vA_degr_m A_m > ∅

MEC * FAAH_m * kcat_FAAH * a_FAAH_A * A_m / (Km_FAAH_A * FAAH_D_m)
vA_degr_r vA_degr_r A_r > ∅

ROB * FAAH_r * kcat_FAAH * a_FAAH_A * A_r / (Km_FAAH_A * FAAH_D_r)
vA_m_p vA_m_p A_m > A_p

MEC * ktr_m_p_A * (A_m - A_p * Ktr_p_m_A) / (A_m + A_p + Km_p_m_A)
vA_r_p vA_r_p A_r > A_p

PLASMA * ktr_r_p * (A_r - A_p * Ktr_p_r_A) / (A_r + A_p + Km_p_m_A)
vA_syn_b vA_syn_b NAPE_b > A_b

BRAIN * PLD_b * k_NA_PE * NAPE_b / Km_NA_PE / den_b
vA_syn_r vA_syn_r NAPE_r > A_r

ROB * PLD_r * k_NA_PE * NAPE_r / Km_NA_PE / den_r
vFAAH_degr_b vFAAH_degr_b FAAH_b > ∅

BRAIN * k_deg_FAAH * FAAH_b
vFAAH_degr_m vFAAH_degr_m FAAH_m > ∅

MEC * k_deg_FAAH * FAAH_m
vFAAH_degr_r vFAAH_degr_r FAAH_r > ∅

ROB * k_deg_FAAH * FAAH_r
vFAAH_inh_b vFAAH_inh_b FAAH_b > FAAHinh_b

BRAIN * k_inh * FAAH_b * PF_b
vFAAH_inh_degr_b vFAAH_inh_degr_b FAAHinh_b > ∅

BRAIN * k_deg_FAAH * FAAHinh_b
vFAAH_inh_degr_m vFAAH_inh_degr_m FAAHinh_m > ∅

MEC * k_deg_FAAH * FAAHinh_m
vFAAH_inh_degr_r vFAAH_inh_degr_r FAAHinh_r > ∅

ROB * k_deg_FAAH * FAAHinh_r
vFAAH_inh_m vFAAH_inh_m FAAH_m > FAAHinh_m

MEC * k_inh * FAAH_m * PF_m
vFAAH_inh_r vFAAH_inh_r FAAH_r > FAAHinh_r

ROB * k_inh * FAAH_r * PF_r
vFAAH_syn_b vFAAH_syn_b ∅ > FAAH_b

BRAIN * FAAH_t * b_FAAH_Brain * k_deg_FAAH
vFAAH_syn_m vFAAH_syn_m ∅ > FAAH_m

MEC * FAAH_t * b_FAAH_MEC * k_deg_FAAH
vFAAH_syn_r vFAAH_syn_r ∅ > FAAH_r

FAAH_t * c_FAAH_ROB * k_deg_FAAH
vL_UE_b vL_UE_b L_b > ∅

BRAIN * b_FAAH_Brain * kcl_L * L_b
vL_UE_r vL_UE_r L_r > ∅

c_NAAA_ROB * kcl_L * L_r
vL_b_m vL_b_m L_b > L_m

MEC * ktr_m_p_L * (L_b - L_m)
vL_degr_b vL_degr_b L_b > ∅

BRAIN * FAAH_b * kcat_FAAH * a_FAAH_L * L_b / (Km_FAAH_L * FAAH_D_b)
vL_degr_m vL_degr_m L_m > ∅

MEC * FAAH_m * kcat_FAAH * a_FAAH_L * L_m / (Km_FAAH_L * FAAH_D_m)
vL_degr_r vL_degr_r L_r > ∅

ROB * FAAH_r * kcat_FAAH * a_FAAH_L * L_r / (Km_FAAH_L * FAAH_D_r)
vL_m_p vL_m_p L_m > L_p

MEC * ktr_m_p_L * (L_m - L_p * Ktr_p_m_L)
vL_r_p vL_r_p L_r > L_p

PLASMA * ktr_r_p * (L_r - L_p * Ktr_p_r_L)
vL_syn_b vL_syn_b NLPE_b > L_b

BRAIN * PLD_b * k_NL_PE * NLPE_b / Km_NL_PE / den_b
vL_syn_r vL_syn_r NLPE_r > L_r

ROB * PLD_r * k_NL_PE * NLPE_r / Km_NL_PE / den_r
vNAPE_syn_b vNAPE_syn_b ∅ > NAPE_b

BRAIN * Vmax_NAT * p_A * a_NAT_A * b_NAT_Brain
vNAPE_syn_r vNAPE_syn_r ∅ > NAPE_r

