Combinatorial Therapy Discovery using Mixed Integer Linear Programming

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1 Bioinformatics Advance Access published January 24, 2014 Combinatorial Therapy Discovery using Mixed Integer Linear Programming Kaifang Pang 1,2,3, Ying-Wooi Wan 1,2,4, William T. Choi 1,2, Lawrence A. Donehower 5, Jingchun Sun 6, Dhruv Pant 7, and Zhandong Liu 1,2,3 1 Computational and Integrative Biomedical Research Center, Baylor College of Medicine, Houston, TX, 2 Jan and Dan Duncan Neurological Research Institute, Texas Children s Hospital, Houston, TX, 3 Department of Pediatrics-Neurology, 4 Department of Obstetrics and Gynaecology, 5 Department of Molecular Virology and Microbiology, Baylor College of Medicine, Houston, TX, 6 School of Biomedical Informatics, The University of Texas Health Science Center at Houston, Houston, TX, 7 Department of Cancer Biology, University of Pennsylvania, Philadelphia, PA, USA Associate Editor: Dr. Igor Jurisica ABSTRACT Motivation: Combinatorial therapies play increasingly important roles in combating complex diseases. Due to the huge cost associated with experimental methods in identifying optimal drug combinations, computational approaches can provide a guide to limit the search space and reduce cost. However, few computational approaches have been developed for this purpose and thus there is a great need of new algorithms for drug combination prediction. Results: Here we proposed to formulate the optimal combinatorial therapy problem into two complementary mathematical algorithms, Balanced Target Set Cover (BTSC) and Minimum Off-Target Set Cover (MOTSC). Given a disease gene set, BTSC seeks a balanced solution that maximizes the coverage on the disease genes and minimizes the off-target hits at the same time. MOTSC seeks a full coverage on the disease gene set while minimizing the off-target set. Through simulation, both BTSC and MOTSC demonstrated a much faster running time over exhaustive search with the same accuracy. When applied to real disease gene sets, our algorithms not only identified known drug combinations, but also predicted novel drug combinations that are worth further testing. In addition, we developed a web-based tool to allow users to iteratively search for optimal drug combinations given a user-defined gene set. Availability: Our tool is freely available for non-commercial use at Contact: Supplementary information: Supplementary data are available at Bioinformatics online. 1 INTRODUCTION Complex diseases, such as cancer, cardiovascular diseases and neurological disorders, usually involve multiple genes whose protein products play pivotal roles in controlling aberrant pathways and networks. In addition, disease pathways and networks are often redundant and robust to single point perturbations. Since To whom correspondence should be addressed. most drugs are designed to selectively target specific proteins, single-drug treatments usually cannot break down the whole disease pathways and networks. This is why the traditional one disease, one gene, one drug treatment often fails (Hopkins, 2008). Multitarget treatments, especially drug combinations, can simultaneously target multiple components of the disease pathways and networks, thus offering hope for treating such complex diseases (Jia et al., 2009). There have already been many successful combinatorial therapies to treat complex diseases. For example, highly active antiretroviral therapy is a potent combination of at least three active antiretroviral drugs targeting reverse transcriptase, protease, and integrase to keep the HIV virus from replicating itself (Lucas et al., 1999). The combination of glyburide and metformin is used to treat type 2 diabetes in complementary ways (Bokhari et al., 2003). Moduretic is the combination of amiloride and hydrochlorothiazide that can effectively treat patients with hypertension (Wilson et al., 1988; Frank, 2008). The combination of anastrozole and fulvestrant is more effective than individual or sequential usage of both drugs for the treatment of ER-positive and/or PR-positive metastatic breast cancer (Mehta et al., 2012). Despite the increasing successes in using drug combinations to treat complex diseases, most of them were developed based on clinical experience or test-and-trial strategy, which is not only time-consuming but also expensive. High-throughput screening methods have also been developed to identify effective pairwise drug combinations (Borisy et al., 2003; Lehár et al., 2009; Tan et al., 2012). However, a systematic analysis of all the possible pairwise combinations is both labor intensive and cost ineffective because of the large combinatorial space needed to explore. Furthermore, most drug combinations may not significantly improve the efficacy over individual drugs. Therefore, large-scale drug combination screening is highly ineffective. In addition, a systematic screening becomes unfeasible if combinations of more than two drugs are considered. The closed-loop control (Wong et al., 2008), stack sequential (Calzolari et al., 2008), and other search algorithms reviewed in Feala et al. (2010) have been developed together with biological experiments to identify the optimal drug combinations from a huge drug-dose space. However, given thousands of individual drugs, The Author (2014). Published by Oxford University Press. All rights reserved. For Permissions, please 1

