Research ArticleCancer

Optimizing drug combinations against multiple myeloma using a quadratic phenotypic optimization platform (QPOP)

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Science Translational Medicine  08 Aug 2018:
Vol. 10, Issue 453, eaan0941
DOI: 10.1126/scitranslmed.aan0941

I’ll have a three-drug combo, please

Combination therapy is a major strategy to circumvent the onset of treatment resistance in cancer patients; knowing which drugs to combine, however, can be difficult. Rashid et al. developed a computational platform to facilitate the discovery and optimization of drug combinations to treat multiple myeloma, a disease that often develops resistance to therapies containing the first-line drug bortezomib. The authors validated the combination treatments and refined the drug dosages in mouse models and ex vivo patient samples. Their platform requires no knowledge of which pathways to target and could more broadly aid drug repurposing efforts.


Multiple myeloma is an incurable hematological malignancy that relies on drug combinations for first and secondary lines of treatment. The inclusion of proteasome inhibitors, such as bortezomib, into these combination regimens has improved median survival. Resistance to bortezomib, however, is a common occurrence that ultimately contributes to treatment failure, and there remains a need to identify improved drug combinations. We developed the quadratic phenotypic optimization platform (QPOP) to optimize treatment combinations selected from a candidate pool of 114 approved drugs. QPOP uses quadratic surfaces to model the biological effects of drug combinations to identify effective drug combinations without reference to molecular mechanisms or predetermined drug synergy data. Applying QPOP to bortezomib-resistant multiple myeloma cell lines determined the drug combinations that collectively optimized treatment efficacy. We found that these combinations acted by reversing the DNA methylation and tumor suppressor silencing that often occur after acquired bortezomib resistance in multiple myeloma. Successive application of QPOP on a xenograft mouse model further optimized the dosages of each drug within a given combination while minimizing overall toxicity in vivo, and application of QPOP to ex vivo multiple myeloma patient samples optimized drug combinations in patient-specific contexts.


Advances in omics tools have led to a greater understanding of the complexity of diseases such as cancer, in which large networks of molecular interactions contribute to both disease progression and therapeutic resistance (1). Inhibition of a single pathway is typically not sufficient to effectively treat such diseases; hence, disrupting multiple pathways through combination therapy may possibly be more effective. Combination therapy approaches have been particularly prevalent in cancer research, with 25.6% of oncology clinical trials from 2008 to 2013 involving the study of combination therapies, whereas only 6.9% of non-oncology trials involved combinations (2). Many cancers, however, remain incurable and continue to require the development of further lines of treatment for use after patient relapse. One such incurable malignancy is multiple myeloma (MM), which is characterized by malignant proliferative plasma cells and has a median overall survival rate of about 8 years despite advances in targeted therapy that have led to incremental improvements in survival rates (3, 4). The development of effective secondary lines of treatment for relapsed and refractory MM patients is particularly important after treatment with the proteasome inhibitor bortezomib (Bort), which is present in 58% of clinically used drug combinations (5). Clinical studies of Bort-containing combinations have shown overall response rates as high as 93% in newly diagnosed patients (6), and the introduction of Bort into MM treatment regimens, particularly in upfront first-line treatment options, has increased relative survival rates at 5 years (7). However, as a result of various intrinsic or acquired mechanisms of resistance to Bort, relapse is inevitable for most MM patients (8). Thus, identifying effective drug combinations against Bort-resistant MM may lead to the development of improved secondary lines of treatment in the context of refractory or relapsed MM after Bort treatment.

The rational design of drug combinations remains a challenge because of the complex molecular networks that contribute to feedback mechanisms of drug resistance and compensatory oncogenic drivers that limit the efficacy of targeted inhibitors (9, 10). Genomics-based cancer drug combination development has identified oncogene-specific synthetic lethality targets or used genomic profiling to identify biomarkers that predict enhanced sensitivity to targeted therapies (11). Rather than using a rationally optimized drug combination design, these targeted therapies are often paired with traditional chemotherapy or added to existing combination therapies (12, 13). Network modeling algorithms and pairwise combination predictive algorithms have sought to rationally identify drug combinations by pairing systematic combinatorial experimentation with an understanding of key biological processes (1416). Although these methods are effective in identifying synergistic drug combinations, they do not identify the true global optimum among a set of drugs and can be reliant on an incomplete understanding of underlying molecular mechanisms. In addition, drug dosages and synergy need to be reoptimized at each stage of development because combinations identified as synergistic in vitro may not be effective in vivo (17, 18). A recent clinical study has shown that drug synergy can be both dose- and time-dependent, which can further confound drug development (19). The need to simultaneously address both drug selection and dosages creates a virtually infinite parameter search space that is insurmountable using conventional approaches such as dose escalation or synergy prediction. To identify the optimal drug combination and drug dosage ratios within a set of nine drugs over a range of three concentrations, traditional high-throughput screening methods would have to test 39 or 19,683 combinations, making this approach prohibitively expensive and virtually impossible to complete in vivo. Recent advances in evolution-guided dosing algorithms can optimize drug dosages over a prolonged period, including in vivo, for increased therapeutic efficacy (20, 21). Current versions of this approach, however, are limited to optimization of a single drug and do not take into account the multiple time, dose, and subject-specific drug interactions that may exist within drug combinations. Pairwise combination predictive algorithms are also incapable of optimizing drug dosages for maximal efficacy while minimizing toxicity.

To overcome these challenges, we developed a quadratic phenotypic optimization platform (QPOP) that is able to identify from a pool of possible drug candidates, without reference to mechanism, the drug composition and doses that collectively mediate the best possible treatment outcomes. The foundation of QPOP is the discovery that the response of biological systems to therapeutic intervention can be represented by smooth parabolic surfaces, via second-order polynomial equations (22). Studies across a wide range of biological applications have suggested that a parabolic surface derived from second-order polynomial equations can accurately identify globally optimal drug combination parameters (2226). Furthermore, the importance of first- and second-order terms in determining parabolic surfaces of therapeutic responses extends from cells to preclinical models to humans and can be used to optimize drug dosage ratios in the clinical setting (19, 27, 28). We hypothesized that mapping a parabolic quadratic surface toward a set of drug responses might be able to optimize both the drugs that comprise the combinations and their respective dosages through continuous optimization across the preclinical drug development pipeline. Whereas conventional optimization approaches such as network modeling algorithms are dependent on predetermined synergies, QPOP does not require this information to globally optimize drug combinations. Here, we used QPOP against Bort-resistant MM to optimize combinations of U.S. Food and Drug Administration (FDA)–approved drugs against Bort-resistant MM in vitro and to reoptimize drug dosage ratios in vivo to minimize systemic toxicity while maintaining drug combination efficacy. We tested optimized drug combinations in a preclinical animal model of Bort-resistant MM and against a range of MM primary patient samples. Our approach revealed the potential for implicitly synergistic tumor suppressor gene reactivation by DNA methyltransferase (DNMT) inhibitors and interstrand cross-linking (ICL) agents to effectively treat Bort-resistant MM.


