# New In Vitro-In Silico Approach for the Prediction of In Vivo Performance of Drug Combinations

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## Abstract

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_{effect}) for the combinations effect, itraconazole was the most effective in combination with either reference anticancer drugs. In addition, cell growth inhibition was itraconazole-dose dependent and an increase in effect was predicted if itraconazole administration was continued (24-h dosing interval). This work demonstrates that in silico methods and AUC

_{effect}are powerful tools to study relationships between tissue drug concentration and the percentage of cell growth inhibition over time.

## 1. Introduction

^{®}(ISEE Systems Inc., Lebanon, PA, USA) is a simulation software application that enables the study of systems through its graphical representation. The program uses Compartments, Flows, Converters, and Connectors as building blocks. “Compartments” accumulate whatever flows into them, net of whatever flows out of them, with “Flows” filling and draining accumulations. The Converter serves a utilitarian role in the software. It holds values for constants, defines external inputs to the model and calculates algebraic relationships. In general, it converts inputs into outputs. Connectors, as its name suggests, connect model elements. Moreover, the use of built-in time functions in converters, such as AND, OR, IF…THEN…ELSE or PULSE, allows a set of rules to be established, which are used by the program to control flow through the model, enabling the construction of more complex models. When the model is complete, the user has only to establish a simulation time period and a time increment (h). Each value calculation can be made using either Euler’s, 2nd, 3rd, or 4th order Runge-Kutta methods, being Euler’s the simplest version of the Runge-Kutta method. These are integration methods that estimate a new value (y

_{i+1}) through the extrapolation of an old value (y

_{i}) following Equation (1). In Euler’s method, φ is the slope in x

_{i}(first derivate in x

_{i}). In the Runge-Kutta method, instead of one single derivation, one or more representative slopes (depending on the order of the method) are determined during an interval, h, to estimate the new value. This equation can be applied step by step and trace out the trajectory of the solution (Figure 1) [10,11,12,13].

^{®}, GastroPlus™ is specifically designed for PK studies, particularly physiologically based pharmacokinetics (PBPK) and physiologically based biopharmaceutics modeling (PBBM). Additionally, its incorporated absorption model, ACAT (Advanced Compartmental Absorption and Transit model), allows the simulation of intravenous, gastrointestinal, ocular, nasal, and pulmonary absorption of molecules. This enables the user to obtain a detailed absorption profile of the molecules in study, since it considers several physiological variables. GastroPlus™ simulations rely on the numerical integration of differential equations that coordinate a set of well-characterized physical events that occur and are interconnected as a result of diverse physicochemical and biologic phenomena. Furthermore, GastroPlus™ has additional modules, including ADMET Predictor™ module for the prediction of physicochemical and pharmacokinetic parameters of compounds, and other modules for deeper insight into the pharmacokinetics of a drug, such as PKPlus™ and PBPKPlus™. Despite its sophistication, GastroPlus™ is relatively easy for someone with a background in ADME to learn and use because it incorporates an intuitive and modern graphical user interface that enables a rapid and smooth transition from setting up inputs to evaluating results [14].

^{®}(Certara UK Limited, Sheffield, UK) or GastroPlus™, now have specific modules to predict drug-drug interaction, using previous knowledge on main metabolizing enzymes of each drug in study [18,19,20]. Although a wide variety of in silico tools is already available for drug combination studies, new approaches can be proposed, and drug combination effect coupled with drug disposition simulation is an example of a gap in the existing resources.

## 2. Materials and Methods

#### 2.1. Chemicals

^{®}/Merck© (2021 Merck KGaA, Darmstadt, Germany) and dissolved in sterile dimethyl sulfoxide (DMSO) at 100, 50, 17, 10 and 10 µM, respectively, as stock solutions. The drugs were stored at −20 °C and diluted with culture medium prior to use.

#### 2.2. Cell Culture

_{2}atmosphere.

#### 2.3. Evaluation of Cell Growth Inhibition with the MTT Assay

#### 2.3.1. Dose-Response Curve Determination for ACDs and ACD-RD Combinations

^{4}cells/mL (for all the cells lines) and was then used in the MTT assays. The cells were incubated for 72 h with different concentrations of ACD or ACD-RD combination. Cells were allowed to adhere to the plate for 24 h and then 100 μL/well of drug solution were added. The multiple serial dilutions tested of each drug solution were prepared in culture medium (RPMI-1640 medium + 10% FBS). The concentrations tested ranged from 0.01 to 50 μM for gemcitabine and from 0.05 to 100 μM for 5-FU. When evaluating drug combinations, 50 μL/well of different concentrations of the ACD (gemcitabine or 5-FU) were added to the cells along with 50 μL/well of a fixed concentration of RD. The same ranges of concentrations for gemcitabine and 5-FU were tested and the chosen concentration of each RD was based on the maximum plasma concentration (C

