- Open Access
A linear programming computational framework integrates phosphor-proteomics and prior knowledge to predict drug efficacy
© The Author(s). 2017
- Published: 21 December 2017
In recent years, the integration of ‘omics’ technologies, high performance computation, and mathematical modeling of biological processes marks that the systems biology has started to fundamentally impact the way of approaching drug discovery. The LINCS public data warehouse provides detailed information about cell responses with various genetic and environmental stressors. It can be greatly helpful in developing new drugs and therapeutics, as well as improving the situations of lacking effective drugs, drug resistance and relapse in cancer therapies, etc.
In this study, we developed a Ternary status based Integer Linear Programming (TILP) method to infer cell-specific signaling pathway network and predict compounds’ treatment efficacy. The novelty of our study is that phosphor-proteomic data and prior knowledge are combined for modeling and optimizing the signaling network. To test the power of our approach, a generic pathway network was constructed for a human breast cancer cell line MCF7; and the TILP model was used to infer MCF7-specific pathways with a set of phosphor-proteomic data collected from ten representative small molecule chemical compounds (most of them were studied in breast cancer treatment). Cross-validation indicated that the MCF7-specific pathway network inferred by TILP were reliable predicting a compound’s efficacy. Finally, we applied TILP to re-optimize the inferred cell-specific pathways and predict the outcomes of five small compounds (carmustine, doxorubicin, GW-8510, daunorubicin, and verapamil), which were rarely used in clinic for breast cancer. In the simulation, the proposed approach facilitates us to identify a compound’s treatment efficacy qualitatively and quantitatively, and the cross validation analysis indicated good accuracy in predicting effects of five compounds.
In summary, the TILP model is useful for discovering new drugs for clinic use, and also elucidating the potential mechanisms of a compound to targets.
- Treatment effect
- Signaling pathway
- Linear programming
- Prior knowledge
In recent years, molecular and cellular biology has significantly improved our understanding of cancers in human, however, the discovery and use of therapeutic drugs still faces major challenges . Particularly, insufficient understanding of pathological and therapeutic mechanisms at a cellular level holds back the growth of the number of new drugs taken for clinical use . More difficulties arise to predict the exact effects of those approved drugs . As a result, patients with serious illnesses are left with few treatment options; and the new medicines are usually extremely expensive. Only 10% of drug molecules entering clinical trials succeed and approximately 3 out of 10 drugs generate enough profit to pay back the investment . The linkage between basic science and useful treatment has to be built based on deep understanding of biological networks, as well as drug-induced molecular changes in these networks . A global view covering the interconnectivity of the signaling proteins and their functional contributions to cancer development is critical for the success of targeted drug anti-cancer therapies. Accordingly, the systems biology approaches, which combine experimental data and mathematical modeling, provide an effective framework to understand cancers and develop new drugs .
Recently, the public LINCS genomic database (Http://www.lincsproject.org/) was established, aiming to create a network-based understanding of biology by cataloging molecular changes in gene expression and signal transduction occurring when cells were exposed to various genetic or drug perturbations . The LINCS is helpful for drug screen and discovery via better understanding intracellular pathways. Particularly, the P100  data in LINCS project, is mass spectrometry (MS) based phosphor-proteomic profiles caused by a wide range of small molecule chemical compounds on several representative cancer cell lines, such as MCF7 (breast cancer) and PC3 (prostate cancer) cell lines . Due to unclear targets or treatment effects, most part of compounds used in P100 is not widely applied as drugs in market. Identifying the treatment effects of a compound on certain cell line is of great significance of discovering new potential drugs and improving the response to therapies in clinic.
Considering the P100 data  was only measured at 6 h after compound perturbations, it is impossible to build ODE-based model of intracellular pathway network to predict drug efficacy . Mitsos and coworkers firstly proposed an integer linear programming method (ILP) to predict drug treatment effect with phosphor-proteomic data, however, their model can only address the signaling networks with simple topology . We recently developed a Binary Linear Programming based approach (BLP) for modeling large-scale signaling pathways . BLP was applied on LINCS dataset (L1000 gene expression profiles  and P100 proteomics ) to identify compound treatment effects via pathway alterations. Different from the ILP approach , our BLP model can address the signaling networks which have complex topologies. However, BLP shows obvious disadvantage: 1) the definition of the state of each protein node with Boolean variable is not sufficient enough to represent the relative changes of the proteins between treatment and un-treatment; 2) BLP model may lead to biased predictions due to the division of the training and testing set of P100 data is fixed in advance.
