Multiscale systems pharmacological analysis of everolimus action in hepatocellular carcinoma

  • Anusha Ande
  • Maher Chaar
  • Sihem Ait-Oudhia
Original Paper


Dysregulation of mTOR pathway is common in hepatocellular carcinoma (HCC). A translational quantitative systems pharmacology (QSP), pharmacokinetic (PK), and pharmacodynamic (PD) model dissecting the circuitry of this pathway was developed to predict HCC patients’ response to everolimus, an mTOR inhibitor. The time course of key signaling proteins in the mTOR pathway, HCC cells viability, tumor volume (TV) and everolimus plasma and tumor concentrations in xenograft mice, clinical PK of everolimus and progression free survival (PFS) in placebo and everolimus-treated patients were extracted from literature. A comprehensive and multiscale QSP/PK/PD model was developed, qualified, and translated to clinical settings. Model fittings and simulations were performed using Monolix software. The S6-kinase protein was identified as critical in the mTOR signaling pathway for describing everolimus lack of efficacy in HCC patients. The net growth rate constant (kg) of HCC cells was estimated at 0.02 h−1 (2.88%RSE). The partition coefficient of everolimus into the tumor (kp) was determined at 0.06 (12.98%RSE). The kg in patients was calculated from the doubling time of TV in naturally progressing HCC patients, and was determined at 0.004 day−1. Model-predicted and observed PFS were in good agreement for placebo and everolimus-treated patients. In conclusion, a multiscale QSP/PK/PD model elucidating everolimus lack of efficacy in HCC patients was successfully developed and predicted PFS reasonably well compared to observed clinical findings. This model may provide insights into clinical response to everolimus-based therapy and serve as a valuable tool for the clinical translation of efficacy for novel mTOR inhibitors.


Quantitative systems pharmacology Hepatocellular carcinoma Everolimus 


Hepatocellular carcinoma (HCC) is the third most common cause of cancer mortality worldwide [1]. Several studies have suggested that the rates of incidence of HCC keep on increasing with more than a two-fold rise between 1985 and 2002, with an average age of 65 years at diagnosis [2, 3, 4]. The 5-year survival rate for untreated HCC is estimated to be less than 5% [4], an indication of poor prognosis for patients with advanced HCC. The existing treatment options are either curative or palliative, where localized treatments (loco-regional) such as surgical resection, liver transplant, and resection are considered curative, while systemic chemotherapy is considered as palliative [5]. However, more than 80% of patients present with unresectable disease or with a high recurrence resected disease [6], which makes it harder to use traditional curative treatments. Sorafenib, a multikinase inhibitor, is the only available targeted systemic therapy proven efficacious in HCC with an improved patients overall survival [7, 8]. However, acquired resistance to sorafenib during or after therapy necessitates the search for alternative effective targeted therapies. Novel therapeutic targets for patients with advanced HCC is still an area warranting further investigations due to its high unmet medical need condition [1].

The phosphatidylinositol 3-kinase/AKT/mammalian target of rapamycin (PI3K/AKT/mTOR) pathway plays an important role in regulating cell growth, angiogenesis, cell proliferation and survival [9]. Activation of the PI3K/AKT pathway leads to the phosphorylation of mTOR, followed by a positive regulation of the ribosomal p70S6 kinase (p70S6K) and the eukaryotic initiation factor 4E (Eif4E) binding protein 1 (4EBP1) [9]. It is reported that the PI3K/AKT/mTOR transduction signaling pathway is activated in 30–50% of HCC patients, and that the p70S6K protein is aberrantly activated in 50% of HCC patients [10]. Altogether, the PI3K/AKT/mTOR pathway plays a pivotal role in HCC, and targeting this pathway has become an attractive therapeutic intervention for this devastating disease.

Everolimus (Afinitor®, Novartis Pharmaceuticals) is an oral inhibitor of mTOR that was originally developed as an immunosuppressive macrolide [11]. It is mainly approved for the treatment of patients with advanced renal cell carcinoma (RCC) after treatment failure with sunitinib or sorafenib [11]. Presently, its clinical use has been expanded to the treatment of breast cancer, progressive neuroendocrine tumors of pancreatic origin, renal angiomyolipoma, and tuberous sclerosis complex [12]. Everolimus acts by binding to the FK binding protein (FKBP-12), resulting in the formation of the mTORC1 inhibitory complex. This leads to the inhibition of the mTOR kinase activity and a reduction in the S6K expression [13]. Preclinical studies have demonstrated the effectiveness of mTOR inhibitors such as everolimus and sirolimus at inhibiting tumor growth and reducing blood vascularity in HCC xenograft mice [14, 15]. In an early phase 1 and phase 2 studies involving patients with advanced HCC, everolimus was found to be well-tolerated with a potential of stabilizing the progression of the disease [16, 17]. Furthermore, it showed a disease control rate of 44% in the phase 1/2 clinical trial [17]. However, in a large randomized, double-blind, phase 3 clinical trial (EVOVLE-1) [18], everolimus failed to improve the overall survival and progression free survival (PFS) of these patients [18], thus, restraining its clinical application in HCC.

In this study, we developed a translational and multiscale computational modeling platform for everolimus in HCC that quantitatively describes: (i) intracellular protein dynamics of the PI3K/AKT/mTOR signaling pathway and HCC cells (Huh7) viability in response to in vitro drug exposure; (ii) time course of plasma and tumor concentrations, and tumor volume reduction under everolimus treatment in xenograft mice; and (iii) clinical PK and PFS. This model allowed to link the delay between in vivo drug exposure and tumor growth inhibition, and clinical drug exposure and PFS. In addition, the model allowed to explore whether increased everolimus delivery to tumor improves PFS. Our study indicates that multiscale and translational systems models of drug action provide insights into the regulation of intracellular biomarkers by everolimus and can connect these regulators to in vivo tumor burden dynamics and clinical PFS. This model may serve as a modeling platform to rationally examine new dosing regimens for everolimus as a single agent and in combination, as well as explore novel therapeutic targets in HCC on the PI3K/AKT/mTOR signaling pathway.

