The chemical-genetic profile can be defined as quantitative values of deletion strains' growth defects under exposure to chemicals. In yeast, the compendium of chemical-genetic profiles of genomewide deletion strains under many different chemicals has been used for identifying direct target proteins and a common mode-of-action of those chemicals. In the previous study, valuable biological information such as protein–protein and genetic interactions has not been fully utilized. In our study, we integrated this compendium and biological interactions into the comprehensive collection of ∼490 protein complexes of yeast for model-based prediction of a drug' s target proteins and similar drugs. We assumed that those protein complexes (PCs) were functional units for yeast cell growth and regarded them as hidden factors and developed the PC-based Bayesian factor model that relates the chemical-genetic profile at the level of organism phenotypes to the hidden activities of PCs at the molecular level. The inferred PC activities provided the predictive power of a common mode-of-action of drugs as well as grouping of PCs with similar functions. In addition, our PC-based model allowed us to develop a new effective method to predict a drug' s target pathway, by which we were able to highlight the target-protein, TOR1, of rapamycin. Our study is the first approach to model phenotypes of systematic deletion strains in terms of protein complexes. We believe that our PC-based approach can provide an appropriate framework for combining and modeling several types of chemical-genetic profiles including interspecies. Such efforts will contribute to predicting more precisely relevant pathways including target proteins that interact directly with bioactive compounds.
The collection of yeast deletion strains has enabled systematic genomewide functional analysis [1]. In addition, strain-specific molecular barcodes allow quantitative functional profiling of pooled deletion strains by using TAG oligonucleotide microarrays [1], [2]. One of several types of functional profiles, the chemical-genetic profile, expresses quantitative values of deletion strains' growth defects under a chemical. The compendium of chemical-genetic profiles of heterozygous and homozygous deletion strains under different chemicals has been successfully used for identifying direct target proteins of those chemicals [3], [4] as well as exploring their common mode-of-actions [5]. By integration of synthetic lethality profiles, the chemical-genetic profiles of homozygous deletion strains were also used to discover genes and pathways targeted by specific chemicals [6]. The chemical-genetic profiles in yeast are undoubtedly a useful resource to infer drug' s action mechanism in human [7]. In the previous study, however, valuable biological information such as protein-protein and genetic interactions has not been integrated with chemical-genetic profiles in a single model for drug' s target pathway prediction. Also, those profiles have not been yet modeled at the molecular level in terms of biological real entity such as protein complexes. As chemical-genetic profiles of many bioactive compounds are accumulating in many species including yeast, such real molecular entity-based modeling becomes essential to the molecular level understanding of phenotypes of the eukaryotic cell exposed to different chemicals. For example, that will allow us to infer drug' s mode-of-action from chemical-genetic profiles more precisely than the previous model-free approach. In order to relate hidden biological activities of some real biological entities at the molecular level to the phenotypes of deletion strains at the organism level, we assume that the growth of a deletion strain is affected by hidden activities of protein complexes in a given condition, which leads to the observable population changes of the strain. This assumption comes from the molecular rationale of protein complexes for gene-to-phenotype relationships [8], by which similar sensitive phenotypes of deletion strains of genes comprising a protein complex were explained in various different conditions. It is plausible that protein complexes can be regarded as functional units for the phenotypes of a deletion strain. If we view the entire cell as a factory comprising various distinct machines efficiently connected for its productivity [9], genomewide protein complexes can be regarded as a collection of “cellular machines” connected with each other for optimal growth and survival of a cell (Figure 1). Based on the assumption that each protein complex should play a proper role as well as communicate efficiently with each other for cell survival and adaptation in various treatments, we developed a Bayesian factor analysis model. Our model is similar to the network models developed in transcription regulation studies [10]–[13] (Figure 2). The basic idea of the model is that the observed growth fitness measurements of each strain are determined by combined effects of the activities of PCs in each cell in a given treatment. To implement this idea, the association relationship between deletion strains and PCs is necessary, which led us to construct the binary (0 or 1) association network between the knockout genes of strains and PCs based on their physical or genetic interactions (Figure 2C). Here, we assume that the relative growth fitness of strains by a chemical are mainly affected by deleterious interactions between the knockout-gene product of a strain and PCs which are physically or genetically linked (Figure 1). By modeling chemical-genetic profiles in terms of protein complexes using physical and genetic interactions as a priori knowledge, we inferred hidden activities of a collection of PCs in each cell exposed to different chemicals. Based on those PC activities, bioactive compounds with similar mode-of-action were clustered together. It means that the binary association network in our model represents biologically meaningful relationship between knockout genes of strains and protein complexes as hidden factors. In addition, we showed that protein complexes with similar function were clustered together, which implies that the unknown functions of protein complexes can be predicted. Finally, we presented a new effective method to predict drug' s target pathway using our PC-based model. For example, we were able to highlight target-protein, TOR1, of rapamycin as well as RUB1, UBA3, UBC12, and ULA1 related to protein neddylation as relevant biological pathway for cellular toxicity of camptothecin. We believe that our protein complex-based approach can provide appropriate framework for combining and modeling several types of chemical-genetic profiles including interspecies. Such efforts will contribute to predict more precisely relevant pathway including target-proteins that interact directly with bioactive compounds.
