A population pharmacokinetic-pharmacodynamic model of navtemadlin, its glucuronide metabolite (M1) and serum macrophage inhibitory cykokine-1 (MIC-1)

Figures & data

Figure 1. Schematic of PPK and PK/PD models. The outline indicates the addition of MIC-1 to the PPK model to create the PK/PD model. PPK model equations: $$\begin{array}{c}\text{dnc}/\text{dt}=I-\left({\mathrm{k}}_{\text{el}}+\mathrm{Q}/\mathrm{V}2\right)*\text{nc}+\mathrm{Q}/\mathrm{V}3*\text{np}+\text{MWTR}*{\text{KBR}}_{\text{MEAL}}*\text{mg}*\text{MEALTIME}\\ +\text{MWTR}*{\text{KBR}}_{\text{BASAL}}*\text{mg}\end{array}$$ $$\text{dmc}/\text{dt}={\mathrm{k}}_{\text{el}}*\text{FM}/\text{MWTR}*\text{nc}-{\mathrm{k}}_{\text{em}}*\text{mc}$$ $$\text{dnp}/\text{dt}=\mathrm{Q}/\mathrm{V}2*\text{nc}-\mathrm{Q}/\mathrm{V}3*\text{np}$$ $$\begin{array}{c}\text{dmg}/\text{dt}=\text{FA}*{\mathrm{k}}_{\text{em}}*\text{mc}-{\text{KBR}}_{\text{MEAL}}*\text{mg}*\text{MEALTIME}-{\mathrm{ }\text{KBR}}_{\text{BASAL}}*\text{mg}\end{array}$$

C: navtemadlin concentration; FA: fraction of rate M1 excreted in the gall bladder to the total M1 elimination rate k_em; FM: fraction of rate navtemadlin metabolised to M1 to the total navtemadlin elimination rate k_el; GB: gall bladder; I: amount from the absorption compartment; k_a: absorption rate; Hill: Hill coefficient; KBR_BASAL: bile acid base release rate in gall bladder; KBR_MEAL: bile acid incremental release rate in gall bladder during meal; k_el: navtemadlin elimination rate; k_em: M1 elimination rate; k_in: response formation rate; k_out: response elimination rate; M1: navtemadlin acyl glucuronide metabolite; mc: M1 amount in metabolite central compartment; MEALTIME: flag for meal time (0 for non-meal time, 1 for meal time); mg: M1 amount in gallbladder compartment; MWTR: molecular weight ratio between navtemadlin and M1; nc: navtemadlin amount in central compartment; np: navtemadlin amount in peripheral compartment; Q: intercompartmental clearance; SC₅₀: drug concentration producing 50% of S_max; S_max: maximum stimulatory effect; t: time; V2: volume of navtemadlin central compartment; V3: volume of navtemadlin peripheral compartment.

Figure 2. Visual predictive checks for the final PPK model over 0–96 h post dose (A) and 0–24 h post dose (B). Dots: observed. Lines: observed and predicted 5th, 50th, and 95th percentiles. Bands: 95% confidence intervals around predicted 5th, 50th, and 95th percentiles.

Table 1. Parameter estimates for PPK model.

Parameter	Description	Unit	Estimate	RSE (%)
ka	Absorption rate	1/hr	0.69	10.22
CL/F	Clearance of navtemadlin	L/hr	36.35	9.66
Q/F	Intercompartmental clearance	L/hr	30.30	12.69
V2/F	Central volume of navtemadlin	L	159.30	11.28
V3/F	Peripheral volume of navtemadlin	L	390.27	13.70
FM	Fraction of navtemadlin metabolism rate to M1 compared to kel	–	1 (fixed)	–
FA	Fraction of M1 entering rate to gallbladder compared to kem	–	0.1 (fixed)	–
Kem	M1 elimination rate	1/hr	36.49	10.97
Vmet	Volume of distribution for M1	L	5 (fixed)	–
KBRMEAL	Additional gallbladder mealtime emptying rate	1/hr	70 (fixed)	–
KBRBASAL	Gallbladder basal emptying rate	1/hr	0.03 (fixed)	–
FOOD_KA	Food effect on ka	–	0.64	18.32
Female_F	Fractional change in relative bioavailability for females	–	1.89	15.38
ω^2(CL/F)	Between-volunteer variance of CL/F	–	0.14	4.42
ω^2(V2/F)	Between-volunteer variance of V2/F	–	0.20	7.04
ω^2(kem)	Between-volunteer variance of Kem	–	0.21	4.75
ω^2(ka)	Between-volunteer variance of ka	–	0.11	3.94
ε^2 (navtemadlin)	Log-additive residual variance of navtemadlin	–	0.67	2.89
ε^2 (M1)	Log-additive residual variance of M1	–	0.60	3.14

ε²: variance of log-additive within-volunteer variability; RSE: relative standard error = SE/estimate × 100%; SE: standard error; ω²: variance of between-volunteer variability for that parameter.