Quadratic phenotypic drug combination optimization against Bort-resistant MM

We designed QPOP to optimize drug combinations in three stages. At stage 1, drug combinations (inputs) were administered to systems of interest ranging from cells grown in vitro to tumor-bearing mice (29). Upon completion of the drug treatments, the corresponding phenotypic readouts such as cell viability and the overall survival of mice were quantified in stage 2. Because the relationship between the administered drugs and the quantifiable phenotypic responses can be determined by a second-order algebraic equation, a quadratic smooth drug response surface is seen when system response is plotted against drug doses (22). Using this approach, a set of drug-dose combinations can be used to describe the system response as a quadratic function (Eq. 1). Because the quadratic function coefficients of the parabolic surface maps are derived from changes in system response following the input of specific drug-dose combinations, QPOP can use these maps to identify optimal drug-dose combinations that are based on experimentally derived data.

We first identified candidate drugs that may be effective against Bort-resistant MM using the Bort-resistant cell line RPMI 8226 (P100v), which exhibited a 70.2 times higher half-maximal growth inhibitory concentration (IC50) and a noticeable reduction in aggresome formation compared to the parental RPMI 8226 cell line after treatment with Bort (Fig. 1A). One hundred fourteen FDA-approved oncology drugs were screened on RPMI 8226 and P100v cell lines at 1 and 5 μM (Fig. 1B). Using a cutoff of less than 0.6 of the normalized viability in both P100v and RPMI 8226 cell lines, dactinomycin (Dac) (30), decitabine (Dec), mechlorethamine hydrochloride (Mech) (31), and mitomycin C (MitoC) were chosen as candidate drugs among inhibitors that demonstrated greater sensitivity toward the Bort-resistant cell line (Fig. 1, C and D, and tables S1 and S2). Dose-response curves were used to identify and compare the IC50 of the candidate drugs between both cell lines to validate these hits (Fig. 1E).

Fig. 1 A high-throughput screen identified four potential drug inhibitors that preferentially targeted Bort-resistant cell lines.

(A) Top: Bort dose-response curve, IC50 analysis in RPMI 8226 and P100v cells. Bottom: Aggresome formation analysis in RPMI 8226 and P100v cells. Aggresome formation (red) is counterstained with DNA dye, Hoechst (blue). Scale bars, 10 μm. DMSO, dimethyl sulfoxide. (B) Schematic outline of drug screen on both the sensitive RPMI 8226 and resistant P100v. (C and D) Results of the high-throughput screening of the 114 compound FDA-approved oncology drugs set V on both RPMI 8226 and P100v cell lines at 1 μM (C) and 5 μM (D). Highlighted red bars indicate the four drugs (Dac, Dec, Mech, and MitoC) that consistently appeared as top hits for the two concentrations used. (E) Dose-response curves and IC50 of the positive hits from drug screen on RPMI 8226 and P100v. All dose-response curves (A and E) are means ± SD of three independent biological replicates.

We sought to identify optimal drug combinations from a set of drugs that included these candidate drugs as well as 10 FDA-approved drugs clinically used in MM therapy (5). We carried out a 14-drug, two-dosage QPOP analysis consisting of 128 combinations, where the two dosages corresponded to different concentrations used (tables S3 and S4). Drug combinations were determined using a method that has been shown to be the least number of combinations required for factor screening and in-depth analyses (29). Drug treatments were evaluated in P100v and a normal epithelial control cell line, THLE-2, to distinguish drug combinations that maximized the killing of Bort-resistant MM cells while minimizing the effect on normal control cells (table S5). Thus, we defined the output as the normalized viability of P100v subtracted from the normalized viability of THLE-2. We then revised our investigation to nine drugs at three dosages consisting of 155 combinations (tables S6 to S8). In this analysis, the top 10 ranked QPOP-optimized two-drug combinations included Bort, Mech, Dec, or MitoC. The top-ranked two-drug combinations were Dec/MitoC followed by Bort/Mech (table S9), whereas Dec/MitoC/Mech was top-ranked for three-drug combinations (table S10). Top-ranked drug combinations were deemed to have synergistic interactions when predicted therapeutic output increased as the concentrations of the drugs both increased (Fig. 2A). QPOP analysis also revealed antagonistic interactions within current clinical drug combinations used against MM, such as Bort with dexamethasone (Dex) as well as Bort with panobinostat (Pano), because increasing the concentrations of the drugs resulted in a decreased output (Fig. 2B). The R2 of the above QPOP analysis was 0.803 (table S8), indicating the close proximity of the data points to the QPOP linear regression analysis. To validate these results, we treated P100v cells with optimized and nonoptimal drug combinations identified by QPOP analysis, including the clinically approved three-drug combination of Bort, Pano, and Dex (D5). The optimized drug combinations (D2, D3, and D4) repressed the viability of P100v cells compared to the nonoptimal drug combinations (D1 and D5; fig. S1). We calculated the combination index (CI) via the Chou-Talalay method after the optimization to determine whether drug combinations were synergistic (CI < 1), additive (CI = 1), or antagonistic (CI > 1) (32). We confirmed synergistic interactions (CI < 1) for all three top-ranked drug combinations (D2, D3, and D4), whereas both nonoptimal drug combinations exhibited antagonistic interactions with CIs > 1 (fig. S1). These data confirm that although QPOP does not use predetermined synergistic or antagonistic interactions in identifying optimal drug combinations, top-ranked combinations were synergistic, whereas previously unknown antagonistic interactions contributed to lower ranks in the QPOP analysis.

Fig. 2 Parabolic response surface maps and validation of QPOP-ranked efficacious drug combinations.

(A) Parabolic response surface maps from top QPOP-ranked two-drug combinations. (B) Parabolic response surface maps from selected low QPOP-ranked two-drug combinations. Axes lengths differ in (A) and (B) to aid visualization. Monotherapy versus combination therapy dose-response curve and IC50 analysis of (C) Bort and Mech; (D) Dec and MitoC; (E) Dec, MitoC, and Mech; and (F) Pano, Bort, and Dex in P100v cells. Data are means ± SD of three independent biological replicates. (G) Bort and Mech and (H) Dec and MitoC were evaluated as single- or dual-drug treatment on relapsed MM patient samples. Data are means ± SD of three independent biological replicates. (I) Combination indices of Dec and MitoC on different patient samples based on the derived IC50.