2 careful pre-selection of a subset of drugs within which to search for optimal combinations in experimental testing is not an easy task. Several systematic computational approaches for predicting drug combinations have recently been developed and could provide a guide to limit the search space for experimental methods. For example, Vazquez (2009) proposed identifying the optimal drug combinations by searching for the minimal number of drugs that can target all the cancer cell lines using the highest-degree-first and simulated annealing algorithms. However, this heuristic search algorithm does not have optimum guarantee and the convergence rate for large-scale data sets could be slow. Wu et al. (2010) integrated a molecular interaction network and gene expression data of individual drugs to identify subnetworks affected by individual or combinatorial drugs. The drug effect on these subnetworks is measured by taking into account both efficacy and side effect and then used to prioritize drug combinations. They successfully identified effective drug combinations used to treat type 2 diabetes, but the dependency on the availability of gene expression data treated with individual and combinatorial drugs as well as the high computational cost when handling the vast combinatorial space makes their approach unsuitable for large-scale application. Zhao et al. (2011) and Xu et al. (2012) proposed two similar computational approaches to prioritize pairwise drug combinations using feature patterns enriched in the known drug combinations and got some promising predictions. However, their approaches rely heavily on the known drug combination data which is of small size, thus biasing their predictions towards those combinations that are similar to the known ones. Therefore, the current computational approaches are very limited and there is a great need to develop new algorithms for drug combination prediction. Drug design is usually specific, but one drug may target multiple proteins due to promiscuous binding (Paolini et al., 2006; Yildirim et al., 2007). One protein can be targeted by multiple drugs as well. The drugs and proteins form an intricate drug-target network. When used to treat diseases, a drug can affect both disease on-target proteins for which it was designed and some off-target proteins that are not related to the diseases. When different drugs are combined, there could be a large number of additive off-targets whose effects are undesired. Thus, given a set of disease genes, the problem of finding the optimum drug combinations that maximize on-target coverage and minimize off-target effects is important and challenging. This is similar to the efficacy maximization and side effect minimization problem in combinatorial therapy. Also, such off-target effects in drug combination have not been considered in the systematic computational studies (Vazquez, 2009; Zhao et al., 2011; Xu et al., 2012) with the exception of the work (Wu et al., 2010). To address the on-target maximization and off-target minimization problem, we first formulated the optimal combinatorial therapy problem using an optimization framework and solved it using mixed integer linear programming. Then, we compared our approach with exhaustive search using simulation and demonstrated a better performance of our approach over exhaustive search. Finally, we demonstrated the good performance of our approach through searching optimal drug combinations for six disease gene sets from a drug-target network. Our approach not only captured the wellknown drugs and drug combinations, but also suggested novel uses for some other drugs. The drug combinations discovered using our approach can target the protein products of disease genes with minimal perturbations to the other proteins and are worthy of further testing to treat such diseases. To make our approach more accessible to the general drug discovery community, we developed a webbased tool to allow users to iteratively search for optimal drug combinations from a user-defined gene set. The remaining part of this article is organized as follows: we first describe the optimization approach in Section 2; in Section 3, application of the approach on both the simulated and real data is presented; the article concludes with a brief discussion on current issues and potential future improvements. 