_{max}) found in the literature. Since gemcitabine is a prodrug, which is phosphorylated into an active drug inside the cells, we assume this conversion is complete, and something similar for 5-FU as well. As such, verapamil, itraconazole and tacrine solutions were prepared and used in this assay with the concentrations of 1, 8.5 and 0.24 μM, respectively [23,24,25,26]. A DMSO control was also included in the experiments (maximum concentration used, 0.2%, was previously considered non-toxic to the cells). After 72-h incubation, the media was removed by aspiration, 100 μL/well of MTT solution (0.5 mg/mL in media) was added to each well and cells were incubated for another 3 h. The MTT solution was then removed by aspiration, cells were washed with 100 μL/well of PBS and 100 μL/well of DMSO were added to dissolve the formazan crystals. Absorbance was read in a spectrometer (Varioskan™ LUX multimode microplate reader) at 540 nm. Results were treated in Microsoft Excel and GraphPad Prism 6. The dose-response curves for each treatment were then plotted in appropriate graphs, differences between treatments were compared and the IC50 value, indicating the concentration resulting in inhibition of 50% of the maximal cell growth, was determined. The percentage of cell growth inhibition resulting from each drug was calculated as: [(OD 540 control cells—OD 540 treated cells)/OD 540 control cells] × 100. These assays were repeated in at least three independent experiments.

#### 2.3.2. Further Studies with Itraconazole in Combination with Gemcitabine or 5-FU

- Range of itraconazole concentrations + fixed concentration of ACD (Gem or 5-FU); itraconazole’s concentrations ranged from 0.07 to 4.25 μM, since the concentration used in the previous experiments was 8.5 μM (note dilution factor of 2 in the well). The concentration chosen for Gem and 5-FU was the one that showed the lowest effect in the previous experiments: 0.01 and 1 μM, respectively. The ACDs were also tested alone for control purposes;
- Range of ACD (Gem or 5-FU) concentrations + fixed concentration of itraconazole (three different concentrations were tested). Different concentrations of ACD (Gem or 5-FU) were added to the wells, as well as a fixed concentration of itraconazole. The multiple serial dilutions tested for ACD ranged from 0.005 to 10 μM for Gem (since in the previous experiments the resulting dose-response curve did not have the ideal shape), and the range was maintained for 5-FU. The concentrations for itraconazole were 2, 4 and 6 μM (concentrations within the range that showed an effect when administered with a very low concentration of ACD). Itraconazole was also tested alone for control purposes.

#### 2.4. Model Development

^{®}10.0.3 (ISEE Systems Inc., Lebanon, PA, USA). The structure of the model, as well as all the equations, variables and constants used for this purpose, are described in detail in the following sections.

#### 2.4.1. WinNonlin: PK Analysis

^{®}models require the input of PK parameters of each drug, such as the volume of distribution in central and tissue compartment (V

_{d1}and V

_{d2}, respectively), clearance (CL) and transfer rate constants from central compartment to tissue compartment and from tissue compartment to central compartment (k

_{12}and k

_{21}, respectively). Ideally, all parameters would belong to the same source: human plasma concentration versus time data (C

_{p}-time data) belonging to the same ethnicity, gender, and age. Due to lack of data available in the literature concerning this issue, the only mandatory conditions were that collected data for this study was from human patients and that all the PK data for each drug belonged to the same literature source.

_{p}-time data of a certain drug, can generate its PK parameters.

_{p}-time data collected were from NSCLC Chinese patients [27]. Briefly, gemcitabine was intravenously infused for 120 min at a rate of 15.7 mg·min

^{−1}and plasma samples were collected until 210 min after infusion start. In relation to 5-FU, C

_{p}-time data collected belonged to English cancer patients [28]. 5-FU was administered over 1 min, by intravenous bolus injection, at a dose of 900 mg. Plasma samples were collected for 90 min. For itraconazole, the data is relative to healthy subjects from The Netherlands, who received 100 mg administered intravenously, over 1 h, and plasma samples were collected for 96 h [29].

#### 2.4.2. Model Structure

#### 2.4.3. Determination of the AUC for Each Drug Combination Effect in Humans

_{effect}” was determined to evaluate the overall effect of each drug combination tested in the NSCLC cell line A549. In current STELLA

^{®}models, AUC is recorded using a separate compartment, but it follows a principle which is mathematically expressed in Equation (2):

_{p}-time profile has a two-compartment distribution. Using gemcitabine and 5-FU C

_{p}-time data for intravenous infusion obtained from literature and the PK/PD modeling program Phoenix WinNonlin (64-bit, version 7.00), the curve that best fitted the experimental values obtained in the experimental in vitro approach was traced and the values for each PK parameter (V

_{d1}, V

_{d2}, CL, k

_{12}and k

_{21}) were obtained. Therefore, with the input of the parameters obtained through WinNonlin, the models developed in STELLA

^{®}describe the disposition of each drug over time, after intravenous infusion. The input dose is also the same as the one reported in the literature source used (infusion of 15.7 mg·min

^{−1}for 120 min for gemcitabine, and bolus injection of 900 mg for 5-FU).