We applied our PC-based Bayesian factor model (see the details in Method Section) to the compendium of chemical-genetic profiles (∼4,800 haploid deletion strains, 82 chemicals) generated in the recent study [5]. This allowed us to infer the hidden activities of 488 PCs in 82 different chemicals (Figure 3A and Figure S3). To compare our model-based approach with the previous strain-based approach for predicting common mode-of-action of drugs using the same compendium, we first performed hierarchical clustering of the inferred PC activities and strains fitness itself (Figure 3, see the details in Method section). For fair comparison, two different dendrograms of 82 drugs should be validated against the gold standard drug-drug associations in the cellular context of Yeast. However, such reliable data were not available enough to measure performance of two dendrograms quantitatively. Therefore, we marked the common clusters and different clusters on the two dendrograms (Figure 3B and 3C) and surveyed their literature evidences, which were categorized as follows: In strain-based clustering of the compendium [5], deletion mutant strains with similar chemical sensitivities are clustered together as well, grouping functionally related genes. Similarly, the protein complexes with a similar function were also clustered together (Figure 3D). For examples, we selected three clusters with at least two protein complexes known for their functions. Their functional annotations of Gene Ontology were summarized in Table S1. Here, we describe more literature evidences for those clusters. As shown in the above examples, the hierarchically clustered groups of protein complexes revealed insights into similar biological processes. In other words, unknown functions of protein complexes could be inferred based on those groups closely clustered. Nonetheless, it was preliminary investigation using simple hierarchical clustering method to highlight the biological essential features of protein complex activities. If chemical-PC profiles are applied to other clustering methods such as biclustering or network reconstruction methods, such results could be different in some cases as well as give more essential features on behaviors of protein complexes perturbed by drugs. To find a drug-target pathway, we first selected significantly sensitive protein complexes to each drug (Figure 4), and then examined the biological processes of deletion genes of strains that were associated with such sensitive protein complexes in our model (see the details in the method; Table S2). This investigation of PC-constrained strains allowed us to highlight more relevant drug-target pathways than that of PC-free strains. In particular, it is clear in cases of camptothecin and rapamycin whose target-pathways are well known (Figures 5 and 6). In a seminal article in the journal Cell entitled, “The cell as a collection of protein machines: preparing the next generation of molecular biologists, ” Bruce Alberts described a cell as a factory: “Indeed, the entire cell can be viewed as a factory that contains an elaborated network of interlocking assembly lines, each of which is composed of a set of large protein machine” [9]. In recent genomewide study of yeast, two independent groups, European Molecular Biology Laboratory (EMBL), Cellzome (a spin-off company from EMBL), and the university of Toronto, have surveyed the first comprehensive protein complexes, called protein machines by Bruce Alberts, using tandem affinity purification (TAP) [8], [44]. Furthermore, Gavin et al. [8] gives molecular rationale of protein complexes for gene-to-phenotype relationship. In our study, those protein complexes are regarded as functional units for yeast cell growth, and then protein complex based Bayesian factor analysis is performed to relate growth fitness of genomewide deletion strains to hidden activities of protein complexes in a cell. In other words, at the organism' s phenotype level, the chemical-genetic profiles representing relative growth fitness of systematic deletion strains are modeled in terms of protein complexes at the molecular levels. To show that our model assumption (Figure 1) is reasonable and the inferred complex activities are reliable, hierarchical clustering analysis and literature survey were performed, which showed predictive power of common mode-of-action of bioactive compounds as well as grouping of protein complexes with similar biological behavior. In addition, we performed drug' s target-pathway prediction based on our model assumption (Figure 1) to show how practical our model framework is. GO analysis and literature survey shows that complex-based way of drug' s target-pathway prediction narrows down lots of drug-sensitive genes involved in various biological pathway to a handful of genes important in the relevant pathway perturbed