Semi-mechanistic modelling of the tumour growth inhibitory effects of LY2157299, a new type I receptor TGF-b kinase antagonist, in mice

Lorea Buenoa, Dinesh P. de Alwisb, Celine Pitoub, Jonathan Yinglingc, Michael Lahnd,
Sophie Glattb, In˜ aki F. Troco´niza,*
aDepartment of Pharmacy and Pharmaceutical Technology, School of Pharmacy, University of Navarra, Pamplona 31080, Spain
bGlobal PK/PD & Trial Simulation, Eli Lilly and Company, Windlesham, Surrey, UK
cDivision of Cancer Research, Eli Lilly and Company, Indianapolis, USA
dOncology Program Phase, Eli Lilly and Company, Indianapolis, USA


Human xenografts Calu6 (non-small cell lung cancer) and MX1 (breast cancer) were implanted subcutaneously in nude mice and LY2157299, a new type I receptor TGF-b kinase antagonist, was administered orally. Plasma levels of LY2157299, percentage of phosphory- lated Smad2,3 (pSmad) in tumour, and tumour size were used to establish a semi-mecha- nistic pharmacokinetic/pharmacodynamic model.An indirect response model was used to relate plasma concentrations with pSmad. The model predicts complete inhibition of pSmad and rapid turnover rates [t1/2 (min) = 18.6 (Calu6) and 32.0 (MX1)]. Tumour growth inhibition was linked to pSmad using two signal transduction compartments characterised by a mean signal propagation time with esti- mated values of 6.17 and 28.7 days for Calu6 and MX1, respectively.The model provides a tool to generate experimental hypothesis to gain insights into the mechanisms of signal transduction associated to the TGF-b membrane receptor type I.

1. Introduction

Since its discovery almost two decades ago1 the transforming growth factor-b (TGF-b) has received considerable attention, being identified as a key element regulating tumour cell growth.2,3 The complex and multifunctional activities of TGF-b endow it with both tumour suppressor and tumour promoting activities, depending on the stage of carcinogene- sis and the response of the tumour cell.4,5Briefly, the TGF-b exerts its regulatory functions binding to the TGF-b type II receptor located in the cell membrane, the constitutively active TGF-b type II receptor recruits a TGF-b type I receptor, to form a heterotetrameric receptor complex, where TGF-b type II receptor phosphorylates the TGF-b type I receptor in the juxtamembrane region, or ‘GS domain’ which is rich in serine and threonine residues.6 Activated TGF-b type I receptor propagates the signal downstream directly by phos- phorylating Smad2 and Smad3, which in turn form com- plexes with Smad4. This combined complex translocates to the nucleus where it regulates numerous gene transcriptions in combination with transcription factors.7
Recently, the in vitro and in vivo pharmacodynamic (PD) characterisation of new TGF-b receptor I kinase inhibitors has been published8,9 as well as a review of the current drug development programmes for TGF-b receptors antagonists.10 However, to our knowledge in vivo characterisation of novel drugs inhibiting TGF-b receptors based on a pharmacoki- netic/pharmacodynamic (PK/PD) approach has not been pub- lished yet.

The objective of the present study was to develop a semi- mechanistic PK/PD model for LY2157299, a new and potent specific TGF-b type I receptor antagonist of the family of pyr- azoles.11,12 The model was formulated with the aim of inte- grating the pharmacokinetics (PK) properties of LY2157299, the percentage of phosphorylated Smad2 and Smad3 (pSmad) considered as a biomarker, and the inhibition of tumour growth.