_{50}”), the effect over time can be determined through a Hill Equation (3) (because tissue concentration will vary over time):

_{effect}was evaluated: Gemcitabine alone; gemcitabine + itraconazole 2 μM; gemcitabine + itraconazole 4 μM and gemcitabine + itraconazole 6 μM; 5-FU alone; 5-FU + itraconazole 2 μM; 5-FU + itraconazole 4 μM and 5-FU + itraconazole 6 μM. All the variables, such as drug plasma concentration, drug tissue concentration, drug amount eliminated, and percentage of effect can be plotted in graphs or tables and evaluated over time.

^{®}. Simulation length and step size (h) were chosen in a way that h was low enough to give accurate results without compromising the speed of the simulation and simulation length was long enough to allow the lower effect value to be reached. Therefore, h = 0.02 and 400 min of simulation length were used for gemcitabine and h = 0.02 and 200 min of simulation length were used for 5-FU.

_{50}” variables were changed, according to each situation.

#### 2.4.4. Itraconazole’s Dose-Dependent Effect, when Combined with Gemcitabine or 5-FU

_{effect}), where the main variable was ACD tissue concentration, itraconazole’s dose-dependent effect was evaluated. At this stage, the exact same 8 dose-response curves were considered: ACD alone; ACD + itraconazole 2 μM; ACD + itraconazole 4 μM and ACD + itraconazole 6 μM. The difference from the previous study lies in the addition of a second two-compartment model (this time for itraconazole) and the itraconazole dose-dependent effect evaluation. For this purpose, three different itraconazole doses were evaluated in the simulations (100, 300 and 500 mg). ACD doses remained the same as in the previous study (1884 mg of gemcitabine and 900 mg of 5-FU).

_{p}-time data. Although itraconazole is most frequently administered orally, the intravenous infusion was selected to avoid the low oral bioavailability characteristic of this drug. Therefore, based on the literature human C

_{p}-time data for intravenous infusion of itraconazole and using the WinNonlin program, all PK parameters needed for two-compartment model construction were collected and the model was built.

^{−1}. In relation to the other variables that describe dose-response curve (“Top”, “Steepness factor” and “EC

_{50}”), the average of the three values (relative to ACD + itraconazole 2, 4 and 6 μM dose-response curves) were used. The model for gemcitabine + itraconazole combination is shown in Figure 4. 5-FU + itraconazole combination model is shown in Figure 5. Again, the exact same layout was used to test three different doses of itraconazole, and 5-FU dose remained the same. All the variables, such as drug plasma concentration, drug tissue concentration, drug amount eliminated, and percentage of effect can be plotted in graphs or tables and evaluated over time. Similar Runge-Kutta 4th order integration methods were used.

#### 2.5. Model Validation

^{®}generated C

_{p}-time curves were plotted against literature C

_{p}-time data and general shape of the curve and fitting was evaluated. AUC plasma concentration was another parameter used to evaluate the accuracy of the models. Therefore, using the exact same dosages and routes of administration as the ones used in the literature experiments, C

_{p}-time curve and AUC plasma concentration were determined and compared with literature data.

_{effect}. Furthermore, the innovative idea developed in this work resides in an in silico study that enables the coupling of cell viability assay data with human drug disposition.

## 3. Results and Discussion

#### 3.1. In Vitro Experiments—Evaluation of Inhibition of Cell Growth

#### 3.1.1. Range of ACD Concentrations + Fixed Concentration of RD

#### 3.1.2. Range of Itraconazole Concentrations + Fixed Concentration of ACD

#### 3.1.3. Range of ACD Concentrations + Fixed Concentration of Itraconazole

#### 3.2. WinNonlin: PK Analysis

_{10}, AUC, C

_{max}and CL values obtained are in accordance with the literature. However, transfer rate constants k

_{12}and k

_{21}and tissue compartment volume of distribution (V

_{d2}) measurements are not very precise, but since no more accurate data was available, the values were included in the STELLA

^{®}model.

_{ss}) is quite lower than the volume of distribution reported in literature source, WinNonlin prediction (blue line) fits all experimental values (red circles) almost perfectly and % CV is fairly small in all parameters determined. Therefore, WinNonlin prediction was assumed to be reliable. In fact, the volume of distribution parameter determined in the literature is V

_{darea}[28], which means that it was determined during the elimination phase and not at steady-state, as in WinNonlin prediction [45]. Therefore, the parameters cannot be compared.