P100 data on 15 chemical compounds were used in this study
Treatment concentration (uM)
The expression of each protein (ρ) in P100 dataset was represented as log2 ratio of treatment to control (un-treatment). Therefore, the raw data of P100 were normalized to ternary values (1, 0, and −1) with threshold 1.2, where 1 corresponds to up-regulation (ρ ≥ log2(1.2)), 0 to no-change (−log2(1.2) < ρ < log2(1.2)), and −1 to down-regulation (ρ ≤ − log2(1.2)). The normalization method reflects the relative changes on signaling proteins after compound perturbation.
Constructing a generic pathway map
The compound targets were proved in the previous literatures
According to Eq. (1–4), four cell functions (cell cycle regulation, DNA repair, cell survival, and cell growth) are quantified as integer variables, and are calculated from their upstream TFs (see Methods).
Inferencing a cell-specific pathway network by TILP
In order to infer the cell-specific network from our constructed generic pathway map that best reproduces the experimental data, we minimized the differences between the model’s predicted values and the corresponding observational values for the subset of protein nodes that are observed, as well as the complexity of network structure. To solve the multi-objective optimization problem, we developed a TILP model of the generic pathway network, and obtained a cell-specific pathway network by optimizing formula (9) shown in Methods. The idea behind TILP is that the states of nodes are normalized to ternary numbers; directed edges between two connected nodes are represented as Boolean numbers; and linear constraints are defined to describe the casual relationship between child and parent nodes. The prior knowledge shown in Table 2 was represented as linear constraints to guide the optimization process. The TILP model of a signaling network was solved by using MATLAB toolbox Gurobi 6.5.1 . The toolbox guarantees to minimize a global error function that combines the requirements of data fit and simplicity. The fitting precision of the inferred specific pathways of MCF7 cells was 83.33%, which demonstrates that TILP fits well on P100 data. The definition of fitting precision is described in Additional file 1: Text S2.
Predicting a compound’s treatment effects
Additional file 2 Figure S1, Additional file 3: Figure S2, Additional file 4: Figure S3, Additional file 5: Figure S4 and Additional file 6: Figure S5 present the response network perturbed by 5 testing compounds: carmustine, doxorubicin, GW-8510, daunorubicin, and verapamil (Table 1). For all 15 measured proteins in the MCF7-specific pathway network, fitting precision of these observed nodes for five compounds were 100%, 80%, 86.67%, 93.33%, and 80%, respectively. According to the pathway alterations, we can qualitatively identify the compound-induced treatment effects on MCF7 cells. From Additional file 2: Figure S1, Additional file 3: Figure S2, Additional file 4: Figure S3, Additional file 5: Figure S4 and Additional file 6: Figure S5, the reactions with red color represent up-regulation, green is for down-regulation, and black is for no-change. The reactions with yellow color did not occur after compound treatment
Carmustine , a potential anticancer agent, activated the MAPK (MEK/ERK, and JNK) pathway via ER→SHC→RAS, and inhibited PI3K/AKT, HSP90/HIF, and AMPK pathways in MCF7 (see Additional file 2: Figure S1). An’s work proved that carmustine induced phosphorylation of the MAPKs, such as ERK, JNK, and p38, etc. .
Doxorubicin , the current front-line therapy for breast cancer, not only activated MAPK pathway as carmustine, but also up-regulated EGFR/PKC pathway. In addition, treatment with Doxorubicin also decreased the expression of ATM/BRCA1, HSP90/NFKB, and PI3K/AKT/BAD pathways (see Additional file 3: Figure S2). Rojo and coworkers proved that ex vivo exposure of breast tumors to doxorubicin down-regulated MKP-1, and up-regulated p-ERK1/2 and p-JNK, in the majority of cases . Liu, et al. also found that the active TGFβ signaling exhibited resistance to the DNA-damaging agent doxorubicin in some breast tumors , and TGFβ induces a DNA-repair deficiency through downregulating DNA-repair genes, such as ATM, and BRCA1 .
Additional file 4: Figure S3 indicates that GW-8510 potentially inhibited most of signaling pathways in the MCF7-specific network expect increase the expression of HDAC1.
Daunorubicin , a market selling heterocyclic anticancer drug, mainly activate MAPK (MEK/ERK, and JNK) pathways via ER→SHC→RAS, and down-regulated cell survival through reduced PI3K/AKT pathway in the inferred MCF7-specific pathway network (Additional file 5: Figure S4). Stulpinas and colleagues observed that daunorubicin treatment induced the activation of JNK and phosphorylation of its direct target c-Jun along with inactivation of AKT . We also noticed from Additional file 5: Figure S4 that, the activation of HDAC1 induced the down-regulation of p53. D’Assoro’s study indicates that treatment on MCF7 cell line with daunorubicin resulted in the arrest of both G1/S cell cycle progression .