To further validate QPOP-optimized drug combinations, we determined the IC50 of these drugs, either as monotherapies or drug combinations, in vitro. When Bort and Mech were administered concurrently, there was a marked shift in the dose-response curve, and the IC50 of the drug combination decreased compared to when drugs were administered alone (Fig. 2C). Although Mech IC50 only saw a moderate reduction from 9.47 ± 0.832 μM to 7.29 ± 1.52 μM, Bort IC50 was significantly reduced from 12.2 ± 2.66 μM to 0.433 ± 0.173 μM (P < 0.0001). This observation suggests that the efficacy of this top-ranked drug combination is likely due to the increase in efficacy of Bort in a Bort-resistant MM cell line. For the Dec/MitoC combination, both Dec and MitoC saw marked reductions in IC50 values (Fig. 2D). For Dec, IC50 was significantly reduced from 41.5 ± 8.64 μM to 0.120 ± 0.211 μM (P < 0.0001). For MitoC, IC50 was significantly reduced from 7.52 ± 2.43 μM to 0.0420 ± 0.00366 μM (P < 0.0001). The combination of these two drugs contributed to a strong synergistic increase in efficacy as evidenced by a CIIC50 of 0.331. For Dec, Mech, and MitoC, significant reductions in IC50 of Dec (P < 0.0001) and Mech (P < 0.0001) contributed to increased efficacy and a CIIC50 of 0.739 (Fig. 2E). Although Pano/Bort/Dex has been approved for use in the clinic for relapsed and refractory MM, this combination was confirmed to be antagonistic on the Bort-resistant P100v cells with a CIIC50 of 11.0 (Fig. 2F) (33). This three-drug combination reduced the efficacy of Pano, with IC50 increasing from 0.0790 ± 0.0888 μM to 0.862 ± 0.304 μM compared to other cell types. We also compared the IC50 derived from P100v cells earlier to the IC50 obtained when these drug combinations were administered on a normal epithelial cell line, THLE-2, or mesenchymal stem cells (MSCs). For both single-drug and combination drug treatments, the IC50 obtained for both THLE-2 and MSC was higher than the IC50 derived from the P100v cells (fig. S2). For instance, the IC50 of Bort in the dual combination was higher in THLE-2 (5 μM) and MSC (1.35 μM), as compared to P100v (0.55 μM; P = 0.0471 and 0.0369, respectively). The same trend was observed for Mech (P = 0.00299 for THLE-2 and P = 0.00962 for MSC). These results demonstrate the ability of the QPOP platform to optimize drug combinations against Bort-resistant MM.

Clinical relevance and disease specificity of QPOP drug combinations

Although QPOP was used to identify optimized drug combinations specifically against Bort-resistant MM, the mechanisms by which Bort resistance arises may be shared across the spectrum of hematological malignancies (34). To investigate the effect of QPOP-optimized drug combinations against other Bort-resistant cancers, we evaluated the two top-ranked QPOP-optimized drug combinations against Bort-resistant acute lymphoblastic leukemia (ALL). Similar to the effects seen with the P100v line, optimized drug combinations had markedly lower IC50 values compared to single-drug treatments and corresponding CIIC50 values of less than 1 (figs. S3 and S4). Using Bort-resistant CCRF-CEM cells (7 nM), there was a significant decrease in the IC50 of Dec when administered dual therapy (0.0570 μM) compared to monotherapy (>100 μM) (P = 0.0221), whereas MitoC decreased from 6.70 to 0.0480 μM (P < 0.0001). For Bort, a significant reduction from 11 to 0.150 μM (P = 0.0349) was observed, and for Mech, IC50 decreased from 8.34 to 1.68 μM (P < 0.0001; fig. S3). Similar patterns were also observed in CCRF-CEM cells (200 nM), a more Bort-resistant cell line, where the IC50 of Dec (P = 0.0027), Bort (P < 0.0001), and Mech (P = 0.00770) decreased significantly, whereas that of MitoC decreased from >50 to 0.0270 μM (fig. S4). These data suggest that QPOP-optimized drug combinations against Bort-resistant MM could also represent viable therapeutic options against other Bort-resistant cancers.

We also examined top-ranked drug combinations ex vivo using primary MM patient samples to evaluate the clinical relevance of the QPOP drug combination optimization approach. The Bort/Mech drug combination was found to be antagonistic (CIIC50 = 1) in a relapsed patient sample, with the IC50 for Bort increasing from 0.00319 to 0.00729 μM (Fig. 2G), suggesting that this drug combination was optimized specifically against highly Bort-resistant cancers and may not be as effective against more Bort-sensitive MM cells. The Dec/MitoC combination, however, resulted in a significantly lower IC50 compared to Dec (P < 0.0001) and MitoC (P < 0.0001) alone (Fig. 2H). Because Dec/MitoC appeared to retain enhanced efficacy compared to single-drug treatments, we evaluated additional samples from both newly diagnosed and relapsed MM patients. In all 13 patient samples tested, the CIIC50 was less than 1 (Fig. 2I). These CIIC50 values were influenced by reductions in IC50 for both Dec and MitoC in 8 of 13 of these patients (table S11), with many of these reductions in IC50 being orders of magnitude less. For instance, patient 11 had a significantly lower IC50, from 316 to 0.231 μM (P = 0.0001) for Dec and a decrease from 1.90 to 0.298 μM for MitoC (P < 0.0001; table S11). These results suggest that QPOP-based drug optimization identified an epigenetic inhibitor-based drug combination where the increased efficacy and implicitly synergistic interactions were retained across a range of MM patients.

After ex vivo testing of Dec/MitoC in MM patient samples, we explored how Dec/MitoC interactions would be mapped onto quadratic surfaces and how this combination compared to other drug combinations tested on ex vivo patient samples. A six-drug, three-level QPOP analysis was carried out across four newly diagnosed patient samples, with the six-drug set comprising Dec, Bort, MitoC, Pano, Dex, and melphalan (Melph; table S12). For all four patients, the combination of Dec and MitoC displayed synergistic interactions in parabolic quadratic surface plots (Table 1). Synergism was further confirmed by determining the IC50 of the drugs decreased in dual therapy as compared to monotherapy (Table 1). The R2 values for all the ex vivo QPOP analysis were >0.9, suggesting the fidelity of the data to the linear regression analysis. Dec/MitoC emerged in the top 10 two-drug ranked combinations for patient samples 1 (Table 2) and 2 (Table 3). Other drug combinations, including clinically used combinations such as Bort/Pano/Dex and Bort/Melph/Dex, were ranked higher than Dec/MitoC for patient samples 3 (Table 4) and 4 (Table 5). For two of four naïve patient samples, Dec/MitoC was identified as a potentially effective and higher-ranked drug combination than two clinically used combinations. For naïve patient samples 3 and 4, lack of previous patient exposure to Bort likely contributed to a higher ranking for Bort-containing combinations. Although interpatient heterogeneity may limit the effectiveness of any drug combination against the total cancer population, ex vivo patient sample validation data suggested that Dec/MitoC is a drug combination that may be effective toward a subset of MM patients, particularly Bort-resistant MM patients. Hence, we subsequently interrogated potential molecular mechanisms driving this drug combination.