Materials and methods

Drugs and cell culture materials

The human HCC cell line Huh7 was purchased from ATCC. Everolimus was purchased from Selleckchem, Houston, TX, USA. Cells were maintained in high-glucose Dulbecco’s modified Eagle’s medium (DMEM; HyClone, Logan, UT) containing 4.0 mM l-glutamine and sodium pyruvate, and supplemented with 10% fetal bovine serum (FBS, Sigma Aldrich, MO), 1% penicillin–streptomycin solution. In all experiments, cells were incubated for 48 h at 37 °C with 5% CO2. Cells were passaged weekly twice to maintain sub-confluency.

Cell cycle assay

Cell cycle assay was performed in Muse™ Cell Analyzer (EMD Millipore, Billerica, MA) using Muse™ Cell Cycle Kit (Catalog No. MCH100106). Samples were prepared by seeding Huh7 cells in a 6-well plate at 0.3 million cells per well. Cells were allowed to adhere for overnight. The next day cells were serum-starved for about 24 h (for synchronization) followed by replacement with complete medium for 6 h. Cells were treated with 50 μM everolimus for 48 h in triplicate. For harvesting, the medium was removed followed by a wash with PBS and trypsinization to detach from the plate. Fresh medium containing serum was added to each well to reach a final concentration of 1 × 106 cells/mL. Cell samples were transferred to a 12 × 75-mm polystyrene tube and centrifuged at 300×g for 5 min. The supernatant was discarded and the cell pellet was washed with PBS, then suspended in 50 μL of PBS by thorough pipetting. Later, the cell suspension was re-suspended in 1 mL of 70% ice-cold ethanol while vortexing at medium speed. Tubes were capped and frozen at − 20 °C for at least 3 h. For staining, 200 μL of above fixed cells were transferred to a fresh polystyrene tube and centrifuged at 300×g for 5 min. The cell pellet was washed with PBS and then resuspended in 200 μL of Muse™ Cell Cycle Reagent. Tubes were incubated for 30 min protected from light followed by analysis for cell cycle phase distribution in Muse™ Cell Analyzer.

Sources of the data

Data were extracted from literature using the WebPlotDigitizer version 3.9 software [19]. They included: (1) The time course of key signaling proteins in the PI3K/AKT/mTOR pathway including pmTOR, pS6, IRS, pAKT, Huh7 cells viability, and xenograft mice tumor volume under everolimus treatment [20]. (2) Everolimus plasma and tumor concentrations time profiles in xenograft mice [21]. (3) Clinical pharmacokinetic (PK) profile of everolimus [22]. (4) Progression free survival in placebo [8] and everolimus treated patients [17].

Step 1: in vitro model

Through intense literature search on the mechanism of action of everolimus, we identified few key signaling proteins in the PI3K/Akt/mTOR pathway to build the protein network model as shown in our research strategy (Fig. 1). Transduction proteins with available experimental data of temporal change in their dynamics are depicted in yellow (Fig. 2). Briefly, everolimus inhibits protein expression of phosphorylated mTOR (pmTOR), which further inhibits two main downstream effectors: the eukaryotic translation initiation factor 4E-binding protein 1 (4eBP1 (EIF4EBP1)) and ribosomal protein S6 kinase 1 (p70S6K). Both proteins, 4eBP1 and p70S6K, are regulators of the translation of mRNA of various proteins stimulating the synthesis of other proteins involved in cell proliferation [23]. The inhibition of pS6 kinase by an mTOR inhibition disturbs the homeostatic feedback loop and leads to a counter AKT activation mediated by upregulation of IRS1 [24].
Fig. 1

Flowchart of the proposed multiscale quantitative systems pharmacology (QSP), pharmacokinetic (PK) and pharmacodynamic (PD) modeling and simulation strategy for the preclinical-to-clinical translation of everolimus action in hepatocellular carcinoma (HCC)

Fig. 2

Intracellular signal transduction pathway depicting the mechanism of action of everolimus on cancer cell proliferation and survival. The observed data available from literature include the time course profiles of the fold change from control in the expression of the proteins colored in yellow, and the inhibition of cellular proliferation of Huh7 cells under everolimus treatment at 100 nM [20]. In brief, everolimus inhibits the expression of the phosphorylated mTOR (pmTOR) protein, which in turn inhibits two main downstream effectors: eukaryotic translation initiation factor 4E-binding protein 1 (4eBP1 (EIF4EBP1)) and ribosomal protein S6 kinase 1 (p70S6K). Both 4eBP1 and p70S6K stimulate the synthesis of several proteins involved in cell proliferation and survival [23]. Inhibition of pS6 kinase leads to a feedback activation of AKT mediated by upregulation of IRS1 [24]