Vmax_NAT * p_A * a_NAT_A * c_NAT_ROB
vNLPE_syn_b vNLPE_syn_b ∅ > NLPE_b

BRAIN * Vmax_NAT * p_L * a_NAT_L * b_NAT_Brain
vNLPE_syn_r vNLPE_syn_r ∅ > NLPE_r

Vmax_NAT * p_L * a_NAT_L * c_NAT_ROB
vNOPE_syn_b vNOPE_syn_b ∅ > NOPE_b

BRAIN * Vmax_NAT * p_O * a_NAT_O * b_NAT_Brain
vNOPE_syn_r vNOPE_syn_r ∅ > NOPE_r

Vmax_NAT * p_O * a_NAT_O * c_NAT_ROB
vNPPE_syn_b vNPPE_syn_b ∅ > NPPE_b

BRAIN * Vmax_NAT * p_P * a_NAT_P * b_NAT_Brain
vNPPE_syn_r vNPPE_syn_r ∅ > NPPE_r

Vmax_NAT * p_P * a_NAT_P * c_NAT_ROB
vNSPE_syn_b vNSPE_syn_b ∅ > NSPE_b

BRAIN * Vmax_NAT * p_S * a_NAT_S * b_NAT_Brain
vNSPE_syn_r vNSPE_syn_r ∅ > NSPE_r

Vmax_NAT * p_S * a_NAT_S * c_NAT_ROB
vO_UE_b vO_UE_b O_b > ∅

BRAIN * b_FAAH_Brain * kcl_O * O_b
vO_UE_r vO_UE_r O_r > ∅

c_NAAA_ROB * kcl_O * O_r
vO_b_m vO_b_m O_b > O_m

MEC * ktr_m_p_O * (O_b - O_m)
vO_degr_b vO_degr_b O_b > ∅

BRAIN * FAAH_b * kcat_FAAH * a_FAAH_O * O_b / (Km_FAAH_O * FAAH_D_b)
vO_degr_m vO_degr_m O_m > ∅

MEC * FAAH_m * kcat_FAAH * a_FAAH_O * O_m / (Km_FAAH_O * FAAH_D_m)
vO_degr_r vO_degr_r O_r > ∅

ROB * FAAH_r * kcat_FAAH * a_FAAH_O * O_r / (Km_FAAH_O * FAAH_D_r)
vO_r_p vO_r_p O_r > O_p

PLASMA * ktr_r_p * (O_r - O_p * Ktr_p_r_O)
vO_syn_b vO_syn_b NOPE_b > O_b

BRAIN * PLD_b * k_NO_PE * NOPE_b / Km_NO_PE / den_b
vO_syn_r vO_syn_r NOPE_r > O_r

ROB * PLD_r * k_NO_PE * NOPE_r / Km_NO_PE / den_r
vP_UE_b vP_UE_b P_b > ∅

BRAIN * b_FAAH_Brain * kcl_P * P_b
vP_UE_r vP_UE_r P_r > ∅

c_NAAA_ROB * kcl_P * P_r
vP_b_m vP_b_m P_b > P_m

MEC * ktr_m_p_P * (P_b - P_m)
vP_degr_b vP_degr_b P_b > ∅

BRAIN * FAAH_b * kcat_FAAH * a_FAAH_P * P_b / (Km_FAAH_P * FAAH_D_b)
vP_degr_m vP_degr_m P_m > ∅

MEC * FAAH_m * kcat_FAAH * a_FAAH_P * P_m / (Km_FAAH_P * FAAH_D_m)
vP_degr_r vP_degr_r P_r > ∅

ROB * FAAH_r * kcat_FAAH * a_FAAH_P * P_r / (Km_FAAH_P * FAAH_D_r)
vP_m_p vP_m_p P_m > P_p

MEC * ktr_m_p_P * (P_m - P_p * Ktr_p_m_P)
vP_r_p vP_r_p P_r > P_p

PLASMA * ktr_r_p * (P_r - P_p * Ktr_p_r_P)
vP_syn_b vP_syn_b NPPE_b > P_b

BRAIN * PLD_b * k_NP_PE * NPPE_b / Km_NP_PE / den_b
vP_syn_r vP_syn_r NPPE_r > P_r

ROB * PLD_r * k_NP_PE * NPPE_r / Km_NP_PE / den_r
vS_UE_b vS_UE_b S_b > ∅

BRAIN * b_FAAH_Brain * kcl_S * S_b
vS_UE_r vS_UE_r S_r > ∅

c_NAAA_ROB * kcl_S * S_r
vS_b_m vS_b_m S_b > S_m

MEC * ktr_m_p_S * (S_b - S_m)
vS_degr_b vS_degr_b S_b > ∅

BRAIN * FAAH_b * kcat_FAAH * a_FAAH_S * S_b / (Km_FAAH_S * FAAH_D_b)
vS_degr_m vS_degr_m S_m > ∅