Table 1 Ex vivo sensitivity of Dec/MitoC.

Parabolic response surface maps of Dec and MitoC on diagnosed MM patient samples (1 to 4) from QPOP analysis, with accompanying R2 values, IC50 values, and CIs. Data are means ± SD (n = 3). Statistical analyses were performed using sum-of-squares F test. NS, not significant.

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Table 2 Top 10 two-drug ranked combinations for patient 1.

Overall rankings are indicated in parentheses.

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Table 3 Top 10 two-drug ranked combinations for patient 2.

Overall rankings are indicated in parentheses.

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Table 4 Top 10 two-drug ranked combinations for patient 3.

Overall rankings are indicated in parentheses.

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Table 5 Top 10 two-drug ranked combinations for patient 4.

Overall rankings are indicated in parentheses.

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Targeting DNA methylation in MM

Dec works by inhibiting DNMTs and promoting DNA hypomethylation (35). Previous studies have found that relapsed MM cases had much higher amounts of global DNA methylation compared to monoclonal gammopathy of undetermined significance and newly diagnosed MM cases (36). We observed that P100v cells had significantly higher DNA methylation than the parental cell line (P = 0.00928), similar to what we observed clinically in relapsed MM cases (Fig. 3A). Single- or dual-drug treatment with Dec and MitoC reduced this DNA methylation, suggesting that increased global DNA methylation may be a targetable feature of relapsed MM (Fig. 3B). We explored the genes and regulatory pathways that were perturbed upon Dec and MitoC treatment by measuring and analyzing changes in genomic methylation. Unsupervised hierarchical clustering analysis identified a clear distinction between the Bort-sensitive and Bort-resistant cell lines (Fig. 3C). Although the amount of global DNA methylation in the treated Bort-resistant cell lines was not vastly different from that in the untreated cell line, specific differences in DNA methylation patterns between the treated samples showed that they were different from each other. Volcano plots, in which the differences in mean methylation were plotted against the significance of those differences, illustrate that majority of differentially methylated loci were hypomethylated for cells treated with 2.5 μM Dec. In addition, the combination of 2.5 μM Dec and 5 μM MitoC also resulted in hypomethylation as compared to the cells treated with 2.5 μM Dec only (Fig. 3D). These differences were also mapped to DNA methylation probes (fig S5), which showed 2022 sites to be hypermethylated in a Bort-resistant cell line (P100v) when compared to a Bort-sensitive cell line (RPMI 8226). Treatment with Dec alone or in combination with MitoC caused decreased methylation on 61 and 95 probes, respectively, suggesting that changes in the DNA methylation pattern in P100v could be one of the mechanisms of resistance to Bort.

Fig. 3 Dec and MitoC synergistically repressed global DNA methylation and reactivated tumor suppressor genes.

(A) Mean relative genomic DNA methylation normalized to RPMI 8226 in RPMI 8226 and P100v cell lines. **P < 0.01. Statistical analyses were performed using two-tailed Student’s t test upon confirming normality using Shapiro-Wilk test. (B) Mean relative genomic DNA methylation normalized to control DMSO when P100v was treated with 2.5 μM Dec (D) and/or 5 μM MitoC (M) for 24 hours. **P < 0.01. (C) Unsupervised hierarchical clustering analysis of both RPMI 8226 and P100v together with the corresponding drug treatments for 24 hours. (D) Volcano plots showing difference in mean methylation (x axis) and significance of the difference (y axis) after Dec treatment compared to untreated control and dual-drug treatment. Relative mRNA expression of (E) CDKN1A and (F) PTPN6. *P < 0.05 and **P < 0.01, compared to P100v. Statistical analyses were performed using two-tailed Student’s t test, upon confirming normality using Shapiro-Wilk test. All bar plots represent means ± SD of three independent biological replicates.

Restoration of CDKN1A and PTPN6 transcripts upon dual therapy of Dec and MitoC

We explored changes in gene expression after combination therapy. Pathway analysis of RNA sequencing showed that Erb-B2 Receptor Tyrosine Kinase 2 (ERBB2) signaling pathways were down-regulated in P100v cells after treatment with Dec alone (table S13), whereas p53-responsive pathways, particularly the p21 activation pathway, were up-regulated in P100v cells treated with Dec and MitoC compared to Dec treatment (table S14). The promoter of the tumor suppressor Src homology region 2 domain–containing phosphatase-1 gene PTPN6, which encodes a nonreceptor tyrosine phosphatase that negatively regulates ERBB2 signaling, has been previously reported to be hypermethylated in MM (37). p53-independent long-term expression of p21-encoding gene CDKN1A may contribute to enhanced genomic instability during tumor progression, and p21 is a cyclin-dependent kinase inhibitor that can drive cell cycle arrest and growth inhibition and has been found to be a critical component of Bort-mediated cytotoxicity (3840). When P100v cells were compared to the parental RPMI 8226 cell line, both CDKN1A and PTPN6 were significantly repressed in the Bort-resistant line (both P < 0.0001; Fig. 3, E and F). Dec and MitoC combination therapy resulted in a complete restoration of both CDKN1A and PTPN6 transcripts (P < 0.0001 and P = 0.00214, respectively; Fig. 3, E and F). These data suggest that this optimized drug combination reactivates key tumor suppressor pathways that may contribute to the observed increased therapeutic efficacy.

Enhanced DNA damage by a QPOP-optimized drug combination

MitoC is an ICL agent that has been shown to induce double-strand breaks (41), and Dec has been demonstrated to induce DNA-protein adducts, eventually leading to DNA damage (35). Thus, we investigated DNA damage and the DNA damage response after treatment with the QPOP-optimized drug combination. DNA strand break formation was quantified by an alkaline comet assay in P100v cells after treatment with Dec and MitoC alone and in combination. A significantly longer tail/head ratio, indicative of greater extent of strand breaks, was observed when Dec and MitoC were administered together [P < 0.0001, against control DMSO and single-drug treatments, one-way analysis of variance (ANOVA) with Dunn’s correction and Student’s t test between two independent groups; Fig. 4A]. To further evaluate the extent of DNA damage induced by both Dec and MitoC, we analyzed the expression of phosphorylated checkpoint kinase 1 (p-Chk1) and phosphorylated histone H2AX (γ-H2AX) protein. Chk1 is a cell cycle checkpoint protein that is activated by phosphorylation in response to DNA damage (42), and H2AX is phosphorylated in response to DNA strand breaks (43). A concerted increase in p-Chk1 was observed upon dual Dec and MitoC treatment of P100v cells (Fig. 4, B and C). The expression of γ-H2AX for drug combination treatment, on the other hand, was comparable to the expression induced by MitoC and Dec treatment alone, suggesting that both equally contribute to the formation of DNA strand breaks (Fig. 4, B and D). These results collectively show that Dec and MitoC can synergistically induce DNA damage as evident from the increased formation of DNA strand breaks and up-regulation of cell cycle checkpoint regulators.