Protein network dynamic model

The time course profiles of all proteins obtained from the literature include the measurements of the fold-change from the control of pmTOR, pS6, IRS and pAKT in Huh7 cells upon treatment with everolimus at 100 nM for durations ranging from 3 to 72 h. The final in vitro protein model is depicted in Fig. 3. The four basic indirect response models [25] were used to build the reduced network model. The model translates such as: everolimus inhibits the production of the pmTOR protein, which is a downstream target that is inherently activated by the pAKT protein. The set of differential equations describing the model are:
$$\frac{{d\left( {pmTOR} \right)}}{dt} = k_{syn\_pmTOR} . \left[ {(1 - \left( {I_{EVE} . C_{EVE} } \right))} \right] - k_{deg\_pmTOR} . pmTOR$$
$$\frac{{d\left( {pS6} \right)}}{dt} = k_{syn\_pS6} .\left( {\frac{pmTOR}{{pmTOR_{0} }}} \right)^{\gamma pmTOR} - k_{deg\_pS6} .pS6$$
$$\frac{{d\left( {IRS} \right)}}{dt} = k_{syn\_IRS} \cdot \left( {\frac{{pS6_{0} }}{pS6}} \right)^{\gamma pS6} - k_{deg\_IRS} \cdot IRS$$
$$\frac{{d\left( {pAKT} \right)}}{dt} = k_{syn\_pAKT} .(1 + (S_{IRS} . IRS)) - k_{deg\_pAKT} . pAKT$$
where \(k_{syn\_i}\) and \(k_{deg\_i}\) are the zero order production rates and first-order degradation rate constants for the ith measured protein. \(C_{EVE}\) is the static in vitro concentration of everolimus (100 nM), \(I_{EVE}\) is the linear inhibitory slope of everolimus on pmTOR, \(S_{\text{i}}\) is the stimulatory slope of the ith protein of interest, \(\gamma^{i}\) is the power coefficient for the ith protein of interest. Since all protein measurements are modeled as fold-change from baseline, all initial conditions of Eqs. 1, 2, 3, and 4 are set equal to 1 \((i\left( 0 \right) = i_{0} = 1)\),  with i0 being \(pmTOR_{0},\) \(pS6_{0},\) \(IRS_{0}, or\) \(pAKT_{0}\), the initial conditions for pmTOR, pS6, IRS and pAKT proteins. Hence, since the secondary parameter \(k_{syn\_i} = i_{0} \cdot k_{{deg_{i} }}\), then \(k_{syn\_i}\) is equal to \(k_{deg\_i}\) for pmTOR, pS6, IRS, while \(k_{syn\_i}\) is equal to \(k_{deg\_i} /(1 + S_{IRS} )\) for pAKT.
Fig. 3

Schematic representation of the mathematical models used for the multiscale QSP/PK/PD analysis. a In vitro cell-based pharmacodynamic model for the mechanism of action of everolimus in hepatocellular carcinoma (HCC). R represents the Huh7 cancer cell proliferation in vitro. b Hybrid physiologically-based pharmacokinetic (PBPK) and pharmacodynamic (PD) model for the characterization of the observed plasma and tumor PK data in xenograft mice. c Clinical translation of the mathematical model using a hybrid-PBPK/PD model for plasma and tumor PK in HCC patients, and model-based simulations for the protein network model, tumor growth profiles, and progression free survival (PFS) to predict the clinical efficacy of everolimus

Inhibition of cell proliferation model

Since pS6 promotes the transcription of cellular proliferation genes, the cell proliferation (R) (Fig. 3) was modulated by the protein pS6 stimulating the growth of Huh7 cells \(k_{g}\) (first order growth rate constant). Both cell proliferation profiles for control (Rc) and everolimus treated Huh7 cells (REVE) are modeled with an exponential growth model:
$$\frac{{d\left( {R_{c} } \right)}}{dt} = k_{g} .R_{c} , \quad R_{c} \left( 0 \right) = R_{c\_0}$$
$$\frac{{d\left( {R_{EVE} } \right)}}{dt} = pS6^{\gamma g } . k_{g} .R_{EVE} ,\quad R_{EVE} \left( 0 \right) = R_{EVE\_0}$$
where kg is the first-order growth rate constant of the Huh7 cells, \(\gamma^{g}\) is the power coefficient for the pS6 effect on cell proliferation, \(R_{c\_0}\) is the initial control cell number (20.15 × 103 cells), \(R_{EVE\_0}\) is the initial everolimus treated cell number (20.42 × 103 cells).

Step 2: in vivo model

Hybrid-physiologically-based pharmacokinetic (PBPK) model

Plasma and tumor time course profiles of everolimus used in the hybrid-PBPK model were obtained from [21]. The hybrid-PBPK model is represented in Fig. 3. It consists of a one compartment systemic model describing the plasma everolimus concentration profile linked to a single tumor compartment characterizing everolimus concentrations in tumor. The differential equations for this model are:
$$\frac{{dA_{a} }}{dt} = - k_{a } . A_{a} , \quad A_{a} \left( 0 \right) = Dose$$
$$\frac{{dA_{c} }}{dt} = k_{a } . A_{a} - Cl_{mice} \left( {\frac{{A_{c} }}{{V_{c} }}} \right),\quad A_{c} \left( 0 \right) = 0$$
$$\frac{{dC_{tu\_mice} }}{dt} = \frac{{Q_{tu\_mice} }}{{V_{tu\_mice} }}. \left( {\frac{{A_{c} }}{{V_{c} }} - \frac{{C_{tu\_mice} }}{{k_{p} }}} \right),\quad C_{tu} \left( 0 \right) = 0$$
where Aa and Ac are the amounts of everolimus in the absorption and central compartments, Vc is the central volume of distribution, Clmice is the linear clearance of everolimus from the central compartment, Ctu-mice is the concentration of drug in the tumor compartment, Qtu-mice is the estimated tumor blood flow, kp is the estimated partition coefficient, Vtu-mice is the tumor volume in xenograft mice treated with a single oral dose of 5 mg/kg everolimus and is equal to 300 mm3.

