Chemicals
Lipopolysaccharides (LPS) from Escherichia coli 0111:B4 was obtained from Sigma (Product number L4391; the same batch 036M4070V was used for both studies). The test-compound A was synthesized at Grunenthal, Aachen, Germany, and the purity of the batch used in this study was ≥ 95%. The physico-chemical properties of test compound A are presented in Table 1. Test-compound A was developed as an inhibitor of PDE4. The rat TNFα Quantikine ELISA kit was purchased from R&D systems (SRTA00, Batches P143557, P118837, and 339837). All other reagents and chemicals were of analytical grade and were obtained from standard vendors.
Table 1 Physico-chemical properties of compound A Animals
The studies were conducted in male Sprague–Dawley rats, approximately 210–260 g of body weight, purchased from Vital River Laboratory Animals Co. LTD. All rats were housed in groups under 12 h light/dark cycle with ad libitum access to food and water. During the study, animals were not fasted, but no food was provided prior to dosing until 3 h after drug dosing. All animals were handled in strict accordance with the Guide for the Care and Use of Laboratory Animals in an AAALAC-accredited facility. All animal studies were approved by an established Institutional Animal Care and Use Committee (IACUC).
Design of in vivo studies
LPS was dissolved in saline at 0.0006, 0.006, and 0.06 mg·mL−1 and 5 mL·kg−1 of the solutions were dosed intravenously via foot dorsal vein injection to give doses of 3, 30 and 300 µg·kg−1, respectively. Test-compound A was suspended in 1% HPMC (5 mPa s, Colorcon) and 0.5% Tween 80 (Sigma) in water at concentrations of 0.06, 0.6, and 6 mg·mL−1. Test-compound A was administered at a volume of 5 mL·kg−1 by oral gavage, resulting in doses of 0.3, 3 and 30 mg·kg−1, respectively.
Forty-eight normal male Sprague–Dawley rats were used in the LPS-induced TNFα-response model in the absence (Study 1) or presence (Study 2) of test-compound A (Fig. 1). The animals were randomly divided into eight groups (n = 6). In Study 1, four groups of animals were given increasing intravenous doses of LPS (0, 3, 30 and 300 μg·kg−1 LPS). In Study 2, four groups of animals received a fixed intravenous dose of LPS challenger of 30 μg·kg−1 and increasing oral doses of test compound (0, 0.3, 3 and 30 mg·kg−1 compound A). Test compound was administered two hours before the challenge with LPS. Blood samples were drawn for quantification of Test-compound A and TNFα before dosing of test compound (at − 2 h) and at − 1, 0, 0.5, 1, 1.5, 2, 3, and 4 h after LPS dosing (Fig. 2). Blood samples were collected into EDTA-2K tubes via tail vein or cardiac puncture for terminal bleeding. Samples were stored on ice and centrifuged at 2000×g for 5 min at 4 °C within 15 min after sampling. Each plasma sample was divided into two aliquots, one for LC-MS/MS analysis to measure test compound concentrations, and one for ELISA analysis to measure the biomarker TNFα concentrations. Until quantification, the plasma samples were stored at −70 °C after snap-freezing of plasma in dry ice.
Table 2 summarizes the experimental design of the two studies. Study 1 was conducted to characterize the dose-response-time relationships of the TNFα-release after LPS challenge and to define an appropriate LPS challenge dose. Study 2 investigated the inhibition of this response by Test-compound A using a fixed LPS challenge dose and three inhibitory test-compound doses. Full response time courses for TNFα were obtained and analyzed by modelling. The test-compound concentrations over time were measured as well, but the actual exposure to LPS could not be quantified due to the nature of LPS, which consists of a poorly defined mixture of different components of the bacterial cell wall.
Table 2 Overview of experimental designs of the two individual studies Bioanalytical methods
Quantification of TNFα concentrations by ELISA
TNFα concentrations in plasma were quantified with the rat TNFα Quantikine ELISA Kit (R&D Systems, SRTA00) according to the instructions provided in the kit, using seven calibrations standards ranging from 12.5 to 800 ng·L−1. The measured concentrations of the quality controls were all in the range as specified in the kit instruction and showed CV % < 20%. The lower limit of quantification (LLOQ) was 12.5 ng·L−1 and lower values were reported as “<LLOQ” and excluded from subsequent evaluation and parameter estimation.