Fig. 4 Dec and MitoC induced synergistic up-regulation of activated DNA damage response and strand breaks.

(A) Alkaline comet assay after single- or dual-drug treatment with Dec (153 nM) and MitoC (306 nM), with accompanying quantification of the tail/head length ratio. Scale bars, 50 μm. Data are means ± SD (n = 3). ***P < 0.001, as compared to control DMSO. Experiments were performed in independent triplicate biological repeats. Statistical analyses were performed using one-way ANOVA with Dunn’s correction for multiple comparisons, with two-tailed Student’s t test applied to two independent groups. (B) Representative immunoblots of Chk-1 and H2AX, indicators of activated DNA damage response, when P100v was treated with Dec and MitoC, singly or in combinatorial therapy, for 6 hours. (C and D) Quantification of the protein expression relative to β-actin expression in (B). Data are means ± SD. *P < 0.05 and **P < 0.01, as compared to control DMSO. Experiments were performed in independent triplicate biological repeats. Statistical analyses were performed using two-tailed Student’s t test upon confirming normality using Shapiro-Wilk test.

QPOP in vivo two-drug dosage optimization

Effective and safe drug concentrations for drug combinations obtained in vitro are often not accurately reflected in vivo (17, 18). To determine the optimal concentrations of drugs required in vivo, we carried out a QPOP analysis of the Dec/MitoC combinations consisting of the two drugs at five dosages, using a total of nine test combinations, in an in vivo P100v xenograft model (table S15). The variation in tumor volume and survival we observed highlights the importance of QPOP analysis in defining optimal dosage concentrations (Fig. 5, A and B). The quantitative output for the in vivo QPOP analysis was defined as efficacy minus toxicity, where efficacy is the mean survival time of the mice and toxicity is the mean loss in body weight (table S16). On the basis of this defined phenotypic output, QPOP analysis generated a ranked list of drug combinations with a calculated optimal drug dosage for each drug, within the dosage range rested, to achieve the greatest overall survival time (table S17). Furthermore, the parabolic surface map revealed that the Dec/MitoC drug combination maintained a synergistic interaction, with the parabola peak at 1.5 mg/kg each for both drugs (Fig. 5C). The R2 for this analysis was lower at 0.680, with the greater variance in data possibly attributable to the more complex nature of an in vivo model; however, the interaction between MitoC and Dec remained significant (P = 0.0489; table S18). The differences in parabola curvature between the in vitro and in vivo QPOP analyses (Figs. 2A and 5C, respectively) reflect differences in the coefficients of the second-order quadratic equation and demonstrate the importance of reoptimization as drug combination development spans different biological systems.

Fig. 5 QPOP identified optimal in vivo dosages of Dec and MitoC.

(A) Tumor volume analysis after treatment with nine different drug combinations (n = 4 per group) of varying concentrations of Dec and MitoC. Data are means ± SD. (B) Kaplan-Meier analysis of drug treatments. (C) Parabolic response surface map from QPOP analysis, where output is defined by the toxicity (mean change in body weight) subtracted from efficacy (mean survival time of the mice). (D) Tumor progression analysis upon administration of the optimal drug concentration of Dec (1.5 mg/kg) and MitoC (1.5 mg/kg), singly or in combination (Dec/MitoC; n = 6 per group). Data are means ± SD (n = 6). *P < 0.05, as compared to DMSO vehicle and Dec, and **P < 0.01, as compared to MitoC. Statistical analyses were performed using two-tailed Student’s t test at the end point, upon confirming normality using Shapiro-Wilk test. (E) Kaplan-Meier analysis of Dec/MitoC treatment versus Bort/Dex/Melph [Bort (0.5 mg/kg), Dex (1 mg/kg), and Melph (2.5 mg/kg)] and Bort/Dex/Lena [Bort (0.5 mg/kg), Dex (1 mg/kg), and Lena (3 mg/kg)]. *P < 0.05. Statistical analyses were performed using log-rank (Mantel-Cox) test. (F) Tumor progression analysis curves. Data are means ± SD (n = 6 per group). *P < 0.05 and ***P < 0.001, as compared to Dec/MitoC. Statistical analyses were performed using two-tailed Student’s t test at the end point upon confirming normality using Shapiro-Wilk test.

Enhanced in vivo efficacy of the QPOP reoptimized drug combination

To validate in vivo QPOP analysis, we treated tumor-bearing mice with 1.5 mg/kg each of Dec and MitoC, either singly or in combination. Prolonged survival and decreased tumor size were observed for the Dec/MitoC drug combination as compared to vehicle DMSO (P = 0.0130) or single-drug administration (P = 0.0121 and 0.00174, compared to Dec and MitoC, respectively; Figs. 5D and 6A). In addition, we compared the efficacy of Dec/MitoC to other drug combinations that either are FDA-approved or have been clinically tested for treatment of MM. We treated subcutaneous P100v tumor-bearing mice with Bort/Dex/Melph or Bort/Dex/lenalidomide (Lena). Bort/Dex/Melph has been reported to be an effective regimen in refractory and relapsed MM, with an overall response rate of 62% and a median overall survival of 33.8 months (44). Bort/Dex/Lena, on the other hand, has been approved for newly diagnosed and relapsed/refractory MM patients, with a median overall survival of 30 months (45, 46). Neither the Bort/Dex/Melph nor the Bort/Dex/Lena treatment group survived longer than the DMSO control group, suggesting that these drug combinations are not efficacious in Bort-resistant MM (Fig. 5E). However, Dec/MitoC treatment resulted in significantly longer survival times compared to both Bort/Dex/Melph treatment (P = 0.0389, Mantel-Cox test) and Bort/Dex/Lena treatment (P = 0.0246, Mantel-Cox test; Fig. 5E). In addition, a significant decrease in tumor volume was observed for Dec/MitoC compared to Bort/Dex/Melph (P = 0.000376) and Bort/Dex/Lena (P = 0.000691), and both Bort/Dex/Melph and Bort/Dex/Lena were not significantly different from the DMSO vehicle (P > 0.05; Fig. 5F). These results collectively provide further evidence that the QPOP-derived optimized combination of Dec/MitoC is more effective than current clinically used drug combinations for Bort-resistant MM.

Fig. 6 Analyses of in vivo optimized Dec/MitoC drug combination.