Preclinical tumor growth inhibition (TGI) model

A TGI model was developed to characterize the time course profiles of the tumor volume in unperturbed (control) and everolimus treated HCC xenograft mice [20]. Everolimus intra-tumor concentrations were simulated using the final hybrid-PBPK model, and used as a driver on the transduction signaling protein network as shown in step 2 in Fig. 1. Since pS6-kinase protein is the critical protein responsible for the cellular proliferation, it is used to drive the tumor growth by acting on the HCC tumor growth. The equation for the TGI model is:
$$\frac{{d\left( {V^{\prime}_{tu\_mice} } \right)}}{dt} = k^{\prime}_{g} .pS6 \cdot V^{\prime}_{tu\_mice} ,\quad V^{\prime}_{tu\_mice} \left( 0 \right) = 42\ {\text{mm}}^{3}$$
where \(k^{\prime}_{g}\) is the first-order net tumor growth rate constant mediated by cycling cells.

Step 3: pre-clinical-to-clinical translational strategy

Clinical pharmacokinetics

In order to obtain the clinical exposure of everolimus, an existing population PK model developed from the PK data of patients treated with a daily dose of 10 mg of everolimus from [22] was used. This plasma PK model was linked to a tumor compartment through a partition coefficient (kp) obtained from our pre-clinical model and a tumor blood flow (Qtu-human) fixed from [26]. The final clinical hybrid-PBPK model [27] for everolimus was used to simulate intra-tumor drug concentrations. The set of differential equations translate as:
$$\frac{{dA_{a} }}{dt} = - k_{a } . A_{a} , \quad A_{a} \left( 0 \right) = Dose$$
$$\frac{{dA_{c} }}{dt} = k_{a } . A_{a} - Cl_{human} \cdot \left( {\frac{{A_{c} }}{{V_{c} }}} \right) - Q_{human} \left( {\frac{{A_{c} }}{{V_{c} }} - \frac{{A_{p} }}{{V_{p} }}} \right),\quad A_{c} (0) = 0$$
$$\frac{{dA_{p} }}{dt} = Q_{human}\left( {\frac{{A_{c} }}{{V_{c} }} - \frac{{A_{p} }}{{V_{p} }}} \right),\quad A_{p} \left( 0 \right) = 0$$
$$\frac{{dC_{tu\_human} }}{dt} = \frac{{Q_{tu\_human} }}{{V_{tu\_human} }}. \left( {\frac{{A_{c} }}{{V_{c} }} - \frac{{C_{tu\_human} }}{{k_{p} }}} \right),\quad C_{tu} \left( 0 \right) = 0$$
where Aa and Ac are the amounts of everolimus in the absorption and central compartments, Vc and Vp are the central and peripheral volumes of distribution, Clhuman is the linear clearance of everolimus from the central compartment, Qhuman is the inter-compartment clearance of everolimus, Ctu-human is the concentration of drug in the tumor compartment, Qtu-human is the tumor blood flow fixed from [26], kp is the estimated partition coefficient from the preclinical hybrid-PBPK model, Vtu-human is the tumor volume from Eq. 10 adapted to patients such as detailed below (Pharmacodynamics section).

Clinical in vitro and in vivo pharmacodynamics

The hybrid-PBPK model was used to simulate the tumor concentrations of everolimus. The latter influenced the temporal changes in the dynamics of the intracellular transduction signaling proteins in the PI3K/Akt/mTOR pathway (Step 1) to simulate the in vivo proteins responses. The TGI model (Eq. 15) was used to simulate the time trajectory of tumor volume in patients with HCC. To adapt the HCC xenograft mice model to HCC patients, a human first-order growth rate constant \(k^{\prime\prime}_{g}\) was calculated from the doubling time of HCC tumor volume in naturally progressing HCC patients [28] such as \(TVDT = \frac{Ln(2)}{{k^{\prime\prime}_{g} }}\). Additionally, the patients initial tumor volume (10.5 cm3) and the maximum achievable tumor volume (870.8 cm3) were obtained from [28] (ICs in Table 3).
$$\frac{{d\left( {V_{tu\_human} } \right)}}{dt} = k^{\prime\prime}_{g} \cdot pS6 \cdot V_{tu\_human} \cdot \left( {1 - \frac{{V_{tu\_human} }}{{V_{{tu\_human_{\hbox{max} } }} }}} \right)$$

Step 4: clinical endpoint—predictions of progression free survival (PFS)

A Monte Carlo simulation with 30% variability on the parameter \(k^{\prime\prime}_{g}\) was performed to generate the tumor volume time course profiles of 250 patients with HCC for three scenarios: (i) placebo (no treatment), (ii) everolimus therapy at 10 mg/day during 24 weeks, and (iii) same regimen as in (ii), but with a 10-fold higher tumor partition coefficient (kp) to examine the effect of an enhanced delivery of everolimus to the tumor on the PFS. The individual tumor volumes (TV) were used to calculate the corresponding tumor diameters (DTumor), assuming a spherical shape of the tumors such as: \(D_{Tumor} = 2 \cdot R_{Tumor} = \left[ {\frac{3 \cdot TV}{4\pi }} \right]^{{\frac{1}{3}}}\), with RTumor being the radius of the tumor. Based on the Response Evaluation Criteria in Solid Tumors (RECIST) criteria [29], tumor progression was recorded when diameter value was greater than 20% of its baseline value. The PFS values were calculated from the simulated tumor diameters every month up to 8 months. For comparison, the simulated PFS profiles were superimposed over the observed data from placebo [8] and everolimus [17] treated patients. Additionally, the 95% confidence intervals on the PFS curves were generated.

Data analysis

All in vitro data were modeled simultaneously including pmTOR, pS6, IRS and pAKT, and cell proliferation. In vivo xenograft PK and PD data were also modeled. The software Monolix 2016 R1 was used [30]. Model parameters were estimated using the SAEM algorithm. A proportional error variance model was used for model fittings of in vitro and in vivo PD variables, with Y = F + bFε, where Y is the observation at time t, F is the model-predicted value at time t, ε is a sequence of independent random variables normally distributed with mean 0 and variance 1, and b is the error parameter. A constant error variance model was used for model fittings of in vivo PK data such as Y = F + aε, where a is the error parameter. Model performance was evaluated by goodness-of-fit parameters including Akaike Information Criterion (AIC), visual inspection of observed vs predicted plots and the % relative standard error (%RSE) of the estimated parameters.