Quantification of test-compound A concentrations by LC-MS/MS
For the quantification of the test compound, acetonitrile which contained dexamethasone as internal standard was added to plasma prepared from the blood samples for protein precipitation. Supernatants were injected onto a C18 reversed phase column for LC-MS/MS analysis. The UPLC separation was carried out using a gradient elution in H2O containing 0.025% formic acid/1 mM NH4OAc (mobile phase A) and methanol that contained 0.025% formic acid/1 mM NH4OAc (mobile phase B). The analytes were quantified on an API5500 mass spectrometer using multiple reaction monitoring with appropriate mass transitions. Each set of samples was run together with two calibration sets containing nine non-zero standard concentrations covering a range of range from 1 to 3000 nM. Quality controls of 3, 500, and 2400 nM were interspersed between the samples. The calculated concentrations of the calibration samples and quality controls were within ± 15% of the nominal values (20% at LLOQ) for at least 75% and 67% of the samples, respectively. Concentrations below 80% of the LLOQ (i.e. below 0.8 nM) were reported as “<LLOQ” and excluded from subsequent evaluation and parameter estimation.
Pharmacokinetic and pharmacodynamic models
Test compound kinetics
The impact of test compound on the TNFα-response is shown conceptually in Fig. 3a and b. The first-order loss of test compound from the gut is given by Eq. 1.
$$ \frac{{{\text{d}}A_{ab} }}{{{\text{d}}t}}\, = \, - \,k_{a} A_{ab} $$
(1)
The plasma exposure to test compound was then described by a one-compartment model with first-order oral input and Michaelis–Menten elimination.
$$ V_{p} \cdot \frac{{{\text{d}}C_{p} }}{{{\text{d}}t}}\, = \,{\text{F}} \cdot k_{a} \cdot A_{ab} \, - \,\frac{{V_{max} \cdot C_{p} }}{{K_{m} \, + \,C_{p} }} $$
(2)
Aab denotes amount of test compound in the gut, Cp exposure to drug in plasma, ka the first-order absorption rate constant, Vmax maximum rate of elimination, Km the Michaelis–Menten constant, and Vp volume of distribution. The bioavailability F was set to unity.
LPS challenge model
The impact of the LPS challenge on the TNFα-response is shown conceptually in Fig. 3b and c. The intravenous LPS dose is injected into plasma as a bolus and cleared from plasma via first-order elimination.
$$ \frac{{dA_{LPS} }}{dt}\, = \, - \,k_{LPS} A_{LPS} $$
(3)
The level of LPS in plasma triggers a series of transduction compartments with a saturable process ALPS / (Km, LPS + ALPS). The S3 signal acts on the build-up of TNFα-response via stimulatory action (S(S)3). The transduction of LPS-induced signal from S1 through S3 is given by Eq. 4.
$$ \begin{aligned} \frac{{{\text{d}}s_{\textit{1}} }}{{{\text{d}}t}}\, & = \,k_{s} \cdot \left( {\frac{{A_{LPS} }}{{K_{m,\,LPS} \, + \,A_{LPS} }} - S_{\textit{1}} } \right) \\ \frac{{{\text{d}}s_{\textit{2}} }}{{{\text{d}}t}}\, & = \,k_{s} \cdot \left( {S_{\textit{1}} \, - \,S_{\textit{2}} } \right) \\ \frac{{{\text{d}}s_{\textit{3}} }}{{{\text{d}}t}}\, & = \,k_{s} \cdot \left( {S_{\textit{2}} \, - \,S_{\textit{3}} } \right) \\ \end{aligned} $$
(4)
ALPS is LPS amount in the biophase and S1 to S3 are a chain of transduction compartments which act as signaling compartments. LPS is thought to be eliminated with rate constant kLPS. Signal S1 is stimulated non-linearly by LPS with Michaelis–Menten constant Km. Rate constant ks describes transfer of signal across S1 to S3 and loss from system.