#### 3.3. STELLA^{®} Models

#### 3.3.1. Input Data for the Model

#### 3.3.2. Model Validation

_{p}-time curve was determined through STELLA

^{®}models and compared with the experimental values. Figure 13 shows that gemcitabine STELLA

^{®}model (Figure 2) is quite accurate in predicting gemcitabine’s plasma concentration over time. Since the input values came from WinNonlin, and WinNonlin C

_{p}-time curve prediction did not fit all experimental values, then C

_{p}-time curve predicted through STELLA

^{®}will not fit them all either. For the 5-FU STELLA

^{®}model, Figure 14 demonstrates C

_{p}-time curve predicted with STELLA

^{®}(blue line) fitting all the experimental values (orange circles). Thus, model accuracy predicting 5-FU’s plasma concentration over time can be assumed. Similarly, itraconazole C

_{p}-time curve predicted with STELLA

^{®}(blue line) is also fitting all the experimental values (orange circles) (Figure 15). Once more, model accuracy predicting itraconazole plasma concentration over time can be assumed. Besides C

_{p}-time curve graphical analysis, to validate STELLA

^{®}models, AUC values were determined and compared with literature sources. In Figure 16, three AUC values are depicted for each drug: AUC calculated from experimental data (literature value), WinNonlin PK analysis, and STELLA

^{®}model simulation prediction. As expected, for each drug, STELLA

^{®}prediction is in perfect accordance with WinNonlin PK analysis, showing the exact same AUC value. Literature values are slightly different from STELLA

^{®}and WinNonlin predictions, probably due to differences in the integration method used for AUC calculation (all literature sources used trapezoidal rule, while STELLA

^{®}and WinNonlin predictions resorted to 4th order Runge-Kutta method).

#### 3.3.3. AUC_{effect}: Drug Combination Effect Comparison

_{effect}was determined in STELLA

^{®}. The effect is calculated through Equation (3), where the only variable is ACD tissue concentration. All the other parameters are constants and characterize the dose-response curve obtained from the in vitro studies, i.e., depending on ACD tissue concentration and the parameters introduced in model converters, “Effect” gets a certain value over time. AUC

_{effect}quantifies the overall effect during simulation. According to the simulations (Figure 17), and in accordance with the in vitro experimental results (Figure 9), the higher the itraconazole concentration, the higher is the AUC

_{effect}value. In gemcitabine combinations, when itraconazole tissue concentration is 4 μM and 6 μM, AUC

_{effect}is about 9% and 22% higher than control (gemcitabine without itraconazole), respectively. In 5-FU combinations, these values reach 12% and 34% improvement relative to control (5-FU without itraconazole), respectively. However, for unknown reasons, when itraconazole concentration is 2 μM, AUC

_{effect}is lower than control, in both combination groups.

_{1/2}) is identical (10 and 12 min, respectively) [27,29], the former is infused at a rate of 15.7 mg per minute, over 2 h, which represents a total dose of 1884 mg, while the latter is administered through a bolus IV injection at a dose of 900 mg. Therefore, the AUC

_{effect}of 5-FU is expected to be much smaller than gemcitabine’s, due to the lower dose and overall reduced exposure time of 5-FU in tissue. Besides the AUC

_{effect,}further analysis was done regarding itraconazole dose-dependent effect. This time, instead of only one variable (ACD concentration), as in the previous study, the percentage of effect will also depend on itraconazole tissue concentration over time. “% Effect” is still calculated through Equation (3), where ACD tissue concentration is the main variable, but “Bottom” parameter is now an equation dependent on itraconazole tissue concentration, instead of being a constant (Equations (4) and (5)).

^{−1}, f(x) increases exponentially, reducing “% Effect” abruptly. Figure 18C shows gemcitabine tissue concentration-time curve:

^{®}simulation program, with the objective of increasing itraconazole tissue concentration, but limitations in the software’s built-in functions did not allow the study.

^{−1}, f(x) increases exponentially reducing “% Effect” abruptly. Figure 18D shows 5-FU tissue concentration-time curve. When the drop in “% Effect” value starts, slight differences between effect-time curves start to be noticed. At this point, itraconazole tissue concentration plays the main role in the overall effect, since “% Effect” equals “Bottom” value (Equation (3), which is directly dependent on itraconazole tissue concentration. As stated above, if higher values of itraconazole tissue concentration were considered, “% Effect” would be equally higher. This can be mathematically explained through Equation (5) analysis:

## 4. Discussing the Limitations in Pharmacokinetics Modeling

^{®}simulation program, namely the impossibility to make multiple dosing regimens (for IV infusion). As mentioned in Section 3.3.3., itraconazole concentration in the tissue compartment was not high enough to significantly influence the overall “% Effect”. The idea of using multiple dosing regimen was to reach steady-state plasma concentration (C

_{ss}), increasing itraconazole accumulation in tissue compartment, and thus, to predict the influence of itraconazole in cell growth inhibition. Thus, alternatives to the STELLA

^{®}simulation program were explored to overcome this problem, which included the use of GastroPlus™ PBPK simulation software and Microsoft Excel.

_{p}-time data of itraconazole in GastroPlus™ was made, but neither uploading itraconazole molecular structure nor inputting experimental parameters could replicate the concentration plasma profile reported in the literature. As shown in Figure 19, itraconazole C

_{max}predicted through this program, for 100 mg, 1 h IV infusion, is about 0.095 μg·mL

^{−1}, while the equivalent value reported in the literature, for the same dosing regimen, is 3.9 μg·mL

^{−1}. GastroPlus™ is a complex software and it is not solely ruled by simple pharmacokinetics equations. To run a simulation in this program, the input of a few parameters is needed. Apart from common parameters input as dose, dosage form, solubility and the pH at which it was measured, logP and pKa’s (if any), it also requires some knowledge about particle radius, particle density and diffusion coefficient. In the simulation presented in Figure 19, most of the parameters used were predicted through itraconazole structure upload. Even with the input of some experimental values, itraconazole C

_{p}-time is quite different from the reported one. Thus, it was impossible to validate the model and multiple dosing regimen could not be evaluated.