As to Verapamil , a calcium channel antagonist, is known as a potential anticancer agent. In Additional file 6: Figure S5, this compound induced up-regulation of ATM/BRCA1 to increase the cell cycle, and down-regulation of MAPK, HSP90/HIF1 to reduce the tumor growth.
In addition, the “cell function” vector consists of four output nodes, which can be potentially used to calculate the similarity between two compounds (Fig. 5e). For example, the outcome vectors of response network, treated by Paclitaxel and Staurosporine, were [0, 0,-3,-1] and [0, 0,-2,-2], indicating that both compounds may potentially induce cell death. Compared to the topological structure of cell-specific pathway network shown in Fig. 4, the similarities of compound-induced network are 91.89% (paclitaxel), and 89.19% (staurosporine), respectively. In Yu’s work, MDA-MB-435 breast cancer cells represent similar cell apoptosis rates after treatment with paclitaxel or staurosporine . Cartee, et al. also found that exposed the BG-1 cells to staurosphorine or paclitaxel exhibited similar apoptotic cell death via caspase activation . Another example is the calculated outcomes of GW-8510-induced response network were similar as digoxin did, that are [−2,-2,-3,-4] and [−2,-2,-1,-4], respectively. Although the predicted inhibition effects of GW-8510 on above four cell functions cannot be confirmed, Chung and coworkers introduced that GW-8510 may have high inhibitory activities against cancer cells. They further confirmed that the novel functional links between GW-8510 and cell cycle inhibition according to the microarray experiments . In summary, most of the above predictions from networks are consistent with the conclusions in previous studies, which implies that TILP model is reliable for identifying compound treatment effects.
In this study, we presented a novel computational modeling approach TILP to reconstruct cell-specific pathway network and predict the system’s response to compound treatment by combining prior knowledge from literature and phosphoproteomic data collected from various types of perturbation experiments. In order to test the power of TILP model, we selected a set of P100 proteomic data of 15 chemical compounds effecting on MCF7 breast cancer cell line. Based on the differential expressed proteins in P100 data, we combined all the top-ranked enriched pathways (P value < 0.01) from IPA with some important pathways reported in previous literatures, to manually construct a generic pathway map related with MCF7 cells, which includes 50 reactions and 35 proteins (15 proteins were observed in P100 dataset). With the TILP model for pathway modeling and optimization, a MCF7-specific pathway network of 35 nodes and 37 edges was finally inferred. Based on the topological structure of optimized MCF7-specific network, we monitored 5 cases of compound-induced response networks to predict the effects of these compounds using TILP again.
An important aspect of our approach is its practicability in inferring cell-specific network. Although continuous modeling approaches (e.g. ODEs ) are commonly used to model dynamics of biological networks ; however, parameter estimation in ODE models is a NP-hard problem . TILP, a parameter-free model, based on the conception of discrete modeling, has simplified both the representation and optimization of signaling network with mathematical constraints. In the TILP model, we defined two types of constraints: (1) the states of connected proteins and reactions were defined with linear constraints; (2) the prior knowledge about the expressions of potential targets corresponding to perturbed compounds was also represented as linear constraints. Thus, the developed constraint system simplifies the optimization process and quickly searches an optimal solution from an allowable subspace. For inferencing the MCF7-specific pathway network, the optimization procedure of TILP model produced about 11,357 constraints and 4950 variables (4600 binary variables, and 350 integer variables). Totally, 4317 constraints and 2032 variables were automatically generated for predicting a compound’s effects. The TILP model is scalable to more complex signaling networks; the efficiency can still be guaranteed because a linear programming problem usually can be solved in linear time when the dimensionality is fixed .
Another important aspect of our approach is to help identify compound treatment effects in two ways: (1) identify the treatment effects through network topological alterations; (2) calculate the similarity of two compounds with their corresponding outcome vectors from pathway network. As described in the experimental results, most of predictions were consistent with the previous studies in the literature. However, there are still a small part of predictions could not be proved from literature, such as, GW-8510, which means it has never been used for breast cancer treatment. In addition, some evidences on other cell lines provided supports to our findings. For example, carmustine enhances chemotherapeutic efficacy by attenuating AKT activity in gliomas . As a protective agent, verapamil  was found to significantly reduce the expression of HIF-1 alpha in many cells . Liu and coworkers work also provided evidence for a crucial role for the over expression of MEK/ERK pathway in protecting kidney SP cells from ischemic/hypoxic injury, and Verapamil treatment reversed MEK-induced cell viability . Further biological experiments (e.g. Western Blot, or Mass Spectrometry) will potentially validate the effectiveness of your model.