For PFS, the simulated tumor diameters from the 250 patients were given a binary score of 0 or 1 at every time point based on the progression criteria outlined in the RECIST criteria. From the above-obtained scores, percentage survival along with the 95% confidence interval at each time point were calculated using Kaplan–Meier method in GraphPad Prism 5 version.

The statistical significance for the  %cell distribution in the phases G0/G1, S, and G2/M under everolimus treatment at 50 µM compared to control (no drug) in the cell cycle arrest experiments was examined using a Student’s t test. A P value < 0.05 was considered to be statistically significant.


The four steps approach adopted in our multiscale QSP/PK/PD model development are depicted in Fig. 1. In the first step, temporal changes of key proteins of the PI3K/AKT/mTOR signaling transduction pathway following everolimus treatment of Huh7 cells were characterized. In the second step, everolimus PK in plasma and tumor tissue of xenograft mice were captured well with a hybrid-PBPK model, and the intra-tumor drug concentrations were used to simulate the time course profiles of the proteins in the protein network built in step 1. The protein pS6 was identified as a driver for the inhibition of the tumor growth and aided at capturing well the xenograft mice tumor volume reduction over time. In the third step, a clinical translation of our pre-clinical model was performed followed with model simulations, where using a clinical hybrid-PBPK model with everolimus tumor concentrations driving the dynamics of intracellular signaling proteins, and the latter driving the tumor volume time trajectory. In the fourth step, PFS of patients with HCC were simulated for placebo, clinical regimen of everolimus, and increased penetration of intra-tumor everolimus concentrations.

Step 1: in vitro model

Protein network

The in vitro cell-based and enhanced pharmacodynamic (ePD) model depicting the interplay between the four major proteins in the PI3K/AKT/mTOR signaling pathway including pmTOR, pS6, IRS, and pAKT is shown in Fig. 3. The model captures well the time course profiles of all four measured proteins (Fig. 4a–d). Further, we simulated the time course of protein responses for different dose levels at 50 and 75 nM as shown in Suppl. Figs. 5a and b.
Fig. 4

Time course profiles of the in vitro molecular and cellular responses post a continuous exposure to everolimus at 100 nM. Relative protein expressions to control profiles are shown for pmTOR (a), pS6 (b), IRS (c), pAKT (d), where observed data are represented with red solid symbols and model fittings are represented with solid red lines. The inhibition of cellular proliferation (e), where solid circles represent observed data with blue for the control (untreated cells) and red for cells treated with everolimus at 100 nM. Solid lines represent model fittings for the control (red line) and treated cells with everolimus at 100 nM (blue line). Solid green and purple lines represent model predictions for the simulated time course profiles of cellular response under everolimus treatment at 50 nM (green) and 75 nM (purple). The measured % cell distribution of cancer cells in the various phases of a cell-cycle (G0, G1, S, M) at 48 h post-exposure to everolimus at 50 µM (f). (**p < 0.01, Student’s t-test)

Inhibition of cellular proliferation and cell cycle arrest

Figures 4e and f recapitulates model fittings related to everolimus inhibition of Huh7 cancer cells proliferation responses (Fig. 4e). The simulated time course profiles of the inhibition of Huh7 cellular proliferation by everolimus at the concentrations of 50 and 75 nM predicted lower responses with increasing dug concentrations. The % cell distribution of Huh7 cells in the various phases of the cell cycle after 48 h exposure to everolimus at 50 µM is depicted in Fig. 4f. From several literature reports and our own results, everolimus is known to exhibit its anti-proliferative activity primarily by blocking cancer cells in the phase G0/G1 of the cell cycle [31, 32], owing to its cytostatic mechanism of action. Our findings demonstrate that 50 µM everolimus treatment caused ~ 11% increase in the number of Huh7 cells in the phase G0/G1 of the cell cycle. This result is further supported with a statistical significance in the difference from the control with a p value < 0.01 using a Student’s t-test. Table 1 summarizes all fitted parameters and their precisions (%RSE). The parameter kg is estimated at 2 × 10−2 h−1, which corresponds to a doubling time of ~ 34.6 h as calculated with the formula: \(\frac{Ln(2)}{{k_{g} }}\). This result is consistent with literature reports on the Huh7 cells doubling time of 24 h [33].
Table 1

Fitted parameters of the in vitro cell-based pharmacodynamic model and their % relative standard errors (%RSE)

Parameter (unit)


Estimate (%RSE)

\(k_{deg\_pmTOR}\) (1/h)

pmTOR first-order degradation rate constant

1 (0.01)

\(I_{EVE}\) (10−1 × 1/Conc)

Linear slope for inhibition of pmTOR due to everolimus

0.09 (2.58)

\(k_{syn\_pS6}\) (1/h)

pS6 first-order degradation rate constant

3.9 (44.18)

\(\gamma pmTOR\)

Power coefficient for mTOR mediated activation of pS6

2.07 (12.57)

\(k_{syn\_IRS}\) (1/h)

IRS first-order degradation rate constant

1 (0.04)

\(\gamma pS6\)

Power coefficient for pS6 mediated inhibition of IRS

0.91 (7.05)

\(k_{syn\_pAKT}\) (1/h)

pAKT first-order degradation rate constant

1 (29.46)


Power coefficient for IRS mediated activation of pAKT

0.016 (15.43)

\(k_{g}\) (1/h)

First-order net Cell growth rate constant

0.02 (2.87)