2 METHODS 2.1 Drug-target Network We extracted the drug-target interactions from the DrugBank database (version 3.0) (Knox et al., 2011) and constructed a bipartite network, in which nodes represent drugs or targets and edges represent drug-target interactions. We further removed the targets with no human gene symbol annotation. The remaining network contains 4,233 drugs, 2,058 target genes, and 9,669 drug-target interactions. We also extracted the adverse drugdrug interaction effects and the drug action information from the DrugBank database. Given an input disease gene set, drugs with the same set of targets, actions, and interacting drugs were merged into a single meta-drug since they are equivalent to our algorithm. Details on drug data processing are provided in Supplementary Text 1. Unless otherwise specified, we used the term drug instead of meta-drug in the remaining text and the term disease gene to represent the protein product of disease gene. 2.2 Optimal Combinatorial Therapy Given a set of disease genes, we first removed those genes that have no associated drugs in the drug-target network. The remaining set of disease genes is called on-target set, denoted as T = {t 1, t 2,..., t p}. We then extracted the drugs associated with the on-target genes from the drug-target network. The set of off-targets, S = {s 1, s 2,..., s q } is the set of genes that are connected with the on-target associated drugs in the drug-target network but does not overlap with T. Mathematically, the associated drugs can be formulated as M = {M i M i T S, i = 1, 2,..., m}, where each drug M i can target some disease genes in T and some off-target genes in S as well. Finding the optimal drug combination for a disease is to maximize the coverage on T and minimize the overlap with S using a subset of M. This problem can be defined as follows. PROBLEM 1. (Balanced Target Set Cover Problem, BTSC). Given a disease D = (T, S) and a collection of drugs M, find a subset C M and C k that minimize the cost(d, C) = α T \( C) +(1 α) S ( C), where C = C C C, k is the upper bound on the cardinality of the solution set C, and α is the weight balance of the coverage between on-target set T and off-target set S. A natural choice of α is 0.5. When α is set to 1, BTSC is equivalent to the maximum coverage problem. In practice, users may have a small set of highly confident drug targets and would require full coverage on these targets while minimizing the number of off-targets. BTSC cannot be used directly to solve this problem. To overcome this limitation, we further propose to fully cover the ontargets in T and minimize the number of off-targets in S. In other words, we require any selected combination of drugs to cover all the on-target disease genes. This can be achieved by setting α to 0 and adding a constraint of full set cover. Mathematically, the restricted problem can be defined as follows: PROBLEM 2. (Minimum Off-Target Set Cover Problem, MOTSC). Given a disease D = (T, S) and a collection of drugs M, find a subset C M that minimize the cost(d, C) = S ( C), where T ( C) = T ( M) and C = C C C. 2

3 Running Time (seconds) 2.3 BTSC and MOTSC Problems are NP-hard The NP-hard property of the BTSC problem can be proved through reduction mapping. By setting α to 1, the maximum coverage problem becomes finding a maximum cover on the disease genes in T using at most k drugs from M. This reduction shows that BTSC is at least as hard as the maximum coverage problem, which is in the NP-hard problem set (Cohen and Katzir, 2008). MOTSC can be viewed as a modified version of the Red Blue Set Cover (RBSC), which is also a generalization of the standard set cover problem (Miettinen, 2009). RBSC is much harder than the standard set cover problem and there exists no polynomial approximation with a factor of 2 (4 log n)1 ϵ for any ϵ > 0 (Peleg, 2007). 2.4 Mathematical Programming Formulation Mathematically, BTSC can be formulated using the Mixed Integer Linear Programming (MILP) as follows: minimize α p i=1 (1 y i) + (1 α) p+q i=p+1 y i (1) subject to (Bx) i y i = 0 (2) by i y i 0 (3) y i y i 0 (4) m j=1 x j k (5) (Lx) 1 (6) y i Z+, y i, x j {0, 1} (7) The formulation has three variables, x, y, and y. The first two are binary, and the last one is nonnegative. The binary solution vector x indicates which drugs are selected. The non-negative cost variable y i counts the times that the i th gene is covered by the selected drugs. The binary cost vector y is derived from y, y i = 1 if y i 1; otherwise, y i = 0. The value of y i indicates whether the i th gene is covered. We note that in vectors y and y, the first p elements are associated with the on-target genes and the next q elements are associated with the off-target genes. The relation between a given disease D and the associated drugs M can be represented using a binary matrix B, where the rows are indexed by the on-targets (p) and off-targets (q), and the columns represent the drugs. B im = 1 if the i th gene in D is covered by the m th drug in M; otherwise, B im = 0. The non-zero elements in the product vector of B and x indicate the corresponding genes targeted by a selection of drugs. The drug-drug adverse interaction effects are encoded in L, a l m binary matrix where, for each row k, L ki = L kj = 1 if the drugs M i and M j have an adverse effect when used together. The intuition of the MILP formulation is the following. The equality constraint (2) counts the number of times that an on-target or an off-target is covered by the selected drug combination. However, y cannot be directly used in the objective cost function (1). Thus, the binary cost y is introduced and related to y by the inequality constraints (3) and (4). The inequality constraint (3) requires y i = 1 if y i 1. For that, the value of b needs to be at least the maximum value of all y