Figure 3. Visual predictive checks for the final PK/PD model for treatments A, B, and C over 0–96 h post dose. Dots: observed. Lines: observed and predicted 5th, 50th, and 95th percentiles. Bands: 95% confidence intervals around predicted 5th, 50th, and 95th percentiles.

Table 2. Parameter estimates for final PK/PD model.

Parameter	Description	Unit	Estimate	SE	RSE (%)
kout	Response elimination rate constant	1/hr	0.05	0.005	10.00
Smax	Maximum stimulatory effect	–	6.82	1.00	14.66
SC50	Drug concentration producing 50% of maximum stimulatory effect	ng/mL	85.22	15.1	17.72
MICBL_Smax	Power effect of baseline MIC-1 on Smax (power for baseline MIC-1 multiplier for Smax: 0 = no multiplier)	–	–1.00	0.08	8.00
MICBL_SC50	Power effect of baseline MIC-1 on SC50 (power for baseline MIC-1 multiplier for SC50: 0 = no multiplier)	–	0.30	0.10	33.33
Hill	Hill coefficient (power for Concentration and SC50: 1 = no power)	–	2.02	0.18	8.91
CRP_kout	Power effect of CRP on kout (power for CRP multiplier for kout: 0 = no multiplier)	–	0.20	0.08	40.00
Female_kout	Female effect on kout (multiplier: 1 + Estimate; 0 = no multiplier)	–	0.46	0.20	43.48
AAG_Smax	Power effect of AAG on Smax (power for AAG multiplier for Smax: 0 = no multiplier)	–	–0.85	0.25	29.41
Age_Smax	Power effect of Age on Smax (power for age multiplier for Smax: 0 = no multiplier)	–	0.77	0.23	29.87
ω^2(kout)	Between-volunteer variance of kout	–	0.29	0.04	13.79
IOV(Smax)	Inter-occasion variance of Smax	–	0.11	0.04	36.36
ω^2(SC50)	Between-volunteer variance of SC50	–	0.38	0.05	13.16
ω^2(Hill)	Between-volunteer variance of Hill coefficient	–	0.40	0.07	17.50
ε^2 (MIC-1)	Log-additive residual variance of MIC-1	–	0.42	0.02	4.76

ε²: variance of log-additive within-volunteer variability; RSE: relative standard error = SE/estimate × 100%; SE: standard error; ω²: variance of between-volunteer variability for that parameter.

Figure 4. Simulated amounts of navtemadlin, M1 (left axis), and MIC-1 (right axis) concentration in various compartments and cumulative M1 excreted in bile over time after a single 60-mg dose.

Figure 5. Model-based simulations of steady state navtemadlin PK (upper panels) and glucuronide metabolite M1 PK (lower panels) for 60–480 mg navtemadlin doses given once daily for 7 days over one 28-day cycle in healthy volunteers. Curves are based on the typical healthy volunteer, i.e. the volunteer with the population parameter estimates from the PK model. The top row demonstrates navtemadlin linear scale (left panel) and a semi-log scale (right panel). The bottom row shows M1 linear scale (left panel) and a semi-log scale (right panel). Navtemadlin and M1 concentrations increase with dose. QD: once a day dosing.

Table 3. Estimated steady state (day 7) navtemadlin and M1 PK parameters (SI units) from model-based population simulations in healthy volunteers.

Navtemadlin/M1	Regimen	N	Cmax (ng/mL)	Cmin (ng/mL)	AUC (ng/mL × h)
Navtemadlin	60 mg QD	30	305 (252, 369)	37 (28, 48)	2398 (1950, 2949)
Navtemadlin	120 mg QD	30	610 (505, 737)	73 (56, 96)	4796 (3899, 5898)
Navtemadlin	180 mg QD	30	915 (757, 1106)	110 (84, 144)	7193 (5849, 8847)
Navtemadlin	240 mg QD	30	1220 (1009, 1474)	147 (112, 192)	9591 (7799, 11795)
Navtemadlin	300 mg QD	30	1525 (1262, 1843)	183 (140, 240)	11989 (9748, 14744)
Navtemadlin	360 mg QD	30	1830 (1514, 2211)	220 (167, 289)	14387 (11698, 17693)
Navtemadlin	480 mg QD	30	2440 (2019, 2948)	293 (223, 385)	19182 (15597, 23591)
M1	60 mg QD	30	80 (65, 97)	10 (7, 13)	627 (510, 771)
M1	120 mg QD	30	159 (131, 194)	19 (15, 25)	1254 (1019, 1543)
M1	180 mg QD	30	239 (196, 291)	29 (22, 38)	1881 (1529, 2314)
M1	240 mg QD	30	319 (262, 388)	38 (29, 50)	2508 (2038, 3086)
M1	300 mg QD	30	398 (327, 485)	48 (37, 63)	3135 (2548, 3857)
M1	360 mg QD	30	478 (393, 583)	58 (44, 75)	3762 (3057, 4629)
M1	480 mg QD	30	638 (523, 777)	77 (59, 100)	5016 (4077, 6172)