Comparing to our BLP model, the proposed TILP model successfully solved the limitations in BLP: 1) we used three states (“up-regulation”, “down-regulation”, and “no-change”) to represent the relative changes of a protein when the cancer cells received extracellular stimuli; 2) the training set is related with 10 compounds, which have been validated effectively for breast cancer treatment. And the five compounds included in the testing set are rare studied in the breast cancer therapy. Therefore, the cell-specific pathways optimized by the training set, has potential to find new drugs for cancer therapy. 3) The TILP model not only qualitatively identify the compound treatment effects via pathway alterations, but also quantitatively evaluate the similarity of a pair of compounds on the same cancer cell line.
In order to prove the reliability of our approach TILP, we tested the effects of leave-one-out cross-validation on the p100 data of the first 10 compounds which were used in model training. For each compound, we extracted phospho-proteomic data of 9 compounds to infer a cell-specific pathway network and then identify the treatment effects of the remaining one by predicting the states of all the proteins via TILP. The mean value of fitting precision for above 10 cases was 84%, suggesting that the inferred cell-specific pathway network is reliable for predicting a compound’s effects. Based on the results of the leave-one-out cross-validation we did on MCF7 cell line, we calculated the similarity of network diagrams among 10 cases (each corresponds to one compound) where each case represents a cell-specific pathway network trained from the remaining 9 compounds after leaving one compound out. In overall, the connected edges in the final inferred cell-specific pathway network (Fig. 4) are 37. The similarity of an inferred cell-specific pathway network based on the different combinations is defined as the ratio of the number of connected edges in cell-specific network of each case to the total number of connected edges (37). The mean value of the similarities of 10 cell-specific networks generated by cross validation was 99.7%. It verifies that our inferred cell-specific pathway network with p100 data of 10 compounds was reliable.
The P100 assay is a mass spectrometry-based targeted proteomic assay that detects and quantifies a representative set of ~100 phosphopeptide probes that are presented in a wide range of cell types and have been demonstrated to be modulated via perturbations https://personal.broadinstitute.org/jjaffe/p100.php. The P100 phospho-profiles are suitable for molecular signature generation, querying of signatures across cell perturbations and types, and modeling of response networks in cellular systems.
P100 data is processed through a combination of scientist review of primary data, automated quality control and statistical calculations to result in assay profiles. Currently, the signature of the assay is the complete profile of all probes measured in the assay. Five types of cells were collected and profiled, such as MCF7 (breast cancer cell), H9 (Human embryonic stem cell), et al.
In our work, we selected the validation dataset of MCF7 cell line in P100, which contains measurements of phosphor-signal treated by 26 different small compounds. The treatments were each monitored for 6 h with two replicates. All raw expression values in P100 experiment represent log2 ratios of the treatment VS. Control.
Ternary status based integer linear programming (TILP)
In this study, the TILP computational framework was applied to systemically model a signaling pathway network with phospho-proteomic data. The developed model was used in two ways: firstly, TILP infers the cell-specific pathway network from the discrete representation of a generic pathway map; secondly, TILP predicts the treatment effects of a small compound based on the inferred cell-specific signaling network. The detail steps of the TILP framework is described as follows:
Discrete representation of the generic pathway map
At first, we selected the differentially expressed proteins (DEPs) from the observational data (LINCS P100). Second, we chose the top-ranked enriched signaling pathways from the database IPA (Ingenuity Pathway Analysis) based on the DEPs. Third, the generic pathway map was manually constructed by merging all the enriched signaling pathways with some important pathways studied in literature.
After determining the topological structure of the generic pathway map, the next step is the discrete representation of the signaling network. In our study, a signaling pathway map was defined as a discrete network , consisting of a set of nodes and directed edges. In order to reasonably describe the relative changes of cells after perturbation by a chemical compound, nodes in the network represented phosphoproteins with their discrete values 1, −1, and 0, which stand for “up-regulation”, “down-regulation”, and “no-change”(no significant change), respectively. The directed edges indicate phosphorylation reactions in the process of signal transduction induced by a compound. Here, we consider two types of reactions: inhibition and activation which were encoded by integer variables (−1 or +1). In our study, we defined a linking pattern of signaling proteins which was commonly seen in most of pathway network structures (Fig. 3). According to Fig. 3, we found that a child protein node can connect with several parent protein nodes, and be activated by at least one of its parents. In our TILP model, the states of all the elements (nodes and edges) in a network were satisfied to our developed mathematical constraints (see the details in Additional file 1: Text S1).