by a drug. For example, we were able to highlight target-protein, TOR1, of rapamycin as well as RUB1, UBA3, UBC12, and ULA1 related to protein neddylation as relevant biological pathway for cellular toxicity of camptothecin. From the purely computational standpoint, our model and Bayesian hidden component analysis (BHCA) developed by Sabatti and James [11] are essentially the same, as we pointed out in Method section. We did not try to improve the BHCA, even though there may be a number of ways to improve the algorithm itself, simply because that was not our main objective. Main focus of this study is to model the chemical-genetic profiles at the molecular level, more specifically using protein complexes, and we found that BHCA is an appropriate computational framework. The reasons are as follows: first, central assumption on a hidden factor is conceptually similar. The goal of BHCA in transcriptional regulation is to infer hidden activities of transcription factors under the assumption of combinatorial regulation of a gene by a set of transcription factors. Similarly, our goal is to infer hidden activities of protein complexes under the assumption of combinatorial effect of cell growth by a set of protein complexes. Under this assumption, we were able to set up BHCA-like Bayesian factor model, as shown in Figure 2. Key component of the model is Z matrix (binary association matrix), which not only allowed us to robustly compute the equation, but also provided a window through which relevant biological information such as protein-protein interactions and genetic interactions can be integrated with experimental data. Second, the estimation of protein complex activities by Bayesian factor model is more robust and stable because estimands are obtained by tens of thousands of samplings. Deterministic factor analysis methods [10], [12], [13] often give rises to numerically unstable solutions especially when improper prior knowledge is used in the analysis. In our modeling, protein complexes and genetic interactions as prior information are still insufficient and inaccurate, which makes it inappropriate to use deterministic methods such as network component analysis (NCA) for our study [10]. To improve the hierarchical clustering, Parsons et al. also utilized a matrix decomposition method known as probabilistic sparse matrix factorization (PSMF). Both PSMF and our factor model all decompose chemo-genomic profiles into some factors and their weights. These decompositions of the two methods contribute to noise-reduction of original data, and so reveal more essential features. For example, Parsons et al. discussed two cases (“factor 6” and “factor 5” in [5]) where PSMF method improved the results over hierarchical clustering. For our method, we have already illustrated a number of those examples in Results and Discussion Section. Moreover, if we compare the results from the strain-based clustering, PSMF, and the present method (PC-based clustering) all together, our PC-based clustering tend to produce the results that are more similar to those of PSMF than those of strain-based clustering (Figure S6), indicating that both decomposition-based methods represent some essential features through noise-reduction from original observation. What is different, however, is that our model uses known protein complexes as factors and fixed relationships between factors and observations, while PSMF infers both of them from observations. Therefore, our model is suitable when prior knowledge on factors and observations is available, and PSMF is suitable in case of no prior knowledge. Direct performance comparison between both methods is difficult because only four blocks in the whole “factorgram” are available from [5]. One distinctive advantage of our method over PSMF, however, is that because we use protein complexes as factors and integrate biological prior knowledge in our model, the inferred results are biologically interpretable, which allowed us to develop an effective way to predict drug' s target pathway. In contrast, in PSMF biological meaning of factors is not clear. In addition, our model provides hidden activities of protein complexes from original data, which are difficult to measure in real wet experiment. In current study, we used only chemical-genetic profiles of viable yeast haploid mutants as observed data for modeling. Consequently, it has a limitation for excluding the data for ∼1,000 essential genes in yeast. This drawback can be overcome by combining chemical-genetic profiles of homozygous and heterozygous deletion strains. We believe that our complex-based approach can provide appropriate framework for modeling such combined fitness data, which might especially contribute to predict more precisely relevant pathway including target-proteins that interact directly with bioactive compounds.