TNFα turnover model
Figure 3b shows conceptually the TNFα turnover R and the impact of both the LPS challenge and the test compound kinetics on the TNFα-response. The dynamics of TNFα-response is divided into a central R and a peripheral Rt pool governed by a first-order inter-compartmental rate constant kt, in order to capture the post-peak bi-phasic decline of response. The irreversible loss of TNFα occurs from its central compartment via a first-order rate process kout· R.
The stimulatory action via S3 of LPS-induced challenge is given by Eq. 5.
$$ {S}\left( {{S}_{\textit{3}} } \right) = \,\frac{{S_{ max } \cdot S_{\textit{3}}^{\gamma } }}{{SC_{\textit{50}}^{\gamma } + S_{\textit{3}}^{\gamma } }} $$
(5)
Smax is the maximum LPS stimulatory production rate of TNFα, and SC50 is the corresponding transducer concentration S3 where 50% of maximum rate occurs. The inhibitory action of test compound I(Cp) on build-up of response is.
$$I(C_p) = 1 - \frac{I_{max} \cdot C_p}{IC_{\textit{50}} + C_p}$$
(6)
The structure of Eq. 6 allows a partial Imax inhibitory effect of the test compound. The IC50 parameter denotes the concentration of test compound resulting in 50% of maximal test-compound inhibitory capacity.
Equations 5 and 6 are then combined in Eq. 7 describing the TNFα-response in the central R and peripheral Rt compartments.
$$ \begin{aligned} \frac{{{\text{d}}R}}{{{\text{d}}t}} & & = S(S_{\textit{3}} ) \cdot I(C_{p} ) - k_{out} R + k_{t} \cdot \left( {R_{t} - R} \right) \\ \frac{{{\text{d}}R_{t} }}{{{\text{d}}t}} & = k_{t} \cdot (R - R_{t} ) \\ \end{aligned} $$
(7)
Smax is the maximum stimulatory capacity, SC50 concentration of S3 at 50% of maximum stimulation, γ a Hill exponent, Imax maximum inhibitory capacity by test compound and IC50 test compound potency. Neither S1, S2 or S3, nor TNFα-response display any baseline concentrations in the proposed model. Without any stimulation from LPS there is no TNFα-response to inhibit with test compound.
The determinants of the TNFα-response at equilibrium are given by Eq. 8.
$$ R_{\text{eq}} = \frac{1}{{k_{out} }} \cdot S(S_{\textit{3}} ) \cdot I(C_{p} ) = \frac{1}{{k_{out} }} \cdot \frac{{S_{ max } \cdot S_{\textit{3}}^{\gamma } }}{{SC_{\textit{50}}^{\gamma } + S_{\textit{3}}^{\gamma } }} \cdot \left( {1 - \frac{{I_{ max } \cdot C_{p} }}{{IC_{\textit{50}} + C_{p} }}} \right) $$
(8)
This expression is presented as a 3D-plot in Appendix 2 using the final parameter estimates from regressing TNFα response time data.
Data analysis
Non-linear mixed-effects modelling (NLME) [13] was used to regress the model in Fig. 3 to TNFα-response data and to capture inter-individual variability (IIV). The number of animals was small (18 and 17 subjects in Study 1 and 2, respectively). Therefore, the IIV estimation was restricted to Vmax, kLPS, SC50, kout, Imax and IC50 (See Appendix). Residual variance of compound exposure was modelled with an additive error model on the log-scale and for response concentrations with a proportional error model.
Model parameters were estimated using Monolix [20], including stochastic approximation for the determination of standard errors. In step 1, parameters in Eqs. 3–5 and 7 were based on TNFα-responses from Study 1. The pharmacokinetic parameters in Eqs. 1 and 2 were estimated from test compound data from Study 2. The pharmacokinetic parameters were then fixed together with systems parameters from Step 1, and Imax and IC50 were estimated from Study 2 data. Further computational details can be found in Appendix 1.