Inference of the cell-specific pathway network
Recently, we have developed a linear programming approach DILP to model signaling pathways with time series proteomics. In the DILP model, we proposed three states for defining the protein nodes under different time points . In this study, some basic conceptions were inherited from our DILP model.
Eq. (10) indicates that the activation reaction i under condition k takes place if x u, k ∙ x d, k = 1. Similarity, the inhibitory reaction i under condition k take place if x u, k ∙ x d, k = − 1(Eq. (11)). Comparing with previous DILP model, TILP greatly simplifies the calculation for adding the “missing edges” in the optimization. The details were described in the Additional file 1: Text S1.
The formulations in TILP model described above were implemented in GUROBI 6.5.1 , which is a well-known a Matlab-based mathematical programming solver. The optimization of Eq. (9) delivers an optimal sub-network of the constructed generic pathways and best reproduces the experimental data.
Prediction of compound treatment effects
qualitatively identify the treatment effects via compound-induced pathway alterations. The states of all the phosphor-proteins and signaling reactions in the network could be inferred, so that we can easily find which pathway is activated (nodes are up-regulated and edges take place in this pathway), inhibited (nodes are down-regulated and edges take place in this pathway), or un-changed (the expression of nodes have no significant changes). Additional file 2: Figure S1, Additional file 3: Figure S2, Additional file 4: Figure S3, Additional file 5: Figure S4 and Additional file 6: Figure S5 provides more details about the five testing cases.
quantitatively evaluate the similarity of treatment effects between two compounds according to the outcome vectors of signaling network. The similarity score (SS) is defined as correlation coefficient, to represent the similarity of treatment effects between compound A and C with their corresponding outcome vectors of response networks.
where T A and T C are the output vectors from compound A and compound C induced response networks, respectively. Based on Eq. (12), we can easily evaluate the treatment effects between any two compounds (see the details in Fig. 5e).
We developed a Ternary status based Integer Linear Programming (TILP) model to identify cell-specfic signaling pathways and predict compoun treatment effects by combining phosphorproteomics data and prior knowledge. To validate the effectiveness, we tested our TILP model on MCF7 cell line with LINCS P100 proteomics. The simulation results indicate that our model is capable of inferring the cell-specific pathway network, and further qualitatively and quantitatively predicting the compound treatment effects. For large-scale biological networks, it is difficult to estimate a large number of parameters from limited observations using ODE-based modeling approaches. As a parameter-free model, the TILP model is more efficient than continuous models (such as ODEs) because all of the elements in the network were defined as discrete variables so that the optimal solusion can be qucikly searched from an allowable subspace with constraints. Although MCF7 is used as a case of disease, the proposed model will be applicable to other disease studies with proteomic data.
We would like to acknowledge Lin Zhu and Feng Chen for discussions about this work.
This work was funded by the Foundation of talent’s start-up project in Zhejiang Gongshang University (1120XJ2116016) and the Foundation of Zhejiang Provincial Department of Education (No. 1120KZ0416255). This work was also partially supported by the National Science Foundation of China (No. 61472282), Science Foundation of Zhejiang Province (LY15F020003), and the Key Laboratory of Metallurgical Emission Reduction & Resources Recycling (Anhui University of Technology), Ministry of Education, under Grant No. KF 17–02.
Availability of data and materials
P100 phosphoproteomics data is freely available from the LINCS Data Portal (http://lincsportal.ccs.miami.edu/datasets/).
About this supplement
This article has been published as part of BMC Systems Biology Volume 11 Supplement 7, 2017: 16th International Conference on Bioinformatics (InCoB 2017): Systems Biology. The full contents of the supplement are available online at https://bmcsystbiol.biomedcentral.com/articles/supplements/volume-11-supplement-6.
Conceived and designed the models: Z.J., B.W., L.D. Performed the simulations: Z.J., K.Y., L.S. Analyzed the experimental data: Z.J., G.M., L.D. Wrote the paper: Z.J. Provided ideas to improve the systems modeling: Z.J., B.W. All authors read and approved the final manuscript.
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