i. The inequality constraint (4) guarantees that y i = 0 whenever y i = 0. The maximum number of drugs for any feasible solution is bounded by the inequality constraint (5). The inequality constraint (6) guarantees any feasible solution to avoid the drug-drug adverse effects encoded in L. In this paper, we solved BTSC problem using the GNU MILP solver GLPK which is based on a branch and cut algorithm. MOTSC can be formulated similarly (Supplementary Text 2). The dual problems of BTSC and MOTSC are further discussed in the Supplementary Texts 3 and Iterative Search and Online Tool To make our approach more accessible in practice, we developed a webbased interactive tool (http://www.drug.liuzlab.org/) that will allow users to iteratively refine the search results. Both BTSC and MOTSC are ES BTSC Number of Drugs Fig. 1. Running time difference between BTSC and ES. The number of associated drugs is simulated from 10 to 30 with a step size equal to 2. Each data point represents the average running time of 10 replicates. For the simulated data with 30 associated drugs, ES takes about 4.7 days, while BTSC only needs 9 seconds. implemented with the options to filter out drugs based on approval status, drug-drug adverse interaction, and drug action direction. In addition, our web tool can also generate the output result files for Cytoscape visualization (Shannon et al., 2003). 3 RESULTS 3.1 Time Complexity and Accuracy Analysis To evaluate the time complexity and accuracy of our algorithm, we compared it to exhaustive search (ES) on a simulated data set. According to the formulation in section 2.4, the simulated data set is controlled by four parameters: (1) the number of columns in B, which represents the number of drugs associated with a disease gene set; (2) the number of rows in B, which represents the total ontarget and off-target space; (3) the density of B, which represents the percentage of genes targeted by a drug; (4) the value of p, which represents the number of on-targets. The first parameter, the number of columns in B, is the most important factor affecting the running time of ES. Therefore, we generated B by varying the column size from 10 to 30 with a step size equal to 2. At the same time, the second parameter was set to 1000 and B was sampled from a Bernoulli distribution with hitting probability equal to 0.01 (the third parameter). In addition, we further removed those rows in B for which the sum across the columns is equal to 0. We sampled p indexes (the third parameter) of the rows in B, with a sampling rate equal to 10%. Then, we simulated the data ten times with each varying number of the columns in B, applied BTSC and ES to find the solution x and compared their differences in the cost and running time. Our results demonstrated that there is no difference in the cost function between the BTSC and ES solutions. The running time of ES however increases exponentially, while BTSC tends to generate the correct results significantly faster (Figure 1). From these results, we found that ES is impractical even for finding combinations among a small number of drugs. For example, a search for combinations among 30 drugs using ES will take about 4.7 days to get the optimal solution. However, BTSC can obtain the 3

4 N Formylmethionine LTF LCN2 DPP6 CTSD COX6C HLA B COX7B MBL2 GLA AMY2B MAN1A1 NPR3 COX6B1 GALNT1 IGHG2 UBC CLPP B2M ITGA4 CEACAM1 CXCL12 EFNB2 VEGFA GZMB BCHE IGF1R CPD IGF2R LDLR RNASE1 PTGS1 COX4I1 COX7A1 COX8A GP1BA SIGLEC7 IGHE COX6A2 ADAM33 CSF2RB CES1 NOS1 Tinzaparin Dalteparin S100B MT CO2 CHI3L1 CGA AZGP1 Alpha D Mannose CD2 COX7C SELP CTLA4 IFNB1 COX5B APOH DPP4 IL12B MT CO3 ACPP Heparin IL6R MT CO1 MT ND1 LYZ RABGGTA IGHG1 Ardeparin Sulodexide MAN1B1 LCT PLA2G1B SERPIND1 DNASE1 COX5A CES1P1 LGALS1 CD209 S100G RABGGTB C1R DB04673 DB CD46 RHO Nadroparin FOS EGF FGA Sucralfate PGA3 FGF2 LRP1 Alteplase Reteplase...3 Tenecteplase Fondaparinux_sodium Enoxaparin COL4A5 COL4A2 COL4A4 FGB FGG SERPINC1 TFPI COL4A6 F3 FCER1A Rivaroxaban DB07207 DB Coagulation_factor_VIIa DB04590 DB COL4A1 COL4A3 F7 F9 GGCX PF4 AHSP F8 HPN Gamma Carboxy Glutamic_Acid PROC AMI BGLAP THBD DB07211 DB PROS1 F5 Drotrecogin_alfa F2R DB07376 PLAT F2 ANXA2 CP DB04134 DB07684 Streptokinase CLEC3B SERPINB6 DB07718 CALR SERPINA5 SERPINB2 PLG Bicine KRT8 CANX PLAUR MIF Beta (2 Naphthyl) Alanine DB03865 PRSS1 Lepirudin Argatroban...72 Iloprost Urokinase DB06854 SERPINE1 PLAU PTGER1 YARS Suramin LRP2 PDE4A Aprotinin PIN1 PDE4D DB01767 DB DB02193 DB PDE4B NID1 ST14 DB00006 DB06695 PTGIR PDE4C FSHR SIRT5 PLA2G2A KLK1 RYR1 P2RY2 CTRB1 F10 RTN4R GUSB PROCR which is collected in the Molecular Signatures Database (version 3.1) (Subramanian et al., 2005; Liberzon et al., 2011). From 35 associated drugs, BTSC predicted that Streptokinase, Fondaparinux sodium Enoxaparin, DB04134, and DB07376 can be combined to target the AMI gene set (Figure 2). In the four-drug combination, Streptokinase is able to dissolve blood clots that have formed in the blood vessels. Fondaparinux, as well as Enoxaparin, is an anticoagulant that helps prevent the formation of blood clots. The co-administration of Streptokinase and Fondaparinux in a published cohort of ST-elevation myocardial