MEC * FAAH_m * kcat_FAAH * a_FAAH_S * S_m / (Km_FAAH_S * FAAH_D_m)
vS_degr_r vS_degr_r S_r > ∅

ROB * FAAH_r * kcat_FAAH * a_FAAH_S * S_r / (Km_FAAH_S * FAAH_D_r)
vS_m_p vS_m_p S_m > S_p

MEC * ktr_m_p_S * (S_m - S_p * Ktr_p_m_S)
vS_r_p vS_r_p S_r > S_p

PLASMA * ktr_r_p * (S_r - S_p * Ktr_p_r_S)
vS_syn_b vS_syn_b NSPE_b > S_b

BRAIN * PLD_b * k_NS_PE * NSPE_b / Km_NS_PE / den_b
vS_syn_r vS_syn_r NSPE_r > S_r

ROB * PLD_r * k_NS_PE * NSPE_r / Km_NS_PE / den_r
vo_m_p vo_m_p O_m > O_p

MEC * ktr_m_p_O * (O_m - O_p * Ktr_p_m_O)

Global parameters

Id Value
AG2_b 0.0
AG_p 0.0
CB1_b 0.0
Dose 10.0
ED50 0.53
Emax_PFM 0.773
FAAH_D_b 0.0
FAAH_D_m 0.0
FAAH_D_r 0.0
FAAH_t 78.0
F_PFM 0.0
F_r 0.0
Gut 1.65
H 0.48
Heart 0.31
Kd_AG2 3424.0
Kd_CB1_A 239.2
Ki_A 230.0
Ki_L 1000.0
Ki_O 240.0
Ki_P 6700.0
Ki_S 840.0
Kidney 0.28
Km_FAAH_A 8200.0
Km_FAAH_L 10800.0
Km_FAAH_O 52200.0
Km_FAAH_P 543000.0
Km_FAAH_S 10000.0
Km_NA_PE 2800.0
Km_NL_PE 1000.0
Km_NO_PE 2900.0
Km_NP_PE 3300.0
Km_NS_PE 3400.0
Km_PFM 26.1
Km_p_m_A 1.0
Kp_b_PF 1.3
Kp_m_PF 1.3
Kp_r_PF 1.5
Ktr_p_m_A 1.89
Ktr_p_m_L 2.77
Ktr_p_m_O 9.07
Ktr_p_m_P 2.65
Ktr_p_m_S 30.01
Ktr_p_r_A 0.62
Ktr_p_r_L 0.89
Ktr_p_r_O 2.8
Ktr_p_r_P 0.85
Ktr_p_r_S 9.19
LEU 0.025
LG_p 0.0
LIVER 1.69
Leucocytes 0.025
Lungs 1.172
MD 0.0
M_A 347.5
M_L 323.5
M_O 325.5
M_P 299.5
M_PF 455.4
M_S 321.5
Muscles 35.0
OG_p 0.0
PFG_p 0.0
PF_b 0.0
PF_m 0.0
PF_p 0.0
PF_r 0.0
PG_p 0.0
PLD_b 10000000.0
PLD_r 10000000.0
Pancreas 0.077
R_PF 0.6
SG_p 0.0
Spleen 0.192
Testis 0.036
Thymus 0.029
Vm_PFM 1511.0
Vmax_NAT 300.0
Vss_PFM 58.328
a_FAAH_A 1.0
a_FAAH_L 1.15
a_FAAH_O 5.7
a_FAAH_P 37.8
a_FAAH_S 1.0
a_NAT_A 1.0
a_NAT_L 8.6
a_NAT_O 13.0
a_NAT_P 0.42
a_NAT_S 1.0
b_FAAH_Brain 0.197
b_FAAH_Gut 0.034
b_FAAH_Kidney 0.069
b_FAAH_Leucocytes 0.0
b_FAAH_Liver 1.0
b_FAAH_Lungs 0.032
b_FAAH_MEC 0.137
b_FAAH_Spleen 0.03
b_FAAH_Testis 0.126
b_NAAA_Brain 0.6
b_NAAA_Gut 0.2
b_NAAA_Heart 0.2
b_NAAA_Kidney 0.6
b_NAAA_Liver 1.0
b_NAAA_Lungs 14.0
b_NAAA_Spleen 8.0
b_NAAA_Testis 0.6
b_NAAA_Thymus 4.0
b_NAT_Brain 1.667
b_NAT_Heart 1.0
b_NAT_Kidney 0.667
b_NAT_Leucocytes 0.0
b_NAT_Lungs 0.033
b_NAT_Muscles 0.333
b_NAT_Pancreas 0.333
b_NAT_Testis 0.667
c_FAAH_ROB 0.0
c_NAAA_ROB 0.0
c_NAT_ROB 0.0
den_b 0.0
den_r 0.0
e1 0.0
k_NA_PE 202.0
k_NL_PE 100.0
k_NO_PE 230.0
k_NP_PE 270.0
k_NS_PE 280.0
k_deg_FAAH 0.0051
k_inh 1.1
kabs_PFM 2.2
kcat_FAAH 18000.0
kcl_A 1.74
kcl_L 1.25
kcl_O 2.5
kcl_P 2.61
kcl_S 1.2
kin_PFM 0.117
klinear_PFM 0.0803
kout_PFM 0.18
ktr_m_p_A 150.0
ktr_m_p_L 0.0
ktr_m_p_O 10.0
ktr_m_p_P 10.0
ktr_m_p_S 10.0
ktr_r_p 100.0
p_A 0.051
p_L 0.016
p_O 0.098
p_P 0.615
p_S 0.191
slag1_b 0.0
slag1_r 0.0
slag2_b 0.0
slag2_r 0.0
t 0.0
tid 0.0