2.1.4. Determination of pSmad in tumour

To measure the target inhibition level, tumours were pro- cessed by Western blot for phosphorylated Smad2 and Smad3 activities. Briefly, the tumour was pulverised in liquid nitro- gen and lysed with 600 ll lysis buffer containing 50 mM Tris–HCl at 7.5, 500 mM NaCl, 1% NP-40, 0.25% Na-dexydolate, 20 mM NaF, protease inhibitor (Roche Diagnostics, Basel) and phosphatase inhibitor cocktail I and II (Sigma, St. Louis). Then 80 lg protein was loaded onto 10% SDS Tris-glycine gel. Western blot was performed with a proprietary phosphorylated the assay was 1.14 ng/ml. The accuracy of the assay was <15% and the intra and interassay coefficients of variation were less than 10%. 2. Materials and methods 106 Calu6 human anaplastic carcinoma lung cells (Calu6) or 106 MX1 human carcinoma breast cells (MX1) were implanted subcutaneously into Charles River nude mice (weight ~25 mg). Experiments started 7–10 days after tumour implantation. Two different experiments were carried out, the PK/PD experiments which provided the pharmacokinetic and bio- marker data, and the tumour growth experiments which pro- vided the tumour size data. The experiments were adhered to the Principles of Laboratory Animal Care (NIH publication #85-23, revised in 1985). 2.1. PK/PD experiments 2.1.1. Calu6 LY2157299 was given orally as a single dose (data from eight independent studies were combined) or in a multiple dosing design (one study). The value of the dose levels given in a sin- gle dose manner was 10 (n = 3), 30 (n = 8), 50 (n = 26), 75 (n = 69), 100 (n = 3), 150 (n = 21) and 300 (n = 3) mg/kg. Animals were sacrificed at the following times: 0.5, 1, 1.5, 2, 4, 8 and 16 h after administration, then the tumour was removed and blood was recovered. In the multiple dosing study, LY2157299 was administered twice a day (bid) at the dose of 75 mg/kg every 12 h for 20 consecutive days to 31 mice. Ani- mals were sacrificed at 2 h after the last administration at days 10, 15, 20 and 25, and the tumour was removed for pSmad determination and the blood was recovered for deter- mination of drug levels in plasma. 2.1.2. MX1 Twelve mice involved in a single study were treated with a single 75 mg/kg dose of LY2157299. Animals were sacrificed at 0.5, 1, 2, 4 and 16 h after drug administration, tumours were removed and the blood was collected. 2.1.3. Determination of LY2157299 in plasma Venous blood samples (1 ml) was drawn into sodium-hepa- rinised tubes for measurement of LY2157299. Plasma sam- ples were analysed using a validated method involving protein precipitation with turbo ion spray LC/MS/MS detec- tion. The validated range of measurement in plasma was 5–1000 ng/ml (a 50-fold dilution was validated to demon- strate the ability of the assay to analyse samples at higher concentrations). The value of the limit of quantification of Smad2 and Smad3 antibodies. 2.2. Tumour growth experiments 2.2.1. Calu6 Data from two studies are presented. The first available data came from a study where 20 mice were treated bid with either saline (control group; n = 10) or 75 mg/kg of LY2157299 (treated group; n = 10) for 20 consecutive days. Tumour size was mea- sured every 4–6 days for one month after the first drug admin- istration and afterwards the animals were sacrificed. The data from this study were used to develop the tumour growth model (index dataset). Later, data from a second study also became available and were used for model validation pur- poses (test dataset). Seventy-six mice were treated bid with either saline (control group; n = 36) or 75 mg/kg of LY2157299 for 10 (n = 10) 15 (n = 10) or 20 (n = 20) consecutive days. Tu- mour size was measured once a week for one month. 2.2.2. MX1 Data were obtained from a single study where mice were trea- ted three times a day with either saline (control group, n = 10) or 75 mg/kg of LY2157299 (treated group; n = 10) for 20 consec- utive days. Tumour size was measured every 3–4 days for one month after the first drug administration and afterwards the animals were killed. 2.2.3. Measurement of tumour size Dimensions of the tumours were measured with the use of a clipper. Tumour size (TS) expressed in mg were calculated as 2 follows: TS ¼ × d, assuming a density (d) = 1 mg/mm3 for tumour tissue. 2.3. Data analysis Data were analysed sequentially in four steps. First the phar- macokinetic data were modelled, then using the model parameter estimates from the pharmacokinetic model, a model describing the time course of pSmad was selected (bio- marker model). The third step consisted in finding the best description of tumour growth in the absence of drug adminis- tration, and finally a model describing simultaneously the kinetics of tumour growth in control and treated animals was developed. Data obtained from different cell lines were fit separately (except for the levels of LY2157299 in plasma that were fit together to develop the pharmacokinetic model). All the analyses were performed using the NONMEM V com- puter program.Pharmacokinetic and pSmad data were fit using the naı¨ve pool approach since each animal contributed with a single measurement and therefore is not possible to distinguish be- tween inter-animal and residual variability. In that approach all the information were considered as coming from the same animal.14 On the contrary, animals used in the tumour growth experiments contributed with several measurements, and in the model were Kout, IMAX, IC50 and n, since pSmad(0) was fixed to 100%. 2.3.3. Tumour growth model in control groups TS did not reach a plateau and therefore variants of the Gom- pertz model were used,18,19 in particular two alternative mod- els were fit to the data. A model assuming an exponential rate of tumour growth,20 and a model allowing for the switch from an exponential to a linear growth21.Inter-animal variability was modelled exponentially and the residual variability – reflecting the difference between the observed and model predicted concentrations – was mod- elled initially with a combined error model; if one of the com- ponents (additive or proportional) of the residual error was negligible, it was deleted from the model. Selection between models was based mainly on the good- ness of fit and residual plots, and precision of parameter esti- mates expressed as coefficient of variation. The minimum value of the objective function (OBJ) provided by NONMEM was also used as a guide during the model building process. A difference in OBJ between two hierarchical models of 3.84,where dTS/dt is the rate of change of TS, Kgrw1 and Kgrw0 are the rate constants representing the exponential and linear growth respectively, and c is a parameter that fixed to the va- lue of 20, allows the system to switch from the exponential to the linear growth sharply enough.21 The parameters to be estimated by the model were Kgrw1, Kgrw0 and TS0, the tumour size at baseline. 2.3.1. Pharmacokinetic model Pharmacokinetics of LY2157299 in plasma was described with compartmental models. Since data included plasma concen- trations obtained after the administration of different doses in a single or a multiple dosing regimen, dose- and time- dependent kinetics were also evaluated. Dose-dependent where INH2 is a 0–1 normalised effect representing an inhib- itory growth signal, originated from the drug-induced inhibi- tion of pSmad (INH0), and propagated through two signal transduction compartments. The time course of INH2 was de- scribed with the following set of equations: pSmad — pSmad pharmacokinetics was explored evaluating the significance of the administered dose level as a covariate in each of the INH0 ¼ dINH1 ð0Þ pSmad ð0Þ ð4Þ pharmacokinetic model parameters. Time dependent phar- macokinetics was evaluated allowing model parameters to change linearly (or non-linearly) with time after the first drug administration. 2.3.2. Biomarker model An indirect response model was used to relate the predicted plasma concentrations of LY2157299 (C) with the observed pSmad data17 Eq. (1). The model assumes the existence of fac- tors within the tumour cell responsible for the synthesis (phosphorylation) and degradation (de-phosphorylation) of pSmad. The activity of such factors is reflected by the zero-or- der rate constant Ksyn, and the first-order rate constant Kout, respectively. LY2157299 exerts its effects by inhibiting Ksyn:At baseline (initial condition) INH0, INH1 and INH2 are equal to 0.Ktrd represents the first-order constant governing the rate of signal propagation and is a parameter derived from the esti- mated parameter MSPT (mean signal propagation time) as follows: Ktrd = (m + 1)/MSPT, where m refers to the number of signal transduction compartments. Other models assuming different mechanisms of action were also fit to the data. Spe- cifically, a model where the drug exerts cell death21 and a model including two mechanisms of action, one inducing cell death and the other exerting tumour stabilisation. The former described the data significantly worse (P > 0.05) than the se- lected model, and the latter did not improve the fit signifi- cantly (P > 0.05).

Fig. 1 shows schematically the complete tumour growth model including the pharmacokinetic and the biomarker form of 1 — I × , IC being the value of C eliciting half of maximal inhibition in Ksyn (IMAX), and n the slope parame- ter controlling the steepness of the Ksyn versus C curve. IMAX was constrained between 0 (no inhibition) and 1 (maximal inhibition). At the baseline dpSmad/dt = 0 and therefore Ksyn = Kout · pSmad(0). The parameters to be estimated by summarised computing the profiles of 0.05, 0.5 and 0.95 per- centiles, and representing them graphically together with the raw data. Agreement between simulated and observed values was judged by visual inspection.

2.3.5. Validation of the model

For each of the different dosing scenarios in the test dataset, five hundred individual tumour size versus time profiles were simulated using the selected model. Simulations.

Fig. 1 – Scheme representing the complete pharmacokinetic- biomarker-tumour growth model. Parameters estimated are represented in boldface and defined in text.

2.3.6. Model simulations

Tumour size versus time profiles were simulated after bid oral administration of a total daily dose of 150 mg/kg of LY2157299 under the following scenarios: alternating (i) one week of treatment with a one week washout period, (1W/0W/1W) and (ii) one day treatment with one day off (1D/0D/1D).

3. Results

3.1. Pharmacokinetic model

Disposition of LY2157299 in plasma was best described with a two compartment model. Absorption process could not be adequately characterised due to the lack of plasma samples for the first 30 min after drug administration. The value of Ka, the first-order rate absorption constant used (8 h)1) was se- lected as a result of a sensitive analysis, where Ka was fixed to different values (ranging from 0.5 to 15 h)1), selecting the one providing the lowest value in OBJ. Dose and time did not show significant effects on the kinetics of LY2157299 in plasma (P > 0.05). The estimates of the pharmacokinetic parameters are listed in Table 1. The upper panel in Fig. 2 shows the plot of the observed versus model predicted plasma LY2157299 concentrations for all data obtained at all dose levels.

3.2. Biomarker model

The time course of pSmad for the two cell lines studied was properly described using an indirect response model. The agreement between observed values and model predictions is presented in the lower panel of Fig. 2. Table 2 lists the model parameter estimates. IMAX showed a value that was not significantly different from 1 (P > 0.05). The short values of t1=2K of 18.6 and 33 min for Calu6 and MX1, respectively, indicate a rapid rate of turnover of pSmad.

Fig. 2 – Upper panel: model predicted versus observed plasma concentration LY2157299 values. Lower panel: model predicted versus observed pSmad values. Each symbol represents a dose level. Solid lines correspond to the lines of identity.

Fig. 3 shows the simulated pharmacokinetic and pSmad profiles after a single 75 mg/kg oral dose of LY2157299, the dose used in the tumour growth experiments. After oral administration of 75 mg/kg, LY2157299 induced a 70% de- crease in pSmad for both types of cell lines. The time at which pSmad recovered 80% of baseline was approximately 6 h after administration.

3.3. Tumour growth model

For both Calu6 and MX1 xenografts, the model allowing for the switch from an exponential to a linear growth provided better fits (P < 0.001) compared to the exponential growth model. 3.4. Model validation The tumour growth kinetics found in the control group from the test dataset resulted different compared to the control group in the index dataset. The estimate of Kgrw0 (51.6 mg day)1) was significantly lower (P < 0.001) with respect to the one obtained previously [111 mg day–1 (see Table 3)]. However, once those differences in the control group were ta- ken into account, the simulations from the model developed were able to capture very well the tumour size observations in the treated groups from the test dataset (Fig. 6). 3.5. Model simulations Fig. 7 represents the time profiles of Kgrw1 (left) and tumour size (right) corresponding to the different dosing schedules simulated. Interestingly, despite the different profiles seen in Kgrw1 for the two alternating schedules, tumour response is similar. 4. Discussion Pharmacokinetics of LY2157299 was described with standard PK models, and neither time nor dose dependencies were de- tected. LY2157299 was rapidly eliminated from the plasma and no accumulation was present.The time course of pSmad was described with an indirect response model,17,22 where the rate of phosphorylation was inhibited by the drug resembling a mechanism that is sup- ported by experimental findings.10,23 It is recognised, how- ever, that the model for biomarker represents an oversimplification of the events occurring at the level of the values of MSPT on the time course of drug effects: longer sig- nal propagation times are associated with longer onset and offset response times. Fig. 3 – Symbols represent observed versus time profiles of LY2157299 concentrations in plasma (upper panel) and pSmad values in tumour [circles (MX1); triangles (Calu6); lower panel]. Solid lines represent model based simulated time profiles assuming a single 75 mg/kg oral dose of LY2157299. Vertical lines represent standard deviations. Fig. 4 shows the mean tumour size versus time profiles ob- tained in the animals from the control and treated groups, to- gether with the predictions from the integrated semi- mechanistic model represented in Fig. 1. The model described not only the mean data very well but also individual animal data (plots not shown). Parameter model estimates are shown in Table 3. The only parameter that differs substantially be- tween the two types of cell lines is the mean signal propagation time with values of 6.17 (Calu6) and 28.7 (MX1) days. Propagation of the signal transduction was modelled with two transduction compartments. Upper panel in Fig. 5 shows the substantial delay between the drug-induced decrease in pSmad reflected by the norma- lised function INH0 and the kinetics of the inhibitory growth signal occurring in each of the transduction compartments. The lower panel in Fig. 5 explores the impact of different receptor. Signal transduction mechanisms have been identified in many areas of pharmacology. In the cancer area those mech- anisms play an important role and much research is focused in the identification of the key elements in the cascade of the events. However, there is a lack of information available regarding the quantitative description of the time course of the propagation of the signal once the drug has reached its target. Such quantitative description implies the acquisition of adequate data and the use of a mathematical model. Signal transduction events are reflected as a delay in the observed response with respects the drug-induced changes in the time course of the biomarker, and therefore experimental design has important implications. For example, a design where the time at which the last measurement of tumour equals the time of last administration, might be enough to confirm a significant reduction in tumour size but not for describing the kinetics of signal transduction. In the current study the drug was given for 20 consecutive days, and once administra- tion was stopped, the tumour size was measured for an addi- tional 10–14 days giving therefore the opportunity to quantify the time at which the rate constants governing tumour growth return to their initial values; nevertheless more pro- longed periods of observation of the tumour growth in treated animals would possibly improve the estimation of the signal propagation related parameters. The model that has been used to handle signal transduc- tion is based on a chain of transduction (transit) compart- ments linked through a first-order rate constant, although other model alternatives exist.24 Models including transit compartments have been used to deal with the delay in the appearance of the nadir during chemotherapy,25 to explain the time dependent response found in cell culture experi- ments26 or to model the cytotoxic effect of several anticancer drugs in mice using human xenografts.21 It should be empha- sised that the model presented in the current work predicts tumour stabilisation and never cell death. Although the mod- el was selected taking into account statistical model fitting criteria and the known mechanism of drug action, it should be taken into consideration the possibility of tumour shrink- age at higher exposures to LY2157299. The model estimates obtained for the MSPT parameter are 6.17 and 28.7 days for the Calu6 and MX1 xenografts, respec- tively. This result suggests that the signal transduction effi- ciency is tumour specific. Despite inter-animal variability was tested for significance in all the model parameters of the integrated tumour growth model, for the case of the parameters Kgrw0 and MSPT resulted non-significant (P > 0.05); however, the simulation exercise performed during the external validation shows that the inter-animal variability terms estimated in our analysis are enough and capable to ac- count for the variability seen in the data.

Fig. 5 – Upper panel, kinetics of the inhibitory growth signal occurring in each of the transduction compartments for a value of MSPT of 6 days. Lower panel, impact of different values of MSPT on the time course of Kgrw1.