infarction patients significantly reduced the risk of death, recurrence and severe bleeding (Peters et al., 2008). The combination of Streptokinase and Enoxaparin is effective in patients with AMI (Simoons et al., 2002; Giraldez et al., 2009). Two experimental compounds, DB04134 and DB07376, were also identified in the solution. DB04134 is an antifibrinolytic agent that acts by inhibiting plasminogen activators which have fibrinolytic properties. DB07376 is an anticoagulant that can prevent blood clotting. Since these two compounds target different AMI genes, the use of these two compounds in combination with Streptokinase and/or Fondaparinux sodium Enoxaparin may exert additional benefits in treating AMI patients. This result indicated that BTSC is able to identify known drug combinations as well as novel compounds that are not covered by existing therapies. Fig. 2. The disease-gene-drug network of AMI. The disease gene set name AMI is represented using a cyan hexagon and there are 20 genes (red, orange or chocolate circles) in AMI gene set. Four (green squares) of 35 associated drugs (green or gray squares) selected by BTSC can cover 7 AMI genes (red circles) with no known off-target. Eight genes (orange circles) have no associated drugs and 5 genes (chocolate circles) associated with drugs are not covered by the selected drug combination. optimal solution within 9 seconds. We also varied the other three parameters in simulation. There is still no cost difference between BTSC and ES and the effects of these three parameters on the running time difference are much less important than that of the first parameter (data not shown). Similar results were obtained on MOTSC (Supplementary Figure 1). Thus, through this simulation, we demonstrated that our algorithms can achieve high accuracy with much fast running time. To demonstrate the power of our approach in searching for optimal drug combinations, we applied it on six disease gene sets: acute myocardial infarction, EGFR-PI3K-AKT-mTOR pathway, hypertension, type 2 diabetes mellitus, Parkinson s disease and schizophrenia. All the search parameters used for the following results are available in the Supplementary Text 5. All the following networks are visualized using Cytoscape (Shannon et al., 2003). Drugs are represented using DrugBank names, except that drugs with long names are represented using DrugBank IDs. Further details are provided in the online document. 3.2 Acute Myocardial Infarction Acute myocardial infarction (AMI) is the irreversible necrosis of heart muscle with the usual cause that a coronary artery is obstructed by an acute thrombus. The AMI related 20 genes were derived from BioCarta AMI pathway (http://www.biocarta.com) 3.3 EGFR-PI3K-AKT-mTOR Pathway EGFR-PI3K-AKT-mTOR (EPAM) pathway plays an important role in a lot of cellular processes and is abnormally activated in a variety of human diseases including cancer and neurological disorders. Eighteen genes in the EPAM pathway were obtained from Hennessy et al. (2005) and Morris et al. (2011). From 41 associated drugs, BTSC predicted that Lapatinib, Everolimus, DB08059, DB07812, and DB06831 can be combined to target the EPAM pathway (Figure 3). In the five-drug combination, Lapatinib is a selective inhibitor developed for both EGFR and ERBB2 (Opdam et al., 2012; Diaz et al., 2010). Everolimus, a derivative of Rapamycin, can act as an mtor inhibitor and block the signal transduction for cell proliferation. Through literature search, we discovered that the combination of Lapatinib and Everolimus shows efficacy in patients with advanced cancers in a phase I study (Gadgeel et al., 2013). This combination is also under a clinical trial (NCT ) in patients with advanced triple negative breast cancer, and under a phase 1b/2 clinical trial (NCT ) for treatment of HER-2 positive breast cancer with CNS metastasis. One consequence of mtor inhibition by Rapamycin or Rapamycin derivatives is the loss of inhibition on PI3K and AKT, resulting increased pathway activity. In addition, patients treated with EGFR inhibitors often develop drug resistance through secondary mutations (Kobayashi et al., 2005). To address these issues, our combinatorial therapy selected DB08059 (wortmannin), a known inhibitor of PI3K, and an experimental inhibitor (DB07812) of AKT and GSK3β. Therefore, simultaneously targeting multiple genes in the EPAM pathway will offer the hope to increase the efficacy of drug treatment and delay the development of drug resistance. 4