Values are the mean estimate with 95% confidence intervals using a t-distribution.

Note: Terminal half-life of navtemadlin is 18.2 hours with 95% confidence interval 16.9–19.5 hours. Time of maximum concentration on Day 7 for navtemadlin and M1 is 2.2 hours (standard deviation = 1.28).

AUC: area-under-the-curve on Day 7; C_max: maximum concentration on Day 7; C_min: minimum concentration on Day 7; QD: once a day dosing; T_max: time of maximum concentration on Day 7.

Figure 6. Model-based simulations of serum MIC-1 excursions for 60–480 mg doses of navtemadlin given once daily for 7 days over one 28-day cycle to healthy volunteers. Curves are based on the typical healthy volunteer, i.e. the volunteer with the population parameter estimates from the PK/PD model with median age, AAG, and CRP. MIC-1 linear scale (left panel) and semi-log scale (right panel). MIC-1 concentrations increase with dose. AAG: alpha-1-acid glycoprotein; CRP: C-reactive protein; QD: once a day dosing.

Table 4. Estimated steady state (day 7) serum MIC-1 PD parameters from model-based population simulations in healthy volunteers.

		Navtemadlin	MIC-1
Regimen	N	AUC (ng/mL × h)	Cmax (pg/mL)	Tmax (h)	Cmin (pg/mL)	AUEC (pg/mL × hr)	% of 480 mg QD dose
60 mg QD	30	2398 (1950, 2949)	710 (602, 838)	7.0 (6.6, 7.5)	665 (570, 776)	16629 (14148, 19544)	60
120 mg QD	30	4796 (3899, 5898)	834 (685, 1015)	7.4 (6.8, 8)	771 (641, 927)	19443 (16043, 23564)	70
180 mg QD	30	7193 (5849, 8847)	924 (746, 1145)	7.6 (6.9, 8.3)	849 (693, 1040)	21489 (17412, 26522)	77
240 mg QD	30	9591 (7799, 11795)	996 (795, 1248)	7.9 (7.2, 8.7)	912 (735, 1132)	23132 (18523, 28889)	83
300 mg QD	30	11989 (9748, 14744)	1057 (838, 1334)	8.2 (7.4, 9)	965 (770, 1209)	24521 (19475, 30873)	88
360 mg QD	30	14387 (11698, 17693)	1111 (875, 1409)	8.2 (7.4, 9.1)	1011 (802, 1276)	25731 (20316, 32588)	93
480 mg QD	30	19182 (15597, 23591)	1200 (939, 1534)	8.3 (7.5, 9.2)	1090 (857, 1388)	27781 (21766, 35458)	100

Values are the mean estimate with 95% confidence intervals using a t-distribution.

AUEC: area-under-the-effect-curve on Day 7; C_max: maximum concentration on Day 7; C_min: minimum concentration on Day 7; QD: once a day dosing; T_max: time of maximum concentration on Day 7.

Figure 7. Simulated dose proportionality of molar navtemadlin and M1 AUC and the MIC-1 AUEC. AUC: area-under-the-curve on Day 7; AUEC: area-under-the-effect-curve on Day 7; PK: pharmacokinetics. Values are the mean estimate with 95% confidence intervals using a t-distribution. Conversion factors from ng/mL to nM use navtemadlin molecular weight (MWt) of 568.6 gm/mole: conversion factor ng/mL to nM = 1/MWt × 1000 = 1.758706. Conversion factors from ng/mL to nM use M1 molecular weight (MWt) of 744.7 gm/mole: conversion factor ng/mL to nM = 1/MWt × 1000 = 1.342823. Conversion from pg/mL to nM uses MIC-1 molecular weight (MWt) of 24,600 gm/mole: conversion ng/mL to nM = 1/MWt × 106 = 40.650407.

Data availability statement

The authors confirm that the data supporting the findings of this analysis are available within the article and its supplementary materials.