_{ss}value was used as the itraconazole plasma concentration. The transfer rate constants k

_{12}and k

_{21}previously obtained through WinNonlin were used to simulate itraconazole flow between plasma and tissue compartment. Then, the “Bottom” value was calculated at every time point, which is dependent on itraconazole tissue concentration on that specific time point (Equation (4) or Equation (5)). Finally, “% Effect” was calculated through Equation (3).

^{®}models developed in this work are simple but innovative, and provided insight on the PK and effect of combinations of anticancer drugs with repurposed drugs. Ideally, parameters used in the model structure should be more consistent, but for a first idea of the general behavior of the drug combinations in human body, the data used is fairly appropriate. There is variability in the populations originating the data, and moreover, the tumor is assumed to behave like the tissues grouped into a tissue compartment, but no such assumption was confirmed or validated. Although in vitro results do not correlate directly with in vivo effect, these preliminary studies might be useful for comparative effect purposes and to provide mechanistic predictions of dosing regimens.

## 5. Conclusions

^{®}modeling program works, one can collect and analyze the necessary data and build the most convenient model. Additionally, the effect of these combinations must be studied using appropriate in vivo models.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

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**Figure 1.**Schematic representation of a model built in STELLA

^{®}modeling program. In this model, mass flows from compartment 1 to compartment 2 and from compartment 2 to compartment 1. Flow rates 1 and 2 are determined by convertor 1 and 2 respectively.

**Figure 2.**Two-compartment model of gemcitabine intravenous infusion administration. The drug is infused to plasma compartment at a rate of 15.7 mg·min

^{−1}for 120 min. The drug is transferred from plasma compartment to tissue compartment and vice versa at a rate defined by “k

_{12}” × ”gemcitabine plasma amount” and “k

_{21}” × ”Tissue amount”, respectively, where “k

_{12}” and “k

_{21}” are transfer rate constants. The drug is eliminated from plasma compartment to elimination compartment at a rate defined by “CL” × ”gemcitabine plasma concentration” where “CL” is a constant and “gemcitabine plasma concentration” is a variable that changes over time. “Gemcitabine plasma concentration” is the result of “gemcitabine plasma amount” divided by “V

_{d1}”, while “gemcitabine tissue concentration” results from “Tissue amount” divided by “V

_{d2}”. “Gemcitabine plasma amount” is the net result of the amount of drug that leaves plasma compartment (to elimination and tissue compartment) and the amount that enters in this compartment (coming from the infusion and tissue compartment). “AUC plasma concentration” is generated through Equation (2), where the variable in study is “gemcitabine plasma concentration”. Considering Equation (3), “gemcitabine tissue concentration” and the four parameters obtained from gemcitabine without itraconazole dose-response curve (“Bottom”, “Top”, “Steepness factor” and “EC

_{50}”), the effect of gemcitabine alone is modelled over time.

**Figure 3.**Two-compartment model of 5-FU intravenous injection administration. The drug is injected into plasma compartment at a dose of 900 mg. The drug is transferred from plasma compartment to tissue compartment and vice versa at a rate defined by “k

_{12}” × ”Plasma amount 5-FU” and “k

_{21}” × ”Tissue amount 5-FU”, respectively, where “k

_{12}” and “k

_{21}” are transfer rate constants. The drug is eliminated from plasma compartment to elimination compartment at a rate defined by “CL” × ”Plasma concentration 5-FU”, where “CL” is a constant and “Plasma concentration 5-FU” is a variable that changes over time. “Plasma concentration 5-FU” is the result of “Plasma amount 5-FU” divided by “V

_{d1}” while “Tissue concentration 5-FU” results from “Tissue amount 5-FU” divided by “V

_{d2}”. “Plasma amount 5-FU” is the net result of the amount of drug that leaves plasma compartment (to elimination” or tissue compartment) and the amount that enters in this compartment (coming from tissue compartment). “AUC plasma concentration” is generated through Equation (2) where the variable in study is “Plasma concentration 5-FU”. Considering Equation (3), “Tissue concentration 5-FU” and the four parameters obtained from 5-FU without itraconazole dose-response curve (“Bottom”, “Top”, “Steepness factor” and “EC

_{50}”), the effect of 5-FU alone is modeled over time.