5 C1S AFG3L2 ABCG1 ARAF ABL1 PIK3C3 HIBCH STK17B ASNA1 NAE1 HCK ATP5B ABL2 ADRBK1 ACSS1 ATP5A1 ATP5C1 MAT1A HSP90AB1 ABCB1 UGT3A1 ATP2A1 HSP90AA1 RNASE2 UCK2 TNK2 ABCC2 ACSS2 ADRBK2 RFC5 RFK ABCB11 ABCA1 Adenosine_triphosphate ACVR1B DB06836 SLC25A4 CYTH3 GUK1 Quercetin KIF3B MYH11 PGK1 HSPA8 ACVRL1 DB02375 DB BCKDK RNASE1 PDK2 MYO1D TAP1 APAF1 HMGCR NME1 PDXK HSP90B1 ACVR1 CDK15 PRKAA1 ASNS KIF5B ADCY1 ACSL1 ABCC8 NT5C2 DDX39B DAPP1 ABCC9 AMHR2 BTK PIK3CG PLEKHA4 DB07335 DB08059 CYTH2 ASS1 DB06831 PKIA Adenosine 5 Diphosphate SRC PIK3R1 PIK3CA PIK3CD TRPM7 DCK AKT1 DB06897 DB MYH14 HSPA1A PMS2 CKM PAPSS1 KIT GLUD1 KIF11 KIFC1 TSC2 DB07662 PIK3CB PIK3R2 EPAM PLK1 AKT2 DB07859 DB DB02656 DB07186 DB01772 DB DB07584 DB07585 CAMK4 ABCE1 PTK2 DB01863 PIM1 GSS CMPK1 DB07676 PDPK1 KIF1A SCN10A SCN5A DB01269 DB07602 PTEN ERBB2 PIK3R3 SCN9A Lidocaine MAPK1 DB07812 GSK3B HK1 ABCA6 PRKACA Staurosporine ITPKA GALK1 VCP MAPKAPK2 ACTA1 KIF2C CFTR DTYMK SYK AURKA PRKCQ LCK CSK PFKFB4 TOP2B DB04395 FCGR2B EGFR TSC1 FCGR2A C1QA Trastuzumab Lapatinib ITK Phosphonothreonine SRPK2 RHO DAPK1 CCT3 ZAP70 MTOR MAPK12 RAD51 C1QC Cetuximab FCGR3B FCGR1A Gefitinib Flavopiridol Everolimus Alsterpaullone PRKACB CSNK2A1 CDK2 S100A11 MAPK10 CDK1 Lithium IGF1R EPHA2 DB07010 EPHB2 C1QB C1R FCGR2C FCGR3A Erlotinib Temsirolimus Purvalanol CDK9 Olomoucine CDK7 Sirolimus INPP1 DB04338 DB08521 MAPK3 IMPA2 MAPK14 NR1I2 DB06877 DB CDK6 CDK4DB08513 Indirubin 3 Monoxime CDK5R1 FGF2 FKBP1A PYGM CDK8 IMPA1 CDK2deltaT GRIA3 Fig. 3. The disease-gene-drug network of EPAM. The disease gene set name EPAM is represented using a cyan hexagon and there are 18 genes (red, orange or chocolate circles) in EPAM gene set. Five (green squares) of 41 associated drugs (green or gray squares) selected by BTSC can cover 10 EPAM genes (red circles) with no known off-target. Six genes (orange circles) have no associated drugs and 2 genes (chocolate circles) associated with drugs are not covered by the selected drug combination. This result indicated that BTSC is effective in identifying optimal drug combination to target multiple components of an aberrant pathway. 3.4 Hypertension Hypertension (HTN) or high blood pressure is a chronic medical condition characterized by the elevated blood pressure in the arteries. Yue et al. (2006) curated a set of 26 HTN related genes including key regulators in the renin-angiotensin pathway, endothelin regulation, natruretic peptide regulation, and bradykininkillikrien pathway. From 77 associated drugs, BTSC predicted that the combination of Bupranolol, Triamterene, Chlorthalidone, Sitaxentan, and Remikiren could be effective for treating HTN (Figure 4). In the five-drug combination, Bupranolol is a non-selective beta blocker, Triamterene is a potassium-sparing diuretic, and Chlorthalidone is a thiazide diuretic. The combination of Bupranolol and Triamterene has been well documented as an effective agent for HTN treatment (Schrey, 1981). The combination of Triamterene and Chlorthalidone shows clinical efficacy in reducing blood pressure, and keeping serum potassium concentration from decreasing too much (Spiers and Wade, 1996). CDK5 IRS1 INSR Two other HTN drugs, Sitaxentan and Remikiren, were also identified in the solution. Sitaxentan is an endothelin receptor antagonist, and Remikiren is a renin inhibitor. Since these two drugs target different pathways, they may provide additional benefits for patients who are not responsive to the above drug cocktails. This result indicated that BTSC is also effective in identifying optimal drug combination to target multiple altered pathways. 3.5 Type 2 Diabetes Mellitus Type 2 diabetes mellitus (T2DM) is a chronic metabolic disorder in which blood glucose is increased to a high level due to altered insulin signaling. We extracted KEGG insulin signaling pathway (http://www.genome.jp/kegg/) and REACTOME insulin receptor signaling cascade pathway (http://www.reactome.org) from the Molecular Signatures Database (version 3.1) (Subramanian et al., 2005; Liberzon et al., 2011). These two pathways share 41 genes, which were used as T2DM related genes for optimal drug combination search. From 13 associated drugs, BTSC predicted that Insulin Aspart Insulin Detemir, Metformin, Everolimus Temsirolimus, and Pegademase bovine could be combined to treat T2DM (Supplementary Figure 2). In the four-drug combination, Insulin Aspart is a fast-acting insulin analogue, while Insulin Detemir is a long-acting insulin analogue. Metformin can help control blood sugar levels. Insulin including Insulin Aspart and Insulin Detemir in combination with Metformin is routinely used in the treatment of T2DM (Wulffelé et al., 2002; Kvapil et al., 2006; Hollander et al., 2011). Inhibition of mtor leads to upregulation of IRS (insulin receptor substrate) and increased activity of AKT (O Reilly et al., 2006), thus being able to ameliorate insulin resistance. Everolimus and Temsirolimus, two inhibitors of mtor selected by BTSC, are worthy of further testing in combination with Insulin and/or Metformin to combat T2DM. This result demonstrated that BTSC has the ability to identify both well-known combination regimen regularly used in disease management and promising combination component with additional beneficial effect. 3.6 Parkinson s Disease Parkinson s disease (PD) is a movement disorder caused by depletion of brain dopamine. We obtained 10 genes involved in dopamine synthesis and metabolism pathway from Youdim et al. (2006). From 28 associated drugs, BTSC predicted that the combination of Levodopa, Carbidopa, Entacapone, Selegiline, and Metyrosine is able to fully cover PD related genes (Supplementary Figure 3). Among the 5 selected drugs, there are several well-known combinations that have already been used to treat PD. For example, the triple combination of Levodopa (a dopamine replacement), Carbidopa (a DDC inhibitor), and Entacapone (a COMT inhibitor) has been approved by FDA for treating PD (Hauser, 2004). In addition, Selegiline (an MAO inhibitor) in combination with Levodopa, Carbidopa, or Entacapone shows improved treatment of PD (Elizan et al., 1991; Cedarbaum et al., 1991; Lyytinen et al., 1997). This result further demonstrated the good performance of BTSC in identifying optimal drug combination. 5