Power coefficient for pS6 mediated cell growth

0.17 (8.86)

\(k_{syn\_i} = i_{0} \cdot k_{{{deg}_{i} }}\), \((i\left( 0 \right) = i_{0} = 1)\), \(k_{syn\_i}\) is equal to \(k_{{{deg}\_i}}\) for pmTOR, pS6, and IRS For pAKT, \(k_{syn\_i}\) is equal to \({\text{k}}_{{{deg}\_{\text{i}}}} /(1 + {\text{S}}_{\text{IRS}} )\)

Step 2: in vivo model


The observed data of everolimus plasma and tumor concentrations versus time profiles were obtained from [21], and used to develop the hybrid-PBPK model. In brief, after a daily oral administration of everolimus at 5 mg/kg, the drug was rapidly absorbed reaching a maximum plasma concentration 1 h post-dosing and a maximum tumor concentration 2 h post-dosing. A simultaneous modeling approach was adopted to concurrently capture plasma and tumor concentrations using a hybrid-PBPK model (Fig. 3). The final model captured well the observed plasma and tumor concentrations time course data (Fig. 5a, b), and the final model parameters were all estimated with reasonable precision (Table 2). The estimated partition coefficient of everolimus to the tumor tissue was quantified at 0.06, which is eightfold lower than the value estimated from a full PBPK model by [34] in xenograft mice bearing patients derived (PDx) pancreatic tumors. These differences in the tumor distributional properties of everolimus may be explained by the differences in the morphological and (patho)physiological characteristics between liver and pancreatic cancers as well as between orthotopic and PDx tumors in xenograft mice [35, 36]. The same determinants may also explain the differences observed in the estimate of the tumor blood flow compared to other xenograft mice studies. Initially, the value for Qtu of 0.1 mL/min was obtained from the literature from a human colon carcinoma tumor [37] and used in the current analysis. However, because orthotopic xenograft liver cancers are poorly perfused compared to human HCC, tumor blood flow Qtu was subsequently estimated in the model [38, 39].
Fig. 5

Model fittings for plasma (a) and tumor (b) concentrations using the hybrid-PBPK model following 5 mg/kg, a single and oral administration of everolimus to KB-31 xenograft mice [21]. Red solid circles represent the mean observed data and red solid lines are model fittings. c Simulated pS6 time course profile in Huh7 cells xenograft mice treated with a single oral dose of everolimus at 1 mg/kg. d Time course profiles of tumor volume reduction. Solid circles represent observed data of control (blue) and xenograft mice treated with everolimus at 1 mg/kg orally (red) [20]. Blue solid line represents the model fitting profile for control mice and red solid line represents the model fitting profile for treated animals. Green and purple solid lines are the simulated time course profiles of tumor volume shrinkage in xenograft mice treated daily and orally during 3 weeks with everolimus at 5 mg/kg (green) and 10 mg/kg (purple). Whereas the black solid line represents the simulated time course profiles of tumor volume shrinkage in xenograft mice treated with 10 mg/kg of everolimus orally and twice a day (bid) for 3 weeks

Table 2

Fitted parameters of the in vivo hybrid-PBPK model and their % relative standard errors (%RSE)

Parameter (unit)


Estimate (%RSE)

\(k_{a }\) (1/h)

First-order absorption rate constant

9.63 (35.17)

\(V_{c}\) (mL)

Volume of the central compartment

48 (5.64)

\(Cl_{mice}\) (mL/h)

Linear clearance from the central compartment

5.75 (10.5)


Tumor partition coefficient of everolimus

0.06 (12.98)

\(Q_{tu\_mice}\) (mL/h)

Blood flow to the tumor

0.011 (27.79)

\(V_{tu\_mice}\) (mm3)

Initial tumor volume

300 fixed from [21]


First-order net growth rate constant

0.007 (3)

Tumor growth inhibition

Figure 5d depicts model fittings of the measured tumor volume data over time from [20]. The TGI model captured well the observed data in both placebo and everolimus treated mice. The protein pS6 was identified as a suitable driver for the Huh7 cells response to everolimus, since its pathway is proven as one of the major mTOR-dependent downstream signaling pathways that mediate mTOR-regulated G1-phase progression [40]. Figure 5c demonstrates the simulated time course profile of pS6 protein expression, using intra-tumor everolimus concentration as the driver in mice treated with 1 mg/kg daily oral dose of everolimus. The first-order growth rate constant \((k^{\prime}_{g} )\) is estimated at 0.7 × 10−2 h−1, which is 2.8-fold less than the estimated value of the in vitro \(k_{g}\), resulting in an approximate in vivo doubling time of 61.8 h. The latter result agrees very well with literature findings of the in vivo tumor volume doubling time for Huh7 cells of 2.5 days. The final in vivo model was utilized to capture the in vivo tumor growth response using various dosing regimen such as 5 and 10 mg/kg daily, and 10 mg/kg twice a day (bid) for three weeks. These higher doses predicted greater TV reductions than the observed data from the tested dose of 1 mg/kg. Model-based simulations for these doses are shown in Fig. 5d and Suppl. Fig. 6.