Various types of factor models have been developed to model the transcriptional regulatory networks [10]–[13]. In factor models for transcriptional regulation, transcription factors are defined as hidden factors so that estimated effects of the factors can be biologically interpreted as the activities of transcription factors directly involved in the transcription. In a similar way, we developed a protein complex based Bayesian factor analysis (PCBA) for modeling chemical-genetic profiles. In essence, our model is similar to Bayesian hidden component analysis (BHCA) model by Sabatti et al. developed for the transcriptional regulation network analysis [11]. For convenience, we used the same notations and equations as described in the original BHCA paper. The central assumption of our model was that the observed growth fitness measurements of each strain were determined by combined effects of the activities of a collection of the protein complexes (PCs) in each cell under different treatments. By log-transforming strains' fitness measurements, a linear model was formulated so that eit = ΣLj = 1 aij*pjt+γit, where eit represented the relative fitness of a strain i in an experiment t; aij the association strength of the protein complex j on the strain i; pjt the relative activity for the protein complex j in the experiment t; L the number of protein complexes as hidden factors; and finally γit the measurement errors and the biological variability. We assumed that γit was an independent and identically distributed Gaussian random variable following N (0, σ2). If the number of strains is N and the number of experiments is M, the model can be rewritten in a matrix notation as follows: (1) Here, E denoted an N×M matrix. A was a matrix and represented unknown association strengths between strains and protein complexes. P denoted the matrix. In our model, there are the following features: (1) the “factors”, row vectors in the P matrix have a clear interpretation, as they correspond to specific protein complexes. (2) The specific value of the pjt is the primary interest for the prediction of drug' s mechanism. (3) The matrix A is known to contain a large number of zeroes, corresponding to the sparseness of the network. This sparseness in our model is very important feature to solve the notorious non-identifiable problem in the factor model, by which multiple sets of different parameter values lead to the nearly identical likelihood. Therefore, the identifiability should be achieved by imposing some sort of constraints in the model. A typical way in biological analysis is to constrain the loading matrix of factors by the same size of the matrix with a specific pattern of zeros. In our factor model, the sparse network topology as such constraints was represented in Z matrix with the same size as the A matrix but with only 0 or 1 values (Figure S4). The procedure for constructing Z matrix was shown in (A) and (C) of Figure 2. The entries, zij were assumed to be independent. If there was the association between the knockout gene of a strain i and at least one of components in a protein complex j, we set zij = 1. Otherwise we set zij = 0. By letting πij = Pr (zij = 1), we assigned 1 to the πij because of limited memory size and computation time. By doing so, we lost the chance to remove false positive associations. The remaining entries of Z were set to zero. The other priors on A, P and σ|Z were also defined as follows: (2) The parameters aij, pjt and were assumed mutually independent. The priors on A, P and σ were mainly used for regularization. To explore the posterior distributions of the four parameter groups Z, A, P, and, we used the collapsed Gibbs sampling based on the full conditional distributions of Z, A, P, and, which were derived from those conjugate-like priors and joint probabilities, and described in the BHCA paper. We used the compendium of chemical-genetic profiles for 82 different bioactive compounds by screening them against the yeast haploid deletion collection, of ∼5,000 viable strains [5]. Each value in the profiles was represented by the combined average log2 ratio (control/experiment) of both barcodes (up tag and down tag) corresponding to each strain. We excluded multidrug-resistant genes [5], and genes of deletion strains not associated with any protein complexes. Finally, the profiles of 3,241 strains were used for our Bayesian factor model. We used the collection of 490 protein complexes (PCs) defined by the first genomewide characterization in an organism, budding yeast, using affinity purification and mass spectrometry [8]. The 488 PCs associated with at least one strains were used for our Bayesian factor model. For PC–strain associations, we used the BioGRID version 2. 0. 20 release containing physical and genetic interactions known in S. cerevisiae [45]. We obtained the posterior distributions of all the parameters of A and P matrices in our models using the collapsed Gibbs sampler derived in the BHCA paper [11]. The following hyperparameters were set for the Gibbs sampling: α = 0. 7 and β = 0. 