6 GAPDH NPPB VEGFA VCAM1 GJA1 SLC6A2 SMPD1 ESR1 NDUFC2 CHRM4 CHRM2 CHRM3 NCOA1 DB08347 CHRM1 DB00901 DB07543 Oxprenolol Desipramine HTR2A ADRA2A ADRA2B Carvedilol DB04652 Progesterone Bevantolol Levobunolol Metipranolol...3 Esmolol Atenolol HRH1 ADRA1B Phenoxybenzamine ADRA2C PGR PLA2G4A CHRM5 Labetalol ADRA1A Betaxolol Penbutolol GLUD2 NDUFA9 NDUFB7 AMT NDUFA13 GLUD1 EHHADH ALDH1A2 NDUFS2 ME2 GSR NDUFA4 ALDH1A1 ALDH1A3 BLVRB IMPDH2 NDUFB6 SC4MOL ALDH7A1 ADH1B NDUFA2 HMOX1 MT ND5 ALDH5A1 OGDH NDUFAB1 HSD17B8 PYCR2 ALDH3A1 NDUFS3 NNT ALDH3A2 HADH NDUFB4 LDHB PDHA1 MT ND4 AGTR2 NDUFB5 ADH4 NDUFA5 HSD17B3 DHCR7 NQO2 PPARG NDUFV2 NDUFC1 TSTA3 ME3 NDUFA12 UGDH LDHA NDUFA7 HSD17B7 MTHFD2 RDH5 HADHA ADH7 ALDH2 H6PD GAPDHS AASS MT ND1 MT ND2 HPGD IDH3B CYP4A11 ADH1A NSDHL NDUFA1 CDO1 HSD17B2 JUN NDUFS8 ALDH4A1 NDUFA3 HMOX2 HSD11B1 Tasosartan QDPR NADH GPD1 Telmisartan DLD ADH5 NDUFS7 HIBADH PYCR1 ME1 HSD17B10 MTHFD1 MDH2 LDHCMT ND6 AKR1B1 PDHB Losartan Candesartan...3 Irbesartan CYP17A1 ALDH3B2 IDH3G ALDH6A1 NDUFB9 ADH1C ALDH3B1 TYR Olmesartan SLC12A6 DHFR NDUFB8 HSD3B2 NDUFS6 Forasartan Saprisartan HMGCR NDUFA10 NDUFA11 MT ND3 AKR1C1 LDHAL6B SLC12A4 SLC12A5 NDUFB2 PDHA2 NDUFV3 NDUFS4 HSD3B1HSD17B1 NDUFB10 BLVRA MDH1 LDHAL6A DB04674 Valsartan SLC12A7 NDUFA4L2 NDUFA8 IDH3A BDH1 AKR1C4 MT ND4L AKR1C3 NDUFB1 SLC12A2 NDUFV1 ALDH1B1 Potassium_Chloride NDUFB3 ACADS PHGDH SORD CYB5R3 ALDH9A1 AGTR1 NR3C1 IMPDH1 Bumetanide AR KCNMA1 CA12 NDUFS1 NDUFS5 ABCC9 NDUFA6 KCNJ5 Benzthiazide HSD17B4 DLAT ABCA1 Fluticasone_Propionate AKR1C2 CA9 Quinethazone Bosentan ABCB11 Metolazone Polythiazide CFTR Hydrochlorothiazide Chlorothiazide Spironolactone Drospirenone Eplerenone Aldosterone ADRB2 Metoprolol Timolol...4 Practolol DB08558 LCT CALM1 ADRB1 Sotalol SLC6A4 Sitaxentan EDNRA KCNH2 Alprenolol NR3C2 CACNA2D2 Bupranolol TNNC1 Propranolol HTR1B PDE1A Felodipine Amiodarone HTR1A CACNG1 CACNB2 CACNA2D1 KCNK6 CACNA1H KCNJ1 EDNRB TNNC2 PDE1B CACNA1D CACNA1S CACNA1C Ibutilide KCNH6 Verapamil ADRB3 CACNA1I KCNK1 Nimodipine ABCC8 CACNA1F CACNB1 CACNB4 CACNA1B KCNH7 Glimepiride AHR CACNA1A CACNB3 SCN5A HSD11B2 HTN KNG1 CACNA1G Thiamylal GABRA1KCNJ8 KCNJ11 Spirapril Candoxatril MME ECE2 CLCNKB ACE Ramipril Fosinopril...7 Trandolapril NPPC DB03740 Glyburide CYP11B2 AGT EDN1 BDKRB2 REN SLC12A3 SCNN1A SCNN1B SCNN1G Icatibant DB07171 SLC12A1 Remikiren Aliskiren...16 DB01180 DB02032 Moexipril Lisinopril Captopril ECE1 Dimethylformamide DB07244 KLK1 NOS3 ACE2 ANPEP CELA1 Bendroflumethiazide Furosemide Methyclothiazide Piretanide Chlorthalidone Triamterene Aprotinin PLG Amiloride CA2 CA1 CA4 Hydroflumethiazide Trichlormethiazide Torasemide SCNN1D ACCN2 CTRB1 PRSS1 ACCN1 SLC9A1 Ethacrynic_acid PLAU ABP1 ATP1A1 GBA SIGLEC7 IGHG1 ACHE MMP2 Fig. 4. The disease-gene-drug network of HTN. The disease gene set name HTN is represented using a cyan hexagon and there are 26 genes (red, orange or chocolate circles) in HTN gene set. Five (green squares) of 77 associated drugs (green or gray squares) selected by BTSC can cover 10 HTN genes (red circles) with only one off-target (blue circle). Seven genes (orange circles) have no associated drugs and 9 genes (chocolate circles) associated with drugs are not covered by the selected drug combination. 3.7 Schizophrenia Schizophrenia (SZ) is a chronic, severe, and disabling brain disorder affecting 1% of the population worldwide and is linked to the dysfunction of dopamine, GABA, glutamate, and serotonin pathways. We extracted 28 SZ related receptor and transport genes involved in these four pathways from the SZGR database (Sun et al., 2008, 2009; Jia et al., 2010). From 102 associated drugs, BTSC predicted that Haloperidol, Sertraline, Dolasetron, Methohexital, and Vilazodone could be combined to treat patients with SZ (Supplementary Figure 4). To validate the prediction, we did a literature search and discovered that the co-administration of Haloperidol and Sertraline to schizophrenics results in clinical improvement of negative symptoms and aggravation of extrapyramidal symptoms (Lee et al., 1998). BTSC also unveiled possible new uses of three FDA-approved drugs that have not been previously used in SZ. In particular, Dolasetron targeting the serotonin pathway has been used to treat nausea and vomiting following chemotherapy. Since the serotonin pathway plays a key role in mood control, this drug may improve the existing treatment schema. Such drugs could be reused to target SZ in a cost-effective way, because their safety and side effect have already been well studied. This result not only further demonstrated the good performance of BTSC in optimal drug combination prediction, but also suggested the potential utility of BTSC in drug repositioning. 3.8 Performance on DCDB We further performed an independent validation of BTSC by applying it to predict the FDA-approved drug combinations in DCDB (Liu et al., 2010). Using the FDA-approved drug combinations derived from DCDB, we first generated an approximately gold standard dataset of 68 known associations between disease gene sets and drug combinations. We then performed search to see the extent to which these approved drug combinations can be recovered by our online tool. Totally, 59 of 68 (accuracy = 86.8%) approved drug combinations can be fully or partly recovered, while 55 of 68 (accuracy = 80.9%) approved drug combinations can be fully recovered. Details are provided in the Supplementary Text 6. This result demonstrated that BTSC is able 6