Local parameters

Id Value Reaction

Assignment rules

Definition
tid = t / 2.400000e+01
CB1_b = (A_b / Kd_CB1_A + AG2_b / Kd_AG2) / (1.000000e+00 + A_b / Kd_CB1_A + AG2_b / Kd_AG2)
SG_p = 1.000000e-03 * S_p * M_S
LG_p = 1.000000e-03 * L_p * M_L
PG_p = 1.000000e-03 * P_p * M_P
PFG_p = 1.000000e-03 * PFM_p / Vss_PFM
F_r = 1.500000e+03 * FAAH_r / (FAAHinh_r + FAAH_r)
FAAH_D_b = 1.000000e+00 + A_b / Km_FAAH_A + O_b / Km_FAAH_O + P_b / Km_FAAH_P + L_b / Km_FAAH_L + S_b / Km_FAAH_S
PF_m = PF_p * Kp_m_PF
PF_r = PF_p * Kp_r_PF
den_b = 1.000000e+00 + slag1_b + slag2_b
MD = PFM_gut + 1.000000e+06 * Dose * F_PFM
PF_b = PF_p * Kp_b_PF
FAAH_D_r = 1.000000e+00 + A_r / Km_FAAH_A + O_r / Km_FAAH_O + P_r / Km_FAAH_P + L_r / Km_FAAH_L + S_r / Km_FAAH_S
den_r = 1.000000e+00 + slag1_r + slag2_r
c_FAAH_ROB = LIVER * b_FAAH_Liver + Gut * b_FAAH_Gut + Spleen * b_FAAH_Spleen + Kidney * b_FAAH_Kidney + Lungs * b_FAAH_Lungs + Testis * b_FAAH_Testis + Leucocytes * b_FAAH_Leucocytes
AG_p = 1.000000e-03 * A_p * M_A
OG_p = 1.000000e-03 * O_p * M_O
FAAH_D_m = 1.000000e+00 + A_m / Km_FAAH_A + O_m / Km_FAAH_O + P_m / Km_FAAH_P + L_m / Km_FAAH_L + S_m / Km_FAAH_S
c_NAAA_ROB = LIVER * b_NAAA_Liver + Gut * b_NAAA_Gut + Spleen * b_NAAA_Spleen + Kidney * b_NAAA_Kidney + Heart * b_NAAA_Heart + Lungs * b_NAAA_Lungs + Thymus * b_NAAA_Thymus + Testis * b_NAAA_Thymus * Testis
slag2_r = A_r / Ki_A + O_r / Ki_O + P_r / Ki_P + L_r / Ki_L + S_r / Ki_S
slag1_r = NAPE_r / Km_NA_PE + NOPE_r / Km_NO_PE + NPPE_r / Km_NP_PE + NLPE_r / Km_NL_PE + NSPE_r / Km_NS_PE
c_NAT_ROB = Pancreas * b_NAT_Pancreas + Kidney * b_NAT_Kidney + Heart * b_NAT_Heart + Lungs * b_NAT_Lungs + Muscles * b_NAT_Muscles + Testis * b_NAT_Testis + Leucocytes * b_NAT_Leucocytes
slag2_b = A_b / Ki_A + O_b / Ki_O + P_b / Ki_P + L_b / Ki_L + S_b / Ki_S
slag1_b = NAPE_b / Km_NA_PE + NOPE_b / Km_NO_PE + NPPE_b / Km_NP_PE + NLPE_b / Km_NL_PE + NSPE_b / Km_NS_PE
PF_p = 1.000000e+00 / M_PF * PFM_p / Vss_PFM
F_PFM = Emax_PFM * Dose / (ED50 + Dose)

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments