Sequential Exposure of Bortezomib and Vorinostat is Synergistic in Multiple Myeloma Cells

Abstract

Purpose

To examine the combination of bortezomib and vorinostat in multiple myeloma cells (U266) and xenografts, and to assess the nature of their potential interactions with semi-mechanistic pharmacodynamic models and biomarkers.

Methods

U266 proliferation was examined for a range of bortezomib and vorinostat exposure times and concentrations (alone and in combination). A non-competitive interaction model was used with interaction parameters that reflect the nature of drug interactions after simultaneous and sequential exposures. p21 and cleaved PARP were measured using immunoblotting to assess critical biomarker dynamics. For xenografts, data were extracted from literature and modeled with a PK/PD model with an interaction parameter.

Results

Estimated model parameters for simultaneous in vitro and xenograft treatments suggested additive drug effects. The sequence of bortezomib preincubation for 24 hours, followed by vorinostat for 24 hours, resulted in an estimated interaction term significantly less than 1, suggesting synergistic effects. p21 and cleaved PARP were also up-regulated the most in this sequence.

Conclusions

Semi-mechanistic pharmacodynamic modeling suggests synergistic pharmacodynamic interactions for the sequential administration of bortezomib followed by vorinostat. Increased p21 and cleaved PARP expression can potentially explain mechanisms of their enhanced effects, which require further PK/PD systems analysis to suggest an optimal dosing regimen.

Introduction

Multiple myeloma is a B-cell neoplasm characterized by abnormal proliferation of plasma cells. It accounts for 20% of deaths related to cancers of the blood and bone marrow and has a five-year relative survival of only about 44%. Clinical manifestations of multiple myeloma include bone diseases, hypercalcemia, renal impairment, increased risk to infections and hematological problems such as anemia, leukopenia, and thrombocytopenia (1, 2). Chemotherapy in multiple myeloma encompasses combinatorial regimens of proteasome inhibitors (e.g., bortezomib), immunomodulatory agents (thalidomide and lenalidomide), steroids (e.g., dexamethasone), and alkylating agents (e.g., melphalan). Bortezomib is one of the most significant agents for multiple myeloma management and has lead to improved overall survival rates (3). It acts by binding to the β5 subunit of 26S proteasome, a large complex regulating degradation of intracellular proteins. Bortezomib inhibits proteolysis, disrupts cellular homeostasis (leading to cellular stress), and subsequently apoptosis. It affects both survival and apoptotic signaling pathways by modulating expression of several proteins, such as up-regulation of p21 (causing cell cycle arrest), p53, caspase-3 (causing apoptosis), and down-regulation of BCLxL and NFκB (decreasing proliferation) (4, 5). However, despite significant improvements in overall response rates in patients and median survival times, multiple myeloma shows repetitive patterns of remission and relapse, with patients ultimately developing drug resistance and refractory disease (6). There is still an unmet need for more effective chemotherapy and optimized dosing regimens.

Hematological malignancies have shown to be sensitive to histone deacetylase (HDAC) inhibitors such as vorinostat, particularly in combination with bortezomib (7–9). Vorinostat is a pan-HDAC enzyme inhibitor, an enzyme family responsible for repression of gene expression of several proteins. By removal of acetyl groups, HDAC enzymes decrease access of transcription factors to DNA and create a compact chromatin structure making it transcriptionally repressive. HDAC inhibition by vorinostat results in the up-regulation of many HDAC enzyme substrate proteins, some of which will in turn inhibit cell proliferation (p21) and others that induce apoptosis (e.g., caspase-3 and BID) (10). The combination of bortezomib and vorinostat shows increased efficacy in several in vitro and preclinical studies with multifactorial mechanisms of interactions, such as up-regulation of pro-apoptotic proteins (e.g., caspase-8, 9, 3, PARP, and cytostatic proteins such as p21) and inhibition of protein degradation via their combined inhibition of proteasome and aggresomes (7–9, 11). However, there are limited systematic studies evaluating the nature of this pharmacodynamic interaction, including concentration- and time-dependent effects.

The quantitative analysis of drug combinations in oncology has been traditionally conducted with empirical methods such as Loewe’s additivity (12), isobologram analysis (13), curve shift analysis (14), and certain three dimensional methods such as the universal response surface approach (15). However, these approaches are non-mechanistic and do not take into account all types of experimental data, such as the time course of any potential interactions. A modified form of the non-competitive interaction equation of Ariens and Simonis (16) has been applied widely, and includes an interaction parameter ψ denoting the nature of interaction (i.e., synergistic, antagonistic, or additive) (17, 18). Empirical interaction parameters have also been combined with semi-mechanistic tumor growth models to ascertain the time-course of drug interactions in murine xenografts (19). Here we evaluate several modeling approaches, and introduce a simple modification to evaluate drug sequence effects, to simultaneously distinguish the different in vitro and in vivo combination sequences of boretzomib and vorinostat. The goal is to determine the nature and extent of bortezomib and vorinostat interactions for in vitro and in vivo multiple myeloma systems via semi-mechanistic pharmacodynamic modeling. This study also evaluates several key cellular biomarkers that may be implicated in regulating these interactions.

Methods

Cell Line and Reagents

The U266 human multiple myeloma cell line was purchased from American Type Culture Collection (ATCC; Manassas, Virginia). Vorinostat was purchased from Selleckchem, and a stock solution was made in dimethylsulfoxide and stored at −80 °C. The clinically available formulation of bortezomib (Millennium Pharmaceuticals, Inc.) was used in all experiments. Cells were cultured in RPMI-1640 medium (Life Technologies, Grand Island, New York) supplemented with 15% fetal bovine serum (FBS; ATCC, Manassas, Virginia) and 1% penicillin/streptomycin (Life Technologies, Grand Island, New York). Cell proliferation reagent WST-1 was purchased from Roche Life Science (Indianapolis, Indiana).

Cell Proliferation Assays

U266 cells were seeded at 10,000 cells/well in 96 well plates for all in vitro cytotoxic and proliferation experiments. For single agent growth inhibition, U266 cells were exposed to vehicle (control), bortezomib (0.01–1000 nM), or vorinostat (0.01–100 μM) for 18, 24, and 48 hours. The concentration range for individual agents was selected based on their in vitro potencies. For drug interaction studies, combination groups were comprised of five treatment regimens for up to 30 different concentration combinations for bortezomib (1– 4 nM) and vorinostat (2–5 μM). The five combination study arms consisted of: bortezomib and vorinostat simultaneous exposure for 24 and 48 hours, bortezomib pre-incubation for 6 hours followed by vorinostat for 18 hours, bortezomib pre-incubation for 24 hours followed by vorinostat for 24 hours and the reverse sequence. Cell viability was measured using WST-1 reagent assay at the end of treatment periods. WST-1 was allowed to incubate for 2 hours, and absorbance was measured at 450 nm with a reference wavelength of 690 nm using a SpectraMax 190 micro plate reader (Molecular Devices, Sunnyvale, California). For the time-course of cellular proliferation, the sequence that resulted in synergistic effects of bortezomib and vorinostat was chosen, cell viability was measured at 0, 24, 48, 72, and 96 hours, and outcomes were compared against identical exposure times of single agents and other combination treatment times. Cell viability was normalized to values for untreated controls and reported with all three replicates.

Semi-mechanistic in vitro PD Modeling

Single Agent Growth Inhibition Modeling

The concentration-effect relationships for bortezomib and vorinostat as single agents were characterized with the sigmoidal Hill function:

$$R=R_0·\left[1-\frac{I_{\mathit{max}}·C^{\gamma }}{I{C}_{50}^{\gamma }+C^{\gamma }}\right]$$ (1)

where R is the cell viability (response), R₀ is the baseline (response when no drug is present), I_max is the maximum inhibition caused by the drug, C is drug concentration, IC₅₀ is drug concentration producing 50% of maximum inhibition effect, and γ is the Hill coefficient.

Combination Drug Effect Modeling

To assess the nature and type of interaction between bortezomib and vorinostat, a modified form of the non-competitive interaction equation originally proposed by Ariens et al. (20, 21) was applied (Eq. 2). Chakraborty and Jusko modified the original equation to include an interaction parameter (ψ) to indicate the type of interaction: in which ψ < 1 suggests a synergistic interaction, ψ >1 suggests antagonism, and ψ = 1 suggests an additive interaction (17). We introduced a multiplicative interaction parameter (μ) that signifies any changes in efficacy of the drug combination due to sequential administration. This term behaves similarly to ψ, such that a value of μ < 1 suggests synergistic interaction, μ >1 suggests antagonism, and μ = 1 suggests additive interaction. This allows for modeling of simultaneous and sequential exposure treatment arms together with one model equation for the same exposure times:

$$R=R_0·\left[1-\frac{\left(\frac{I_{\mathit{max},B}·C_B^{\gamma B}}{{(\mu ·\psi ·I{C}_{50,B})}^{\gamma ,B}}\right)+\left(\frac{I_{\mathit{max},V}·C_V^{\gamma V}}{{(\mu ·\psi ·I{C}_{50,V})}^{\gamma ,V}}\right)+I_{\mathit{max},B}+I_{\mathit{max},V}-I_{\mathit{max},B}·I_{\mathit{max},V}\times \left(\frac{C_B^{\gamma B}}{{(\mu ·\psi ·I{C}_{50,B})}^{\gamma ,B}}\right)·\left(\frac{C_V^{\gamma V}}{{(\mu ·\psi ·I{C}_{50,V})}^{\gamma ,V}}\right)}{\left(\frac{C_B^{\gamma B}}{{(\mu ·\psi ·I{C}_{50,B})}^{\gamma ,B}}\right)+\left(\frac{C_V^{\gamma V}}{{(\mu ·\psi ·I{C}_{50,V})}^{\gamma ,V}}\right)+\left(\frac{C_B^{\gamma B}}{{(\mu ·\psi ·I{C}_{50,B})}^{\gamma ,B}}\right)·\left(\frac{C_V^{\gamma V}}{{(\mu ·\psi ·I{C}_{50,V})}^{\gamma ,V}}\right)+1}\right]$$ (2)

with the B and V super- or subscripts referring to bortezomib and vorinostat, ψ is the interaction parameter reflecting the nature of the interaction after simultaneous exposures, and μ is the multiplicative parameter indicating changes in efficacy owing to sequential treatment.

Cellular Proliferation Modeling

For modeling the in vitro kinetics of cellular growth under bortezomib and vorinostat treatment, a prior combination model was adapted (19) and altered to include a multiplicative parameter (μ) for changes on sequential administration:

$$\frac{dR}{dt}=k_g·R-(k_{\mathit{VORT}}·C_V+\mu ·\psi ·k_{\mathit{BORT}}·C_B)·RR(0)=1$$ (3)

with k_g as a first-order growth rate constant, and k_BORT and k_VORT are second-order kill constants of bortezomib and vorinostat. As vorinostat is added to enhance the efficacy of bortezomib, ψ and μ were set to alter the efficacy parameter for bortezomib (k_BORT), but were also tested on vorinostat effects, revealing no change in the type of interaction. As one set of concentrations for each drug was tested, based on modeling a range of exposure times and concentrations with Eq. 2, the model has linear efficacy parameters for drug effects. Consequently, values of ψ or μ >1 would indicate synergy, ψ or μ =1 would indicate additivity, and ψ or μ < 1 would indicate antagonism. μ is estimated only when sequential administration is analyzed concurrently with the simultaneous administration of both drugs.

A transit compartment was also needed to capture the delay in vorinostat effects as a single agent on U266 cell proliferation. The differential equations are defined as:

$$\frac{d{K}_1}{dt}=(k_{\mathit{VORT}}·{\mathrm{C}}_{\mathrm{V}}-K_1)/\mathrm{\tau }{K}_1(0)=0$$ (4)

$$\frac{dR}{dt}=k_g·R-K_1·RR(0)=1$$ (5)

with τ as a mean transit time, and K₁ is the transit compartment.

All in vitro PD modeling was conducted using a naïve pooled approach with the maximum likelihood estimation method in ADAPT 5 (22). For modeling combination effects, single agent parameters were fixed to estimates from fitting the individual drug profiles first, and only interaction parameters were estimated (ψ and μ). The variance model was defined as: VAR = (σ₁+σ₂•Y)², with σ_i representing estimated variance parameters, and Y is the model predicted value for cell viability. Model evaluation and selection was guided by goodness of fit criteria that included: Akaike information criteria (AIC), precision and confidence intervals on parameter estimates, visual inspection of model fits, and examination of residuals.

Xenograft PK/PD Modeling

Mean PK data for vorinostat following a single i.v. dose of 10 mg/kg to female BALB/c nude mice were obtained from Yeo et al. (23), and bortezomib PK data were obtained from Zhang and Mager (24), in which male BALB/c mice were given a 0.25 mg/kg i.v. bolus dose. Tumor growth profiles were taken from Campbell et al. (7), in which SCID mice bearing LAGκ-1B tumors (patient derived) were treated twice weekly with bortezomib (0.5 mg/kg), vorinostat (100 mg/kg), or their simultaneous combination for 35 days. Bortezomib PK data were in-house, and all other data were digitized from the literature using GraphClick software (http://www.arizona-software.ch/graphclick/).

A sequential PK/PD modeling approach was used for modeling the in vivo interaction, in which PK data were modeled first, and then PK parameters were fixed for modeling of the tumor growth kinetics. For both drugs, a two-compartment model with first-order elimination rate and inter-compartmental distribution rate constants was used to describe the PK data (supplemental Fig. S1).

The base model structure for modeling the anti-cancer effects of both drugs, as single agents and in combination, is similar to the one used for in vitro modeling of cell proliferation (Eq. 3); however, instead of static in vitro drug concentrations as the driver for cell kill, we have incorporated in vivo PK of each agent as the drivers for cytotoxic effects. An exponential growth rate model was used to describe tumor growth, and a second-order kill constant for each drug was included. The tumor kinetic data were extracted from Campbell et al., and only simultaneous dosing of bortezomib and vorinostat was tested. Therefore, ψ is the only interaction parameter was included in the model. Based on the parameterization of the model, a value of ψ >1 would indicate synergy, ψ =1 would indicate additivity, and ψ < 1 would indicate antagonism. ψ was tested to affect the kill rate constant of each agent individually; however, no differences in the model fitting performance or interpretation of the interaction were observed. Subsequently, ψ was retained on the bortezomib efficacy parameter as vorinostat is being tested to enhance the efficacy of bortezomib and the structure is consistent with the in vitro modeling. As only one dose level was tested, non-linear functions for drug efficacy could not be tested. Based on model selection criteria (including Akaike information criteria (AIC), precision and confidence intervals on parameter estimates, model fits, and inspection of residuals), no transit compartments (or temporal delays) were needed to describe drug effects. The differential equation for the combination effect is defined as:

$$\frac{dR}{dt}=k_g·R-(k_{\mathit{VORT}}·C{(t)}_{\mathit{VORT}}+\psi ·k_{\mathit{BORT}}·C{(t)}_{\mathit{BORT}})·RR(0)=w(0)$$ (6)

For characterizing single agent data, the efficacy parameter of the second drug was set to zero.

Parameter estimation was achieved with maximum likelihood estimation in ADAPT 5 (22). The variance model was defined as: VAR = (σ₁+σ₂ •Y)², with σ_i representing variance parameters, and Y is the model predicted value for drug concentration (PK) or tumor volume/weight (PD). Separate variance models were specified for PK and PD variables.

Immunoblotting Analysis

U266 multiple myeloma cells were plated in 10 cm² culture dishes at a density of 5 × 10⁶ cells/10 mL culture medium. The cell treatment groups were: bortezomib (3 nM) and vorinostat (2 μM) as single agents for 48 hours, bortezomib (3 nM) and vorinostat (2 μM) simultaneously in combination for 48 hours, and bortezomib (3 nM) for the first 24 hours followed by vorinostat (2 μM) for another 24 hours (sequential administration). Cells were collected at 0, 12, 24, 36, and 48 hours over the duration of treatment, lysed for 30 minutes on ice in RIPA lysis buffer (Cell Signaling Technology, Danvers, Massachusetts) supplemented with Halt^™ protease and phosphatase inhibitor cocktail and phenylmethylsulfonyl fluoride (Thermo Fisher Scientific, Waltham, Massachusetts). The samples were centrifuged at 14,000 rpm for 20 minutes at 4 °C and stored at −80 °C until analysis. After protein concentration analysis by the Bradford method (Bio-Rad Protein Assay Kit; Bio-Rad, Hercules, California), equal amount of proteins for each sample were electrophoresed, separated on SDS-PAGE gel, and transferred onto a nitrocellulose membrane. The primary antibody incubation was done over night (12–16 hours) followed by one-hour incubation with secondary antibody through washes with TBST (Tris-buffered saline + 0.1% Tween 20) in between. Cleaved PARP, total PARP, and p21 expression were measured for all treatment arms. Rabbit primary monoclonal antibodies (Cell Signaling Technology, Danvers, Massachusetts) and horseradish peroxidase (HRP) conjugated goat anti-rabbit secondary IgG (Santa Cruz Biotechnology, Santa Cruz, California) were used for all biomarkers. Protein bands were visualized with enhanced chemiluminescence (ECL) with Pierce ECL Western Blotting Substrate (Thermo Fisher Scientific, Waltham, Massachusetts) and relatively quantified by Image Lab Software (Bio-Rad, Hercules, California). The protein expression profiles were normalized to untreated controls (vehicle) and time point 0 (i.e., first time point). Additionally, cleaved PARP was normalized by total PARP. All experiments were performed in triplicate and reported values are average ± standard deviation.

Results

Single Agent Growth Inhibition

The concentration-effect relationships with the fitted profiles to the sigmoidal Hill function (Eq.1) for borteozmib and vorinostat are shown in Fig. 1. In general, both drugs exhibit a time- and concentration-dependent effect, with the profiles shifting left for longer exposure times. The parameter estimates for single agent growth inhibition modeling are given in Table I. Bortezomib follows a steeper inhibition curve than vorinostat in the U266 cell line (γ = 5 vs. 0.66 and 1.55). Bortezomib is also more potent with lower IC₅₀ values than vorinostat for 24 hours (4.57 nM vs. 3.98 μM) as well as 48 hours (3.38 nM vs. 0.97 μM). I_max for both drugs was fixed to 1 as they showed maximum inhibition and was estimated to be 1 during model fitting (except for the bortezomib estimate of 0.817 at 24 hours). All model parameters were estimated with reasonable precision and the data were described well.

Figure 1.

U266 cell growth inhibition by bortezomib (a) and vorinostat (b). Symbols represent experimental observed values, and lines are model-fitted profiles (Equation 1).

Table 1.

Parameter Estimates for Single Agent Growth Inhibition Modeling

EXPOSURE TIME(HOURS)	PARAMETER
	BORTEZOMIB				VORINOSTAT
	Imax	IC50(nM)	R0	γ	Imax	IC50(μM)	R0	γ
24	0.817	4.57	1.03	5	1	3.98	1.00	0.66
	(1.96)	(3.42)	(1.84)	(N/A) a	(N/A) a	(19.3)	(4.47)	(7.50)
48	1	3.38	0.881	5	1	0.97	1.00	1.55
	(N/A) a	(3.26)	(3.68)	(N/A) a	(N/A) a	(24.8)	(N/A)a	(13.8)
18	-	-	-	-	1	237	0.99	0.50
					(N/A) a	(13.2)	(2.38)	(6.70)

CV% are given in parentheses below the parameter estimates.

N/A- not applicable

^afixed parameter value

Combination Drug Effects

The combination study concentrations were chosen based on the single agent growth inhibition profiles and IC₅₀ values (Figure 1 and Table I). The range for bortezomib was 1– 4 nM and 2–5 μM for vorinostat, which are considerably lower than greater concentrations of 10–1000 nM and 10–1000 μM, where total growth inhibition was achieved for each agent (Fig. 1). A total of 30 different concentration combinations for five diverse treatment exposure times and sequences were fitted to Equation 2 (Table II). The simultaneous and sequential arms for the identical exposure times were modeled simultaneously with the inclusion of an added interaction parameter μ (Eq. 2). I_max, IC₅₀, and γ for each agent were fixed to the estimates obtained from fitting their single agent growth inhibition data (Table I), and only the interaction parameters ψ and μ were estimated. For the 24 and 48 hour simultaneous combinatorial regimens, ψ was estimated to be 0.976 and 0.949 with confidence intervals of 0.855–1.10 and 0.806–1.05. μ was estimated to be 0.874 and 0.704, with confidence intervals of 0.756–0.993 and 0.660– 0.756, for the sequential treatment arms of bortezomib exposures for the first 6 and 24 hours followed by vorinostat for another 18 and 24 hours. For the schedule of vorinostat pre-incubation for 24 hours followed by bortezomib for another 24 hours, μ was estimated to be 0.982 with a confidence interval of 0.909–1.05. Thus, based on the confidence intervals of the estimated interaction parameters, amongst all the in vitro combination treatment arms, only bortezomib pre-incubation treatments had estimates of μ significantly different than 1, indicating a potential synergistic interaction between sequential borteozmib and vorinostat exposures (Table II). Representative modeling fittings for combination data are shown in Fig. 2. A comparison between U266 cells after 48 hours of treatment with bortezomib and vorinostat in simultaneous combination (additive interaction) and sequential treatment of U266 cells with bortezomib only for the first 24 hours followed by vorinostat for another 24 hours (synergistic interaction) is depicted in Figs. 2a and 2b. The plots show the observed data and a three-dimensional response surface created with the final parameter estimates obtained after analyzing the data (Eq. 2). The surface represents the model fitted efficacy response for a value of ψ = 0.949 and μ = 0.708 for simultaneous and sequential combination data. The goodness of fit plots for all treatment arms (observed vs. predicted plots) are included in supplemental Fig. S2. No systematic bias in the fitting of the simultaneous or sequential combination effects was observed.

Table 2.

Combination Treatment Regimens with Nature of Interaction and Parameter Estimates

REGIMEN	PARAMETER		INTERACTION
	ψ	μ
Simultaneous (24 hours)	0.976 (6.16) [0.855, 1.10]	NA	Additive
Simultaneous (48 hours)	0.949 (6.61) [0.806, 1.05]	NA	Additive
Sequential: Bortezomib pre-incubation for 6 hours; Vorinostat added later for 18 hours	0.976 (6.16) [0.855, 1.10]	0.874 (6.78) [0.756, 0.993]	Synergistic
Sequential: Bortezomib pre-incubation for 24 hours; Vorinostat added later for 24 hours	0.949 (3.99) [0.873, 1.02]	0.708 (3.37) [0.660, 0.756]	Synergistic
Sequential: Vorinostat pre-incubation for 24 hours; Bortezomib added later for 24 hours	0.982 (3.68) [0.909, 1.05]	1.01 (8.58) [0.839, 1.19]	Additive

CV% and confidence intervals are given in parentheses below the parameter estimates.

Figure 2.

Fitted 3D response surface (Equation 2) for combination effects in U266 cells treated with bortezomib and vorinostat simultaneously for 48 hours (a) and sequentially with bortezomib alone for the first 24 hours followed by vorinostat for another 24 hours (b). The mesh surface represents model fitting with the final estimates of ψ (0.976) and μ (0.708). Green symbols are experimental data above the surface, and red symbols are experimental data below the surface.

Time-course of Cellular Proliferation

As the sequential combination of bortezomib exposure for 24 hours followed by vorinostat for another 24 hours resulted in the lowest estimated value of μ, this regimen was selected to further evaluate the cellular responses over time and compare against equivalent single and combination dosing schedules. Concentrations of 3 nM and 2 μM were chosen for bortezomib and vorinostat based on maximum growth inhibition in single time point combination experiments. Cell viability over four days was measured for effects for drugs given as single agents, in simultaneous combination (both dosed continuously for 96 hours), and in sequential combination (vorinostat added 24 hours after pre-incubation with bortezomib for 24 hours). The observed time-courses of cell proliferation and model fitted profiles (Eq. 3–5) for these regimens and control conditions (vehicle) are shown in Fig. 3. The model captured the trends in the data well, and all parameters were estimated with reasonable precision (Table III). Bortezomib appears to be more potent than vorinostat, with an estimated second-order efficacy parameter for bortezomib (k_BORT = 0.0143 nM/hr) being greater than for vorinostat (k_VORT = 2.4 × 10⁻⁵ nM/hr). This is in agreement with the IC₅₀ values at single time points (Table I). According to model selection criteria, no transit compartments were needed to capture bortezomib effects, where as one transit compartment was necessary to characterize the delay in vorinostat effects on U266 cell viability (τ = 12. 3 hours). The sequential treatment arm followed a similar profile to bortezomib single agent and simultaneous combinations initially but deviated after 24 hours once vorinostat was added (Fig. 3b). The estimated value of ψ was 0.138 with a confidence interval of 0.06838–0.2077, and μ was 8.96 with a confidence interval of 4.376–13.55. The estimate of μ is significantly different from 1, suggesting a synergistic interaction between bortezomib and vorinostat holds for the entire time-course when the drugs are given sequentially (with a temporal window of 24 hours). Additionally, ψ was significantly less than 1, suggesting that over an extended time-course, bortezomib and vorinostat could likely have an antagonistic interaction when given concurrently.

Figure 3.

Model-fitted profiles of U266 cellular proliferation time-course with (a) vehicle control, and (b) bortezomib (3 nM) and vorinostat (2 μM) as single agents, on simultaneous exposure (bortezomib 3 nM and vorinostat 2 μM), and a 24-hour sequential regimen (bortezomib 3nM exposure alone for the first 24 hours followed by vorinostat 2 μM for next 24 hours). Symbols represent experimental observed values, and lines represent model-fitted profiles.

Table 3.

In vitro Cellular Proliferation Modeling Parameter Estimates

PARAMETER	DEFINITION	ESTIMATE	(CV%)	CONFIDENCE INTERVAL
kg (hr−1)	Growth rate	0.01993	0.121	[0.01988, 0.01998]
kVORT(1/nM•hr)	Kill term Vorinostat	2.4 × 10−5	4.75	[2.16× 10−5, 2.62× 10−5]
kBORT(1/nM•hr)	Kill term Bortezomib	0.0143	2.03	[0.01372, 0.01488]
τ (hr)	Transit time (Vorinostat single agent only)	12.3	28.6	[5.128, 19.47]
ψ	Interaction parameter	0.138	25.2	[0.06838, 0.2077]
μ	Interaction parameter(Sequential effect)	8.96	25.6	[4.376, 13.55]

Combination In Vivo Drug Effects

A sequential PK/PD approach was utilized to model the exposure-response relationships of vorinostat and bortezomib as single agents and in combination in murine xenografts. Pharmacokinetic model fitting and parameter estimates for both agents are given in supplemental Fig. S1 and supplemental Table S1. A simple two-compartment PK model was suitable to capture the plasma concentration-time profile of both agents. Though bortezomib is known to exhibit target-mediated drug disposition in mice (24), no differences in PK profiles were observed between simulations from a linear PK model and a target-mediated model (24) at the dose level of interest. Hence a linear PK model was deemed sufficient to drive the PD.

Tumor reduction in LAGκ-1B xenografts was captured suitably using a combination effect model (Eq. 6). The model fit the data well (Fig. 4), and all estimated parameters were obtained with good precision (Table IV). Model selection criteria suggested no need for a delay (transit compartments) to model the drug effects. A similar trend for the in vivo potency of both agents was observed in vivo as compared to our in vitro IC₅₀ values (Table I) and in vitro cell proliferation effects (Table III). For the given doses and dosing schedule, bortezomib exhibited a greater tumor kill constant than vorinostat (Table III, k_VORT = 7.37 × 10⁻⁶ L/ng·hr vs. k_BORT = 1.10 × 10⁻⁴ L/ng·hr). The estimated value of the interaction parameter ψ was 1.39, but was not significantly different from 1, as the confidence interval [0.816, 1.97] overlapped 1, suggesting that no enhanced effects are likely in pateint derived xenografts when vorinostat and bortezomib are given simultaneously. To test the model, we simulated tumor reduction with the final estimated model parameters (Table IV), but with a value of 1 for ψ (implying additivity for the vorinostat and bortezomib interaction). The resultant simulation is shown as a dashed black line in Fig. 4, and there is little to no separation between the simulated, model-fitted, and experimentally observed tumor volumes. The in vitro and in vivo modeling results concur, indicating that a simultaneous combination of these drugs does not exhibit a synergistic interaction. In addition, a simulation was also conducted using a dosing regimen similar to the one used in the xenograft study, but with vorinostat administration 24 hours post bortezomib (sequential regimen). The value of the interaction parameter μ was kept as 8.96 for the simulation, based on the model-estimated value of μ for the time-course of in vitro cell proliferation (Table III). Instead of using the value of μ from the non-competitive interaction model (Equation 2), which is only for a single time point, the value from the time-course model (Equation 3) was deemed more appropriate for this simulation. The model structure is similar to one used for describing in vivo tumor growth, thus allowing a reasonable translation of in vitro parameters to in vivo conditions. As shown in Fig. 4, the model predicts a greater reduction in tumor volume with the sequential regimen, rather than the simultaneous regimen, of bortezomib and vorinostat.

Figure 4.

Model-fitted profiles of effects on tumor progression in LAGκ-1B tumor xenografts treated with vehicle (control), borteozmib (0.5 mg/kg twice weekly), vorinostat (100 mg/kg twice weekly), and their simultaneous combination (bortezomib 0.5 mg/kg twice weekly and vorinostat 100 mg/kg twice weekly) for 35 days. Symbols represent digitized data from the original publication (7), and lines represent fitted profiles or model simulations with ψ =1 and μ = 8.96 (black dashed and pink lines).

Table 4.

Xenograft PK/PD Model Parameter Estimates

PARAMETER	DEFINITION	ESTIMATE	(CV%)	CONFIDENCE INTERVAL
kg (hr−1)	Growth rate	3.79 × 10−3	3.47	[3.52 × 10−3, 4.07× 10−3]
R0 (mm3)	Initial Tumor Volume	35.1	10.2	[27.6, 42.6]
kVORT(1/nM•hr )	Kill term Vorinostat	1.95 × 10−3	20.2	[3.95 × 10−6, 1.08 × 10−5]
kBORT(1/nM•hr )	Kill term Bortezomib	0.0422	28.9	[3.67 × 10−5, 1.84 × 10−4]
ψ	Interaction parameter	1.39	19.8	[0.816, 1.97]

Intracellular Protein Analysis for Single and Combination Effects

The time-courses of intracellular proteins that are critical in regulating cellular responses to bortezomib (3 nM) and vorinostat (2 μM) were measured. The temporal profiles for relative expression of p21, a central protein affecting cell cycle progression, and cleaved PARP, an important marker of apoptosis, for five different treatment exposures are shown in Fig. 5. The peak response for p21 was around 24 hours for vorinostat, whereas the peak for bortezomib was lower in magnitude and later in time (about 36 hours). This was also reflected in the simultaneous combination, such that p21 progression behaved comparable to vorinostat for the first 24 hours but plateaued later instead of decreasing in value. This could be a consequence of increased p21 owing to the presence of bortezomib. Correspondingly, for the sequential treatment arm, the p21 profile was identical to bortezomib as a single agent, but once vorinostat was added at 24 hours, there was a sustained increase in p21 expression, which was greater than the simultaneous combination. Cleaved PARP expression exhibited a similar trend, except that the peak responses for all four treatment arms were around 36 hours. Furthermore, the differences in magnitude of the fold change amongst vorinostat single agent and both combination arms were not as pronounced as the differences between bortezomib single agent and combination schedules.

Figure 5.

Cellular protein dynamics across different treatment arms in U266 multiple myeloma cells. Time-course of relative expression and representative western blots for p21 (a) and cleaved PARP (b) are shown for vehicle control, continuous exposure of bortezomib (3 nM), vorinostat (2 μM), simultaneous exposure (bortezomib 3 nM and vorinostat 2 μM) for 48 hours, and a 24-hour sequential regimen (bortezomib 3 nM exposure alone for the first 24 hours followed by vorinostat 2 μM for next 24 hours). Symbols represent the mean of three replicates, and error bars represent standard deviation. Groups not statistically different; Kruskal-Wallis One-Way ANOVA on Ranks with Tukey (data do not follow a normal distribution).

Discussion

Combination chemotherapy has become an indispensable approach to the management of multiple myeloma treatment (2, 3). This requires a critical evaluation of drug combinations and dosing sequences at early in vitro and xenograft experimental stages before moving into clinical trials. Semi-mechanistic PK/PD modeling has been increasingly used to study the nature of drug interactions (17–19). Although raw data can be used to imply the nature of combinatorial drug interactions, mathematical models allow for an objective assessment and a quantitative platform to explore combination regimens in cellular studies (25). Assessing intracellular protein expression for probing altered signaling pathways by different targeted agents has also provided insights into potential mechanisms of single agent and combination drug regimens (8, 9, 26, 27). Here, we utilize both of these approaches to evaluate the nature and temporal dependency of vorinostat and bortezomib interactions in multiple myeloma cells and xenografts.

A step-wise modeling approach was followed, in which the combinatorial interaction of bortezomib and vorinostat was evaluated in vitro and then in vivo. For robust estimation of parameters, single agent model estimates were fixed while analyzing the combination data instead of modeling all the data simultaneously. All of the combination data were co-modeled to better inform the interaction parameter estimates. Thus a hybrid sequential-simultaneous modeling approach was applied. Separate modeling for in vivo data was conducted to allow for estimation of system-specific in vivo parameters. In contrast to the often used empirical methods of assessing oncology in vitro drug combinations over limited concentrations and single time points, we evaluated a range of concentrations and total exposure times, diverse dosing schedules, comprehensive protein dynamics, and quantitative semi-mechanistic modeling to study vorinostat and borteozmib combinatorial regimens. Bortezomib was identified to be more potent with a steeper concentration-effect relationship relative to vorinostat (Fig. 1). Based on these findings and parameter estimates (Table I), combinations of bortezomib and vorinostat were evaluated at concentrations in the range of IC₅₀ values to allow for discernable enhanced effects, especially at lower than maximal inhibitory concentrations. Five varied treatment schedules (Table II) were modeled using a novel form (Eq. 2) of Ariens non-competitive interaction (17, 20, 21). Although others have applied this model for analyzing drug combinations (17, 18, 25), the modified form allows the simultaneous modeling of all the data simultaneously, including an evaluation of sequential drug treatments. In our study, sequential exposure of borteozmib prior to vorinostat was suggested to be synergistic based on values of ψ and μ (Table II). A temporal window of 6–24 hours was identified to be optimum for dosing bortezomib prior to vorinostat, with 24 hours providing the most enhanced effects (μ = 0.708). Pre-incubation of U266 cells for 24 hours with vorinostat prior to bortezomib exposure also yielded an additive effect, and therefore this sequence was not pursued further with shorter pre-incubation times. Interestingly, all simultaneous exposure treatments were found to be additive in nature. Model based analysis of the time-course of cell proliferation also suggested greater inhibition by the 24 hour sequential regimen in comparison to single agents or the simultaneous regimen for the entire duration of 4 days (Table III). This affirms that the concentration combinations and dosing schedules for vorinostat and bortezomib inferred from the single time point analysis were indeed synergistic and had persistent effects. The simultaneous dosing in xenografts was also simply additive, as suggested by the value of the interaction parameter ψ (Table IV) and model simulation (Fig. 4). Although a sequential in vivo regimen was not tested experimentally, model simulation with the in vitro parameters suggested greater reduction in tumor volume for the sequential regimen of bortezomib and vorinostat in comparison to their simultaneous regimen (Fig. 4). It is also promising that the in vitro-in vivo combination modeling results were in good agreement, even for different total drug exposures. In addition, owing to reduced vorinostat exposure times, sequential regimens offer the possibility of decreased toxicity, increased tolerability, and enhanced efficacy.

The mechanistic support for the temporal dependency of bortezomib and vorinostat maximal effects could stem conceivably from the well-characterized hypothesis of synergy through protein degradation. Proteasome is required for the degradation of unfolded and misfolded proteins in the cell. Inhibition of proteasome by bortezomib results in the accumulation of ubiquitin protein aggregates, which drives cellular processes for removal of these unwanted proteins. Proteolysis by lysosommal degradation entails the formation of aggresomes for which HDAC6 enzyme is a prerequisite. Vorinostat inhibition of the HDAC6 enzyme works in tandem with proteasome inhibition by bortezomib to shutdown protein degradation mechanisms, leading to increased cellular stress and eventually enhanced apoptosis (8, 11). A delay in the administration of vorinostat could augment this effect, as vorinostat action on the proteolysis pathway only occurs in the presence of protein aggregates. After pre-exposure to bortezomib, myeloma cells might reach a new ‘state’, in which ubiquitin protein aggregates are already formed and cells are readily susceptible to vorinostat effects. Concurrent administration of both drugs might interfere with this pharmacological priming hypothesis, as aggresomes are formed only when myeloma cells are treated with bortezomib or bortezomib and vorinostat combination (not when vorinostat is given as a single agent), with significantly less aggresome formation in the combination (8). In addition, Pei et al. showed that sequential exposure of bortezomib 6 hours before the addition of vorinostat for another 20 hours in two different multiple myeloma cell lines (i.e., U266 and MM1S) results in a synergistic induction of apoptosis (9). The reverse sequence (vorinostat before borteozmib) was not tested, but the simultaneous combination for 26 hours exhibited less pronounced effects as the bortezomib pre-incubation sequence. Our 6 hour sequential bortezomib exposure study is in agreement; however, the lower value of the interaction parameter (μ) suggested that 24 hour pre-incubation with borteozmib is superior (Table II). Although Pei et al. (9) only tested one concentration combination (1 μM vorinostat and 2.4 nM bortezomib) and did not evaluate other sequential regimens, various intracellular proteins were measured via western blotting at the end of the study, which showed increased expression of cell cycle regulatory proteins p21 and p27, apoptosis proteins caspase 3, 9, and cleaved PARP, and stress pathway markers pJNK and reactive oxygen species (ROS). Instead of an end measure, we pursued the dynamic changes of p21 and cleaved PARP, just two of the many regulatory proteins of the vorinostat and bortezomib interaction, over the time-course of all dosing schedules (i.e., controls, single agents, simultaneous 48 hours, and bortezomib 24 hour sequential regimens; Fig. 5). The time-courses of p21 and cleaved PARP suggest that vorinostat and bortezomib interact through these pathways and might form a mechanistic basis for their synergy. More notably, levels of both proteins showed a trend of increased expression in the sequential regimen compared to all other dosing regimens. Although assessing the time-course of more signaling proteins is warranted (and the subject of current research), our findings suggest that bortezomib pre-exposure potentially lowers the threshold for vorinostat mediated myeloma cell growth inhibition and cell death.

There are similar sequence-dependent regimens appearing in the literature with increasing frequency. Some examples include: combinations of epidermal growth factor receptor (EGFR) inhibitors and DNA damaging agents such as doxorubicin and camptothecins (28), combination of paclitaxel and liposomal doxorubicin (29), and the combination of the targeted agent birinapant (antagonist of inhibitor of apoptosis proteins) and gemcitabine (25). The quantitative modeling approach here is based on the general pharmacological premise of non-competitive interaction; hence it could be applied to different tumor types in oncology and other therapeutic areas. It is applicable for testing different exposure conditions and drug schedules for combinatorial therapy and requires only standard in vitro experimental endpoints (e.g., cell viability). It could thus be used as a first-pass tool to check for the nature of drug interactions and temporal dependencies, after which more mechanism-based models can be applied to further explore dosing schedules (25, 28, 29). Measurements of critical intracellular proteins, in addition to p21 and cleaved PARP, that regulate vorinostat and borteozomib interactions to extend our current model to a more mechanism-based model and will be reported separately.

The results of this study should be considered in light of certain limitations. Firstly, the PK/PD modeling is semi-mechanistic and based only on one in vitro cell line. The in vitro results agreed with in vivo dosing schedules in murine xenografts bearing patient derived LAGκ-1B tumors; however, only mean in vivo data were modeled, and the in vivo study evaluated only one dose level for each drug. Nevertheless it offered confirmation for the need of further optimization of dosing schedules for vorinostat and bortezomib with an appropriate temporal window. The interaction parameters ψ and μ are still empirical in nature and cannot be attributed to specific pathways or biomarkers. Although p21 and cleaved PARP profiles lend insight into mechanistic details, more measurements of critical proteins (e.g., Bcl-xL and p53) are needed to bridge gaps and eliminate the need for empirical interaction terms. These signaling components can then be linked through a dynamic pharmacodynamic model to explain the synergy of the study drugs (30). Finally, the translation of the suggested dosing schedules from in vitro and preclinical models to humans is a formidable challenge and requires further research to incorporate aspects of inter-individual variability in pharmacokinetics, tumor micro-environment, and the appropriate scaling of model parameters.

Conclusions

In summary, a semi-mechanistic PK/PD model based approach was successfully developed and applied to assess vorinostat and bortezomib interactions in multiple myeloma cells and xenografts. A novel characteristic of the model was the incorporation of a multiplicative interaction term (μ) signifying effects of sequential drug administration. This provided a simultaneous fitting of combination regimens to distinguish concurrent and time-staggered drug exposure-responses. An optimal temporal window of 24 hours was identified for bortezomib pre-incubation prior to vorinostat to achieve maximal synergistic effects. Semi-mechanistic modeling of both the single time point responses as well as time-course of cell proliferation suggested that the sequential regimen is synergistic and that the temporal dependency of the interaction has a sustained effect. The lack of a synergistic interaction for simultaneous dosing schedule of vorinostat and borteozmib in vitro is in agreement with in vivo patient derived tumor xenografts. Increased up-regulation of complementary pathway proteins of growth inhibition (p21) and apoptosis (cleaved PARP) in the sequential regimen could be representative central factors regulating the temporal nature of the multifactorial mechanisms of the vorinostat and borteozmib interaction. However, detailed protein profiling of supplementary critical biomarkers and cellular-signaling based pharmacodynamic models are required to fully elucidate the mechanisms regulating the synergistic sequential effects. The modeling framework developed in this study may serve as a platform to assess different drug combinations and dosing regimens at early in vitro and preclinical stages and emphasizes the necessity to study the often-overlooked issue of dosing schedules in combination chemotherapy.

Supplementary Material

11095_2017_2095_MOESM1_ESM

Supplemental Figure S1 Pharmacokinetic Model Fittings for (A)0.25 mg/kg Bortezomib IV Bolus and (B)10 mg/kg IV Bolus Vorinostat in BALB/c Mice. Symbols represent data digitized from original publications [1,2] and lines represent model fits

Supplemental Figure S2 Goodness of fit Plots (observed vs. predicted) for combination regimens (A) Bortezomib pre-incubation for 6 hours followed by vorinostat for 18 hours and their simultaneous combination for 24 hours (B) Bortezomib pre-incubation for 24 hours followed by vorinostat for 24 hours and their simultaneous combination for 48 hours and (C) Vorinostat pre-incubation for 24 hours followed by bortezomib for 24 hours and their simultaneous combination for 48 hours. Blue symbols represent simultaneous data and red symbols represent sequential data

Supplemental Table S1 Pharmacokinetic Parameter Estimates for (A) 0.25 mg/kg IV Bolus Bortezomib and (B) 10mg/kg IV Bolus Vorinostat in BALB/c Mice

ABBREVIATIONS

PK

Pharmacokinetics

PD

Pharmacodynamics

PARP

Poly ADP Ribose Polymerase

HDAC

Histone deacetylase