Step 3: pre-clinical-to-clinical translational strategy

Model simulations of plasma and tumor concentrations time course profiles in HCC patients are shown in Suppl. Figs. 1 and 2. Everolimus intra-tumor concentration time course profiles were used as a driver to simulate human protein dynamics. The protein pS6 protein dynamic profile (Suppl. Fig. 3), influenced HCC tumor volume reduction over time (Suppl. Fig. 4), and the patients’ PFS as shown in Fig. 6. The fitted parameters of the clinical hybrid-PBPK model were all estimated with reasonable precision and are summarized in Table 3.
Fig. 6

a Model-predicted median progression free survival (PFS) in placebo treated HCC patients (solid yellow line) and 95% confidence intervals (dashed yellow lines) overlaid with observed PFS (solid black line) from the clinical trial [8]. b Model-predicted median PFS in everolimus treated HCC patients (solid green line) and 95% confidence intervals (dashed green lines) overlaid with observed PFS (solid red line) in the clinical trial [17]. c Model-predicted median PFS in everolimus treated HCC patients using a 10-fold higher kp value for everolimus (solid purple line) and 95% confidence intervals (dashed purple lines)

Table 3

Fitted parameters of the clinical hybrid-PBPK model for everolimus and their % relative standard errors (%RSE)

Parameter (unit)


Estimate (%RSE)

\(Cl_{human}\) (L/h)

Linear clearance from central compartment

17.4 (8.4)

\(V_{c}\) (L)

Volume of the central compartment

25.2 (17.8)

\(k_{a }\) (1/h)

First-order absorption rate constant

0.647 (6.2)

\(Q_{human}\) (L/h)

Clearance of distribution

51.1 (7.3)

\(V_{p}\) (L)

Volume of the peripheral compartment

400 (9.1)

\(k^{\prime\prime}_{g}\) (x10−3 1/h)

HCC clinical growth rate constant

0.18 Fixed from [28]

\(V_{tu\_human} (0)\) (cm3)

Initial tumor volume

10.5 fixed from [28]

\(V_{{tu\_human_{\hbox{max} } }}\) (cm3)

Maximum achievable tumor volume

870.8 fixed from [28]

\(Q_{tu\_human}\) (L/h/g)

HCC tumor blood flow

0.06 fixed from [26]

Step 4: clinical endpoint—predictions of progression free survival

Model predictions of the median PFS were 5.5 months for the placebo arm and 4.5 months for the everolimus treated patients. Our results are in good agreement with observed PFS for placebo (5 months [8]) and everolimus-treated patients (4 months [17]) (Fig. 6a, b). Additionally, model-based simulations of the PFS time course profiles for similar dosing regimen of everolimus (10 mg/kg every day for 24 weeks) with a 10-fold higher value of tumor partition coefficient (kp = 0.6 vs. 0.06) predicted the median PFS for these patients at 6 months as depicted in Fig. 6c.


Despite significant efforts to enhance the development of novel targeted anti-cancer agents, the attrition rate for their clinical translation remains high [41]. As evident with everolimus detailed in our study, the failure occur in most cases at the late stages of drug development such as in a phase 3 trial [42, 43]. This leads to a huge loss of economy and the time invested in the development of these drugs. Specifically, in the EVOLVE-1 trial, despite the two successful phase 1/2 studies, everolimus still failed to show an improvement in the overall survival of HCC patients who were intolerant to sorafenib therapy [18]. Among the multiple reasons associated with this failure, one may be attributed to the lack of predictive pharmacodynamic biomarkers that aid to adequately predict clinical outcome in this population. Another reason may be the lack of efficient utilization of preclinical data to inform clinical translation for a better usage of these agents. In this regard, we designed our modeling strategy with an overarching goal of integrating and reconciling multiscale pre-clinical data to predict clinical response in HCC patients treated with everolimus.

Preclinical models in oncology primarily xenograft tumor models display the potential to inform early clinical development through PK/PD relationships obtained from the preclinical PK and tumor growth inhibition data generated from these model systems [44]. However, they lack information on the underlying pharmacology of the examined drugs. Hence, incorporating the molecular and cellular mechanisms of action of drugs as a bridge between the time course of plasma and/or tumor exposure and the time trajectory of tumor volume shrinkage allow for more mechanism-based PK/PD models that establish best the exposure–response relationships. In our modeling strategy, we constructed a QSP/PK/PD model utilizing existing literature data from preclinical PK and PD studies on everolimus exposures in plasma, tumor, as well as its anti-tumor effects in HCC xenograft mice [20, 21]. The uniqueness of our approach lies in the incorporation of the PI3K/AKT/mTOR signaling protein network model along with the cellular response of liver cancer cells (Huh7 cells) to bridge between drug exposure and downstream pharmacological responses in xenograft mice. This stands as an example of the growing field of QSP for linking drug exposure to network models of biological pathways modulation [27, 45, 46, 47]. Another exclusive feature of our adopted strategy is in linking the tumor exposure rather than the plasma exposure to simulate the targeted protein network to the mTOR signaling protein network. Although this has become possible in case of preclinical PK/PD models owing to the practical feasibility of measurement of tumor drug concentrations in animal tumor tissues, and through the applicability of PBPK models, translatability of this step to the clinic is a major challenge. To address this concern, we constructed a clinical hybrid-PBPK model for everolimus in HCC patients. The model integrates plasma and tumor compartments, both linked through the measured clinical tumor blood flow (QT) [26] and our estimated in vivo everolimus partition coefficient (kp). This hybrid-PBPK model allowed to simulate HCC patients tumor concentrations that drives the dynamics of proteins in the PI3K/AKT/mTOR signaling pathway, and subsequently the PFS in HCC patients (Step 4).