(A) Representative tumor images after treatment with Dec and MitoC at 1.5 mg/kg each, in monotherapy or combination therapy, together with clinically used combinations, Bort/Dex/Melph and Bort/Dex/Lena (n = 6 per group). Scale bars, 1 cm. (B) Representative images of TUNEL and Ki67 staining performed on tumors after drug treatments. All statistical analyses were performed using two-tailed Student’s t test upon confirming normality using Shapiro-Wilk test. Scale bars, 50 μm (TUNEL) and 20 μm (Ki67). Quantification of (C) Ki67 and (D) TUNEL staining. Data are means ± SD (n = 6). *P < 0.05, **P < 0.01, and ***P < 0.001, as compared to DMSO. Relative mRNA expression, normalized to GAPDH, of the perturbed genes, (E) CDKN1A and (F) PTPN6, after drug treatments (n = 4 per group). Data are means ± SD (n = 3). *P < 0.05, **P < 0.01, and ***P < 0.001, as compared to DMSO vehicle. All statistical analyses were performed using two-tailed Student’s t test upon confirming normality using Shapiro-Wilk test.

Further investigation into the effects of these drug combinations on Bort-resistant MM in vivo revealed specific tumor responses to Dec/MitoC that were not shared by the clinical controls. Ki67 analysis revealed that Dec/MitoC treatment resulted in significantly impaired cell proliferation compared to vehicle control (P = 0.00477), Dec (P = 0.0112), and MitoC (P = 0.0376) single-drug treatments as well as both clinically used drug combinations (P = 0.0215 for Bort/Dex/Melph and P = 0.00943 for Bort/Dex/Lena) (Fig. 6, B and C). Terminal deoxynucleotidyl transferase–mediated deoxyuridine triphosphate nick end labeling (TUNEL) analysis revealed that Dec/MitoC resulted in significantly more apoptosis compared to the vehicle control (P = 0.00222), single Dec drug treatment group (P = 0.00244), and Bort/Dex/Lena (P = 0.0424; Fig. 6, B and D). Notably, Bort/Dex/Melph, which has shown some clinical efficacy in refractory and relapsed MM cases, exhibited a similar apoptotic response to Dec/MitoC (Fig. 6, B and D). This suggests that although clinically used combinations such as Bort/Dex/Melph may have an apoptotic effect on Bort-resistant MM, optimizing drug combinations for Bort-resistant MM resulted in a combination that can both induce apoptosis and inhibit proliferation. Furthermore, both CDKN1A and PTPN6 transcripts were up-regulated in vivo only after treatment with the optimized drug combination (Fig. 6, E and F). This recapitulates the in vitro results and provides further evidence that reactivation of key tumor suppressor pathways may contribute to the enhanced therapeutic efficacy seen by the QPOP drug combination but not the monotherapies or currently clinically used drug combinations.

As a follow-up to the synergism observed in the earlier ALL in vitro data, we investigated whether the ability of Dec/MitoC to outperform clinically used drug combinations observed in our Bort-resistant MM model could also be observed in an intravenous in vivo Bort-resistant ALL model, when compared against the clinically used combinations Dex/cyclophosphamide (Cyclo) (47, 48) or Dex/Melph (49). The Dec/MitoC combination did not result in significant increases in survival compared to vehicle control, single-drug treatments, or clinically used combinations (fig. S7, A and B). It is likely that QPOP reoptimization is required to identify the optimal dosages for the intravenously seeded Bort-resistant ALL xenograft mouse model because the distribution of tumor cells and dosage-specific responses likely differ from the subcutaneous Bort-resistant MM xenograft mouse model.


QPOP overcame many of the hurdles associated with drug combination design and optimization, identifying optimal drug combinations and optimal drug dosages by applying experimental data to a deterministic model independent of molecular mechanistic assumptions. Here, QPOP was able to identify from a set of 14 drugs, in a mechanism-blind manner, a more globally optimized drug combination as well as the optimal dosages of each drug for effective treatment of Bort-resistant MM. This was achieved through multiple iterations of QPOP optimization, from in vitro cell lines through to a more complex in vivo system. As demonstrated in this study, in vivo QPOP reoptimization of drug combinations identified in vitro may be needed to identify the dosages required for the most effective therapeutic results. The need to reoptimize dosages in vivo lies in changes to the effects of drugs in a more complex biological system, where differences in pharmacokinetic properties, such as biodistribution, between drugs will ultimately affect how much of each drug is made available to the target tumors compared to other organs where they may confer toxic effects. The in vivo doses that were identified by QPOP reoptimization directly correlated to therapeutic efficacy and safety and implicitly accounted for the pharmacokinetic properties of the drug combination that affected in vivo drug exposure. Thus, whereas in vitro QPOP was effective in identifying the components of the optimized drug combination, in vivo QPOP reoptimization of the drug dosage ratios was able to identify the globally optimal drug-dose combination.

The ability of QPOP to continuously optimize drug combinations across multiple systems of interest in a mechanism-blind manner makes QPOP an attractive platform for combination therapy development that addresses many of the challenges that currently confront the drug development community. For example, drug repurposing is considered a promising approach toward reducing or recovering drug development costs while expanding treatment options for a wide range of diseases, including cancer (50, 51). The clinical success of drug repurposing, however, often relies on the drugs’ appropriate incorporation into drug combinations. The application of approaches such as dose escalation or other conventional strategies that sample the expansive dosing space can result in combinations with suboptimal dosing ratios. Because conventional approaches seek clinically acceptable increases in efficacy response from near-maximum tolerated doses, this could result in minimal increases in efficacy and even downstream clinical trial failure due to patient toxicity and mortality. Increasingly, specifically targeted drugs also necessitate the development of combination therapies to fully realize the efficacy of these targeted approaches. Therefore, QPOP may have a role in decreasing drug development costs by rapidly identifying optimal administration parameters at different phases of drug development.

We would note that QPOP achieves global optimality under certain assumptions that biological response to therapeutic intervention is a robust process that can be mapped by a parabolic smooth map. QPOP may not achieve global optimality in all general situations, including settings with a large nonbiological component. Pairing of QPOP with fully automated high-throughput technology could allow for experimental validation of all possible combinations to demonstrate that the globally optimal drug combination was identified by QPOP, which was not done in this study. Although this study was able to reposition existing clinical drugs for use in MM, the pool of drug candidates from which QPOP was performed comprised only 14 drugs, including drugs selected after an initial screen of the FDA-approved oncology drug set V. More effective drug combinations might result from using drugs that were not included within this 14-drug set. Again, pairing QPOP with fully automated high-throughput technology could allow for expanded in vitro QPOP analysis to identify globally optimal drug combinations from larger sets of drugs. Furthermore, other drug compounds selected on the basis of complementary approaches, such as genome-guided drug selection, would markedly expand the range of derived combinations and provide more immediate insight into drug combinations for established genomic biomarker-positive patients. Another limitation of the QPOP work presented in this study is that the optimized drug combinations did not take into account the effects of sequential drug treatment. A number of studies have demonstrated that certain drug combinations exhibit sequence-dependent efficacy as well as sequence-dependent synergy or antagonism. Although the most well characterized of these sequence-dependent drug combinations are linked to first modulating expression of key drug transporters or priming the tumor microenvironment to improve tumor uptake of cytotoxic drugs, there is preclinical and clinical evidence that even combinations of general cytotoxic drugs may benefit from sequential treatment (5255). In vivo or low-throughput optimization of drug combinations that include optimization of drug treatment sequence would likely be limited to smaller drug sets with the current QPOP platform. Although limited to smaller focused drug sets, optimization of sequential drug combinations by QPOP would be a logical next study to identify the optimal in vivo sequence of two to three drug combination treatments, as well as the optimal dosages by which these drugs mediate maximal efficacy. Finally, the work presented here demonstrated QPOP optimization in MM, which is characterized by a single solid tumor site. Application of QPOP toward other cancers, especially cancers with multiple tumor sites or hematological malignancies that do not have solid tumor foci, requires further investigation, as evidenced by Dec/MitoC response in the Bort-resistant ALL xenograft mouse model.