**Figure 4.**Two-compartment PK model for gemcitabine with IV infusion, two-compartment PK model for itraconazole with IV infusion and the relation of their tissue concentration with percentage of cell growth inhibition in A549 cancer cell line. Gemcitabine’s model has been described in Figure 2. For itraconazole compartmental model, drug is infused to plasma compartment at a rate of 8.3, 5 or 1.7 mg·min

^{−1}during 1 h (500, 300 or 100 mg doses, respectively). It is transferred from plasma compartment to tissue compartment and vice versa at a rate defined by “k

_{12}” × ”Itraconazole plasma amount” and “k

_{21}” × ”Itraconazole tissue amount”, respectively, where “k

_{12}” and “k

_{21}” are transfer rate constants. The drug is eliminated from plasma compartment to elimination compartment at a rate defined by “CL” × ”Itraconazole plasma concentration”, where “CL” is a constant and “Itraconazole plasma concentration” is a variable that changes over time. “Itraconazole plasma concentration” is the result of “Itraconazole plasma amount” divided by “V

_{d1}” while “Itraconazole tissue concentration” results from “Itraconazole tissue amount” divided by “V

_{d2}”. “Itraconazole plasma amount” is the net result of the amount of drug that leaves plasma compartment (to elimination and tissue compartment) and the amount that enters in this compartment (coming from infusion and tissue compartment). “AUC plasma concentration” is generated through Equation (2), where variable in study is “Itraconazole plasma concentration”. Considering Equation (3), “Gemcitabine tissue concentration”, the average of gemcitabine + itraconazole dose-response curve parameters “Top”, “Steepness factor” and “EC

_{50}”, and Equation (4), itraconazole dose-dependent effect was modelled.

**Figure 5.**Two-compartment PK model for 5-FU with IV injection (described in Figure 3), two-compartment model for itraconazole with IV infusion and the relation of their tissue concentration with percentage of cell growth inhibition in A549 cancer cell line. For itraconazole, compartment model drug is infused to plasma compartment at a rate of 8.3, 5 or 1.7 mg·min

^{−1}during 1 h (500, 300, or 100 mg doses, respectively). It is transferred from plasma compartment to tissue compartment and vice versa at a rate defined by “k

_{12}” × ”Itraconazole plasma amount” and “k

_{21}” × ”Itraconazole tissue amount”, respectively, where “k

_{12}” and “k

_{21}” are transfer rate constants. The drug is eliminated from plasma compartment to elimination compartment at a rate defined by “CL” × ”Itraconazole plasma concentration”, where “CL” is a constant and “Itraconazole plasma concentration” is a variable that changes over time. “Itraconazole plasma concentration” is the result of “Itraconazole plasma amount” divided by “V

_{d1}”, while “Itraconazole tissue concentration” results from “Itraconazole tissue amount” divided by “V

_{d2}”. “Itraconazole plasma amount” is the net result of the amount of drug that leaves plasma compartment (to elimination and tissue compartment) and the amount that enters in this compartment (coming from infusion and tissue compartment). “AUC plasma concentration” is generated through Equation (2) where variable in study is “Itraconazole plasma concentration”. Considering Equation (3), “Tissue concentration 5-FU”, the average of 5-FU + itraconazole dose-response curve parameters “Top”, “Steepness factor” and “EC

_{50}”, and Equation (5), itraconazole dose-dependent effect was modelled.

**Figure 6.**Dose-response curve of gemcitabine in combination with RD. Percentage of cell growth inhibition of human lung carcinoma A549 cell line ((

**A**)—top left), human prostate adenocarcinoma PC-3 cell line ((

**B**)—right top) and normal human prostate epithelium PNT2 cell line ((

**C**)— bottom left), treated with a wide range of concentrations of gemcitabine (Gem) alone (black line) or Gem in combination with a fixed concentration of RD (verapamil, V, green line; itraconazole, I, blue line; or tacrine, T, orange line), during 72 h, determined with MTT assay. The results are the mean of at least three independent experiments. The DMSO control did not present toxicity to the cells (data not shown).

**Figure 7.**Dose-response curve of 5-FU in combination with RD. Percentage of cell growth inhibition of human lung carcinoma A549 cell line ((

**A**)—top left), human prostate adenocarcinoma PC-3 cell line ((

**B)**—top right) and normal human prostate epithelium PNT2 cell line ((

**C**)—bottom left), treated with wide range of concentrations of 5-fluorouracil (5-FU) alone (black line) or 5-FU in combination with a fixed concentration of RD (verapamil, V, green line; itraconazole, I, blue line; or tacrine, T, orange line), during 72 h, determined with MTT assay. Results are the mean of at least three independent experiments. The DMSO control did not present toxicity to the cells (data not shown).

**Figure 8.**Dose-response curve of itraconazole in combination with ACD. Percentage of cell growth inhibition of human lung carcinoma A549 cell line treated with a range of concentrations of itraconazole alone (black line) or itraconazole in combination with a fixed concentration of ACD (Gem (blue line) or 5-FU (green line)), during 72 h, determined with MTT assay. The results are mean of at least three independent experiments. The DMSO control did not present toxicity to the cells (data not shown).