QSP bridges systems biology models comprised of molecular and cellular models with conventional PK/PD models. The cell-based network model shown in the first step of our modeling strategy is one such example of the application of QSP. In our own previous studies, we have demonstrated that, for targeted therapies such as sunitinib, bridging their exposure to clinical outcome through mathematical modeling of biomarkers serves as a reliable predictor for estimating drug’s anti-tumor activity and time-to-tumor progression in HCC patients [48]. In the current work, we developed a cell-based protein network model with key proteins regulated by everolimus in the PI3K/AKT/mTOR pathway using in vitro data [20]. Although, we were able to incorporate model parameters obtained from the in vitro cell-based protein network model to simulate the temporal changes in proteins dynamics in in vivo settings (xenograft mice and patients) models, and drive the tumor growth inhibition, these simulated profiles still need qualification against observed data. While such model qualification can be performed in xenograft mice models, it is a real challenge to obtain measurements of such biomarkers from human tumors due to the repeated biopsies required from the patients. An alternative approach would be to search for readily accessible biomarkers such as proteins circulating in bloodstream. Such approach was explored by [49], where the inhibition time profiles of serine/threonine kinase p70S6 kinase1 (S6K1) were measured in human PBMCs following everolimus treatment, and S6K1 was used as a circulating biomarker that helped select an optimal dosing regimen [49]. Similarly, in our analysis, the phosphorylated form of S6 protein (pS6), which is the downstream target of S6K1 protein, was used as a driver in both: the in vitro and in vivo cytostatic effects of everolimus as well as the HCC patients’ progression free survival. Based on our clinical simulations, everolimus treatment failed to achieve inhibition of pS6 (Suppl. Fig. 3), demonstrating the lack of efficacy in clinical response for this patients population.

Another major challenge for the clinical translation is the access to intra-tumor concentrations of the tested drugs. To overcome this limitation, a well-stirred, hybrid-PBPK model was used to simulate HCC patients’ intra-tumor concentrations of everolimus. In this model the partition coefficient (kp), a drug-specific parameter, quantifying the distribution of everolimus from plasma to tumor was fixed to the estimated value from the in vivo hybrid-PBPK model. One limitation from this assumption is that the difference in the unbound fraction (fu) of drug between mice (fu = 1%) and human (fu = 25%) is embedded in the value of kp. An alternative strategy to overcome this limitation is to use the corresponding fu from mice and human in the hybrid-PBPK model. The latter was attempted in our modeling exercise; however, both parameters kp and Qtu_mice were not identifiable in xenograft mice data; probably due to the very low tumor free drug concentrations. Hence, total drug concentration was carried forward as a driver of the downstream pharmacodynamics. Similarly, the tumor blood flow was fixed to a measured value in HCC patients [26]. Since it is not feasible to measure drug’s intra-tumor concentrations in the clinic to compare against our model-based predictions, the present approach relies heavily on the preclinical and clinical measures used for the translation. A full-PBPK model developed using animal models with concentration time course profiles from various tissues including the tumor will allow better estimation of the kp in the different tissues including the tumor that can be used for clinical translation. With the improving clinical diagnostic techniques such as advanced computed tomography, blood flow measures and changes in tumor size over time in HCC patients can be more reliably measured, and hence, better inform the clinically translated models.

The final step of our translational strategy involves the predictions of HCC patient outcome (i.e., PFS) when treated with everolimus using the clinically translated multiscale model (Step 4). Since PFS is the primary endpoint for clinical trials and serves as a surrogate endpoint for the overall survival, model qualification of the clinically translated model was performed by comparing the simulated PFS profiles with clinical observations. One of the most important parameters for the clinical model predictions is the tumor growth rate. Since the growth rate constant of clinical tumors are much different from those observed in preclinical models, the value for the clinical observed growth rate constant of HCC was obtained and fixed from literature report [28]. The initial tumor size and the maximum achievable tumor burden were also obtained from the same source of literature. A Monte Carlo simulation was performed by introducing variability on the growth rate constant to account for a range of HCC patients’ responses to everolimus. The validity of our predictions using literature derived tumor growth rate parameters was evaluated by simulating PFS in the placebo treated HCC patients, and comparing it with clinically observed PFS in non-treated patients [8]. Overall, model-predicted PFS values were quite similar to the observed ones. One of the reasons behind the slight over prediction of PFS compared to observed clinical trial data may be due to the misspecification of unperturbed tumor growth kinetics that were adapted from Taouli et al. [28]. According to their report, there is a huge variability of tumor growth between different patients monitored within the study itself. In an attempt to identify enhanced anti-tumor activity with everolimus and a longer PFS for HCC patients, the final qualified multiscale model was used to perform simulations with higher tumor partition coefficient. The model predicted that a 10-fold higher kp results in a higher inhibition of pS6 protein, and extends further HCC patients PFS (4.5 vs. 6 months using model-predicted kp = 0.06 vs using a 10-fold kp = 0.6). Although this result is encouraging, it is acknowledged that this slight improvement in PFS may also pertain to the uncertainty from some of the PD parameters.

In summary, we present a QSP/PK/PD modeling and simulation based strategy that integrates multiscale data for a translation of the lack of efficacy of a small molecularly targeted inhibitor in HCC, everolimus. Although, we utilized the PD data obtained from the same cell line in both in vitro and in vivo conditions, the PK data were obtained from a xenograft mouse model diseased with a different HCC cell line. Considering the heterogenous nature of the disease itself (i.e. HCC), even using the same cell lines throughout the in vitro and in vivo studies, the likelihood of variability in response is very high. Thus, our final QSP/PK/PD model cannot be generalized to all HCC cell lines and xenografts responses. In this study, we have demonstrated the capability of our translated QSP/PK/PD model to a priori predict PFS of HCC patients treated or not (placebo) with everolimus. This type of strategy may be extended to predict combinatorial therapies effects for everolimus given the availability of preclinical data, and may serve as a valuable tool to optimize the dosing regimen of these combinations owing to its multiscale and systems-based features.


Compliance with ethical standards

Conflict of Interest

The authors declare that there is no conflict of interest.

Supplementary material

10928_2018_9590_MOESM1_ESM.docx (403 kb)
Supplementary material 1 (DOCX 397 kb)


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pharmaceutics, Center for Pharmacometrics and Systems Pharmacology, College of PharmacyUniversity of FloridaOrlandoUSA

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