A key advantage of the QPOP platform over conventional approaches is that QPOP does not use predetermined drug synergy information that can confound preclinical and clinical development, given the dose-dependent nature of drug antagonism and synergy. There are several factors that can affect optimal drug combination design, such as the individual drugs having mutually exclusive targets, individual efficacies, and possibly having overlapping toxicities. Results from this study demonstrated that synergistic interactions can be identified and they contribute to the efficacy of drug combinations. However, synergy is not the sole determinant for the identification of globally optimized drug combinations. In the case of the ex vivo QPOP analysis of naïve MM patient samples, the drug set was built around Dec/MitoC and two clinically used combinations, Bort/Pano/Dex and Bort/Melph/Dex. We observed that the efficacies of these drug combinations were differently ranked across patient samples, in accordance with the fact that interpatient heterogeneity will always limit the efficacy of any single proposed drug combination. Clinical results for both Bort/Pano/Dex and Bort/Melph/Dex bear this out as well (13, 44).

QPOP identified a drug combination that may provide increased efficacy and benefit for a subset of patients after development of resistance to Bort or other proteasome inhibitors. Further studies of patient response to this combination, paired with genomic or DNA hypermethylation analysis, may be used to identify the most appropriate subset of patients based on a putative genomic or hypermethylation biomarker. The identification of a DNA hypermethylation biomarker could potentially be determined through supervised cocluster analysis. A similar supervised cocluster analysis of Dec/MitoC drug response to genomic data might reveal unique genomic signature subtypes that are more sensitive to the newly described combination (56). Beyond population-specific optimized drug combinations, ex vivo QPOP analysis of primary MM patient samples presented evidence that QPOP could also be applied toward identifying the best drug combination for specific patients. This would be particularly valuable for malignancies such as MM where the yield from bone marrow is low and not easily obtainable and optimized drug combination analysis must be highly efficient.

Although QPOP does not rely on mechanistic assumptions to derive optimal drug combinations, we were able to identify a potential mechanism to treat MM, that is, by targeting DNA hypermethylation and promoting the reexpression of the tumor suppressor genes CDKN1A and PTPN6. The increase in global DNA methylation in the resistant cell lines mirrored the clinical phenomenon where DNA hypermethylation is observed in relapsed MM (36). Although epigenetic drugs such as DNMT inhibitors and histone deacetylase (HDAC) inhibitors have been approved for clinical use, this approval is limited to a handful of hematological malignancies (57, 58). The vast majority of clinical trials for epigenetic inhibitors have failed because of a lack of patient response or toxicity (30). These clinical studies often use epigenetic inhibitors as monotherapies or in nonoptimized drug combinations with standard preexisting therapeutic regimens. Epigenetic drug combinations based on in vitro synergistic activities have also thus far not successfully translated into the clinic. Although HDAC and DNMT inhibitors have shown synergistic activity in vitro, multiple clinical trials demonstrated no clinical benefits and, in some cases, even pharmacodynamic antagonism for these combinations (5961). These studies highlight the need for continuous optimization of drug combinations and dosages throughout the entire drug development pipeline.


Study design

Here, we described a process to identify and rank optimal drug-dosage combinations as a continuous optimization platform, QPOP, based on the concept that biological responses to external perturbations can be mapped to smooth parabolic surfaces (22). This study aimed to use QPOP to identify effective optimal drug-dosage combinations from a diverse set of 14 FDA-approved oncology drugs in Bort-resistant MM. We performed QPOP analysis in vitro to identify drug combinations from this pool of candidates that were effective against a Bort-resistant human MM cell line. We then performed QPOP analysis in an in vivo xenograft model to reoptimize the drug combination to identify the optimal drug dosages for efficacy and reduced toxicity, thus providing a globally optimal drug-dosage combination. This study further aimed to evaluate the application of QPOP toward ex vivo patient sample drug combination optimization and to evaluate the sensitivity of individual MM patient samples toward QPOP-optimized drug combinations. Human primary MM cells used for in vitro validation and ex vivo QPOP experiments were obtained from naïve or relapsed MM patients from the National University Hospital. Treatment groups were not blinded; however, drug combinations for all QPOP analyses were prepared by an automated liquid handler. Details of replicate experiments are included in the figure legends. All animal studies were performed in accordance with animal research protocols approved by the National University of Singapore Institutional Animal Care and Use Committee, Singapore. Mice were randomly assigned to each treatment group. Minimum mouse treatment group sample sizes were determined by power analyses based on an expected minimum 2× difference with a 0.5 SD, a power of 80%, and a statistical significance of <0.05. Mice were euthanized when tumors reached 15 mm in diameter. Bone marrow samples from myeloma patients were collected after informed consent. The collection of bone marrow samples from myeloma patients for research performed under Domain Specific Review Board (DSRB) protocols 2007/00173 and 2012/00058 was approved by the National Healthcare Group DSRB that governs research ethics in Singapore that involves patients, staff, premises, or facilities of the National Healthcare Group and any other institutions under its oversight.

QPOP analysis

The results of the QPOP analysis were correlated into a second-order quadratic series. For in vitro experiments, the viability of the cells was used for the fitting, whereas for in vivo experiments, the toxicity subtracted from the efficacy was used for the optimization process. The second-order quadratic series is as follows:Embedded Image(1)where y represents the desired output, xn is the nth drug dosage, β0 is the intercept term, βn is the single-drug coefficient of the nth drug, βmn is the interaction coefficient between the mth and nth drugs, and βnn is the quadratic coefficient for the nth drug. This second-order quadratic series was coded with MATLAB software (MathWorks Inc.), where each drug combination was represented as a vector and coded dosages were used in the analysis (data file S1). For in vitro experiments, the relative viabilities of the Bort-resistant cell line RPMI 8226 were subtracted from the relative viabilities of the Bort-sensitive THLE-2 cell line for each combination and used as data for correlation into the second-order linear regression process. For in vivo experiments, the optimization metric was calculated as the mean weight loss of the mice (fig. S6) subtracted from the mean survival time of the mice (table S16).