A mechanistic interpretation can be proposed for the two signal transduction compartments. The first one might be reflecting changes occurring at the level of the cytoplasma (i.e. phosphorylation of other proteins), and the second, events occurring at the nucleus, such as gene expression. Re- cently, it was presented the first PK/PD analysis of altered gene expression in rat liver using gene microarrays after a single administration of prednisolone to rats.27 The model comprises membrane receptor and cytoplasm events, and in general the time course of gene expression was modelled with an indirect response model using receptor dynamics as the driving force. The turnover process expressed as half-life (days) varied from 0.01 to 0.5 days, depending on the cluster. These values are shorter than the derived half-life associated to the second transduction compartment [1.41 days (Calu6) and 6.9 days (MX1)] found in the current report. Interestingly, other authors found that the derived values of the half-life associated to k1, the first rate constant responsible of propa- gating the cytotoxic effects in mice ranged from 1.34 to 12.4 days.

Fig. 6 – Results from the model validation exercise. In each of the panels the symbols represent observations from the test dataset, and lines represent the outcome of the simu- lations based on the selected model. The median profile is represented by the middle lines and the lower and upper lines in each panel correspond to the 5 and 95 percentiles. The thick horizontal line in each panel shows the duration of the 75 mg/kg bid treatments.

Delays in signal transduction have a dual effect as it is shown in Fig. 5. Faster signal propagation implies faster onset but also faster offset in response. The time course of the inhibitory signal associated to the Type I receptor TGF-b ki- nase antagonism highlights the possibility of having a benefit combining signal transduction modulators acting on different pathways with different dynamics.

In Fig. 8, the general behaviour of the integrated tumour growth model is explored relating the sensitivity of the re- sponse as a function of drug potency and transduction sys- tem efficiency, the latter represented by MSPT. Response was expressed as tumour growth inhibition [TGI (%), com- puted as percentage change in tumour size in the treated group with respect to the control group at the end of the treat- ment] and tumour growth delay (TGD, calculated as the time at which the tumour in the treated group achieves a size equal to the size in the control group at the time of the stop of the treatment). Drug potency was expressed as the ratio be- tween Cee and IC50, where Cee is the steady state plasma con- centration of LY2157299 corresponding to three weeks of continuous intravenous infusion. Independent of the value of MSPT, TGI increases as Cee/IC50 increases, however, for each value of drug potency TGI decreases as MSPT increases. With respect to TGD, Cee/IC50 and MSPT behave similarly.

Fig. 8 – Model based simulated percentage of tumour growth inhibition [TGI; left panel] and tumour growth delay [TGD; right panel] as a function of steady state plasma concentrations of LY2157299 (Cee) relative to IC50, and mean signal propagation time (MSPT). IC50 is the level of LY2157299 in plasma eliciting half of maximal inhibition in the rate of pSmad phosphorylation.

The model developed so far has potential applications in the drug development of Type I receptor TGF-b kinase antag- onists. For example and for LY2157299, simulations varying the dose schedule and exploring the impact on the time course of the response were performed (Fig. 7). With respect to follow-up compounds, and taking into account that the kinetics of the signal transduction is a drug independent pro- cess, the model can be used together with PK and biomarker information to simulate tumour response of new compounds with the same mechanism of action.

In conclusion, this report shows the first PK/PD analysis of the anti-tumour effects of LY2157299, a new Type I Receptor TGF-b kinase antagonist. The integrated model contains four major components: the PK model, the biomarker model, the model dealing with signal transduction and the tumour re- sponse model.

Conflict of interest statement

The authors are employees of Eli Lilly and Company (Dinesh P. de Alwis, Celine Pitou, Jonathan Yingling, Michael Lahn and Sophie Glatt) or have received financial research support from this company (Lorea Bueno and In˜ aki F. Troco´ niz).


This work was supported by Eli Lilly and Company, Windle- sham, Surrey, UK


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