**Figure 9.**Dose-response curves of ACD in combination with itraconazole. (

**A**): Percentage of cell growth inhibition of human lung carcinoma A549 cell line treated with wide range of concentrations of gemcitabine (Gem) alone (control) or Gem in combination with a fixed concentration of itraconazole (I), during 72 h, determined with MTT assay; (

**B**): Percentage of cell growth inhibition of human lung carcinoma A549 cell line, treated with wide range of concentrations of 5-FU alone (control) or 5-FU in combination with a fixed concentration of I, during 72 h, determined with MTT assay. The results are the mean of at least three independent experiments. The DMSO control did not present toxicity to the cells (data not shown).

**Figure 10.**Gemcitabine C

_{p}-time curve prediction through two-compartment model fitting of its observed C

_{p}-time data. Red circles correspond to the experimental data, obtained from the literature, and the continuous blue line corresponds to the in silico C

_{p}-time curve prediction. Plasma concentration is given in μg·mL

^{−1}and time in minutes.

**Figure 11.**5-FU C

_{p}-time curve prediction through two-compartment model fitting of its observed C

_{p}-time data. Red circles correspond to the experimental data, obtained from the literature, and the continuous blue line corresponds to the in silico C

_{p}-time curve prediction. Plasma concentration is given in μg·mL

^{−1}and time in minutes.

**Figure 12.**Itraconazole C

_{p}-time curve prediction through two-compartmental model fitting of its observed C

_{p}-time data. Red circles correspond to the experimental data, obtained from the literature, and the continuous blue line corresponds to the in silico Cp-time curve prediction. Plasma concentration is given in μg·mL

^{−1}and time in minutes.

**Figure 13.**Graphical representation of experimental C

_{p}-time data of gemcitabine and C

_{p}-time curve generated in silico for this drug over 210 min.

**Figure 14.**Graphical comparison between experimental C

_{p}-time data of 5-FU and C

_{p}-time curve generated in silico for this drug over 90 min.

**Figure 15.**Graphical comparison between experimental C

_{p}-time data of itraconazole and C

_{p}-time curve generated in silico for this drug over 5000 min.

**Figure 16.**Graphical representation of AUC plasma concentration of gemcitabine, 5-FU, and itraconazole when determined experimentally, through WinNonlin or STELLA

^{®}models.

**Figure 17.**Graphical representation of AUC

_{effect}for gemcitabine + itraconazole and 5-FU + itraconazole combinations.

**Figure 18.**ACD + itraconazole (I) combination STELLA

^{®}simulation. (

**A**,

**B**): Effect curves for gemcitabine + itraconazole and 5-FU + itraconazole combinations, respectively. Three itraconazole doses were tested, (

**C**,

**D**): Tissue concentration-time curves of gemcitabine and 5-FU, when intravenously administered at a dose of 1884 mg (infusion), and 900 mg (injection), respectively; (

**E**): Tissue concentration-time curve of itraconazole for three different doses of intravenous infusion.

**Table 1.**Dose-response curve parameters for gemcitabine and itraconazole combinations, obtained from GraphPad. (N.A.: non-applicable.).

Gem + I ^{a} | Bottom (%) | Top (%) | Steepness Factor | EC_{50} (μg·mL^{−1}) |
---|---|---|---|---|

I = 6 μM | 34.33 ± 2.43 | 80.39 ± 1.71 | 4.30 ± 1.30 | 0.0016 ± 3.2 × 10^{−7} |

I = 4 μM | 12.83 ± 2.79 | 73.07 ± 1.97 | 4.37 ± 0.99 | 0.0018 ± 3.1 × 10^{−7} |

I = 2 μM | −5.51 ± 1.83 | 67.47 ± 1.29 | 5.35 ± 1.12 | 0.0022 ± 1.6 × 10^{−7} |

I = 0 μM | −1.06 ± 2.35 | 70.12 ± 1.67 | 23.14 ± 4.20 × 10^{5} | 0.0026 ± 2.2 × 10^{5} |

Average | N.A. | 72.76 | 4.67 | 0.0021 |

^{a}I is the drug itraconazole. Gem + I = 2 μM for “Bottom (%)” and Gem + I = 0 μM for “Steepness factor” were not included in the calculation of the average.

**Table 2.**Dose-response curve parameters for 5-FU and itraconazole combinations, obtained from GraphPad. (N.A.: non applicable.).

5-FU + I ^{a} | Bottom (%) | Top (%) | Steepness Factor | EC_{50} (μg·mL^{−1}) |
---|---|---|---|---|

I = 6 μM | 33.22 ± 1.58 | 63.24 ± 1.62 | 2.77 ± 1.23 | 0.36 ± 0.01 |

I = 4 μM | 13.42 ± 3.09 | 56.05 ± 2.87 | 2.90 ± 2.40 | 0.20 ± 0.0071 |

I = 2 μM | −6.99 ± 2.14 | 57.52 ± 2.11 | 1.70 ± 0.26 | 0.27 ± 0.002 |

I = 0 μM | −0.47 ± 1.32 | 57.80 ± 1.32 | 2.19 ± 0.27 | 0.28 ± 0.001 |

Average | N.A. | 58.65 | 2.39 | 0.28 |

^{a}I is the drug itraconazole. 5-FU + I = 2 μM for “Bottom (%)” was not included in the calculation of the average.