Stepwise regression was initialized with first-order drug terms, interaction terms between drugs, and second-order drug terms, with their corresponding estimated coefficients. Interaction terms and second-order drug terms were removed sequentially based on the highest P values in F test variance comparisons between the reference equation and the subsequent equation with the removed interaction or second-order drug term.

The predictive power of the generated outcomes was also calculated via adjusted R2 and correlation coefficients to confirm the fidelity of QPOP optimization considering the number of drug and drug-drug interaction terms. Correlation coefficients (measures of the strength of the linear association between two variables ranging in value between zero and one) were derived from the experimental output values and projected output values for the corresponding drug combinations.

Statistical analysis

All experiments were performed in at least triplicate biological repeats, unless otherwise stated, with data presented as means ± SD. Normal distributions were first determined using the Shapiro-Wilk normality test. Student’s two-tailed t test was used for the comparison of two independent groups, whereas one-way ANOVA (with Dunn’s correction) was used for multiple comparisons. IC50 curves were compared using a sum-of-squares F test. For tumor volume analysis, Student’s t test was carried out between two independent groups at the end point of the experiment. Kaplan-Meier curves were compared using the log-rank Mantel-Cox test. P < 0.05 was considered statistically significant. Primary data are shown in table S19.


Materials and Methods

Fig. S1. Validation of QPOP-optimized combinations on P100v cells.

Fig. S2. IC50 comparison of QPOP-ranked efficacious drug combinations across different cell lines.

Fig. S3. QPOP-optimized drug combinations are efficacious against 7 nM Bort-resistant ALL cells.

Fig. S4. QPOP-optimized drug combinations are efficacious against 200 nM Bort-resistant ALL cells.

Fig. S5. Venn diagram showing common significant probes between three treatment groups.

Fig. S6. Mean weight of tumor-bearing mice for identification of optimal in vivo drug concentrations via QPOP analysis.

Fig. S7. Analysis of QPOP-optimal drug combination in a Bort-resistant ALL in vivo model.

Table S1. Top hits from the high-content screening of the FDA-approved oncology drug set at 1 μM on P100v.

Table S2. Top hits from the high-content screening of the FDA-approved oncology drug set at 5 μM on P100v.

Table S3. QPOP analysis using a design consisting of 128 combinations for 14 drugs at two levels (−1 and 1).

Table S4. Concentrations of drugs used for first iteration consisting of 14 drugs at two levels (1 and −1).

Table S5. Estimates and significance of QPOP analysis for first iteration (14 drugs at two levels).

Table S6. QPOP analysis using a design consisting of 155 combinations for nine drugs at three different levels (−1, 0, and 1).

Table S7. Concentrations of drugs used for second iteration consisting of nine drugs at three levels (1, 0, and −1).

Table S8. Estimates and significance of QPOP analysis for second iteration (nine drugs at three levels).

Table S9. Top 10 ranked QPOP-optimized two-drug combinations.

Table S10. Top 8 ranked QPOP-optimized three-drug combinations.

Table S11. Validation of Dec/MitoC on MM patient samples.

Table S12. Drugs and corresponding concentrations used for ex vivo QPOP.

Table S13. RNA sequencing pathway analysis upon treatment with 2.5 μM Dec versus DMSO control.

Table S14. RNA sequencing pathway analysis comparing Dec-treated and Dec/MitoC-treated P100v cells.

Table S15. Concentrations of Dec and MitoC used for in vivo QPOP analysis at five levels.

Table S16. Output used for in vivo QPOP analysis.

Table S17. Ranked list of in vivo QPOP drug dosage optimizations.

Table S18. Estimates and significance of in vivo QPOP analysis (four drugs at five levels).

Table S19. Primary data from figures shown (Excel file).

Data file S1. MATLAB code for quadratic series.


Acknowledgments: We thank the patients under the care of the National University Cancer Institute, Singapore (NCIS) for providing samples for the ex vivo portion of this study. Funding: This work was supported by the National Research Foundation Singapore and the Singapore Ministry of Education under its Research Centers of Excellence initiative to the Cancer Science Institute of Singapore (to E.K.-H.C., S.J., and W.J.C.) as well as the RNA Biology Center at the Cancer Science Institute of Singapore, National University of Singapore, as part of funding under the Singapore Ministry of Education’s Tier 3 grants, grant number MOE2014-T3-1-006 (to S.J. and W.J.C.). Additional support was received from the Singapore Ministry of Education Academic Research Fund (MOE AcRF Tier 2 MOE2015-T2-2-126 to E.K.-H.C. and MOE AcRF Tier 1 T1-2012 Oct -04 to S.J.). This work was supported by the NCIS Yong Siew Yoon Research Grant through donations from the Yong Loo Lin Trust (to E.K.-H.C.) and by the National Medical Research Council (NMRC) with the NMRC CBRG-NIG BNIG11nov001 (to S.J.) and NMRC Singapore Translational Research Investigatorship (to W.J.C.). This work was also supported by the Ben Rich–Lockheed Martin Professor endowment fund (to C.-M.H.) and by the NSF CAREER Award (CMMI-1350197), Center for Scalable and Integrated Nanomanufacturing (DMI-0327077), CMMI-0856492, DMR-1343991, V Foundation for Cancer Research Scholars Award, Wallace H. Coulter Foundation Translational Research Award, National Cancer Institute (U54CA151880), Society for Laboratory Automation and Screening Endowed Fellowship, and Beckman Coulter Life Sciences (to D.H.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NCI or the NIH. Author contributions: M.B.M.A.R., T.B.T., L.H., A.S., S.J., C.-M.H., W.J.C., D.H., and E.K.-H.C. designed the overall study. M.B.M.A.R., T.B.T., L.H., A.S., C.-M.H., D.H., and E.K.-H.C. performed the QPOP optimization design and validation portion of the study. M.B.M.A.R., T.B.T., L.H., Y.Z., A.L.T., P.F.T., and N.K. performed the biological characterization portion of the study. W.J.C. prepared the DSRB application to obtain patient samples. M.B.M.A.R., S.J., C.-M.H., W.J.C., D.H., and E.K.-H.C. wrote the manuscript. Competing interests: M.B.M.A.R., T.B.T., A.S., C.-M.H., W.J.C., D.H., and E.K.-H.C. are co-inventors of patent application WO2016179306 A1 entitled “Improved drug combinations for drug-resistant and drug-sensitive multiple myeloma.” C.-­M.H. is a co­inventor of pending patent WO2014113714 entitled “Rapid identification of optimized combinations of input parameters for a complex system.” All other authors declare that they have no competing interests. Data and materials availability: All data associated with this study are present in the paper or the Supplementary Materials. Cell lines are available from W.J.C. and E.K.-H.C. under a material transfer agreement with the National University of Singapore.

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