3 for the gamma distribution as a prior of inverse, and σa = 1,10,30,60,70,90,100 and σp = 1,10,30,50 for a priori standard normal distributions of aij and pjt. We first ran the Gibbs sampler for 11,000 iterations written in statistical language R [46] to select the optimal hyper-parameters, σa and σp. The initial 1000 iterations were discarded as burn-in, and the results of one per ten iterations were recorded, as suggested by Sabatti and James [11]. To assess the overall chain behavior, we monitored the sum of squared error (SSE). Given hyper parameters, σa = 30 and σp = 1, the convergence of SSE was best (Figure S5) so that we obtained multiple chains by Gibbs sampler under such hyper-parameter condition. For each chain of those multiple chains, we collected about 400 to 500 samples, one per ten iterations, after discarding initial 5,000 iterations as burn-in. All of samples obtained from each chain were merged so that they were used as each posterior (or sample) distribution of each parameter. Then, posterior means and posterior variances of each posterior distribution were used as estimands of each parameter. In this study, we focused on the analysis of posterior mean of each element in P matrix because our goal is to infer the hidden relative activities of protein complexes. Hierarchical agglomerative clustering was performed by Gene Cluster 3. 0 [47] for (A) and (D) of Figure 3 or by hclust function of standard R package stat [46] for (B) and (C) of Figure 3 using Pearson' s correlation as a distance measure, and average linkage for compounds and complete linkage for protein complexes as an agglomeration method. The figures of clustering results were generated by Java TreeView [48] or by plclust function of standard R package stat. To estimate the significance of the effect of a drug on a protein complex, we modified the error model used for haploinsufficiency-based direct drug-target identification in Yeast [4]. For this, first, the relative activities of all the protein complexes under different compounds were expressed as a matrix P with rows of 1…i…488 complexes and columns of 1…j…82 compounds, and the reference set of each complex was defined as a collection of activities of each protein complex under different 82 compounds, {Pi, j = 1‥82}. For every activities (Pij) of a given protein complex under a given compound, the drug effect (eij) on a protein complex was calculated by subtracting the mean (X̅i) of its reference set from Pij, and the uncertainty () of the drug effect was obtained by pooling of the variance () of its reference set and sample variance () of Pij obtained from tens of thousands of Gibbs sampling (Equations 3 and 4). (3) (4) where N represented the number of compounds, 82. The drug effect (eij) on a protein complex and its pooled variance () were applied to error function (Equation 5) so that significance of the effect of a given compound to a given complex was scored as a real value in the range of 0 to 1. (5) When error function scores of complexes were less than 0. 25, such complexes were regarded as being significantly affected by a given compound. When a protein complex has relatively positive value of activity, it was called a “sensitive complex”. In the opposite case, it was called a “resistant complex”. In similar way, we defined “sensitive strain” and “resistant strain”, all of whose relative fitness values had greater than 0. 5 or less than −0. 5. Based on known biological associations between “sensitive/resistant complexes” and “sensitive/resistant strains”, Gene Ontology (GO) analysis for all of 82 compounds were performed, and those results were available at http: //pombe. kaist. ac. kr/CMA/ModeOfAction. pl. Each set of genes of sensitive/resistant strains associated with sensitive/resistant complexes was used for GO analysis, which was also performed against all of genes of sensitive strains to compare complex-based with strain-based GO results in terms of highlighting relevant cellular pathway targeted by a compound.
Finding the specific targets of chemicals and deciphering how drugs work in our body is important for the effective development of new drugs. Growth profiles of yeast genomewide deletion strains under many different chemicals have been used for identifying target proteins and a common mode-of-action of drugs. In this study, we integrated those growth profiles with biological information such as protein–protein interactions and genetic interactions to develop a new method to infer the mode-of-action of drugs. We assume that the protein complexes (PCs) are functional units for cell growth regulation, analogous to the transcriptional factors (TFs) for gene regulation. We also assume that the relative cell growth of a specific deletion mutant in the presence of a specific drug is determined by the interactions between the PCs and the deleted gene of the mutant. We then developed a computational model with which we were able to infer the hidden activities of PCs on the cell growth and showed that yeast growth phenotypes could be effectively modeled by PCs in a biologically meaningful way by demonstrating that the inferred activities of PCs contributed to predicting groups of similar drugs as well as proteins and pathways targeted by drugs.
computational biology/systems biology
computational biology/genomics
Inference of Protein Complex Activities from Chemical-Genetic Profile and Its Applications: Predicting Drug-Target Pathways