Gemcitabine Parameters | Estimate | CV (%) | Literature Values [27] |
---|---|---|---|

k_{10} (min^{−1}) | 5.54 × 10^{−2} | 144.9 | 7.00 × 10^{−2} |

k_{12} (min^{−1}) | 6.64 × 10^{−4} | 45,998.6 | - |

k_{21} (min^{−1}) | 1.02 × 10^{−1} | 29,203.6 | - |

AUC (μg·mL^{−1}·min) | 499.58 | 10.3 | 453.00 |

C_{max} (μg·mL^{−1}) | 4.16 | 10.5 | 4.92 |

CL (mL·min^{−1}) | 3771.20 | 10.3 | 3940.05 |

V_{ss} (mL) | 68,464.40 | 37.4 | - |

V_{d1} (mL) | 68,019.62 | 148.8 | - |

V_{d2} (mL) | 444.79 | 19,137.5 | - |

_{10}: elimination rate constant; k

_{12}: transfer rate constant from central compartment to tissue compartment; k

_{21}: transfer rate constant from tissue compartment to central compartment; AUC: area under the plasma concentration-time curve; C

_{max}: maximum plasma concentration; CL: clearance; V

_{ss}: steady state volume of distribution; V

_{d1}: volume of distribution of central compartment; V

_{d2}: volume of distribution of tissue compartment.

5-FU Parameters | Estimate | CV (%) | Literature Values [29] |
---|---|---|---|

k_{10} (min^{−1}) | 9.17 × 10^{−2} | 4.9 | - |

k_{12} (min^{−1}) | 3.21 × 10^{−2} | 29.5 | - |

k_{21} (min^{−1}) | 1.07 × 10^{−1} | 28.1 | - |

AUC (μg·mL^{−1}·min) | 1058.81 | 1.6 | 926.80 |

C_{max} (μg·mL^{−1}) | 97.14 | 5.1 | - |

CL (mL·min^{−1}) | 850.01 | 1.6 | 1069.20 |

V_{ss} (mL) | 12,056.99 | 4.9 | 15,912.00 |

V_{d1} (mL) | 9265.14 | 5.1 | - |

V_{d2} (mL) | 2791.84 | 14.2 | - |

_{10}: elimination rate constant; k

_{12}: transfer rate constant from central compartment to tissue compartment; k

_{21}: transfer rate constant from tissue compartment to central compartment; AUC: area under the plasma concentration-time curve; C

_{max}: maximum plasma concentration; CL: clearance; V

_{ss}: steady state volume of distribution; V

_{d1}: volume of distribution of central compartment; V

_{d2}: volume of distribution of tissue compartment.

Itraconazole Parameters | Estimate | CV (%) | Literature Values [28] |
---|---|---|---|

k_{10} (min^{−1}) | 2.80 × 10^{−2} | 8.8 | 2.66 × 10^{−2} |

k_{12} (min^{−1}) | 2.38 × 10^{−2} | 9.4 | - |

k_{21} (min^{−1}) | 2.34 × 10^{−3} | 15.3 | - |

AUC (μg·mL^{−1}·min) | 437.73 | 7.9 | 449.88 |

C_{max} (μg·mL^{−1}) | 3.88 | 0.6 | - |

CL (mL·min^{−1}) | 228.45 | 7.9 | 246.67 |

V_{ss} (mL) | 90,922.24 | 20.9 | 558,000.00 |

V_{d1} (mL) | 8145.37 | 2.6 | - |

V_{d2} (mL) | 82,776.88 | 22.9 | - |

_{10}: elimination rate constant; k

_{12}: transfer rate constant from central compartment to tissue compartment; k

_{21}: transfer rate constant from tissue compartment to central compartment; AUC: area under the plasma concentration-time curve; C

_{max}: maximum plasma concentration; CL: clearance; V

_{ss}: steady state volume of distribution; V

_{d1}: volume of distribution of central compartment; V

_{d2}: volume of distribution of tissue compartment.

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Correia, C.; Ferreira, A.; Santos, J.; Lapa, R.; Yliperttula, M.; Urtti, A.; Vale, N.
New In Vitro-In Silico Approach for the Prediction of In Vivo Performance of Drug Combinations. *Molecules* **2021**, *26*, 4257.
https://doi.org/10.3390/molecules26144257

**AMA Style**

Correia C, Ferreira A, Santos J, Lapa R, Yliperttula M, Urtti A, Vale N.
New In Vitro-In Silico Approach for the Prediction of In Vivo Performance of Drug Combinations. *Molecules*. 2021; 26(14):4257.
https://doi.org/10.3390/molecules26144257

**Chicago/Turabian Style**

Correia, Cristiana, Abigail Ferreira, Joana Santos, Rui Lapa, Marjo Yliperttula, Arto Urtti, and Nuno Vale.
2021. "New In Vitro-In Silico Approach for the Prediction of In Vivo Performance of Drug Combinations" *Molecules* 26, no. 14: 4257.
https://doi.org/10.3390/molecules26144257