7 to identify known drug combinations with high accuracy in a large scale. Taken together, these results indicated that BTSC has good performance in predicting both known and novel drug combinations. In addition, MOTSC identified similar but slightly different drug combinations when applied to the five disease gene sets which are not fully covered by BTSC (Supplementary Figures 5-9). The difference between the results of BTSC and MOTSC further indicated that MOTSC is more applicable if the user has a specific requirement on the full coverage of the input genes. Thus, BTSC and MOTSC provided two complementary ways to identify optimal drug combination. 4 CONCLUSION Optimal combinatorial therapy discovery is an important and challenging problem. In this article, we introduced two complementary approaches for this problem and solved them using mixed integer linear programming. There are many heuristic search algorithms that can provide greedy solutions for this problem. However, we are interested in finding the global optimum solution and these heuristic search algorithms cannot provide such accuracy. Therefore, we excluded this category of algorithms in solving the optimal combinatorial therapy problem and did not compare our approaches to any heuristic search algorithms. Instead, we compared our approaches to exhaustive search and demonstrated that our algorithms can obtain the same optimum solution with much faster running time. Application of our approach on real disease gene sets demonstrated its good performance in identifying known drug combinations as well as predicting novel drug combinations. In addition, our approach has the potential to unveil new functions of existing drugs for drug repositioning. We have developed an online tool for our proposed algorithms. The online tool provides many features, such as exclusion of adverse drug-drug interaction, constraint on the number of drugs, iterative search, highly efficient solver and notification. In addition, the online tool allows the user to assign the weight balance on the on-target and off-target set as well as to choose how to handle drugs with opposite actions on input genes. The online tool is also flexible to include new constraints, such as the importance weight of input disease genes and the penalty weight of potential off-target genes. The availability of the online tool will make our algorithm accessible not only to the computational biologists but also to the bench scientists. The mathematical analysis presented here provides a general framework for the solution of multi-target therapeutic design. Although running our algorithm on arbitrarily large set of drugs is not possible due to the nature of NP-hard problem, most of the real applications fall into the small and mid-size categories. In practice, our algorithm and online tool demonstrate accurate and fast performance on those applications. One weakness of our approach stems from its use of incomplete drug-target interaction data. However, in recent years, a significant amount of effort has been devoted to drug target annotation and prediction. With the improved size and quality of such data, we believe that our approach and web-based tool will play an increasing role in drug discovery and development. In addition, personal variants in protein-coding genes can be easily obtained with the advances in next-generation sequencing technologies. Due to the heterogeneity of complex diseases, even individual patients with the same disease may have a distinct set of causal genes and thus will need different treatment strategy. This problem is very challenging and cannot be resolved in an effective way now. But our tool offers one way to help predict optimal drug combination for targeting individual set of disease genes, which will have a nontrivial contribution to personalized medicine. ACKNOWLEDGMENTS The authors would like to extend their gratitude to Drs. Juan Botas, Huda Zoghbi, and James Alverez. The authors would also like to thank the reviewers for their valuable suggestions on improving the manuscript. Funding: This project is supported by the Houston Bioinformatics Endowment and NIH 5DP5OD Zhandong Liu is also partly supported by NSF/DMS Jingchun Sun is supported by Cancer Prevention & Research Institute of Texas (CPRIT) Rising Star Award to Dr. Hua Xu. Conflict of Interest: none declared. REFERENCES Bokhari,S.U., Gopal,U.M. and Duckworth,W.C. (2003) Beneficial effects of a glyburide/metformin combination preparation in type 2 diabetes mellitus. 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